The prediction and avoidance of cracking in long product hot rolling. Phase II (Pacrolp-II)
Research and Innovation
EUR 26321 EN
EUROPEAN COMMISSION Directorate-General for Research and Innovation Directorate G — Industrial Technologies Unit G.5 — Research Fund for Coal and Steel E-mail:
[email protected] [email protected] Contact: RFCS Publications European Commission B-1049 Brussels
European Commission
Research Fund for Coal and Steel The prediction and avoidance of cracking in long product hot rolling. Phase II (Pacrolp-II)
J. M. Rodriguez-Ibabe, M. C. Revilla, N. Gonzalez CEIT P. M. Lardizabal 15, 20018 San Sebastian, SPAIN
D. C. J. Farrugia, Z. Husain, G. Claxton, D. Wilcox, M. Whitwood, E. McGee, B. Cheong TATA Steel UK LTD Swiden Technology Centre, Moorgate, Rotherham S60 3AR, UNITED KINGDOM
M. Llanos, V. Santisteban Gerdau I+D Barrio Ugarte s/n, 48970 Basauri, SPAIN
J. H. Bianchi, F. Macci, F. D. Vici CSM Via di Castel Romano 100/102, 00128 Roma, ITALY
P.-O. Bouchard, M. Bernacki, E. Roux ARMINES CEMEF Ecole des Mines de Paris, R. Claude Daunesse, BP 207, 06904 Sophia-Antipolis Cedex, FRANCE
Grant Agreement RFSR-CT-2009-00007 1 July 2009 to 31 December 2012
Final report Directorate-General for Research and Innovation
2013
EUR 26321 EN
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TABLE OF CONTENTS Page Final summary
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1.
Introduction
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1.1.
Aims and objectives
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1.2.
Conformity with plan
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2
Description of activities and discussion
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2.1.
WP1: Envelope of industrial conditions and material acquisition
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2.2.
WP2: Reheating, industrial rolling and sampling of defects
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2.3.
WP3: Experimental laboratory study of damage nucleation, growth, coalescence and healing
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2.4.
WP4: Characterisation of through process microstructures, defects and mechanically deformed samples
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2.5.
WP5: Multiscale modelling and validation of high temperature ductile damage
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2.6.
WP6: Regime maps, sensitivities and industrial validation for defect-free rolling
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3.
Exploitation and impact of research results
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4
List of figures
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5.
List of tables
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6.
List of acronyms and abbreviations
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7.
References
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Appendix A: Detailed results of micro-tensile tests with digital image correlation
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Appendix B: SKIZ technique application in inclusions characterisation
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Appendix C: TEM analysis of inclusions
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Appendix D: Summary of influence of reheating on surface features
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Appendix E: Thermal etching and microgrid analysis of RPS tests
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Appendix F: Characterisation of inclusions from mechanical tests
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Appendix G: New FEM based Matlab image analysis software
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Appendix H: Micro RVE with CPFE constitutive material models
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Appendix I: Description of different phases, remeshing strategy and constitutive equations for modelling
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Appendix J: Examples of applications of the models developed by Cemef
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Appendix K: Void and defect welding
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FINAL SUMMARY 1. INTRODUCTION Free cutting steels belong to a family usually associated with hot ductility (workability) problems. Other typical grades prone to surface defects are peritectic and microalloyed steels. In all these cases, exhaustive analyses have been done in the past to identify and modify main process/microstructural parameters intervening in defects nucleation and propagation. A major characteristic of these previous studies is that they have mainly focused on a single aspect of the industrial process with minimum consideration of the multiscale (heterogeneities) and through process nature of damage mechanisms. Taking into account these limitations, the previous RFCS PACROLP I project [1] laid down the foundation for through process tracking of high temperature ductile damage for free cutting steels (FCS), therefore representing a step forward from previous studies. This project was mainly focused on studying conditions during hot rolling, establishing various approaches (modelling, characterisation) and improving the understanding of high temperature ductile cracking theory. The results obtained converged in proposing a methodology for damage assessment and minimisation in rolling mills. Free cutting steels need simultaneously to fulfil two opposite conditions. First, as machinability of these grades is their major singularity, this requirement must be fulfil by assuring a minimum fraction of inclusions, mainly MnS, combined in some cases with other low melting elements, able to favour cutting operations. Secondly, these inclusions and additives are the main responsible for surface defects during hot rolling. A proper balance of these two opposite conditions can be achieved with a high control of all the main actors intervening in both machinability and ductility properties. This only can be done through process either as expensive plant trials or more efficiently by an adequate modelling. On the other hand, the advance that is taken place in Materials Science, both in the development of experimental techniques and in multiscale modelling, provides new opportunities to better understand the complexity associated with the damage nucleation and evolution during casting/reheating/hot rolling of steels. In this context was undertaken Pacrolp II project with six different WPs. 2. WORK CARRIED OUT AND MAIN CONCLUSIONS WP1: Envelope of industrial conditions and material acquisition The main objectives of WP1 were: a) Production of as-cast materials of selected steel grades (blooms and billets). b) Generate as-cast material for laboratory thermal-mechanical simulation. c) Generate material for further pilot hot rolling. d) Envelope of processing conditions at each key process stage (reheating, rolling). Several steel grades were selected and produced to fulfil the a) to c) objectives. The selection was done considering these aspects: - Steels with Mn/S relationships close to the critical value proposed by Alvarez et al. [2] to avoid FeS formation. - BOS and EAF routes in order to evaluate possible negative interactions between MnS inclusions and residual elements (Cu) - Presence, in some cases, of other alloying additions (Pb, Bi, Te) in order to analyse their incidence on damage generation. - Microalloying addition in two cases to analyse possible additional negative effects of precipitates in combination with inclusions. - Austenitic stainless steels and Fe30%NiS laboratory heat to maintain austenitic microstructure at room temperature and study interactions occurring during hot working between austenite grains and inclusions. On the other hand, as one of the mains aspects of the project was the “through process” evaluation of damage, a total of 6 industrial rolling mills, each one with their peculiarities concerning reheating
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furnaces and rolling schedules, were taken into account. In addition, a laboratory rolling mill was included in order to explore with more flexibility the effect of process conditions on damage. Concerning envelope of industrial conditions, data acquisition and required calculations were done in both furnaces conditions (atmospheres and heating cycles) and initial rolling passes. An important aspect was the evaluation of stress triaxiality-plastic strain evolution during rolling passes. These results were required for a proper support of laboratory tests and subsequent modelling simulations. WP2: Reheating, industrial rolling and sampling of defects The objectives of this WP were: a) Identification of process windows considering: • Avoidance of post-casting defect formation. • Minimisation of previous small defects and their interaction with new weak formed regions. • Reduction of thickness of as-cast cortical region and relevance of sub-surface defects. b) Obtain industrial damaged samples for characterisation. Task 2.1: Reheating and industrial rolling Tata, Gerdau and CSM were responsible for the collection of plant parameters, obtain industrial as-cast and rolled samples for defect inspection and also provide material for laboratory tests. Both partially and fully rolled intermediate stocks were obtained, the former by stopping rolling with the stock still pressed below the 4 roughing stands. Task 2.2: Effects of reheating on as-cast integrity The reheating step can have two opposite effects, depending on the initial as-cast surface conditions and on the furnace parameters. It can serve to eliminate previous surface defects formed during casting or it can induce new weak points that can evolve negatively during initial rolling passes. In order to identify these possibilities, a wide range of laboratory tests were done, including aspects as: oxidation kinetics and scale morphology, evolution of artificially damaged samples during reheating and low stress creep tests (low stress levels that can be present in the billet during its presence in the furnace). In addition, small billet pieces of studied stainless steels were attached to a transport billet to analyse surface evolution in real industrial conditions. The oxidation kinetics confirmed the risks of presence of FeS in the scale/matrix interphase (filtering to the interior) and also in the matrix subsurface region. This presence of FeS was scarcely observed prior to reheating in LFCS steels, while some amount was present in 9SMn28 grade (smaller than 200 µm). During reheating partial oxidation of MnS inclusions (to MnO) and their evolution into (Mn,Fe)S or FeS particles has been detected. In contrast, in 38MnSiVS5 steel FeS was not identified. In this case, the Mn/S ratio is significantly higher than in the rest of steels considered, confirming the relevant role of this relationship. In addition, in the case of EAF route, segregation of Cu can appear combined with FeS in regions close to the oxide/steel interfase. The analysis of the evolution of the artificial cracks during reheating shows that it is possible to clean small defects (< 200 µm) coming from the continuous casting, but large cracks remain after reheating with internal oxidation in the surrounding regions, which implies a risk of presence of low melting products at some distance from the surface (after reheating). The low stress creep tests under different atmospheres indicate that these conditions favour the opening of grain boundary/oxidation and that this effect increases with time in furnace (at similar temperature). The EPMA analysis indicates that there are Mn depletion bands which favour the penetration of FeS at grain boundaries and that this is enhanced by stress application and oxidising atmospheres.
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Task 2.3: Defect sampling In this task, Tata, Gerdau and CSM extracted industrial cracked samples that were analysed in WP4. This selection provided valuable information (including the identification of different origins) to properly evaluate the predictions obtained with the models in WP5. WP 3: Experimental laboratory study of damage nucleation, growth, coalescence and healing The objectives were: a) Study factors affecting damage nucleation, growth, coalescence and healing. b) Obtain complementary information of defect evolution for feeding information to damage models. c) Tailored tests to develop and validate modelling approach and results. d) Validation of modelling approach. Task 3.1: Laboratory mechanical techniques to study damage nucleation, growth, coalescence and healing A proper analysis of damage evolution during industrial conditions requires the application of a set of different tests able to cover the stress/strain/temperature range. In addition, other specific tests are necessary to study the parameters involved in each damage step (nucleation, growth, coalescence) and their interaction with matrix (mean values and local microstructural heterogeneities) at different scale levels. These are the reasons of the selection of a wide range of different tests and thermo-mechanical conditions (revised plain strain compression, tensile, 3-4 point bending, torsion and compression). A high number of revised plain strain compression (RPS) tests with different geometries (based on previous Pacrolp I knowledge) were done, providing different levels of stress triaxiality- plastic strain ratios and locations in relation to as-cast surface. In some conditions, as-cast faces were preserved to analyse their behaviour during deformation. In order to analyse the interaction between matrix (austenite grain boundaries) and inclusions during deformation, a set of RPS specimens were thermal etched and deformed under vacuum. Similarly, in several RPS specimens deposit gold microgrids were applied. The material selected to perform these types of tests were the austenitic Fe30%Ni and Fe30NiS laboratory heats. The objective of the tests with microgrids was the study of inhomogeneous deformation at the scale of microstructure. These results could help to validate micro-FEM models of deformation. A wide range of different tensile tests was studied, including conventional and new micro-tests. The results carried out with conventional tests (including some of them with in situ remelting) provided hot ductility curves at different testing conditions and microstructures to evaluate damage. These results were considered in WP5 for modelling and also to propose some rules for safe rolling. On the other hand, micro-tensile tests done with Taboo machine (including specimens with drilled holes) have been a key factor to understand (and they provide results for modelling validation) the interaction between holes (voids machined at different locations) as a function of their dimensions and special configuration. It is worth emphasising the relevance of the study on high temperature damage evolution during tension by 3D X-ray tomography performed on the LFCS grades. This has allowed the study of damage nucleation and evolution and the interaction with MnS inclusions at high temperature. The analysis of the spatial location of the inclusions and how this combines with triaxiality in damage start and progression has been one of the main objectives to consider the application of this technique to free cutting steels. Interrupted torsion and tensile tests were done to quantify the evolution of MnS deformation as a function of applied strain. Similarly, three point bending tests at high temperature machined from billet corners were tested. The objective of these tests was to analyse the evolution of defects and geometrical singularities present in the as-cast surfaces of the billets under high deformation conditions.
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In summary, a high number of tests with different geometries and thermo-mechanical conditions have been done, providing material for analysing microstructure/damage evolution in WP4 and data for validation of models in WP5. Task 3.2: Pilot mill rolling Samples from 9MnS28 and 38MnSiV5 grades were flat rolled in a pilot mill at conditions close to the industrial situation and the influences of the initial reheating temperature, total strain and rolling speed were explored. In order to enhance damage, in a set of rolling trials the lateral surface geometries were modified to provoke high tensile strains. At the end of the tests, the material was quenched in order to study the interaction between damage evolution and microstructure. WP4: Characterisation of through process microstructures, defects and mechanical deformed samples The objectives of this WP were: a) Detailed characterisation of key features in crack sensitive grades. b) Detailed characterisation on all industrial and laboratory samples. c) Generate process and product data for validation/input from/to the numerical methods. Task 4.1: As-cast and as-cast reheated materials characterisation A detailed analysis of as-cast and as-cast reheated samples has been done from the point of view of features that can intervene in damage processes during hot rolling. This analysis has focussed mainly on the cortical region. The as-cast analysis has revealed the possible presence of FeS and alignment of MnS inclusions close to the as-cast surface (both features can lead to incipient damage nucleation at the roughing passes). These features change significantly from one to another analysed steel grade. Similar results were obtained when the MnS local area fraction was quantified at different distances from the as-cast surface. TEM analysis demonstrates that an important fraction of small particles are combinations of (Fe, Mn)S or (Mn,Cu)S and not only single MnS inclusions. In addition, in the stainless steels Cr also is present as (Mn,Cr)S. All these elements in solution will increase inclusion hardness during hot rolling in comparison to MnS. It is worth emphasising that all these aspects, relevant from the point of view of damage during hot working, are very dependent on the solidification and post-solidification conditions and on chemical composition (mainly Mn/S relationship). The presence of possible defects formed before reheating (simulated by the production of artificial cracks) and their evolution during reheating have been evaluated for some specific steel heats (considering dry and wet conditions and schedules similar to those in industrial plants). The results indicate the risks of the appearance of other “weak points”, as Cu segregation (in the EAF route), in the vicinities of these defects. Local oxidation also can enhance the appearance of FeS. It is important to indicate that after reheating, the austenite grain has relatively low mean values (in the range from 25 to 40 µm) compared to other steel grades (> 150 µm if no Ti additions of other microalloyed elements (Nb) are added to avoid grain growth). This is due to the fact that the high volume fraction of MnS inclusions is exerting a pinning effect (although they are not very fine particles, the high volume faction is sufficient to control the grain growth). As a consequence, an important fraction of MnS inclusions will be at grain boundaries and triple points. This implies that “two weak” microstructural features (particles and boundaries) can interact during damage nucleation and propagation. This is one of the singularities of FCS in comparison to other poor hot workability steel grades. Nevertheless, this situation is different when compared FCS with stainless steels. While in the first case there is a change (at least in cold charging) from austenite/ferrite and ferrite/austenite prior rolling (leading to equiaxed austenite grain), in austenitic stainless steels at the first rolling pass the columnar as-cast microstructure is present.
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EPMA analysis has shown that there is a depletion in Mn content following reheating, as well as Pb, with Mn/S ratio reducing to lower value than 3.5 (critical value for avoidance of formation of FeS) in the case of LCFS grades. On the other hand, the reheating in the normal industrial conditions has not a relevant influence in the structure of the as-cast structure of AISI 303 and AISI 304L stainless steels. However it is possible to appreciate a dilution of delta ferrite particularly in the cortical zone, and the globulisation of the net shape delta ferrite in the columnar zone. Tasks 4.2-4.3: Wrought structures characterisation and Defect sampling The activity in this Task has focussed mainly on free cutting and austenitic stainless steel grades. In the case of wrought conditions, besides the possible effects due to reheating, the main features are the elongation of MnS inclusions and delta ferrite islands in the rolling direction. In relation to defect analysis in rolled material, different cases ranging from intergranular cracking to ductile breaks with scaled branched defects have been observed. These cracks can be potentially associated with casting defects originated from off-corner/corner of billets. In the case of stainless steels, several defects observed have been identified with microcracks of oscillation marks in the billet corners that undergo compression in transversal direction and tension in rolling direction. A detailed analysis of interaction between orientation of inclusions in relation to cracks and applied strain has been done. Task 4.4: Characterisation of mechanical deformed samples (lab + pilot rolling) A complete characterisation of samples tested in WP 3 has been done. In the case of RPS specimens, in combination with microscopy analysis and identification of damage state, thresholds of triaxiality and strain for nucleation and cracking were obtained. This leads to some conclusions concerning maximum and minimum (reheating) temperature for minimising damage in high strain conditions when tensile triaxiality and strain, similar to those resulting in rolling, are acting. The RPS results also confirmed that BOS cast structure shows enhanced ductility compared to EAF. On the other hand, an improvement in ductility was observed after reheating, compared to as-cast, in EAF route. Finally, the detailed microstructural analysis of inclusions and their relevance in damage nucleation, clearly demonstrated that spacing to diameter ratio of inclusions is critical, indicating that cluster and large inclusions are more prone to damage (for a given triaxiality state). In these compression tests it was also possible to observe, with EPMA analysis, that cracking and initial voiding took place in depleted Mn bands with MnS inclusions with bands running at an angle to the direction of maximum principal stresses, suggesting that potentially offer easy path for crack propagation. The presence of iron oxide, probably formed during reheating, and associate with MnS inclusions is another source of easy path for crack propagation. The thermal etching RPS tests confirmed that microvoids are originated very early around austenite grain boundaries and inclusions. Similarly, microgrid tests clearly confirmed the big differences in strain localisation at the surrounding of grain boundaries when MnS inclusions were present or not. 3D X-ray tomography confirms the relevance of triaxiality and MnS inclusion clustering on damage nucleation and evolution. Quantitative analysis of void volume fraction evolution with applied strain indicates rapid void coalescence in a very short strain interval as approaches to strain-to failure conditions. Similarly, Kernel Average Misorientation measurements (in the case of austenitic steels) confirmed that there are strain concentrations in the matrix surrounding inclusions, increasing significantly when clustering of particles is present. Internal defects at inclusions (as porosity identified by FIB technique) and surface heterogeneities can also intervene in this behaviour. In summary, a lot of experimental evidences clearly indicate the relevance of clustering of MnS inclusions as factors promoting strain concentrations that favour damage nucleation. Probably, if compared to other steels with particles, in FCS grades one of the main differences (in addition to the nature of MnS inclusions) will be the localisation of a high fraction of these inclusions at grain boundaries. This clearly introduces an additional problem.
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The plasticity of MnS inclusions at different strain levels and temperatures was quantified. The results indicate that there is not a linear relationship between aspect ratio of inclusions and nominal applied strain. As the total strain increases, there is a decrease in inclusion deformability. On the other hand, for a given strain level, the plasticity of inclusion in steels with Pb, Bi or Te is smaller. This suggests the relevant role of the interface of MnS inclusions with matrix in their deformability and, as a consequence, in the tendency to nucleated voids. In addition, the evolution of the polycrystalline nature of inclusions with deformation was quantified, observing that this factor affects inclusion plasticity. The microstructural characterisation of industrial defects has allow to identify mechanisms of interaction between as-cast damage (small cracks at oscillation marks and subcutaneous damage) with MnS inclusions along the rolling schedule leading to cracking. WP5: Multiscale modelling and validation of high temperature ductile damage In this WP the list of objectives was: a) Modelling of damage mechanisms at the microscopic scale. b) Enhancement of the Damage models and multiscale approach developed in PACROLP project, linking Continuum Damage Mechanics (CDM) models to microstructural evolution. c) Implementation within the analysis of initial and emerging geometrical and micro/meso-structural heterogeneities. d) Develop customised damage models interfaced to FEM platform Tasks 5.1 and 5.2: Micro-mesoscale and Meso-macro modelling The multi-scale modelling approach developed during PACROLPI has been further developed by Tata with: - Assessment of simple damage criteria for RPS test. Parameters such as triaxiality, principal stress and strain rations have been considered. A range of simple post processing damage criteria has been coded and integrated into the post processor C++ script. - Further development of the micromechanics models of inclusions for both imposed, random distributions, boundary conditions applied to RVE (representative volume element) and finally possibility to run in both formulations of ABAQUS (Explicit and Standard). Generation of inclusions based on a library of MnS shape/morphology can be done randomly. Inclusions can also be imposed to extract knowledge about influencing zone, strain and stress localisation based on an initial periodic or specific location or based on an initial spacing to diameter ratio. Inclusions can be edited and translated/rotated/scaled and the relative distances between inclusions are a controllable feature. - Further application of RVE models to range of distributions with comparison of effect of inclusion on strain localisation compared to far field strain. - Influence of inclusion spacing to diameter ratio and strength on damage linkage using simplistic microRVEs with porosity constitutive model. This analysis has confirmed that the inclusion s/d relationship (spacing to diameter) is the most significant parameter. Nevertheless, as inclusions hardening increases (in relation to matrix) effect of strain shielding decreases. - New FEM based Matlab image analysis software to quantify statistics of microRVE models (major development). - Assessment of differential thermal expansion effect between MnS and matrix Cemef has developed a new robust finite element (FE) strategy based on a level set framework to describe the nucleation, void growth and coalescence stages occurring during ductile damage mechanisms in 2D or 3D. The initial FE mesh, independent of the different phases, is coarse and isotropic. This initial mesh is anisotropically adapted to accurately describe the geometry of the constituents and to deal with discontinuities in material properties. This new approach was used to study the effect of several parameters on ductile damage mechanisms. Results are in a good agreement with those obtained experimentally and found in the literature. Several cases, including different properties of matrix and inclusions have been applied to a real microscopical domain. These developments represent a real step forward in the comprehension and modelling of ductile damage mechanisms at the microscale.
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The Self-Consistent Strain Model (SCSM), previously developed by CSM, has been extended to describe the hot working behaviour of an austenite matrix containing inclusions. The modelling allows to obtain both a constitutive equation for MnS inclusion and quantify the decohesion strain difference between matrix and inclusion. For the calibration of the model, compression and tensile tests were done in the temperature range corresponding to hot working. Two damage models for sound material have been developed using hybrid experimental-simulation procedures. The simplest macro-damage model is based on bounds obtained from conventional isothermal tension in terms of temperature and strain. The second is a mesoscopic model constructed in a similar way, but in terms of the temperature-dependent matrix-inclusion decohesion strain. The macro damage model, in contrast with the mesoscopic one, makes no microstructural assumption on failure origins and the macro behaviour is extracted directly from the tensile test. Task 5.3: Multiscale modelling For multiscale modelling, The CAFE model as originally developed by Sheffield University has been further developed to be more appropriate for the hot rolling applications. The set of ordinary differential equations describing the viscoplastic-damage constitutive Model and the CAFE Framework were combined into a hybrid multiscale model during PACROLPI project. The constitutive model is physically based and capable of modelling both the macro, i.e. stress, strain, material hardening, etc, and microscopic, i.e. average grain size, fraction of recrystallisation, damage, etc, aspects of a material during deformation. The Sheffield CAFE model allows more than 1 CA array, each of which encapsulating a given material law, to be combined and made use of within a Finite Element (FE) simulation. The resulting hybrid of the two cutting-edge modelling capabilities allows the modelling of “real life” deformation processes that are traditionally very difficult to deal with and require the consideration of non-uniformity within material microstructure. The meso and macro-damage models developed by CSM were produced under isothermal conditions and considering a mean MnS volume fraction. The extension to rolling conditions involve several implementations: non isothermal and complex loading along the deformation path, microstructural softening mechanisms (recrystallisation), suppression of spurious damage reversal due to thermal recovery in the interpass and welding under the rolling gap, all aspects which were taken into account. Task 5.4: Knowledge encapsulation and transfer Based on the results obtained in WP3-5, by combining experimental tests with microstructural analysis and modelling, key significant MnS inclusions parameters involved in damage mechanisms were catalogued. These factors are: volume fraction, crystallographic orientation, morphology, size, spacing/diameter ratio, plasticity, role of oxides, clustering, triaxiality, matrix plasticity, thermal stresses and chemistry of surrounding matrix (Mn depletion zones) and localization of solidification incipient damage. Examples of how each factor intervenes have been summarised. WP6: Regime maps, sensitivities and industrial validation for defect-free rolling The objectives were: a) Apply and validate models developed to: • Mechanical testing and pilot mill rolling. • Industrial line cases and validation against partially rolled industrial samples. b) Optimisation of the reheating through a reduction of the holding time compatible with industrial conditions in order to assure superficial defect/heterogeneity removal at minimum cost. c) Develop simulation tools on FEM platform for a quick assessment of damage risk in terms of industrial rolling parameters including roll-groove geometries. d) Define criteria and procedures for defects free rolling in terms of process and material parameters.
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Task 6.1: Simulation and calibration against controlled mechanical testing and pilot rolling Each partner involved in modelling has performed different tests and simulations for a proper validation of the models. Task 6.2. Optimisation of reheating conditions and industrial rolling Considering the three main steel families studied in this project (LFCS, microalloyed grades and austenitic stainless steels), recommendations concerning reheating and rolling operations has been obtained on: - Proper definition of the chemical composition of steel (minimum Mn/S relationship). - Definition of temperature interval in reheating furnace. This will depend on steel grade. Very high temperatures will enhance oxidation problems provoking grain boundary opening and Mn oxidation (formation of FeS in Mn depleted regions). In contrast, a minimum temperature is required to assure a minimum ductility in the steel. Time also needs to be considered as a factor controlling oxidation. In the case of EAF route steels, attention of Cu enrichment at matrix/scale interface needs to be included. - In those grades prone to have subcortical damaged segments, a minimum cortical zone should be achieved during casting, provided the cooling conditions do not magnify residual stresses and worsen cracking risks. - Transfer from furnace to rolling mill and descaling. Overcooling or residual scale are both potential problems. - Identify both material and industrial geometric/process parameters leading to damage generation, the interaction of this with pre-existing solidification defects and assess cracking risk. - Analysis of roughing pass conditions (stress triaxiality-strain) in order to minimise corner/off-corner mechanical conditions. Depending on steel grade the criteria for maximum allowed triaxiality-strain will change. If minimum requirements are not achieved, redesign of rolling pass should be required. Task 6.3. Final analysis, conclusions and recommendations The main singularity of this project has been a multiscale analysis combined with a through process evaluation (casting/reheating/rolling) of damage nucleation, coalescence and propagation by experiments. This approach has allowed obtaining different conclusions and recommendations (some of them described in previous Tasks) that can be summarised as follows: - The study of as-cast cross sectional structure provided a good knowledge of microstructural features that were identified as relevant in subsequent process steps: location of as-cast incipient damage, grain distributions, nature, distribution size and location (clustering) of MnS inclusions, depleted Mn regions, among others. - The reheating step prior to hot rolling has been identified as a key factor that can eliminate, enhance or provoke surface defects. The laboratory heat tests with samples with artificial defects, the TGA analysis and the low stress creep tests indicate that small defects can disappear but, depending on the conditions, a new set of defects and weak points can be formed at the billet/bloom surfaces. As oxidation of MnS can occur, temperature and time needs to be limited. - A wide range of mechanical tests was analysed, including innovative techniques able to provide different scale approaches. These tests, combined with fine microstructural evaluation and FEM models for analysis of state of damage, have allowed: the definition of thresholds of triaxiality and strain for nucleation and cracking, the evolution of plasticity of inclusions with applied strain, a better understanding on the interaction between austenite grain boundaries and MnS inclusions in the early stages of damage nucleation (included relevance of recrystallisation softening), the relevance of inclusions spatial distribution in all the steps of damage evolution. - A complete multiscale modelling has been developed to study the effects of macro processing conditions and MnS inclusions at the scale of interest. Some of the most relevant aspects are the following: the techniques at micro level range from automatic RVE models to extract regimes and
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distributions of field of interest (strain, triaxiality, principal stresses, etc.), CPFE with/without grain boundaries, cohesive zone models (CZM), extended FEM (XFEM), cellular Automaton FEM (CAFE), a new FEM image analysis based on Matlab was developed to extract histograms of key state or field variables function of deformation, new robust finite element strategy based on a level set framework to describe the nucleation, void growth and coalescence stages occurring during ductile damage mechanisms in 2D or 3D and an extension of Self-Consistent Strain Model (SCSM) to hot working conditions. - Both experimental results and model predictions clearly emphasize the relevant role of triaxiality/strain path during rolling, in order to reduce damage in FCS. This implies that some guidelines for rolling FCS need to be taken into account. In fact, proper design of entry bite and groove radius appear as a key factor to minimise damage risks. The project has allowed the definition of very specific and practical rules for direct application in steel plants. On the other hand, the recommendations done in order to better define furnace conditions, avoiding excessive oxidation (temperature and time combinations) rules, will also have an indirect effect on energy consumption. Finally, based on the results obtained in this project, a total of 16 papers and communications at conferences have been done.
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1. Introduction 1.1. Aims and objectives The appearance of surface/sub-surface defects during casting/reheating/rolling industrial sequences continues being an unresolved problem in crack susceptible grades, such as improved machinable steels. The previously completed RFCS PACROLP-I [1] project has laid down the foundation for through process and product influence on high temperature ductile damage. PACROLP-I project also ended with a set of recommendations/further work which will contribute to further understand through process damage mechanisms (from the exit of casting, reheating, descaling and hot rolling) in apparently sound as-cast FCS long product steels. These included the relevance of the metallurgical nature and microstructural evolution of the as-cast cortical zone during the overall reheating/rolling process, the incidence of weak regions at grain boundaries and triple points on damage nucleation/evolution, the 3D configuration of inclusions and particles including particle free zones, the combined effect of geometrical features (hooks, oscillation marks,..) and microstructural weak regions, the Mn loss due to oxidation, the inclusion/matrix texture and plasticity. It is worth emphasising that in last years new characterisation and mechanical techniques, together with more sophisticated multiscale models are being developed in the field of Materials Science. Some of these techniques (X-Ray tomography including in-situ testing at high temperature, 3D FIB characterisation, micro-hardness tests and micro-testing at high temperature) will be considered in PACROLP-II in order to develop finer multiscale models implementing the influence of local heterogeneities. PACROLP-II will focus on a better understanding of the factors intervening from exit of casting to rolling and their incidence in damage nucleation/evolution would permit to optimise the reheating process/soaking cycle. Some of the main objectives and innovations of PACROLP-II project are: -
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-
Detailed characterisation of as-cast, reheated and wrought industrial products with special emphasis on local heterogeneities, identifying the evolution through the industrial process of those possible factors affecting damage. Conventional and innovative techniques as FEG-SEM, EBSD, TEM, FIB and X-Ray tomography will be used on production and simulation material. Performance of a wide range of laboratory thermal-mechanical tests to bring a multiscale understanding of damage mechanics in enhanced machinable steels. Emphasis will be placed on covering a wide range of length scale required to feed multiscale material damage models. Development of more precise constitutive material models able to incorporate local heterogeneities for different length scales to help constructing process regime maps. Development of rules/guidance/defect-free process maps for steel producers for resulphurised crack sensitive steel grades.
1.2. Conformity with plan (1 July 2009 - 31 December 2011) PACROLP-II project is divided into six work packages that interact as shown in the flow chart. The main results of each WP and corresponding discussion are described in the following sections.
14
WP 1 Envelope of Industrial Conditions and Material Acquisition
WP 2 Reheating, Industrial Rolling and Sampling of Defects crostructures
WP 5
Work packages of PACROLP-II and interactions between them.
Multiscale Modelling and Validation
WP 3
WP 4
Experimental Laboratory Study of Damage
Microstructure Characterisation
WP 6 Regime maps, sensitivities and industrial validation
The Gantt chart indicating the real situation of each WP against initial plan is show below.
Work Work packages’ title packages WP 1
Deliverabl Hours on project/Contractor(s) es 1 2 3 4 5 200
250
Task 1.1
Envelope of industrial conditions and material acquisition Grade acquisition D1
50
100
50
Task 1.2
Envelope of processing conditions
150
150
100
350
250
450
300
50
150
50
350
100
150
150
100
150
100
Experimental laboratory study of damage 1200 nucleation, growth, coalescence and healing Laboratory mechanical techniques D6 1200 to study damage Pilot mill rolling D7
1000
700
600
900
1000
700
400
900
2850
1800
1800
750
1400
800
600
400
50
400
WP 2 Task 2.1 Task 2.2 Task 2.3 WP 3 Task 3.1 Task 3.2 WP 4
Task 4.1 Task 4.2 Task 4.3 Task 4.4 WP 5 Task 5.1
D2
Reheating, industrial rolling and sampling of defects Industrial rolling D3 Effects of reheating on as-cast integrity Defect sampling
D4 D5
Characterisation of through process microstructures, defects and mechanical deformed samples As-cast and as-cast reheated D8 materials characterisation Wrought structures D9 characterisation Characterisation of defects D10
300
150
700
200
400
150
Characterisation of mechan. D11/D12 850 deformed samples Multiscale modelling and validation of high 150 temperature ductile damage Micro-mesoscale modelling D13
800
700
400
800
1700
600
2000
2800
500
1400
600
200
600
600
400
Task 5.2
Meso-macroscale modelling
D14
500
Task 5.3
Multiscale modelling
D15
600
In conformity with plan
IV
I
3rd year II III
200
200
Knowledge encapsulation and D16 transfer WP6 Regime maps, sensitivities and industrial validation for defect free rolling Task 6.1 Simulation and calibration against D17 mechanical testing, pilot rolling Task 6.2 Optimisation of reheating D18 conditions and industrial rolling Task 6.3 Final analysis, conclusions and D19 recommendations Total Hours on project
I
2nd year II III
150
500
Task 5.4
1st year III IV
400
200
150
200
200
300
600
600
900
850
1100
700
100
400
300
500
200
200
300
350
350
200
300
200
200
250
300
5150
5850
4650
4900
5800
Start/end data extended
15
Behind plan
IV
4th year I II III IV
2. DESCRIPTION OF ACTIVITIES AND DISCUSSION 2.1. WP1: Envelope of industrial conditions and material acquisition Task 1.1: Grade acquisition (Tata, Gerdau and CSM) The following industrial steel grades were selected in the project (see compositions in Table 1): low carbon free cutting steels (Tata and CSM) medium C microalloyed steel (CSM) free cutting austenitic stainless steels (Gerdau) Table 1. Chemical composition of selected steels. Grade
C
Mn
LCFS (nominal)
0.07 1.05
9SMn28
0.08
Si -
S 0.32
1.1 0.02
0.42
38MnSiV5 0.38 1.35 0.51 0.045 AISI 304L 0.026 1.8 0.40 0.042 AISI 303
0.070 1.6 0.27 0.284
Pb 0.31 -
Cr
Ni
Mo
Cu
Ti
V
Mn/S
(Mn/S)c
Conditions
-
-
-
-
-
-
3.28
3.32
BOS and EAF (180 mm billet)
0.18
0.22
0.09
0.20
-
0.11
2.62
2.67
EAF (140x140 mm bloom)
30
16
0.045 0.136 0.019 0.176 0.019 0.088 18.25
8.25
0.39
-
-
-
42.8
16.6
18.25
8.26
0.43
-
-
-
5.6
3.6
EAF (240x200 mm bloom) EAF (155 mm billet) EAF (155 mm billet)
In addition, a laboratory heat was produced (Fe-30%Ni-S(0.3-0.4%). This steel remains austenitic during all temperature range and has recrystallisation kinetics similar to low C free cutting steels. Tata UK has obtained as-cast, as-cast reheated and wrought low carbon free cutting steels (LFCS). Both EAF and BOS routes have been selected in order to evaluate the influence on the level of residuals on embrittlement at high temperature during reheating. The study has focused on the Thrybergh Combination Mill (TCM) which is a 24 stand continuous single strand bar mill. Main area for investigation is the 5 stand close-coupled rougher, where the transition between as-cast to a wrought structure occurs during HV box rolling. As-cast, as-cast reheat and wrought at various sampling shear positions on the mill and finished products have been acquired. In the case of BOS route, samples with varied casting conditions (powder and speed) have been selected (see Table 2). Table 2. Material range and type including code (Tata). Material LFCS EAF Cast 1697H QA code 9TZ9/B1 or /A1 Cast 51440 QA code 9TZ9/B2 or /A2 LFCS BOS Cast 51441 9TZ7/204, 9TZ7/209 Cast 51150 9TZ7/202, 9TZ7/211 Simulation material Previous PACROLP-I BOS material from BBM, Scunthorpe inc. lead substitutes (Bi,Te,Telby+)
Conditions As-cast Before (B1)/After reheat (A1) & wrought pedigree specimens (shear 5/8/finished rolled)
Status Machined to bars Machined to RPS/Creep/micro-tensile
9TZ7/204 casting powder1 fast speed 9TZ7/209 casting powder1 slow speed 9TZ7/202 casting powder2 fast speed 9TZ7/211 casting powder2 slow speed
Machined to bars Machined to RPS/ Creep/micro-tensile
Fe30%Ni S (0.3-0.4%)
Initial trial cast
Gerdau has analysed two stainless steel grades (AISI 304L and AISI 303, see Table 1), being the main difference between them the high amount of S in the case of steel AISI 303. In relation to hot ductility other important parameter is delta ferrite weight (DFW). This value is determined as follows: DFW = - (99.7 x R) + 138 with R = ( Ni(eq) + 36.5 ) / ( Cr(eq) + 17.6 ) The Ni(eq) and Cr(eq) amounts are calculated with the following expressions:
16
Ni(eq) = (%Ni) + 30(%C) + 0.5 (%Mn) + 30 (%N) and Cr(eq) = (%Cr) + (%Mo) + 1.5 (%Si) + 0.5 (%Nb) The selected heats have a delta ferrite content of 5.0% and 2.7% that correspond to low crack susceptibility. On the other hand, several modes explain the stainless steel solidification:
Mode A: Liquidus → Liquidus + Feδ → Liquidus + Feδ + Feγ Mode B: Liquidus → Liquidus + Feδ + Feγ→ Feγ + Feδ Mode C: Liquidus → Liquidus +Feγ → Feγ
→ Feγ + Feδ
f0
where f = Nieq – 0.75 x Creq + 0.257 [3]. According to the value of f (see Table 3), the solidification of both steel grades is in mode A, that is, the initial solidification is in delta ferrite that decomposes into austenite as the solidification progresses. Finally only a residual quantity of delta ferrite remains in the solid austenitic matrix. Table 3. Creq, Nieq and f factor of the selected heats. Heat 38039 41064
Grade AISI 304L AISI 303
Creq (%) 19.393 19.253
Nieq (%) 11.032 11.708
f -3.255 -2.474
Fig. 1 shows the solidification path of the selected heats. The calculations have been done with IDS software and in the figure the fraction of each phase is represented as a function of temperature. Also the precipitation of MnS is indicated. In this case, a small quantity of ferrite can be observed in the final stages of the solidification that completely disappears below 1250ºC. The main differences between both steel grades, in terms of solidification, are the final delta ferrite content, a delay in the solidification of the AISI 303 and that the precipitation of MnS starts earlier in this steel grade when only delta ferrite is present.
Fig. 1. Phase diagram at high temperature of the selected heats at a cooling rate of 1ºC/s.
In the case of CSM, two V microalloyed steels have been selected: a low carbon free cutting steel (9SMn28 having a 0.65% wt MnS) and a medium carbon microalloyed steel (38MnSiV5 with a 0.17%wt MnS). An equilibrium analysis by Jmatpro® [4] indicates that in addition to MnS inclusions present in both steels in the whole hot rolling range, small amount of precipitates are expected. These are 0.01 to 0.03 % Ti-V nitrides in the hot rolling span for the 38MnSiV5 steel, 0.1% V- carbonitrides fully dissolved above 900 °C in both steels and 0.03 % Al nitrides disappearing above 1213 °C in the 38MnSiV5 steel (Fig. 2).
In Table 1, together with the chemical compositions of the selected steel grades, the Mn/S ratio and the (Mn/S)c critical value, defined as (Mn/S)c=1.345⋅S-0.7934 are included [2]. A ratio between Mn/S and (Mn/S)c lower than the unity denotes susceptibility to hot shortness and cracking during solidification/deformation due to low-melting temperature interdendritic FeS.
17
Fig. 2. Precipitation and transformation equilibrium temperatures.
Task 1.2: Envelope of processing conditions (Tata, Gerdau and CSM)
In this Task, all the processing conditions, including the definition of parameters involved in both reheating and rolling of as-cast billets/blooms, were acquired and modelled. This information is necessary as input to the mechanical testing programme. The rolling mills considered are: TCM by Tata, Basauri, Vitoria and Azkoitia rolling mills by Gerdau and Mills 1 and 2 by CSM. In these analyses different approaches have been selected, mainly based on previous experience by each partner. Several examples of measurements and modelling of processing parameter parameter are illustrated in the following figures. The 5-stand roughing block of TCM was analysed by Tata using the macro-mesoscale FEM methodology developed in PACROLP-I [1] and others [5]. Critical a-dimensional parameters such as triaxiality (STR), principal stress ratios (SPR), etc. have been derived. Triaxiality-strain plots along projected length of contact, together with frequency plots and mean distribution of mechanical properties have been obtained. For definition of these criteria, please refer to [1 [1,5,6,7]. Fig. 3 shows typical strain (equivalent), triaxiality and principal stress distribution distribution in steady state section (strain only) and at entry bite for the first entry pass of the roughing block. Typical triaxiality-strain plots along projected length of contact, together with frequency plots and mean distribution of mechanical parameters have been extracted and derived at both surface and within the full cross section.
(a)
(b)
(d)
(c)
18
Fig. 3. (a) Typical 3D FEM rolling with partition and submodelling option for TCM box pass (b-d) 2D cross section FEM plots of (b) equivalent strain at steady state (pass1), (c) entry bite triaxiality STR (d) entry bite principal stress and (e) entry bite equivalent strain. (e) The triaxiality-strain plots are very important as they show not only the triaxiality inversion within the projected length of contact but also the magnitude of strain-triaxiality developed according to Rice and Tracey [8] and Bandstra [9]. This will directly affects nucleation and growth of micro-cracks and the conditions to be imposed during mechanical testing both in terms of magnitude but also evolution. Fig. 4 summarises the triaxiality inversion in both longitudinal but also through the cross section. Fig. 5 shows three types of triaxiality-strain profile integrated through the bite at three locations, mid top vertical face, corner/off-corner and mid vertical face (opened collar gap). These profiles in terms of magnitude, gradient and area are a first key step for understanding damage during rolling and provide ways for optimisation. These will be dependent on billet profile (inc. corner radius), pass design profile (roll corner radius, pass width, etc.) and reduction. It can be observed that corner/off corner possesses higher tensile triaxiality-strain profiles (i.e. tensile triaxiality but also principal stresses) carried over a longer time, exposing the as-cast microstructure to longer detrimental conditions.
Fig. 4. Evolution of triaxiality and principal stress ratio along the contact length from entry bite and through the cross section at entry bite.
Fig. 5. Example of triaxiality inversion at 3 positions on perimeter of billet showing mid vertical face (at collar) being positive due to spread, large inversion at billet corner, off-corner but also inversion at mid top vertical face due to billet presentation/pass profile and entry conditions. Heating furnace profiles corresponding to different rolling mills are illustrated in Fig. 6. In summary, the thermo-mechanical conditions associated with the mills have been mapped with respect to temperature, strain rate, triaxiality-strain and other critical parameters. These envelopes have been used as input to the laboratory testing programme (WP2 and WP3). 19
(a) TMC with 5% oxygen
(b) Gerdau rolling mills Stand 1 (R1) vertical axis
Stand 1 (R1) vertical axis 1400 1200
140 mm
1000 T [°C]
T [°C]
1200
240 mm
1000
140 mm
200 mm
1400
800
(b) (a)
Core
600
Core
600
Skin - Top side
400
800
(a) (b)
Skin - Bottom side
400
Skin - Top side
Skin - Bottom side
200
200
Section average
Section average
0
0 0
0.5
1
1.5
2
2.5
0
3
0.5
1
1.5
2
2.5
3
Time [h]
Time [h]
(c) Mill_1 (blooms 240 mmx200 mm)
(d) Mill_2 (140 mmx140 mm)
Fig. 6. Typical industrial heating cycles of different rolling mills. Summary of WP1 The main objectives of this WP were the production of as-cast materials (blooms and billets) for microstructural analysis and for laboratory tests and pilot hot rolling. Different steel grades were selected in order to provide a wide range of possibilities concerning interactions between chemical composition and process variables (casting/reheating/rolling). Based on plant measurements and model applications, the most relevant process conditions were determined to provide required information for the rest of WP (mainly those related to laboratory tests and model simulations).
2.2. WP2: Reheating, industrial rolling and sampling of defects
Tasks 2.1: Reheating and industrial rolling (Tata, Gerdau and CSM) A first series of trials to acquire as-cast, as-cast reheat and wrought at three key positions within the TCM mill (exit roughing block, shears 5 and 8) was carried out by Tata, but focus of study was on effect of production reheat on as-cast structure rather than wrought structure. All pass designs and schedules were obtained for the range of straight and coil bar size with specific attention to the close coupled 5 stands H/V roughing block. Feedstock for LFCS was 180 mm billet which are reheated in a walking beam furnace (max throughput 200t/h) which which includes 3 top and bottom fired zones – preheat, heating, soak with a typical residence time 60 minutes. Trials consisted in obtaining as-cast and as-cast reheat divert billets as input to the project for the EAF route. For the BOS route, 4 different as-cast conditions of LFCS steel billet were obtained. Crops of wrought LFCS at shear positions 5 (crop & cobble pendulum shear) and 8 (Crop and cobble flying shear) were also obtained.
The cobbles produced in the Basauri rolling mill (Gerdau) were studied to evaluate the effect of reheating and rolling on defect generation on stainless steels, as they are more prone to this problem than carbon steel grades. Considering all the production in a given period, Table 4 shows that the
20
cobbles in the rolling of resulphurised (3.8%) and not resulphurised (3.7%) austenitic stainless steels are very similar. However, in the case of steels with Ti the percentage is significantly higher (8.5%). The opposite happens with the martensitic grades (1.0%). Taking into account these results, it can be concluded that sulphur is not involved in the cobbles formation. Table 5 shows the cobbles produced at the different points of the rolling mill. It is obvious that the majority are located at the roughing mill. Additionally, it was confirmed that the cobbles identified in the continuous mill are due to previous problems in the roughing stand and to a poor reheating. Going more in detail, passes 4 (14.7% of all cobbled bars), 6 (22.3%) and 7 (17%) are more prone to form cobbles when the stainless steel is rolled. These passes are associated with higher reductions. Table 4. Cobbled bars distribution in function of the stainless steel grade. Kg of % of cobbles cobbles Austenitic + S 43808 3,8 Austenitic 79040 3,7 Austenitic + Ti 23125 8,5 Martensitic 3490 1,0
Table 5. Cobbled bars distribution in the rolling mill. N. of % cobbled bars Roughing 74 73 Stand 4 vertical 7 7 Shear 5 5 Stand 11 horizontal 3 3 Stand 8 vertical 2 2 Others 10 10
In the case of CSM, because of the lower speeds and interstand distances leading to a better accessibility for monitoring defect generation, this work was mainly carried on Mill_1, starting from ascast blooms of 240 mm x 200 mm. A batch was interrupted with the rolling stock still under the tandem roughing stands, to obtain partially rolled and intermediate stand specimens. In Mill_2, the on-line detection system® [10] was used to capture defects past the 5th and 6th tandem roughing stands. Task 2.2: Effects of reheating on as-cast integrity (CEIT, Tata, Gerdau and CSM) In this task several types of tests were carried out: - TGA (thermo-gravimetric analysis) to study oxidation kinetics and scale morphology - Low stress creep testing under oxidising atmosphere to replicate reheating conditions of LFCS ascast billets. - Low stress creep testing on wrought FCS in both N2 and oxidising atmosphere. - Low stress creep testing in Gleeble (wrought C-Mn and as-cast LFCS grades). - Laboratory reheating of artificially damaged samples - Billet pieces of AISI 303 and 304 L attached to a transport billet and reheated. TGA (thermo-gravimetric analysis) LFCS oxidation kinetics was studied by Thermo-gravimetric Analysis (TGA) to measure weight gain due to oxidation as well as profile of detailed scale morphology. Heating profile of Fig. 7 was imposed under controlled reheating atmosphere (2% O2). Optical microscopy (LOM) and SEM/EDAX was also carried out on TGA samples (Fig. 8). Presence of FeS can be clearly observed in the EDAX maps. The EDAX chemical map analysis included spot analysis starting from blistered magnetite (assuming thin hematite layer was spallated) (1) then dense magnetite (2) followed by non-stoichiometric wustite (FexO) with lower FeO composition close to the magnetite than the steel including presence of large nodules/rosette clusters (Fe, Si), then most importantly FeS (11, 13) and (Mn,Fe)S formation (14) in the scale ingress/grain boundary but also steel matrix sub-surface (14). Using a simple linear conversion between weight gain and scale thickness (ideally a parabolic conversion should be used), for 1g oxide gain/cm2 equivalent to 7230 µm of scale thickness, the total scale thickness can be estimated at 1480 µm [11]. From LOM micrographs the maximum scale thickness was ~1900 µm.
21
Fig. 7. Heating profile selected in thermogravimetric analysis (TGA) tests.
Fig. 8. SEM/EDAX analysis on thermogravimetric analysis samples corresponding to LFCS steel Low stress creep tests under oxidising atmosphere similar to TCM Low stress creep tests under oxidising atmosphere similar to TCM industrial conditions (2% excess O2 (dry)) were done. Non standard creep test specimens were used with specific weight in order to impose a ~1 MPa stress during reheating/soaking. Two conditions were studied: 1/ heating to 1220ºC in argon followed by a 40 min- soak in a simulated 2% excess O2 atmosphere, 2/ heating to 1220ºC and soak sample at 1220ºC for a total time of 80 min. Following testing, LOM observation of surface/sub-surface state in both cross transverse and longitudinal sections was carried out. Fig. 9 shows the oxidation state and sub-surface oxide penetration within the LFCS steel through the gauge length and grip section, respectively. In summary, as time under uniform temperature (1220ºC) increases (double), oxidation penetration/embrittlement increases from 100 µm to 330 µm below the oxide scale layer. It is also clear that opening of grain boundary/oxidation is accelerated under stress (1 MPa) between the gauge section and upper grip of sample at the longer soaking time.
22
SEM-EDAX and EPMA characterisations indicate that Mn depletion bands are created with grain boundary penetration of FeS under oxidising atmosphere and stress much below the scale metal interface therefore creating a change in sub surface (~200 µm) in chemical profile. The quantitative analyses and qualitative maps show that the P and Mn content of the steel matrix dropped towards the surface and that MnS tend to be oxidised to MnO. Low stress creep testing on wrought FCS in both N2 and oxidising atmosphere One series of tests were carried out on wrought FCS submitted to a temperature of 1220ºC, and 1 and 10 MPa tensile stresses in both inert (nitrogen) and TCM atmosphere. Microstructural characterisation was also carried out to assess ferrite grain size and any sign of damage/oxidation state. Oberhoffers reagent and careful etching was used to reveal the microstructure, inc. a polish-etch technique where the etched surface is polished partially back after etching to remove staining that occurred during etching. The analysis indicated that oxidation penetrates the grain boundary and may promote formation of FeS. Damage was not present, except along closely spaced and large MnS inclusions. Low stress creep tests on both C-Mn and LFCS grades Controlled tests in the Gleeble 3800 based on gauge free low C-Mn and LFCS 209 G4A type specimens were carried out. Range of stress magnitude studied varied from 5 and 20 MPa within a temperature range from 1180 to 1250ºC with a mean of 1220ºC (mean temperature for LFCS). Stress, strain and creep rate can be calculated and derived (see Fig. 10). The results indicate that at a stress of 4.5 MPa, creep rate for LFCS is still in regime II at 1220ºC after 1h test. As load increases regime III appears for load of 60 kg after 1000 s. Regime II for LFCS operates within limit of a strain of 0.05 and stress of max 4.5 MPa. These tests are useful to understand limit during reheating of potentially opening grain boundaries and promoting damage under creep. It shows as temperature increases (1250ºC), creep rate increases and therefore stress has to be maintained at a lower level to minimise creep damage. Lower reheating temperature is potentially preferable to minimise damage cavitation. Heating profile 2
cross section (grip section)
longitudinal section (gauge length)
Heating profile 1
Fig. 9. Optical micrographs of creep tests under oxidised atmosphere.
23
Fig. 10. Strain and stress response as a function of time (max 1h) for C-Mn and LFCS grades. Laboratory reheating of artificially damaged samples In order to evaluate the evolution (during ulterior reheating and strain application) of small previous defects in the as-cast microstructure, 3 and 4 point bending (3PB and 4PB) fatigue tests were done to obtain very fine flaws emanating from the as-cast surface. The samples have been machined from steel billets 9SMn28, 38MnSiVS5 and AISI 303. Cracks with length smaller than 1 mm have been obtained. Although in some cases larger cracks were induced, the initial objective was to produce not very profound defects. Several examples are illustrated in Fig. 11.
9SMn28 AISI 303 38MnSiVS5 Fig. 11. Artificial cracks on as-cast surface after 4PB fatigue tests. In the case of 3PB specimens machined from 9SMn28 material, although the tendency of crack nucleation should be maximum at the centre of the specimen, in almost all the cases the nucleation of the cracks is related to the presence of oscillation marks and superficial oxides through the inner of the billets. In the 4PB samples, the cracks are also associated with defects and oxides. However, it must be pointed out that no all the marks and oxides have cracks associated after performing the tests. AISI 303 specimens have cracks associated with defects and regions of MnS type II inclusions. In the case of 38MnSiVS5 steel, small cracks appear in some cases associated with segregation of Ni and Cu near the as-cast surface. These artificial damaged materials have been used to analyse the evolution of flaws and their interaction with microstructure during reheating. As a consequence, some of these samples with cracks and also samples with no cracks (LFCS 9TZ9: 202 and 211) have been reheated simulating conditions of a billet in an industrial furnace (information provided from D2). Different schedules have been used. The reheating conditions are listed in the following table. Table 6. Laboratory reheating conditions. Laboratory reheating conditions
Materials
Atmosphere: Air-Room atmosphere Time = 4 h 15 min., temp 1170ºC Atmosphere: Dry conditions (%CO2 =10.68, %N2 =87.21, %O2 =2.10) ~10% excess air. Time = 4 h 30 min. (heating: + 5ºC/min), temp. 1200ºC Atmosphere: Wet conditions (%CO2 =8.85, %N2 =72.22, %O2 =1.74, %H2O=17.19). ~10% excess air Time = 4 h 30 min. (heating: + 5ºC/min), temp. 1200ºC
24
9SMn28 - 3PB samples 9SMn28 , AISI 303,38MnSiVS5 - 4PB samples LFCS 9TZ7 202/16; 211/16 9SMn28, AISI 303, 38MnSiVS5 - 4PB samples LFCS 9TZ7 202/16; 211/16
Billet pieces of AISI 303 and AISI 304 steels Billet pieces of AISI 303 and AISI 304 L attached to a transport billet have been reheated in the reheating furnace of Vitoria rolling mill (Gerdau). After reheating, the transport billet has been discharged from the furnace and the steel samples removed for characterisation (Task 4.1).
Task 2.3: Defect sampling (Tata, Gerdau and CSM) Typical production billet defects are presented in Fig. 12 ranging from intergranular cracking to ductility breakups with scaled branched defects up to 1 mm deep potentially associated with casting defects (blowholes, etc.) originated from offcorner/corners of billets.
Fig. 12. Examples of typical casting and hot ductility breakup production surface defects (LFCS steel). Another example of defect sampling (from industrial hot rolling) is indicated in Fig. 13 for the case of 38MnSiV5 steel: in spite of the presence of oscillation marks, no evidence of surface defects were found in the as-cast-RH stock; transverse cracks ((a1) and (c)) at edge in stand R2 and others fully developed at R5 (b1); a mid-face, short longitudinal crack at stand R3 ((a2) and (d)). Longer longitudinal cracking was detected in the 90 mm bar by NDT Magnetoscopy (b2). The observed edgetransverse and mid-face short longitudinal cracks had 0.5 to 2 mm depth (b1-c), while the few long cracks (b2) were of the order of 1 mm deep.
(a1)
(a2)
(b2)
(b1)
25
(c)
(d) Fig. 13. Industrial rolling of 38MnSiV5 steel: (a1) transverse edge cracks past stand R2; (a2) mid-face short longitudinal cracks past R3; edge cracks past R5 (b1) and longitudinal crack R9 (b2); (c) and (d) cracking details stands R2 and R3. Summary of WP2 In addition to industrial rolling of as-cast material collected in WP1 and defect sampling, the other main activity of this WP was the analysis of the relevance of reheating on as-cast microstructure. Thermogravimetric analysis clearly indicated the risks of presence of FeS and (Mn,Fe)S low melting products located at the scale ingress/grain boundary and at the steel matrix sub-surface. In addition, the results obtained with the low stress crept tests indicate that small stresses acting during reheating will enhance the oxidation penetration favouring the opening of grain boundaries. This effect is more notorious as temperature and soaking time increase.
Finally, with the help of 3 and 4 point bending fatigue tests, small cracks were nucleated at as-cast surfaces. These samples were heat treated at different simulated industrial conditions to analyse the evolution of these defects and their surrounding area. All the the samples were microscopically studied in WP4.
2.3. WP3: Experimental laboratory study of damage nucleation, growth, coalescence and healing Task 3.1: Laboratory mechanical techniques to study damage nucleation, growth, coalescence and healing (all partners) Different mechanical (macro/micro) testing techniques have been used to study the damage mechanisms with respect to existing or newly developed heterogeneities acting at the scale of interest. In this context, there are two main aspects that are considered: Wide range of mechanical conditions of the tests providing micro and macro scale analysis. Specific location of the samples in relation to the as-cast microstructure. Table 7 summarises the different mechanical tests selected. One of the main aspects is the location of the specimens in relation to the as-cast material. This allows capturing relevant information concerning changes in the microstructure from the surface to the inner part (local heterogeneities...). Fig. 14 shows some examples about how this has been done. In addition to the differences in mechanical conditions and locations, several thermomechanical schedules were applied (see Fig. 15). Referring to the 26
mechanical conditions, it is worth emphasising that a wide range of triaxiality has been obtained, starting from those achieved with the different geometries of the revised plain strain compression (RPS) specimens to that of null triaxiality in the case of torsion conditions. Some of the main features are described in the next paragraphs.
Table 7. List of different (thermo)mechanical tests performed in WP2 and 3. Revised plane strain compression RPS tests: Different taper angles alloying several triaxiality-strain paths with/without retained as-cast surface. Deposited gold microgrids on RPS specimens with simulation material (Tata).
Tensile tests: - Conventional specimen: machined very close to as-cast surface. Different thermomechanical cycles (reheating temperature, deformation temperature and strain rate) (Gerdau and CSM). - Conventional specimen: specific tests with in situ melting (or incipient melting) prior testing (CSM). - Taboo specimen: flat microsamples extracted from chilled zones. Speckle technique. Singular specimens with holes drilled (strain field measurements) (CEMEF). - Creep tests (Tata). - Micro specimen (flat and round): high temperature 3D X-ray in-situ and ex-situ tomography (Tata). 3 or 4 point bending (3PB, 4PB) tests: - Small specimens to nucleate small cracks from as-cast surface (fatigue precracking) (CEIT). - Hot bending of specimens with as-cast surface under flexion (Gerdau). Torsion tests: Monotonic tests with different reheating temperatures and strain rates. Interrupted tests (CEIT). Axisimetric compression tests: - Tests to determine constitutive laws (CSM). - Small specimens to evaluate inclusion deformability (CEIT).
(a) RPS specimens
(b) EDM flat specimens
(c) Torsion specimens
(d) flat micro-tensile specimen (Taboo) (e) Diamond beamLine flat specimen Fig. 14. Examples of specimen geometries and locations in relation to the as-cast condition.
27
1100, 1200ºC
1200oC,
5 s-1
5min
Temperature
(5 min)
880oC 16 oC/s, 30s
5ºC/s 1s-1 25,40,50%
1 ºC/s
Air Water Quenching
time
RPS
Torsion
1000-1300ºC
10 s-1
Temperature
(1 min) 10 ºC/s
Air
time
Micro-tensile (Taboo) Tensile (conventional) Fig. 15. Examples of thermomechanical cycles selected for the mechanical tests. Revised plane strain compression RPS tests (Tata)
RPS compression specimens with/without retained as-cast surface The RPS geometry can be composed of one to four tapered faces with specific inclination (10 to 60o) to promote required level of triaxiality-strain ratios on both orthogonal faces. By machining inclined front and backend faces as denoted by the first taper index, together with side faces (second index), one can generate in a single test at least two states of stress-strain conditions, i.e. mid triaxiality and strain together with high triaxiality-low strain regions as shown in Fig. 16c and d. Path plots of interest will be at front (path3) and side (path2) mid horizontal planes (dashed lines in Fig. 16e-f). As compared with Pacrolp I, a full as-cast face was preserved on RPS samples.
(a)
(b)
(e)
(f)
(c)
(d)
(g)
Fig. 16. RPS specimens with specific tapers: (a) 45/30º and (b) 10/45º, (c) Equivalent strain (PEEQ) for 30% reduction, (d) STR (triaxiality) predictions for 30% reduction case 45/30º, (e) Path plots for transverse denoted path 2, (f) path plot for front mid horizontal planes, respectively denoted path 3, (g) machined RPS specimens with 3 tapers. It can be observed that the level of triaxiality (paths 2 & 3) is established early in the test and shows an inversion at ~1.8 to 2.4 mm from the external surfaces of both sides of the specimen as shown in Fig. 17a. Influence of taper of the RPS specimen has been studied with respect to its effect on a-dimensional
28
mechanical parameters such as SPR, STR, etc. Fig. 17b-c shows evolution of triaxiality (STR) and maximum principal stress (SPR) on path 3. It can be seen that a minimum taper of 45o is required on the front plane to promote triaxiality and stress principal ratios of relevance to rolling conditions. Inversion of triaxiality function of position (from external surface) reduces as taper decreases. The external side face (path 2) does not show any dependency on taper, only affecting the central core of the plane strain plane (Fig. 17d).
(a)
(b)
(c) (d) Fig. 17. a) Triaxiality (STR) vs. distance in mm for 3 reductions (5, 25 and 50%) plotted on paths 2 and 3 (solid line) (case of 45/30º), (b-c) STR, SPR ratios at 30% function of taper (10,30,45º) plotted for path, (d) STR ratios at 30% function of taper (10,30,45º) plotted for path 2 (side face). Deformation imposed in this series of tests ranged from 25, 40 to 50%, under three strain rates of 0.1, 1 and 10 s-1, with deformation temperature, following conditioning of austenite at 1200ºC, from 880 to 1180ºC,at interval of 60ºC. A 5ºC/s heating rate to 1200ºC was imposed whilst a cooling rate of 16ºC/s to deformation temperature was used. Argon atmosphere was used and therefore this type of tests will not be representative of the reheating profiles under production reheat oxidising atmosphere shown in WP2. In total more than 157 tests were carried out with varying reduction, temperature and speed. Thermal etching based on machined RPS with one micropolished face deformed in vacuum (10-5 torr) The method of thermal etching consists in revealing the prior austenite grain boundaries (GB) in a prepolished sample by formation of grooves in the intersection of austenite grain boundaries when the steel is exposed to high temperature in vacuum or inert atmosphere. These grooves decorate the GBs and make it visible at room temperature under optical microscopy. This equilibrium between triple junction and the free polished surface is set-up quickly at high temperature so that the free surface adjacent to the line where the GB emerges becomes tightly curved. The aim is therefore to use this technique on polished RPS samples on the face of interest normal to path 3 (see Fig. 16f). Conditions applied range from 5 to 25% for samples reheated to 1000ºC and deformed either at 1000ºC or 880ºC.
29
Deposited gold microgrids on RPS specimens with simulation material A simulation material was selected to suppress transformation effect whilst retaining similar recrystallisation kinetics and flow stress characteristics to CMn/FCS steel grades. Based on previous work published on suitability of Fe30%Ni in wrought condition to replicate CMn steels, it was decided to cast a 60 kg melt of Fe30%Ni 0.3%S (0.07C 30% Ni, 1.05%Mn) with specific conditions to promote formation of MnS whilst reducing porosity formation. Two 60 kg casts were made during the course of the project. Microgrid technique is a technique to study the inhomogeneous deformation at the scale of the microstructure using an electron micro-lithography technique (see Fig. 18) [12]. It is used as a complementary technique to 3D Xray tomography to measure distribution of local strains brought about by the presence of grain boundaries but mostly MnS inclusions. The aim is to validate microFEM models of deformation with MnS as well as at later stage damage. Strain maps can then be plotted over representative areas of the microstructures together with strain distributions within each phase of the microstructure. Gold microgrids have revealed to be best suited for studying strain distribution at high temperature on the assumption that oxidation is prevented. By combining the microgrid technique with a simulation material, avoiding solid state transformation, strain maps should remain during cooling of samples. As series of tests have been carried out on the Gleeble 3800 under high vacuum (10- 5 torr) and are reported in WP4. In addition, microgrids were also deposited on LFCS to check whether these will resist transformation during natural cooling.
Fig. 18. Example of microgrid deposited on LFCS BOS steel (pitch 2.5 µm)
Hot tensile tests Conventional hot tensile tests (Gerdau and CSM) Different types (geometries and thermomechanical cycles) of tensile tests have been done with “conventional” specimens. Hot tensile tests were performed on austenitic stainless steels to study the influence on ductility of the sulphur content (AISI 303 vs. AISI 304L), the region of the billet (faces vs. corners), the hot work (billet vs. roughed bar) and the rolling mill (Basauri vs. Azkoitia). Fig. 19 shows the differences between AISI 303 and AISI 304L steels. Sulphur reduces hot ductility around 10% in terms of area reduction. This difference can look small, but it means that AISI 304L is over 60% of area reduction at any rolling temperature; however, AISI 303 must be deformed at least at 1150ºC to reduce cracking susceptibility. With regard to corners and faces, the behaviour is very similar up to 1200ºC in both steels. The ductility of corners and faces is different at higher temperatures: for both steel grades the ductility of faces is better than the ductility of corners. This result is opposite to the behaviour observed in other steel grades (see Pacrolp I final report) in which the billet corners have worse ductility due to oscillation marks, solidification defects, etc The cooling rate of the corners is higher than the faces and consequently there can be more delta ferrite in the corners. Taking into account that the safe level of delta ferrite is 2-5%, in the case of AISI 303 (DFW=2.7%) an increment of delta ferrite is good and the observed ductility of corners increases continuously with the temperature. The faces of this steel grades can be closer to the lower limit of the 30
safe level and a fall in the ductility is found at 1300ºC. The AISI 304L is in the other extreme of the safe level (DFW=5.0%) so an increment of delta ferrite in the corners involves the fall of the ductility at 1300ºC, however the faces continues inside the safe level and the ductility keeps at high temperature. For the study of wrought material, roughed bars form two rolling mills were sampled (rolling conditions in Table 8). In the case of wrought material (Fig. 20), the difference between the steel grades continues evident. However the difference is not constant. At lower temperatures the difference is around 10% but the ductility of both steels is the same at 1300ºC. The behaviour of corner and faces is very similar. Table 8. Rolling conditions of the sampled roughed bars for wrought material characterisation. Rolling mill Basauri Azkoitia
Number Pass schedule passes 5 D-D-S-D-S 6 B-B-D-D-D-S
Bar size (mm) 98x98 91x91
Reheating time (min) 160 180
Reheating temp. (ºC) 1200-1295-1295 1100-1240-1240
The ductility of the billet and the roughed bar are compared in Fig. 21 in the case of AISI 303 roughed in Azkoitia. It is evident that there is an important increment of ductility after the 6 passes in the roughing stand. The effect of the rolling mill can be analysed in Fig. 22, where some differences can be found between Azkoitia and Basauri mill for AISI 303. At high temperatures, the ductility is better in the bars roughed in Azkoitia. The main difference between Basauri and Azkoitia roughing stand is that in the second one there is one pass more and a lower average reduction per pass.
Fig. 19. Hot ductility curves of 155x155 mm billet corners and faces. AISI 303 and AISI 304L.
Fig. 20. Hot ductility curves of 91x91 mm bars roughed at Azkoitia rolling mill.
Fig. 21. Hot ductility curves of billets and 91x91 mm bars roughed at Azkoitia rolling mill.
Fig. 22. Hot ductility curves of bars at Azkoitia rolling mill and Basauri rolling mill.
Interrupted tests at different steps of deformation were performed to analyse damage evolution. Fig. 23 shows the stress-strain curve with the point at which the tests were interrupted and the values of strain and reduction of area. The material comes from the selected AISI 303 billet corners. In order to expand the analysis conditions of the tensile tests, CSM tested re-fused and solidified in situ several specimens as well as rolled specimens. They were next pre-treated (Table 9) as follows: (a) Pre-reheated at industrial cycles and rolled (9SMn28 and 38MnSiV5-1) (b) Re-fused and solidified in situ (38MnSiV5-0) (c) Reheated to 1425°C to solubilise and spheroidise some MnS (its wt% reduced from 0.16 to 0.06) and (Ti,V) nitrides, in an environment with incipient 8 % liquid phase. (38MnSiV5-1-TT)
31
Fig. 23. Interrupted hot tensile tests of AISI 303. Points indicate interruption of deformation. Billet corners. Temperature 1250ºC. Strain rate 10 s-1. The first group were intended to break the dendrite structure and obtain the base ductility trough, as well as hot working behaviour after grain refinement. The last two aimed to modify austenite microstructure and shape of inclusions. Cylindrical specimens were cut after preconditioning and reheated again once mounted at Oulu University Gleeble machine for testing. Standard isothermal tension testing of cylindrical specimens was performed on both grades. The main work was done on the samples (a) and the testing conditions are described in Table 9. The low C steel results show a general trend of a much lower ductility respect to the medium C steel (Fig. 24), and a higher sensitivity to strain rates in the range 0.1 to 5 s-1 representative of the roughing conditions.
Table 9. Pre-mechanical testing treatments (CSM). ID
9SMn28
38MnSiV5-0
Fig. 24. Experimental ductility of the two steels studied by CSM.
starting conditions
as cast
as cast
RH conditions • RH0: 2 hours @1180 °C • Rolling:1090 °C/45%/0.5 ms-1; Air cooled.
-- --
• RH0: 2 hours @1275 °C • Rolling:1230 °C/15%/0.5 ms-1; Air cooled to 650 °C 38MnSiV5-1 as cast • RH00:1 hour @1250 °C; Rolling:1164 °C/25%/0.5 ms-1; Air cooled to Room Temperature • RH: Load @ 1350 °C, steady @ 1425 °C in 3’ 50”, 38MnSiV5-1-TT 38MnSiV5-1 • 10 minutes holding; Unload+Air Cooling
Testing • RH @ 10°C/s to 1150°C, 2 minutes soak, cool @ 5°C/s to Tdef, hold for 15 s, • Tensile deformation+ jet Air Cooling • RH@ 5°C/s to 1500°C, 3 min. @1500 °C • Drop to Tdef in 1 minute, hold 1 minute, • Tensile and compresive deformation, jet Argon cooling.
• RH @ 10°C/s to 1200°C, 5 min soak, cool @ 5°C/s to Tdef, hold for 1min, • Tensile deformation+ jet Air Cooling
• RH @ 10°C/s to 1200°C, 5 min soak, cool @ 5°C/s to Tdef, hold for 1min, • Tensile deformation+ jet Air Cooling
The 38MnSiV5-0 specimens were melted in situ to obtain liquid phase as well as MnS and carbonitrides into solution, cooled to deformation temperature and tested at slow speed. In spite of some scattering, the ductility above 1040°C conforms to the group (a), but it drops significantly below that temperature. At equal testing conditions than the group (a), the TT material showed small ductility differences up to 1040°C, but significant scattering beyond this temperature (Fig. 24). Micro tensile tests (CEMEF) Micro tensile tests at high temperature were done by CEMEF with the Taboo machine for the case of AISI 303 steel. The Taboo machine is a tensile machine developed at CEMEF which allows testing very small specimens. The different parameters (temperature, strain rate) were fixed in order to localize strain in the central part of the samples (20 mm length zone). In order to get accurate surface field 32
measurements with the speckle technique it was necessary to avoid oxidation. An inerting procedure was developed for the Taboo system with two inerting chambers (see Fig. 25).
Fig. 25. Taboo system: (a) the largest inerting chamber and (b) the local inerting chamber.
a)
b)
In a first experimental campaign eight samples were tested (Fig. 14). S-specimens were extracted in the flat part of the considered bloom at two different depths from the surface whereas C-specimens were extracted in the corner of the bloom, at two different depths from the surface. The first step of the analysis was to study the rheological behaviour of each steel grade. The S4 sample (Fig. 26) shows an important decrease of the load at t=1010 s. This test had to be stopped because the thermocouple welding broke during the tensile stage (the second part of the curve is not valid). S1 and S2 samples exhibit the same behaviour. No difference due to the sample location can be observed. The hardening of sample S3 is a little bit lower than the one of sample S1 and S2. Analysis of the C series samples shows that close samples (C1-C2 and C3-C4) have a relatively “similar” behaviour (Fig. 26). The heterogeneity of the material due to the different location of the sample seems to have more influence than the heterogeneity due to the location of the sample in the bloom skin. However, a small difference can be observed in between the two samples extracted in the same corner. In addition to macro analysis of the results, full filed measurements were done (see Appendix A). 160 Stress (MPa)
C3
Stress (MPa)
160
S1
S2
140
C4
140 C1
120
120
S3 S4
100
C2
100 S4 S1 S3 S2
80
60
80
C4 C1 C3 C2
60
40
40
20
20 Strain
Strain
0
0 0
a)
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
b) Fig. 26. Stress-strain curves of a) S-series samples and b) C-series samples.
In a second campaign of tests, Taboo micro-tensile tests on drilled sample were realized with the same stainless steel grade used for the first Taboo campaign and with the same dimensions. These tests were very useful to visualize and to understand the appearance of damage mechanisms but also to validate numerical developments realized in WP5. The thermo-mechanical conditions used for this new campaign were slightly different from those used for the first campaign and are described in Fig. 27 (left side). Samples were drilled with two holes of 1mm diameter, the positions and locations considered are summarized in Fig. 27 (right side). These samples were extracted in the rolling direction and from the centre area of the bloom. It was decided to drill the holes at specific locations so as to preserve a ligament of material equals to the hole diameter between the two holes. Thus, the area with defect has a characteristic length equal to 3 mm. This value is non-negligible compared to the sample length and some border effects could have slightly influenced the obtained results.
33
Fig. 27. Thermo-mechanical conditions for the drilled samples and geometries for the holes positions. The three configurations were tested on the Taboo machine and repeated two times with repeatability of the obtained trends. In the following, only the results corresponding to the 90º configuration will be described (Fig. 28) as follows: (a) The first experimental images where a crack appears. (b) The strain fields computed using the digital image correlation (DIC) technique. (c) The macro stress/strain curve. The macro value refers to the analysis of the load/elongation curve. This analysis is done by considering a non-drilled sample.
Fig. 28. Drilled samples results corresponding to 90º configuration. The following trends have been obtained:
o Fracture appears first between the two holes (Fig. 28a, E4-333 image), the strain localisation is also observed between the two holes Fig. 28c – img=333 image). The equivalent strain reaches a value of 0.43 when the crack occurs. o Before the crack appearance, the shape of the two holes evolves from circle to elliptic shape. However, no clear interaction is observed (Fig. 28a – E4-333 image).
34
o A second crack location appears in Fig. 28a – E4-478 image. The two new cracks are located between the holes and the sample border. In Fig. 28c – img=400 the strain localisation is also observed in this area, the equivalent strain value at rupture reaches 0.66. Thermal effects could explain the difference between the two strain crack values. Indeed, the sample section decreases when crack occurs, thus the local current density increases. This increasing leads to increase the joule effect power and so the temperature. For a higher temperature, the equivalent strain to fracture is higher. o In Fig. 28b, the macro stress/strain curve is described. The two cracks initiation times can be observed. In fact, the curve exhibits two deflection points (arrows in Fig. 28b) which can be linked to the initiation of the two cracks. The study of the different drilled samples allows obtaining the following remarks: • the ratio between the diameter of the holes and the dimension of the sample must be reduced in order to avoid border effects. • The 45° configurations allow observing a shear band mechanism between the 2 considered holes. This shear band is finally a preferential way for the sample fracture. This specific configuration induces an interaction between the 2 holes. • The 0° and 90° configurations do not show clear interaction between the 2 holes. • The maximal equivalent strain reaches for the three configurations are quite similar (equal to ~0.65). A lower value is measured on the 90° configuration; this difference may be due to a nonhomogenous thermal field. It may also come from a difference in terms of stress triaxiality ratio higher between the voids than in the section between voids and borders of the sample. This experimental study with three different configurations shows the importance of the position of voids. A quantitative study of the impact of the position remains difficult, due to border effects and due to the non-homogeneous thermal field induced by this border effect. However, these experimental tests and observations have been crucial in order to validate the numerical model developed at the voids scale. This validation is related to the WP5 and particularly to the D16 deliverable. High temperature tensile in-situ and ex-situ synchrotron Xray microtomography (Tata) In collaboration with Imperial College and University of Manchester, in situ ultra-fast synchrotron Xray tomographic of FCS steel during hot deformation was done. The material was a BOS 209 grade from bar 10 which was cut 45.5 mm from an as-cast billet wide-face surface. The material was machined into a uniaxial tensile test piece with 1 mm diameter and 6 mm length at the gauge. Synchrotron X-ray microtomography during in situ tensile tests were performed at Beamline I12 at the Diamond Light Source using a 53 keV monochromatic beam. A Phantom camera with 800x600 pixels at a spatial resolution of 12.22 µm was used to acquire radiographic images during the experiment. At the beginning of the experiment, the sample was heated to 860 ºC to simulate the typical hot forming temperature of FCS acting at steel surface. Then, the load was applied at a constant cross-head displacement of 5 µm/s using a bespoke rig and furnace. The radiographs were continuously acquired at an integration time of 16 ms while the sample was continuously rotated and under load. This experiment configuration resulted in a full 3D tomographic volume every 12 s and 24 3D volumes were acquired from the undeformed to fracture stages. Using this set-up, minimum resolution is 12µm, not enough to distinguish damage (void) to inclusion (except large ones). In view of acquisition of under load (full tomographic volume every 12 s), the strain rate had to be very low (less 10-3 s-1). The previous experiments were supplemented with interrupted Gleeble tensile testing carried out at Imperial College which were then fully tomographed to provide higher spatial resolution down to 1.8µm. Gleeble tensile specimens were machined with a notch diameter of 6 mm to fit the X-ray field of view. Before testing, the samples were reheated to the upper range (1200ºC) of the typical industrial hot forming operations, and then cooled and held at 1000ºC during deformation. Two different levels of strain-to-failure (ε/εf) of 78% and 90% after necking were analysed by interrupting the test before failure. In order to freeze the level of damage evolution within the microstructure, samples were quenched in water immediately after the desired level of deformation was reached. Specimens were scanned using a monochromatic X-ray beam of 76.5 keV at beamline I12, Diamond Light Source. A camera with a resolution of 1.8 µm was used to obtain a high resolution of the evolution of the damage
35
in the interrupted microstructure. A series of 1441 projections was taken over 180 degrees at an exposure time of 1 s, resulting in a full set of data required for reconstructing a 3D volume. Three point bending tests (Gerdau) Three point hot bending tests have been carried out on specimens machined form billet corners. Despite the temperature of the furnace was 1250ºC, the temperature at bending ranged 991-1180ºC (small size of the specimens and transport time from furnace to press). These temperatures are low compared to industrial conditions, but they could be helpful because the formation of defects is forced. The first observations refer to the general surface appearance. In both steel grades the surface is rough but in particular the surface of AISI 304L is described as very rough (Fig. 29). In this last case very small cracks are present and they can be due to hot shortness. It is possible to observe how the small cracks penetrate at the back of the specimens. Regarding important defects, only AISI 303 presents cracks due to oscillation marks opening. Monotonic torsion tests (CEIT)
AISI 304L
Monotonic hot torsion tests have been done with AISI 303 steel at different conditions (Fig. 15). In order to study the ductility and damage evolution, some tests were interrupted at different deformation levels before failure occurred. At the end of the test, the specimens were water quenched in order to study the interaction between damage evolution and microstructure. In the tested range conditions, strain to failure is higher as temperature increases and strain rate decreases.
Oscillation marks not opened
Cracks at the back of the specimen
Rough surface cracks free
Oscillation marks opening
Back of specimen free of cracks
AISI 303
Very rough surface with small cracks
Fig. 29. Detailed view of the surface of three point hot bending tested specimens. Compression tests (CSM and CEIT) Isothermal, constant strain rate axisymmetric compression tests up to 0.55 strain were performed by CSM on both 38MnSiV5-1 and 9SMn28 steels pre-conditioned as in Table 9. Typical experimental data for the 38MnSiV5 steel are shown in Fig. 30. A limited number of stress relaxation experiments were carried out to assess the effect of static (SRX) and metadynamic (MDRX) recrystallisations under the basic operating conditions of Mill_1. The results indicated that recrystallisation is complete for the temperatures and interstand times up to R4 for both steels. CEIT has performed hot compression tests with 9SMn28 as-cast steel to study the influence of deformation mode on the plasticity behaviour of MnS inclusions. Cylindrical specimens (10 mm length and 5 mm diameter) were machined parallel to the casting direction at different distances to the surface: close to the as-cast surface and at 5 cm from the surface. In order to study the damage and plasticity evolution of inclusions tests were performed up to ε= 0.2, 0.5 and 1 in the case of samples machined 36
near surface, and ε=1 in the case of samples machined from the inner region. The samples were heated up to 1150ºC (5 min) and then deformed up to the selected deformation level and quenched.
Fig. 30. Constitutive law and its fitting (in black) to hot compression results for the 38MnSiV5 steel. Task 3.2. Pilot mill rolling (CSM) The objective of these trials is to provide complementary material/information to that obtained from industrial rolling conditions. The thickness of the cortical zone prevents inner cracks propagation to the surface [1]. In order to capture generation of new cracks, pieces were cut away from the central porosity zone and an hc=13 mm layer was removed from their as-cast surface, thus eliminating the cortical zone (of mean thickness 7 mm). The experiments were carried out as flat partial rolling rolling for tracking defect generation during deformation, using a 60 % rolling reduction, with the initial geometry, reheating conditions, temperatures and speeds detailed in Table 10. Table 10. Pilot mill rolling conditions.
38MnSiV5
9SMn28
cross section geometry
Ho/Wo mm
dendritic grain axis vs. roll axis
RH °C/min (core)
20/100
†
1100/60
---
960 °C core, 0.5 m/s 60 % red
YES
--
29/100
†
1150/60
---
1041°C core, 0.5 m/s 60 % red
YES
--
16/100
†
1190/60
---
1146 °C core, 0.5 m/s 60 % red
NO
--
29/68
||
• Load at 1275 °C 1275/20 • Re-stabilization in15-20'
Notes
• Tdrop on table ready to roll: min=1180 °C • Tdrop to 900°C in 2' 40''
rolling
CRACKING
NDT
1000 °C core, 0.3 m/s 60%red setup-57%real
NO
900 °C core, 0.3 m/s 65% red set up
NO
(-)
950 °C core, 0.3 m/s 60% red set up
NO
(-)
(-)
29/68
||
1275/10
29/50
||
1275/90 • T tail surface =840 °C
29/50
†
1200/90
• (20' load+90'steady) • edge(Tail measure):820 °C
950 °C core ,0.2 m/s 60% red set up
NO
(-)
29/50
†
1275/90 • edge(Tail measure):750 °C
901 °C core, 0.2 m/s 60 % red
NO
(-)
29/50
†
1275/90 • edge(Tail measure):830 °C
950 °C core, 0.2 m/s 60 % red
NO
(-)
29/50
†
1275/90 • edge(Tail measure):1040 °C
1200 °C core, 0.5 m/s 60 % red
NO
(-)
37
Fig. 31. Effect of rolling temperature on edge cracking of steel blooms for a hc=13 mm removed cortical layer, 60% roll pass reduction, experimental mill. The experiments with the 9MnS28 steel on initially squared edges stocks, showed visible edge and surface crack generation below 1040 °C, more profuse as temperature diminished (Fig. 31, Fig. 32). Similar geometry rolling experiments on 38MnSiV5 did not produce any cracking, either visible or searched by Magnetoscopy with a resolution up to 1 mm in depth, for two orientations orientations of the original dendrite grains respect to the roll axis. Subsequently, modified lateral surface geometries aiming to enhance the tensile strains due to bulging and hence accelerate cracking, were tried for this second steel (Table 10). However, neither eye-inspection nor Non Destructive Testing (NDT) revealed any cracking in the second steel (Fig. 31, Fig. 32). The pilot mill results are in agreement with the difference in ductility levels shown by both grades in Fig. 24.
Summary of WP3 A significant high number of mechanical tests with different testing conditions (state of triaxiality, strain rate, temperature…) have been done. The selection of specific locations locations (close to the as-cast surface...) of the specimens is another main aspect that has been considered (this mainly affects geometrical characteristics of MnS inclusions and also, possibility of presence of segregations/heterogeneities, see WP4). This wide range of testing conditions allows having a good interval of relevant parameter values for modelling validation (for example damage models comparisons with the results achieved with RPS tests) considered in WP5. As the main results of these tests proceed from the corresponding microstructural and damage analysis in WP4, the most important conclusions will be addressed in this WP. The specific conditions applied in the pilot rolling mill trials provide addition information, compared to industrial hot rolled material. For example, with these trials it has been possible to evaluate the behaviour when there is not at the surface the microstructure associated with the cortical zone.
38
Fig. 32. Effect of temperature on rolled surface of steel blooms for a hc=13 mm removed cortical layer, 60 % single pass reduction, experimental mill.
2.4. WP4: Characterisation of through process microstructures, defects and mechanically deformed samples Task 4.1: As-cast and as-cast reheated materials characterisation The objective of this task is to analyse the microstructures of the as-cast surface and cortical zone in order to identify features that could enhance the appearance/propagation of defects. This analysis will help to properly define the location of the specimens to be machined for the mechanical tests. Macro-etching of as-cast samples (Tata, Gerdau and CSM) In order to differentiate the cortical, equiaxial and columnar regions of the as-cast geometries, macroetching analysis was done by the partners involved in this task. Some of the main aspects concerning each steel grade are described in the following paragraphs. Sulphur prints were taken on all relevant casts by Tata. This was followed by deep etching in hot hydrochloric acid solution for a given immersion time to study shell formation profiles and potential distortion. Chilled zones have been marked on etched images but using this technique it is difficult to differentiate between the metallurgical chill zone (ideally equiaxed grain) and surface disruption due to EMS coil for instance. The analysis done indicates that slow casting speed and powder (grade 211) gave the best results with respect to shape (rhomboid) and defects. EAF samples quantified after reheating seem to show more porosity.
39
In the case of 38MnSiV5 steel (CSM), details of the as-cast structure on a cross-section of the bloom, after Ammonium Persulphate etching, are shown in the macrographs in Fig. 33. It can be seen the cortical zone with its mean thickness around hco = 7 mm, the concentration of porosity at the bloom centre and the presence of linear segments of macro-damage. These last lay mainly along the diagonals of the section where dendrite grains growing at orthogonal directions of adjacent faces meet each other. A few of them perpendicular to the bloom faces were also observed. They were as long as 30 mm, do not emerge through the cortical zone, were arrested at about 7 mm from the skin and have a minimal component in the as-cast direction. There were no signs of initial surface cracks.
Fig. 33. Macroscopic inspection after Baumman’s etchings of 38MnSiV5 as-cast and industrially rolled workpieces.
Transversal slices from the 155x155 mm billets of the stainless steels have been studied by Gerdau. Fig. 34 shows the slices after acid etching. Solidification structure is similar in both cases and corresponds to the solidification patter found in austenitic stainless steels. The equiaxial cortical zone is not even around all the perimeter of the slices. In some zones, it is difficult to distinguish this structure or the transition with the columnar structure. Other zones show a clear equiaxial structure of very few millimetres (2-4 mm).
Fig. 34. Billet slices after acid etching. 303
304L
Microstructural characterisation of surface/cortical regions Roughness/oscillation marks, surface uniformity, general microstructural features (CEIT) A detailed microstructural characterisation of the surface and cortical regions of all the as-cast materials has been done. There are several common defects in all steel grades studied that are summarised in the scheme of Fig. 35. A summary of this analysis is shown in Table 11 for the case of LFCS steels (similar analysis has been done with the rest of steels). The results in yellow correspond to the characterisation of defects present in as-cast surfaces (cracks and small flaws, surface roughness, oxidation, possible presence of FeS and Ni or Cu segregation). The lower part (not coloured) corresponds to the inclusion and austenite grain characterisation of the cortical zone up to 5-6 mm from the surface.
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Fig. 35. Scheme of the different defects identified in the ascast surface.
Table 11. Summary of microstructural characterisation of cortical zone, LFCS steels (BOS and EAF). LFCS 209 (EAF)
LFCS 207 (BOS) Cracks, small flaws OM/Roughness
202
204
209
211
No
No roughness 1 cm not much depth CZM
n) Micro parametric RVE for rule generation under IsightFD® DoE (ABAQUS Explicit)
Elastoplastic with Gurson
m) same as k) but with Gurson porosity model within grain boundary to simulate damage and presence of secondary oxide
ABAQUS/Explicit
o) Micro XFEM model using ABAQUS standard 6.96.10 with pre-existing micro-crack (model used in compression with friction and tension)
(p) New OOFEM CPFE + XFEM model as developed by Imperial College using open access code showing single inclusion modelling (q) Multiscale CAFE technique coded within ABAQUS/Explicit VUMAT allowing statistical and physical behaviour to be incorporated with Gauss points of FEM
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(r) Digimat 3D inclusion model (Extreme)
Fig. 68. Various modelling approaches across length scale developed and further refined Post processing damage calculation A high-performance C++ postprocessor was developed with the use of the Abaqus C++ Application Programming Interface to allow for the visualisation of material information that is not readily available in the “standard” Abaqus field output. This postprocessor is compiled and linked using the Abaqus make utility and can be run using the Abaqus execution procedure. A range of simple post processing damage criteria has been coded and integrated into the post processor C++ script. These ductile damage criteria have their benefits in highlighting zones where damage might be initiated but most of them are either empirical or macroscopic and do not differentiate on microstructural features (inclusions, dynamic recrystallisation, grain size, etc.). They all tend to combine effect of either triaxiality or principal stress with the accumulated strain to predict where damage/fracture might be initiated based on intensity (magnitude) of the damage factor. The damage criteria considered were: Cockcroft-Latham, Lemaitre, McClintock, Ghosh, Brozzo, Freudenthal, Rice and Tracey and Oyane with A =1. These integral damage equations have been applied to a partition (3x4x5mm) of the RPS mechanical test (see details of the procedure in [17]). It can be concluded that the phenomenological damage criteria are specimen dependent and for the RPS test McClintock, Ghosh, Brozzo, Cockroft and Latham and, to some extent the Rice and Tracey, and Oyane are the most suitable criteria. Only Ghosh model predicts an inversion which is close to experimental results. However, none of these criteria account for inclusion/microstructure feature as well as minimum threshold of triaxiality. Only Brozzo and Ghosh criteria account for effect of triaxiality and principal stress which is to be related to Fig. 4 (see triaxiality and principal stress inversion). A further improvement of the application of these models should also involve imposing an average spatial distribution of inclusion spacing via the parameter s/d or ω=(d/s)2 (s: spacing; d: diameter of MnS inclusions) using a field variable to further differentiate zones where damage might be initiated. The aforementioned damage criteria have been applied to a partition (3x4x5mm) of the RPS mechanical test as shown in Fig. 69a, for a deformation of 40% and 50%, respectively. This partition represents the region of interest for ductility breakup with the RPS being a test where damage is nucleating at surface/sub-surface and then propagating from surface up to triaxiality and principal stress threshold (function of inclusions) (several examples are indicated in Fig. 69f-k).
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a)
b)
d) Triaxiality plot (40% reduction)
e)
c)
f) Cockroft Latham damage g) Ghosh damage factor 40% factor 40%
h) Ghosh damage factor (50%)
k) Rice and Tracey damage factor 40% Fig. 69. Assessment of several damage criteria in RPS mechanical test zone of interest
i) Lemaitre damage factor 50%
j) Brozzo damage factor 40%
Micro RVE modelling with full parametric DoE capability A new automated procedure (using python scripting within ABAQUS/CAE) to enable the study of matrix and MnS inclusion material response within a 2D representative volume (RVE) has been developed. MnS inclusions are “controllable” objects with respect to position, size, orientation (rotation, x, y position) and mechanical properties within an RVE volume (200 µm x 200 µm) of FCS steel grade. Generation of inclusions based on a library of MnS shape/morphology can be done randomly. Inclusions can also be imposed to extract knowledge about influencing zone, strain and stress localisation based on an initial periodic or specific location or based on an initial spacing to diameter ratio. Inclusions can be edited and translated/rotated/scaled and relative distances between inclusions (i.e. spacing) is a controllable feature.
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New FEM based Matlab image analysis software Following execution, DoE FEM micro RVE runs usually create hundreds of thousands of discrete results for specific state or field variables, making it difficult to assess the statistics as well as the general effect of changing inclusion variables. Therefore a new Python script has been developed to output each discretised FEM plot into TIFF greyscale format image files. A description of the results achieved considering then influence of different parameters is done in Appendix G. All outputs are saved automatically to an Excel file. The layout of the GUI Matlab code is shown in Fig. 70.
Fig. 70. Matlab FEM image based analysis software.
From the analysis summarised in Appendix G, the following conclusions can be made: • It can be concluded that the greater the strength of MnS is as compared to matrix (index of plasticity reducing well below 1), the lower the % of area affecting by high triaxiality as the matrix tend to accommodate the deformation. Also as inclusion strength increases, greater shielding is developed in % of area. • Hard inclusions are not deforming, and increase strengthening effect as the matrix needs to accommodate the material flow. In reality, interface properties will be such that inclusion might rotate. • Soft inclusion (ratio 1:2 v matrix) shows formation of shear bands (45º to tensile direction) with inclusion acting as nucleation sites. 4 poles at 45º tend to be formed with linkage occurring/growing at 45º. Strain tend to be shielded at pole as these inclusions are deforming more than the matrix creating regions of high triaxiality at 90º to the direction of stretch. • Harder inclusions (2:1 ratio versus matrix) show an opposite behaviour. Tensile triaxiality is greatest at pole of inclusions in the direction of the tensile stretch, creating conical gaps. Minimum stress is developed at 90º and therefore stress linkage between inclusions cannot be developed at 90º.These particles will tend to deflect cracks and promote greater void cleavage in the direction of the tensile axis. • Strain localisation or shielding at spacing to diameter less than 2.33 shows that for soft inclusions, local strain increase at 90deg with an increasing effect as inclusion size increases. A strain decrease in the axis parallel to the elongation axis can be observed between inclusions. This shielding intensifies as inclusions interact. • Results of strain partitioning (Increase and Decrease) can therefore be plotted on a single graph comparing far field strain (or bulk strain) with local strain for both circular and oval inclusions (Fig. 71). This is an important graph showing effect of inclusion function of spacing to diameter ratio and strength parallel to the direction of tension and this result has been incorporated into the mesoscale models of the viscoplastic Model 2 (see Flowchart Fig. 67). • The strength of inclusion affects localisation as s/d increases but effect is second order compared to s/d. • At low s/d, shielding increases for softer inclusions in the direction of the elongation axis as the inclusion deforms.
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• Linkage for periodic inclusion spacing occurs at 90º to the elongation axis as per experiments of Weck on Al drilled samples. • For harder inclusion also, the s/d parameter varies less than for softer inclusions.
ref. [39] a) Relation between bulk strain and strain localised at inclusions assuming circular inclusions
b) Relation between bulk strain and strain localised at inclusions assuming ellipsoidal inclusions Fig. 71. Relation between bulk strain (or far field strain) and localised strain brought about by presence of MnS inclusions function of initial spacing to diameter ratio and plasticity index for both circular and ellipsoidal inclusions A summary of the mechanisms that have been considered is illustrated in Fig. 136 (Appendix G). Micro RVE with CPFE constitutive material models All other models included above micro RVEs assume Von Mises elasto or visco plasticity to study strain and stress state acting on matrix, inclusion and interfaces between MnS and austenite matrix under the assumption that both austenite and MnS inclusions exhibit isotropy during deformation. This is a simplifying assumption as austenite has an FCC crystal structure with 12 slip systems, and MnS can be approximated by a cubic configuration with only 6 slip systems. The role of crystal plasticity based micro-mechanic model is to target the prediction of local stress and strain state due to the different crystallographic orientation, by considering the action of the shear stresses in slip planes according to specific slip directions. Three different approaches have been done: - Oxford based Implicit CPFE (UEL (User Element Fortran subroutine) - Imperial College based explicit CPFE model (VUMAT) - Variant of Imperial College based explicit CPFE model A description and some results of the models are summarised in Appendix H. 64
Micro-mesoscale modelling (CEMEF) Cemef was concerned by the development of a new numerical FE (finite element) strategy in order to model, at the microscopic scale, voids nucleation (by inclusions fragmentation or inclusion/matrix debonding), growth and coalescence of the resulting porosities. These developments were intended to improve damage models and multiscale approach developed in PACROLP I previous project. The main idea was to base the approach on Level Set Methods (LSM) method (proposed by Osher and Sethian [18] and described in more detail by Sethian [19]) but, contrary to X-FEM, to track discontinuities by using anisotropic mesh adaptation in order to deal with large strains. A level set framework was used to model particles and voids interfaces in an implicit way. The initial FE mesh, independent of the different phases, is coarse and isotropic. This initial mesh is anisotropically adapted to accurately describe the geometry of the constituents and to deal with discontinuities in material properties. The procedure developed for the description of the different phases (matrix, inclusion and void), the remeshing strategy and the definition of the constitutive laws are described in Appendix I. In the following, the aspects related to modelling of void growth and void nucleation and coalescence will be described. Void growth modelling In the first part of the project, the immerged strategy was developed and used to model void growth of preexisting porosity. This approach was validated in 2D academic configuration by comparison with explicit method (without immersion of the porosity phase). These results are described in [20] and constituted really a new innovative numerical strategy in order to model void growth due to ductile damage. More interesting results were obtained by modelling void growth in the context of a real microstructure containing several MnS inclusions. The developed level set framework and anisotropic remeshing strategy was used to model this real microstructure under tensile loading. Fig. 72a shows a SEM image of the considered microstructure given by TATA steel. This image is then processed in order to extract the level set distance function. Fig. 72b describes the zero iso-value of the φi distance function which is used to perform the anisotropic mesh adaptation. Fig. 72c describes the resulting mesh. Initially, the mesh is only refined around inclusions interfaces whereas during the simulation it is adapted to the interface and to the von Mises stress field. Due to the re-meshing strategy the number of nodes is controlled and varies between 30000 and 35000 during the simulation. The domain is then submitted to a vertical loading and lateral sides of the square domain are free of boundary conditions. The material parameters of the phases are given in Table 12.
Fig. 72. Developed immerged method applied to a SEM image: (a) SEM image (MnS inclusions in green), (b) zero isovalue of the φi function and (c) mesh of the microstructure adapted initially to the inclusion interfaces thanks to the metric M d .
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Table 12. Material parameter values for the 2 phases. Material parameters Matrix Inclusions
ν
E (GPa) 100 150
0.3 0.3
σy (MPa) 200 1000
K (MPa) 100 100
n 0.5 0.3
On this configuration two simulations were performed: one with a bi-phase material configuration without any void and a second one with initial voids located at matrix/inclusion interfaces. These voids were created at the initial stage in the model. The localization of these voids was fixed thanks to the results of the first simulation (interfaces area for which a given threshold in terms of normal stress was reached were selected for introducing the void phase). The initial configuration of the second simulation is described in Fig. 73. This manual nucleation method leads to model the void growth stage under tensile loading. At the end of the project, an automatic nucleation stage to account for interfaces debonding or particles failure was developed and it is described in the next subsection.
Fig. 73. Position of initial
void layers.
Results obtained with these two configurations are shown in Fig. 74, Fig. 75 and Fig. 76. In Fig. 74 and Fig. 75 the von Mises stress and plastic strain fields are plotted for two macro strain values. In Fig. 76, load/displacement curves are plotted for both configurations and void volume fraction evolution is plotted for configuration 2. Several remarks can be done on these results:
Fig. 74. Uni-axial tensile test on real microstructure (macro strain = 5%).
Fig. 75. Uni-axial tensile test on real microstructure (macro strain = 10%)
• The global behaviour (macro-strain/ macro-stress curves) Fig. 76a shows that the configuration with initial voids is softer than the configuration without any void. Indeed the maximal macro-stress is lower for the second configuration that has initial voids. These initial voids have also an influence on the macro-strain value corresponding to the decrease of the load. For the configuration with initial voids, this softening behaviour starts for a macro-strain value of 0.095, whereas for the
66
configuration without initial voids, this softening behaviour starts for a higher higher macro-strain value of 0.145. This result shows the impact of the initial void and their growth on the macro behaviour of the microstructure. It must be noted that this phenomenon should also be enhanced when coalescence will be taken into account.
Fig. 76. Real microstructure uniaxial tensile
test: (a) stress-strain curves and (b) voids volume fraction.
• Fig. 76b shows that the initial void volume fraction of configuration 2 is equal to 0.3 10-3. This void volume fraction value is equal to 4.4 10-3 when the load starts to decrease (Fig. 76a). • The local analysis of von Mises stress fields (Fig. 74-Fig. 75a-b) shows that the presence of voids creates very non-homogenous stress distribution. distribution. The stress concentrations are located at triple points. These triple points should give rise to additional debonding. • The analysis of von Mises stress field on the configuration without void shows that important stress values are reached in particles. The higher stress value can be observed in the bigger inclusion, located in the top left part of the microstructure in Fig. 74a and Fig. 75a. This high stress would certainly give rise to the failure of the particle, thus leading to a stress relaxation after fracture. • The study of equivalent plastic strain fields shows the strain localisation phenomenon (Fig. 74c-d and Fig. 75c-d). Comparison between both cases shows that the existence of voids increases the localisation phenomenon. Indeed for the second configuration, with initial voids, the strain localisation leads to an increase of the void growth rate. This increase can be observed in Fig. 75b. • In Fig. 75d high equivalent plastic strain values are reached (higher than 1). These values are observed between two voids located in the top left quarter of the domain in Fig. 75d. Coalescence is not modelled, but this plastic ligament would undoubtedly be a preferential area for coalescence. These simulations show the ability of this model to work with real microstructures based on experimental observations. This approach was extended to 3D representations as illustrated in Fig. 77 where a 3D cubic domain with two spherical inclusions and initial void layers is considered. The material parameters of the phases are given in Table 12. Boundary conditions are similar to the one used in the previous 2D simulations. Symmetrical boundary conditions are applied to the two large faces of the domain (Sym planes in Fig. 77a). Results for a macro strain of 0.15 are displayed in Fig. 78. Fig. 78c shows the mesh adaptation to the equivalent von Mises stress field. This mesh adaptation allows obtaining an accurate evaluation of the mechanical field around the inclusion (Fig. 78b). Fig. 78c illustrates the ability of this method to track track the interfaces between the two phases. Void nucleation and coalescence
The nucleation stage leads to the creation of new free surfaces in the microstructure. It is well-known that nucleation stage during ductile damage is due to two physical phenomena: the matrix/inclusion interface debonding, and the brittle fracture of the inclusions. Two models were developed in order to take into account these phenomena in the simulation. Concerning debonding phenomenon, a stress criterion based model was developed. The debonding will appear when the interfacial stress σint reaches the interfacial critical strength σc. Concerning the brittle fracture of an inclusion, another stress criterion was developed, assuming that a brittle fracture occurs when the critical critical tensile strength of the inclusion S I c is reached. Fig. 79 illustrates the methodology developed for void nucleation by matrix/inclusion interface debonding or by brittle fracture of an inclusion.
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Fig. 77. Simple 3D microstructure – (a) cubic domain with two spherical voids/inclusions, (b) position of initial void layers.
Fig. 78. 3D cubic case – Macro strain = 15%: (a) global view of von Mises stress field, (b) zoom around inclusions and (c) detailed view of the FE mesh displayed on a cutting plane with the zero isovalue of the different LS in black.
The coalescence phenomenon appears for high strain values after the growing stage. The coalescence stage leads to a quick collapse of voids. This phenomenon leads therefore to the creation of new free surfaces in the microstructure. It was developed a methodology, based on the equivalent plastic strain value ε , to model the coalescence stage as ductile fracture of the matrix by addition of multiple void germs or by a fracture plane in the matrix phase in the zones where ε exceeds the critical value εc . The micro-voids approach is more progressive than the fracture plane approach, but it induces a small volume loss in the matrix phase. Fig. 80 illustrates both methodologies.
Fig. 79. Ductile damage mechanisms: (a) matrix/inclusion interface debonding, (b) brittle fracture of an inclusion and (c) meshing adaptation.
(b)
(a)
Fig. 80. Coalescence criteria: (a) coalescence thanks to micro voids and (b) coalescence thanks to a fracture plane. Applications
In Appendix J several applications of the models have been done considering different conditions (nucleation or no) and matrix and inclusion properties.
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In summary, all the developments realized enabled to build a new robust finite element strategy based on a level set framework to describe the nucleation, void growth and coalescence stages occurring during ductile damage mechanisms in 2D or 3D. These results are clearly innovative regarding the state of art and constitute one of the remarkable achievements of the PACROLPPACROLP-II project. This new approach was used to study the effect of several parameters on ductile damage mechanisms. Results are in a good agreement with those obtained experimentally and found in the literature. An extension to more complex microstructure was realized in the last part of the project to illustrate the ability of the adopted numerical model to deal with real microstructures. These developments developments represent a real step forward in the comprehension and modelling of ductile damage mechanisms at the microscale. Micro-mesoscale modelling (CSM) The compression testing results from both 9SMn28 and 38MnSiV5 steels in WP3 have been used to obtain viscoplastic constitutive laws related to the temperature, compensated strain rate and a historydependent variable. This last incorporates strain hardening, hardening, dynamic recovery and dynamic recrystallization; Fig. 30 describes the model and shows its fitting to the original isothermal-constant strain rate experimental data. The application of this constitutive law to FEM tensile tests simulations beyond necking provides reference behaviour of a hypothetic solid not undergoing damage. By comparing the tensile force vs. strain results from the numerical predictions predictions against experiments, a strain εond at which both these traces separate themselves, is identified as the onset of damage (Fig. 81). This εond has been found to be: ≈ 1.25
.
ε ond
εu
Eq. 1 where εu is the uniform strain computed from the constitutive law at strength equalling its hardening rate. A second characteristic strain is the fracture strain εfr defined as the area reduction referred to the broken section.
Fig. 81. Distributed macro-damage model DM: (a) construction procedure from isothermal tension experiments and its FEM simulation using the constitutive law from isothermal compression; (b) implementation for non-isothermal paths (rolling).
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The microstructures in Fig. 65 clearly show the temperature dependent elongation of MnS inclusions not accompanying the steel nominal strain. A Self-Consistent Strain Model (SCSM), previously applied to predictions of multiphase-steels mechanical properties at room temperature [21,22,23], has been modified to describe the hot working behaviour of an austenite matrix containing inclusions and applied to 9MnS28 steel. The modelling allows to obtain both a constitutive equation for MnS and quantify a decohesion strain difference between matrix and inclusion, by using the mechanical testing results from WP3 and incremental strain partition data [23]. Hot strength of components
The SCSM is applied by using the circuit (1) of Fig. 82a, as described in the procedure below: Input: (a) MnS mean volume fraction of inclusions ( fi ), testing temperature T and strain rate ε& . (b) Experimental knowledge of the incremental strain partition:
χ = ∆ε / ∆ε i i
Eq. 2
for calibration temperatures (extracted from the data of Charles and Baker [24, 25], converted to the volume fraction of the 9MnS28 steel under study. (c) The steel experimental flow stress data from compression (WP3) or its extracted constitutive equation σ (ε , ε& , T ) (Fig. 30) for the same temperatures than in (b). Output: For each set of (T , ε& ) conditions, the inclusion stress σ i in terms of its evolving strain ε i is extracted (i.e.: Fig. 82c). A numerical regression over all these curves curves allows obtaining a constitutive equation for the inclusion, applicable to intermediate hot working conditions. Best fitting was obtained by using a Voce type of equation: Eq. 3 σ i = σ i ,* + (σ i , o − σ i ,*). exp ( − ε i / ε i ,*) where: σ i , o , σ i ,* , ε i ,* are temperature-dependent. For the very low inclusion volume fractions of both Charles and Baker [24,25] and 9MnS28 steels, the σ m matrix stress is practically equal to the steel flow stress σ as given in Fig. 30.
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Fig. 82. Self Consistent Strain Model (SCSM): (a) procedures to obtain: (1) inclusion hot working properties and (2) matrix-inclusion decohesion strain. Application to 9SMn28 FC steel: (b) initial and SCSM-predicted enlarged set of strain partition data; (c) inclusion hot strength predictions; (d) resulting matrix/inclusion stress ratio, (e) validation against literature data. Validation of predictions against additional mechanical testing
The SCSM was next applied to additional compression and tensile tests for which the calibration data (b) above were not available, in a temperature range intermediate to 800 -1200 °C, by using the circuit (2) in Fig. 82a as follows: Input: (a) MnS volume fraction of inclusions fi and (T , ε& ) testing conditions. (b) Constitutive laws for both steel (Fig. 30) and inclusion (Eq. 3) Output in terms of the steel strain: (c) Inclusion strain εi (d) Decohesion strain difference between austenite matrix and MnS inclusion:
∆ ε dc = ε m − ε i
Eq. 4
Fig. 82b shows the original data [24,25] and new results in terms of inclusion and steel strains. The incremental strain partition χi used in the model Eq. 2) is given by the slope of the plotted curves. Fig. 82c shows inclusion strain-stress predictions for the temperature-enlarged set of data.
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Mesoscopic damage model
Because of the smaller strain taken by the MnS inclusions respect to the austenite matrix, they become locally under tension (Fig. 82a), which occurs even under compressive stresses (e.g.: compression testing, rolling deformation). The computed ∆εdc decohesion strain shows a linear dependency with the steel strain under isothermal testing, but its coefficients are temperature-dependent (Fig. 83a).
Fig. 83. Distributed meso-damage model dm: (a) Isothermal analysis: behaviour of decohesion strain ∆εdc with steel strain and temperature. Bounds on ∆εdc at damage onset and fracture are obtained from the respective characteristic strains in tensile testing and related to temperature, (b) Procedure for nonisothermal paths (rolling). The envelopes of the tensile characteristic macro-strains at damage onset and failure (Fig. 24), as a function of temperature, were next over imposed upon the path of the decohesion strain ∆εdc to obtain corresponding bounds for damage start ∆ε dc, ond and end ∆ε dc, fr (Fig. 83a).
A fractional matrix-inclusion decohesion strain after the start of damage:
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∆ε dc − ∆ε dc,ond ≤1 0 ≤ η d (ε ) = Eq. 5 ∆ε dc, fr − ∆ε dc,ond was next computed for each isothermal test. Finally, a 2-parameter meso-damage d m model was defined as: α
Eq. 6
0 ≤ d m = sinh (k.η d ) ≤ 1 with the parameters k and α as for the macro-damage model DM in Task 5.2. Task 5.2: Meso-macroscale modelling ( CSM, Gerdau)
In the case of meso-macroscale, a rather simpler macroscopic damage model was developed by CSM from the tensile strains at uniform deformation and fracture. For each isothermal, constant strain rate test, by using tensile experiments data and its simulation as in Fig. 81a, they were determined: (a) Bounding strains εond and εfr for damage start and fracture and their temperature dependency extracted as a polynomial fitting over the whole set of isothermal tests. (b) The stress loss due to damage, evolving with the steel strain:
∆σ D (ε ) = σ . D M
Eq. 7
Then, the fractional strain after damage start:
ε − ε (T ) ond ≤1 0 ≤ η D (ε ) = ε fr (T ) − ε ond (T )
Eq. 8
was determined for each test. Finally, the best fit to the tabular data of stress losses ∆σD for the whole set of tests at different temperatures, was obtained by using a 2-parameter macro-damage DM model: α
0 ≤ DM = sinh (k.η D ) ≤ 1
Eq. 9
In contrast with the dm mesoscopic damage based on the difference in strain between matrix and inclusion, the DM macro damage makes no microstructural assumption on failure and the macrobehaviour is extracted directly from the tensile test in (Fig. 81a). Concerning Gerdau activity in this field, the the eight passes of the roughing stand (2-high reversing) of Azkoitia rolling mill have been modelled with DEFORM software. For example, the results in terms of strain rates of the first and the second passes are in Fig. 84. The maximum value of strain rate is 10 s-1 and takes place on the surface and in the subsurface of the bar at the beginning of the deformation in the contact area between rolls and bar. The values of the second pass are slightly lower and penetrate less into the centre of the bar. The deformation takes place mainly in the contact are between bar and rolls, this is between the groove bottom and the top face of the bar. However it extends by the corners but not by the lateral faces.
a) Surface (lengthwise)
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b) Horizontal and vertical section (lengthwise)
Fig. 84. Strain rate distribution at pass 1 and 2. Azkoitia roughing stand. Task 5.3. Multiscale modelling (Tata, CSM) CAFE model The CAFE model as originally developed by A. Shterenlikht [26] has been further developed to be more appropriate for the applications at Tata Steel. The set of ordinary differential equations describing the viscoplastic-damage constitutive Model 1 of Fig. 68d and the CAFE Framework taken from Shterenlikht were combined into a hybrid multiscale model during PACROLPI project [1]. The constitutive model is physically based and capable of modelling both the macro, i.e. stress, strain, material hardening, etc, and microscopic, i.e. average grain size, fraction of recrystallisation, damage, etc, aspects of a material during deformation. The Sheffield CAFE model allows more than 1 CA array, each of which encapsulating a given material law, to be combined and made use of within a Finite Element (FE) simulation. The resulting hybrid of the two cutting-edge modelling capabilities allows the modelling of “real life” deformation processes that are traditionally very difficult to deal with and require the consideration of non-uniformity within material microstructure. The sophistication in using the user subroutine in a hybrid mode is that it allows for layers of damage mechanisms to be incorporated seamlessly into the modelling. At present, two categories of damage mechanisms are implemented: (1) ductile damage based on viscoplastic-damage Constitutive Equations of Model 1; and (2) brittle damage based on fraction stress. The CAFE model has been applied (ductile regime only; the initial version includes also brittle fracture) to the RPS with a central network of CA ductile cells located in the region of interest (mid plane) implemented within a VUMAT user-subroutine. In a first approach and to aid developments of the CAFE model, a simplified RPS test was developed to run under less than 30 min. CPR time. The model includes a 150 element partition which is applied to the CA formulation, the rest of the model works with the viscoplastic model 1 without links to the CA. First improvement of the model dealt with the constitutive response which was fitted to LFCS stress-strain relationship from uniaxial compression testing.
Fig. 85. Application of CAFE to RPS test: (a) initial damage distribution showing wrong distribution (b) new improved distribution with corrected threshold/trigger Deactivation of the brittle part of the CAE was also trialled to give the same result than that of the full model. A new threshold for triaxiality as determined by RPS testing was also added to ensure that not only the damage areas predicted by the model are correct, but also it follows experimental observation. The following damage factor can now be output from the subroutine (Fig. 85). Work is still under way to enhance initialisation of initial distribution of strain strain concentration factor and replacing the brittle
74
carbide part to MnS with known diameter and spacing. The post processing routine has also been incorporated into the CAFE VUMAT user subroutine. Self-Consistent Strain Model (SCSM) The ∆εdc strain difference, the dm and DM damage models developed by CSM, have been produced under isothermal conditions, from initially single stress state and considering a mean MnS volume fraction. Applications to rolling involve: (a) Non isothermal paths due to heat generation by mechanical work, with radiation and conduction to the rolls at the surface layers. (b) Complex loading along the deformation path, with presence of hydrostatic pressure gradients. (c) Dynamic recrystallization within the pass under non-isothermal, varying strain rate conditions. (d) Non uniform distribution of inclusions The condition (a) requires accumulating decohesion strains and damage contributions generated at different temperatures. To these purposes, the models are re-cast in incremental form and integrated quasi-isothermically along the deformation paths (Fig. 81b and Fig. 83): ∆ ε dc (ε , T ) | accum = d m (ε , ∆ ε dc , T ) | accum =
∫
∂ ∆ ε dc (ε , T )
Eq. 10
∂ d m (ε , ∆ ε dc , T )
Eq. 11
∫
D M (ε , T ) | accum =
∫
∂ D M (ε , T )
Eq. 12
and implemented in the FEM rolling schedule simulation. The decohesion strain is considered to accumulate during any particle lengthening, this occurring under tensile or compressive state. In applying condition (b), damage contributions are added up for all increments where either the hydrostatic stress or its forward gradient is tensile. A consolidation model previously developed [1] has been applied to simulate closure of defects and porosity. Because the models are active in the whole rolling simulation, spurious damage reduction due to thermal recovery in the interpass has to be prevented by an irreversibility constraint (Fig. 81b and Fig. 83b). The spatial distributions of Continuum, damage and microstructural variables at exit of a given rolling stand are next exported to an interstand module tracking thermal and static recrystallisation. The resulting distributions on the cross section of the intermediate product at the end of the interstand time are then imported as initial condition for the subsequent rolling stand entry. The dynamic recrystallisation model from mechanical testing in Fig. 30 also needs to be recast in incremental form to be applied to the non-isothermal, varying strain rates profiles along the deformation paths developing in rolling: X DRX (ε , ε& , T ) =
∫
∂ X DRX (ε , ε& , T , X DRX )
Eq. 13
At any degree of deformation under the rolling gap, a residual strain after DRX is then defined as:
ε r = ε p .(1 − X DRX )
Eq. 14
where ε p is the nominal value provided by the viscoplastic FEM model in absence of microstructural changes. The mesoscopic models for ∆εdc and dm have been obtained assuming a mean fi =0.65 wt %, but this is bound to exhibits local variations. An estimation obtained from the work of Charles-Baker (fi=0.44%) and current 9MnS28 experimental data indicates a safe region of applicability is between 0.4 %< fi strip near as-cast surface rich in Si, Mn, O FeO --> strip near as-cast surface rich in Si, Mn, O
Dry Wet Dry Wet
FeO+(Fe, Mn, P)O FeO+(Fe, Mn, P)O Yes Yes
O, Mn, Si, Fe, P O, Mn, Si, Fe, P Yes Yes
Fe, Mn, Si, O Fe, Mn, Si, O,V No No
Dry
No
Ni around oxide network
Ni and Cu in external oxide layer and around oxides
Wet
No
Ni and Cu in external oxide layer and around oxides
oxide layer
Dry
------no tested---------
0.7 mm close surface
125 µm
thickness
Wet
------no tested---------
Ni around oxide network small flaws no detected after oxidation small flaws no detected after oxidation
Cr, O, Mn, Fe Cr, O, Mn, Fe Yes Yes Ni:surrounding oxides// Ni rich areas -->Cr, Mn depletion Si enrichment surrounding oxides Yes Ni surrounding oxides, Cu segregation
Dry
----------------------------
--------------------------
Fe, Mn, Si, O
Wet
---------------------------
---------------------------
---------
Dry Wet
---------------------------- ---------------------------------------------------- -----------------------------
Dry
---------------------------
--------------------------
No detected
Wet
---------------------------
--------------------------
---------
internal oxides As-cast surface
FeS
Ni Cu segregation
Artificial
oxide layer composition
38MnSiV5
very thin crack
cracks FeS
Ni, Cu segregation
105
No
AISI 303 --------Cr,Mn,O,Fe,Cu
close suface 50 µm-->crack tip: 25 µm (Mn, O, Cr)Fe and (Cr, Mn)S Si enrichment surrounding oxides Mn, O, Cr, Fe Si enrichement surrounding oxides Yes Yes Ni:surrounding oxides// Ni rich areas -->Cr, Mn depletion Ni:surrounding oxides//Ni rich areas ->Cr, Mn depletion
APPENDIX E THERMAL ETCHING AND MICROGRID ANALYSIS OF RPS TESTS Thermal etching Optical microscopy characterisation of RPS samples deformed at 5 and 10% at 1000ºC are shown in Fig. 113. The prior austenite grain boundaries can be clearly observed, together with damage. The results obtained indicate that microvoids are created quickly around grain boundaries (GB) and inclusions even under 5% bulk deformation of the RPS sample. It should be noted that in view of the shape of the specimen, the tensile triaxiality is established quickly of the order of 0.37 (for 45deg taper RPS specimen) and that the local strain (not accounting for strain localisation due to inclusions) is of the order of 3.4% with a low strain rate on ~0.5 s-1.
5% deformed – damage grain boundary and inclusion
10% deformed – damage grain boundary and inclusion.
Fig. 113. Examples of micro-etching characterisation following 5 and 10% deformation at 1000ºC on external face of RPS specimens.
Microgrid Microgrids deposited on external faces (path 3) of RPS samples of both simulation material (Fe30%Ni, Fe30%NiS) and LFCS have been deformed in the Gleeble 3800 under vacuum and characterised. This work is part of a PhD scheme at the University of Sheffield. Some examples are illustrated in Fig. 114. It can be observed that strain localisation (shielding and increase) is developed due to the presence of MnS inclusions as compared to only grain boundary (Case Fe30%Ni). A strain increase up to x2 can be visualised in the deformation map computed following distortion of the microgrid.
a)
106
b) Fig. 114. Microgrid technique on RPS samples: a) Fe30%Ni, 15% deformation, b) Fe30%NiS, 25% deformation.
107
APPENDIX F CHARACTERISATION OF INCLUSIONS FROM MECHANICAL TESTS Torsion tests Different procedures have been used to characterise torsion samples. Microstructural analysis was carried out at the position defined as sub-surface (0.9 of the radius of the torsion specimen). The first aspect to consider is that the deformation of both matrix and inclusions is not homogeneous in all the sample length, especially at low strain levels. There are some areas where the deformation is accumulated (recrystallisation is not activated), and other regions where the austenite is completely recrystallised. On the other hand, there are regions where MnS inclusions remain globular, whereas in other regions inclusions are elongated (Fig. 115). The inclusions that remain globular after deformation are mainly located in regions where microstructure is not recrystallised.
(1100ºC, 5 s-1, ε =1.5) Fig. 115. Micrograph of AISI 303 steel torsion sample.
(1200ºC, 5 s-1, ε= 1)
A characterisation of inclusions at different strain levels has been done and the results have been compared with those obtained in PACROLP I. The inclusions aspect ratio of AISI 303 steel deformed at 1 s-1 is similar to the values obtained for other steel grades at equivalent testing conditions, as it is shown in Fig. 116. The deformation of inclusions under shear stress conditions has been calculated as a function of the total applied strain. Deformation of AISI 303 inclusions is similar to that obtained in steels S-1 and S-2, that is, steels without Pb, Bi or Te. Those elements appear usually surrounding MnS inclusions and can modify their deformation behaviour. As can be observed in the figure, the inclusions of steels containing these elements appear less deformed. Dotted line represents the conditions of relative plasticity of 1, i.e inclusion deformation similar to total deformation. At a given total strain level, the plasticity of inclusions without Pb, Bi or Te is higher, and in general the relative plasticity of inclusions decreased with total strain. Therefore, the presence of some elements and also the difference matrix strength can influence in void nucleation. 7
1.2 ν=1
1
5 4
S1 S2 SPb1 ext SPb1 int SPb-2 SPbBiTe ext. SPbBiTe int 1 s-1 1100ºC 1 s-1 1200ºC 5 s-1 1100ºC 5 s-1 1200ºC
T = 1150ºC Strain Rate = 1 s-1
3 2
AISI 303
1 0
1
2
ε total
3
ε inclusion
Aspect Ratio
6
4
0.8 0.6
S1 S2 SPb1 ext SPb1 int SPb-2 SPbBiTe ext. SPbBiTe int 1 s-1 1100ºC 1 s-1 1200ºC 5 s-1 1100ºC 5 s-1 1200ºC
T = 1150ºC -1 Strain Rate = 1 s
0.4 AISI 303
0.2
5
0
1
2
ε total
3
4
5
Fig. 116. MnS aspect ratio and deformation as a function of total applied strain (torsion test). Fig. 117 shows the mean aspect ratio of MnS inclusions (normalized by the as-cast inclusion aspect ratio) at different strain levels. There are many factors that can affect inclusion plasticity and
108
consequently, on void nucleation by matrix-inclusion debonding. Some of them will be considered in the following paragraphs.
Fig. 117. MnS inclusions aspect ratio normalized at increasing strain levels.
- According to Fig. 117, inclusion deformation behaviour can be divided into different groups depending on steel composition. Inclusions that appear more elongated are those of steels without any addition of these elements - Inclusion plasticity is also affected by inclusion hardness. Nanoindentation tests have been performed at room temperature on MnS inclusions of AISI 303, LFCS and S-1 as-cast steels. Fig. 118 shows the mean nanohardness values. Considering the error, MnS inclusions of AISI 303 and LFCS steels have similar hardness values ~3.2 GPa, whereas inclusion hardness of S-1 steel is lower than 3 GPa. If it is assumed that this tendency is similar at testing conditions (1150ºC) then, there is a good agreement with the higher values of aspect ratio of this steel (see Fig. 117, inclusions of S-1 are more elongated than those of SPb-1/LFCS for similar strain level). Regarding MnS inclusions of AISI 303 steel, it could be expected the aspect ratio to be similar to that of LFCS steel, but it must be taken into account that matrix strength is higher than the rest of steel grades, which likely affects inclusion plasticity.
Fig. 118. Nanohardness of non deformed inclusions at room temperature.
- Inclusion hardness depends on inclusion composition. It is reported in literature that the presence of elements as Fe or Cr in solid solution increase inclusion hardness in comparison with single MnS. The EDS and TEM analysis done clearly indicate that not all the particles are single MnS inclusions. In fact, in the case of AISI 303 the inclusions have Cr (Cr, Mn)S, which agrees with the higher values of nanohardness. - It has been observed that in as-cast conditions, MnS inclusions can be monocrystals or assembly of crystals. Thus, it is reasonable to consider that during deformation their behaviour can be different. As it
109
is shown in Fig. 119, in AISI 303 and in LFCS 1_05 steels, at increasing strain levels, most inclusions appear elongated and they are more polycrystalline inclusions. In Fig. 120 is depicted the misorientation profile of an elongated inclusion in a sample tested at ε=1. It can be distinguished high and low angle boundaries inside the inclusion.
Fig. 119. Crystallographic evolution of MnS inclusions of LFCS/SPb-1 and AISI 303 steels at increasing strain levels.
Fig. 120. Misorientation profile along a deformed inclusion (ε=1, 1100ºC, 5 s-1, AISI 303). To quantify the crystallographic evolution of the inclusions as a function of the applied strain, at least 150 inclusions at each strain level have been analysed by detecting changes in diffraction patterns through EBSD technique. Fig. 121 shows that the percentage of inclusions that have high angle boundaries (>15º) is higher as deformation increases. - The presence of internal defects is another aspect that can affect inclusion deformability. Torsion samples have also been characterised by cross-section technique with FIB. Fig. 122 shows an example of the slices obtained for AISI 303 torsion samples. It can be distinguished that voids, which apparently are associated only with an inclusion, are also connected with other inclusions in all directions.
110
100
% Inclusions HIGH angle boundaries
90 80
AISI 303 1s-1 y 1100ºC
AISI 303 1s-1 1200ºC
AISI 303 5 s-1 1100ºC
AISI 303 5 s-1 y 1200ºC
SPb_LFCS 1s-1 1150ºC
S1 1s-1 1150ºC
S2-9MnS28 1s-1 y 1150ºC
70
Fig. 121. Percentage of inclusions with internal high angle boundaries.
60 50 40 30 20 10 0 0
1
2
3
4
5
6
Total Strain
Fig. 122. Micrographs of AISI 303 torsion samples obtained through cross section with FIB. - In all the previous analysis, it has not been considered the interaction between neighbour inclusions. Some torsion samples at different increasing deformation levels were characterised with EBSD technique. Examples of Inverse Pole Figure (IPF) and Kernel Average Misorientation (KAM) maps are shown in Fig. 123. The kernel average misorientation technique allows the possibility of identifying regions between inclusions that could have strain concentrations (there is a direct correlation between the KAM value and the dislocation density [38]. The kernel maps of Fig. 124 correspond to a sample deformed at 1150ºC to ε= 0.5. In the figure, the mean KAM values of different regions are indicated. As observed, KAM is higher in those regions were inclusion agglomeration is present in comparison to the situation of isolated inclusions. This will affect inclusions deformability deformability and damage nucleation.
111
fcc and MnS Strain = 0.5
Strain = 1
Fig. 123. IPF and Kernel Average Misorientation maps of torsion samples at 1200ºC and 5 s-1.
Fig. 124. Inverse pole figure (IPF) and KAM maps of AISI 303 steel (ε = 0.5, 1100ºC and 5 s-1).
RPS tests In addition to conventional microstructural analysis, detailed crystallographic orientation measurements were done in RPS tested specimens. The regions were selected as indicated in Fig. 57. In the case of ferritic microstructures (as occurs in LFCS), EBSD analysis of MnS is challenging as the crystal structure has a lattice parameter close to a multiple of that of ferrite, so distinguishing between the two can be problematic. Fig. 125a-b shows SEM+IPF of all points with boundaries >5° and segmented IPF data from Mn-rich points overlaid on the SEM signal for RPS sample (corresponding to EAF as-cast prior reheating). In general, it appears as if MnS inclusions 5 mm from the crack tip show fewer voids around them but increased polycrystallinity and orientation variation than those around the crack tip. Polycrystallinity arises from the fact that the inclusions are not voided (still attached to matrix). Fig. 125b shows detailed EBSD acquisition at 0.1-0.15µm step. Fig. 126 shows a series of EBSD scans for EAF RPS deformed samples with proper indexing for orientations (Euler angles). Tabular data of crystallographic orientation areas are appended below following deformation of RPS samples 9TZ9A112 (uncracked) and 9TZ9A115 (Fig. 127) together with initial orientations for as-cast and as-cast reheat samples (average across all areas).
112
a) SEM + IPF for boundaries >5º
b) MnS EBSD analysis
Fig. 125. EBSD scans (SEM + IPF inc Mn rich points to properly index MnS).
Uncracked samples as-cast
Cracked samples post reheated Fig. 126. EBSD and indexing for crystallographic orientation (Euler or Bunge angles). RD: direction along the direction of maximum principal stress (width direction of sample). It can be observed that misorientation has not been affected between 39 and 45deg angle, only the angle phi seems to have been drastically changed from 30º to 85-90º together with angle phi2 between uncracked sample 9TZ9A112 and 9TZ9A115 at surface 152 versus 193º. It should be noted that for all specimens as cast and as-cast deformed, the RD orientation has been maintained. Voids are formed along the RD direction (direction of maximum principal stress) in line with the MnS inclusion index of plasticity being lower than the matrix.
113
Fig. 127. EBSD Euler angles for RPS deformed samples Areas A,B and C from surface to 5mm below surface) inc. EAF as-cast and as-cast reheat – Samples bar 4 EAF 9TZ9A1 RPS samples 12 and 15. Focusing on A112 surface and A115 surface image analysis to further extra key parameters to explain why 9TZ9 EAF A115 cracked, the following statistics have been derived and are expressed in Table 16. It can be clearly observed that the sample which did crack during RPS testing has a lower mean spacing to diameter ratio due to larger inclusion size/area with a mean s/d below critical threshold of 2.7. The % volume fraction of MnS was also larger and although the lead concentration was similar, the % of voids was greater. Table 16. Key feature extraction from image analysis
Features area fraction (MnS, void, Pb) (%) MnS area fraction (%) Pb area fraction (%) Void area fraction (%) Mean orientation of MnS (deg) MnS Mean diameter (µm) MnS Mean diameter below s/d threshold of 2.7 (µm) MnS mean distance below s/d threshold of 2.7 (µm) MnS mean area (µm2) MnS mean s/d (below threshold of 2.7)
114
9TZ9A112 (uncracked) 1.58 1.05 0.21 0.31 71.52 (sd 0.6) 1.56 1.91 3 2.84 1.6 (sd 0.51)
9TZ9ZA115 (cracked) 2.37 1.55 0.23 0.58 66 (Sd 0.57) 1.67 2.16 2.39 3.93 1.6 (sd 0.51)
APPENDIX G NEW FEM BASED Matlab IMAGINE ANALYSIS SOFTWARE Following execution, DoE FEM micro RVE runs usually create hundred of thousands of discrete results for specific state or field variables, making it difficult to assess the statistics as well as the general effect of changing inclusion variables. Therefore a new Python script has been developed to output each discretised FEM plot into TIFF greyscale format image files. The inclusion properties are characterised by the following four quantities: -Size: equivalent diameter. The equivalent diameter is calculated as (4.Area/π)0.5, where Area is the number of pixels covered by the inclusion. - Morphology: ratio of the length of longest axis over the length of shortest axis. - Spacing: two different definitions are used as visualized in Fig. 128. Note that the inclusion spacing is not necessarily equal for both definitions; centre-centre spacing is set by i - j1 while edge-edge spacing is set by i - j2. - Size over spacing ratio
Fig. 128. Definition of inclusion spacing.
Influence of MnS strength A series of DoE microRVE runs with random distribution for two volume fractions (5 and 1%) and imposed MnS strength properties has been carried out. Random distribution was imposed for two MnS volume fractions of 5 and 1% respectively with varied spacing to diameter ratios (see Fig. 129) within a 100x100 µm square area. 50% tensile elongation was imposed giving a bulk strain of 0.405. A typical strain plot considering soft inclusions and hard inclusions is shown in Fig. 130. Fig. 131 shows the results for hard inclusions in terms of strain and stress histograms (equivalent strain and triaxiality) at 5% volume fraction. Fig. 129. MnS distributions with two volume fractions (5 and 1%) within 100x100 µm square RVE. a)
115
b)
Fig. 130. Typical plots: (a) soft inclusion MnS1 50% elongation and (b) hard inclusion – Equivalent strain plot capped to bulk strain (or 0.468) showing strain localisation (increase) and shielding.
a) Fig. 131. Output of subset DoE micro RVE analysis with Matlab image analysis software (deformed plot, inclusion morphology histogram, MnS spacing to diameter histogram equivalent strain (PEEQ) and triaxiality (TRIAX) histograms) 850ºC, hard inclusion 5% fv.
It can be concluded that the greater the strength of MnS is as compared to matrix (index of plasticity reducing well below 1), the lower the % of area affecting by high triaxiality as the matrix tend to accommodate the deformation. Also as inclusion strength increases, greater shielding is developed in % of area. Hard inclusions are not deforming, and increase strengthening effect as the matrix needs to accommodate the material flow. In reality, interface properties will be such that inclusion might rotate. Influence of inclusion strength and porosity for same inclusion morphology, distribution and density Example below has been especially selected to clearly demonstrate the influence of inclusion strength on strain/stress and damage. Two extreme MnS inclusion strengths have been imposed for a 6 inclusion RVE model (volume fraction 1%, inclusion morphology a/b=1.8, inclusion average diameter=28 µm, spacing distribution between 40 and 400 µm, spacing to diameter ratios between 2 to 13). 4 inclusions are isolated, two inclusions with initial s/d ratio of 2-3 will be interacting. For simulating damage nucleation/growth, a porous plasticity constitutive model based on Gurson-Tvergaard has been imposed on the matrix using ABAQUS/Standard and an elongation of 17%. It can be clearly observed from Fig. 132 and Fig. 133 that the soft inclusion (ratio 1:2 v matrix) shows formation of shear bands (45º to tensile direction) with inclusion acting as nucleation sites. 4 poles at 45º tend to be formed with linkage occurring/growing at 45º. Strain tend to be shielded shielded at pole as these inclusions are deforming more than the matrix creating regions of high triaxiality at 90º to the direction of stretch. In comparison, harder inclusions (2:1 ratio versus matrix) show an opposite behaviour. Tensile triaxiality is greatest at pole of inclusions in the direction of the tensile stretch, creating conical gaps. Minimum stress is developed at 90º and therefore stress linkage between inclusions cannot be developed at 90º.These particles will tend to deflect cracks and promote greater void cleavage in the direction of the tensile axis.
116
a) Hard particle b) Soft particle 85 MPa Fig. 132. Comparison of effect of inclusion strength on void volume fraction (damage) of matrix (17% elongation).
Fig. 133. Comparison of effect of inclusion strength on strain (Equivalent PEEQ) and stresses (STR=Triaxiality) of matrix. STR has been capped above 0.33 (triaxiality plain tensile test).
Influence of MnS spacing to diameter ratio (s/d) Influence of inclusion interaction was further studied using a defined periodic configuration. A similar methodology was used with spacing to diameter ratio being varied from 2.33 to 0.1 (circular inclusion) and 0.24 to 3.1 for ellipsoid inclusion. A DoE studying effect of temperature (850, 1050, 1200ºC), relative plasticity of MnS and diameter to spacing ratio was carried out. Fig. 134 shows typical DoE results following 50% uniaxial elongation for 2 initial spacing/diameter ratios and a relative strength ratio of 2 (strength matrix/strength inclusion, i.e. soft inclusion).
From this analysis, the following conclusions can be made: Strain localisation or shielding at spacing to diameter less than 2.33 shows that for soft inclusions, local strain increase at 90º with an increasing effect as inclusion size increases. A strain decrease in the axis parallel to the elongation axis can be observed between inclusions. This shielding intensifies as inclusions interact. It is also clear that when the inclusion hardens (in relation to matrix), effect of strain shielding reduces except as low s/d which is the most significant parameter. Heterogeneity within inclusion increases with its size.
117
Mises equivalent stress for s/d=2.33 (top), 1.22 PEEQ equivalent strain for s/d=2.33 (top), 1.22 (middle) and 0.11(bottom) (middle) and 0.11(bottom) Fig. 134. Effect of soft inclusion interaction based on initial spacing/diameter ratio and relative strength of 2 (strength matrix/strength inclusion). Results of strain partitioning (increase and decrease) can therefore be plotted on a single graph comparing far field strain (or bulk strain) with local strain for both circular and oval inclusions (Fig. 135). This is an important graph showing effect of inclusion function of spacing to diameter ratio and strength parallel to the direction of tension and this result has been incorporated into the mesoscale models of the viscoplastic Model 2. In addition, results of strain partitioning on uniform drilled hole Al tensile specimens have been added (Weck [39]), representing an upper bound for effect of localisation. Note this effect will be dependent on inclusion neighbourhood and orientation to the deformation axis.
Fig. 135. Relation between bulk strain (far field strain) and strain localised at inclusions assuming circular inclusions.
A list of the different mechanisms identified is shown in teh following figure:
118
Soft Inclusion (index of plasticity > matrix) Strain shielding mostly for deformable inclusion when index of plasticity is greater than 1, strain at pole of inclusion is minimum. Linkage is operating at 90º or 45º from tensile axis depending on s/d ratio.
Triaxiality and maximum principal stress are maximum at 90º from direction of straining with triaxiality doubling as s/d reduces (x2)
Shear band, straining at 45º from tensile axis for soft inclusions
Hard Inclusion (index of plasticity < matrix) Straining is maximum at pole of inclusion within inclusion spacing gap further away of inclusion pole where triaxiality is maximum i.e. parallel to tensile axis for low index of plasticity inclusions (i.e. harder
119
inclusions). Minimum straining at 45º promoting conical gap in direction of elongation Triaxiality is minimum at 90º to direction of straining (opposite behaviour to soft inclusion) and maximum at pole
Fig. 136. Strain and stress localisation mechanisms function of MnS inclusion strength.
Influence of thermal effect Using the microRVE presented above, a simple heat transfer analysis was developed to assess development of stress prediction based on differential expansion between MnS and austenite matrix. In these simulations, elasticity Modulus /Poisson ratio was similar between MnS and matrix. This simplified model simulates typical cooling at surface (no cracks and no oxide simulated). An HTC at top boundary of 20kW/m2.K was applied with an inward heat flux imposed at the bottom surface to minimise in RVE (200x200 µm) drastic heat loss (simulating adjacent material). The model is allowed to contract in the horizontal direction upon cooling. An initial temperature of 1100ºC was imposed for both matrix and inclusion. The transient analysis was run for two simulation times (2 s and 200 s). Analytically the radial stress will vary function of distance to particle and inclusion size (or radius). The following set of equations is shown below:
=
.
=− .
+ +
! − − %
Eq. 16
+
"
! "#$
Eq. 17
With σr: radial stress [MPa], σt: thermal stress [MPa], r: distance from particle centre, R: MnS particle radius, G1 and G2, shear modulus of both MnS particle [MPa] and matrix, ν1 and ν2, Poisson ratios of both particle and matrix, α1 and α2, thermal expansion coefficient of both particle and matrix [/ºC], ∆T: temperature differential [ºC]. A typical plot for radial stress is shown below in Fig. 137. The radial stress increases as distance from particle reduces up to a “safety” margin of r=1.02*R. It can be observed that interaction starts when distance ~ 5 times the particle radius or ~2.5 times the particle diameter which is in line with previous data from Rhines [15] (although dealing with only mechanical interaction).
120
Fig. 137. Typical radial stress evolution function of normalised distance ∆T=40ºC – case of MnS (blue curve with α1=4.3E5/ºC).
Upon cooling, when the thermal expansion of the particle (in our case MnS) is greater that the matrix (4.3E-5 v 2.3E-5/ºC), internal tensile stresses will arise in the particle whilst the matrix will be in compression in order to satisfy dimensional match (case of no voiding). In cases where stresses are sufficient to promote decohesion, voiding can occur at particle/matrix interface. On the other hand, if the thermal expansion of the particle is less than the matrix, tensile stresses will develop in the matrix creating stress raising potential. The analytical equation above (Eq. 17) has been input into Isight-FD® for studying the sensitivity to input factors. It can be observed that the thermal expansion and distance are the most significant factors affecting the radial stress from the Pareto chart and effects plots (Fig. 138). For MnS inclusions, radial stresses should be tensile upon cooling. This field requires further development and may be interesting as a check to interface strength.
Fig. 138. DoE analysis for radial stress input factor effects.
Fig. 139 shows typical FEM coupled thermo-mechanical simulations using assumptions described above. In addition, a porous plasticity model was used to check whether damage could be initiated (assuming no effect of recovery/recrystallisation).
121
(a) transient thermal cooling 2s simulating surface chilling from 1150oC.
(b) Low strength MnS1, fast cooling time 2s, with higher thermal expansion coefficient than matrix (4.3E-5) – Plot of stress in 1 direction and max principal stress
(c) High Strength MnS inclusions with higher thermal expansion coefficient than matrix (4.3E-5) – Plot of stress in 1 direction and max principal stress Fig. 139. Thermal-mechanical simulation of MnS submitted to rapid cooling (simulating roll gap conductance/water cooling).
122
APPENDIX H MICRO RVE WITH CPFE CONSTITUTIVE MATERIAL MODELS Oxford based Implicit CPFE (UEL) The role of crystal plasticity based micro-mechanic model is to target the prediction of local stress and strain state due to the different crystallographic orientation, by considering the action of the shear stresses in slip planes according to specific slip directions. Although this model does not integrate cohesive zone modelling or XFEM to predict decohesion and growth, it can be used to estimate the interfacial stress and slip at interfaces between MnS inclusions and matrix. The theory and assumptions of the model have been well outlined in paper from Dunn et al [40]. The approach relies on the determination of the critical resolved shear stress CRSS at a given temperature or τα as shown in Fig. 140. Up to now the CRSS was fitted to a true stress-strain curve at 1100ºC using a macro RVE presented in Fig. 68g, assuming a hardness ratio of 1.7 between MnS and the austenite. Recently, this approach has been enhanced by expressing the critical resolved shear stress function of dislocation density ρ as follows:
τ c = τ i + αGb ρ
Eq. 18
(a) FCC slip systems
Fig. 140. CPFE based Oxford model assumptions
(b) MnS cubic systems
Expression of shear modulus G and Burgers vector for austenite have been taken from data fitted by Nadai [41] and Onink [42]. Relative plasticity or plasticity index as studied by Bakers and Charles [24] between inclusions and matrix has been re-assessed and quantitatively described as shown in Fig. 141. A DoE analysis using IsightFD® and the micro RVE CPFE based Oxford model has been carried out to study interfacial stress development between MnS and austenite grain as shown in Fig. 142. Python extraction result scripts have been written to extract information at the external perimeter MnS inclusions as shown in Fig. 142b. Model comprises of 4 austenite grains and a MnS inclusion (in red see Fig. 142a). 10% strain is being imposed into the microRVE via displacement control (5 microns). Both austenite and MnS have been given initial random orientations but the MnS has then been rotated in the 2D plane (about z axis, i.e. normal to Fig. 142a) from initial 0º to 90º at increment of 15º. Fig. 142c shows the interfacial stress developed at the interface as the MnS inclusion is rotated. A maximum interfacial stress is developed when MnS is rotated 45o from its initial configuration. Therefore in addition to diameter/spacing influence dealing with interactions between inclusions, the MnS orientation will also be critical mostly at the nucleation/initial growth stage. From the graph plotting the loading-direction interfacial stress function of perimeter position, it can be observed that from 30 to 60º to the loading direction, the interfacial stresses increase from based line (dashed line)
123
peaking at 45º to the tensile direction ahead of the inclusion (Fig. 142e) consistent with some of the finding of the initial voiding mechanism at inclusion interface. This will depend on the morphology of the inclusion. Effect of temperature is also visible in Fig. 142d and Fig. 142f with a non-linear behaviour predicted in view of the plasticity index of Fig. 141b.
(a) T (ºC) CRSS austenite [MPa] 850 25.6 900 24.4 1000 22 1200 18
CRSS MnS [MPa] 51.3 40.6 36.7 46
c) (b) Fig. 141. (a) Relative Plasticity, (b) hardness ratio function of temperature (c) tabulated CRSS for both austenite and MnS at various temperature of interest.
Imperial College based explicit CPFE model (VUMAT) This new model developed by Imperial College is based on the work of Kalindi and Anand [43,44] and incorporates all CPFE theory based on the Schmid law (i.e. plastic deformation is the sum of the crystalline slip in all activated slip systems) within a VUMAT ABAQUS Explicit routine. Note that grain boundary effect is also accounted for within the RVE. The shear strain increment for each slip system is assumed function of the ratio of corresponding resolved shear stress over current strength, and of the time step. The resolved shear stress (CRSS) is the double product of stress tensor with the slip deformation tensor (Schmid factor). The increment of current strength is related to the shear strain increments over all slip systems through self- (active along diagonal of slip systems) and latenthardening (off-diagonal) functions. Two kinds of hardening law can be used which differ from the Taylor’s model which implies that all slip systems harden equally. The first law, proposed by Asaro, and Pierce et al. [45] assumes a hyperbolic secant relation for the self-hardening modulus function of shear strains to reach saturation to CRSS. The Bauschinger effect is neglected. The second is Bassani's hardening law [46], which gives an explicit expression of slip interactions between slip systems. Both self and latent hardening depends on the shear strains on all slip systems with a simple linear relationship between self and latent hardening. The classical three stage hardening for FCC single crystal could be simulated, i.e. initial hardening to reach the critical resolved shear stress, then saturation and then again hardening due to cross hardening between slip systems (secondary slip systems). A typical micro RVE is shown in Fig. 143 with grain boundary.
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(b)
(a)
c)
(d)
(e)
(f) Fig. 142. CPFE Oxford-based model main results with high temperature data.
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(b) Material assignment within two opposite grains based on 12 slip systems of {111} and two different orientations (1 active slip system only)
(a) 4 austenite grains, 1MnS inclusion and grain boundary/inclusion interface as a cohesive zone model (c) total accumulated shear strain on all slip systems for RVE submitted to pure shear - Note MnS inclusion is modelled with an elastoplastic constitutive
(d) Equivalent stress in pure shear Fig. 143. VUMAT RVE CPFE model with 1 MnS inclusion and 4 austenite grain inc. grain boundary and grain boundary decohesion (CZM model).
Variant of Imperial College based explicit CPFE model One variant is to suppress the CPFE implementation and use only the mesh topology with an elastoplastic implementation and various ductile damage models from the previous PACROLPI project. These models are based on nucleation and growth either at inclusion/matrix or within also the matrix itself. Fig. 144 shows various implementation of this model. Model below simulates a simple uniaxial tension from left to right (max displacement of 25 µm (25% reduction)).
(a) Equivalent strain with maximum predicted at triple point grain boundary and interface during uniaxial tension- case of hard inclusion
(b) Stiffness degradation SDEG – hard inclusion (ABAQUS) during uniaxial tension
(c) Stiffness Degradation SDEG – soft inclusion (d) Stiffness Degradation SDEG – pure (ABAQUS) during uniaxial tension. Note shear deformation of grain boundaries Fig. 144. Variant RVE models.
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APPENDIX I DESCRIPTION OF DIFFERENT PHASES, REMESHING STRATEGY AND CONSTITUTIVE EQUATIONS FOR MODELLING - Description of the different phases and remeshing strategy A level set framework was used to model particles and voids interfaces in an implicit way. The initial FE mesh, independent of the different phases, is coarse and isotropic. This initial mesh is anisotropically adapted to accurately describe the geometry of the constituents and to deal with discontinuities in material properties. In fact, the set of particles and the matrix are described, respectively, by a signed distance function, φi and φ m , defined over the domain Ω which gives at any node x of the finite element mesh the distance to the corresponding interface ( Γi and Γm ). Furthermore, the sign convention φi ≥ 0 (resp. φm ≥ 0 ) inside the part of the domain corresponding to the inclusions denoted Ωi (resp. inside the part of the domain corresponding to the matrix denoted Ωm ), and φi ≤ 0 (resp. φm ≤ 0 ) outside the inclusions (resp. outside the matrix) is adopted. In turn, both types of interfaces are given by the zero level of the corresponding distance function:
(
)
(
)
φ (x) = χ ( x) − χ ( x) d(x, Γ ), φ (x) = χ ( x) − χ ( x) d(x, Γ ), x ∈ Ω Ωi i m Ωm m Ωi Ωm i Eq. 19 Γ i = ∂Ωi = { x ∈ Ω / φi (x) = 0} Γ m = ∂Ωm = { x ∈ Ω / φm (x) = 0} where d(x,Γ) defines the distance between node x and interface Γ and
χ D ( x) corresponds to the
characteristic function of the domain D. As the set of the different phases correspond to a partition of the domain, it is easy to determine to which phase each nodes belongs using the following rules:
x ∈ Ω ⇔ φ ( x) ≥ 0 i i x ∈ Ωm ⇔ φm (x) ≥ 0 Eq. 20 x ∈ Ωv (void part of the domain) ⇔ φv ( x) = −max (φi ( x), φm (x)) ≥ 0 r r Finally, the normal to the interfaces, ni and nm , are defined using the gradient of the corresponding level set function. Thus functions φi and φ m satisfy the following properties:
r
r
r ∇φi r ∇φ m ni = , nm = , ∇φi ∇φ m
Eq. 21
with ni (resp. nm ), the inside unit normal to the inclusions interfaces (resp. to the matrix interface). It is important to underline the fact that working with only one level set function for the set of inclusions implies that these inclusions cannot be differentiated during the finite element simulation. Hence, the physical properties of theses inclusions must be identical. However, it is simple to extrapolate our approach for different set of inclusions by considering one level set function per set of inclusions. Concerning remeshing strategy, an isotropic refinement of the mesh can be used to reach a desired accuracy in the interfaces description. However, this strategy leads to a significant increase of computation resources. An adaptive anisotropic meshing and re-meshing technique is therefore preferred.
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There are different ways of generating adapted anisotropic meshes. The most common approach consists in using an a posteriori error estimator in order to obtain an optimal mesh for a given number of nodes [47,48]. However this approach could be insufficient in our case when large deformation is reached. Indeed, the use of a posteriori error estimator on a physical field, such as for example pressure or equivalent stress, leads to a mesh refinement in the zones of intense variation of this field. If these zones correspond generally to matrix/inclusions/voids interfaces, they do not necessarily concern the whole interfaces. This can lead to a de-refinement of the mesh close to interfaces areas, which is inconsistent with the PACROLP-II objective concerning modelling at the mesoscopic scale, i.e. to track accurately matrix/inclusions/voids interfaces during the ductile damage mechanisms and could be also synonym of convergence difficulties for the FE solver in these zones where mechanical properties are strongly discontinuous. In order to overcome this difficulty, the developed methodology consists in building several metrics by using a posteriori error estimator for several fields and to mix them thanks to arithmetic operations, or thanks to area selection. Therefore to use our strategy, several tools are necessary: a topological mesher, a posteriori error estimator and a method to melt the several obtained metrics. The remeshing strategy is described below for 2D or 3D configurations. Anisotropic meshes are built using the topological MTC mesher/re-mesher developed by Coupez [49]. It is based on local mesh topology optimization techniques and works for all meshing applications from adaptive remeshing to mesh generation by using a minimal volume principle. MTC improves the mesh topology by considering the quality of the elements. The quality of an element is defined through a shape factor which takes into account the considered metric. A metric is a symmetric positive defined tensor which represents a local base modifying the way to compute a distance, such that:
r u
M
=
t
r r r r r tr u M u , < u , v > M = u Mv
Eq. 22
If M is the identity tensor, the distance corresponds to the usual one in the Euclidean space. As M is a symmetric positive defined tensor, it is diagonalizable in an orthonormal basis of eigenvectors, and all the eigenvalues are strictly positive. The metric M can be interpreted as a tensor whose eigenvalues are linked to the mesh sizes, and with eigenvectors defining the directions in which these mesh sizes are applied. Therefore the MTC mesher needs a metric field as an input. An efficient way to compute this metric is presented in the work of Mesri [47] and Almeida [48]. The metric is computed thanks to an a posteriori error analysis based on physical fields and with a fixed number of nodes. Besides, this refinement operator by a posteriori error estimator is based on the interpolation error calculation thanks to the Hessian of the physical fields. This method leads to very fine mesh where gradient of fields have the higher variation. In our new approach, we have used this method to compute two metrics. The first metric is based on the distance to interface in order to track the interface. And the second metric is based on a mechanical field (such as the equivalent stress) in order obtain an accurate resolution of the mechanical problem. Thus we can directly compute the metric Mm adapted to the mechanical fields. Whereas the computation of the metric Md based on the distance to interface need a specific treatment. In fact the distance function is by definition linear, and so a posteriori error estimator cannot be applied directly to this field. A simple solution consists to filter the distance function in order to track the interface. The used filter function is:
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~ if φ ( x) < −e φ ( x) = 0 ~ if φ ( x) > e φ ( x) = 1
Eq. 23
π * φ ( x) sin 1 φ ( x) e else φ ( x) = 1 + + 2 e π ~
where e is the characteristic thickness of the filter where the mesh is adapted around the interface. The ~ obtained filtered distance φ has the right properties to track the interface. In fact the higher variations ~ of the gradient of φ are located in a narrow zone near the interface. Therefore the obtained metric Md is adapted to track the interface. The next stage to construct the global metric M is to melt the two metrics Mm and Md. We made the choice to melt these two metrics using a geometric criterion based on a linear transition. This melting law is described in: if φ ( x) < Dmin
M =Md
if Dmin ≤ φ ( x) ≤ Dmax if Dmax < φ ( x)
M=
Md −Mm φ ( x) − Dmin + M d Dmin − Dmax
(
)
Eq. 24
M = Mm
where Dmin and Dmax are the characteristic lengths of the melting law. In practice Dmin is chosen to be equal to e (see Eq.23). When dealing with many inclusions/voids, the mesh has to be adapted to many interfaces. Therefore a global distance has to be defined, which is equal to the maximum of each distance functions φ glob ( x ) = max (φ i ( x ), φ m ( x )) . In our case this global distance is the opposite of the void distance φv . This anisotropic meshing/re-meshing strategy leads to a very high accuracy near interfaces and lead to an adapted mesh to the mechanical problem in the whole domain without increasing dramatically the computation resources. Fig. 145 illustrates the adapted mesh for two 2D different configurations. The results are obtained for a domain containing an elliptical inclusion with a void layer. In Fig. 145a-b, the 2D anisotropic mesh is generated thanks to the metric M defined by Eq. 24 for D min = e = 0.003 mm, D max = 0.012 mm . Far from the interfaces the mesh is adapted to the von Mises equivalent stress field. Fig. 145a shows a mesh adapted to the matrix/void interface (blue dash line) and the void/inclusion interface (red line). This figure illustrates an anisotropic mesh adapted exclusively to the interface as we focus on a narrow zone (inferior to Dmin). Fig. 145b shows the same configuration but at a larger scale. Thanks to our strategy, far from the interfaces (superior at Dmax), the anisotropic mesh is adapted to a mechanical field, which corresponds here to the von Mises equivalent stress. This mesh adaptation does not impact the mesh refinement near interfaces, so that a fine mesh is conserved to track both types of interfaces. It must be underlined that the methodology developed, in terms of virtual generation, implicit description of the interfaces and meshing adaptation, was validated in 2D and 3D for a large variety of VERs as illustrated by the Fig. 146.
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Fig. 145. Mesh adaptation with a metric defined thanks to Eq. 23: (a) Zoom at the interfaces where the metric is adapted on the filtering φv level-set function and (b) global view where the metric is defined thanks to the equivalent von Mises stress field combined to the interface adaptation.
a)
b)
Constitutive equations in our immerged context In the microstructure we assume that three phases are present: matrix, inclusion, and void. To describe the behaviour of each phase, specific constitutive laws have to be defined. And the use of an implicit description of the interface requires the use of transition laws between each phase. Therefore these two points are described below.
Fig. 146. Some 3D
a)
b)
c)
d)
RVEs respecting initial statistical or exact data: (a) a 304L powder, (b) semi-solid granular with liquid in blue, FE mesh is anisotropically adapted to the interfaces, (c) 304L polycrystal with anisotropic finite element mesh in white, (d) cluster of MnS inclusions in a homogeneous steel matrix.
Ductile fracture mechanisms appear in elastic-plastic media. Therefore an elastic-plastic constitutive law is used. This constitutive law is based on the strain tensor ε decomposition in two parts, the elastic part ε e and the plastic part ε p : ε =εe +ε p Eq. 25
130
The elastic law is computed using the objective Jaumann derivative of the strain tensor rate:
dσ = λ tr ε& e I d + 2 µ ε& e dt
( )
where λ and µ are the Lame coefficient, I d the identity matrix and part of the strain rate tensor is computed using the following flow rule:
2 ε& p s= σ 0 (ε ) 3 ε&
Eq. 26
σ
the stress tensor. The plastic
Eq. 27
where s is the deviator part of the stress tensor, σ 0 the flow stress, ε the equivalent strain and ε& the equivalent strain rate. The flow stress is driven by a hardening law. The following form is chosen: σ 0 (ε ) = σ y + K ε n Eq. 28 n where K , σ y and are material parameters, and represent, respectively, the consistency, the yield stress and the hardening exponent. More details about the constitutive modelling are given in [50]. For all simulations, a mixed velocity–pressure formulation with an enhanced (P1+/P1) element is used to solve the considered elastic-plastic problem. This mixed formulation is well adapted to solve incompressible or quasi incompressible flow as elastic-plastic problem [51]. Due to the level set framework, some elements are crossed by the interface. These elements are therefore made of two different phases. In order to account for these different phases within an element, a linear melting law is used between the phases which have the same constitutive behaviour (matrix/inclusion). The linear melting law is defined by:
Pm = α 1 (φ )P1 + (1 − α 1 (φ ))P2
Eq. 29
where Pm corresponds to the melted parameters, P1 and P2 the phase parameters, and α 1 (φ ) is the fraction phase function associated with phase one. In practice, the parameters P which are melted are: the elastic coefficients ( λ and µ ), the plastic hardening law parameters ( K , σ y and n ). This fraction phase function is computed with a “volume of fluid” technique. For elements crossed by the interface, this function evaluates the proportion of each phase thanks to the level set function φ . When the two phases have different constitutive laws (void/matrix interface or void/inclusion interface) a switching rule is used. If the fraction of solid phase (matrix or inclusion) is different from zero the elastic-plastic constitutive law is used, if the fraction of void is equal to one, the void (solid fraction phase equal to zero) constitutive law is used. Finally, the void phase is modelled by a compressible Newtonian flow with a viscosity coefficient equal to 1 MPa.s-1. Tests were done in order to check that this viscosity coefficient is optimal.
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APPENDIX J EXAMPLES OF APPLICATIONS OF THE MODELS DEVELOPED BY CEMEF In the first application, the impact of the inclusion fracture properties has been evaluated. Same geometry and boundary conditions for the case studied in Fig. 72 are considered. A domain reduction is used, as illustrated in Fig. 147.
Fig. 147. (a) Description of the considered domain and (b) work hardening curves of matrix and inclusions. In order to test the robustness of the proposed void nucleation model and its ability to separate the two nucleation mechanisms (debonding or particle fracture), five configurations were considered with different values for the critical values σ c (relative to debonding) and S I c (relative to fracture of inclusions) (see Table 17): • Case 1: no nucleation • Case 2: reference case where brittle fracture of inclusions is the easier nucleation mechanism • Case 3: case where matrix/inclusion interfaces debonding is the easier nucleation mechanism • Case 4: reference case with higher values for σ c and S I c •
Case 5: reference case with lower values for σ c and S I c Table 17. Nucleation critical values for the five tested configurations. Case 1 (no nucleation)
Case 2 (Reference)
Case 3 (Inverse Ref.)
Case 4 (Ref. * 1.5)
Case 5 (Ref. * 0.5)
SI c
∞
200 MPa
300 MPa
300 MPa
100 MPa
σc
∞
300 MPa
200 MPa
450 MPa
150 MPa
Fig. 148 describes, for the different configurations, the evolution of the void volume but also the equivalent stress/equivalent strain curve. For the first case, as no nucleation is considered, the work hardening curve of the homogenized RVE without softening was obtained. Evolution of the void volume and equivalent stress/equivalent strain curves are quite similar for the second case, where debonding is preferred and for the third case, were brittle fracture of inclusions is preferred. The fourth case exhibits, as expected, a delayed nucleation start which results in a lower void volume fraction than for cases 2 and 3. Finally, the opposite behaviour is well observed for the last case. Fig. 149 describes, for the five cases, the equivalent stress field for 0.1 of macro strain.
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Fig. 148. Evolution of the volume of porosities and the equivalent stress/equivalent strain curve for the different configurations.
A second application was considered in order to study the impact of shear loading for the mechanical configuration of the previous cases 3 and 5. The results obtained are described in Fig. 150. Nucleation and void growth phenomena are really different from those observed in previous simulations for the same cases in tension. For the third case, nucleation by debonding is favorized as for the tension configuration. However, the void growth is radically different. For the fifth case, the nucleation is mixed but no multi fracture of inclusions is observed contrary to the tension configuration.
Fig. 149. Equivalent stress field at 0.1 of macro strain for the five considered cases.
The last application illustrates the capability of the developed methodology, in terms of nucleation, growth and coalescence, to deal with 3D configurations. The idea was to use the configuration described in Fig. 77 but without the initial void layers. Nucleation is now considered thanks to our models of nucleation by debonding or fracture of inclusion. Fig. 151 illustrates the appearance of void by debonding at the inclusion interfaces and the subsequent void growth and coalescence between the two inclusions.
133
Fig. 150. Results of the shear loading for the cases 3 and 5.
Fig. 151. Growth and coalescence of porosities in a 3D configuration.
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APPENDIX K VOID AND DEFECT WELDING Fig. 152 details the consolidation model used for both porosity and defect closure and its effect on central line porosity. As in the central zone in Fig. 99, there is still some incomplete void closure up to the examined R4 stand. The simulations have been produced considering interstand tension-free optimal conditions and consequently damage predictions are bound to increase, should mismatching rolling speed develop between stands as consequence of deterioration of presetting conditions (i.e.: by wear). Fig. 152. Consolidatio n model for closure of void and defects (9SMn28).
EFFECT OF DRX ON RESIDUAL STRAINS
Fig. 153. Effect of dynamic recrystallisation on residual strain gradients at the rolling stock outer layers. Edge surface set in tension by subcutaneous layer (profile type B). Prior austenite grain size: cortical 35 µm, internal 60 µm (9SMn28, Mill_1, basic Case 1).
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European Commission EUR 26321 — The prediction and avoidance of cracking in long product hot rolling. Phase II (Pacrolp-II) Luxembourg: Publications Office of the European Union 2013 — 136 pp. — 21 × 29.7 cm ISBN 978-92-79-34585-2 doi:10.2777/50283
137
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KI-NA-26321-EN-N
Pacrolp-II project is aimed at minimising ductility break-ups on ‘apparently sound’ as-cast semis (blooms/billets), which are prone to surface cracking during reheating/rolling. The main singularity of this project has been a multiscale analysis combined with a through process evaluation (casting/ reheating/rolling) of damage by experiments and simulation. The study of as-cast structures has lead to identify the microstructural features that are relevant in subsequent process steps (grain distributions, nature, distribution size and location of MnS inclusions, incipient solidification damage ...). The reheating is an important step that can eliminate, enhance or provoke surface defects, depending on the steel grade and furnace conditions. A wide range of mechanical tests, combined with fine microstructural evaluation and FEM models for analysis of damage levels, have allowed: the definition of thresholds of triaxiality and strain for nucleation and cracking, the evolution of plasticity of inclusions with applied strain, a better understanding on the interaction between austenite grain boundaries and MnS inclusions in the early stages of damage nucleation and the relevance of inclusions spatial distribution in all the steps of damage evolution. Multiscale modelling has been developed to study the effect of macro processing and as-cast conditions on the MnS inclusions at the scale of interest. These models, in combination with laboratory tests and analysis, have allow the identification and quantification of a high number of factors (micro-macro) intervening in the damage process. The relevant role of stress triaxiality/strain path suggests the convenience of proper design of entry bite geometry and grove radius in roughing passes.
Studies and reports
doi:10.2777/50283
