An Integrated Computational Materials Engineering ...

HONORARY VOLUME IN MEMORY OF PROFESSOR VASSILIOS PAPAZOGLOU NATIONAL TECHNICAL UNIVERSITY OF ATHENS, 2015

Alloyneering: An Integrated Computational Materials Engineering Approach to Alloy Design G.N. Haidemenopoulos Laboratory of Materials, Department of Mechanical Engineering, University of Thessaly, Greece Author’s note: I first met Vassilios Papazoglou in September 1983 when I enrolled at MIT to work with the late Prof. Koichi Masubuchi. Vassilios not only helped me to get along at the welding lab, but provided valuable advice during my first year at MIT. Since then he had been one of my most valuable friends and colleagues. Vassilios knew my interest in computational alloy design and encouraged me to work and contribute to this scientific field. The present paper reflects this effort and is dedicated to his memory. Vassilios’ record of achievement and service to the University was unique and immeasurable. His work was characterized by ingenuity, patience and dedication beyond the ordinary. I will remember him not only as a good friend but also as a visionary working for a better higher education in our country.

Abstract Alloyneering is a generic term, developed at the Laboratory of Materials at University of Thessaly. It combines the words Alloy and Engineering and describes a concise knowledge-based methodology leading to the design and development of engineered alloys. Alloyneering encompasses the application of computational alloy thermodynamics and kinetics on one hand, which can describe the microstructure evolution, with suitable strength models on the other hand, which link strength with microstructure, for the design of metallic alloys with tailored properties. The present paper is a review of this integrated computational materials engineering approach. Recent applications to the development of new alloy systems and processing conditions are presented.

1. INTRODUCTION The development of new materials is traditionally a very tedious process involving extensive experimental investigations by which composition and processing conditions are varied in a more or less erratic manner until the desired properties are achieved. The properties of materials depend on phases present, their composition and how they are geometrically arranged in the microstructure, involving structural elements on micro, nano and atomic scale. Therefore a detailed information about temperature and stability ranges of the different phases as well as their transformations and equilibria are indispensable not only for the modeling and simulation but more importantly for the computational design of materials and processes. For many simple alloys a large amount of constitutional information is to be found in databases and reference books. If critically evaluated, such constitutional, thermodynamic and kinetic data develop predictive power when appropriate thermodynamics and kinetics calculation software and model descriptions are applied. Several software packages that allow calculation of phase equilibria as well as other thermodynamic quantities are now commercially available. Calculations considered a cutting edge a few years ago may now be performed on a routine basis by personnel without much expertise in thermodynamics or computations. A more ambitious approach is to combine the thermodynamic calculations with kinetic models, e.g. diffusion calculations and thereby predict the rate of reactions and transformations. This approach is extremely powerful and may be used to simulate a wide range of different phenomena in materials including precipitation, homogenization, diffusional interactions between substrate and coatings, welding, etc. With this approach it could be possible to treat multi-component alloys with realistic thermodynamic and kinetic properties and it could become possible to take anisotropy, elastic stresses etc. into account as long as the computational work can be afforded. Although there is much progress in modeling and simulation, there still remain a lot to be done in order to use these tools in materials and process design. When computational alloy thermodynamics and kinetics tools are combined

with other software packages in the area of mechanics of materials, such as Finite Element codes, inverse analysis programs, or more general multipurpose computational tools such as Matlab, then it is possible to apply these tools towards the design of alloys and processes. Alloyneering is a generic term, developed in the Laboratory of Materials at University of Thessaly. It combines the words Alloy and Engineering and describes a concise knowledgebased methodology leading to the development of engineered alloys. Alloyneering encompasses the application of computational alloy thermodynamics and kinetics on one hand (which can describe the microstructure evolution) with a suitable strength model on the other hand (which links strength with microstructure) for the design of metallic alloys with tailored properties. The same approach can be used for the design of the required processing conditions to achieve the corresponding microstructure and thus to achieve the required properties. In its full development, Alloyneering will enable the computer-aided design of both alloy composition and processing. This could lead to a situation where the development of new alloys will take only a fraction of time and cost associated with the empirical (trialand-error) development. This constitutes a breakthrough step which takes the alloy development process from an entirely empirical to a knowledge-based platform. The proposed approach is in line with the directives of the European Materials White Book on the microstructure of materials, which was published in 2002 (Max Planck Institute 2002). More specifically the white book in section 5.1.5 states that “a very significant approach is to combine the thermodynamic calculations with kinetic models, e.g. diffusion calculations, and thereby predict the rate of reactions. This approach is extremely powerful and may be used in the future to simulate a wide range of different phenomena, including precipitation, homogenization, solidification, etc.” Almost 15 years from the publication of the white book, the above directives are applied, not only for simulation of different phenomena but for alloy design as well. This approach is now termed Integrated Computational Materials Engineering (ICME) and is organized in the US under TMS (TMS 2014) as well as in Europe (ICMEg 2014). The Materials Genome Initiative (MGI) launched in 2011 by the Obama administration in the US (White House 2011) is a multi-agency initiative designed to create a new era of policy, resources and infrastructure that support US institutions in the effort to discover, manufacture and deploy advanced materials twice as fast, at a fraction of the cost. Since the launch of MGI, $250 million have been invested in new R&D and innovation infrastructure to enable the application of ICME approach. The present paper summarizes recent developments of the ICME approach as applied at the Laboratory of Materials at the University of Thessaly. A brief description of the methodology and the associated computational tools will be presented first followed by example applications of the Alloyneering-ICME approach. 2. METHODOLOGY 2.1 CALPHAD approach for alloy thermodynamics and kinetics The methodology is based on two pillars, computational alloy thermodynamics and computational kinetics of materials. The core of the methodology is the CALPHAD approach (Spencer 2008). It is based on mathematically formulated models, such as the quasichemical model or the sublattice model, to describe the thermodynamic properties of individual phases, such as the Gibbs free energy. The model parameters are evaluated from thermochemical data of the individual phases. The available thermodynamic data are stored in thermodynamic databases. Under typical experimental conditions of constant temperature and pressure, phase equilibrium is obtained by minimization of the Gibbs energy of a closed system. The relevant software (Thermo-Calc) is described in the following section. In addition to thermodynamic calculations, diffusion calculations in multicomponent alloy systems can be performed once diffusivity data are available. In this case the relevant kinetic databases contain mobility data and the program calculates the diffusion coefficient by multiplying the mobility with the thermodynamic factor. In this way not only the temperature, but also the composition

dependence of diffusivity is taken into account. The mobility data are stored in relevant databases and the data scheme follows the standard CALPHAD approach for modeling the mobility of the elements in individual phases. 2.2 Description of Software tools A short description of the software tools to be used within the Alloyneering methodology, are described below: Thermo-Calc (Andersson et al. 2002) is a software and database package for all kinds of phase equilibrium, phase diagram and phase transformation calculations and thermodynamic assessments; with its application-oriented interface, many types of process simulations can also be performed. It has been developed for complex heterogeneous interaction systems with strongly non-ideal solution phases and can be applied to any thermodynamic system in the fields of chemistry, metallurgy, material science, alloy development, geochemistry, semiconductors etc. depending on the kind of database it is connected to. It allows explicit conditions to be set on individual phases such as activities and chemical potentials of the components, volumes, enthalpies and entropies. DICTRA (Borgenstam et al. 2000) is a software package for simulation of diffusion controlled transformations in multicomponent alloys. It is closely linked with the ThermoCalc, which provides all necessary thermodynamic calculations. The geometries treated are one-dimensional (planar, cylindrical and spherical). These geometries can successfully be used to model many processes of practical and scientific interest. DICTRA simulations make use of databases containing data for multicomponent thermodynamics and diffusion. Diffusion coefficients are calculated from the mobilities in the databases for diffusion and thermodynamic factors from the thermodynamic databases. The different models in DICTRA are then based on a solution of the multicomponent diffusion equations. Precipitation modeling. The majority of phase transformations, which take place in alloys, are diffusional and proceed by thermally activated movements of atoms across a concentration gradient. Of significant importance in relation to thermal industrial processing, are phase transformations involving precipitation reactions resulting to a second phase in the form of a particle population. During these transformations three basic physical mechanisms are taking place, the nucleation of new particles, the growth of the nucleated particles and the coarsening of the particles resulting to a particle population which can be described by a particle size distribution (PSD). The material final mechanical properties depend on the particles volume fraction and size and consequently on the shape of the PSD. The PSD is readily calculated with the KWN model (Kampmann et al. 1987) which treats nucleation, growth and coarsening concurrently. Strength modeling. Considering age hardening, the yield strength of an alloy consists of the contributions of lattice resistance, work hardening, grain boundary (Hall-Petch) hardening, solid solution strengthening, and precipitation hardening. A model has been developed to perform the necessary calculations. The input is the PSD calculated by the KWN model. A Matlab code for the calculation of the PSD with the KWN model and the final alloy strength has been developed in the Laboratory of Materials at the University of Thessaly and has been used for the calculation of the aging curve of aluminum alloys under isothermal conditions (Serafeim and Haidemenopoulos 2012). The model is currently under further development in order to perform strength calculations after non-isothermal conditions such as after cooling from the homogenization temperature of aluminum alloys (Sarafoglou 2015, Fanikos 2015). 3. EXAMPLE APPLICATIONS The Alloyneering methodology has evolved in the Laboratory of Materials of the University of Thessaly through several research projects encompassing a large range of materials and processes. The approach has been applied to model the austenite stability in TRIP steels (Haidemenopoulos & Vasilakos 1996, 1997), laser transformation hardening (Katsamas et al.

1997, Katsamas & Haidemenopoulos 1999) and laser carburizing of steels (Katsamas & Haidemenopoulos 2001, Haidemenopoulos & Katsamas 2015), intercritical annealing (Katsamas et al. 2000) and strain-induced transformations in low-alloy TRIP steels (Haidemenopoulos et al. 2014), HAZ microstructure and hardness in laser welding of Alalloys (Zervaki & Haidemenopoulos 2007), microsegregation and homogenization in Alalloys (Samaras & Haidemenopoulos 2007, Haidemenopoulos et al. 2012) and design of AlMg-Sc-Zr alloys (Haidemenopoulos et al. 2010). Some example applications of more recent activities are described below. 3.1 Medium-Mn steels: Intercritical annealing and solute partitioning The first example deals with the kinetics of austenite formation and solute partitioning in medium-Mn steels. These steels belong to the 3rd generation, advanced high-strength steels and are a substitute to 1st (low alloy) and 2nd generation (high-Mn) steels aiming at improved combinations of strength and ductility. In medium-Mn steels, the manganese content is reduced, relative to the high-Mn steels, in the range between 3 and 12 wt% and the microstructure consists of an ultrafine ferrite-austenite mixture. The transformation-induced plasticity (TRIP) of the retained austenite is responsible for the enhanced formability in these steels and several processing routes have been developed in order to stabilize the austenite phase for optimum TRIP interactions. For steels containing 5 to 12 wt% manganese, intercritical annealing, following the cold rolling of the martensitic microstructure, is investigated as a means of stabilizing the austenite by carbon and manganese partitioning. The retained austenite fraction and stability depend, therefore, on the intercritical annealing temperature and time. Simulations have been carried out on Fe -0.18C-11Mn-3.8Al steel (Kamoutsi et al. 2015). The austenite fraction is shown in Fig.1a as a function of annealing time for several intercritical annealing temperatures. The evolution of austenite consists of three stages. In stage I, the initial rapid increase of austenite fraction is due to growth under no-partitioning local equilibrium conditions (NPLE mode), where the growth is controlled by carbon diffusion. In stage II the intermediate slow growth of austenite takes place under local equilibrium with partition of manganese and aluminum (PLE mode), controlled by Mn diffusion in ferrite. In stage III the final very slow equilibration is controlled by Mn diffusion in austenite and is associated with the shrinkage of austenite. Points B in Fig.1a indicate the NPLE to PLE transition, for each annealing temperature, points C mark the maximum austenite volume fraction corresponding to the transition between PLE growth controlled by diffusion of Mn in ferrite and PLE growth controlled by Mn diffusion in austenite. Points D mark the final stable volume fraction of austenite corresponding to the equilibrium volume fractions computed by Thermo-Calc (points E). Mn partitioning during austenite growth is shown in Fig.1b. Austenite growth under PLE mode (stage II) is controlled by Mn diffusion in ferrite.

(a) (b) Fig.1 (a) Austenite fraction as a function of annealing time for several intercritical annealing temperatures, (b) Mn partitioning between ferrite and austenite under PLE growth mode. Austenite is on the left and ferrite on the right of the moving interface.

There is a significant enrichment of austenite in manganese at the interface with ferrite. This is attributed to the low diffusivity of manganese in austenite, which does not allow the accommodation of the Mn diffusive flux from ferrite. This Mn enrichment of austenite leads in austenite stabilization. The simulations presented above allow the selection of optimum heat treatment conditions in order to achieve the desirable microstructure in terms of austenite amount and stability for enhanced TRIP interactions in these steels. 3.2 Medium-Mn steels: Cyclic transformations In addition to isothermal intercritical annealing discussed above, the study of cyclic α!γ and γ!α transformations in the intercritical range is a good method to investigate the growth kinetics in medium-Mn steels. There are certain advantages in studying cyclic phase transformations. The first is that growth can be isolated and studied exclusively without the intervention of nucleation. The second stems from the fact that α!γ and γ!α transformations proceed at different rates isothermally, and, therefore, cyclic transformations can provide insight in the growth kinetics. The cyclic transformations were studied in a Fe-0.2C-5Mn steel (Sarafoglou et al. 2015). The cyclic thermal treatment considered is depicted in Fig.2a. The cycle starts with an isothermal holding at Tis=675oC followed by temperature cycling between Tmax=710oC and Tmin=640oC. The heating and cooling rates were 10oC/min. It is important to note that the time were the cyclic transformations starts is important, since the cyclic transformations depend on the previous conditions established during isothermal holding at Tis. Therefore, isothermal intercritical annealing was simulated first and then the start of the cyclic transformations was chosen accordingly. The isothermal α!γ and γ!α transformations are depicted in Fig.2b. Compared with the α!γ, the γ!α transformation is much slower. Two specific times, ts, were identified as the start of the cyclic transformations. In the first case ts=1x108 sec after equilibrium volume fractions for both austenite and ferrite have been established in the isothermal transformation. In the second case, ts=2x103 sec, where the α!γ transformation is evolving while the γ!α transformation is very sluggish. These times are depicted by dotted lines in Fig.2b.

(a) (b) Fig.2 (a) The thermal cycle considered for the study of cyclic transformations in Fe-0.2C-5Mn steel, (b) Volume fractions of austenite and ferrite for the α!γ and γ!α isothermal transformations respectively for the temperatures indicated.

The cyclic transformations are depicted in Fig. 3a and 3b for the times ts=1x108 sec and ts=2x103 sec respectively. In Fig.3a the volume fraction forms hysteresis loops. Point A marks the beginning and point B the end of the cyclic transformation. The loops move upwards indicating that more austenite forms at every cycle. An additional feature of the cyclic behavior is the “inverse” transformation, where the transformation proceeds to a direction opposite to the temperature change. This behavior is depicted by CD for Tmax and EF for Tmin in Fig.3a. The cyclic transformation for ts=2x103 sec is depicted in Fig.3b. Since in this case at ts=2x103 sec, the γ!α transformation during the isothermal treatment (Fig.2b) is sluggish, the volume fraction during cyclic transformation does not form hysteresis loops. On the

contrary, the volume fraction increases in each cycle, both in the heating and cooling part. In this case, austenite forms by inverse transformation during the cooling part of the cycle.

(a) (b) Fig.3 Evolution of austenite volume fraction during cyclic transformations for the times (a) ts=1x108 sec and (b) ts=2x103 sec.

3.3 Carburization of heat resistant steels Carburization is a high-temperature corrosion problem experienced in industrial processes such as ethylene production, natural gas reforming and coal gasification. The phenomenon takes place mainly in the petrochemical industry, where ethylene is produced in pyrolysis furnaces by thermal cracking of hydrocarbons in a steam hydrocarbon mixture at temperatures up to 1100oC. In this cracking process, coke deposition occurs at the inner walls of the cracking tubes. Carbon is transferred from the gas atmosphere through the porous coke at the alloy surface, where it diffuses in the interior and forms alloy carbides. Despite the theoretical and experimental work as well as the failure cases reported in the literature, carburization is not taken into account quantitatively in the design codes. For example, the API 530 standard used for the calculation of heater-tube thickness in petroleum refineries provides guidelines for selection of tube materials based solely on criteria for creep resistance. Carburization is only mentioned as a potential mechanism that could limit the service life of the tubes. In this example the ranking of carburization resistance of the steels listed in the API 530 standard was made possible through a simulation of the carburization process (Samaras & Haidemenopoulos 2015). The simulation for the 316 austenitic stainless-steel is shown in Fig.4a. The volume fraction of carbides is plotted as a function of distance from the surface. The time required for the carbides front to reach the mid-thickness was used as a criterion of carburization resistance. The calculated carburization mid-thickness time for the API 530 steels is shown in Fig.4b. The austenitic grades exhibit a higher carburization resistance than the ferritic grades. Among the austenitic grades the stabilized steels 321 and 347 exhibit the highest carburization resistance.

(a) (b) Fig.4 (a) The volume fraction of carbides as a function of distance from the surface for 316 stainless-steel carburized at 800oC, (b) carburization mid-thickness time for the API 530 steels.

3.4 Bainite transformation under para-equilibrium Bainite is playing a major role in the microstructure and mechanical properties in a variety of advanced high-strength steel steel grades. Optimization of the production and exploitation of bainite-involving steel grades and, more importantly, optimization of the design of new alloy compositions and/or processing routes, necessitate the clarification of the effect of chemical composition and heat-treatment conditions on the evolution of the bainitic transformation. This in turn creates a necessity for the development of appropriate models, with the highest possible degree of accuracy and applicability. Of all known models describing the evolution of bainitic transformation the most integrated one, is that proposed by Azuma (2005). It takes into account and quantifies the precipitation of cementite during the bainitic transformation, which allows a more realistic modelling of the bainitic transformation. This makes necessary the evaluation of the driving forces of formation for all participating phases, cementite precipitating from austenite and ferrite as well as ferrite forming from austenite. The evolution of bainite transformation is under paraequilibrium control, so the aforementioned driving forces were calculated under paraequilibrium conditions. This was made possible by modifying the thermodynamic solution database SSOL of the commercial thermodynamic software Thermo-Calc, following the methodology established in an earlier work (Grujicic & Haidemenopoulos 1988). The thermodynamic functions describing a pseudo-binary system of a fictitious element Z with carbon were incorporated into the database. Z accumulates all the thermodynamic functions of the substitutional elements in the initial alloy. Driving forces calculated for the phases of the pseudo-binary system of Z-C in equilibrium are driving forces of the respective phases of the initial alloy in paraequilibrium (Fig.5a). The paraequilibrium driving forces were inserted into the Azuma model and the kinetics of the bainitic transformation were modelled (Fig.5b). Several steel grades were studied and the calculated transformation kinetics for each one was in good agreement with experimental dilatometric results.

(a) (b) Fig.5 (a) Graphical representation of the paraequilibrium driving force for precipitation of cementite from austenite, (b) Comparison of model with experimental data for a Silicon TRIP steel transformed at 450oC.

The influence of parameters such as nucleation-site densities, interfacial energies, transformation temperature, parent austenite grain-size, etc, on the kinetics of the bainitic transformation was studied extensively. This is a more realistic modeling of the bainitic transformation and widens the range of applicability of the model to practically any steel composition. It is anticipated that the development of such reliable modeling tools will enhance the capabilities related to the design and optimization of new alloy compositions. 3.5 Computational-based design of Extrudable Al-alloys In recent years there has emerged a growing need for the development of high-strength Alalloy extruded profiles of complex shape for the needs of the transportation industry. This means that high strength should be combined with high extrudability in the 6xxx series alloys (Al-Mg-Si-Fe-Mn). The usual route followed so far is through increased alloying, for the formation of higher volume fractions of the strengthening Mg2Si phase. At the same time this

leads to the formation of higher volume fractions of Fe-bearing intermetallics, αAl12(FeMn)3Si and β-Al5FeSi, called α-AlFeSi and β-AlFeSi respectively. The α-AlFeSi has a cubic crystal structure and globular morphology while the β-AlFeSi possesses a monoclinic structure and a plate-like morphology, limiting the extrudability of the as-cast billet by inducing local cracking and surface defects in the extruded material. To cope with these effects, prolonged homogenization treatments (up to 12 h just below the solidus temperature) are employed, after casting and prior to extrusion, in order to transform the β-AlFeSi to αAlFeSi, which has a much lesser impact on extrudability, raising the production cost substantially. The computational design of these alloys has two aims: (a) to identify alloy compositions for the maximization of the strengthening phase Mg2Si and the minimization of β-AlFeSi and (b) to identify industrially feasible homogenization processes through the kinetics modeling of the homogenization process. Towards the first target, a mapping of Mg2Si and β-AlFeSi phase fractions in the as-cast microstructure of Al-Mg-Si-Fe-Mn (6xxx series) alloys has been performed over the useful composition range (0-1.2 mass%) of the principal alloying elements Mg and Si (Sarafoglou & Haidemenopoulos 2014). The calculations were based on the Scheil-Gulliver assumption of infinite diffusion in the liquid and limited diffusion in the solid state. The computed phase fractions (Fig. 6a) were validated with experimental measurements of phase fractions. An example of such a map is shown in Fig. 6b. The mapping procedure allows the control of intermetallic phases in the as-cast microstructure, the minimization of the β-AlFeSi phase in particular, which is a significant prerequisite in obtaining enhanced extrudability, combined with high strength in this alloy series. Construction of maps for different levels of Mn has shown that addition of Mn could allow for higher alloying with Mg and Si, in order to obtain higher amounts of Mg2Si, without at the same time increasing the β-AlFeSi phase in the as-cast microstructure.

(a) (b) Fig.6 (a) Microsegregation of phases in the as-cast microstructure of a 6082 alloy, (b) Map of fractions of Mg2Si (dotted lines) and β-AlFeSi (full lines) in the as-cast microstructure in 6xxx alloys containing 0.2Fe and 0.03Mn.

Towards the second target, a two-grain composite homogenization model has been developed (Sarafoglou 2015) for the simulation of the homogenization process. The simulation includes the dissolution of Mg2Si, the transformation of β-AlFeSi to α-AlFeSi, the removal of solute microsegregation and the reprecipitation of Mg2Si during cooling. Representative results from these simulations are depicted in Fig.7a for the temporal evolution and Fig.7b for the spatial evolution of the relevant transformations.

(a) (b) Fig.7 (a) Temporal evolution of phase transformations during the homogenization of a 6082 alloy, (b) Spatial evolution of β!α-AlFeSi transformation during homogenization for times 15 and 45min

The above results are useful in designing new alloy compositions as well as heat treatment schedules in order to shape the desirable microstructures and properties in these alloy systems. Conclusions The potential of the Alloyneering methodology has been presented as an integrated computational materials engineering approach to alloy design. Computational alloy thermodynamics and kinetics have been applied for the simulation of microstructure evolution in several alloy systems. The effect of alloy chemistry and processing can be systematically mapped and appropriate selections can be made. From the examples presented in this paper, it appears that Alloyneering can be a promising route towards fully computerized alloy design in the near future. Acknowledgement This work would not be possible without the valuable contribution of my former and current students. The assistance of P.I. Sarafoglou in the preparation of the manuscript is appreciated. The financial support by several agencies including GSRT, IKY, EU-ECSC and EU-RFCS is greatly appreciated. References Andersson, J.O., Helander, T., Höglund, L., Shi, P., Sundman, B. (2002). Thermo-Calc & DICTRA, computational tools for materials science. Calphad 26, pp.273-312. Azuma, M. (2005). Modelling upper and lower bainite trasformation in steels. ISIJ International, 45(2), pp.221-228. Borgenstam, A., Höglund, L., Ågren, J., Engström, A. (2000). DICTRA, a tool for simulation of diffusional transformations in alloys. Journal of Phase Equilibria 21, pp.269-280. Fanikos, J. (2015), M.Sc. thesis, in progress, Laboratory of Materials, University of Thessaly, Greece. Grujicic, M. & Haidemenopoulos, G.N. (1988). A treatment of paraequilibrium thermodynamics in AF1410 steel using the thermocalc software and database. Calphad, 12(3), pp.219-224. Haidemenopoulos, G.N. & Vasilakos, A. (1996). Modeling of Austenite Stability in LowAlloy Triple-Phase Steels, Steel Research, 67, Nο.11, p. 513-519. Haidemenopoulos, G.N. & Vasilakos, A. (1997). On the Thermodynamic Stability of Retained Austenite in 4340 Steel , J. of Alloys and Compounds, 247, p.128-133, 1997

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