Science Foundation Ireland, Grant/Award. Number: 14/IA/2604. Abstract. This paper presents a crystal plasticity model to predict the tensile response and.
Received: 18 September 2017
Revised: 4 December 2017
Accepted: 22 December 2017
DOI: 10.1111/ffe.12768
ORIGINAL CONTRIBUTION
The effect of ferrite phases on the micromechanical response and crack initiation in the intercritical heat‐ affected zone of a welded 9Cr martensitic steel M. Li1
| F. Sun2 | D.F. Li3 | P.E. O'Donoghue1 | S.B. Leen1* | N.P. O'Dowd2*
1
National University of Ireland Galway, Galway, Ireland 2
Bernal Institute, University of Limerick, Limerick, Ireland
Abstract This paper presents a crystal plasticity model to predict the tensile response and crack initiation in a mixed ferrite‐martensite material with a low volume fraction
3 Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China
of pro‐eutectoid ferrite, representative of a welding‐induced intercritical heat‐ affected zone. It is shown that small volume fractions of ferrite can have a significant
Funding information Science Foundation Ireland, Grant/Award Number: 14/IA/2604
effect on material strength and ductility depending on the ferrite grain orientation. For relatively “soft” ferrite grains, microcracks can grow across interferrite ligaments with damage accumulating in the ferrite, leading to a reduction in strength and strain hardening, but with little influence on ductility; in contrast, relatively “hard” ferrite grains act to accelerate microcrack initiation, leading to reduced ductility, with negligible influence on strain hardening up to the maximum load. KEYWORDS crystal plasticity, crystallographic orientation, damage, dual phase, IC‐HAZ
1 | INTRODUCTION P91 is a tempered martensitic steel (containing 9% chromium, 1% molybdenum) that has been widely used in high‐temperature piping systems for fossil fuel power plant, due to its high creep resistance, low thermal expansion, and good weldability. P91 is also a candidate material for next generation ultrasupercritical thermal plant.1,2 Welding plays a pivotal role in the manufacture of complex piping system in such power plant.3 The thermal history experienced at each material point within a welded joint
depends on the distance from the welding heat source, leading to heat‐affected zones (HAZs) in the weld. These are further classified, according to their characteristic microstructure into coarse‐grained, fine‐grained, and intercritical (IC‐HAZ). 4 Under complex operational loading conditions, failures can often initiate within the IC‐ HAZ, a phenomenon known as type‐IV cracking.5-10 Figure 1 (adapted from Abe et al6) shows the relationship between peak temperature, Tp, and the key phase transformation temperatures for a P91 weld. For the coarse‐grained HAZ, Tp is significantly greater than Ac3
Nomenclature: C, material elastic stiffness; C0, material elastic stiffness without damage; d, define the width of the damage transition region; Dp, plastic strain rate; F, deformation gradient; Fe, elastic deformation gradient; Fp, irreversible deformation gradient; F0, total free activation energy; hαβ, hardening matrix; hs, material constant for all slip systems (active and inactive); Jσ, Kirchhoff stress; k, Boltzmann constant; mα, lip direction; nαslip plane normal; N, total number of slip systems; p, q, exponents; Sα, the slip resistance; Ssat, saturated slip resistance; S0, initial value of slip resistance; T, absolute temperature; T*, stress elastically work‐conjugate; α, a given slip system; β, non‐active slip system; γ_ α , inelastic slip rate; γ_ 0 , pre‐exponent constant; τα, resolved shear stress; τ0, lattice friction stress at absolute temperature; τ0m, martensite lattice friction stress; τ0f, ferrite lattice friction stress; δαβ, Kronecker delta; εpl eq , the accumulated equivalent plastic strain; εc, the critical strain; σyy, predicted stress in y direction; σ, Cauchy stress; ω1, ω2, isotropic crystallographic hardening constants; ω, a microstructural damage variable * Joint senior authors
Fatigue Fract Eng Mater Struct. 2018;1–15.
wileyonlinelibrary.com/journal/ffe
© 2018 Wiley Publishing Ltd.
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FIGURE 1
A schematic of the weldment regions as corresponding to the equilibrium Fe─C binary phase diagram adapted from Abe et al.6 The dash line shows the carbon content of P91
(the upper austenite transition temperature) so that significant austenite grain growth occurs, whereas in the fine‐grained HAZ region, recrystallization dominates leading to grain refinement; in the IC‐HAZ region, Ac1 < Tp < Ac3, leading to partial transformation to austenite and the development of a mixture of ferrite and tempered martensite following cooling.6,7 The temperature in this region is not sufficiently high to cause dissolution of carbides, leading to the formation of carbide‐free ferrite in the IC‐HAZ region.8 It is important to understand the influence of the IC‐ HAZ microstructure on mechanical behaviour as failure generally occurs in the IC‐HAZ under long‐term service.9-11 Limited information is available on the effect of weld microstructure on inelastic deformation in P91 and related materials, due to the complexity of the IC‐ HAZ microstructure and the difficulty of extracting test samples from IC‐HAZ. However, it is reported that the IC‐HAZ material has the lowest hardness compared with the other regions of the weld after PWHT.12,13,8-10 The IC‐ HAZ is a partially transformed region, resulting in a mixture of metallurgical features.12-14 In Paul et al,15 the existence of small amounts of proeutectoid ferrite in the IC‐ HAZ is reported. The low values of microhardness in the IC‐HAZ have been attributed to the presence of this soft ferrite phase within a martensite matrix. (Transmission electron microscope images indicate that IC‐HAZ exhibits a lower dislocation density than parent material,16,17 which is another possible explanation for the lower hardness of the IC‐HAZ.) In this work, we examine the influence of a low volume fraction of ferrite within a martensite matrix on the microstructural deformation and the initiation of microcracks under tensile loading. Modern modelling techniques provide the opportunity to gain unique insight into, and quantify, specific microstructure effects on constitutive response. For example, a continuum damage mechanics model18 was used to
account for multiple precipitate types within a 9Cr steel, and the results indicate that the volume fraction of MX carbide is a vital factor for creep behaviour of 9Cr steel at elevated temperature.19 Crystal plasticity finite element (CPFE) approaches have provided information on inelastic deformation at the microscale.20-22 A dislocation‐density grain boundary interaction scheme has been developed and incorporated into a CPFE approach by Shanthraj and Zikry,20 to analyse crack nucleation and evolution based on the unique variant morphologies and inherent orientation relationships in martensitic microstructures. The extended FE model approach was used in Ramazani et al23 to simulate martensite cracking in a dual phase steel. A combined CPFE and continuum damage model for a single crystal superalloy showed that effects such as crystallographic orientation, self‐ and latent‐hardening, and rate sensitivity can significantly influence creep and damage.24 The authors are not aware of any previous work on modelling of the failure mechanisms for IC‐HAZ using the CPFE approach, especially for 9Cr steels. Therefore, this work investigates the application of a crystal plasticity model combined with a strain‐controlled damage model at the microscale, to investigate the failure response of P91 steel under monotonic tensile loading. Small amounts of ferrite can induce significant stress concentrations and associated strain gradients at the ferrite‐martensite grain boundaries, as shown in our previous work.7 This may lead to premature microcrack initiation and influence the fatigue life of welded joints. It has been shown experimentally that the presence of soft ferrite grains in a hard martensite matrix has a detrimental effect on the low cycle fatigue life of 9Cr‐1Mo steel, leading to acceleration of fatigue crack initiation.25 In this work, a modified 2‐dimensional Voronoi tessellation (VT) model is implemented, which explicitly accounts for the packet/block microstructure of the martensite. The
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Kurdjumov‐Sachs (K‐S) orientation relationship26 is used to describe the crystallographic orientation of the martensite grains at each material point.l27 A strain‐controlled damage model is incorporated to assess the influence of the soft ferrite phase on the development of microplasticity and damage to provide insight into the mechanical behaviour of welded joints.
2 | FINITE ELEMEN T MOD ELL I NG FRAMEWORK 2.1 | Implementation of finite element model for IC‐HAZ A typical tempered martensite grain has a body‐centred cubic (BCC) lattice structure composed of 3 different types of slip systems (see Table 1), twelve {110} slip systems, twelve {112} slip systems, and twenty‐four {123} slip systems. Figure 2 shows examples of a slip system for each of these slip families. The hierarchical microstructure of martensite grains is shown schematically in Figure 3. The prior austenite grain (PAG) is divided into martensite packets containing blocks with specific misorientations as described in Kitahara et al,26 while each block consists of collections of laths with similar orientations separated by low‐angle grain boundaries.28 In recent work,29 the K‐S relationship was introduced into a VT code, providing a physical description of the orientation relationship between the neighbouring blocks and packets within a PAG. TABLE 1
Slip systems of body‐centred cubic (BCC) structure
BCC Slip Systems 1
2
3
Slip normal
{110}
{112}
{123}
Slip direction
Number of slip systems
12
12
24
Figure 4A shows a micrograph of the IC‐HAZ region from a sample of ex‐service P91. The micrograph shows a region, without internal block boundaries, which may be identified as a ferrite region within a matrix of martensite grains.30 Similar microstructures have been reported in Paul et al and Hsiao et al.15,31 The present work is focused on assessing the influence of such an isolated ferrite region within a martensite matrix. The corresponding idealized FE representation derived from the modified VT code is shown in Figure 4B, including 1 randomly distributed ferrite grain (approximately 5% by volume based on experimental observations15). The colour contours correspond to 1 of the Euler angles for each martensite block, obtained from the K‐S relation based on a random distribution of PAGs. The grain size of the martensite PAG in the IC‐HAZ is typically 10 μm,2 whereas the mean block width within the PAG is ~1.5 μm.32 In this paper, attention is focused on the tensile response of the IC‐HAZ material, with particular focus on the in‐plane interactions among grains, packets, and blocks within the PAG and between the ferrite and martensite phases. Hence, it is assumed here that the grains are columnar in the out‐of‐plane direction (with 1 element in that direction), following the approach adopted previously for modelling of single‐phase P91 martensitic steel.21 Three‐ dimensional, linear brick elements are used within the framework of the fully 3‐dimensional user material constitutive model presented below, with periodic boundary conditions in both the in‐plane and out‐of plane directions, as described below (Section 3) and illustrated in Figure 4C. The present quasi‐2D representation is considered appropriate to capture the dominant in‐plane interactions of the ferrite‐martensite phase mixture in the IC‐HAZ, at least as a first step toward more detailed application of a full 3D modelling approach, which would be actually be prohibitively onerous, in computational overheads. Previous work21 has directly compared 3D columnar, 3D equiaxed, and test data, for the same boundary conditions and deformation mode as used here, for a stainless steel;
FIGURE 2 Examples of slip systems for body‐centred cubic structure corresponding to each slip system family. In each figure, the arrow and the blue lines indicate the slip plane and slip direction, respectively [Colour figure can be viewed at wileyonlinelibrary.com]
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the in‐plane directions are accounted for. The present quasi‐2D gives the same response as the columnar 3D. The key differences will, of course, be in fracture and failure modes; eg, clearly, 3D aspects of the fracture surfaces and crack morphology will not be captured in the quasi‐ 2D approach. It is intended to develop 3D models of the martensite‐ferrite grain interactions in future work. The crystal plasticity model used to represent the constitutive response is discussed in Section 2.2.
FIGURE 3 Schematic illustration of the hierarchical microstructure in P91 martensitic steel including prior austenite grain, packet, block, and lath
it was shown that the 3D columnar gave almost identical tensile stress‐strain response to the 3D equiaxed up to 10% strain, as the most important grain interactions in
2.2 | Micromechanical crystal plasticity constitutive formulation The CPFE model describes the microstructural deformation at the block level, accounting for elastic and plastic flow anisotropies for each block, without considering a size effect (length scale dependent plasticity) for simplicity. Length scale effects may be important when block size is lower than ~1 μm,33 which will be considered in our
(A)
(B)
(C) A, Intercritical heat‐affected zone microstructure morphology measured by scanning electron microscopy.30 B, Distribution of Euler angle in a polycrystal finite element model; the blue region indicates α‐ferrite embedded in martensite matrix. C, Illustration of quasi‐2D (columnar microstructure) model with periodic boundary conditions [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 4
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future work. Martensite laths are not explicitly modelled; the constitutive model at the block level accounts implicitly for the lath contributions, as described in Li et al.21 Following Asaro and Rice,34 the deformation gradient F is decomposed into components, Fe and Fp, as follows: F ¼ Fe Fp ;
(1)
where Fe is the elastic deformation gradient due to the reversible response of the lattice to external loadings and rotation, while Fp is an irreversible deformation gradient due to slip. The inelastic slip rate on a slip system α, γ_ α is represented by a thermally activated flow rule35 dependent on the resolved shear stress τα, as follows: α q F0 jτ j−Sα p γ_ α ¼ γ_ 0 exp − 1− ; kT τ0
(2)
In Equation 2, T and k are absolute temperature and Boltzmann constant, respectively. The material constants are as follows: F0, the total free activation energy needed to overcome the lattice resistance; τ0, the lattice friction stress at absolute temperature; and p, q, and γ_ 0 , the exponents and preexponent constant, respectively. The resolved shear stress τα on a given slip system is defined as follows: τ α ¼ ðFe ÞΤ Fe T* :ðmα ⊗nα Þ; α
(3)
ω1 = 1, ω2 = 1, all slip systems harden equally, irrespective of whether active or not, leading to isotropic crystallographic hardening (Taylor hardening36). Based on recent studies,37,38 this model (ω1 = 1, ω2 = 1) has been used here.
2.3 | Damage model The accumulated equivalent plastic strain (εpl eq ) has been proposed by a number of authors as an important indicator parameter for crack initiation.39,40 In this paper, we adopt a strain‐controlled damage progression model in conjunction with microplasticity to describe the localized deformation. This damage model has previously been applied for austenitic stainless to account for damage development.41 The accumulated equivalent plastic strain εpl eq is defined as t
εpl eq ¼ ∫ 0
2 p p D :D 3
12 dt;
(7)
where t is the current simulation time and Dp is plastic strain rate, expressed as Dp ¼
i 1 N αh e α ∑ γ_ F m ⊗nα ðFe Þ−1 þ ðFe Þ−T nα ⊗mα ðFe ÞT ; 2 α¼1 (8)
α
where m and n are unit vectors to define slip direction and slip plane normal in the reference configuration; N denotes the total number of slip systems. In Equation 3, T* indicates the stress elastically work conjugate to the elastic Green strain
A microstructural damage variable, ω, varying from 0 (no damage) to 1 (fully damage), is adopted to describe the degradation of the elastic stiffness. The modified local elastic stiffness matrix is written as follows:
T* ¼ ðFe Þ−1 JσT* ðFe Þ−T ;
C ¼ C0 ð1−ωÞ;
(4)
where J = det(F), σ, and Jσ are the Cauchy and Kirchhoff stress, respectively. The slip resistance Sα in Equation 2 is defined as N Ssat −Sβ β S_ α ¼ ∑ hαβ γ_ ; Ssat −S0 β¼1
(5)
where hαβ in Equation 5 is the hardening matrix and Ssat is the saturated slip resistance with initial value S0. The hardening matrix, hαβ, can be written as
hαβ ¼ hs ω1 þ ð1−ω2 Þδαβ ;
(6)
where hs is a material constant for all slip systems (active and inactive) and δαβ is the Kronecker delta. The slip resistance hαβ depends not only on the active slip systems α (self‐hardening) but also on the nonactive slip system β (latent hardening), through the constants ω1 and ω2.27 If
(9)
where C0 is the material elastic stiffness without damage. A continuously varying ω is assumed by using a modified Cauchy‐Lorentz cumulative distribution function42 as follows: ω¼1 ! # " ε −1 1 εpl 1 1 1 eq −εc c − : (10) þ þ arctan arctan d d 2 π π 2 The Cauchy‐Lorentz function in Equation 10 provides a phenomenological description of a damage transition pl with ω = 0 at εpl eq ≤0 and ω → 1 as εeq →εc and εc is the critical strain. The width of the damage transition region is defined by d. The material model defined in Sections 2.2 and 2.3 is implemented in a material user subroutine (UMAT) in the nonlinear commercial FE code Abaqus (2016).43
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3 | M O D E L C A L I B R A T IO N A N D MATERIAL P ARAMETER IDENTIFICATION A methodology to obtain the viscoplastic constitutive response in heterogeneous (welded P91) material by using digital image correlation is described in Touboul et al.44 The material parameters for the constitutive model described in Section 2 were determined by fitting to the experimental data in Touboul et al44 for the IC‐HAZ at room temperature. The representative volume element (RVE), constructed as described in Section 2.1, has been checked to establish a sufficient number of blocks to give a consistent macroscopic response by using the polycrystalline FE model.7,29,45 Two RVEs were first generated: an all‐martensite RVE and an all‐ferrite RVE as shown in Figure 5. The all‐martensite RVE consists of 20 PAG grains, containing 444 blocks; the smallest element size is about 0.24 μm, giving about 4 or 5 elements across the width of each block (see Figure 5A, inset). The model contains about 30,000 elements. The all‐ferrite RVE
FIGURE 6 Identification of parameters for martensite by fitting the intercritical heat‐affected zone data from Touboul et al;44 the predicted ferrite response is also included
(A)
(B) FIGURE 5 Illustration of the micromechanical finite‐element (FE) model for dual‐phase constitutive parameter identification: (A) single‐ phase martensite model showing FE mesh and (B) single‐phase ferrite model (from Li et al7) [Colour figure can be viewed at wileyonlinelibrary.com]
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TABLE 2 C11 (GPa) 219.7
TABLE 3
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Elastic constants and flow rule parameters used in the polycrystal model (room temperature) C22 (GPa)
γ_ 0 (s−1)
C44(μ) (GPa)
112.2
140.0
p (−)
450
0.5
Strain hardening parameters used in the polycrystal
model S0 (MPa) 2.2
TABLE 4
Ssat (MPa)
hs (MPa)
ω1 (−)
ω2 (−)
250
520
1
1
Twelve slip systems list used in the crystal plasticity
model System
Plane Normal
Slip Direction
1
(011)
[111]
2
(101)
[111]
3
(110)
[111]
4
(011)
[111]
5
(101)
[111]
6
(110)
[111]
7
(011)
[111]
8
(101)
[111]
9
(110)
[111]
10
(011)
[111]
11
(101)
[111]
12
(110)
[111]
q (−) 1.25
F0 (J) 0.43 * 10
(−18)
τ0m (MPa)
τ0f (MPa)
305
244
Microhardness indentation tests for the ferrite and martensite phases in the IC‐HAZ demonstrated a hardness value for martensite of approximately 1.25 times that of the ferrite phase.31 In the CPFE model, the lattice friction stress (Equation 2) largely controls the material strength. Therefore, in this work, the constitutive response of the ferrite phase is represented by scaling τ0 according to the microhardness ratio between the 2 phases; the martensite and ferrite lattice friction stresses are given by τ0m and τ0f, respectively. The resulting predictions of the macro stress‐strain responses of both martensite and ferrite phases are shown in Figure 6, taken from the RVEs of Figure 5. Table 2 presents the identified elastic constants and flow parameters used in the analysis. Table 3 gives the parameters associated with the strain hardening for both phases. Numerous researchers, eg, Chen and Maddin,46 have argued that for BCC crystals; the slip along {110} slip planes is the dominant deformation mode at room temperature. Therefore, only the dominant twelve {110} slip systems of BCC are considered in the remainder of this paper. Table 4 gives the list of {110} slip systems used in the UMAT.
4 | R E SUL T S (see Figure 5B, inset) consists of 200 PAG grains with 35,000 elements, following our previous work.7 In both cases, periodic boundary conditions (see Figure 4C) are used to represent the overall material microstructure, as in Li and Sun et al and Li and Golden et al.7,21
4.1 | Crystal orientation effect on global response The global and local deformation mechanical responses induced by different ferrite orientations are first investigated.
FIGURE 7 A, Isolated ferrite grain embedded within a martensite matrix; B, 3 typical ferrite orientations chosen for ferrite grain [Colour figure can be viewed at wileyonlinelibrary.com]
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Figure 7A illustrates the approach with an isolated ferrite grain embedded within the martensite matrix. The darkest lines correspond to the PAGs (or ferrite phase), the heavy lines correspond to packet boundaries, and the lightest lines are the block boundaries. The
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regions A, B, C, and D in Figure 7A and the path have been identified for further analysis in Sections 4.2 and 4.3. Three orientations are chosen for the single crystal ferrite grain, as shown in Figure 7B; the loading direction is [010] in all cases.
(B)
FIGURE 8
Comparisons of stress‐strain responses for the ferrite with different orientations. A, Global responses for the representative volume element including ferrite with different orientations; B, single crystal response for the ferrite with different orientations [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 9 Stress distribution (σyy) at 5% macroscopic tension for the ferrite with different orientations. A, No ferrite; B, ferrite with orientation; C, ferrite with orientation; D, ferrite with orientation [Colour figure can be viewed at wileyonlinelibrary.com]
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Figure 8A shows a comparison of the global tensile stress‐strain responses obtained from the FE analysis for the 3 different ferrite orientations up to a strain of 5%. Also included is the measured IC‐HAZ response from Touboul et al.44 It is clear that, at the macroscale, the influence of the ferrite orientation is weak, with the orientation giving a slightly softer response than the other 2 orientations and all 3 cases are similar to the all‐martensite response at the macroscale (Figure 6). Figure 8B provides a comparison of the single crystal stress‐strain responses for the 3 orientations, showing the softest response for the orientation, which is also significantly softer than a typical martensite‐only response (compare to Figure 6). The hardest response is for the orientation, which is a similar response to that of martensite.
4.2 | Crystal orientation effect on local micromechanical response Figure 9 shows the σyy distribution at 5% macroscopic strain. The thick solid white lines indicate the PAG
FIGURE 10
pl
boundaries or ferrite boundary, the thin solid lines are the packet boundaries, and the dash lines are block boundaries. The predictions show a complex pattern of stress due to the orientation mismatch between neighbouring packets and blocks and, for Figure 9B to D, the influence of the ferrite grain with different applied orientations. Figure 9B shows that the introduction of a “soft” ferrite grain causes reduced stress within the grain, compared with the equivalent PAG in Figure 9A; the average σyy in the ferrite region decreases from ~610 MPa for single phase martensite RVE to ~500 MPa for the mixed‐phase RVE. There is some increase in the local stress in transversely adjacent martensite grains of the A and B regions (defined in Figure 7A) and, concomitantly, reduced stresses in C and D regions. In contrast, Figure 9C shows that the introduction of a “hard” ferrite grain increases the local stress in the C and D regions but slightly decreases local stresses in the A and B regions. Figure 9 D shows that the introduction of the intermediate hardness ferrite grain gives an almost identical inter‐
Accumulated equivalent plastic strain distribution (εeq ) at 5% macroscopic tension for the ferrite with different orientations. A, No ferrite; B, ferrite with orientation; C, ferrite with orientation; D, ferrite with orientation [Colour figure can be viewed at wileyonlinelibrary.com]
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and intragranular stress distribution to the “no ferrite” case, Figure 9A. Figure 10 shows the equivalent plastic strain distribution (εpl eq ) for the cases examined in Figure 9. As before, the results are presented at the same macroscopic strain level of 5%. As discussed in Section 2.3, εpl eq is a key variable controlling prediction of microcrack initiation for the strain‐based damage model. It can be seen from Figure 10B that the introduction of a “soft” ferrite grain leads to an increase in average εpl eq from 0.054 to 0.069 in this grain (relative to Figure 10A) and, more importantly, an associated reduction in εpl eq in the transversely adjacent B region and, especially, in the block and packet of maximum εpl eq . In other words, the high plastic strain experienced by this martensite block in region B of Figure 10A is “shared” with the ferrite phase in this configuration. In contrast, Figure 10C and D shows that the “hard” ferrite grain (and to a lesser extent the ferrite grain) further accentuates the εpl eq concentration in the most highly strained block
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location, relative to the original single‐phase martensite microstructure. This trend is consistent with CPFE simulations of hard‐soft grain interactions for titanium alloy polycrystals.47 To further examine this issue and to quantify the trends illustrated in the contour plots of Figures 9 and 10, Figure 11 shows the predicted σyy and εpl eq distributions (at 5% macroscopic strain) plotted along the path identified in Figure 7A for the all‐martensite and mixed‐phase analyses. The path traverses the single‐phase martensite microstructure from region A to region B. Significantly inhomogeneous distributions of σyy and εpl eq are predicted in Figure 11A and B, due to traversing of multiple block boundaries within the fully martensitic microstructure. Figure 11C shows the increased stresses within adjacent martensite grains for the “soft” case, relative to both the and martensite‐only cases; the highest localization of stress occurs at the ferrite‐martensite grain boundaries for the case of the “soft” ferrite grain, leading to accentuated microstress concentration factors
(A)
(B)
(C)
(D)
FIGURE 11 Effect of ferrite orientation on local stress and strain distributions at 5% global strain for path identified in Figure 7A. A, pl pl All‐martensite analysis σyy; B, all‐martensite analysis εeq ; C, mixed‐phase analysis σyy; D, mixed‐ phase analysis εeq [Colour figure can be viewed at wileyonlinelibrary.com]
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of ~1.8 (relative to the global stress of Figure 8). This type of microstress “hot spot” at a grain boundary is potentially detrimental with respect to fatigue crack nucleation. Figure 11D shows the peak εpl eq localization in the martensite packet‐block is adjacent to the ferrite grain (region B). For the ferrite with orientation case, the peak strain is significantly higher than that in the martensite‐only and ferrite cases. Note that this is the location of predicted failure for the martensite‐only and the cases; the latter is shown below to have a lower ductility than the former, which is consistent with the relative strain localizations; viz. the higher
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localization in the case gives lower ductility. It may be noted that the value of peak strain at the failure location for the case (not shown here in the interest of space) is ~0.13, which is lower than the martensite‐only and cases, as highlighted in Figure 11B and D, resulting in higher predicted ductility.
4.3 | Prediction of microcrack initiation of IC‐HAZ The preceding analyses have been for strain levels up to 5% with the damage model inactive. Figure 12A shows a
(A)
FIGURE 12 Prediction of tensile damage and microcrack initiation in tensile test for single‐martensite phase representative volume element: (A) comparison of crystal plasticity finite element (CPFE) tensile stress‐strain response with intercritical heat‐affected zone data from Touboul et al44 and (B) CPFE‐predicted damage distribution showing predicted failure locations [Colour figure can be viewed at wileyonlinelibrary.com]
(B)
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(B)
(C)
FIGURE 13 Prediction of damage and microcrack initiation for the mixed‐phase martensite‐ferrite representative volume element: A, comparisons of predicted responses against measured intercritical heat‐affected zone data;44 B, damage distribution for “soft” ferrite; C, damage distribution at failure for “hard” ferrite [Colour figure can be viewed at wileyonlinelibrary.com]
comparison of the CPFE‐predicted tensile stress‐strain response to failure, for the single‐phase martensite (assuming no ferrite in the IC‐HAZ), with the measured IC‐HAZ response.44 The predicted response shown is for a range of critical strain values, εc, in the damage model of Equation 10 up to εc = 0.3. For critical strain values above 0.3, it was found that a converged solution was not obtained in the FE analysis, and therefore, the critical strain value of εc, which is closest to the measured value for the IC‐HAZ, has been used in the subsequent analysis. The value of the damage transition parameter d TABLE 5
is fixed at 0.1. Figure 12B shows the predicted damage distribution at failure. Intergranular cracking is predicted generally, ie, along PAG boundaries and block boundaries. Figure 13 shows a comparison of the CPFE‐predicted tensile stress‐strain responses for the 2‐phase martensite‐ferrite IC‐HAZ microstructures with “soft” and “hard” ferrite grains with the measured IC‐HAZ response from Touboul et al44 and the corresponding damage distributions at failure. It can be seen from Figure 13A that the effect of the “soft” ferrite
Comparison of crystal plasticity finite element results with measured intercritical heat‐affected zone data Tensile Strength (MPa)
Ductility εf (%)
Experiment 44
665
10.2
CPFE‐single phase
615
9.0
CPFE‐mixed phase: ferrite
590
9.3
CPFE‐mixed phase: ferrite
600
8.5
Method
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grain is to cause a softer overall response with reduced hardening, leading to a discernible reduction in tensile strength and marginal effect on ductility for εc = 0.3 (see Table 5). In contrast, the most significant effect of the “hard” ferrite grain is to reduce predicted ductility with negligible effect on hardening response (up to the maximum stress). Although the single‐phase martensite model has been calibrated (in Figure 12) to correlate closely to the measured IC‐HAZ stress‐strain response, on the assumption of no ferrite phase, the purpose of the mixed‐phase models is to investigate the global (tensile stress‐strain) and local (inhomogeneity of local stress‐strain distributions and cracking‐fracture behaviour) effects of inclusion of such a ferritic phase (material imperfection), specifically, in the context of premature creep or creep‐fatigue failure of P91 weldments. Small amounts of ferrite can be seen in the IC‐HAZ region after welding. Figure 13B and C shows the predicted microcracking patterns for the “soft” and “hard” ferrite cases, respectively. It can be clearly observed that the ferrite grain can strongly influence the location of crack initiation with the “soft” ferrite grain causing a significant change in microcracking pattern, ie, transgranular, relative to the single‐phase martensite case (Figure 12B). Figure 13C shows that the damage distribution for the “hard” is more consistent with that for the single‐phase martensite, ie, intergranular, though with increased damage at the same level of macroscopic strain (see also Figure 10A and C). Some additional observations are as follows. Although the present quasi‐2D modelling approach can match the overall stress‐strain response, the predicted local (detailed) fracture morphology and fracture characteristics will undoubtedly be different to what would be predicted by a full 3D microstructure model (with microstructure variation in the out‐of‐plane direction, as opposed to the columnar assumption of the present approach). Specifically, 3D aspects of the fracture surfaces and crack morphology will not be captured in the quasi‐2D approach. A 3D RVE model equivalent to the present quasi‐2D RVE would contain about 7,525,000 elements, as opposed to the 30,100 required here. With damage and large‐deformation effects, this would require prohibitively enormous run times, particularly for the range of sensitivity analyses presented. Nonetheless, the present quasi‐2D approach has provided a key first step in crystal plasticity modelling of IC‐HAZ failure under tensile loading. It is argued that this simplification allows more accessible interpretation of the trends in predicted inter‐ and intragranular cracking vis‐à‐vis in‐ plane grain‐block‐packet and ferrite‐martensite phase interactions.
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5 | C ON C L U S I ON S A micromechanical modelling methodology is presented for tensile damage and crack initiation in the intercritical HAZ in 9Cr steels, due to the ferrite‐martensite inhomogeneity. A damaged model based on accumulated plastic strain, but independent of stress history, has been examined. The key conclusions are as follows: 1. The predicted ductility and strength are shown to be in general agreement with previously published measured test data for the IC‐HAZ material. 2. The crystallographic orientation of ferrite grains significantly affects the localization of strain and the behaviour of crack initiation in the IC‐HAZ. 3. Small volume fractions of softer ferrite are shown to have a detrimental effect on material strength, as expected. However, the effect on ductility can be detrimental or marginally beneficial, depending on ferrite grain orientation.
ACKNOWLEDGEMENTS This publication has emanated from research conducted with the financial support of Science Foundation Ireland under grant no. 14/IA/2604 and the College of Engineering and Informatics at NUI Galway. The authors are grateful to the Irish Center for High‐End Computing (ICHEC) for supporting the computational work (uleng040b). The authors are grateful for the helpful discussions with the Mechanics team (NUI Galway and UL). The assistance of Mr Edward Meade of the Bernal Institute at UL is also gratefully acknowledged. ORCID M. Li
http://orcid.org/0000-0002-0869-8971
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How to cite this article: Li M, Sun F, Li DF, O'Donoghue PE, Leen SB, O'Dowd NP. The effect of ferrite phases on the micromechanical response and crack initiation in the intercritical heat‐affected zone of a welded 9Cr martensitic steel. Fatigue Fract Eng Mater Struct. 2018;1–15. https://doi.org/ 10.1111/ffe.12768
