- Email: [email protected]
Modeling the strongly localized deformation behavior in a magnesium alloy with complicated texture distribution
Materials Science & Engineering A 762 (2019) 138103
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Modeling the strongly localized deformation behavior in a magnesium alloy with complicated texture distribution
T
Weijie Rena, Renlong Xina,*, Dejia Liub a b
Joint International Laboratory for Light Alloys (MOE), College of Materials Science and Engineering, Chongqing University, Chongqing, China College of Materials Science and Engineering, East China Jiaotong University, Nanchang, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Mg alloys CPFEM Friction stir welding Bending Strain heterogeneity
A crystal plasticity finite element model (CPFEM) was developed to simulate the bending behaviors of a friction stir welded (FSW) Mg joint. The joint was divided into 12 sub-regions in the model to represent the observed complicated texture distributions. Twinning was modeled as pseudo slip and the predominant twin reorientation scheme was used. Two kinds of three-point bending geometries were applied. The present study aims to understand the underlying mechanisms of the strain heterogeneity and fracture localization commonly occurred in FSW Mg joints during bending deformation. It reveals that the strongly localized texture in conjunction with the different activities of slip and twinning in each sub-region cause severe strain heterogeneity in welding direction (WD), which results in the “concave-convex” appearance as observed on the longitudinal section. Besides, fracture initiates from the outer edge of thermomechanical affected zone (TMAZ) during Surface test due to the highly localized activation of basal slip, and crack likely propagates into the region of easy to activate basal slip (EABS) in a later stage. Crack initiates in crown zone (CZ)-side during Base test with a small distance away from the TMAZ/CZ interface. The huge differences in the activities of slip and twinning modes in each sub-region cause deformation incompatibility in the FSW Mg joint and initiates fracture in the area with maximum strain.
1. Introduction
alloys. Bending is one of the most widely used operations in forming of Mg sheet. Recently, Liu et al. [21,22] carried out two kinds of bending tests on a FSW AZ31 Mg alloy. They investigated the relationship between textural variation, twinning activity and fracture path in bending tests by Schmid factor analysis. However, unlike simple uniaxial deformation, the stress state and deformation behaviors for three-point bending are more complicated [23]. Therefore, it is necessary to conduct an indepth study on the underlying deformation mechanisms (e.g. the activities of deformation modes and local strain state) of the sub-regions of FSW Mg joints during bending. As a type of time and cost saving tool, crystal plasticity finite element model (CPFEM) provides a new research approach [24–27]. However, CPFEM has seldom been applied on the deformation behavior of FSW Mg joints due probably to their complicated textures and twinning behaviors [28–30]. To fill this research gap, CPFEM was employed in this work to simulate the deformation and fracture behaviors in an FSW Mg joint. To represent the observed complicated texture distributions, the joint was divided into 12 sub-regions in the model. Two kinds of three-point bending tests were simulated. The present work aims to investigate the underlying mechanisms for the strain heterogeneity and fracture
As one of the lightest structural materials, Mg alloy has promising application potential in automotive and aerospace industries [1–3]. The wider use of Mg alloys need to overcome several problems, one of which is the joining problem. Friction stir welding (FSW) is an innovative solid state joining technique, which can avoid surface distortion and grain coarsening, and is especially suitable for the welding of light metals such as Al and Mg [4–7]. However, sharp and inhomogeneous texture is usually formed in Mg welds, which results in strain heterogeneity during subsequent deformation [8–12], and significantly deteriorates the strength as well as ductility [13–15]. Moreover, fracture usually occurred in stir zone (SZ)-side or the transition region between SZ and base material (BM) during transverse tensile tests [1,16,17]. Some researchers correlated the fracture position with the sub-region of joint having the c-axis oriented favorable for basal slip [18,19]. Some other researchers attributed fracture to the incompatible plastic deformation at thermomechanical affected zone (TMAZ)/SZ interface because of a sudden texture change over there [1,10,20]. Accordingly, it is meaningful to understand the mechanism of strain heterogeneity as well as its relationship with the fracture of FSW Mg
*
Corresponding author. Sha Zheng Jie 174, Sha Ping Ba District, Chongqing, China. E-mail address: [email protected] (R. Xin).
https://doi.org/10.1016/j.msea.2019.138103 Received 10 April 2019; Received in revised form 1 July 2019; Accepted 2 July 2019 Available online 03 July 2019 0921-5093/ © 2019 Elsevier B.V. All rights reserved.
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
s *α = F *⋅s0α and m *α = m 0α⋅F * − 1
behaviors observed in FSW Mg alloys during the two kinds of bending tests.
(5)
γ˙ α
The shear rate on each slip system is calculated using a ratedependent formulation proposed by Asaro and Needleman [39,40]:
2. Experimental procedures
τα gα
γ˙ α = γ˙0
A hot-rolled commercial AZ31 Mg alloy (Mg–3%Al–1%Zn) sheet with a thickness of 6 mm was joined by FSW. The detailed welding parameters were reported in a previous work [21].The welding direction (WD) was along the rolling direction of the rolled sheet. After welding, the cross-section vertical to the WD of the FSW joint was examined. Microstructure was characterized by optical microscopy (OM). The samples for OM were etched with a solution consisting of 2 ml distilled water, 2 ml glacial acetic acid, 14 ml ethanol and 0.84 g picric acid. Electron backscatter diffraction (EBSD) was used to analyze the local texture variation in various regions of the joint. The EBSD detector used was an HKL Channel 5 System equipped in a field emission gun scanning electron microscope (FEG-SEM, FEI Nova 400). Three-point bending tests were applied along two directions with respect to the FSW joint and are designated as Surface test and Base test, respectively, as shown in Fig. 2. Strips with dimensions of 84 (transverse direction, TD) × 10 (WD) × 4.5 (normal direction, ND) mm3 were cut from the FSW plates for bending tests. The bending tests were performed on an AG-X50kN machine at a displacement rate of 2.0 mm/min. The span distance was set as 50 mm.
1/ m
sign(τ α )
(6)
Due to the polar nature, the shear rate due to twinning is described by
⎧ γ˙ α =
τα gα
γ˙0
1/ m
τα > 0
⎨ α ⎩0 τ ≤ 0
(7)
where γ˙0 is the reference shear rate and m is the strain rate sensitivity index. τ α and g α are the resolved shear stress on slip/twin system α and the strength of this system, respectively. The relative activity n (γ˙ α / ∑β = 1 γ˙ β ) of each system α is also used for analysis. The elastic constitutive equation for a crystal is: ∇*
σ
+ σ tr(D *) = C: D *
(8)
where C is the tensor of elastic moduli, tr(D *) denotes the trace of ∇* tensor D*, σ is the Jaumann rate of the Cauchy stress σ based on the lattice spin tensor Ω* and can be written as: ∇*
(9)
σ = σ˙ − Ω*σ + σ Ω*
3. Crystal plastic finite element method
The rate of resolved shear stress is specified by: A code describing the constitutive formulation of Mg crystals was developed and implemented in the commercial finite element code ABAQUS/Standard as a user material (UMAT) subroutine [31]. This code is based on the code initially developed by Huang [32] to capture slip based deformation in FCC polycrystals. For a detailed description, readers are referred to previous papers [33–39]. The framework of Huang's code was described in detail in Ref. [32]. In the following, we will briefly summarize the constitutive formulation of the modified code used here.
τ˙ α
n
hαα = h 0 sec h2
n
n
ntw
a=1
V acc =
(4)
= n sl + ntw
s0α
∑ γ t /γ0
(13)
t =1
is the shear rate on slip system α. Unit vectors and are where the slip direction and normal to slip plane in the reference configuration, respectively. n sl and ntw are the total number of available slip and twin systems, respectively. It is convenient to define s *α , lying along the slip direction of the system α and m *α , normal to the slip plane in the deformed configuration by
γ˙ α
γ˙ (α ) dt and hαβ = qhαα (α ≠ β )
α=1
Twinning is essentially modeled as pseudo slip. The model for reorientation is based on the ideas of Van Houtte [42] and the predominant twin reorientation Scheme (PTR) [43]. We keep track of the shear strain γ t contributed by each twinning system t, and of the associated volume fraction γ t / γ0 ( γ0 = 0.129 is the characteristic twin shear) within each element. By summation of all twin systems in each element, the accumulated twin volume fraction V acc can be calculated as:
with
γ˙ αs0α ⊗ m 0α
t
3.2. Incorporation of twinning
(3)
∑
n
∑ ∫0
(12)
where the symmetric stretching rate D and the antisymmetric spin tensor Ω can be decomposed into elastic (superscript *) and plastic (superscript p) parts as follows:
D * + Ω* = F˙ *F *−1 and D p + Ω p =
h0 γ , γ= τs − τ0
where h0 is the initial hardening modulus, τs is the break-through stress where large plastic flow initiates, τ0 is the initial value of strength gα, and γ is the Taylor cumulative shear strain on all slip/twin systems. q is a constant, which is set as one in this work.
(2)
D = D * + D p and Ω = Ω* + Ω p
(11)
where hαβ is the hardening modulus, which empirically accounts for the obstacles on system α associated with system β. The self hardening moduli hαα and the latent moduli hαβ can be written as [37]:
(1)
= D + Ω
hαβ γ˙ β , α = 1, 2, …, n
β =1
where F p denotes plastic shear of the material to an intermediate reference configuration in which lattice orientation and spacing are the same as in the original reference configuration, and where F * denotes stretching and rotation of the lattice. The velocity gradient L in the current state is:
L =
∑
g˙ α =
A crystalline material undergoes elastic stretching, rotation and plastic deformation. The total deformation gradient F is given by:
˙ −1 FF
(10)
For both slip and twinning, the strain hardening is characterized by the evolution of the strengths g α through an incremental relation [41]:
3.1. Constitutive equations
F = F *F p
= m*α (C: D * − D *σ + σD *) s *α
m 0α
After each incremental step, the accumulated twin volume fraction is compared with a threshold fraction V th defined as: (14)
V th = Ath1 + Ath2 ⋅V acc Ath1
Ath2
Ath1
where and are material constants with being the minimum volume fraction to reorient the grain, and Ath2 determining the 2
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
(CZ), respectively. Clearly, the grains in SZ are significantly refined compared to that in BM due to the severe plastic deformation caused by the stir pin. TMAZ contains a number of recrystallized grains and some coarse grains. This is because TMAZ suffered severe plastic deformation in addition to the frictional heat generated during FSW. A distinct interface is noticed between TMAZ and SZ in advancing side (AS), while such kind of interface is less clear in retreating side (RS). This may result in different fracture behaviors between AS and RS during tests. CZ is subjected to the shear not only from the rotating pin but also from the tool shoulder. This might result in a higher temperature. Hence, the grain size in CZ is slightly larger than that in SZ. Based on the geometries of different sub-regions in the FSW Mg joint displayed in Fig. 1a, two kinds of finite element models for bending tests were established, as shown in Fig. 2a and b. The deformation zones of bending are magnified in Fig. 2c. A 3-D C3D8R (ABAQUS) element type with eight nodes and one integration point was used, and the total number of elements was 14,476. Each element represents one grain. The indenter is taken as a rigid body meshed with R3D4 elements. The contact between the sample and the indenter was simply assumed to be frictionless. To represent the observed texture variations in FSW Mg plates, the joint was divided into 12 sub-regions. For simplicity, SZ and CZ were divided into 5 equal volume zones. The textures corresponding to the 12 sub-regions are shown as the insets in Fig. 2c, which were extracted from the EBSD result on a FSW Mg joint. It is seen that BM has a typical basal texture with the c-axis of most grains parallel to ND. Besides, strong basal texture is formed in SZ and it tends to tilt from TD to WD with the position moving from SZ-side to SZ-center. Previous studies demonstrated that, in the case of simple shear deformation of Mg alloys (e.g. extrusion [46] or equal channel angular extrusion (ECAE) [47]), < a > dislocations align the {0002} basal planes to the macroscopic shear plane. Park et al. [8] revealed that basal slip system preferentially operates during FSW of Mg alloys. The material in SZ is sheared by the rotation pin surface, causing {0002} basal planes to align with the pin column surface, i.e., the shear plane [4,8,48]. Thus, this {0001} < uvtw > β-fiber texture became predominant in SZ. In addition, Xin et al. [49] reported that SZ-side could be further divided into two micro-regions based on the orientation of c-axis. One was
Table 1 Hardening parameters used for CPFEM simulations. Mode
τ0 (MPa)
τs (MPa)
h0 (MPa)
Ath1
Ath2
Basal < a > Prismatic < a > Pyramidal < c+a > Extension twin
10 70 121 28
50 200 128 30
80 130 50 10
– – – 0.42
– – – 0.4
evolution of twin volume fraction during plastic deformation. For a detailed description, readers are referred to a previous paper [44]. If the accumulated twin fraction is greater than the threshold fraction V th , the lattice orientation at each integration point is allowed to reorient according to the following equation:
Qtw = 2N tw ⊗ N tw − I
(15)
where N tw is the twinning plane normal vector for the predominant twin system of the integration point. For Mg alloys, (0001) < 11–20 > basal slip, (1–100) < 11–20 > prismatic slip, (11-2-2) < 11–23 > pyramidal slip and (10–12) < -1011 > extension twinning are assumed as the potential modes that may be activated. Secondary twinning is not allowed in this work. The reference shear rate γ˙0 and rate sensitivity m are assumed to be the same for all slip/twinning systems, and are taken as γ˙0 = 0.001 s−1 and m = 0.05. The set of parameters listed in Table 1 was used for the simulation. The room temperature elastic constants of Mg single crystal are taken to be (GPa): C11 = 58.58, C12 = 25.02, C13 = 20.79, C33 = 61.11 and C44 = 16.58 [45]. 4. Results and discussion 4.1. Initial microstructure and finite element model Fig. 1a shows the cross-section of the FSW Mg joint. The white dashed lines mark the boundaries between different sub-regions. The OM images from various regions are shown in Fig. 1b–f. By a linear intercept method, the average grain size was measured to be about 28 μm, 7.8 μm, 22 μm and 10 μm in BM, SZ, TMAZ and crown zone
Fig. 1. (a) Macroscopic image of the cross-section of a FSW Mg joint; OM images of various regions in joint: (b) BM, (c) TMAZ/SZ interface in AS, (d) SZ-center, (e) TMAZ/SZ interface in RS and (f) CZ. 3
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
Fig. 2. Finite element models for bending tests on the joint: (a) Surface test, (b) Base test; (c) 12 sub-regions considered in the models and their corresponding (0001) pole figures.
not affect the understanding of the key problem of this paper, i.e. the strain and fracture localization in an FSW Mg weld.
adjacent to the TMAZ/SZ interface where the c-axis was almost parallel with TD. The other was slightly away from the TMAZ/SZ interface where the c-axis was tilted about 45° towards TD. The latter was defined as “EABS” since basal slip most likely activated when the joint was subjected to transverse tensile tests [49,50]. The texture distribution in RS of the WZ was almost symmetrical with that in AS [8,49]. The texture in TMAZ was also affected by the stir pin. It is shown that the < 0001 > direction in TMAZ of AS is tilted ~20° anticlockwise to ND, and is tilted ~30° clockwise to ND in TMAZ of RS. The < 0001 > direction in CZ slightly deviates from ND due to the compressive stress from the tool shoulder. Fig. 3 shows the applied bending load vs. IDt for Surface and Base tests. Both curves exhibit a concave down shape, which is considered as the feature of {10–12} twinning-induced hardening. The simulated curves are also shown in Fig. 3 for comparison. The twinning-induced hardening feature is noted in the simulated curves as well. Moreover, the experimental and simulated curves consistently reveal that Base test requires a higher bending load in the early stage. The simulated curves exhibit stronger strain hardening trends than the experimental ones. The major reason is possibly that the sub-regions where twinning are activated in the model have relatively larger sizes than that in the real weld (will be presented later). We believe that such difference should
4.2. Twinning and texture Indeed profuse {10–12} twinning was observed in several sub-regions of the bended samples, as shown as the insets in Fig. 3. Detailed experimental reports on the activation of twinning and texture evolution in sub-regions of an FSW Mg weld can be found in Ref. [21]. In the following, we focus on the simulated ones. Fig. 4 shows the distribution of twinned regions, which is in good agreement with the EBSD results reported before [21]. Note that a few {10–12} twins also appear in CZside of the Base test sample, whereas no twin is observed in other subregions of CZ. These twins may have great impacts on the fracture behavior during Base test as will be discussed later in section 4.5. The measured [21] and simulated textures in various regions of FSW joints after 5% bending strain on outer surface are compared in Fig. 5. Clearly, the simulated (0001) pole figures can capture the main features of the measured ones. For Surface test, the texture in SZ-center changes little from the initial state. A few extension twinning occurred in the region of easy to activate basal slip (EABS), while profuse twinning was activated in both SZ-side and CZ-center [21]. It is worth to mention that six {10–12} twin variants can be equally activated in SZ-side as the caxis of grains was subjected to a tension along LD [51]. However, the caxis of most twinned grains was rotated to ND. The reason for this phenomenon will be discussed in section 4.4. For Base test, the c-axis of many grains tilts toward TD in SZ-center due to the activation of extension twinning. Unexpectedly, the measured texture in EABS is similar to that in SZ-center. This may be related to that the selected EBSD scan area is closer to SZ-center than expected. Besides, a few extension twinning occurred in both SZ-side and CZcenter (will be discussed below). 4.3. Deformation mechanisms To understand the observed experimental phenomenon, the relative activities of deformation modes are calculated as a function of indenter displacement (IDt) in sub-regions of FSW plates during bending (Figs. 6 and 7). For Surface test (Fig. 6), BM-outer (outer indicates the outer side of bending) and SZ-center are dominated by prismatic < a > slip over the entire range of plastic strain. Note that the activity of basal slip in BM-outer is much higher than that in SZ-center, which is ascribed to the presence of a more diffuse basal texture in BM-outer than that in SZcenter (see Fig. 2c). Additionally, the activity of pyramidal < c+a > slip is pronounced in both regions. Basal slip dominates the whole deformation process in EABS, but extension twinning is also active. Extension twinning dominates the early stage of deformation in SZ-side
Fig. 3. The applied bending load vs. IDt for Surface and Base tests and the orientation maps confirming the activation of profuse twinning in several subregions (Red lines indicate {10–12} twin boundaries). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 4
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
Fig. 4. The distribution of twinning regions in the simulated bending models after 5% bending strain on outer surface: (a) Surface test, (b) Base test.
increased, respectively with the area moving from CZ-center to CZ-side. As twin activity drastically decreased, pyramidal < c+a > slip increased in the sub-regions of CZ. For Base test (Fig. 7), twinning contributes most to the plastic strain at the beginning in both SZ-center and BM-inner (inner represents the inner side of bending) due to the preferred initial grain orientation. However, the activity of twinning is higher in SZ-center than that in BM-inner because the former has a stronger initial texture (Fig. 2c). Basal slip dominates through the whole deformation in both EABS and SZ-side. The main deformation mode at the early stage and later stage of bending is basal slip and prismatic slip, respectively in the various outer regions presented in Fig. 7e–h. Basically, the activity of basal slip
and its activity is much higher than that in EABS. This is consistent with the recent experimental results that twin volume fraction in SZ-side (~53.6%) is much larger than that in EABS (~9.3%) [21]. The activity of extension twinning decreased in both sides with the applied IDt, while prismatic slip increased gradually. Then, prismatic slip together with basal slip becomes the main deformation modes. The relative activities of the slip and twinning modes simulated in TMAZ-outer (outer indicates the outer zone of bending) have similar features to that in EABS. However, the maximum activity of extension twinning in the former is slightly reduced compared to the latter. The activities of the simulated deformation modes are similar among the various sub-regions of CZ. Extension twinning and basal slip gradually decreased and
Fig. 5. Measured and simulated (0001) pole figures in various regions of FSW Mg joints after 5% bending strain on outer surface: (a) Surface test and (b) Base test. 5
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
Fig. 6. Relative activities of deformation modes as a function of IDt in sub-regions of the FSW joint during Surface test: (a) BM-outer, (b) SZ-center, (c) EABS, (d) SZside, (e) TMAZ-outer, (f) CZ-center, (g) CZ-adjacent and (h) CZ-side.
For Base test (Fig. 8b), the strains of εxx, εyy and εzz distribute uniformly across SZ. This is because the plastic strain in SZ-center and other sub-regions (EABS and SZ-side) are dominated by extension twinning and basal slip, respectively; both have very low CRSS. Strains in both sides of CZ are larger than that in CZ-center for the two kinds of bending samples. This is due probably to that basal slip becomes more and more active with the area moving from CZ-center to CZ-side (Figs. 6 and 7). Besides, a contraction strain parallel to the z-axis is observed through CZ, which explains the activation of twinning in CZ-center, as shown in Fig. 5b. Strain localization causes an obvious “concave-convex” appearance on the ND-TD plane of FSW samples after bending, as shown in Fig. 9a and b. To quantitatively analyze the “concave-convex” appearance, the surface depth in the regions of the white dashed boxes was measured. Note that the positive and negative values represent the “convex” and “concave” appearances relative to BM, respectively. Concave appearance (~-40 μm) was observed after Surface test (Fig. 9a) on the two sides of SZ, while convex apperance (~60 μm) was in SZ-center. The depth difference between the two regions is about 100 μm. Differently to SZ, no obvious strain localization is seen in CZ. The whole region in SZ is convex after Base test (Fig. 9b) compared with that in BM. The convex feature is most obvious (~120 μm) on the
in CZ-side and CZ-adjacent is higher compared to that in TMAZ-outer and CZ-middle. Moreover, twinning is slightly more active in CZ-side (Fig. 7h) than that in CZ-adjacent (Fig. 7g). These make CZ-side become the preferred area for necking and fracture.
4.4. Strain localization The drastic texture change in the various regions of WZ caused different macroscopic strain [14]. CPFEM can identify the spatial distribution of specific strain components. As shown in Fig. 8, the black dotted lines mark the boundaries between different sub-regions. It is seen that severe and complex strain localization occurs after both Surface and Base tests on FSW samples. For Surface test, localized strains are found in EABS and SZ-side, which are attributed to the high activity of basal slip and extension twinning, respectively. The texture in SZ-center is favorable for prismatic slip and pyramidal slip. However, their critical resolved shear stress (CRSS) values are relatively high. Therefore, the strain in SZcenter is very small. It is worth to mention that εyy (~0.04) is significantly larger than εzz (~0.02) in SZ-side (absolute value). This can explain why the twinned grains in SZ-side have the c-axis//ND texture (Fig. 5a).
Fig. 7. Relative activities of deformation modes as a function of IDt in sub-regions of the FSW joint during Base test: (a) BM-inner, (b) SZ-center, (c) EABS, (d) SZ-side, (e) TMAZ-outer, (f) CZ-center, (g) CZ-adjacent, (h) CZ-side. 6
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
Fig. 8. Distribution of strain components after 5% bending strain on outer surface for (a) Surface test and (b) Base test.
two sides of SZ, while it is relatively small in SZ-center (~80 μm). Unlike SZ, the two sides of CZ are obviously concave (~-60 μm), while little change was induced in CZ-center. Fig. 9c and d shows the simulation results of surface displacement along WD (the z axis) for the two bending tests. For Surface test (Fig. 9c), the outer regions of bended samples all move along the negative direction of the z-axis, while such movement is very small in SZcenter. Thus SZ-center appears obviously convex compared with other sub-regions. Moreover, the simulated height difference between SZcenter and SZ-side (or EABS) is about 80 μm. This is similar with the experimentally abserved value (~100 μm). The displacement along Path 1 in Fig. 9c was further examined, and a “w” -shaped profile is seen. Additionally, it is found that a small region in CZ-center moves in the positive x direction (not in the range of experimental measurement), exhibiting a convex feature relative to the other regions of CZ. Althougth the plastic strain in both SZ-center and BM-outer are dominated by prismatic slip (Fig. 6a and b) during Surface bending, the spatial distributions of the strains caused by prismatic slip is different in
the two regions (Fig. 8a). The activation of prismatic slip in BM-outer generates a contraction in WD due to the initial favarable orientation (i.e., c-axis//ND). Moreover, the activity of basal slip is higher in BMouter compared with that in SZ-center, which also generates a contraction in WD. The c-axis in SZ-center is nearly parallel to WD. The strain along WD can only be accommodated by pyramidal slip or contraction twin that have much higher CRSS compared to prismatic slip and extension twinning. This caused a very samll strain in WD. Both basal slip and primatic slip activated in EABS and SZ-side can accommodate the contraction in WD very well. Furthermore, the twinned grains in SZ-side mainly exhibit the c-axis//ND texture, implying that extension twinning mainly accommodates the strain on the ND-TD plane. For Base test, the whole region of SZ moves in the positive direction of the z-axis (Fig. 9d). By contrast, the materials in BM-inner move slightly to the negative z-axis direction. Thus, the surface in SZ appears convex compared to that in BM-inner. This agrees well with the experimental results (Fig. 9b). The displacement along Path 2 in Fig. 9d
Fig. 9. “Concave and convex” appearances on the ND-TD plane of the FSW samples with 5% bending strain on outer surface, experimental results: (a) Surface test and (b) Base test; simulation results: (c) Surface test and (d) Base test. 7
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
with an experimental study [49]. Besides, the strain in EABS is also very large due to the high activity of basal slip. Hence crack may propagate to EABS in a later stage. Considering the fact that the width of EABS is only ~100 μm in a typical FSW Mg joint [49], it seems that fracture occurs in SZ-center (dashed oval). The maximum strain appears in CZ-side (black arrow) of AS for Base test (Fig. 10b), implying that crack likely initiates over there. Moreover, crack would spread on a plane parallel to the TMAZ/CZ interface, exhibiting a sharp corner on the ND-TD section. This is in good agreement with the observed fracture morphology shown in Fig. 10b. Interestingly, the maximum strain does not locate at the TMAZ/CZ interface but in CZ-side, with a small distance away from the TMAZ/CZ interface. The experimental measurement shows that the distance is ~1.8 mm [22]. Note that the maximum strain in CZ of Surface test also occurs in CZside, with a small distance away from the TMAZ/CZ interface. As seen from Fig. 7, the activities of basal slip and extension twinning are higher in CZ-side compared to that in other sub-regions. Thus, fracture likely initiates in CZ-side due to the large plastic deformation attributed to basal slip and extension twinning. The above analyses confirm that strongly localized texture in each sub-region of WZ is responsible for the deformation incompatibility, which largely deteriorates the joint performance. Since the activity of basal slip and extension twinning is highly dependent on grain orientation, tailoring the texture of Mg joints could be an effective way to reduce this deformation incompatibility [50]. Xin et al. [52] observed that profuse extension twinning was activated in SZ-side during postweld rolling of a FSW AZ31 alloy. The twinned grains have a texture with c-axis nearly parallel to ND. The strain incompatibility of the rolled specimens was significantly reduced during transverse tensile tests. Moreover, fracture position was moved from the TMAZ/SZ interface to BM. Other post-weld deformation techniques such as postweld tension along TD [53], post-weld compression along ND or WD [54] and additional pass of friction stir process (FSP) [55] can also effectively randomize the strongly localized texture of Mg joints and hence reduce the strain incompatibility. Welding parameters also have influences on texture distribution in Mg joints [13,15,56]. Shang et al. [15] found that the non-uniform deformation of Mg joints could be suppressed by modifying the texture through increasing the tool rotation rate. Chen et al. [12] joined an AZ31B Mg alloy by a double-sided FSW technique. They found that the texture in SZ was randomized compared to that produced by the conventional one-sided FSW technique. Correspondingly, the ductility of the joint produced by the double-sided technique is improved. As a summary, both the simulation and previous experimental work indicate that the deformation incompatibility can be alleviated by controlling the texture distribution in a FSW Mg joint.
was further examined. It reveals that the height difference between SZcenter and EABS is smaller than the experimental results (~40 μm). This may be attributed to that the volume of each sub-region used in the model does not exactly agree with the real one. In addition, the whole region of CZ moves toward the negative z-axis direction. However, the displacement in CZ-side is larger than that in CZ-center, exhibiting an obvious concave appearance. This is consistent with the experimental result shown in Fig. 9b. Althouth extension twinning is dominant in both BM-inner and SZcenter (Fig. 7a and b), its contribution to strain is different in these regions. The strain caused by twinning is mainly on the ND-TD plane in BM-inner (Fig. 8b), which is responsible little for the strain generated in WD. By contrast, twinning can accommodate the tensile strain along WD in SZ-center very well. The plastic strains caused by twinning is related to the texture and variant selection. This is a complicated topic and will not be discussed further here. The plastic strains in SZ-side and EABS are dominated by basal slip. Considering the initial grain orientations, basal slip primarily accommodates the tensile strain in WD. As a result, the surface in SZ exhibits a convex feature compared to that in BM-inner. In general, the texture characteristics together with the different deformation modes in each sub-region of FSW Mg joints are responsible for the severe strain heterogeneity in WD, which results in the “concave-convex” appearance observed on the longitudinal section. 4.5. Fracture behavior The fracture behavior of FSW Mg alloys is a hot topic under investigation. Unlike simple uniaxial deformation, the fracture mechanisms during bending are more complicated. Fig. 10 shows the simulation results for maximum-principal-strain distribution after IDt of 10 mm and the observed fracture morphologies for two kinds of bending tests [22]. It is seen that the maximum strain locates on the outer surface in AS for both bending tests, but the corresponding positions are largely different. The simulation results show that the maximum strain occurs in the transition region between BM-outer and SZ (i.e., TMAZ-outer) for Surface test. As seen from Fig. 6, there are large differences in the activity of deformation modes among BM-outer, TMAZ-outer and SZ-side due to the large differences in texture among them. Moreover, the activity of basal slip is much higher in TMAZ-outer than that in BM-outer and SZ-side. The activation of different deformation modes in such a narrow area may cause plastic deformation incompatibility and initiate fracture in the position with maximum strain, i.e., TMAZ-outer. This is consistent with the observed fracture location indicated by the white arrow in Fig. 10a. The above analyses indicate that the texture in TMAZ determines the fracture morphology for Surface test. This implies that the joint strength of Mg alloys can be further improved by optimizing the texture in TMAZ, being consistent
Fig. 10. Simulation results for the distribution of maximum-principal-strain after IDt of 10 mm and the observed fracture morphologies [22]: (a) Surface test, (b) Base test. 8
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
5. Conclusions
[7] A.H. Feng, Z.Y. Ma, Acta Mater. 57 (2009) 4248–4260. [8] S.H.C. Park, Y.S. Sato, H. Kokawa, Metall. Mater. Trans. A 34 (2003) 987–994. [9] S.H. Chowdhury, D.L. Chen, S.D. Bhole, X. Cao, P. Wanjara, Metall. Mater. Trans. A 44 (2012) 323–336. [10] R. Xin, B. Li, A. Liao, Z. Zhou, Q. Liu, Metall. Mater. Trans. A 43 (2012) 2500–2508. [11] J. Yang, D. Wang, B.L. Xiao, D.R. Ni, Z.Y. Ma, Metall. Mater. Trans. A 44 (2013) 517–530. [12] J. Chen, H. Fujii, Y. Sun, Y. Morisada, R. Ueji, Mater. Sci. Eng. A 580 (2013) 83–91. [13] R. Xin, D. Liu, X. Shu, B. Li, X. Yang, Q. Liu, J. Alloy. Comp. 670 (2016) 64–71. [14] D. Liu, R. Xin, Y. Xiao, Z. Zhou, Q. Liu, Mater. Sci. Eng. A 609 (2014) 88–91. [15] Q. Shang, D.R. Ni, P. Xue, B.L. Xiao, Z.Y. Ma, Mater. Sci. Eng. A 707 (2017) 426–434. [16] N. Afrin, D.L. Chen, X. Cao, M. Jahazi, Mater. Sci. Eng. A 472 (2008) 179–186. [17] S. Lim, S. Kim, C.G. Lee, S.J. Kim, C.D. Yim, Metall. Mater. Trans. A 36 (2005) 1609–1612. [18] W. Woo, H. Choo, D.W. Brown, P.K. Liaw, Z. Feng, Scripta Mater. 54 (2006) 1859–1864. [19] S.H.C. Park, Y.S. Sato, H. Kokawa, Scripta Mater. 49 (2003) 161–166. [20] R. Xin, B. Li, Q. Liu, Mater. Sci. Forum 654 (2010) 1195–1200. [21] D. Liu, R. Xin, Z. Li, Z. Liu, X. Zheng, Q. Liu, Mater. Sci. Eng. A 646 (2015) 145–153. [22] D. Liu, R. Xin, L. Zhao, Y. Hu, J. Alloy. Comp. 693 (2017) 808–815. [23] J. Singh, M.S. Kim, S.H. Choi, Int. J. Plast. 117 (2019) 33–57. [24] W. Huang, Q. Huo, Z. Fang, Z. Xiao, Y. Yin, Z. Tan, X. Yang, Mater. Sci. Eng. A 710 (2018) 289–299. [25] C.S. Hyun, M.S. Kim, S.H. Choi, K.S. Shin, Acta Mater. 156 (2018) 342–355. [26] H. Ovri, D. Steglich, H. Dieringa, E.T. Lilleodden, Mater. Sci. Eng. A 740–741 (2019) 226–234. [27] W. He, L. Zheng, R. Xin, Q. Liu, Mater. Sci. Eng. A 687 (2017) 63–72. [28] X. He, F. Gu, A. Ball, Prog. Mater. Sci. 65 (2014) 1–66. [29] M.S. Kim, J.Y. Jung, Y.M. Song, S.H. Choi, Int. J. Plast. 94 (2017) 24–43. [30] B. Sadeghian, A. Taherizadeh, M. Atapour, J. Mater. Process. Technol. 259 (2018) 96–108. [31] ABAQUS User's Manual, Version 6.5, Hibbit, Karlsson and Sorenson, Inc., 2004. [32] Y. Huang, A User-Material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program, Cambridge, Massachusetts, (1991). [33] R. Hill, J. Mech. Phys. Solids 14 (1966) 95–102. [34] J.R. Rice, J. Mech. Phys. Solids 19 (1971) 433–455. [35] R.J. Asaro, J. Mech. 50 (1983) 921–934. [36] R.J. Asaro, J.R. Rice, J. Mech. Phys. Solids 25 (1977) 309–338. [37] D. Peirce, R.J. Asaro, A. Needleman, Acta Mater. 30 (1982) 1087–1119. [38] D. Peirce, R.J. Asaro, A. Needleman, Acta Mater. 31 (1983) 1951–1976. [39] R.J. Asaro, A. Needleman, Acta Mater. 33 (1985) 923–953. [40] J.W. Hutchinson, P Roy Soc. Lond. A. Mat. 348 (1976) 101–127. [41] S.R. Kalidindi, C.A. Bronkhorst, L. Anand, J. Mech. Phys. Solids 40 (1992) 537–569. [42] P.V. Houtte, Acta Mater. 26 (1978) 591–604. [43] C.N. Tomé, R.A. Lebensohn, U.F. Kocks, Acta Mater. 39 (1991) 2667–2680. [44] S.H. Choi, D.H. Kim, H.W. Lee, E.J. Shin, Mater. Sci. Eng. A 527 (2010) 1151–1159. [45] R.F.S. Hearmon, Rev. Mod. Phys. 18 (1946) 409–440. [46] Y.N. Wang, J.C. Huang, Acta Mater. 55 (2007) 897–905. [47] S. Li, Acta Mater. 56 (2008) 1031–1043. [48] Z. Yu, H. Choo, Z. Feng, S.C. Vogel, Scripta Mater. 63 (2010) 1112–1115. [49] R. Xin, D. Liu, B. Li, L. Sun, Z. Zhou, Q. Liu, Mater. Sci. Eng. A 565 (2013) 333–341. [50] W. Ren, J. Li, R. Xin, Scripta Mater. 170 (2019) 6–10. [51] S.G. Hong, S.H. Park, C.S. Lee, Acta Mater. 58 (2010) 5873–5885. [52] R. Xin, D. Liu, Z. Xu, B. Li, Q. Liu, Mater. Sci. Eng. A 582 (2013) 178–187. [53] R. Xin, L. Sun, D. Liu, Z. Zhou, Q. Liu, Mater. Sci. Eng. A 602 (2014) 1–10. [54] Z. Liu, R. Xin, D. Li, L. Sun, Q. Liu, Sci. Rep. 6 (2016) 39779. [55] Q. Shang, D.R. Ni, P. Xue, B.L. Xiao, K.S. Wang, Z.Y. Ma, J. Mater. Process. Technol. 264 (2019) 336–345. [56] N. Xu, Q. Song, H. Fujii, Y. Bao, J. Shen, Mater. Lett. 219 (2018) 93–96.
A CPFEM model was developed to simulate the bending behaviors of an FSW Mg joint. The joint was divided into 12 sub-regions representing the complicated texture distributions as observed experimentally. Two kinds of three-point bending tests were simulated. Several conclusions can be made based on the simulated results as follows: (1) The observed twinning behavior, texture evolution, “concaveconvex” appearance and crack nucleation sites in FSW Mg alloys during bending can be successfully predicted by CPFEM. (2) The strong localized texture in conjunction with the different deformation modes in each sub-region of the joint causes severe strain heterogeneity in WD, which results in the “concave-convex” appearance observed on the longitudinal section. (3) Fracture initiates in TMAZ-outer during Surface test due to the highly localized activation of basal slip, and crack likely propagates into EABS in a later stage. Moreover, the fracture morphology can be changed by adjusting the texture in TMAZ during Surface test. Crack initiates in CZ-side during Base test, with a small distance away from the TMAZ/CZ interface. (4) The huge differences in the activities of slip and twinning modes in each sub-region cause plastic deformation incompatibility, which initiates fracture in the area with maximum strain in the FSW Mg joint. Acknowledgements This project was financially supported by the National Natural Science Foundation of China (Project No. 51571045, 51871036 and 51421001) and the National Key Research and Development Program of China (2016YFB0301102). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.msea.2019.138103. References [1] [2] [3] [4]
J. Yang, B.L. Xiao, D. Wang, Z.Y. Ma, Mater. Sci. Eng. A 527 (2010) 708–714. L. Commin, M. Dumont, J.E. Masse, L. Barrallier, Acta Mater. 57 (2009) 326–334. J.D. Robson, N. Stanford, M.R. Barnett, Acta Mater. 59 (2011) 1945–1956. U.F.H.R. Suhuddin, S. Mironov, Y.S. Sato, H. Kokawa, C.W. Lee, Acta Mater. 57 (2009) 5406–5418. [5] H.N.B. Schmidt, T.L. Dickerson, J.H. Hattel, Acta Mater. 54 (2006) 1199–1209. [6] A. Steuwer, M. Dumont, J. Altenkirch, S. Birosca, A. Deschamps, P.B. Prangnell, P.J. Withers, Acta Mater. 59 (2011) 3002–3011.
9
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Modeling the strongly localized deformation behavior in a magnesium alloy with complicated texture distribution
T
Weijie Rena, Renlong Xina,*, Dejia Liub a b
Joint International Laboratory for Light Alloys (MOE), College of Materials Science and Engineering, Chongqing University, Chongqing, China College of Materials Science and Engineering, East China Jiaotong University, Nanchang, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Mg alloys CPFEM Friction stir welding Bending Strain heterogeneity
A crystal plasticity finite element model (CPFEM) was developed to simulate the bending behaviors of a friction stir welded (FSW) Mg joint. The joint was divided into 12 sub-regions in the model to represent the observed complicated texture distributions. Twinning was modeled as pseudo slip and the predominant twin reorientation scheme was used. Two kinds of three-point bending geometries were applied. The present study aims to understand the underlying mechanisms of the strain heterogeneity and fracture localization commonly occurred in FSW Mg joints during bending deformation. It reveals that the strongly localized texture in conjunction with the different activities of slip and twinning in each sub-region cause severe strain heterogeneity in welding direction (WD), which results in the “concave-convex” appearance as observed on the longitudinal section. Besides, fracture initiates from the outer edge of thermomechanical affected zone (TMAZ) during Surface test due to the highly localized activation of basal slip, and crack likely propagates into the region of easy to activate basal slip (EABS) in a later stage. Crack initiates in crown zone (CZ)-side during Base test with a small distance away from the TMAZ/CZ interface. The huge differences in the activities of slip and twinning modes in each sub-region cause deformation incompatibility in the FSW Mg joint and initiates fracture in the area with maximum strain.
1. Introduction
alloys. Bending is one of the most widely used operations in forming of Mg sheet. Recently, Liu et al. [21,22] carried out two kinds of bending tests on a FSW AZ31 Mg alloy. They investigated the relationship between textural variation, twinning activity and fracture path in bending tests by Schmid factor analysis. However, unlike simple uniaxial deformation, the stress state and deformation behaviors for three-point bending are more complicated [23]. Therefore, it is necessary to conduct an indepth study on the underlying deformation mechanisms (e.g. the activities of deformation modes and local strain state) of the sub-regions of FSW Mg joints during bending. As a type of time and cost saving tool, crystal plasticity finite element model (CPFEM) provides a new research approach [24–27]. However, CPFEM has seldom been applied on the deformation behavior of FSW Mg joints due probably to their complicated textures and twinning behaviors [28–30]. To fill this research gap, CPFEM was employed in this work to simulate the deformation and fracture behaviors in an FSW Mg joint. To represent the observed complicated texture distributions, the joint was divided into 12 sub-regions in the model. Two kinds of three-point bending tests were simulated. The present work aims to investigate the underlying mechanisms for the strain heterogeneity and fracture
As one of the lightest structural materials, Mg alloy has promising application potential in automotive and aerospace industries [1–3]. The wider use of Mg alloys need to overcome several problems, one of which is the joining problem. Friction stir welding (FSW) is an innovative solid state joining technique, which can avoid surface distortion and grain coarsening, and is especially suitable for the welding of light metals such as Al and Mg [4–7]. However, sharp and inhomogeneous texture is usually formed in Mg welds, which results in strain heterogeneity during subsequent deformation [8–12], and significantly deteriorates the strength as well as ductility [13–15]. Moreover, fracture usually occurred in stir zone (SZ)-side or the transition region between SZ and base material (BM) during transverse tensile tests [1,16,17]. Some researchers correlated the fracture position with the sub-region of joint having the c-axis oriented favorable for basal slip [18,19]. Some other researchers attributed fracture to the incompatible plastic deformation at thermomechanical affected zone (TMAZ)/SZ interface because of a sudden texture change over there [1,10,20]. Accordingly, it is meaningful to understand the mechanism of strain heterogeneity as well as its relationship with the fracture of FSW Mg
*
Corresponding author. Sha Zheng Jie 174, Sha Ping Ba District, Chongqing, China. E-mail address: [email protected] (R. Xin).
https://doi.org/10.1016/j.msea.2019.138103 Received 10 April 2019; Received in revised form 1 July 2019; Accepted 2 July 2019 Available online 03 July 2019 0921-5093/ © 2019 Elsevier B.V. All rights reserved.
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
s *α = F *⋅s0α and m *α = m 0α⋅F * − 1
behaviors observed in FSW Mg alloys during the two kinds of bending tests.
(5)
γ˙ α
The shear rate on each slip system is calculated using a ratedependent formulation proposed by Asaro and Needleman [39,40]:
2. Experimental procedures
τα gα
γ˙ α = γ˙0
A hot-rolled commercial AZ31 Mg alloy (Mg–3%Al–1%Zn) sheet with a thickness of 6 mm was joined by FSW. The detailed welding parameters were reported in a previous work [21].The welding direction (WD) was along the rolling direction of the rolled sheet. After welding, the cross-section vertical to the WD of the FSW joint was examined. Microstructure was characterized by optical microscopy (OM). The samples for OM were etched with a solution consisting of 2 ml distilled water, 2 ml glacial acetic acid, 14 ml ethanol and 0.84 g picric acid. Electron backscatter diffraction (EBSD) was used to analyze the local texture variation in various regions of the joint. The EBSD detector used was an HKL Channel 5 System equipped in a field emission gun scanning electron microscope (FEG-SEM, FEI Nova 400). Three-point bending tests were applied along two directions with respect to the FSW joint and are designated as Surface test and Base test, respectively, as shown in Fig. 2. Strips with dimensions of 84 (transverse direction, TD) × 10 (WD) × 4.5 (normal direction, ND) mm3 were cut from the FSW plates for bending tests. The bending tests were performed on an AG-X50kN machine at a displacement rate of 2.0 mm/min. The span distance was set as 50 mm.
1/ m
sign(τ α )
(6)
Due to the polar nature, the shear rate due to twinning is described by
⎧ γ˙ α =
τα gα
γ˙0
1/ m
τα > 0
⎨ α ⎩0 τ ≤ 0
(7)
where γ˙0 is the reference shear rate and m is the strain rate sensitivity index. τ α and g α are the resolved shear stress on slip/twin system α and the strength of this system, respectively. The relative activity n (γ˙ α / ∑β = 1 γ˙ β ) of each system α is also used for analysis. The elastic constitutive equation for a crystal is: ∇*
σ
+ σ tr(D *) = C: D *
(8)
where C is the tensor of elastic moduli, tr(D *) denotes the trace of ∇* tensor D*, σ is the Jaumann rate of the Cauchy stress σ based on the lattice spin tensor Ω* and can be written as: ∇*
(9)
σ = σ˙ − Ω*σ + σ Ω*
3. Crystal plastic finite element method
The rate of resolved shear stress is specified by: A code describing the constitutive formulation of Mg crystals was developed and implemented in the commercial finite element code ABAQUS/Standard as a user material (UMAT) subroutine [31]. This code is based on the code initially developed by Huang [32] to capture slip based deformation in FCC polycrystals. For a detailed description, readers are referred to previous papers [33–39]. The framework of Huang's code was described in detail in Ref. [32]. In the following, we will briefly summarize the constitutive formulation of the modified code used here.
τ˙ α
n
hαα = h 0 sec h2
n
n
ntw
a=1
V acc =
(4)
= n sl + ntw
s0α
∑ γ t /γ0
(13)
t =1
is the shear rate on slip system α. Unit vectors and are where the slip direction and normal to slip plane in the reference configuration, respectively. n sl and ntw are the total number of available slip and twin systems, respectively. It is convenient to define s *α , lying along the slip direction of the system α and m *α , normal to the slip plane in the deformed configuration by
γ˙ α
γ˙ (α ) dt and hαβ = qhαα (α ≠ β )
α=1
Twinning is essentially modeled as pseudo slip. The model for reorientation is based on the ideas of Van Houtte [42] and the predominant twin reorientation Scheme (PTR) [43]. We keep track of the shear strain γ t contributed by each twinning system t, and of the associated volume fraction γ t / γ0 ( γ0 = 0.129 is the characteristic twin shear) within each element. By summation of all twin systems in each element, the accumulated twin volume fraction V acc can be calculated as:
with
γ˙ αs0α ⊗ m 0α
t
3.2. Incorporation of twinning
(3)
∑
n
∑ ∫0
(12)
where the symmetric stretching rate D and the antisymmetric spin tensor Ω can be decomposed into elastic (superscript *) and plastic (superscript p) parts as follows:
D * + Ω* = F˙ *F *−1 and D p + Ω p =
h0 γ , γ= τs − τ0
where h0 is the initial hardening modulus, τs is the break-through stress where large plastic flow initiates, τ0 is the initial value of strength gα, and γ is the Taylor cumulative shear strain on all slip/twin systems. q is a constant, which is set as one in this work.
(2)
D = D * + D p and Ω = Ω* + Ω p
(11)
where hαβ is the hardening modulus, which empirically accounts for the obstacles on system α associated with system β. The self hardening moduli hαα and the latent moduli hαβ can be written as [37]:
(1)
= D + Ω
hαβ γ˙ β , α = 1, 2, …, n
β =1
where F p denotes plastic shear of the material to an intermediate reference configuration in which lattice orientation and spacing are the same as in the original reference configuration, and where F * denotes stretching and rotation of the lattice. The velocity gradient L in the current state is:
L =
∑
g˙ α =
A crystalline material undergoes elastic stretching, rotation and plastic deformation. The total deformation gradient F is given by:
˙ −1 FF
(10)
For both slip and twinning, the strain hardening is characterized by the evolution of the strengths g α through an incremental relation [41]:
3.1. Constitutive equations
F = F *F p
= m*α (C: D * − D *σ + σD *) s *α
m 0α
After each incremental step, the accumulated twin volume fraction is compared with a threshold fraction V th defined as: (14)
V th = Ath1 + Ath2 ⋅V acc Ath1
Ath2
Ath1
where and are material constants with being the minimum volume fraction to reorient the grain, and Ath2 determining the 2
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
(CZ), respectively. Clearly, the grains in SZ are significantly refined compared to that in BM due to the severe plastic deformation caused by the stir pin. TMAZ contains a number of recrystallized grains and some coarse grains. This is because TMAZ suffered severe plastic deformation in addition to the frictional heat generated during FSW. A distinct interface is noticed between TMAZ and SZ in advancing side (AS), while such kind of interface is less clear in retreating side (RS). This may result in different fracture behaviors between AS and RS during tests. CZ is subjected to the shear not only from the rotating pin but also from the tool shoulder. This might result in a higher temperature. Hence, the grain size in CZ is slightly larger than that in SZ. Based on the geometries of different sub-regions in the FSW Mg joint displayed in Fig. 1a, two kinds of finite element models for bending tests were established, as shown in Fig. 2a and b. The deformation zones of bending are magnified in Fig. 2c. A 3-D C3D8R (ABAQUS) element type with eight nodes and one integration point was used, and the total number of elements was 14,476. Each element represents one grain. The indenter is taken as a rigid body meshed with R3D4 elements. The contact between the sample and the indenter was simply assumed to be frictionless. To represent the observed texture variations in FSW Mg plates, the joint was divided into 12 sub-regions. For simplicity, SZ and CZ were divided into 5 equal volume zones. The textures corresponding to the 12 sub-regions are shown as the insets in Fig. 2c, which were extracted from the EBSD result on a FSW Mg joint. It is seen that BM has a typical basal texture with the c-axis of most grains parallel to ND. Besides, strong basal texture is formed in SZ and it tends to tilt from TD to WD with the position moving from SZ-side to SZ-center. Previous studies demonstrated that, in the case of simple shear deformation of Mg alloys (e.g. extrusion [46] or equal channel angular extrusion (ECAE) [47]), < a > dislocations align the {0002} basal planes to the macroscopic shear plane. Park et al. [8] revealed that basal slip system preferentially operates during FSW of Mg alloys. The material in SZ is sheared by the rotation pin surface, causing {0002} basal planes to align with the pin column surface, i.e., the shear plane [4,8,48]. Thus, this {0001} < uvtw > β-fiber texture became predominant in SZ. In addition, Xin et al. [49] reported that SZ-side could be further divided into two micro-regions based on the orientation of c-axis. One was
Table 1 Hardening parameters used for CPFEM simulations. Mode
τ0 (MPa)
τs (MPa)
h0 (MPa)
Ath1
Ath2
Basal < a > Prismatic < a > Pyramidal < c+a > Extension twin
10 70 121 28
50 200 128 30
80 130 50 10
– – – 0.42
– – – 0.4
evolution of twin volume fraction during plastic deformation. For a detailed description, readers are referred to a previous paper [44]. If the accumulated twin fraction is greater than the threshold fraction V th , the lattice orientation at each integration point is allowed to reorient according to the following equation:
Qtw = 2N tw ⊗ N tw − I
(15)
where N tw is the twinning plane normal vector for the predominant twin system of the integration point. For Mg alloys, (0001) < 11–20 > basal slip, (1–100) < 11–20 > prismatic slip, (11-2-2) < 11–23 > pyramidal slip and (10–12) < -1011 > extension twinning are assumed as the potential modes that may be activated. Secondary twinning is not allowed in this work. The reference shear rate γ˙0 and rate sensitivity m are assumed to be the same for all slip/twinning systems, and are taken as γ˙0 = 0.001 s−1 and m = 0.05. The set of parameters listed in Table 1 was used for the simulation. The room temperature elastic constants of Mg single crystal are taken to be (GPa): C11 = 58.58, C12 = 25.02, C13 = 20.79, C33 = 61.11 and C44 = 16.58 [45]. 4. Results and discussion 4.1. Initial microstructure and finite element model Fig. 1a shows the cross-section of the FSW Mg joint. The white dashed lines mark the boundaries between different sub-regions. The OM images from various regions are shown in Fig. 1b–f. By a linear intercept method, the average grain size was measured to be about 28 μm, 7.8 μm, 22 μm and 10 μm in BM, SZ, TMAZ and crown zone
Fig. 1. (a) Macroscopic image of the cross-section of a FSW Mg joint; OM images of various regions in joint: (b) BM, (c) TMAZ/SZ interface in AS, (d) SZ-center, (e) TMAZ/SZ interface in RS and (f) CZ. 3
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
Fig. 2. Finite element models for bending tests on the joint: (a) Surface test, (b) Base test; (c) 12 sub-regions considered in the models and their corresponding (0001) pole figures.
not affect the understanding of the key problem of this paper, i.e. the strain and fracture localization in an FSW Mg weld.
adjacent to the TMAZ/SZ interface where the c-axis was almost parallel with TD. The other was slightly away from the TMAZ/SZ interface where the c-axis was tilted about 45° towards TD. The latter was defined as “EABS” since basal slip most likely activated when the joint was subjected to transverse tensile tests [49,50]. The texture distribution in RS of the WZ was almost symmetrical with that in AS [8,49]. The texture in TMAZ was also affected by the stir pin. It is shown that the < 0001 > direction in TMAZ of AS is tilted ~20° anticlockwise to ND, and is tilted ~30° clockwise to ND in TMAZ of RS. The < 0001 > direction in CZ slightly deviates from ND due to the compressive stress from the tool shoulder. Fig. 3 shows the applied bending load vs. IDt for Surface and Base tests. Both curves exhibit a concave down shape, which is considered as the feature of {10–12} twinning-induced hardening. The simulated curves are also shown in Fig. 3 for comparison. The twinning-induced hardening feature is noted in the simulated curves as well. Moreover, the experimental and simulated curves consistently reveal that Base test requires a higher bending load in the early stage. The simulated curves exhibit stronger strain hardening trends than the experimental ones. The major reason is possibly that the sub-regions where twinning are activated in the model have relatively larger sizes than that in the real weld (will be presented later). We believe that such difference should
4.2. Twinning and texture Indeed profuse {10–12} twinning was observed in several sub-regions of the bended samples, as shown as the insets in Fig. 3. Detailed experimental reports on the activation of twinning and texture evolution in sub-regions of an FSW Mg weld can be found in Ref. [21]. In the following, we focus on the simulated ones. Fig. 4 shows the distribution of twinned regions, which is in good agreement with the EBSD results reported before [21]. Note that a few {10–12} twins also appear in CZside of the Base test sample, whereas no twin is observed in other subregions of CZ. These twins may have great impacts on the fracture behavior during Base test as will be discussed later in section 4.5. The measured [21] and simulated textures in various regions of FSW joints after 5% bending strain on outer surface are compared in Fig. 5. Clearly, the simulated (0001) pole figures can capture the main features of the measured ones. For Surface test, the texture in SZ-center changes little from the initial state. A few extension twinning occurred in the region of easy to activate basal slip (EABS), while profuse twinning was activated in both SZ-side and CZ-center [21]. It is worth to mention that six {10–12} twin variants can be equally activated in SZ-side as the caxis of grains was subjected to a tension along LD [51]. However, the caxis of most twinned grains was rotated to ND. The reason for this phenomenon will be discussed in section 4.4. For Base test, the c-axis of many grains tilts toward TD in SZ-center due to the activation of extension twinning. Unexpectedly, the measured texture in EABS is similar to that in SZ-center. This may be related to that the selected EBSD scan area is closer to SZ-center than expected. Besides, a few extension twinning occurred in both SZ-side and CZcenter (will be discussed below). 4.3. Deformation mechanisms To understand the observed experimental phenomenon, the relative activities of deformation modes are calculated as a function of indenter displacement (IDt) in sub-regions of FSW plates during bending (Figs. 6 and 7). For Surface test (Fig. 6), BM-outer (outer indicates the outer side of bending) and SZ-center are dominated by prismatic < a > slip over the entire range of plastic strain. Note that the activity of basal slip in BM-outer is much higher than that in SZ-center, which is ascribed to the presence of a more diffuse basal texture in BM-outer than that in SZcenter (see Fig. 2c). Additionally, the activity of pyramidal < c+a > slip is pronounced in both regions. Basal slip dominates the whole deformation process in EABS, but extension twinning is also active. Extension twinning dominates the early stage of deformation in SZ-side
Fig. 3. The applied bending load vs. IDt for Surface and Base tests and the orientation maps confirming the activation of profuse twinning in several subregions (Red lines indicate {10–12} twin boundaries). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 4
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
Fig. 4. The distribution of twinning regions in the simulated bending models after 5% bending strain on outer surface: (a) Surface test, (b) Base test.
increased, respectively with the area moving from CZ-center to CZ-side. As twin activity drastically decreased, pyramidal < c+a > slip increased in the sub-regions of CZ. For Base test (Fig. 7), twinning contributes most to the plastic strain at the beginning in both SZ-center and BM-inner (inner represents the inner side of bending) due to the preferred initial grain orientation. However, the activity of twinning is higher in SZ-center than that in BM-inner because the former has a stronger initial texture (Fig. 2c). Basal slip dominates through the whole deformation in both EABS and SZ-side. The main deformation mode at the early stage and later stage of bending is basal slip and prismatic slip, respectively in the various outer regions presented in Fig. 7e–h. Basically, the activity of basal slip
and its activity is much higher than that in EABS. This is consistent with the recent experimental results that twin volume fraction in SZ-side (~53.6%) is much larger than that in EABS (~9.3%) [21]. The activity of extension twinning decreased in both sides with the applied IDt, while prismatic slip increased gradually. Then, prismatic slip together with basal slip becomes the main deformation modes. The relative activities of the slip and twinning modes simulated in TMAZ-outer (outer indicates the outer zone of bending) have similar features to that in EABS. However, the maximum activity of extension twinning in the former is slightly reduced compared to the latter. The activities of the simulated deformation modes are similar among the various sub-regions of CZ. Extension twinning and basal slip gradually decreased and
Fig. 5. Measured and simulated (0001) pole figures in various regions of FSW Mg joints after 5% bending strain on outer surface: (a) Surface test and (b) Base test. 5
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
Fig. 6. Relative activities of deformation modes as a function of IDt in sub-regions of the FSW joint during Surface test: (a) BM-outer, (b) SZ-center, (c) EABS, (d) SZside, (e) TMAZ-outer, (f) CZ-center, (g) CZ-adjacent and (h) CZ-side.
For Base test (Fig. 8b), the strains of εxx, εyy and εzz distribute uniformly across SZ. This is because the plastic strain in SZ-center and other sub-regions (EABS and SZ-side) are dominated by extension twinning and basal slip, respectively; both have very low CRSS. Strains in both sides of CZ are larger than that in CZ-center for the two kinds of bending samples. This is due probably to that basal slip becomes more and more active with the area moving from CZ-center to CZ-side (Figs. 6 and 7). Besides, a contraction strain parallel to the z-axis is observed through CZ, which explains the activation of twinning in CZ-center, as shown in Fig. 5b. Strain localization causes an obvious “concave-convex” appearance on the ND-TD plane of FSW samples after bending, as shown in Fig. 9a and b. To quantitatively analyze the “concave-convex” appearance, the surface depth in the regions of the white dashed boxes was measured. Note that the positive and negative values represent the “convex” and “concave” appearances relative to BM, respectively. Concave appearance (~-40 μm) was observed after Surface test (Fig. 9a) on the two sides of SZ, while convex apperance (~60 μm) was in SZ-center. The depth difference between the two regions is about 100 μm. Differently to SZ, no obvious strain localization is seen in CZ. The whole region in SZ is convex after Base test (Fig. 9b) compared with that in BM. The convex feature is most obvious (~120 μm) on the
in CZ-side and CZ-adjacent is higher compared to that in TMAZ-outer and CZ-middle. Moreover, twinning is slightly more active in CZ-side (Fig. 7h) than that in CZ-adjacent (Fig. 7g). These make CZ-side become the preferred area for necking and fracture.
4.4. Strain localization The drastic texture change in the various regions of WZ caused different macroscopic strain [14]. CPFEM can identify the spatial distribution of specific strain components. As shown in Fig. 8, the black dotted lines mark the boundaries between different sub-regions. It is seen that severe and complex strain localization occurs after both Surface and Base tests on FSW samples. For Surface test, localized strains are found in EABS and SZ-side, which are attributed to the high activity of basal slip and extension twinning, respectively. The texture in SZ-center is favorable for prismatic slip and pyramidal slip. However, their critical resolved shear stress (CRSS) values are relatively high. Therefore, the strain in SZcenter is very small. It is worth to mention that εyy (~0.04) is significantly larger than εzz (~0.02) in SZ-side (absolute value). This can explain why the twinned grains in SZ-side have the c-axis//ND texture (Fig. 5a).
Fig. 7. Relative activities of deformation modes as a function of IDt in sub-regions of the FSW joint during Base test: (a) BM-inner, (b) SZ-center, (c) EABS, (d) SZ-side, (e) TMAZ-outer, (f) CZ-center, (g) CZ-adjacent, (h) CZ-side. 6
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
Fig. 8. Distribution of strain components after 5% bending strain on outer surface for (a) Surface test and (b) Base test.
two sides of SZ, while it is relatively small in SZ-center (~80 μm). Unlike SZ, the two sides of CZ are obviously concave (~-60 μm), while little change was induced in CZ-center. Fig. 9c and d shows the simulation results of surface displacement along WD (the z axis) for the two bending tests. For Surface test (Fig. 9c), the outer regions of bended samples all move along the negative direction of the z-axis, while such movement is very small in SZcenter. Thus SZ-center appears obviously convex compared with other sub-regions. Moreover, the simulated height difference between SZcenter and SZ-side (or EABS) is about 80 μm. This is similar with the experimentally abserved value (~100 μm). The displacement along Path 1 in Fig. 9c was further examined, and a “w” -shaped profile is seen. Additionally, it is found that a small region in CZ-center moves in the positive x direction (not in the range of experimental measurement), exhibiting a convex feature relative to the other regions of CZ. Althougth the plastic strain in both SZ-center and BM-outer are dominated by prismatic slip (Fig. 6a and b) during Surface bending, the spatial distributions of the strains caused by prismatic slip is different in
the two regions (Fig. 8a). The activation of prismatic slip in BM-outer generates a contraction in WD due to the initial favarable orientation (i.e., c-axis//ND). Moreover, the activity of basal slip is higher in BMouter compared with that in SZ-center, which also generates a contraction in WD. The c-axis in SZ-center is nearly parallel to WD. The strain along WD can only be accommodated by pyramidal slip or contraction twin that have much higher CRSS compared to prismatic slip and extension twinning. This caused a very samll strain in WD. Both basal slip and primatic slip activated in EABS and SZ-side can accommodate the contraction in WD very well. Furthermore, the twinned grains in SZ-side mainly exhibit the c-axis//ND texture, implying that extension twinning mainly accommodates the strain on the ND-TD plane. For Base test, the whole region of SZ moves in the positive direction of the z-axis (Fig. 9d). By contrast, the materials in BM-inner move slightly to the negative z-axis direction. Thus, the surface in SZ appears convex compared to that in BM-inner. This agrees well with the experimental results (Fig. 9b). The displacement along Path 2 in Fig. 9d
Fig. 9. “Concave and convex” appearances on the ND-TD plane of the FSW samples with 5% bending strain on outer surface, experimental results: (a) Surface test and (b) Base test; simulation results: (c) Surface test and (d) Base test. 7
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
with an experimental study [49]. Besides, the strain in EABS is also very large due to the high activity of basal slip. Hence crack may propagate to EABS in a later stage. Considering the fact that the width of EABS is only ~100 μm in a typical FSW Mg joint [49], it seems that fracture occurs in SZ-center (dashed oval). The maximum strain appears in CZ-side (black arrow) of AS for Base test (Fig. 10b), implying that crack likely initiates over there. Moreover, crack would spread on a plane parallel to the TMAZ/CZ interface, exhibiting a sharp corner on the ND-TD section. This is in good agreement with the observed fracture morphology shown in Fig. 10b. Interestingly, the maximum strain does not locate at the TMAZ/CZ interface but in CZ-side, with a small distance away from the TMAZ/CZ interface. The experimental measurement shows that the distance is ~1.8 mm [22]. Note that the maximum strain in CZ of Surface test also occurs in CZside, with a small distance away from the TMAZ/CZ interface. As seen from Fig. 7, the activities of basal slip and extension twinning are higher in CZ-side compared to that in other sub-regions. Thus, fracture likely initiates in CZ-side due to the large plastic deformation attributed to basal slip and extension twinning. The above analyses confirm that strongly localized texture in each sub-region of WZ is responsible for the deformation incompatibility, which largely deteriorates the joint performance. Since the activity of basal slip and extension twinning is highly dependent on grain orientation, tailoring the texture of Mg joints could be an effective way to reduce this deformation incompatibility [50]. Xin et al. [52] observed that profuse extension twinning was activated in SZ-side during postweld rolling of a FSW AZ31 alloy. The twinned grains have a texture with c-axis nearly parallel to ND. The strain incompatibility of the rolled specimens was significantly reduced during transverse tensile tests. Moreover, fracture position was moved from the TMAZ/SZ interface to BM. Other post-weld deformation techniques such as postweld tension along TD [53], post-weld compression along ND or WD [54] and additional pass of friction stir process (FSP) [55] can also effectively randomize the strongly localized texture of Mg joints and hence reduce the strain incompatibility. Welding parameters also have influences on texture distribution in Mg joints [13,15,56]. Shang et al. [15] found that the non-uniform deformation of Mg joints could be suppressed by modifying the texture through increasing the tool rotation rate. Chen et al. [12] joined an AZ31B Mg alloy by a double-sided FSW technique. They found that the texture in SZ was randomized compared to that produced by the conventional one-sided FSW technique. Correspondingly, the ductility of the joint produced by the double-sided technique is improved. As a summary, both the simulation and previous experimental work indicate that the deformation incompatibility can be alleviated by controlling the texture distribution in a FSW Mg joint.
was further examined. It reveals that the height difference between SZcenter and EABS is smaller than the experimental results (~40 μm). This may be attributed to that the volume of each sub-region used in the model does not exactly agree with the real one. In addition, the whole region of CZ moves toward the negative z-axis direction. However, the displacement in CZ-side is larger than that in CZ-center, exhibiting an obvious concave appearance. This is consistent with the experimental result shown in Fig. 9b. Althouth extension twinning is dominant in both BM-inner and SZcenter (Fig. 7a and b), its contribution to strain is different in these regions. The strain caused by twinning is mainly on the ND-TD plane in BM-inner (Fig. 8b), which is responsible little for the strain generated in WD. By contrast, twinning can accommodate the tensile strain along WD in SZ-center very well. The plastic strains caused by twinning is related to the texture and variant selection. This is a complicated topic and will not be discussed further here. The plastic strains in SZ-side and EABS are dominated by basal slip. Considering the initial grain orientations, basal slip primarily accommodates the tensile strain in WD. As a result, the surface in SZ exhibits a convex feature compared to that in BM-inner. In general, the texture characteristics together with the different deformation modes in each sub-region of FSW Mg joints are responsible for the severe strain heterogeneity in WD, which results in the “concave-convex” appearance observed on the longitudinal section. 4.5. Fracture behavior The fracture behavior of FSW Mg alloys is a hot topic under investigation. Unlike simple uniaxial deformation, the fracture mechanisms during bending are more complicated. Fig. 10 shows the simulation results for maximum-principal-strain distribution after IDt of 10 mm and the observed fracture morphologies for two kinds of bending tests [22]. It is seen that the maximum strain locates on the outer surface in AS for both bending tests, but the corresponding positions are largely different. The simulation results show that the maximum strain occurs in the transition region between BM-outer and SZ (i.e., TMAZ-outer) for Surface test. As seen from Fig. 6, there are large differences in the activity of deformation modes among BM-outer, TMAZ-outer and SZ-side due to the large differences in texture among them. Moreover, the activity of basal slip is much higher in TMAZ-outer than that in BM-outer and SZ-side. The activation of different deformation modes in such a narrow area may cause plastic deformation incompatibility and initiate fracture in the position with maximum strain, i.e., TMAZ-outer. This is consistent with the observed fracture location indicated by the white arrow in Fig. 10a. The above analyses indicate that the texture in TMAZ determines the fracture morphology for Surface test. This implies that the joint strength of Mg alloys can be further improved by optimizing the texture in TMAZ, being consistent
Fig. 10. Simulation results for the distribution of maximum-principal-strain after IDt of 10 mm and the observed fracture morphologies [22]: (a) Surface test, (b) Base test. 8
Materials Science & Engineering A 762 (2019) 138103
W. Ren, et al.
5. Conclusions
[7] A.H. Feng, Z.Y. Ma, Acta Mater. 57 (2009) 4248–4260. [8] S.H.C. Park, Y.S. Sato, H. Kokawa, Metall. Mater. Trans. A 34 (2003) 987–994. [9] S.H. Chowdhury, D.L. Chen, S.D. Bhole, X. Cao, P. Wanjara, Metall. Mater. Trans. A 44 (2012) 323–336. [10] R. Xin, B. Li, A. Liao, Z. Zhou, Q. Liu, Metall. Mater. Trans. A 43 (2012) 2500–2508. [11] J. Yang, D. Wang, B.L. Xiao, D.R. Ni, Z.Y. Ma, Metall. Mater. Trans. A 44 (2013) 517–530. [12] J. Chen, H. Fujii, Y. Sun, Y. Morisada, R. Ueji, Mater. Sci. Eng. A 580 (2013) 83–91. [13] R. Xin, D. Liu, X. Shu, B. Li, X. Yang, Q. Liu, J. Alloy. Comp. 670 (2016) 64–71. [14] D. Liu, R. Xin, Y. Xiao, Z. Zhou, Q. Liu, Mater. Sci. Eng. A 609 (2014) 88–91. [15] Q. Shang, D.R. Ni, P. Xue, B.L. Xiao, Z.Y. Ma, Mater. Sci. Eng. A 707 (2017) 426–434. [16] N. Afrin, D.L. Chen, X. Cao, M. Jahazi, Mater. Sci. Eng. A 472 (2008) 179–186. [17] S. Lim, S. Kim, C.G. Lee, S.J. Kim, C.D. Yim, Metall. Mater. Trans. A 36 (2005) 1609–1612. [18] W. Woo, H. Choo, D.W. Brown, P.K. Liaw, Z. Feng, Scripta Mater. 54 (2006) 1859–1864. [19] S.H.C. Park, Y.S. Sato, H. Kokawa, Scripta Mater. 49 (2003) 161–166. [20] R. Xin, B. Li, Q. Liu, Mater. Sci. Forum 654 (2010) 1195–1200. [21] D. Liu, R. Xin, Z. Li, Z. Liu, X. Zheng, Q. Liu, Mater. Sci. Eng. A 646 (2015) 145–153. [22] D. Liu, R. Xin, L. Zhao, Y. Hu, J. Alloy. Comp. 693 (2017) 808–815. [23] J. Singh, M.S. Kim, S.H. Choi, Int. J. Plast. 117 (2019) 33–57. [24] W. Huang, Q. Huo, Z. Fang, Z. Xiao, Y. Yin, Z. Tan, X. Yang, Mater. Sci. Eng. A 710 (2018) 289–299. [25] C.S. Hyun, M.S. Kim, S.H. Choi, K.S. Shin, Acta Mater. 156 (2018) 342–355. [26] H. Ovri, D. Steglich, H. Dieringa, E.T. Lilleodden, Mater. Sci. Eng. A 740–741 (2019) 226–234. [27] W. He, L. Zheng, R. Xin, Q. Liu, Mater. Sci. Eng. A 687 (2017) 63–72. [28] X. He, F. Gu, A. Ball, Prog. Mater. Sci. 65 (2014) 1–66. [29] M.S. Kim, J.Y. Jung, Y.M. Song, S.H. Choi, Int. J. Plast. 94 (2017) 24–43. [30] B. Sadeghian, A. Taherizadeh, M. Atapour, J. Mater. Process. Technol. 259 (2018) 96–108. [31] ABAQUS User's Manual, Version 6.5, Hibbit, Karlsson and Sorenson, Inc., 2004. [32] Y. Huang, A User-Material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program, Cambridge, Massachusetts, (1991). [33] R. Hill, J. Mech. Phys. Solids 14 (1966) 95–102. [34] J.R. Rice, J. Mech. Phys. Solids 19 (1971) 433–455. [35] R.J. Asaro, J. Mech. 50 (1983) 921–934. [36] R.J. Asaro, J.R. Rice, J. Mech. Phys. Solids 25 (1977) 309–338. [37] D. Peirce, R.J. Asaro, A. Needleman, Acta Mater. 30 (1982) 1087–1119. [38] D. Peirce, R.J. Asaro, A. Needleman, Acta Mater. 31 (1983) 1951–1976. [39] R.J. Asaro, A. Needleman, Acta Mater. 33 (1985) 923–953. [40] J.W. Hutchinson, P Roy Soc. Lond. A. Mat. 348 (1976) 101–127. [41] S.R. Kalidindi, C.A. Bronkhorst, L. Anand, J. Mech. Phys. Solids 40 (1992) 537–569. [42] P.V. Houtte, Acta Mater. 26 (1978) 591–604. [43] C.N. Tomé, R.A. Lebensohn, U.F. Kocks, Acta Mater. 39 (1991) 2667–2680. [44] S.H. Choi, D.H. Kim, H.W. Lee, E.J. Shin, Mater. Sci. Eng. A 527 (2010) 1151–1159. [45] R.F.S. Hearmon, Rev. Mod. Phys. 18 (1946) 409–440. [46] Y.N. Wang, J.C. Huang, Acta Mater. 55 (2007) 897–905. [47] S. Li, Acta Mater. 56 (2008) 1031–1043. [48] Z. Yu, H. Choo, Z. Feng, S.C. Vogel, Scripta Mater. 63 (2010) 1112–1115. [49] R. Xin, D. Liu, B. Li, L. Sun, Z. Zhou, Q. Liu, Mater. Sci. Eng. A 565 (2013) 333–341. [50] W. Ren, J. Li, R. Xin, Scripta Mater. 170 (2019) 6–10. [51] S.G. Hong, S.H. Park, C.S. Lee, Acta Mater. 58 (2010) 5873–5885. [52] R. Xin, D. Liu, Z. Xu, B. Li, Q. Liu, Mater. Sci. Eng. A 582 (2013) 178–187. [53] R. Xin, L. Sun, D. Liu, Z. Zhou, Q. Liu, Mater. Sci. Eng. A 602 (2014) 1–10. [54] Z. Liu, R. Xin, D. Li, L. Sun, Q. Liu, Sci. Rep. 6 (2016) 39779. [55] Q. Shang, D.R. Ni, P. Xue, B.L. Xiao, K.S. Wang, Z.Y. Ma, J. Mater. Process. Technol. 264 (2019) 336–345. [56] N. Xu, Q. Song, H. Fujii, Y. Bao, J. Shen, Mater. Lett. 219 (2018) 93–96.
A CPFEM model was developed to simulate the bending behaviors of an FSW Mg joint. The joint was divided into 12 sub-regions representing the complicated texture distributions as observed experimentally. Two kinds of three-point bending tests were simulated. Several conclusions can be made based on the simulated results as follows: (1) The observed twinning behavior, texture evolution, “concaveconvex” appearance and crack nucleation sites in FSW Mg alloys during bending can be successfully predicted by CPFEM. (2) The strong localized texture in conjunction with the different deformation modes in each sub-region of the joint causes severe strain heterogeneity in WD, which results in the “concave-convex” appearance observed on the longitudinal section. (3) Fracture initiates in TMAZ-outer during Surface test due to the highly localized activation of basal slip, and crack likely propagates into EABS in a later stage. Moreover, the fracture morphology can be changed by adjusting the texture in TMAZ during Surface test. Crack initiates in CZ-side during Base test, with a small distance away from the TMAZ/CZ interface. (4) The huge differences in the activities of slip and twinning modes in each sub-region cause plastic deformation incompatibility, which initiates fracture in the area with maximum strain in the FSW Mg joint. Acknowledgements This project was financially supported by the National Natural Science Foundation of China (Project No. 51571045, 51871036 and 51421001) and the National Key Research and Development Program of China (2016YFB0301102). Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.msea.2019.138103. References [1] [2] [3] [4]
J. Yang, B.L. Xiao, D. Wang, Z.Y. Ma, Mater. Sci. Eng. A 527 (2010) 708–714. L. Commin, M. Dumont, J.E. Masse, L. Barrallier, Acta Mater. 57 (2009) 326–334. J.D. Robson, N. Stanford, M.R. Barnett, Acta Mater. 59 (2011) 1945–1956. U.F.H.R. Suhuddin, S. Mironov, Y.S. Sato, H. Kokawa, C.W. Lee, Acta Mater. 57 (2009) 5406–5418. [5] H.N.B. Schmidt, T.L. Dickerson, J.H. Hattel, Acta Mater. 54 (2006) 1199–1209. [6] A. Steuwer, M. Dumont, J. Altenkirch, S. Birosca, A. Deschamps, P.B. Prangnell, P.J. Withers, Acta Mater. 59 (2011) 3002–3011.
9