Fatigue crack propagation across grain boundary of Al-Cu-Mg bicrystal based on crystal plasticity XFEM and cohesive zone model

doi:10.1016/j.jmst.2022.03.020

Abstract

Abstract:

In this paper, a methodology integrating crystal plasticity (CP), the eXtended finite element method (XFEM) and the cohesive zone model (CZM) is developed for an Al-Cu-Mg alloy to predict fatigue crack propagation (FCP) across grain boundary (GB) of Al-Cu-Mg alloy during stage ІІ. One GB model is incorporated into FCP constitutive law to describe grain interaction at GB. A bicrystal containing GB is built up to simulate FCP behavior through L participated GBs. Modelling features including GB characteristic, cumulative plastic strain (CPS) distribution and crystal slipping evidence can be identified. The numerical results are compared with published experimental data to check the accuracy of model. This work demonstrates that the combination of CP containing GB constitutive laws, XFEM and CZM is a promising methodology in predicting twist angle-controlled crack deflection through GBs.

Key words: Grain boundary, Twist angle, Crystal plasticity, Extended finite element method, Fatigue crack propagation, Cumulative plastic strain

QiZhao, Magd Abdel Wahab, Yong Ling, Zhiyi Liu. Fatigue crack propagation across grain boundary of Al-Cu-Mg bicrystal based on crystal plasticity XFEM and cohesive zone model[J]. J. Mater. Sci. Technol., 2022, 126: 275-287.

Figures/Tables 13

Table 1. Implanted CP parameters for Al-Cu-Mg crystal [18].

Parameter	Unit	Value
C₁₁	[GPa]	112
C₁₂	[GPa]	59.5
C₄₄	[GPa]	26.7
γ˙0	[s⁻¹]	1×10⁻³
n	[-]	10
μ	[GPa]	26.5
b	[nm]	0.285
K	[-]	38
yc	[nm]	0.957
h	[MPa]	3600
hd	[-]	380

Fig. 1. Decomposition diagram of a cracked element with nodes 1-4 into two elements; the solid circles are original nodes and the hollow circles are phantom nodes [33].

Fig. 2. Multiscale model of CP containing GB, XFEM and CZM: (a) CT shape model, (b) buffer region and (c) CP zone composed by two grains.

Fig. 3. Schematic diagram showing twist angle and tilt angle, (a) definition of twist angle (α) and tilt angle (β) for grain orientation, and (b) twist angle (α') and tilt angle (β') for slip system, where saand sbrepresent slip directions of grain a and b, respectively, and naand nbrepresent slip plane normals of grain a and b, respectively.

Fig. 4. Orientation relationship between two grains in bicrystal model, and the corresponding determination of GB characteristic.

Fig. 5. The flowchart of CP, XFEM and CZM model.

Fig. 6. Simulated FCP paths within L/L (a, b) and L/Goss (c, d) bicrystal grains. (a) and (c) are the FCP paths with von Mises stress distributions, and (b) and (d) are the FCP paths within bicrystal model.

Fig. 7. Simulated FCP paths within bicrystal grains with different twist angle (α). The bicrystal in (a-d) is L/Goss-Brass, L/Brass, L/r-Brass, and L/P, respectively. (e, f, g, h) is the magnification view near GB from (a, b, c, d), respectively.

Fig. 8. Simulated FCP paths within L/Cube bicrystal grains: (a) the FCP path with Mises stress distribution, (b) the FCP path within bicrystal.

Fig. 9. Simulated FCP paths within L/Goss-Brass bicrystal grains. The number represents the average size of the 3 nearest mesh to GB at vertical direction. The average size is 18 μm (a), 11.5 μm (b), and 8.89 μm (c), respectively.

Fig. 10. Cumulative plastic strain (CPS) of simulations and experiments: (a-c) CPS distribution within bicrystals with different effective twist (αe), and the αe is 0° (a), 20° (b) and 35° (c), respectively; (d, e) Experimental results about CPS distribution along different GBs, and these data are from Ref. [3].

Fig. 11. Comparison between simulation and experimental results for the relationship between CPS and αe. The experimental data are from Ref. [3].

Fig. 12. {111} pole figures of L/Brass bicrystal corresponding to different FCP stage: (a) the original {111} pole figure, and (b-d) the {111} pole figures after 9 cycles, 12 cycles and 21 cycles, respectively.

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