Fatigue crack propagation across grain boundary of Al-Cu-Mg bicrystal based on crystal plasticity and XFEM combining cohesive zone model
Qi Zhao
a, c, Magd Abdel Wahab
b, c,*,Yong Ling
c, Zhiyi Liu
da School of Materials Science and Engineering, Hubei University of Automotive Technology, Shiyan 442002, PR China
b CIRTech Institute, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Viet Nam
c Soete Laboratory, Faculty of Engineering and Architecture, Ghent University, Technologiepark Zwijnaarde 903, B-9052 Zwijnaarde, Belgium
d School of Materials Science and Engineering, Central South University, Changsha 410083, PR China
The authors are grateful for the financial support from National Natural Science Foundation of China (51901073), China Scholarship Council (201808420393), and PhD Research Startup Foundation of Hubei University of Automotive Technology (BK201702).
Abstract
Introduction
Methodology Results
Conclusion
Acknowledgements
A method combining CP (crystal plasticity), XFEM (eXtended Finite Element) and CZM (cohesive zone model) with traction separation law is developed to predict fatigue crack propagation (FCP) across grain boundary of Al-Cu-Mg alloy during fatigue stage ІІ. For this model, the ideal constitutive law about dislocation interaction at GB is implanted on CP model. A bicrystal containing GB is built up to model FCP behavior at typical L participated GBs. Corresponding modelling results are also compared with published experimental results to check the accuracy of model. This CP containing GB constitutive laws, XFEM and CZM model is suggested to be a promising method in predicting slip-controlled crack deflection at GBs.
Keywords: Goss texture; grain boundary; fatigue crack propagation; crystal plasticity; extended finite element method; cohesive zone model
.
-Grain boundary (GB) plays an important role in affecting fatigue crack propagation (FCP) behavior.
From the micro-perspective, FCP behavior is a reflection of FCP resistance. Large FCP deflection at GB represents the correspondingly high FCP resistance.
-GB characteristic can be descripted by the twist and tilt angles. Compared with tilt angle, twist angle is a predominated factor in determining the magnitude of FCP deflection. GB with large twist angle will be beneficial for large FCP deflection.
-From experimental observation, it is well known that Goss was easy to induce FCP deflection at GB because of its large twist angle with neighboring grains. Cube grain presented a great FCP deflection when it had twist angle component boundary with neighboring grains, but little one when it had a small tilt angle component boundary with neighboring grains.
-Although the effect of twist angle on FCP deflection behavior has been revealed by experimental observation, the corresponding numerical methods are still not available.
-To this end, a method combining CP (crystal crystal), XFEM (eXtended Finite Element) and CZM (cohesive zone model) with traction separation law is developed to predict fatigue crack propagation (FCP) across GB
-The present numerical methods includes the constitutive law of crystal plasticity (CP), and eXtended Finite Element (XFEM).
-The crystal plasticity is a dislocation-based constitutive law combined with grain boundary (GB) model. The corresponding description of this CP constitutive law can be found at the Ref. (Q. Zhao, M.
Abdel Wahab, Y. Ling, Z. Liu, Mater. Des. 206 (2021) 109794).
-The XFEM is comprised by cohesive zone model (CZM) with traction separation law. This XFEM is suitable for the fatigue behavior of Al-Cu-Mg alloy with elastic-plastic deformation behavior.
-The multiscale model is as follows:
-Both the twist and tilt angles for L/L GB are 0, and as expected the crack fails to deflect at GB. In this case, the L-L bicrystal can be actually as a single crystal.
-The twist angle for L/Goss GB is 90°. Considering the strong symmetry of FCC slip system, the effective twist angle for this GB is 0°, and correspondingly there is no FCP deflection at this GB.
-We have developed a method combining CP, XFEM and CZM with traction separation law, and this model has good accuracy in predicting slip-controlled fatigue crack deflection at GBs.
-When the bicrystal model is comprised by the same two orientations, it can be regarded as a single crystal and correspondingly there is no fatigue crack deflection at GBs.
-Twist angle of GB has a great effect on FCP deflection behavior at GB. The large twist angle will be beneficial for the formation of large FCP deflection angle at GBs.
As compared with twist angle, the effect of tilt angle on FCP deflection can be ignored.
-When calculating the effective twist angle, the symmetry of FCC structure should be considered. It is suggested that the effective twist angle of GB related to slip system is not larger than 35°.
-FCP path within L grain has a slight difference for different L-participated bicrystals. This attributes to the different grain interaction behavior at different bicrystal models.
CP zone Buffer zone
47.5×45.6 mm
9.87×6.58 mm
L/L boundary L/L L/Goss
-The effective twist angle for L/Goss-Brass GB is 20°. It is observed that crack propagates through GB with obvious deflection.
-When the effective twist angle reaches 35° (L/Brass GB), the deflection angle also further increases. A similar deflection angle is also observed for L/P GB with 35° twist angle.
L/Goss-Brass: 20° L/Brass: 35° L/P: 35°
GB GB
GB GB GB
Results
L/Cube boundary, with 45° tilt
47.5×45.6 mm
9.87×6.58 mm
360×360 μm
