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A finite-deformation dislocation density-based crystal viscoplasticity constitutive model for calculating the stored deformation energy

M. Jafari, M. Jamshidian and S. Ziaei-Rad

International Journal of Mechanical Sciences, Volumes 128–129, May 2017, Pages 486-498



A previously-developed infinitesimal strain and dislocation density based crystal viscoplasticity constitutive theory is reformulated in the finite deformation regime in a thermodynamically consistent manner. The constitutive equations are then numerically implemented into the Abaqus/Standard finite element package. The constitutive model is primarily verified and calibrated with respect to single crystal aluminum experiments and then the distribution of stored deformation energy in aluminum bicrystals and polycrystals is investigated to estimate the driving forces for grain boundary migration due to the stored energy difference across grain boundary. Our statistical analysis shows that the onset of strain induced grain boundary migration in a polycrystalline microstructure is basically dependent on the spatial distribution of the stored deformation energy rather than the overall stored deformation energy value; and it preferably occurs in a few predictable specific regions where certain grain orientations meet at a grain boundary across which high values of stored energy difference happens.



A. Constitutive equation; B. Stored deformation energy; C. Dislocation density; D. Crystal viscoplasticity; E. Finite elements


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