Refined analysis of elastic-plastic crystals

doi:10.1016/0020-7683(92)90191-U

International Journal of Solids and Structures

Volume 29, Issue 16, 1992, Pages 2013-2021

https://doi.org/10.1016/0020-7683(92)90191-U Get rights and content

Abstract

The concept of the rigid-ideally plastic crystals with interacting slip systems is extended for the case of the elastic-plastic crystals with work hardening. It allows the crystal analysis to be performed in a similar way to the case of elastic-plastic continuum at large strains i.e. on the basis of the complete system of equations. As in classical plasticity, the flow rule is expressed in terms of the Kirchhoff stress increment and the strain rate tensor. Three additional constitutive relations between the plastic spin and stress components help to describe the lattice rotations. A smooth but highly nonlinear yield condition is assumed as an approximation of the Schmid law. The hardening law describing the self-hardening and the latent hardening is considered within the isotropic and the kinematic approach. The complete model is applied to an analysis of the drawing process of f.c.c. single crystals. By comparison with the numerical procedure based on the conventional rate-independent approach, the calculations are simplified considerably.

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Citation Excerpt :
Therefore, the polycrystal response can be slightly altered. To evaluate the effect, we compare the results from this procedure with the results based on the regularized Schmid law (Gambin, 1992). The latter approach is summarized next.
Slip system hardening behavior of a given slip system is influenced more by shearing on another slip system known, as latent hardening, than by shearing on itself, known as self-hardening. This paper extends a recently developed dislocation-based hardening law within the elasto-plastic self-consistent polycrystal plasticity model to incorporate the latent hardening effects for predicting anisotropic response of polycrystalline face-centered cubic metals. In doing so, a new approach to overcome singularities associated with the self-consistent Eshelby solution procedure is proposed. The new approach is validated using a regularized Schmid law, where the singularity in Eshelby tensor calculation is intrinsically suppressed. Moreover, the solution procedure for single crystal stress increment is advanced to be based on a methodology involving the singular value decomposition to solve for shear increments. It is found that modeling crystallographic texture evolution and latent hardening successfully captures the anisotropic behavior of polycrystalline AA6022-T4 alloy. The model is subsequently successfully applied to predict large strain cyclic deformation of the same material. The implementation and insights from these predictions are presented and discussed in this paper.

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Refined analysis of elastic-plastic crystals

Abstract

Acta Metall.

Scripta Metall.

J. Mech. Phys. Solids