Multi-laminate plastic-strain organization for non-uniform TFA modeling of poly-crystal regularized plastic flow

Abstract A recently presented single plastic-potential, microstructure-based model of poly-crystal plasticity by the authors considers a globally regularized Schmid law (RSL) as the slip flow criterion of a homogeneous equivalent super-crystal. The homogenization scheme that is taken of affine type is specialized to the transformation field analysis (TFA) framework. The relevancy of the TFA here results from a description of intra-crystalline slip in terms of hierarchical multi-laminate (HML) structures that ensure the request of piece-wise homogeneous plasticity. This RSL–TFA–HML modeling has been shown efficient for heterogeneous intra-crystalline plastic slip in terms of overall stiffness estimates when laminates are parallel to slip planes or normal to slip directions. It is also suitable for twinning modes of crystal plasticity as stressed in this paper. The performed superposition of all possible HML plastic strain modes makes the TFA of the non-uniform (NTFA) and coupled type proposed by Michel and Suquet [Michel, J.C., Suquet, P., 2003. Non-uniform transformation field analysis. International Journal of Solids and Structures 40, 6937–6955; Michel, J.C., Suquet, P., 2004. Computational analysis of nonlinear composite structures using the non-uniform transformation field analysis. Computer Methods in Applied Mechanics and Engineering 193, 5477–5502]. In this new contribution, we investigate further our extension of this modeling to poly-crystals. It is interpreted as based on a description of the aggregate morphology in terms of the distribution of the crystallographic orientations of the grain boundary and sub-boundary facets, rather than in terms of a mean grain or domain shape. In its initial form, our extension amounted to assuming all these facets oriented either parallel to slip planes or normal to slip directions, what is proved convenient for large enough grains. In order to extend the relevancy of the modeling down to ultra-fine grains, we introduce a graded form of the modeling that is made grain size dependent from specifying the conditions for which the TFA accommodation hardening is negligible according to the range of the physical one. Some numerical stiffness comparisons from this graded RSL–TFA–HML modeling are provided.

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