Spectral non-local crystal plasticity modelling of size effects in polycrystals

Abstract eng:
The numerical implementation of a non-local polycrystal plasticity theory using the FFT-based formulation of Moulinec and Suquet [l] is presented. Gurtin’s [2] non-local formulation has been incorporated in the elasto-viscoplastic (EVP-FFT) algorithm of Lebensohn et a1. [3]. Numerical procedures for the accurate estimation of higher order derivatives of micromechanical fields, required for feedback into single crystal constitutive relations, are identified and applied. A simple case of a periodic laminate made of two fcc crystals is first used to assess the soundness and numerical stability of the proposed algorithm. Different behaviors at grain boundaries are explored, and the one consistent with the micro-clamped condition gives the most pronounced size effect. The new formulation is applied to the case of 3-D fcc polycrystals, illustrating the possibilities offered by the proposed scheme to accurately solve large problems in reasonable computing times.

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