Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations
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In this chapter, we review two crystal plasticity methodologies based on Green’s functions for the prediction of microstructure-property relations in polycrystalline aggregates. The first, known as the viscoplastic self-consistent (VPSC) formulation, is a mean-field theory. The second, known as the viscoplastic fast Fourier transform-based (VPFFT) formulation, is a full-field method. The assumptions and main equations of these Green’s function-based crystal plasticity formulations are presented using a unified notation, pointing out their similarities and differences and cross-validating their predictions.
This chapter contains results of the author’s collaboration with C.N. Tomé, P. Ponte Castañeda, R. Brenner, O. Castelnau, P. Gilormini, M. Zecevic, M. Knezevic, and R.J. McCabe. Parts of this work were supported by Los Alamos National Laboratory’s Laboratory-Directed Research and Development (LDRD) program, project 20180441ER.