Micromechanical analysis of a unimodal and a bimodal polycrystal with paired microstructures of ultrafine grains, 2D & 3D

Abstract

Both experimental and numerical evidence supports that blending grains of different sizes within a polycrystalline materials allows to increase the alloy strength while maintaining its ductility. Microstructure-based modeling approaches have been developed to uncover the mechanisms governing the strength–ductility synergy, thereby assisting in the strategic design of alloys with multimodal grain size distributions. Due to significant differences in grain size and the need for statistical representativity, many approaches resort to simplifying hypotheses regarding the transition from ultrafine to macroscopic scales. Although the limitations of these simplifications in unimodal polycrystals are well documented, their biases associated with the micromechanical analysis of multimodal systems have not been addressed. To tackle this general question, this paper considers the model problem of a bimodal polycrystal with a single coarse grain embedded in a matrix of ultrafine grains. To ensure unbiased representation and enable systematic multi-scale comparisons, the analyses are based on a unimodal ultrafine grain polycrystal and its paired bimodal polycrystal, both of which have an identical microstructure of ultrafine grains. In order to distinguish structural effects of a classical matrix inclusion problem from crystal related interactions, two types of constitutive behavior have been investigated, both in 2D and 3D: isotropic macro-homogeneous for each grain population or full-field crystal plasticity. The four related configurations of a bimodal polycrystal all share the same macro-scale constitutive behavior. The distortions introduced by each of the above simplifying hypothesis and their combinations have thus been comprehensively evaluated, paying a particular attention to the specific patterns of localization of stress, strain and plastic activity. The 2D approach has been confirmed to be efficient in describing characteristic interaction mechanisms, yet with a propensity to accentuate localization phenomena. However the volume fraction of the coarse grain to achieve a given macro-scale stress–strain behavior has been found to be different from that in 3D.