Optimization of mechanical properties of bi-crystals via a genetic algorithm (GA) combined with FFT-based Dislocation Mechanics

Recently, an enhanced polycrystal plasticity elasto-viscoplastic FFT (fast Fourier transform) formulation coupled with a mesoscale continuum dislocation mechanics theory (MFDM) was developed to predict gran size effects on the flow stress of polycrystals [1]. Here, we consider different bi-crystalline configurations with fixed grain size, and fixed grain boundary planes parallel or perpendicular to the loading direction. We seek to optimize the crystallographic orientations of both grains to maximize the elastic limits of these bi-crystals by using a genetic algorithm (GA) of global optimization. GA is a meta-heuristic method for stochastic search of optimal solutions imitating the theory of biological evolution by genetic selection [2]. It is here coupled with numerical simulations using MFDM-FFT and CP-FFT (classic crystal plasticity). Considering different initial populations for GA, the results given by both crystal plasticity models are analyzed and compared based on different features of the optimized configurations: maximum Schmid factors in both crystals, misorientation angles, grain boundary types (tilt / twist) and slip transmission factors. Numerical results are provided and discussed for different crystallographic structures with different slip system families, like face-centered cubic and body-centered cubic structures.