Variety of scaling behaviors in nanocrystalline plasticity

Abstract: We address the question of why larger, high symmetry crystals are mostly weak, ductile and statistically sub-critical, while smaller crystals with the same symmetry are strong, brittle and super-critical. We link it to another question of why intermittent elasto-plastic deformation of sub-micron crystals features highly unusual size sensitivity of scaling exponents. We use a minimal integer-valued automaton model of crystal plasticity to show that with growing variance of quenched disorder, which can serve in this case as a proxy for increasing size, sub-micron crystals undergo a crossover from spin-glass marginality to criticality characterizing the second order brittle-to-ductile (BD) transition. We argue that this crossover is behind the non-universality of scaling exponents observed in physical and numerical experiments. The non-universality emerges only if the quenched disorder is elastically incompatible and it disappears if the disorder is compatible.