Variety of scaling behaviors in nanocrystalline plasticity

Abstract

We address the question of why larger, high-symmetry crystals are mostly weak, ductile, and statistically subcritical, while smaller crystals with the same symmetry are strong, brittle and supercritical. We link it to another question of why intermittent elasto-plastic deformation of submicron 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, submicron 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 nonuniversality of scaling exponents observed in physical and numerical experiments. The nonuniversality emerges only if the quenched disorder is elastically incompatible, and it disappears if the disorder is compatible.

Fluctuations in crystalline plasticity

“…We have shown above that the dimensionless ratio R = L/l appears as the key controlling parameter, encompassing the external size effect ("smaller is wilder") as well as the disorder through the internal scale l ∼ 1/τ pin [67]. Below, we show how the effects of system size and disorder can be analyzed in a single setting using a minimal model of crystal plasticity.…”

“…The obtained agreement with observations indicates a sound basis of the underlying theoretical ideas. While the individual scaling exponents turn out to be nonuniversal [62,67], the ensuing dependence of exponents on wildness appear to be universal. The theoretical ideas behind the proposed framework, which justify such a generalized notion of universality, will be discussed in Section 5.…”

“…The recent discovery that the reported scaling in crystal plasticity is not universal, and that the measured power law scaling exponents depend on lattice structure, crystal orientation in the loading machine, the size of the crystal, its purity, and the presence or the absence of hardening [33,[62][63][64][64][65][66], reveal rich and complex physics of the underlying self-organization process that still remains largely unexplored [67]. Without attempting to make a comprehensive exploration of the elemental plasticity mechanisms, we concentrate on the recent work addressing: (i) experimental tracking of plastic fluctuations either directly from stress-strain records [64,68], or from acoustic emission (AE) in bulk materials [62,66,69]; (ii) numerical simulations based on the minimal automaton model of plastic flow in crystals proposed in [67,70]; (iii) stochastic modeling of mesoscale crystal plasticity introducing rheological closure relations with multiplicative noise [62]. Our various comments on the recent progress in the field are therefore highly biased by our own experimental and computational work and are presented in the perspective of the studies performed in our group.…”

“…Figure 1 shows experimental results: in (a) the true stress-true strain relations, and in (b) the cumulative distributions of displacement burst sizes X (in nm). In (c) we illustrate the deformation morphology for compression tests for µm to sub-µm pillars of a high-purity BCC material, Mo [67]. In these experiments, the loading configuration was designed to ensure that twinning was absent, i.e.…”

“…For the larger pillars (L = 1500 nm), the relatively smooth mechanical response (Figure 1(a)) produces a distribution of plastic fluctuations which clearly has nothing to do with power law, instead revealing a characteristic size X 0 (see more below) and corresponding to a sub-critical regime. At an intermediate sample size L = 1000 nm, the nature of plastic fluctuations changes drastically, with a power law distribution [67]. Copyrighted by American Physical Society.…”