Statistical physics of elastoplastic steady states in amorphous solids: Finite temperatures and strain rates

Abstract

The effect of finite temperature T and finite strain rateγ on the statistical physics of plastic deformations in amorphous solids made of N particles is investigated. We recognize three regimes of temperature where the statistics are qualitatively different. In the first regime the temperature is very low, T < Tcross(N ), and the strain is quasi-static. In this regime the elasto-plastic steady state exhibits highly correlated plastic events whose statistics are characterized by anomalous exponents. In the second regime Tcross(N ) < T < Tmax(γ) the system-size dependence of the stress fluctuations becomes normal, but the variance depends on the strain rate. The physical mechanism of the crossover is different for increasing temperature and increasing strain rate, since the plastic events are still dominated by the mechanical instabilities (seen as an eigenvalue of the Hessian matrix going to zero), and the effect of temperature is only to facilitate the transition. A third regime occurs above the second cross-over temperature Tmax(γ) where stress fluctuations become dominated by thermal noise. Throughout the paper we demonstrate that scaling concepts are highly relevant for the problem at hand, and finally we present a scaling theory that is able to collapse the data for all the values of temperatures and strain rates, providing us with a high degree of predictability.

Elasticity in Amorphous Solids: Nonlinear or Piecewise Linear?

“…Also at finite temperatures one sees in Fig. 2 the change from small stress drops to large ones [15]. The highly serrated nature of the stress vs. strain curves is masked by the averaging of many realizations shown in Fig.…”

Crossover from random three-dimensional avalanches to correlated nano shear bands in metallic glasses

“…Furthermore, the anelastic regime studied here is far off the region where macroscopic-and system-spanning shear bands appear, both in time and stress. It is known from simulational approaches that correlated STZ activity, that is, inhomogeneous deformation, typically occurs at temperatures below T g and high stresses 23,32 . Hence, we attribute the 15 nm length steps to the occurrence of the so-called 'nano shear bands'.…”

“…Hence, at a given temperature, the applied stress plays an important role. Only when assisted by the stress, the random thermal activation of STZs might trigger small plastic avalanches in certain directions mediated by short-range interactions 23 . These nano shear bands are created independently and are distributed randomly in the three-dimensional sample.…”

“…Finally, their collective activation is responsible for the emergence of macroscopic shear bands 22 , and hence plasticity and failure. On the length scale of such interacting local plastic rearrangements, avalanche statistics have been studied in theoretical efforts and numerical simulations 2,4,[23][24][25][26] .…”

Universality of the Plastic Instability in Strained Amorphous Solids

“…One immediate consequence is that the barrier ∆E between the minimum in which the system resides and the saddle that it eventually collides with tends to zero like [11] ∆E ∝ (γ P − γ) 3/2 .…”