Effective temperature dynamics of shear bands in metallic glasses

Abstract

We study the plastic deformation of bulk metallic glasses with shear transformation zone (STZ) theory, a physical model for plasticity in amorphous systems, and compare it with experimental data. In STZ theory, plastic deformation occurs when localized regions rearrange due to applied stress and the density of these regions is determined by a dynamically evolving effective disorder temperature. We compare the predictions of STZ theory to experiments that explore the low-temperature deformation of Zr-based bulk metallic glasses via shear bands at various thermal temperatures and strain rates. By following the evolution of effective temperature with time, strain rate, and temperature through a series of approximate and numerical solutions to the STZ equations, we successfully model a suite of experimentally observed phenomena, including shear-band aging as apparent from slide-hold-slide tests, a temperature-dependent steady-state flow stress, and a strain-rate- and temperature-dependent transition from stick-slip (serrated flow) to steady-sliding (nonserrated flow). We find that STZ theory quantitatively matches the observed experimental data and provides a framework for relating the experimentally measured energy scales to different types of atomic rearrangements.

Dynamic properties of major shear bands in Zr–Cu–Al bulk metallic glasses

“…In fact, it has been shown theoretically (see Appendix D in Ref. [41]) that Q app is about three times the activation energy for aging in Vit105.…”

“…Pronounced thermally-activated relaxation has been suggested as being responsible for lowering the strain-rate sensitivity (SRS) when temperature is increased or strain rate decreased, eventually turning it negative [32,40]. Using a detailed theoretical approach [41] it has meanwhile been demonstrated that upon lowering the strain rate, the required athermal driving stress decreases while relaxation processes are dynamically less suppressed. Therefore an additional stress contribution that works against relaxation is required to maintain the applied strain rate.…”

Coarse graining atomistic simulations of plastically deforming amorphous solids

“…Although χ is a dimensionless form of T eff we shall henceforth refer to it as simply "the effective temperature" for readability. Some limited attempts to experimentally measure an effective temperature for disordered materials have been made [58], as well as other direct, quantitative comparisons with experiments of bulk metallic glasses [59]. For a monotonically loaded, athermal amorphous system where there are no rate-dependent processes such as aging, which compete with the STZ-transition rates described in Sec.…”

A small-gap effective-temperature model of transient shear band formation during flow

“…In this paper we use data from the aforementioned experiments in [26] to determine the physical parameters of the theory and make precise experimental connections. A distinguishing feature of the STZ theory is that it is based on a specific model of molecular rearrangements, which have been observed directly in numerical simulations and analog experiments [43,47,48]. The present formulation of the STZ theory has been extended from the original work of Argon [49,50] and his proposal of "shear transformations" to explain plastic deformation in metallic glasses, as well as from the free-volume and flow-defect theories of Turnbull, Cohen, Spaepen, and others [51,52].…”

“…vibrational degrees-of-freedom, but the configurational degrees-of-freedom are typically out of equilibrium. Some limited attempts to experimentally measure an effective temperature for disordered materials have been made [53], as well as other direct, quantitative comparisons with experiments of bulk metallic glasses [48]. Atomistic simulations of two-dimensional glasses have already suggested that T eff is linearly related to the local potential energy per atom [54], and earlier many arguments were made for the existence of the notion of an effective temperature, related to the entropy, that characterizes the number of phase-space paths available to the system [42,[55][56][57].…”