Cooperative Shear Model for the Rheology of Glass-Forming Metallic Liquids

Abstract

A rheological law based on the concept of cooperatively sheared flow zones is presented, in which the effective thermodynamic state variable controlling flow is identified to be the isoconfigurational shear modulus of the liquid. The law captures Newtonian as well as non-Newtonian viscosity data for glassforming metallic liquids over a broad range of fragility. Acoustic measurements on specimens deformed at a constant strain rate correlate well with the measured steady-state viscosities, hence verifying that viscosity has a unique functional relationship with the isoconfigurational shear modulus. DOI: 10.1103/PhysRevLett.97.065502 PACS numbers: 61.43.Fs, 61.66.Dk Over the last three decades, several phenomenological theories have been proposed to explain flow in metallic glasses, most of which were founded on two hypothetical flow mechanisms: dilatation [1] and cooperative shear [2]. By analogy to granular materials, metallic glasses were thought to flow by deformation-induced dilatation, which results in the creation of a microstructural ''free volume'' leading to flow localization and consequent softening [1]. Owing to their ability to effectively capture the flow characteristics of metallic glasses, free volume models have been regarded as good phenomenological flow models and have been widely embraced. Even though experimental assessment of excess molar volume provided certain evidence of deformation-induced dilatation [3,4], it has not been possible to quantitatively link measurable free volume to flow as predicted by free volume models. To some extent, this can be attributed to the lack of a fundamental thermodynamic definition of ''free volume'' leading to constitutive models that possibly lack thermodynamic consistency. In an alternative approach [2], flow in amorphous metals was thought to be accommodated by cooperative shearing of atomic clusters, referred to as ''shear transformation zones.'' In a recent study [5], it has been shown that plastic yielding in metallic glasses can be effectively accounted for by adopting a cooperative yielding analysis for these flow zones similar to the one developed by Frenkel [6] for dislocation-free crystals. In the present study, we employ such cooperative shear flow analysis to investigate the rheology of metallic glass-forming liquids.Following [5], a periodic energy density versus strain can be formulated as = 0 sin 2 =4 c , where 0 is the barrier energy density, and c is a critical shear strain limit shown to be a universal scale for metallic glasses. Considering that the shear modulus is given by the curvature of the energy density function, i.e., G d 2 =d 2 j 0 , a linear relationship between barrier energy density and shear modulus can be formulated as 0 8= 2 2 c G. Multiplying by an effective zone volume , the total energy barrier for configurational hopping between inherent states, which can be regarded as the activation barrier for shear flow, can be expressed as W 8= 2 2 c G . Acknowledging that the variables contributing to barrier softening are G an...

A thermodynamic unification of jamming

“…(A flow sweet spot is observed nearγ ≈ 200 s −1 .) The shear-softening scenario presented above has been observed in driven metallic 5 and colloidal 6 glasses, substances that are disordered solids that lack the periodicity of crystals. Why do granular fluids flow like glassy liquids?…”

“…Broadly speaking, it considers the elastic, the entropic, the free volume and the hydrodynamic bases of other glass theories presented so far. This view of jamming applies to phenomena such as stick-slip nucleation in seismic fault ruptures 24 , shear banding in metallic alloys 5 , strain softening in colloidal glasses 6 and even stop-and-go driving in traffic jams 25 . These types of flow, defiant of conservative fluid models, are closely governed by dynamics that straddle the tipping point of jamming.…”

“…In contrast, other variations 14,15 of the theory rely on an effective granular temperature that is unrelated to the architectural arrangement of particles. Ultimately, the state variables that govern the isothermal states of jamming are pressure, shear rate 5 and the free volume 16 . Moreover, the EOS for dense granular flows has provided strong evidence for the unification of jamming in fragile materials.…”

Compositional landscape for glass formation in metal alloys

“…The rate at which atomic configurations are sampled in an undercooled liquid is taken to be proportional to the liquid fluidity, or inverse viscosity η −1 . Viscous flow is taken to be an activated process that may be characterized by a temperature and composition dependent barrier, W ðT; cÞ (17,18). The characteristic time for the nucleation of an α-crystal takes the general form…”

Properties of Bulk Metallic Glasses

“…Было, например, отмечено, что разные исто-рии обработки объемных металлических стекло-образных сплавов (режимы отжига и скорости охлаждения) приводят к изменению химического и топологического атомных порядков и, следователь-но, к изменению механических свойств [72][73][74]. Такие структурные изменения были объяснены с точки зрения свободного объема и конфигураци-онной потенциальной энергии [75,76]. Компью-терное моделирование показало, что изменения скорости охлаждения сплава Cu-Zr сопровожда-лись изменением доли икосаэдрических кластеров и их влиянием на пластичность [77].…”