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...

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The change in the configurational enthalpy of metallic glass forming liquids induced by mechanical deformation and its effect on elastic softening is assessed. The acoustically measured shear modulus is found to decrease with increasing configurational enthalpy by a dependence similar to one obtained by softening via thermal annealing. This establishes that elastic softening is governed by a unique functional relationship between shear modulus and configurational enthalpy. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2717017͔In the recent work of Johnson and co-workers, 1-4 a link between elastic softening and configurational changes in metallic glass forming liquids has been proposed. The steepness of the viscosity dependence on temperature in the vicinity of the glass transition, i.e., the liquid fragility, has been known to be associated with the stored configurational enthalpy since the early work of Angell and co-workers. [5][6][7] Furthermore, the effect of strain rate on viscosity induced by mechanical deformation has also been linked to changes in configurational enthalpy. 8 However, attributing the deformationally induced softening of liquids to a unique functional relation between shear modulus and stored configurational enthalpy is a concept that has just recently been brought to attention. 3 This concept essentially suggests that conversion of mechanical work into stored configurational enthalpy induces softening via a dependence of shear modulus on configurational enthalpy. The thermodynamic state variable controlling flow in this concept is identified to be the isoconfigurational shear modulus. Experimental validation of earlier concepts based on the "free volume" hypothesis 9 has not been possible, mainly due to the lack of a fundamental thermodynamic definition of free volume. In contrast, the isoconfigurational shear modulus is a thermodynamically well-defined and experimentally accessible property, rendering this concept experimentally verifiable. In the present study, the change in configurational enthalpy induced by mechanical work and its effect on the softening of metallic glass forming liquids is evaluated by means of compressive experiments, ultrasonic measurements, and enthalpy recovery tests.For the loading experiments we utilized cylindrical specimens of Pt 57.2 Ni 5.3 Cu 14.7 P 22.5 ͑Refs. 10 and 11͒ and Pd 43 Ni 10 Cu 27 P 20 , 3,12 which we deformed isothermally at constant strain rates. The loading setup described in Ref. 13 is utilized. Deformation was performed for a period of time sufficient to allow a steady flow stress state in the nonNewtonian regime to be attained. Upon unloading, the specimens were quenched as rapidly as possible to capture the configurational state associated with that flow stress.We assessed the elastic softening induced by mechanical deformation by evaluating the isoconfigurational shear modulus at the high-frequency "solidlike" limit G. We evaluated G of the quenched unloaded specimens ultrasonically, 14 and extrapolated the room temperature m...

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