The Thermal Shear-Transformation-Zone Theory: Homogeneous Flow and Superplasticity in Bulk Metallic Glasses
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The Thermal Shear-Transformation-Zone Theory: Homogeneous Flow and Superplasticity in Bulk Metallic Glasses Michael L. Falk1, James S. Langer2 and Leonid Pechenik2 Department of Materials Science and Engineering, University of Michigan Ann Arbor, MI 48109-2136, U.S.A. Department of Physics, University of California, Santa Barbara, CA 98106 U.S.A. ABSTRACT We present an extended version of our earlier shear-transformation-zone theory of amorphous plasticity that takes into account thermally assisted molecular rearrangements. As in the previous low-temperature theory a transition is predicted between jammed and flowing states at a well defined yield stress. In the new theory the jammed state below the yield stress exhibits thermally assisted creep. The theory accounts for the experimentally observed strain-rate dependence of the viscosity of a bulk metallic glass. In particular it models the onset of superplastic behavior at high strain rates as the system approaches the yield stress. The theory also captures many of the details of the transient stress-strrain response of the metallic glass at temperatures near the glass transition. INTRODUCTION Bulk metallic glasses possess exemplary mechanical properties such as high strength while potentially enabling near-net-shape processing of metallic parts. Being able to adequately model such processes requires a thorough understanding of the constitutive behavior of the metallic glass in the high temperature regime. Ideally any theory of such processes should be based on a microscopic picture of the mechanisms of deformation in the metallic glass. The sheartransformation-zone (STZ) theory of amorphous plasticity presented here is based on ideas originated by Cohen, Turnbull, Spaepen, Argon and others [1-4] who postulated that plastic deformation in amorphous materials occurs at localized sites often called flow defects. A number of computational studies (e.g. [5,6]) have provided support for this ideas that a model based on localized defects can capture the dynamics of deformation in such systems. The STZ theory specifically requires that these defects must be dynamic entities that carry orientational information. The most persistent consequence of this model is that the equations of motion for such a system imply a transition from between a jammed and flowing state at a critical stress that we identify as a yield stress. Most defect-based theories of deformation in glassy materials begin with the standard Eyring form in which the plastic strain rate is related to the number of defects multiplied by the difference between forward and backward transitions: ∆G k BT
ε& pl = ν n R ( s ) − R ( − s ) = 2ν n exp −
Ωs sinh 2k B T
(1)
here ν is a molecular vibrational frequency; R is the de-dimensionalized rate of transition of a flow defect; ∆G is an activation barrier; kB is Boltzmann’s constant; T is the temperature; Ω is an
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atomic volume, and s is the deviatoric stress. These theories then attempt to describe the dynamics of de
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