John Hopkins University
Multiscale Modeling of Plastic Flow and Failure in Amorphous Solids: The Role of Effective (Fictive) Temperature as a Measure of Disorder
We have undertaken to develop multiscale models of plastic flow and failure processes in amorphous solids, materials that exhibit a complete lack of crystalline order. In this we have taken metallic glass as an exemplar material and applied molecular dynamics simulation to examine the physics at the atomic scale. This has allowed us to uncover the statistics of the shear transformation zone (STZ) defects that control plastic deformation. We have then sought to relate this defect structure to statistical mechanics models of “effective temperature” that characterize the degree of glass disorder in an effort to build a constitutive model of plastic deformation. The constitutive model has been incorporated into a high-fidelity 3D viscoplastic finite differencing scheme that adapts techniques originally developed for solving the Navier-Stokes equation. A novel machine learning algorithm then utilizes the atomistic data to guide the parameterization of the constitutive model so as to inform the continuum method. In doing so we have begun to ask some fundamental questions about the concept of “effective temperature.”
The concept of fictive-temperature has long been utilized to characterize the processing dependence of glass structure, and has recently been shown to be predictive of metallic glass ductility. Some theories have hypothesized that it is actually a real temperature related to the configurational degrees of freedom of the glass, i.e. an “effective-temperature,” notably the shear-transformation-zone (STZ) and soft-glassy-rheology (SGR) theories. We derive a thermodynamic integration scheme for calculating effective-temperature based on a 2-temperature hypothesis. To test this scheme we simulate a binary Cu-Zr metallic glass modeled with an EAM potential. Measures of the energy fluctuations associated with both the fast and slow degrees of freedom are measured during the glass quench. The resulting effective-temperature is consistent with estimates of fictive-temperature obtained from simulation in more heuristic ways. The results indicate that effective-temperature can be understood as a purely structural quantity. The method provides a means to measure the effective-temperature in the absence of fluctuations induced by shear and without resorting computationally expensive and impractical methods for explicitly measuring the configurational entropy.