Spatial and temporal heterogeneity of Kohlrausch–Williams–Watts stress relaxations in metallic glasses

Abstract

Abstract We perform a molecular dynamics (MD) stress relaxation simulation for Zr 50 Cu 40 Al 10 metallic glass to confirm that the time dependency of stress relaxation conforms with the Kohlrausch–Williams–Watts (KWW) equation, and to derive the temperature dependency of the Kohlrausch exponent β KWW . We also calculate local plastic deformation based on atomic strain, then discuss the morphology of relaxation and calculate the probability density of stress relaxation with respect to the characteristic time of relaxation from the number of deformed atoms. Afterward, we derive the time dependency of stress relaxation as a mode-averaged decay function, which expresses spatial and temporal heterogeneity. Both the results of simulation and calculation reproduce the KWW relaxation form and are in good agreement, confirming the spatially and temporally heterogeneous nature of KWW relaxation. The heterogeneity of the stress relaxation of metallic glass is determined by local stress changes caused by microscopic local plastic deformation.