Creep failure of amorphous solids under tensile stress

TL;DR

This paper investigates the creep failure process in amorphous solids under tensile stress, developing a scaling theory to predict the distribution of collapse times across different material conditions.

Contribution

The study introduces a universal scaling framework for the probability distribution of collapse times in amorphous solids, applicable to both ductile and brittle materials, based on simulation data.

Findings

Scaling concepts enable data collapse for collapse time distributions.

Universal functions predict failure times across different parameters.

Scaling theory successfully describes brittle material failure.

Abstract

Applying constant tensile stress to a piece of amorphous solid results in a slow extension, followed by an eventual rapid mechanical collapse. This "creep" process is of paramount engineering concern, and as such was the subject of study in a variety of materials, for more than a century. Predictive theories for $\tau_w$, the expected time of collapse, are lacking, mainly due to its dependence on a bewildering variety of parameters, including temperature, system size, tensile force, but also the detailed microscopic interactions between constituents. The complex dependence of the collapse time on all the parameters is discussed below, using simulations of strip of amorphous material. Different scenarios are observed for ductile and brittle materials, resulting in serious difficulties in creating an all-encompassing theory that could offer safety measures for given conditions. A central aim of this paper is to employ scaling concepts, to achieve data collapse for the probability distribution function (pdf) of $\ln{\tau_w}$. The scaling ideas result in a universal function which provides a prediction of the pdf of $\ln{\tau_w}$ for out-of-sample systems, from measurements at other values of these parameters. The predictive power of the scaling theory is demonstrated for both ductile and brittle systems. Finally, we present a derivation of universal scaling function for brittle materials. The ductile case appears to be due to a plastic necking instability and is left for future research.