Effect of quenched heterogeneity on creep lifetimes of disordered materials

TL;DR

This paper investigates how quenched heterogeneity and elastic interactions influence creep failure times in disordered materials, revealing an effective temperature concept that impacts lifetime variability and interpretation of creep tests.

Contribution

It introduces a generalized effective temperature framework accounting for complex elastic kernels and heterogeneity effects on creep lifetimes in disordered materials.

Findings

Creep failure time follows an Arrhenius law with an effective temperature increased by heterogeneity.

Elastic interactions and memory effects modify the effective temperature dependence.

Lifetime variability is proportional to mean lifetime and influenced by heterogeneity and elastic kernel.

Abstract

We revisit the problem of describing creep in heterogeneous materials by an effective temperature by considering more realistic (and complex) non-mean-field elastic redistribution kernels. We show first, from theoretical considerations, that, if elastic stress redistribution and memory effects are neglected, the average creep failure time follows an Arrhenius expression with an effective temperature explicitly increasing with the quenched heterogeneity. Using a thermally activated progressive damage model of compressive failure, we show that this holds true when taking into account elastic interactions and memory effects, however with an effective temperature $T_{eff}$ depending as well on the nature of the (non-democratic) elastic interaction kernel. We observe that the variability of creep lifetimes, for given external conditions of load and temperature, is roughly proportional to the mean lifetime, therefore depends as well on $T$, on quenched heterogeneity, and the elastic kernel. Finally, we discuss the implications of this effective temperature effect on the interpretation of macroscopic creep tests to estimate an activation volume at the microscale.