A Model for Fracture Probability as a Function of Stress and Strain

Abstract

Distributions of ultimate stress (σ m) and strain (ε m) are obtained by Monte-Carlo simulations with a chain-of-bundles (COB) model. The COB contains linear-elastic elements, for which the fracture probability distribution of stress and strain is varied. Various entities describing the combined distribution of σ m and ε m for the COB are calculated. Simulated σ m - ε m distributions resemble those observed experimentally for various materials. Experimental trends for the combined σ m - ε m distributions, which are observed when, e.g., changing material parameters or processing conditions, can be interpreted in terms of changes in critical substructures, and simulations like those presented here may be useful in such studies.