Size effects in statistical fracture

TL;DR

This paper reviews statistical theories and numerical methods to understand how sample size influences the failure strength distribution in disordered materials, comparing analytical, energetic, geometric, and simulation approaches.

Contribution

It provides a comprehensive overview of existing models and simulations addressing size effects in fracture, highlighting their limitations and interrelations.

Findings

Analytical predictions of extreme value statistics and fiber bundle models are discussed.

Numerical simulations of lattice models are compared with theoretical models.

Limitations of current models in predicting size effects are identified.

Abstract

We review statistical theories and numerical methods employed to consider the sample size dependence of the failure strength distribution of disordered materials. We first overview the analytical predictions of extreme value statistics and fiber bundle models and discuss their limitations. Next, we review energetic and geometric approaches to fracture size effects for specimens with a flaw. Finally, we overview the numerical simulations of lattice models and compare with theoretical models.