Data-driven extreme-value statistics for fracture size effects

Abstract

Micro- and nanoscale materials exhibit complex fracture size effects, often modeled using phenomenological extreme value theories like Weibull and Gumbel distributions. However, the predefined functional forms of these traditional theories largely rely on assumptions that lack robust justification, leading to debated applicability, particularly in the crucial low-strength tail. Here, we propose a data-driven extreme value approach that overcomes these limitations by directly deriving the survival distribution from raw data, thereby bypassing predefined functional forms. Validated via large-scale atomistic simulations of carbon nanotubes across lengths (10 nm–1 μm), our approach demonstrates superior accuracy over traditional theories in capturing the full fracture strength distribution, including the critical low-strength tail governing rare failure events. This work establishes a robust, assumption-minimal, universally applicable framework for understanding and predicting fracture size effects.