Dynamic fragmentation of residually stressed solids: From microscopic instabilities to universal scaling

TL;DR

This study explores how residual stress influences dynamic fracture patterns in solids, revealing a universal fragment size distribution law and microscopic mechanisms behind crack speed anomalies.

Contribution

It introduces a novel micromechanical model incorporating residual stress and uncovers a universal scaling law for fragment sizes across various conditions.

Findings

Fragment size distribution follows an exponential decay.

Universal scaling law collapses data from different conditions.

Micro-instabilities cause apparent crack speeds exceeding $c_r$.

Abstract

The dynamic fragmentation of residually stressed solids involves a complex interplay between stored elastic energy, stress wave propagation, and crack instabilities. In this work, we investigate the fracture mechanics of chemically toughened glass through high-velocity projectile impact experiments and a novel micromechanical network model. We rigorously incorporate residual stress into the discrete lattice framework via a prescribed inelastic strain (eigenstrain) distribution, formulated as equivalent body and surface forces to ensure mesh-independent fracture paths. Our experiments and simulations demonstrate that while the fracture topology shifts from coarse to fine with increasing impact energy, the cumulative fragment size distribution consistently follows an exponential decay. Crucially, we reveal a universal scaling law: fragment size distributions from diverse loading conditions and stress profiles collapse onto a single master curve when normalized by the mean fragment area. Furthermore, the model elucidates the determinants of fragmentation, showing that the resulting fragment size is governed not only by the magnitude of residual stress but also by the steepness of the stress gradient. At the microscopic scale, we identify a mechanism for dynamic instability where non-sequential bond breaking ahead of the crack tip leads to apparent local crack speeds exceeding the Rayleigh wave speed ($c_r$). These arrested micro-branches, analogous to the Burridge-Andrews mechanism, provide a physical explanation for the "tongue-like" features and hackle zones observed in post-mortem fractography.