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

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.

Figures (12)

• Figure 1: (a) Projectile geometry and (b) projectile-glass impact configuration, and (c) image processing of the fragmented sample for fragment detection.
• Figure 2: Schematic of the triangular network discretization. Insets depict: (Right-Red) network connectivity and bond stiffness; (Bottom-Blue) inelastic nodal forces; and (Left-Green) surface forces on boundary nodes.
• Figure 3: (a) Schematic showing the simulated tensile mid-plane, (b) Residual stress field after static equilibration. (c) Crack initiation via hole excision and radial expansion.
• Figure 4: (a) Cumulative fragment area distribution with insets showing representative fracture patterns. (b) Radial variation of fragment count, $N_c(r)$. Blue and orange data correspond to impact velocities of 20 and 35 m/s, respectively. The inset in (b) shows the fragments (solid yellow) that contribute to $N_c(r)$ at a given $r$ (red circle).
• Figure 5: (a) Simulated cumulative fragment area distribution with insets showing representative fracture patterns. (b) Radial variation of fragment counts, $N_c(r)$. Blue and orange data correspond to radial loading rates of 8 m/s and 15 m/s, respectively (Cases 1 and 2 in Table \ref{['Tab:sim_parameter']}). The inset in (b) shows the fragments (solid blue) that contribute to $N_c(r)$ at a given $r$ (red circle).