On the Origin of Crack Bifurcation in Dynamic Brittle Fracture
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Fragmentation in brittle materials is a central problem in dynamic fracture mechanics, with implications ranging from impact-resistant structural design and semiconductor packaging reliability to planetary collisions. It is governed by the instability of rapidly propagating cracks and their tendency to bifurcate. Classical analyses, most notably Yoffe’s moving crack solution, predict that beyond a critical crack speed the angular stress distribution ahead of the crack tip favors off-axis growth . Alternative explanations invoke material heterogeneity, inherent flaws, or energetic arguments associated with increased fracture surface. Resolving these competing mechanisms requires direct simulation of dynamic crack bifurcation. Traditional continuum-based approaches, such as X-FEM or phase-field methods, face severe challenges in this regime as computational cost grows rapidly with crack multiplication. We therefore employ peridynamics, a nonlocal formulation introduced by Silling that naturally accommodates discontinuities . In particular, the bond-based peridynamic model (PMB) provides a particle-based framework for simulating dynamic brittle fracture without explicit crack tracking or remeshing . The PMB formulation implemented in LAMMPS is used to study elastic response, crack propagation, and bifurcation in soda-lime glass. Elastic fidelity is validated through two independent approaches. Quasi-static uniaxial tension yields an effective Young’s modulus of approximately 72.1 GPa, while dynamic stress-wave propagation estimates the modulus as about 65.4 GPa. The validated model is then benchmarked against canonical experiments. Simulations of the Kalthoff–Winkler experiment reproduce the observed crack deflection angle of approximately 55°, and impact-induced conical crack patterns reported by Chaudhri are captured. Finally, dynamic wedge-loading experiments of Tippur and Sundaram are simulated, reproducing crack acceleration, bifurcation, and experimentally consistent crack speeds . Near-tip polar stress fields are compared with Yoffe’s predictions, providing insight into crack-tip instability and branching mechanisms underlying brittle fragmentation.
