Expression of Quenched Disorder in Lattice Fracture

Fracture in disordered materials remains one of the most compelling examples of emergent organization in driven, non-equilibrium systems. We explore this phenomenon in two dimensional lattices where quenched disorder - introduced through Weibull distributed breaking thresholds - governs the nucleation and evolution of damage around a pre-existing defect. Through statistical modelling and numerical simulations, we identify distinct failure regimes that emerge in the space of disorder strengths and lattice geometries. By elucidating how these regions are shaped by the competition between crack-tip stress concentration and material heterogeneity, we discuss how disorder imprints itself on the spatial and statistical structure of the fracture. Our findings motivate a continuum description of damage accumulation, that link diffuse failure events to crack-tip shielding, and offering insights into the formation and scaling of the process zone - the region of distributed damage that governs crack propagation.