Scaling and spatial correlations in the quasibrittle process zone

We describe a scaling theory for the spatial distributions of damage and stress in the process zone of cracks propagating through quasibrittle materials. Brittle but disordered, these materials are ubiquitous in everyday life, including concrete, shell, and bone. Like in ductile materials, propagating cracks in quasibrittle materials have an extended process zone surrounding the crack surface, but unlike ductile materials this zone is comprised of a large complicated region of microfracture with correlated damage across many length scales. As a result, fracture in these materials exhibits strong sample size and shape dependence whose underlying nature evades standard analysis. Motivated by simulations of disordered fuse networks, our results work towards explaining the way damage and stress are correlated in and around the process zone and use renormalization group ideas first developed by Shekhawat et al. (PRL 110(18), 185505) to grapple with their system size dependence.