Fracture spacing in layered materials and pattern transition from parallel to polygonal fractures

We perform three-dimensional simulations of fracture growth in a three-layered plate model with an embedded heterogeneous layer under horizontal biaxial stretch (representing stretch from directional to isotropic) by the finite element approach. The fractures develop under a quasistatical, slowly increasing biaxial strain. The material inhomogeneities are accounted for by assigning each element a failure threshold that is defined by a given statistical distribution. A universal scale law of fracture spacing to biaxial strain in terms of principal stress ratio is well demonstrated in a three-dimensional fashion. The numerically obtained fracture patterns show a continuous pattern transition from parallel fractures, laddering fracture to polygonal fractures, which depends strongly on the far-field loading conditions in terms of principal stress ratio lambda = sigma(2)/sigma(1), from uniaxial (lambda = 0), anisotropic (0 < lambda < 1) to isotropic stretch (lambda = 1). We find that, except for further opening of existing fractures after they are well-developed (saturation), new fractures may also initiate and propagate along the interface between layers, which may serve as another mechanism to accommodate additional strain for fracture saturated layers.