Numerical Simulation on Fracture Formation on Surfaces of Bi-Layered Materials

Abstract

Fracture formation on surfaces of bi-layered materials is studied numerically. A simplified two-layered materials model like growing tree trunk is present. This work is focused on patterns of fractures and fracture saturation. We consider the formation of crack pattern in bark as an example of pattern formation due to expansion of one material layer with respect to another. As a result of this expansion, the bark stretches until it reaches its limit of deformation and cracks. A novel numerical code, 3D Realistic Failure Process Analysis code (abbreviated as RFPA3D) is used to obtain numerical solutions. In this numerical code, the heterogeneity of materials is taken into account by assigning different properties to the individual elements according to statistical distribution function. Elastic-brittle constitutive relation with residual strength for elements and a Mohr-Coulomb criterion with a tensile cut-off are adopted so that the elements may fail either in shear or in tension. The discontinuity feature of the initiated crack is automatically induced by using degraded stiffness approach when the tensile strain of the failed elements reaching a certain value. The different patterns are obtained by varying simulation parameters, the thickness of the material layer. Numerical simulation clearly demonstrates that the stress state transition precludes further infilling of fractures and the fracture spacing reaches constant state,i.e. the socalled fracture saturation. It also indicates that RFPA code is a viable tool for modeling fracture formation and studying fracture patterns.