Elastic and plastic fracture analysis of a crack perpendicular to an interface between dissimilar materials

Abstract

Elastic and plastic fracture analysis of a Mode I crack perpendicular to an interface between dissimilar materials is carried out. Continuously distributed dislocations are used to simulate the crack. The simulation will cause singular integral equations with Cauchy kernel. By solving the singular integral equations numerically, the effects of crack depth (distance from the interface to the crack middle point) and Dundurs' parameters on the Mode I stress intensity factor are investigated systematically. Then, based on the Dugdale model, the plastic zone size, and the crack tip opening displacement of the crack under uniform loadings are investigated. The effects of uniform loadings, crack depth, and Dundurs' parameters on the plastic zone size and the crack tip opening displacement are examined. Numerical results show that when the crack is embedded in a stiffer material, the values of both the normalized plastic zone size and the normalized crack tip opening displacement are larger than 1. On the contrary, if the crack is embedded in a softer material, the values of both the normalized plastic zone size and the crack tip opening displacement are less than 1.

Fracture analysis-based mode-I stress intensity factors of crack under fracture grouting in elastic–plastic soils

“…Theoretical investigations three-dimensional finite boundary crack problems began in late 1980s, Nakamura et al 7 , 8 based on very detailed full-field finite element analysis of the near tip region of a thin isotropic elastic/ductile plate, the three-dimensional stress state in the vicinity of a through-crack front is characterized. More recent analytical solution to depict the relationship among out-of-plane constraints, three-dimensional J -integrals and stress intensity factors have been presented by Yi 9 , 10 and· Wang 11 , who combined with three-dimensional Maxwell stress functions, the principle of minimum complementary potential energy and three-dimensional J -integrals, respectively. Simple solution methods solving the SIFs of elastic–plastic soils under fracture grouting has attracted the attention from many researchers.…”