Analytical J-integral model for mode-I cracks in ductile materials with three-dimensional constraints

The J-integral is widely used in fracture analysis to characterize the stress-strain field at the crack tip. To describe the dimensionless relationships between the J-integral and the load for mode-I cracks in ductile materials, a novel model based on the energy density equivalence is proposed by introducing the three-dimensional constraint functions. The model-obtained relationships between the J-integral and the load are shown to be consistent with those obtained via finite element analysis. Moreover, the dimensionless relationships provided by the proposed model are shown to be only related to the constitutive parameters and independent of the geometric dimensions of mode-I cracks.