Micromechanical consideration of tensile crack behavior based on virtual internal bond in contrast to cohesive stress

Abstract

A modified version of the virtual internal bond model (VIB) is presented. This involves the introduction of a R-bond restricting the relative rotation freedom of pairwise mass particle. Such a modification allows the VIB model to consider arbitrary values of the Poisson ratio. A linear elastic cohesive law considering both the R-bond and L-bond are assumed. The constitutive relationship is derived using the Cauchy–Born rules. The derived constitutive associates the bond stiffness with the Young’s modulus and Poisson ratio of materials. This gives the bond stiffness in terms of the Young’s modulus and Poisson ratio of materials. The modified VIB model is then used to analyze the tensile crack behavior. In contrast to the cohesive stress method, the deformation-governed concept will be used. The local materials failure is assumed to coincide with the reduction of the bond density due to the local deformation rather than by the local cohesive stress. A phenomenological relationship between the bond density and the deformation is established. The criterion which is applied to determined crack initiation and propagation is built into the constitutive model. As an example, the method is used to study the crack initiation and propagation behavior under tensile loading.