A parameter to represent a local deformation mode and a fracture criterion based on the parameter in ordinary-state based peridynamics

Abstract

It is known that a local deformation mode affects the fracture behavior. First, a parameter that represents the deformation mode is defined for a fracture criterion that can consider the deformation mode in ordinary state-based peridynamics. This parameter is analogous to stress triaxiality in conventional continuum mechanics. The calculated values of the parameter agree well with the theoretical values under uniaxial compression, pure shear, uniaxial tension, and equi-biaxial tension. Then, modified fracture strain by a function using the parameter is proposed as a fracture criterion. The intended fracture strains of uniaxial tensioned cubes and those of equi-biaxial tensioned cubes were well reproduced by calculations with the criterion. Further, the intended ratio of fracture strain of a uniaxial tensioned round bar to that of an equi-biaxial tensioned thin plate was reproduced by calculations with the criterion. In a pipe bending simulation, the crack propagation behavior was reproduced by the proposed criterion.