Uncoupled numerical method for fracture analysis

Abstract

An uncoupled numerical method for the analysis of dynamic crack propagation is proposed. The approach consists of two main steps. Firstly, the internal stresses in the intact, unfractured, elastic body are calculated with the use of the finite element method. In this calculation it is assumed that no cracks are present and that fracture does not occur. Secondly, a theoretical crack is initiated and possible crack paths are derived from the elastic stress data. The stress-intensity factors for the planar fracture modes I and II, for the anti-plane mode III, and for the bending modes 1 and 2 are calculated from the well-known, linearized expressions for arbitrary, slightly curved cracks in thin plate-like and shell-like structures. The direction and speed of crack propagation are determined from a dynamic fracture criterion based on the energy release rate. Several applications of the uncoupled numerical method are presented, concerning standard fracture specimens loaded by tensile forces and bending moments, a single-edge notched beam loaded by shear forces, and a three-dimensional cylindrical tube loaded by torsional moments. Good agreement with both experimental and numerical results from the literature has been obtained. The major advantages of the uncoupled approach are its ease-of-use and the limited computational effort.