Crack initiation and growth in contact problems

The problem of crack initiation and growth in contact problems is studied by the strain energy density theory. This is accomplished by considering each point of the body as a possible source of crack initiation. The direction of crack initiation is determined by calculating the minimum value of the strain energy density function along a circular core area surrounding the point. The crack initiates from the point with the maximum of the local minimum values of the strain energy density function. Considered is a circular disc subjected to two equal and opposite forces and a circular cylindrical body pressed by a cylindrical punch. The stress field for the first case is obtained from the classical elasticity solution, while a finite element code is used for the second case. The locations of fracture initiation and the subsequent fracture trajectories for fast unstable fracture are determined.