FINITE STRESS-CONCENTRATIONS AND J-INTEGRALS FROM NORMAL LOADS ON A PENNY-SHAPED CRACK

The stress concentrations around a penny-shaped crack contained in a three-dimensional body under axi-symmetric loads are analyzed in this paper. The basic solution with infinite stress concentrations around the crack fringe is derived using the Legendre's function. Then, a method is presented to construct a transition zone (similar to the process zone or the softening zone) around the crack tip, where the crack opening displacement appears accompanied with finite stress concentrations. Finally, the J-integrals Ja and Jb (the rates of decrease of total potential energy with respect to the real crack length and the transition zone length in an elastic body, respectively) are revealed. It shows that the model may appropriate to fracture mechanics for soil, rock or concrete materials.