Non-Uniform Distribution of Energy Density Near a Crack Tip in the Framework of HRR Model

The energy density distribution in the frame work of HRR model (Hutchinson, 1968a; Rice and Rosengren, 1968) is obtained. The analysis indicates that within a sector ahead of a crack, the hydrostatic stresses are very high while the effective stresses are very small, near to the yield stress, so the elastic strain energy density of volume deformation prevails in the forward sector. However, this sector is nearly a "rigid area" in HRR field (Hutchinson, 1968b). Meanwhile, a large amount of plastic dissipation distributes out of the sector, where the plastic dissipation makes up the main part of the J value. The high constraint means that the high elastic volume energy is stored in the local sector, thus the one-parameter fracture criterion based on J is invalid.