Comparison of several path independent integrals including plasticity effects

Proceeding from the work of Eshelby, a path independent integral, J, is developed which is the negative of the rate of change of total energy for a material characterized by an incremental plasticity model. This integral is compared to several well known integrals to indicate that those integrals, for such a material, are deficient in certain terms with regard to the rate of change of total energy. The various integrals are compared on the three point bend specimen. The J integral was found to be very sensitive to the finite element idealization and limited studies indicate that under certain conditions that other more easily calculated integrals can be substituted for J. 24 ref.--AA