Energy release rate in the presence of residual and thermal stresses

This paper presents a thermodynamic formulation of the J-integral in the presence of residual stress and thermal stress. First, the Helmholtz free energy and the internal energy are derived considering residual and thermal stresses. With the use of these thermodynamic potentials, the energy release rate, J-integral, is derived for thermo-elastic body with residual stresses in isothermal condition. It is verified that the resulting J-integral in the absence of residual stress is identical with the definition of J reported earlier. Furthermore, it is shown that the J-integral in the presence of residual and thermal stresses does not depend on the integration path and domain.