Elastic-plastic analysis of crack in thermally-loaded structures

The stress or strain field near a crack-tip in a thermally-loaded structure has the HRR singularity and its amplitude is determined by the path-independent $\text{J}\text{?}\text{-}\text{integral}$. The $\text{J}\text{?}\text{-}\text{integral}$ is an extension of Rice's $\text{J-}\text{integral}$ and is related to the energy-release rate in thermal stress field. The finite element calculations have been carried out for a plate and a cylinder subjected to transient thermal loading with the temperature dependence of material properties taken into consideration. The computed $\text{J}\text{?}\text{-}\text{values}$ are almost path-independent as predicted theoretically. In an elastic problem, the stress intensity factor estimated from the $\text{J}\text{?}\text{-}\text{integral}$ agrees well with the analytical one. It is concluded that the $\text{J}\text{?}\text{-}\text{integral}$ has a potential ability to evaluate the integrity of structures such as nuclear pressure vessies that are subjected to thermal loading as well as mechanical one.