On the Calculation of Stress Intensity Factors and $J$-Integrals Using the Submodeling Technique

In the present paper, calculations of the stress intensity factor (SIF) in the linear-elastic range and the $J$-integral in the elastoplastic domain of cracked structural components are performed by using the shell-to-solid submodeling technique to improve both the computational efficiency and accuracy. In order to validate the submodeling technique, several numerical examples are analyzed. The influence of the choice of the submodel size on the SIF and the $J$-integral results is investigated. Detailed finite element solutions for elastic and fully plastic $J$-integral values are obtained for an axially cracked thick-walled pipe under internal pressure. These values are then combined, using the General Electric/Electric Power Research Institute method and the reference stress method, to obtain approximate values of the $J$-integral at all load levels up to the limit load. The newly developed analytical approximation of the reference pressure for thick-walled pipes with external axial surface cracks is applicable to a wide range of crack dimensions.