\(J^*\) integral of the specific deviator strain energy and its application (Q1890329)

The authors propose a path-independent line integral \(J^*\). The motive force of crack growth in elastic-plastic case comes from the deviator strain energy release due to the volume strain energy, and does not contribute to crack growth. The authors discuss the problem of critical plane-crack growth. The conservation of the \(J^*\) integral is proved strictly, and \(J^*\) integral is formulated for mode-I crack. It is shown that under the linear elastic condition, the \(J^*\) integral equals to release rate of deviator strain energy. The considered numerical examples (bending and tension of a beam with edge crack and tension of a beam with center crack) agree well with the corresponding examples from the literature.