A Practical Method to Calculate Elasto-Plastic J-Integral

Abstract

For Ramberg-Osgood elasto-plastic material, under the premise that integration path is limited through the Gaussian integration points, the finite element expressions of the J- integral were deduced in detail. Using the method of coordinate transformation, integration was conducted through the plane rs of the shell element local coordinate system rst (t for shell element thickness direction). The integration points on mid-surface of the shell element were considered. Thus the finite element expressions of the J- integral can be applied to shell elements, the J- integral calculation problem of the shell structure with crack can be solved. A lot of standard sample results comparisons show that the calculation precision of the method proposed in this paper meet the requirements of engineering. Finally, the J- integral of a pressure vessel (a cylindrical shell with a hole and unilateral axial crack) was calculated. The obtained results are recognized by a pressure vessel research institution and referenced in the design. In the conventional finite element calculation, users can, at the same time, obtain the J- integral of the component with crack. So the method in the paper has strong practicability and high engineering application value.