Critical Plane Orientation Under Biaxial Fatigue Loading Conditions

The thermal loadings in the pipe wall of the residual heat removal systems in pressurized water reactors can be generally regarded as biaxial fatigue loadings, which may lead to multidirectional thermal fatigue cracks on the inner surface of the pipe wall. In this paper, the orientation of the critical plane defined by maximum damage under biaxial fatigue loading conditions are investigated by analytical and computational approaches. The analytical solutions of the critical plane orientation for the Matake's and Fatemi–Socie's criteria are first derived using an elastic material law. The computational results obtained from Code_Aster are used to validate the analytical solutions. The analytical solutions of the critical plane orientation using an elastic material law appear to be consistent with the computational results obtained from Code_Aster by using an elastic material law or a Chaboche-type elasto-plastic material law. An analytical derivation is performed to investigate the effect of the plasticity on the critical plane orientation by using a simple elasto-plastic material law with one linear isotropic hardening term. It is concluded that for the loading path of applied biaxial stress considered in this study where the maximum and minimum stresses in both directions are reached simultaneously, the critical plane orientation is not effected by the plasticity within the considered elasto-plastic material laws.