Expected position of the fatigue fracture plane by using the weighted mean principal Euler angles

The expected principal stress axes under multiaxial fatigue loading are determined by averaging the instantaneous Euler angles through suitable weight functions. Then, the fracture plane position is derived from such expected principal stress directions. Three weight functions based on stress parameters are discussed by comparing theoretical predictions with available test results related to six metallic materials under proportional and non-proportional loading. The fatigue fracture plane position under multiaxial loading may be established on the basis of the averaged direction of the maximum principal stress, with such a direction deduced by employing proper weight functions.