Critical Plane Search Method for Biaxial and Multiaxial Fatigue Analysis

Abstract

For complex cyclic loadings, stress- or strain-based critical plane search methods are commonly used for fatigue analysis of the structural components. Complex loadings can result in a non-proportional type loading in which it is difficult or impossible to determine the plane with maximum shear stress/strain amplitude. ASME Sec VIII, Div-3 fatigue analysis for non-welded components is a shear stress based fatigue analysis method and, for non-proportional loading, uses the critical plane search method to calculate the plane with maximum shear stress amplitude. For a two-dimensional non-proportional stress state, analytical stress transformation equations can be used to calculate the shear stress or strain amplitude on any plane at a point. The shear stress range on each plane is the difference between the maximum and minimum shear stress. For a three-dimensional stress state, shear stress amplitude calculations are much more complicated because the shear stress is a vector and both magnitude and direction change during the loading cycle. In ASME VIII-3, the maximum shear stress range among all planes, along with the normal stress on the plane, is used to calculate the stress amplitude. This paper presents a method to calculate the shear stress/strain amplitude using 3D transformation equations. This method can be used for any stress- or strain-based critical plane search method. This paper also discusses ASME proportional and non-proportional fatigue analysis methods in detail.