On the application of polar representation for investigating high and low cycle fatigue of metals

Stress and strain analyses on eight materials tested under multiaxial stress- and strain-controlled conditions are performed. Stress and/or strain fields are generated using plane stress-strain transformation. Maximum stress and strain loci are plotted in polar diagrams. For low cycle fatigue tests, normal stress and shear strain are normalized with their yield counterparts to allow plotting them in one polar diagram. The roles of shear strain and normal stress in fatigue can be examined using such a representation. For high cycle fatigue, normal and shear stresses are plotted in a single polar diagram. Observed crack planes are superimposed on all polar diagrams. In general, observed cracks are found to be aligned with the plane of both maximum shear strain and normal stress. Polar representations of Fatemi-Socie fatigue damage for strain-controlled tests show that significant numbers of planes experience high damage value especially for 90° out-of-phase loading.