Cyclic plasticity in three-dimensional notched components under in-phase multiaxial loading at R = −1

•The incremental cyclic plasticity theory is extended to the study of three dimensional effects.•The analytical frame has been validated considering bi-dimensional problems.•The analytical frame has been modified to consider the out-of-plane 3D-effects.•A link between the strain energy density and the area of the hysteresis loop has been found.

In this work a comprehensive theoretical and numerical study on the cyclic elastic–plastic notch stress and strain distributions is carried out. In more detail, the incremental cyclic plasticity theory, already proposed by other authors to determine the actual stress and strain state arising in two-dimensional or axis-symmetric notched components, is extended to the study of three dimensional effects at the tip of rounded notches in plates of finite thickness. The analytical frame is initially validated considering some bi-dimensional problems and later modified to consider the out-of-plane 3D-effects. Different notch geometries and loading conditions are investigated, such as axis-symmetric specimens weakened by a circumferential U-notch, subjected to cyclic torsional and multiaxial (tension–torsion) in-phase loading, and plane specimens with finite thickness, weakened by rounded V-notches and subjected to cyclic mode II loading. A nominal load ratio R = −1 has been taken into account in all cases. Theoretical results based on the incremental cyclic plasticity theory are compared with time-consuming elastic–plastic finite element analyses carried out with a commercial FE code showing a very satisfactory agreement.Finally, a link between the averaged strain energy density (SED) criterion and the area inside the hysteresis loops tied to the different stress and strain components acting at the notch tip has been investigated.