Cyclic plasticity modeling and finite element analyzes of a circumferentially notched round bar under combined axial and torsion loadings

A cyclic plasticity model suitable for fatigue damage modeling of metallic structures is presented and its finite element (FE) implementation is described within the small strain plasticity framework. The model uses the von Mises yield surface in stress space whose evaluation follows an Armstrong–Frederick type of nonlinear kinematic hardening rule, and the normality hypothesis in conjunction with the associative flow rule is assumed. An incremental implicit-iterative algorithm was employed for the numerical solution of resulting stress–strain equations, and the continuum tangent obtained from plasticity model was used in FE implementation. The developed FE computational model is applied in the cyclic deformation analysis of a circumferentially notched specimen in combined axial force-torsion loading tests. The computed notch root deformations were compared with measured notch root strain histories. An assessment of model predictions showed that non-proportional loading tests have been simulated with a good accuracy. The computed strain loops were in accord with experimental data and matched qualitatively with measured shear – axial strain histories irrespective of loading path of the test. In proportional balanced torsion-axial loading, the nonlinear shear strain – axial strain loops were also simulated properly. The errors in notch root strains were dependent on the loading path shape, and compared to axial strains, the shear strain errors were relatively greater. The computer solution times were also acceptable.