A CDM-like constitutive law for predicting degradation of strength and ductility of steel subjected to cyclic loading

This paper presents a continuum-damage-model-like constitutive law embedding cohesive cracks with plasticity-induced damage to represent the degradation of strength and ductility of steel under cyclic loading. The proposed constitutive law accommodates an arbitrary hyperelasticity-based plastic model with the use of the deformation gradient multiplicatively decomposed into separation-induced, elastic and plastic parts, and incorporated with an additional isotropic hardening rule endowed with a memory surface. While the elastic–plastic deformation along with isotropic and kinematic hardening is represented by a Hencky-type model, the separation-induced deformation gradient due to material separation is employed to embed an arbitrary cohesive traction separation law (CTSL) into the hyperelasticity-based plastic model. Also, a plasticity-induced damage variable is added to the selected CTSL to degrade the critical energy release rate. In addition, a new material constant is introduced to adjust the ratio between the critical values of cohesive traction and material separation width in the CTSL. On the other hand, the additional hardening rule depending on memory surface is appended in conjunction with the conventional isotropic and kinematic hardening rules to reflect the difference in plastic deformation with various ranges of cyclic loading. Several experiments are conducted to identify the material parameters and verify the validity of the proposed model. By reference to the experimental results, the capability of our proposed constitutive law is demonstrated in predicting the degradation of tensile strength and breaking elongation of a steel after cyclic loading.