Damage mechanics incorporating two back stress kinematic hardening constitutive models

In the present work, damage mechanics is incorporated into the plastic constitutive relation in order to describe the localized plastic deformation and damage experienced in a tensile test of the high strength VascoMax 300 steel specimen. The results obtained on the VascoMax 300 steel are also compared with 1080 steel. In order to identify the effect of damage on the shear band formation, one-dimensional simple shear analysis is carried out with non-isothermal visco-plasticity using a finite difference modeling assuming isotropic hardening. The results depicts that the damage evolution within a work piece accelerates the plastic deformation localization and the temperature variation plays less significant role in a shear band formation compared with damage mechanics. A coupling between damage mechanics and isothermal rate independent plasticity is proposed using the kinematic hardening constitutive relation which in turn is formulated by combining the nonlinear Armstrong–Frederick rule and the linear Phillips rule. The effects of the various hardening parameters on plastic deformation localization are investigated within the J2 deformation theory. The material with a lower hardening exponent results in a rapid shear band formation, and the results from the numerical analysis reflected closely with the micro-structures around the fractured regime. However, the material with a higher hardening exponent is less affected by damage evolution in the plastic deformation behavior. Moreover, as the nonlinear strain rate description in the back stress evolution becomes dominant, the plastic strain localization becomes intensified as well as damage. It is also possible to describe a wide range of plastic deformation and damage behavior by selecting a simple combination of two back stress evolution rules.