A Continuum Model of Deformation and Damage for API X70 Steel Based on the Theory of Strain Gradient

This work shows the results of a continuum model of deformation and damage for API X70 steel based on the strain gradient theory. The model is developed according to the continuum mechanics of the elastic/viscoplastic framework. The constitutive equations of the model include the dislocation theory according to the roles of the statistically stored and geometrically necessary stored dislocation densities during plastic deformation. In addition, effects of nucleation and growth of voids are considered within the constitutive equations as a ductile failure based on a classical isotropic damage model. Then, the model is examined for scale and strain rate effects. The developed model is implemented into LS-DYNA® by writing a subroutine within USER_DEFINED_MATERIAL_MODELS (UMAT). A ASTM tensile test is simulated to examine the validity of the model. The results show a good agreement with experimental data found in the literature.