Incremental strain gradient plasticity model and torsion simulation of copper micro-wires

Experimental observations show that the torsional deformation of copper micro-wires exhibits obvious sample and grain size effects. In this work, based on the framework of the cyclic plastic J2 flow rule, an incremental higher-order strain gradient constitutive model is established to describe the size effect observed in the torsional deformation of copper micro-wires. A novel kinematic hardening evolution rule is constructed in which the coupling effect of sample and grain sizes on the plastic hardening has been considered. In terms of numerical implementation, a finite element iterative algorithm which can independently solve the gradient field and plastic strain increment is proposed. Finally, the proposed model is implemented into the finite element software ABAQUS using a three-dimensional user-defined element and user-defined material subroutine. Simulated results show that the proposed model can capture the size-dependent torsional deformation of copper micro-wires since both the effects of sample and grain sizes are considered reasonably. This provides a good basis for the combination of strain gradient plasticity theory and cyclic plasticity constitutive model.