Dislocation-based constitutive model of crystal plasticity for the size effect of single crystalline micropillar samples

Abstract

In this study, based on the Orowan equation and the principle of Bergstrom dislocation evolution, the plastic mechanical response of single crystalline micropillars is investigated by considering dislocation evolution. According to the single-arm source model, a physically revised Peirce-Asaro-Needleman (PAN) hardening model is proposed that can describe size-dependent hardening flow. The dislocation evolution parameters greatly affect the size-dependent plastic behavior of the single crystalline micropillars. Linking to the crystal plasticity finite element (CPFE) method, a physical plastic constitutive model with the framework of the CPFE method is proposed to solve the size-dependent boundary value problem. Compared with the results based on the original PAN hardening model, the proposed constitutive model can provide mechanical responses in different sizes, depending on the shear strain in each slip plane. If the non-friction condition between the rigid punch and the top surface of the pillar under uniaxial compression is considered, the results show that the shear band of the pillar mainly results from shear deformation on the slip plane with the maximum Schmid factor. Otherwise, the actual shear band deformation of the micropillars is complicated and combined with the other slip planes, that is, a multislip system. The results also indicate that friction affects size-dependent hardening.

Keywords

• bergstrom dislocation evolution
• orowan equation
• size effect
• constitutive equation
• elastic-plastic deformation