Modeling size effects in microwire torsion: A comparison between a Lagrange multiplier-based and a [formula omitted] gradient crystal plasticity model

Abstract

The size-dependent response of metallic microwires under monotonic and cyclic torsion is modeled taking a reduced-order strain gradient crystal plasticity approach involving a single scalar-valued micromorphic variable. It is compared with the response predicted by the CurlFp model proposed in Kaiser and Menzel (2019a), which is based on the complete dislocation density tensor. It is shown that, in cyclic non-uniform plastic deformation processes, the gradient of the scalar-valued internal variable in the reduced-order model predicts isotropic hardening in contrast to kinematic-type hardening produced by the CurlFp model due to a dislocation-induced back-stress component. The arising size effect in the monotonic torsion tests is described by the normalized torque T/R3 as a function of the ratio of the microwire radius R and the characteristic length scale ℓ. In the size-dependent domain, characterized by an inflection point on the corresponding curve, the scaling law T/R3∼(R/ℓ)n can be identified, and explicit relations are found for the power n. The relative evolution of Statistically Stored Dislocation (SSD) and Geometrically Necessary Dislocation (GND) densities during torsion is described in detail.