Modeling size effects in microwire torsion: A comparison between a reduced-order micromorphic and the CurlFp strain gradient crystal plasticity models

The size-dependent response of metallic microwires under monotonic and cyclic torsion is modeled using a reduced-order strain gradient crystal plasticity model involving a single scalar micromorphic variable. It is compared with the response predicted by the CurlF p model proposed in Kaiser and Menzel (2019a), which is based on the full dislocation density tensor. It is shown that in cyclic nonuniform plastic deformation, 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 the dislocation induced back-stress component. The arising size effect in the monotonic torsion tests is described by the normalised torque T /R3 as a function of the ratio of the radius of the microwire R and material length scale l. In the size-dependent domain, characterized by an inflection point on the corresponding curve, the scaling law T/R^3 ∼ (R/l)^n can be identified. Explicit relations are found for the power n and compared for the reduced-order micromorphic and Lagrange multiplier based models.
(PDF, DOI)