MULTISCALE MODELING OF MICROCRYSTALLINE MATERIALS

Abstract

Materials with micrometer dimensions and their distinct mechanical properties have generated a great interest in the material science community over the last couple of decades. There is strong experimental evidence showing that microcrystalline materials are capable of achieving much higher yield and fracture strength values than bulk mesoscopic samples as they decrease in size. Several theories have been proposed to explain the size effect found in micromaterials, but a predictive physics-based model suitable for numerical simulations remains an open avenue of research. Since the successful design of micro-electro-mechanical systems (MEMS) and novel engineered materials hinges upon the mechanical properties at the micrometer scale, there is a compelling need for a quantitative and accurate characterization of the size effects exhibited by metallic micromaterials. This work is concerned with the multiscale material modeling and simulation of strength in crystalline materials with micrometer dimensions. The elasto-viscoplastic response is modeled using a continuum crystal plasticity formulation suitable for large-deformation problems. Crystallographic dislocation motion is accounted for by stating the crystal kinematics within the framework of continuously distributed dislocation theory. The consideration of the dislocation self-energy and the step formation energy in the thermodynamic formulation of the constitutive relations renders the model non-local and introduces a length scale. Exploiting the concept of total variation we are able to recover an equivalent model that is local under a staggered approach, and therefore amenable to time integration using variational constitutive updates. Numerical simulations of compression tests in nickel micropillars using the proposed multiscale framework quantitatively capture the size dependence found in experimental results, showcasing the predictive capabilities of the model.