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Abstract: When nanoindenting dislocation-free regions of single crystals a so-called pop-in phenomenon is commonly observed. Molecular dynamics (MD) studies have revealed homogeneous nucleation of dislocations in a perfect crystal as a mechanism causing such pop-in behavior. In this work we transfer this knowledge gained on the atomic scale into a dislocation nucleation model that is applied within a dislocation density based crystal plasticity description. Furthermore, we develop a non-local formulation of a crystal plasticity model that is devised to yield a valid description of plasticity also in situations where the dislocation density is small or even vanishing and where conventional plasticity models fail. This is accomplished by studying the evolution of statistically stored and geometrically necessary dislocation densities separately. We apply this non-local crystal plasticity model to investigate the evolution of dislocation densities in the early stages of nanoindentation. The results of our continuum model show good agreement with MD simulations for cases where nanoindentation into an initially dislocation-free crystal is studied, i.e. where a pop-in occurs when the critical stress underneath the indenter reaches the critical value for homogeneous dislocation nucleation. After thus validating our model we study the influence of pre-existing homogeneous and local dislocation densities. Both cases show a good qualitative agreement with recent experimental findings and it is concluded that pre-existing local dislocations densities reduce the load at which a pop-in occurs and – more importantly – change the mechanism from homogeneous dislocation nucleation to rapid dislocation multiplication. In general, our results show that continuum plasticity formulations can be extended such that applications to nanoscale volumes become possible. [Copyright &y& Elsevier]

Abstract: The glide of screw dislocations with non-planar dislocation cores dominates the plastic deformation behavior in body-centered cubic iron. This yields a strong strain rate and temperature dependence of the flow stress, the breakdown of Schmid’s law and a dependence of dislocation mobility on stress components that do not contribute to the mechanical driving force of dislocation glide. We developed a constitutive plasticity model that takes all these effects into account. The model is based on the crystal plasticity approach and parameterized by performing molecular statics calculations using a semi-empirical potential. The atomistic studies yield quantitative relations between local stress tensor components and the mobility of dislocations. Together with experimental stress–strain curves obtained for two different orientations of iron single crystals taken from the literature, the constitutive law is completely parameterized. The model is validated by comparing numerical single crystal tension tests for a third orientation to the equivalent experimental data from the literature. We also provide results for the temperature and strain rate dependence of the new atomistically informed constitutive model. [Copyright &y& Elsevier]

Abstract: Several strain gradient plasticity formulations have been suggested in the literature to account for inherent size effects on length scales of microns and submicrons. The necessity of strain gradient related terms render the simulation with strain gradient plasticity formulation computationally very expensive because quadratic shape functions or mixed approaches in displacements and strains are usually applied. Approaches using linear shape functions have also been suggested which are, however, limited to regular meshes with equidistanced Finite Element nodes. As a result the majority of the simulations in the literature deal with plane problems at small strains. For the solution of general three dimensional problems at large strains an approach has to be found which has to be computationally affordable and robust. For this goal a strain gradient Finite Element approach is suggested where elements with linear shape functions are applied in combination with a patch projection technique well known from error indication and adaptive mesh procedures. This approach is applied to a strain gradient crystal plasticity formulation where strain gradients are incorporated in terms of geometrically necessary dislocation densities. Simulation results of size dependent problems, including laminates in simple shear and a three dimensional contact problem, are presented and discussed to assess the performance of the suggested approach. [Copyright &y& Elsevier]