Microstructural finite element modeling of metals

The mechanical properties of metals have been investigated.This has been done by creating micromechanical models based onthe microstructural data available for the materials ofinterest. Thus, models containing a grain structure withappropriate constitutive equations have been created. Periodiccells on the micrometer scale have been shown to be sufficientto represent the materials, when macroscopic properties areevaluated. Micromechanical modeling by the finite element method can bedivided into three different parts: geometry, boundaryconditions and constitutive equations. These parts have more orless been illustrated and used in the seven appendedpapers. The geometric outlines of the grain structures arerepresented by the Voronoi algorithm. Hence, polyheadrons areused to represent three-dimensional grain structures, whiletwo-dimensional models are represented by polygons. Twodifferent approaches are used. Either, space is divided intograins by application of the Voronoi algorithm. Thus, grainboundaries are represented by planes or lines. Thereafter, thegrains are meshed with an adaptive mesh generator.Alternatively, a mesh is created before the Voronoi algorithmis applied. The grain boundaries will in the latter case bekinky, since the outline of the predefined mesh is followedwhen grains are formed. The former method results in smallerelements close to grain boundaries. This fact is used to studytwo-phase ferrite-pearlite steels, since pearlite and the smallelements have the same location. Representative volume elements (RVEs) of the materials arecreated by considering a sufficient number of grains, and it isshown how this number depends on anisotropy and loading. Toavoid edge effects in the models, the volume elements are madeperiodic and periodic boundary conditions are utilized toconstrain the models. In the present implementation of periodicboundary conditions, average stresses and/or average strainsare prescribed over the periodic cell. A non-local crystal plasticity theory that incorporates slipgradients in the hardening has been implemented. It is shownthat this concept can be used to account for the effect\u93smaller is harder\u94. Furthermore, the effect ofnon-local plasticity on the deformation of a free surface isinvestigated in detail. It is shown that the surface roughnessdecreases as an effect of strain gradients. Lastly, all numerical work done here aims to mimicexperiments that have been performed. This includes microscopicinvestigations, tensile testing, investigations by atomic forcemicroscopy, but also experimental data from the literature.NR 2014080