On the Role of Interfaces in Small Scale Plasticity

Abstract: The strong evidence for a size dependence of plastic deformation in polycrystalline metalsis the basis for the research presented in this thesis. The most important parameter for this, and arguably also the most well known, is the grain size. As the size of the grains in a microstructure is decreased the yield stress increases. This is known as the Hall–Petch relation and have been confirmed for a large number of materials and grain sizes. Other structural dimensions may also give rise to a similar strengthening effect, such as the thickness of films and surface coatings, the widths of ligaments and localization zones and the diameter of thin wires, to mention a few. The work presented in this thesis is shown to be able to model these effects.Size dependent plastic deformation have here been modeled in a continuum mechanical setting by an extension of the standard theory of solid mechanics. Specifically, the work in this thesis is formulated in terms of the higher order strain gradient plasticity (SGP) theory presented by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids, 52]. This allows size dependent plasticity phenomena to be modeled and a yield stress that is proportional to the inverse of the geometric dimension of the problem is predicted.The ability to model interfaces have been of specific importance to the work presented here. The state at internal interface is shown, via a physically motivated constitutive description, to be of great importance to capture size effects. The surface energy at grain boundaries is shown to influence both the local and the macroscopic behavior. At the smallest scales an additional deformation mechanism have been introduced at the internal boundaries. This allowed the strengthening trend associated with decreasing grains size to be halted, in qualitative agreement with reported experiments on the behavior of ultrafine and nanocrystalline polycrystals. In the later part of the thesis the focus is aimed at modeling grains structures to bring some insight into the different regions of deformation mechanisms in relation to grainsize and interface strength. A deformation mechanism map for polycrystals is suggested based on the results from structures with both hexagons and log-normal size distributed Voronoi tessellations, and the implication of a statistical variation in grain size have been explored.A finite element implementation of the theory have been developed that is a fully implicit backward-Euler algorithm with tangent operators consistent with the stress update scheme, which give excellent convergence properties and is numerically very stable. Higher order finite elements have been implemented for modeling of both bulk material and internal interfaces. A plane strain version have been used to model metal-matrix composites and explore the implication of some of the more exotic features of the theory.