A 3D Distributed Dislocation Loop Model Of Nanoindentation Of Single Crystals And Study Of Interaction Between Dislocation Loops And Free Surfaces

Motivited by the elastic theory of three-dimensional dislocation loop in anisotropic media, a model of nanoindentation of anisotropic single crystals is established and the interaction of dislocation-free surface in anisotropic single crystal films is investigated. Using the elastic fields induced by 3D dislocation loops in anisotropic materials, this thesis has performed two problems as follows:1. An anisotropic dislocation loop model is proposed for simulation of nanoindentation of single crystals based on the recently available solution of the elastic displacement and stress fields due to a polygonal dislocation within an anisotropic homogeneous half-space. The present investigation is a direct extention of the approach established by Mura et al., and its recent application to triangular dislocation loop model, which is only capable of describing the indentation processes of isotropic materials, thus ruling out the possibility of characterizing the nanoindentation of elastically anisotropic single crystals. By following Mura's procedure, we adopt square and triangular prismatic dislocation loops as building blocks and with Burgers vectors normal to the free surface to simulate the Vickers and Berkovich indentation, respectively. However, we place all the dislocation loops within a semi-ellipsoidal volume rather than a semi-spherical region as adopted by Mura after analysing the existing simulation results based on dislocation density formulation. The nanoindentation is performed in [001] and [111] crystallographic directions employing Vickers and Berkovich indentors, respectively, and different magnitude of pile-up, sink-in and spring-back is observed in different directions, in addition that the residual stress is simulated after unloading in [001] crystallographic direction, clearly demonstrating the elastic anisotropy of the indented single crystals, hence an further improvement of Mura's model.2. Based on the superposition principle in discrete dislocation plasticity and the recently available solution of the elastic displacement and stress fields due to a polygonal dislocation loop within an anisotropic homogeneous full-space, the anisotropic elastic field induced by a 3D prismatic dislocation loop in a bounded thin single crystal film is obtained. The anisotropic image stress tensor and the corresponding tractions on the free surface, taken as a continuously distributed surface loading, are firstly calculated at the four Gaussian points of the 4-sided surface element attached to a hexahedron element by using the full-space solution due to the dislocation loop. And then the distributed loadings are equivalently reduced to those of nodes of the finite element. With the nodal loadings obtained and the elastic anisotropy of the bounded single crystal films taken into account, the FEM solver is invoked to calculate the solution corresponding to the image stress on the free surface. It is demonstrated that crystal elastic anisotropy plays an important part in the image stress induced 3D elastic fields. One of the main advantages of the present approach by employing the FEM over that relying on the FFT is the ability to calculate elastic fields in bounded and/or voided crystals without resorting to the condition of periodicity of the calculation region.