Stiffness of Contacts Between Rough Surfaces

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal and lateral stiffnesses rise linearly with the applied load, and the load rises exponentially with decreasing separation between surfaces. Results for a wide range of roughnesses, system sizes and Poisson ratios can be collapsed using Persson's contact theory for continuous elastic media. The atomic scale response at the interface between solids has little affect on the area or normal stiffness, but can greatly reduce the lateral stiffness. The scaling of this effect with system size and roughness is discussed.Comment: 4 pages, 3 figure

Dislocation interactions with interfaces

In this dissertation work, our main focus was to investigate the interactions of dislocation with interfaces. Plastic deformation in polycrystalline materials and multi-layered metallic composites, on a microscopic scale, involve interaction of dislocations with grain boundaries and bi-material interfaces respectively. Towards the end of investigating the interaction of dislocations with bi-material interface, we have derived analytical expressions for the stress field due to an arbitrary dislocation segment in an isotropic inhomogeneous medium. We have developed a new approach as compared with attempts made in the literature. One of the main advantages our derivation is separation of solution into homogeneous and image parts which facilitates an easy modification of existing dislocation dynamics simulation codes to incorporate the image stress effect. In the case of polycrystalline materials, as grain boundaries are major obstacles to plastic deformation, it is of fundamental importance to study the interactions of dislocations with grain boundaries. Towards this goal, in chapter four, we have investigated the basic phenomena of transmission of dislocation through a pure tilt wall. In this work, we have studied the structure of the symmetric tilt wall acquired after transmission of several dislocations and modeled the structures to which it relaxes. In chapter five, digressing from the main theme of the dissertation, we have studied the kinematic and thermodynamics effect of representing discrete dislocations in terms of continuously distributed dislocations. In this work, we have considered infinite stacked double ended pile-ups in an isotropic elastic homogeneous medium. The error in number of dislocations, microstructural energy and slip distribution between discrete and semi-discrete representation was quantified. The asymptotic expressions are derived and threshold values of certain key parameters are also deduced. In the appendix, we have investigated the deformation of single crystal micropillars under uniaxial compression using a multi-scale model for plasticity. Our simulation results are qualitatively and quantitatively comparable with that of experiments. Dislocation arm operation was found to be the prominent mechanism to plastic deformation in micron to submicron size specimens. The observed strain hardening is attributed to the formation of entangled dislocation structures and stagnation of dislocations

Numerical analysis of plane cracks in strain-gradient elastic materials

The classical linear elastic fracture mechanics is not valid near the crack tip because of the unrealistic singular stress at the tip. The study of the physical nature of the deformation around the crack tip reveals the dominance of long-range atomic interactive forces. Unlike the classical theory which incorporates only short range forces, a higher-order continuum theory which could predict the effect of long range interactions at a macro scale would be appropriate to understand the deformation around the crack tip. A simplified theory of gradient elasticity proposed by Aifantis is one such grade-2 theory. This theory is used in the present work to numerically analyze plane cracks in strain-gradient elastic materials. Towards this end, a 36 DOF C1 finite element is used to discretise the displacement field. The results show that the crack tip singularity still persists but with a different nature which is physically more reasonable. A smooth closure of the structure of the crack tip is also achieved