| Contact mechanics is critical to understanding some tribological phenomena such as friction, wear, contact fatigue, adhesion, and sealing. The morphology of a rough surface is essential for predicting contact area, pressure, and subsurface stress and strain fields. At the microscopic level, real machined surfaces are not perfectly smooth; hence contact occurs at discrete contact spots, where the contact pressure and subsurface stresses tend to be extremely high, often causing plastic deformation near these spots.; Recently, advances in computer science and technology have allowed investigators to simulate computationally contact problems with real measured surfaces. The finite element methods (FEM) and semi-analytical methods (SAM) are two main techniques employed in these numerical models. Typically, SAM is computationally faster than FEM, especially for three dimensional (3D) rough contacts.; Previous SAM models only consider a purely elastic or elastic-perfectly plastic constitutive law. However, for real rough surfaces these assumptions may be inaccurate for two reasons: first, since the stress level is concentrated and extremely high at the local contact spots, it will undergo some level of plastic deformation even under the lightest of loads; second, most metal or alloy materials exhibit plastic hardening behavior during the process of plastic deformation. Thus it is more appropriate to consider this hardening behavior in the elastic-plastic contact model.; In this thesis, a modified SAM model is developed to simulate 3D elastic-plastic contact. A purely elastic contact field and a residual field arising from the plastic deformation are simulated to gain iteratively the final approximate solution. This approach can simulate elastic-plastic contact with different hardening behaviors, which is an advantage over other SAM methods. Some sophisticated mathematical techniques, such as the fast Fourier Transform and the fast convergence method, are applied to increase the speed of computation.; 3D smooth and rough contact problems are simulated and analyzed using the developed model. The simulation accurately predicts the development of area and magnitude of the plastic strain along the loading process. Effects of the topography of real machined surfaces and hardening behavior; upon the distribution of contact pressures, contact area, and subsurface fields are analyzed. |
