Quasi-Static Contact and Sliding of Crystalline Materials

The mechanical properties of solid-solid contact are important in both engineered systems and in the explanation of everyday phenomena. However, predicting those properties from the surface geometry is a challenge for several reasons. The surface of a solid is typically rough, exhibiting effectively random geometry extending from the long-wavelength topography down to the atomic-scale structure. The surfaces often remain separated over most of their area. Even within a single region of contact, the solids can deform into one of many possible configurations. In this thesis we use quasi-static molecular dynamics simulation to determine the mechanical properties of crystalline contacts. We help develop the Green's function molecular dynamics method to enable simulations to reach the necessary wide range of length-scales. We focus on simple interatomic potentials and models to isolate the underlying mechanical phenomena. We design simulations that test with atomic-scale resolution the normal contact of rough solids and the quasi-static sliding of clean crystalline contacts. We find for rough solids at typical normal loads that the average surface separation decreases as a logarithm of load. Correspondingly, the mechanical stiffness associated with the rough surface is proportional to the load. In both the continuum case and the atomistic case, the fraction of the surface in repulsive contact increases approximately linearly with load. In the atomistic case, the dimensionless proportionality constant can be increased several times by nanometer-scale features. Surface steps frequently found on crystalline materials can dramatically increase contact area by increasing the amount of plastic rearrangement and, in turn, decreasing the average surface stress. The static friction of a contact between elastic crystals depends sensitively on contact size, crystal orientation, and the microscopic friction law at the interface. In non-adhesive commensurate simulations, we show that the friction coefficient decreases over several decades as $(a^2/Rb)^{-2/3}$ where a is the contact radius, $R$ is the sphere radius, and $b$ is the Burgers vector of dislocations that are produced. Incommensurate contacts, despite exhibiting complex deformations while sliding, show surprisingly universal characteristics in the large size limit. We discuss the elastic breakdown of superlubricity by showing the rapid rise in friction from lowering the material modulus of large incommensurate contacts