Plasticity under rough surface contact and friction

Abstract

The ultimate objective of this work is to gain a better understanding of the plastic behavior of rough metal surfaces under contact loading. Attention in this thesis focuses on the study of single and multiple asperities with micrometer scale dimensions, a scale at which plasticity is known to be size dependent. The asperities have very simple geometries, either rectangular or sinusoidal and they are pressed into contact with a rigid platen. The analysis is performed using the discrete dislocation (DD) plasticity method, given its accuracy to describe microscale plasticity and its capability of predicting size effects. In DD, plasticity is modeled as the collective motions of discrete dislocations dislocations, which are modeled as line singularities in an otherwise isotropic linear elastic medium. The dislocation Burgers vector is the material length scale that allows to capture plasticity size effects. In Chapter 2, simulations are performed to investigate the flattening of a sinusoidal surface, for different dimensions and shape of the sinusoid. A size dependent response is found for asperities with the same amplitude-to-period (A/w) ratio. The smaller asperities are more difficult to deform plastically due to the limited dislocation density at the same strain. It is observed that the mean contact pressure can reach values up to about 40 times the yield pressure, thus significantly higher than what is predicted by the classical plasticity theory. This is mainly caused by the fact that the area of intimate contact is discontinuous and therefore the distribution of contact pressure is highly non homogeneous. Smaller contact regions are characterized by a very high stress concentration. The simulation results are rather insensitive to the contact conditions used, i.e. frictionless or sticking. When flattening periodic sinusoidal waves, it is not possible to assess a possible size dependence related to the spacing between asperities, since decreasing asperity spacing also reduces asperity size. Therefore in Chapter 3, simulations are performed for the flattening of an array of equally spaced sinusoidal asperities. This allows to investigate the effect of plastic interaction between neighboring asperities on the contact pressure. It is found that the mean contact pressure necessary to flatten closely spaced asperities is larger than that required to flatten widely separated asperities. The so-called asperity density effect is already present in purely elastic materials, and becomes more pronounced when plasticity is described by discrete dislocations. The origin of the asperity density effect is found to be a combination of plastic strain gradients, dislocation limited plasticity and interaction between plastic zones. In Chapter 4, simulations are performed to investigate the effect of flattening on the subsequent shearing behavior of a rectangular asperity protruding from a large single crystal. The shearing is applied after the pillar is flattened to different depths. In large asperities, i.e. a couple of square micrometers, the dislocations generated during flattening promote early plasticity upon shearing, i.e the contact shear stress is reduced, when plastic deformation takes place upon flattening. However, flattening smaller asperities to the same displacement, instead, does not affect subsequent plastic shearing. Despite there are many dislocations in the asperities, they are closely packed on a few active slip planes and therefore have smaller mobility. The simulations are also performed for on multiple asperities to investigate the effect of spacing on their shearing behavior. It is found that closely spaced asperities are easier to plastically shear than isolated asperities. This effect is mainly triggered by the fact that shearing closely spaced asperities in the elastic regime gives rise to a wide region in the subasperity where the shear stress is large and therefore facilitates dislocation nucleation. This effect fades when asperities are very protruding, and plasticity mainly occurs inside of the asperities. In Chapter 5, simulations are performed to investigate the static frictional behavior of a metal asperity on a large single crystal, in contact with a rigid platen. The focus of this chapter is on understanding the relative importance of plasticity and contact sliding in a single asperity at a scale where plasticity is size dependent. Sliding of a contact point is taken to occur when the shear traction exceeds the normal traction at that point times a friction coefficient. Plasticity initiates through the nucleation of dislocations from Frank-Read sources in the metal and is modeled as the collective motion of edge dislocation. Results show that at large contact pressures and friction coefficients, plasticity controls the frictional behavior of a single asperity. When self-similar asperities of different size are flattened to the same depth while loaded tangentially, there is no trace of a size effect in their frictional behavior. However, when they are submitted to the same contact pressure smaller asperities slide while larger asperities deform plastically.