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Discrete dislocation plasticity simulations are carried out to investigate the static frictional response of sinusoidal asperities with (sub)-microscale wavelength. The surfaces are first flattened and then sheared by a perfectly adhesive platen. Both bodies are explicitly modelled, and the external loading is applied on the top surface of the platen. Plastic deformation by dislocation glide is the only dissipation mechanism active. The tangential force obtained at the contact when displacing the platen horizontally first increases with applied displacement, then reaches a constant value. This constant is here taken to be the friction force. In agreement with several experiments and continuum simulation studies, the friction coefficient is found to decrease with the applied normal load. However, at odds with continuum simulations, the friction force is also found to decrease with the normal load. The decrease is caused by an increased availability of dislocations to initiate and sustain plastic flow during shearing. Again in contrast to continuum studies, the friction coefficient is found to vary stochastically across the contact surface, and to reach locally values up to several times the average friction coefficient. Moreover, the friction force and the friction coefficient are found to be size-dependent. [ABSTRACT FROM AUTHOR]

It is customary to simplify the analysis of contact between two elastically deformable bodies by treating an equivalent problem where only one body is deformable and the other is rigid. This is possible provided that the gap geometry and the effective elastic modulus of the bodies in the simplified problem are the same as in the original problem. However, the question arises on whether – and to which extent – the simplification is still valid even when (size-dependent) plasticity occurs. Studies using discrete dislocation plasticity have also, so far, addressed simple contact problems where only one body can deform plastically. Here, we extend the analysis to two bodies in contact that can both deform by dislocation plasticity and investigate under which conditions the response agrees with that of an equivalent simplified problem. The bodies in contact are metal single crystals with sinusoidal and flat surface. It is found that the response of two plastically deformable bodies in contact can be simplified to an equivalent problem where one body is rigid and the other can deform plastically. Also, a plasticity size effect is observed, but the effect fades when the platen becomes more plastically deformable. [ABSTRACT FROM AUTHOR]

Discrete dislocation plasticity 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 study is on understanding the relative importance of contact slip opposed to plasticity in a single asperity at the micrometer size scale, where plasticity is size dependent. Slip of a contact point is taken to occur when the shear traction exceeds the normal traction at that point times a microscopic 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 dislocations. Results show that plasticity can delay or even suppress full slip of the contact. This generally happens when the friction coefficient is large. However, if the flattening depth is sufficiently large to induce nucleation of a large dislocation density, slip is suppressed even when the friction coefficient is very small. This study also shows that when self-similar asperities of different size are flattened to the same depth and subsequently loaded tangentially, their frictional behavior appears size independent. However, when they are submitted to the same contact pressure, smaller asperities slip while larger asperities deform plastically. [ABSTRACT FROM AUTHOR]

Discrete dislocation plasticity simulations are performed to investigate the role of interaction between neighboring asperities on the contact pressure induced by a rigid platen on a rough surface. The rough surface is modeled as an array of equispaced asperities with a sinusoidal profile. The spacing between asperities is varied and the contact pressure necessary to flatten the surface to a given strain is computed. Plasticity in the asperities and in the crystal below is described by the collective glide of dislocations of edge character. Results show that the mean contact pressure necessary to flatten closely spaced asperities is larger than that required to flatten widely separated asperities. A small dependence on asperity density is already observed for a purely elastic material, but it is enhanced for small asperities, in the presence of dislocation plasticity. Plastic strain gradients, dislocation limited plasticity and interaction between neighboring plastic zones all contribute to what we will call the asperity density effect. Since dislocation limited plasticity plays a dominant role, the asperity density effect will mainly be relevant for surfaces having small asperity roughness. [ABSTRACT FROM AUTHOR]

Abstract: The plastic flattening of a sinusoidal metal surface is studied by performing plane strain dislocation dynamics simulations. Plasticity arises from the collective motion of discrete dislocations of edge character. Their dynamics is incorporated through constitutive rules for nucleation, glide, pinning and annihilation. By analyzing surfaces with constant amplitude we found that the mean contact pressure is inversely proportional to the wavelength. For small wavelengths, due to interaction between plastic zones of neighboring contacts, the mean contact pressure can reach values that are about 1/10 of the theoretical strength of the material, thus significantly higher than what is predicted by simulations that do not account for size dependent plasticity. Surfaces with the same amplitude to period ratio have a size dependent response, such that if we interpret each period of the sinusoidal wave as the asperity of a rough surface, smaller asperities are harder to be flattened than large ones. The difference between the limiting situations of sticking and frictionless contacts is found to be negligible. [Copyright &y& Elsevier]