A molecular dynamics study of scale effects on the friction of single-asperity contacts

A micro-mechanical dislocation model of frictional slip between two asperities was presented by Hurtado and Kim [1], which predicts that the friction stress is constant and of the order of the theoretical shear strength, when the contact size is small. However, at a critical contact size there is a transition beyond which the frictional stress decreases with increasing contact size, until it reaches a second transition where the friction stress gradually becomes independent of the contact size. Hence, the mechanisms of slip are size-dependent, or in other words, there exists a scale effect. Before the first transition, the constant friction is associated with concurrent slip of the atoms without the aid of dislocation motion. The first transition corresponds to the minimum contact size at which a single dislocation loop is nucleated and sweeps through the whole contact interface, resulting in a single-dislocation-assisted slip. This mechanism is predicted to prevail for a wide range of contact sizes, from 10 nm to 10 μm in radius for typical dry adhesive contacts; however, there are no available experimental data in this size range. The second transition occurs for contact sizes larger than 10 μm, beyond which friction stress is once again constant due to cooperative glide of dislocations within dislocation pileups. The above dislocation model excludes wear or plastic deformation of either surface. On the other hand, on the atomic scale, based on molecular dynamics modelling, Zhang and Tanaka [2] proposed a mechanism with four transition regimes, that is no-wear, adhering, ploughing and cutting regimes, when the radius of the asperity is kept constant but the depth of asperity indentation is increasing. In this case, the contact size increases due to the increment of the indentation depth of the asperity and thus both wear and plastic deformation consequently occur. In the present study, a molecular dynamics simulation is carried out to analyze the mechanism of sliding when the asperity radius varies from 5 to 30 nm but the indentation depth is kept unchanged, so that any variance in the mechanisms of sliding is solely due to the different contact size. The molecular dynamics models consist of a single cylindrical asperity (rigid diamond and copper) of various radii, sliding across the face of a copper workpiece on its (111) plane with a speed of 5 m/s. The indentation depth, d , was 0.46 nm and −0.14 nm (0.14 nm above the workpiece), respectively, where d is the distance between the surfaces of the asperity and specimen defined by the envelopes at the theoretical radii of their surface atoms [2–4]. As usual [2–4], two layers of thermostat atoms are arranged around the Newtonian copper atoms of the specimen to ensure that the heat generated during sliding can conduct out of the control volume properly. The boundary atoms are fixed to the space to eliminate the rigid body motion of the copper specimen. The velocities of atoms in the initial configuration of the model follow the Maxwell distribution. The modified Morse potential used by Zhang and Tanaka in their simulation of sliding between a diamond tool and copper workpiece [2] was applied to describe the interactions between the atoms. The simulation model is shown schematically in figure 1. It must be noted that the molecular dynamics simulation cannot cap-