Scale dependence of interface dislocation storage governing the frictional sliding of single asperities

Abstract

Single-asperity friction tests have found a critical dependence of friction stress on the nanoscale contact size, as successfully explained by the nucleation of interface dislocations as opposed to concurrent sliding of all the interfacial atoms in contact. Modeling and simulation results, however, vary when the motion and interactions of multiple dislocations dominate at a larger scale regime. A Rice-Peierls framework is employed to investigate the multiplication and storage of interface dislocations, and the critical conditions for dislocation initiation and steadystate gliding are determined numerically. Our findings identify the key parameters that govern various friction mechanisms in the Hurtado-Kim and Deshpande-Needleman-van der Giessen models. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 2 Keywords IntroductionFriction is an inherently multiscale problem [1,2], because of the geometric irregularities (i.e., roughness, asperities) that prevail over multiple decades of length scales [3][4][5], the plastic responses that depend on intrinsic and extrinsic length scales such as geometrically necessary dislocations or material microstructures [6][7][8][9], and a variety of time-dependent processes that render peculiar rate-dependent, collective responses of multi-asperities at micro-and macroscales [10]. Much of the above complexities can be removed if a smooth single asperity can be examined at nanoscale. Along this line, frictional force microscopy tests have found the high friction stress (i.e., friction force divided by the contact area) that is a large fraction of the material shear modulus, the reduction of friction stress due to interface incommensurability, and the increase of the friction force with the increase of sliding velocity, among many others [2,[11][12][13][14]. The one-dimensional Tomlinson model, as commonly used in surface physics and tribology [1,2], assumes a point contact that is connected to the faraway loading apparatus by a compliant spring and traverses on a periodic potential that represents the atomic structure on the surface.Although the stick-slip behavior on the shear load-displacement curves can be successfully explained, it inexorably constrains all the atoms in contact moving concurrently. Although several dislocation-based models [11,[15][16][17] have emerged recently to resolve this limitation in the Tomlinson model, they appear to conflict each other in the underlying assumptions, as will be explained in Figs. 1 and 2. The present work aims to reconcile, and provide justifications for, the discrepancies in the Hurtado-Kim model [15,16] and the Deshpande-Needleman-van der Giessen model [17].In the Hurtado-Kim model in Fig. 1(a), the contacting bodies are equivalent to an external circular crack subjected to a tangential loading, thus leading to stress singularity at the contact edg...

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