This talk will explore the interplay of structure and elasticity in determining contact area A and friction F between a nominally spherical tip of radius R and a clean, flat elastic substrate. An efficient Greens function technique allows study of R up to ~mm and reveals new behavior as the contact radius a increases from nm to μm scales. When elasticity is neglected, most bare tips are predicted to exhibit superlubricity: F∝Ax with x≤0.5. Friction and area are only proportional (x=1) in the rare case of commensurate surfaces with the same period and orientation. We find that interfacial dislocations lead to quantitative deviations from these rigid results when a is greater than the dislocation core width b, which scales inversely with the shear modulus. For a&gt;b, the ratio F/A for commensurate surfaces drops, while F/A rises for incommensurate surfaces. In the limit of large a, all crystalline surfaces have F/A near the Peierls stress for dislocation motion. Dislocations do not form for amorphous tips but there is still a crossover to linear scaling of F with A for compliant surfaces. The talk will conclude with a study of tips with locally self-affine surfaces. For small R and high loads the contact area follows predictions for single-asperity contacts. For large R and low loads, contact is described by theories for flat rough surfaces and contact area is proportional to load. Simple analytic formulae capture the crossover between these regimes for nonadhesive and adhesive contacts.

Scale dependence of friction and contact of nanometer to millimeter radius tips

253rd National Meeting (2017)

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