Abstract
Adhesive contact of a rigid flat surface with an elastic substrate having Weierstrass surface profile is numerically analyzed using the finite element method. In this work, we investigate the relationship between load and contact area spanning the limits of non-adhesive normal contact to adhesive contact for various substrate material properties, surface energy and roughness parameters. In the limit of non-adhesive normal contact, our results are consistent with published work. For the adhesive contact problem, we employ Lennard-Jones type local contact interaction model with numerical regularization to study the transition from partial to full contact including jump-to-contact instabilities as well as load-depth hysteresis. We have investigated evolution of bonded contact area and pull-off force for various surface roughness parameters, substrate material properties and surface energy. We have identified two non-dimensional parameters to adequately explain experimentally observed adhesion weakening and strengthening phenomena. A design chart of the relative pull-off force as function of non-dimensional parameters is also presented.
Highlights
Adhesive contact of a rigid flat surface with an elastic substrate having Weierstrass surface profile is numerically analyzed using the finite element method
We study the contact between a flat rigid surface and an elastic substrate with rough surface characterized by a Weierstrass function
We discuss the evolution of contact area in the presence of adhesion and the limiting case of non-adhesive contact
Summary
Adhesive contact of a rigid flat surface with an elastic substrate having Weierstrass surface profile is numerically analyzed using the finite element method. The loss of adhesion with an increase in roughness is observed in several experiments[5,6,7,8,9,10,11] These experiments can be grouped based on a nondimensional parameter β = (γ/E⁎α), the ratio of surface energy density γ to product of modulus E∗ and range of interaction α. The seminal work by Fuller and Tabor[9] was one of first comprehensive efforts in developing a model to explain the experimental results of adhesion loss due to increase in roughness. In all the above-mentioned studies, the adhesive contact was at the individual asperity scale and the asperities are non-interacting These models cannot capture the important observed phenomena such as the jump-to-contact instabilities and hysteresis in loading and unloading due to surface roughness. Komvopoulos[24] used constitutive relations between interfacial force and separation at the asperity level exhibiting jump-in instability in conjunction with GW multi-asperity model and introduced a new adhesion parameter which is the ratio of rms roughness to equilibrium interatomic distance
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