Mechanics of non-slipping adhesive contact on a power-law graded elastic half-space

Abstract

a b s t r a c tIn previous work about axisymmetric adhesive contact on power-law graded elastic materials, the contact interface was often assumed to be frictionless, which is, however, not always the case in practical applications. In order to elucidate the effect of friction and the coupling between normal and tangential deformations, in the present paper, the problem of a rigid punch with a parabolic shape in non-slipping adhesive contact with a power-law graded half-space is studied analytically via singular integral equation method. A series of closed-form analytical solutions, which include the frictionless and homogeneous solutions as special cases, are obtained. Our results show that, compared with the frictionless case, the interfacial friction tends to reduce the contact area and the indentation depth during adhesion. The magnitude of the coupling effect depends on both the Poisson ratio and the gradient exponent of the half-space. This effect vanishes for homogeneous incompressible as well as for linearly graded materials but becomes significant for auxetic materials with negative Poisson's ratio. Furthermore, influence of mode mixity on the adhesive behavior of power-law graded materials, which was seldom touched in literature, is discussed in details.

The JKR-type adhesive contact problems for power-law shaped axisymmetric punches

“…The non-slipping contact problems were discussed by many researchers, see a discussion by Borodich and Keer (2004b), Zhupanska (2009) and Guo et al(2011). The analysis of the nonslipping contact problems was performed first incrementally for a growth in the contact radius a (Mossakovskii 1954(Mossakovskii , 1963.…”

“…In the general formulation (see, e.g. Popov 1973, Guo et al 2011, it is assumed that in the system subjected to a normal contact force P , the displacements u r (r, 0, P ) and u z (r, 0, P ) are known within the contact region, and the solids are not loaded outside the contact region, i.e. u r (r, 0, P ) = s(r), u z (r, 0, P ) = g(r), for r ≤ a;…”

Sliding Contact Between a Cylindrical Punch and a Graded Half-Plane With an Arbitrary Gradient Direction

“…Further discussion on the plane strain adhesive model was given by Chen et al [21], As for a rigid sphere in adhesive contact with a graded half-space, a very simple closed-form analytical solu tion was achieved by Chen et al [22], which could be well reduced to the classical Johnson-Kendall-Roberts (JKR) solution as well as that for Gibson soil materials. Considering a similar JKR-Derjaguin-Muller-Toporov (DMT) transition, axis-symmetrically adhe sive contact models for graded half-spaces were further analyzed by Guo et al [23] and Jin et al [24,25].…”

Frictional contact of a rigid punch on an arbitrarily oriented gradient half-plane

“…A closed-form analytical solution of a rigid sphere contacting with a graded elastic half-space was successfully given by Chen et al [25]. A further non-slipping adhesive contact model of FGMs was reasonably analyzed by Guo and his coauthors [26][27][28][29].…”