In this note, we explore the possibility of simple extensions of the heuristic El Haddad formula for finite life, as an approximate expression valid for crack-like notches, and of the Lukas and Klesnil equation for blunt notches. The key starting point is to assume, in analogy to the Basquin power-law SN curve for the fatigue life of the uncracked (plain) specimen, a power law for the finite lifeintrinsic El Haddad crack size. The approach has similarities with what recently proposed by Susmel and Taylor as a Critical Distance Method for Medium-Cycle Fatigue regime. Reasonable agreement is found with the fatigue data of Susmel and Taylor for notches, and in particular the error seems smaller in finite life than for infinite life, where these equations are already used. In these respects, the present proposal can be considered as a simple empirical unified approach for rapid assessment of the notch effect under finite life.

In this paper, the classical JKR theory of the adhesive contact of isotropic elastic spheres is extended to consider the effect of anisotropic elasticity. The contact area will then generally be non-circular, but in many cases it can reasonably be approximated by an ellipse whose dimensions are determined by imposing the energy release rate criterion at the ends of the major and minor axes. Analytical expressions are obtained for the relations between the contact force, the normal displacement and the ellipse semi-axes. It is found that the eccentricity of the contact area decreases during tensile loading and for cases when the point load solution can be accurately described by only one Fourier term, it is almost circular at pull-off, permitting an exact closed form solution for this case. As in the isotropic JKR solution, the pull-off force is independent of the mean elastic modulus, but we find that anisotropy increases the pull-off force and this effect can be quite significant.

Analyses of rough surface contact sometimes study the two-dimensional problem to avoid some of the difficulties of three-dimensional contacts, or to reduce the size of the calculations in numerical work. But two-dimensional elastic contacts introduce their own difficulties. The mean real contact pressures will be much lower than in three dimensions, and will depend strongly on the thickness of the 'slab' used to represent the elastic half-space. (C) 2010 Elsevier B.V. All rights reserved.

If the nominal contact tractions at an interface are everywhere below the Coulomb friction limit throughout a cycle of oscillatory loading, the introduction of surface roughness will generally cause local microslip between the contacting asperities and hence some frictional dissipation. This dissipation is important both as a source of structural damping and as an indicator of potential fretting damage. Here we use a strategy based on the Ciavarella-Jager superposition and a recent solution of the general problem of the contact of two half spaces under oscillatory loading to derive expressions for the dissipation per cycle which depend only on the normal incremental stiffness of the contact, the external forces and the local coefficient of friction. The results show that the dissipation depends significantly on the relative phase between the oscillations in normal and tangential load a factor which has been largely ignored in previous investigations. In particular, for given load amplitudes, the dissipation is significantly larger when the loads are out of phase. We also establish that for small amplitudes the dissipation varies with the cube of the load amplitude and is linearly proportional to the second derivative of the elastic compliance function for all contact geometries, including those involving surface roughness. It follows that experimental observations of less than cubic dependence on load amplitude cannot be explained by reference to roughness alone, or by any other geometric effect in the contact of half spaces. (C) 2011 Elsevier Ltd. All rights reserved.

We consider the problem of a cyclic Hertzian indentation between elastically dissimilar materials. In the case of loading, the problem was solved by Spence in a series of seminal papers, where he proved a relationship between the solution for a rigid square-shaped punch, to that for a power-law indenter. For example, the stick area is a constant ratio of the contact area, independently on the shape of the punch. “Unfortunately”, on unloading, many of the simple properties of the self-similar loading case are lost, there is a complicated development of an external region of slip which cycles in the two directions (forward and back-slip), and an inner region which continues to slip in the forward direction of the first loading cycle. However, this inner region gradually disappears, and further cyclic loading generates a convergence to a steady state solution which involves residual “locked-in” tangential slip displacements in a permanent stick zone, provided the contact is not fully unloaded. Dissipation in the steady state therefore occurs only in the external region of slip, and we provide some results for the energy dissipation per cycle, as a function of the governing parameters: coefficient of friction, Dundurs’ dissimilarity constant, normal load amplitude. We also show the likely independence of energy dissipation on initial conditions, limited to the possible scenario of overloading. It is seen that dependence of energy dissipation per cycle on load amplitude is closer to quadratic than to cubic, and this may explain some experimental findings which so far were not expected from oscillatory loading of elastically similar half-spaces.