D.A. Hills

Mechanics of fretting fatigue

Abstract Several aspects of the mechanics of cracks originating at sites of fretting are considered. It is argued that the problem may be distilled into three separate parts: the contact problem itself in full or partial slip, the initiation of a crack from a surface suffering severe distress, and the propagation of a crack under combined contact and bulk loading. The first of these may be solved by either a classical or numerical means, whilst the last merely requires the careful use of fracture mechanics. However, it is the second element which remains elusive to quantify, and the influence of the intrinsic length scales in the problem, including contact length, surface roughness and amplitude of relative tangential displacement on initiation conditions, is discussed and explored.

Solution of Crack Problems: The Distributed Dislocation Technique

Preface. 1. Introduction to Fracture Mechanics. 2. Distributed Dislocation Fundamentals. 3. Further Topics in Plane Crack Problems. 4. Interface Cracks. 5. Solution of Axi-Symmetric Crack Problems. 6. Three-Dimensional Cracks: An Introduction. 7. Three-Dimensional Cracks: Further Concepts. 8. Concluding Remarks. A: Dislocation Influence Functions. B: Numerical Solution of SIEs with Cauchy Kernel. C: Plane and Ring Dipole Influence Functions. D: Contour Integral and Kernel Function. References. Index.

The influence of rounded edges on indentation by a flat punch

Abstract The contact problem and stress state for indentation by a flat punch with rounded edges is studied. For the contact problem itself analytical solutions are obtained for both surface pressure and interior stress fields. Cases of normal indentation and frictional contact, the latter in both sliding or partial slip conditions, are all treated. The transition from the Hertzian configuration to the contact between a nominally flat pad and contacting flat surface is discussed, and it is found that the strength of the contact decays surprisingly slowly. Regarding the von Mises yield parameter, there is a range of configurations for which the strength is actually higher than the Hertzian one, and the strength decays only when the corner radii are very small. The present solution is therefore a realistic alternative to the classical rigid-flat punch idealization, and has particular application to fretting fatigue tests.

Mechanics of fretting fatigue tests

Abstract A popular fretting fatigue test, in which oscillating tension is applied in phase with the fretting force, is analysed. The configuration is a generalization of the well-known Mindlin contact problem, and it is shown that the addition of bulk tension has a substantial effect on the stick-slip geometry and the shear traction at the interface. The largest tension induced, which is thought to be responsible for the initiation of fatigue cracks, is also slightly increased.

Crack initiation criteria in fretting fatigue

Abstract This paper is a description of a series of fretting fatigue tests on an Al/Cu alloy in which the contact size was varied while the other relevant parameters were held constant. The fretting fatigue life was found to be infinite below a certain critical contact width. The configuration has been analysed using elastic stress analysis and stresses and displacements have been calculated. The variation of life with contact size can be explained by a variation in amplitude of micro-slip. Composite parameters proposed by Ruiz et al. are shown to characterize the severity of fretting damage and the probability of crack initiation, and hence explain the observed results. The physical basis of these parameters and their use in design calculations is discussed.

Contact problems incorporating elastic layers

Abstract In this paper, plane elastic contact between a thin strip and symmetric rollers is considered. Various loading regimes, including factional sliding, frictionless and frictional indentation, and the effect of applying a tangential force less than that necessary to cause sliding are treated. For each case, the surface tractions are found, and, for the last two problems, a detailed analysis of the stick and slip zones is presented.

On the initiation of fretting fatigue cracks

This paper discusses macroscopic and microscopic approaches for prediction of the initiation of fretting fatigue cracks. A novel series of fretting fatigue tests is described, involving the cycling of fretting force and specimen load at different frequencies. This technique attempts to determine the proportions of specimen life consumed in initiation and propagation. The experimental contact configuration is analysed and the variation of subsurface stresses calculated. The use of shear stress amplitude as a parameter for characterising the initiation of fretting cracks is discussed.

The application of asymptotic solutions to characterising the process zone in almost complete frictionless contacts

A method is developed for characterising the nature of the plastic zone which develops along the boundary of any notionally complete frictionless contact but where, in practice, there is some small rounding. The approach consists of an outer asymptote, the solution for a semi-infinite square ended rigid punch, whose validity sets the upper limit to the load, and a nested inner asymptote, the solution for a semi-infinite rounded punch, which sets the lower limit to the load. The technique is applied, as an example, to a circular punch, and explicit values of the load given to ensure that the singular field characterises the local stress field to within a given degree of accuracy.

Contact mechanics of wedge and cone indenters

Abstract Several aspects of the mechanics of indentation of a half-space by an elastic indenter which is either conical or wedge-shaped are addressed. These include elucidation of the contact law, the state of stress induced when the indenter is either pressed normally or sliding with Coulomb friction, the strength of the contact, and the influence of shearing forces less than those necessary to cause sliding, including those induced by elastic mismatch.

Brief note: Some observations on oscillating tangential forces and wear in general plane contacts

For general plane contact of elastically similar materials, including cases where there are multiple regions of contact, general properties of the partial slip solution for conditions of constant normal force and monotonically increasing shearing force have been found recently by the first author. An extension is given here to cover the unloading and cyclic loading cases. Further, it is shown that, if the tangential load varies between two fixed limits, the region of stick does not change, even if relative microslip causes wear, changing continuously the profile of the indenter. The contact area will change, but wear will not enter the original region of adhesion. The theoretical limit to which wear will eventually, asymptotically proceed is established, viz. almost complete contact over what is the initial stick zone, although it may, in practice, take a long time to reach this state.