A. Sackfield

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.

A shrink-fit shaft subject to torsion

The problem studied is an elastic, circular shaft, fitted into a cavity normal to the free surface of a half-space. The cavity is smaller than the shaft, so that there is a residual radial stress. A torque is applied to the shaft, giving rise to a region of slip between the shaft and the socket. Its extent is determined by forming an integral equation whose kernel is given by a circular ring dislocation, which has a Burgers vector whose magnitude is constant, oriented in the tangential direction. The problem has direct application to the study of shrink fitted shafts in wheels, whose diameter is large compared with the shaft.

The tilted punch under normal and shear load (with application to fretting tests)

The use of a tilted fretting fatigue pad in experimental investigations of fretting fatigue is discussed, and a concise, closed-form analysis of the resulting contact law, pressure distribution and partial slip regime found. The salient physical quantities controlling the size and characteristics of the contact are deduced. Preliminary tests using pads of this form have shown them to be very useful in applying carefully graded slip damage in a controlled way.

The influence of an edge radius on the local stress field at the edge of a complete fretting contact

The state of stress adjacent to the corner of a complete or almost complete fretting contact pad is studied using the corresponding Muskhelishvili potentials. Three potential are employed; that for a semi-infinite rigid punch, that for a finite square-ended rigid punch, and that for a punch having a flat form with radiused corners. It is shown that the asymptotic stress field (the semi-infinite punch) matches the finite punch well over a large region. Further, the edge radius which can be tolerated, but still giving rise to a local stress field which can be approximated by the asymptotic solution is found. The implication of these results for the application of an asymptotic approach to the design of almost complete fretting contacts is described.

Analysis of a Rocking and Walking Punch—Part I: Initial Transient and Steady State

A rigid, square-ended punch resting on a incompressible half-plane, and subjected to a constant shearing force, together with a normal force, constant in magnitude, but moving backwards and forwards over the face, is studied. The shearing force is insufficient to cause sliding, but the presence of a slip region which migrates in from each contact edge as the punch rocks back and forth may permit a steady rigid-body motion to occur The conditions for this are found, both for the early transient problem, starting from complete adhesion, and in the steady state.

Asymptotic Solutions for Contact Problems: The Effect of an Internal Discontinuity in Surface Profile

Abstract The contact pressure adjacent to the apex of a tilted punch is studied and used to form a refined, two-term asymptote for the contact pressure at a point of discontinuous gradient interior to a half-plane contact problem. The asymptote is compared with the full solution for an example problem, the wheel with a flat.

Torsional loading of a finite shrink-fit shaft

Abstract This paper treats the problem of a shaft of finite depth, shrink-fitted into a cavity and subject to remote torsion. The evolution of slip regions along the curved surface of the shaft is discussed and the effect of finite depth is investigated. The end face of the shaft is traction-free, which is achieved by distributing special axisymmetric dislocations giving a relative twist displacement over the end plane. This permits the conditions for no-slip along the curved surface to be found explicitly.

A stepped, shrink-fitted shaft subject to torsion:

Abstract A circular shaft having an enlarged boss is shrink-fitted into a large plate. The shaft is subject to torsion and the conditions are established for continued adhesion of the interface to the free surface, together with the depth of penetration of slip when this occurs. Lastly, the development of protective residual shear tractions is discussed and the frictional shakedown of the assembly is studied.

Closed-form solutions for the stress fields induced by blunt wedge-shaped indenters in elastic half-planes

Department of Mathematics, Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, UK Closed-form expressions are given for the Muskhelishvili potentials created by wedge-shaped indenters contacting elastic halfplanes. The potentials are given for normal and sliding contact of both similar and dissimilar materials. Surface values of the tension σ 0 xx are also presented.