Analysis of the asymptotic response of complete contacts

Complete contacts are a rich area of study and are of significant interest. These contacts arise when one of the contacting bodies has a sharp corner, such as if machining burrs have not been removed, or if previous damage has resulted in material loss, leaving a sharp corner. The state of stress induced by the loading of a complete contact is singular in the neighbourhood of the contact edge. The inherent coupling in the problem and the inability to treat the problem, other than by asymptotic or numerical means, makes the study of these contact interactions more challenging.
This thesis aims to investigate the response of these contacts. The behaviour of these contacts must be investigated by asymptotic methods, using distributed dislocation techniques. This requires the development of existing and new asymptotic methods. As such, this thesis begins by defining and classifying contact properties. Asymptotic methods and phenomena such as crack growth and partial slip are reviewed.
The response of a general complete contact, emerges as a key research challenge, together with the understanding of how and when zones of partial slip form, or a crack grows. This is very important as partial slip will inevitably lead to wear, which not only damages the surfaces but can lead to further problems by debris ejection or by reducing the load bearing contact area. A growing crack is a more obvious concern, long cracks and short cracks behave differently, but if a short crack, such as those modelled here is allowed to grow without control it can lead to several different problems. A short crack can of course grow into a long crack, which then result in total component failure, a short crack may instead branch, depending on material microstructure, and all cracks will weaken the material so it will not sustain as much load as intended.
This thesis presents predictive tools to indicate when a growing crack may form, or when a large partial slip zone will form at the edge of a complete contact. First of all we classify the response, to determine a priori whether a slip zone will exist, and whether or not intimate contact is maintained, a {necessary} condition for the use of the asymptotic method. Once the response type is known, we must also develop a dislocation method.
Crystalline dislocations induce stresses in bodies where they are present. However, the state of stress induced is described in closed form for an infinite plane, so using dislocations as strain nuclei in the presence of other features, such as free surfaces or the contact edge, requires a determination of the state of stress induced when interacting with the other features. This makes the stress kernel position dependent and more complex than a simple infinite plane kernel. These kernels can not be expressed in closed form, so a numerical method is described which allows the use of the distributed dislocation theory.
The asymptotic solution and the numerical solutions for the dislocation kernels are then used to enforce the conditions required to model a crack, and to model a zone of partial slip. The state of stress at the crack tip, characterised by the crack tip stress intensity factors is calibrated to remote loading to determine under what conditions the crack will grow. The size of the slip zone will also be found, for a given loading, and how this is affected by changes in the angle of the contact, and the coefficient of friction. This gives an estimate of the depth to which slip, and by {extension} wear, penetrates.
This work is original and no part of it has been submitted for a degree at this university or any other. Some of the work described here has been published or is under consideration for publication in the following journals:
1. Riddoch, D. J. and Hills, D. A., Necessary conditions for near edge stick of Complete Contacts, The Journal of Strain Analysis for Engineering Design 55: 172-180, March 2020
2. Riddoch, D. J. and Hills, D. A., Dislocations in an arbitrary angle wedge. Part I: The dislocation kernel, The Journal of Strain Analysis for Engineering Design: 03093247211042539, October 2021
3. Riddoch, D. J., Cwiekala, N. and Hills, D. A., Dislocations in an arbitrary angle wedge. Part II: Cracks in the wedge, The Journal of Strain Analysis for Engineering Design: 03093247211047785, October 2021.
4. Riddoch, D. J., Slip at the edge of complete contacts, The Proceedings of the iMeche, Part C: Journal of Mechanical Engineering Science, https://doi.org/10.1177/09544062221142695, January 2023
5. Riddoch, D. J., Distributed dislocation problems in wedge shaped domains, European Journal of Mechanics/ A Solids, https://doi.org/10.1016/j.euromechsol.2023.104941, February 2023
In addition to these publications and the work detailed above, other work has been completed during the course of this D. Phil. This has resulted in the publication of: Riddoch, D. J., Cicirello, A. and Hills, D. A., Response of a mass-spring system subject to Coulomb damping and harmonic base excitation, International Journal of Solids and Structures 193 (2020), 527-534.
This paper is included in appendix D, along with a brief outline of previous related work and an explanation of the developments found.
Much of the analysis contained within this thesis, including almost all numerical work was performed using MATLAB. The code used to produce these results and figures has been partially published in relation to certain papers. However, it has now been compiled completely and is made available along with instructions for its use at: https://doi.org/10.5287/bodleian:dXRdVJEAa

Advisor: Hills, D
Cicirello, A