Contact mechanics and impact dynamics of non-conforming elastic and viscoelastic semi-infinite or thin bonded layered solids
The thesis is concerned with the contact mechanics behaviour of non-conforming solids. The geometry of the solids considered gives rise to various contact configurations, from concentrated contacts with circular and elliptical configuration to those of finite line nature, as well as those of less concentrated form such as circular flat punches. The radii of curvature of mating bodies in contact or impact give rise to these various nonconforming contact configurations and affect their contact characteristics, from those considered as semi-infinite solids in accord with the classical Hertzian theory to those that deviate from it. Furthermore, layered solids have been considered, some with higher elastic modulus than that of the substrate material (such as hard protective coatings) and some with low elastic moduli, often employed as tribological coatings (such as solid lubricants). Other bonded layered solids behave in viscoelastic manner, with creep relaxation behaviour under load, and are often used to dampen structural vibration upon impact. Analytic models have been developed for all these solids to predict their contact and impact behaviour and obtain pressure distribution, footprint shape and deformation under both elastostatic and transient dynamic conditions. Only few solutions for thin bonded layered elastic solids have been reported for elastostatic analysis. The analytical model developed in this thesis is in accord with those reported in the literature and is extended to the case of impact of balls, and employed for a number of practical applications. The elastostatic impact of a roller against a semi-infinite elastic half-space is also treated by analytic means, which has not been reported in literature. Two and three-dimensional finite element models have been developed and compared with all the derived analytic methods, and good agreement found in all cases. The finite element approach used has been made into a generic tool for all the contact configurations, elastic and viscoelastic. The physics of the contact mechanical problems is fully explained by analytic, numerical and supporting experimentation and agreement found between all these approaches to a high level of conformance. This level of agreement, the development of various analytical impact models for layered solids and finite line configuration, and the development of a multi-layered viscoelastic transducer with agreed numerical predictions account for the main contributions to knowledge. There are a significant number of findings within the thesis, but the major findings relate to the protective nature of hard coatings and high modulus bonded layered solids, and the verified viscoelastic behaviour of low elastic modulus compressible thin bonded layers. Most importantly, the thesis has created a rational framework for contact/impact of solids of low contact contiguity.