|Ph.D Thesis||Department of Aerospace Engineering|
|Supervisor:||Prof. Durban David|
|Full Thesis text|
Cavity expansion theory is concerned with the stress and displacement fields around internally and externally pressurized spherical or cylindrical cavities embedded in either linear or nonlinear media. This fundamental problem is of considerable interest in the mechanics of solids from both theoretical and practical points of view. A good example for theoretical and practical application is the problem of material hardness which is discussed in this research. For the extreme case of a cavity embedded in an infinite medium (or the expansion of cavities from zero initial radius), it is expected that by increasing the internal pressure it will approach an asymptotic value for both spherical and cylindrical cavities. The spontaneous steady-state expansion induced by the constant asymptotic pressure is known as quasi-static cavitation and the asymptotic pressure is known as the quasi-static cavitation pressure. This problem has no characteristic length and hence will possess a similarity solution, in which the continuing deformation is geometrically self-similar. By increasing the internal pressure beyond the quasi-static cavitation pressure a dynamically self-similar steady-state cavity expansion will develop with constant expansion velocity sufficiently high not to neglect material inertia effects. This kind of media response is known as dynamic cavitation and the pressure that drives it is known as dynamic cavitation pressure. In recent years there has been increasing interest in dynamic elastoplastic cavitation as a basic physical model underlying penetration behavior because one can consider the penetrator as an external source of energy to drive dynamic cavitation in the target material.
The present research has been aimed to achieve a better understanding of quasi-static cylindrical cavitation and dynamic spherical cavitation phenomena in Mises and Tresca materials. The analysis is based on the self-similar deformation pattern induced by the steady expansion of spherical or cylindrical cavities. This self-similar pattern enables a simple analysis according to plastic flow theory with no need to trace the entire straining history. Another goal of this research was to apply our new dynamic spherical cavitation results to simulate penetration mechanics and to use the spherical cavity expansion model to investigate hardness of strain-hardening materials. Most of the study in this thesis has been published in journals and a sum up of the main achievements can be found in the thesis extended abstract.