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published_or_final_version / Dentistry / Doctoral / Doctor of Philosophy

A combined theoretical and experimental study of the criteria governing the failure analysis of pressure vessels with defects has been performed. The fields of fracture mechanics (linear elastic and elastic-plastic behaviour), failure governed by large scale plastic deformation and energy balance methods are critically reviewed. All three approaches are shown to have relevance in the complete failure analysis of a structure with defects. An experimental study of the failure mechanisms of precracked polycarbonate and maraging steel plates and model polycarbonate vessels is presented. Room temperature, static loading tests are performed on 85 mm wide, 5 mm thick compact specimens of polycarbonate (0.013 andle; ^aandfrasl;_W andle; 0.810). For comparison, 51 mm wide maraging steel compact specimens are monotonically loaded at room temperature. The influence of through-thickness constraint on the fracture toughness and slow crack growth characteristics of the steel is investigated using plates of varying thickness (3.1 mm-25.4 mm) and initial crack length (0.386 andle; ^aandfrasl;_W andle; 0.766 for 3.1 mm thick sheet); various ancillary studies (scanning electron microscopy, surface deformation studies) complement the results. The crack growth behaviour of longitudinal through (0.704 ≤ c / andradic;‾DT/2</span> ≤ 1.434) and deep part-through (^dandfrasl;_T = 0.700 and 0.878) cracks in 50.8mm and 102mm diameter (5mm and 6mm wall thickness) polycarbonate cylinders is also studied. Bowling and Townley's two-criteria approach to failure i.e. LEFM on the one hand and limit analysis on the other, is shown to provide a useful method for assessing the relative importance of crack initiation, in the presence of limited crack tip plasticity and general yield as failure criteria for a given sized defect. Thus, for crack tip plasticity fully contained by an outer elastic field i.e. not general yield, the LEFM parameter, K_Ic (with the possibility of a plasticity correction factor for thin sheet) can be used to predict crack initiation. For the low strain-hardening maraging steel, Irwin's plane strain plasticity correction, ¹andfrasl;_6π (K_{Ic/σ_y})² is shown to be applicable to sheet thicknesses comparable to ¹andfrasl;_π (K_{Ic/σ_y})² i.e. twice Irwin's plane stress plastic zone radius.

In this dissertation, first the experimental and theoretical observations on the deformational characteristics of brittle geomaterials are reviewed and discussed. A basic conclusion is that special features such as strain softening can not be considered as true material (continuum) properties. These conclusions created a renewed emphasis on the constitutive modelling of such materials. A model that accounts for structural changes is developed. Such changes are incorporated in the theory through a tensor form of a damage variable. It is shown subsequently that formation of damage is responsible for the degradation in strength (softening) observed in experiments, for the degradation of the elastic shear modulus and for mechanical, damage induced anisotropy. A generalized plasticity model is incorporated for the so-called topical or continuum part of the behavior, whereas the damage part is represented by the so-called stress-relieved behavior. The question of uniqueness in the strain-softening regime is examined. It is shown that the constitutive equations lead to a unique solution for the case of rate dependent as well as rate independent formulation. Its implementation in finite element analysis shows mesh size insensitivity in the hardening and softening regimes. The general order of bifurcation of differential equations is employed in order to study the effect of damage accumulation on formation of narrow, so-called shear bands. It is shown that as the damage accumulates, the material approaches localization of deformation. The theory of mixtures is employed for further theoretical establishment of the proposed model. Energy considerations show the equivalence of the two-component damage body to an elastoplastic body containing cracks; the equivalence is considered in the Griffith sense. The mechanisms of failure are considered and discussed with respect to multiaxial stress pads. An explanation of failure, at the micro level, is given. The material constants involved in the theory are identified and determined from available experimental data. The model is then verified by back-predicting the observed behavior.