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This lecture begins with a overview of applied fracture mechanics pertinent to safety of pressure vessels. It then progresses to a chronological panorama of experimental and analytical results. To be useful and dependable in safety analysis of real structures, new analysis developments must be physically realistic, which means that they must accurately describe physical cause and effect. Consequently, before mathematical modeling can begin, cause and effect must be established from experimental data. This can be difficult and time consuming, but worth the effort. Accordingly, the theme of this paper is that the search for patterns is constant and vital. This theme is illustrated by the development of small, single-specimen, fracture toughness testing techniques. It is also illustrated by the development, based on two different published large-strain, elastic-plastic, three-dimensional finite-element analyses, of a hypothesis concerning three-dimensional loss of constraint. When a generalization of Irwin`s thickness-normalized plastic-zone parameter, reaches a value close to 2{pi}, the through-thickness contraction strain at the apex of the near-tip logarithmic-spiral slip-line region becomes the dominant negative strain accommodating crack opening. Because slip lines passing from the midplane to the stress-free side surfaces do not have to curve, once these slip lines are established, stresses near the crack tip are only elevated by strain hardening and constraint becomes significantly relaxed. This hypothesis, based on published three-dimensional elastic-plastic analyses, provides a potentially valuable means for gaining additional insight into constraint effects on fracture toughness by considering the roles played by the plastic strains as well as the stresses that develop near a crack tip. |
