37 research outputs found
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Patterns and perspectives in applied fracture mechanics
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
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New method for analyzing small-scale fracture-specimen data in the transition zone
Among the problems related to the use of small specimens for measuring fracture toughness, those concerning size effects and data scatter are perennial. An attempt was made to find a suitable method for adjusting individual small specimen fracture toughness values for size effects in the transition range of temperature. The method selected was one already proposed by Irwin. Irwin's ..beta../sub Ic/ equation recognizes an interaction between toughness and size. If either toughness increases or size decreases, the ratio K/sub c//K/sub Ic/ will increase. This interaction magnifies the scatter inherent in plane strain K/sub Ic/ values. Although the more common application of the ..beta../sub Ic/ formula is the estimation of K/sub c/ values from known values of B and K/sub Ic/, the original application was the one considered here, i.e., the estimation of K/sub Ic/ from measured values of B and K/sub c/. So the new aspect of the application described here is mainly the use of small specimen test data, analyzed inelastically
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Engineering approaches to the application of fracture toughness data in the nuclear industry
The procedures for measuring the plane strain fracture toughness, K{sub Ic}, of metals were originally developed for relatively high yield strength materials, the toughnesses of which were not affected by strain rate. The application of these procedures to lower yield strength and higher toughness structural and pressure vessel steels have since revealed a perplexing combination of problems involving the effects of geometry, stable crack growth and strain rate on the measured values of toughness. Only the geometric problems were encountered in the development of the procedures for measuring K{sub Ic}. For fracture in the linear elastic range of the load-displacement curve, these problems were overcome by specifying specimen dimensions sufficiently large with respect to the plastic zone size at fracture. However, in the case of structural and pressure vessel steels, it is not always possible to test specimens large enough for fracture to occur prior to general yielding. Therefore, in these cases, the effects of large-scale yielding prior to fracture cannot be avoided, but since they presently have no analytical explanation they are being treated empirically. The problems of geometry and strain rate effects on toughness discussed herein are complex and difficult to solve. However, taking advantage of the improvements that have recently been made in the hardware and software available for performing three-dimensional elastic-plastic and viscoplastic stress analysis, it should be possible to significantly improve the analysis of small-specimen, elastic-plastic fracture toughness data
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Approximate method of elastic--plastic fracture analysis for nozzle corner cracks
Two intermediate test vessels with inside nozzle corner cracks have been pressurized to failure at ORNL by the HSST Program. Vessel V-5 leaked without fracturing at 88/sup 0/C (190/sup 0/F), and Vessel V-9 failed by fast fracture at 24/sup 0/C (75/sup 0/F) as expected. The nozzle corner failure strains were 6.5 and 8.4 percent, both considerably greater than pretest plane strain estimates. The inside nozzle corner tangential strains were negative, implying transverse contraction along the crack front. Therefore, both vessels were reanalyzed, considering the effects of partial transverse restraint by means of the Irwin ..beta../sub Ic/ formula. In addition, it was found possible to accurately estimate the nozzle corner pressure-strain curve by either of two semiempirical equations, both of which agree with the elastic and fully plastic behavior of the vessels. Calculations of failure strain and fracture toughness corresponding to the measured final strain and flaw size are made for both vessels, and the results agree well with the measured values
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Evidence concerning crack-tip constraint and strain-rate effects in fracture-toughness testing
The procedures for measuring the plane strain fracture toughness, K/sub Ic/, of metals were originally developed for relatively high yield strength materials, the toughnesses of which were not affected by stain rate. The application of these procedures to lower yield strength and higher toughness structural and pressure vessel steels have since revealed a perplexing combination of problems involving the effects of geometry, stable crack growth and strain rate on the measured values of toughness. Only the geometric problems were encountered in the development of the procedures for measuring K/sub Ic/. For fracture in the linear elastic range of the load-displacement curve, these problems were overcome by specifying specimen dimensions sufficiently large with respect of the plastic zone size at fracture. However, in the case of structural and pressure vessel steels, it is not always possible to test specimens large enough for fracture to occur prior to general yielding. Therefore, in these cases, the effects of large-scale yielding prior to fracture cannot be avoided, but since they presently have no analytical explanation they are being treated empirically
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Evaluations of the Irwin. beta. /sub Ic/ adjustment for small specimen fracture toughness data
When small specimens are used to measure the cleavage fracture toughness of pressure vessel steels in the transition range of temperature, specimen thickness size effects and large amounts of data scatter are often observed. The size effects are manifested by an increase in the average value of fracture toughness with decreasing specimen thickness, eventually resulting in a change in fracture mode from cleavage to ductile tearing. It has been shown that a semiempirical adjustment for the interacting effects of specimen thickness, yield stress and toughness originally proposed by Irwin is capable of reducing the calculated values of toughness and data scatter to levels consistent with large specimen test data. This is true for dynamic as well as for static initiation toughness values. The nature of the size effect described by the Irwin ..beta../sub Ic/ equation is illustrated and specific cases are shown in which ..beta../sub Ic/ adjustment has eliminated size effects, for both static and dynamic fracture toughness data
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Development of the present reference fracture toughness curves in the ASME nuclear code
Since the early 1970's, the Sections of the ASME Boiler and Pressure Vessel Code concerned with nuclear power plant components have included fracture mechanics procedures to analyze the effects of postulated or detected flaws. These procedures are contained in Appendix G of Section III and in Appendix A of Section XI of the Code. Specifically, Appendix G procedures are concerned with designing for protection against nonductile failures while Appendix A procedures are for evaluating the disposition of flaws detected during in-service inspection. An important element of the procedures is the inclusion of recommended material fracture toughness values. This paper describes the origin and development of these recommended fracture toughness values. Since these values appear in the Code in a graphical format, the values are often referred to as reference toughness curves. In the context of Code terminology, reference toughness means the allowable values of fracture toughness for the materials of concern that can be used in conjunction with the analytical procedures of Appendices G and A. The paper discusses the basis and rationale underlying the original formulation of these reference toughness curves and the modifications incorporated into them in the course of their adoption into the Code