Actual Stress Field Research Articles

Reliability Against Defect Generated Fracture

ABSTRACT The subject of this study is the reliability determination for structures that may fail due to fracture generated from some material defect among a random number of small random defects distributed in some way throughout the body of the structure. The considered failure mechanism may be characterized as a weakest link mechanism with a random number of links. The calculation technique is based on some previously published general narrow probability bounds for unions of small probability events. In the case of high reliability structures, as are usually of interest in structural engineering, some very useful conclusions may be drawn from the study. Given only the defect fracture probability corresponding to the actual stress field and the mean number of defects per unit volume both as functions of the space coordinates, a sufficiently accurate assessment of the total reliability may be calculated. With rare exceptions, no dependency information is needed and no information about the defect point process is needed except its mean function. The reliability is insensitive to very large variations of these properties. If there is doubt about the dependency level being too high to neglect it, conditioning followed by fast probability integration may be useful. This is illustrated in the last section of the paper.