Possibilities of Estimation of Fracture Probabilities and Allowable Sizes of Defects of Structural Elements According to the Criteria of Fracture Mechanics

This article discusses the possibilities of estimation of safe sizes of integrity defects on the basis of risk criteria. Such defects occur at all stages of the lifetime of structures. In most cases the estimation of their hazard and determination of allowable sizes attract attention when the defects can lead to brittle or quasi-brittle fractures. In this case, the models of linear and nonlinear destruction mechanics are applied, when the defects are considered as internal elliptical or surface semielliptical cracks. The stochastic variety of shapes, sizes, locations, and orientations of defects has a significant influence on the failure mechanisms. Therefore, the probabilistic problem of estimating allowable sizes of defects according to the criteria of risk of failure is relevant. This paper examines a general approach to estimation of the hazards of defects according to risk criteria. Two formulations of the probabilistic problem of risk estimation are presented: on the basis of single-parameter and two-parameter failure criteria. The risk function is used as the calculated characteristic, represented as the probability of failure according to a given criterion. An equation of the risk function based on single-parameter failure criteria is presented. The main focus is on the probabilistic model based on the two-parameter Morozov failure criterion. This criterion provides a wide range of opportunities for analyzing various failure mechanisms with variations in the size of defects. An expression for the risk function based on the family of two-dimensional Lu–Bhattacharya probability distributions of Weibull type is derived. It is shown that correlations between failure mechanisms can significantly influence the probabilities of failure and, consequently, the allowable size of defects.