Development of the strength statistical characteristics of materials, which takes into account the features of their brittle fracture

Abstract

The object of the research is the algorithm for determining the finding of the most probable, mean value, dispersion and coefficient of failure loading variation of a stochastically defective plate under conditions of comprehensive tensile-compression. The material of the plate is considered as a continuous medium in which evenly distributed defects such as rectilinear cracks that do not interact with each other. It is isotropic and has the same crack resistance. Let’s believe that the plate consists of primary elements, each of which can be weakened by one defect. To predict the strength and failure conditions of plates made of such material, it is natural to use, on the one hand, the results of the theory of limit equilibrium of individual determined defects and their development, and on the other hand, probabilistic-statistical methods that take into account the randomness of defects. This comprehensive approach makes it possible to calculate the statistical characteristics of strength and fracture based on data on the structure of the material defect and its resistance to the emergence and development of cracks. The main content of this paper is the algorithm for calculating and research the strength statistical characteristics of stochastically defective plate structural elements taking into account some deterministic features of their brittle fracture. Based on the deterministic failure criterion, which takes into account the initial direction of crack propagation, the ratio is obtained to find the most probable, mean value, dispersion and coefficient of variation of failure loading. The dependences of the specified strength statistical characteristics on the type of applied loading, the number of defects (body size) and structural inhomogeneity of the material, as well as the effect of taking into account the initial direction of crack propagation are investigated. The obtained results allow to more adequately assessing the reliability of structural materials under conditions of complex stress state, taking into account the stochastic of their structure. This is due to the fact that the use of the approach to determine the limit applied stresses, which takes into account the initial direction of the crack propagation, improves the algorithm for finding strength statistical characteristics.