Reliability prediction of composite materials with random elastic inclusions

Abstract

The object of the research is the construction of an algorithm that allows finding a number of strength (failure loading) statistical characteristics of a composite material plate under the conditions of a complex stress state. The relationships that determine the most probable value, mean value, dispersion and coefficient of variation of strength for an elastic homogeneous plate in which elliptical inclusions of another elastic material are uniformly distributed are written. Inclusions do not interact with each other and their geometric parameters are statistically independent random variables whose distribution laws are written for certain physical reasons.
 The combination of the known deterministic solution of the composite materials failure theory and probabilistic statistical methods that take into account the randomness of the material structure makes it possible to study the failure of composite materials taking into account the stochasticity of their structure.
 The main content of this article is the construction and analysis of the strength statistical characteristics algorithm of two-component lamellar composite materials. The mechanism of composite plate’s failure initiation in the inclusion is considered. The recorded relationships make it possible to calculate the most probable value, mean value, dispersion and coefficient of variation of strength and to investigate their dependence on the type of applied loading, structural heterogeneity of the composite and its dimensions (number of inclusions).
 The obtained results allow effective assessment of the reliability of stochastically defective two-component composite structural materials under complex stress conditions. This is due to the fact that the combined consideration of defectiveness and randomness in the composite material structure as interconnected, inseparable phenomena open new opportunities for researching of the strength problem and failure of composite materials under various types of applied loading.