General principles and criteria of failure of solids on different scale-structural levels under static and alternating loading

Experimental and theoretical studies of the fracture regularities under monotonic and alternating loadings, including stress-corrosion fracture, revealed the main scale-structural levels of the brittle fracture (formation of a strip structure, nucleation of microcracks, microstructurally short non-propagating cracks and short propagating cracks, merging of short cracks with a macrocrack nucleation) and viscous fracture (an evolution of dislocation in slip bands, cellular structure formation, nucleation of a pit relief with micropores, merging of pores with a formation of meso-shear bands and initiation of a viscous crack, growing of a viscous crack under inelastic deformation) of crystal bodies. A transition from one level to another is determined by changes in the fracture mechanisms and occurs with varying degrees of probability. The necessity of considering the destruction as a hierarchical random step-by-step process on all scale-structural levels is substantiated. The fracture of plastic materials is considered as the sum of independent or dependent events, namely the initiation and growing of brittle cracks and evolution of pores through various mechanisms. Attaining of the limit states is determined by the statistics of the distribution of inhomogeneities throughout the entire body volume. The results of physical studies (using electron microscopy, X-ray structural analysis, etc.) provide determination of the geometry and density of defects, dislocations, pores, cracks at different levels. Macrocharacteristics of static, long-term and fatigue strength are determined using methods of mechanical tests. The regularities of the fracture evolution of engineering structures are determined using methods of non-destructive testing (ultrasonic analysis, acoustic emission analysis, magnetic flaw detection, etc.). A brief analytical review of the main known physical approaches — dislocation and energy structural theories, dislocation continuous theories, dilaton-frustron models, stochastic physical theories, and phenomenological approaches, including continuum damage theory and fracture mechanics — is presented. The analysis of gained data leads to the necessity of describing fracture in the framework of stochastic multilevel models. We consider the approach according to which the probability of reaching limit sates at each level under arbitrary multiaxial loading is determined by linear functionals of the loading process, kernels of the functionals being random functions of time. For simple proportional loading, the theory of brittle fatigue scale-structural failure is presented.