13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Statistical Model of Submicrocrack Evolution under Cyclic Loading Oleg Plekhov*, Oleg Naimark Institute of continuous media mechanics Ural Branch Russian academy of science, 614013, Perm, Russia *poa@icmm.ru Abstract To describe the damage evolution under high- and gigacyclic fatigue we develop a generalization of statistical model of microcrack evolution. The statistical model combined with a stochastic description of damage accumulation process allows us to describe the interaction of microplastisity and damage (submicrocracks) under cyclic deformation and propose a model of fatigue crack initiation. Considering a fatigue crack initiation as a blow-up regime of damage accumulation we propose a method for prediction of SN-curves of materials. The SN-curve has dual form caused by shift the location of crack initiation from surface to the bulk of specimen. Keywords statistical model of defects, gigacyclic fatigue, dual Woller curve 1. Introduction It is now well known that real metals have complex structure, which is a hierarchy of different levels. Under deformation process the structural evolution observed at all scale levels and leads to irreversible deformation and destruction. The most interesting situation observed under gigacyclic fatigue when the stress amplitude is less than the yield stress of materials and fracture emergence under macroscopic “pure” elastic conditions. One of most critical issue of the gigacyclic fatigue is the location of fatigue crack initiation. The decreasing of stress amplitude leads to the shift of crack initiation from specimen surface to the bulk. To develop a model of defect evolution under small stress amplitude we have to choice of the basic physical level of description of the material microstructure and describe the geometry of the elementary defects. Analysis of the experimental results of the study of structural levels of plastic deformation and fracture [1,2] and resent experimental investigation of damage evolution of fine grain metals can hypothesize that scale level with the size of submicrocracks 0.1-0.3 mm plays a key role in this process [3]. The failure process includes both the nucleation of new microcracks and their development. The contribution of these processes in the failure varies depending on the structure of the material conditions of its loading. The defect kinetics is different near specimen surface and in the bulk. The rate of microcracks nucleus initiation in the surface layers of one to three orders of magnitude higher than in the bulk material. It is also well known that for high concentration the defect ensemble exhibits both collective and nonlocal effects. One of the possible descriptions of defect kinetics is the statistical model of defect ensample. This model has to take into account the stochastically properties of defect initiation, their nonlinear integration and link between micropalsticity and damage accumulation. This work is devoted to the development of such model in the application to cyclic loading of metals. The paper is organized as follow. The first part is devoted to the statistical description of submicrocrack ensemble. The statistical description was developed based on the mean field approximation of defect interaction and allows us to investigate the effect of initial nucleus concentration of defect evolution process and determine the equilibrium state of materials with
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