PSI - Issue 5

Mikhail Tashkinov et al. / Procedia Structural Integrity 5 (2017) 608–613 Mikhail Tashkinov/ Structural Integrity Procedia 00 (2017) 000 – 000

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In general case, such statistical approach can be used for investigation of the influence of spread of the microstructure parameters as well as the constants of an inhomogeneous medium on the strength characteristics of the material. The question is whether it is possible to assess failure probability of the entire RVE on the basis of the probability of microscale fracture. There are a number of approaches that make it possible to establish a relationship between the probability of phases, the number of destroyed microparticles, and experimental data. Thus, by introducing parameters determined experimentally for each material, it is possible to obtain relationships that directly connect the probabilities of micro- and macro-scale fracture. There are also approaches based on basic mathematical theories, such as percolation theory (Kesten (1982)) and beam theory (Bredon (1997)), which determines which pattern of failed micro-scale elements will lead to failure of the whole element. The criteria for the components represented in the form of the laws of distribution of stress and strain tensors can correspond to one or another failure mechanisms, which makes it possible to use the fracture model with a set of criteria. The research is supported by the Grant of the President of Russian Federation for state support of young Russian scientists (MK-2395.2017.1). References Aboudi, J., Arnold, S.M., Bednarcyk, B. a., 2013. The Generalized Method of Cells Micromechanics, Micromechanics of Composite Materials. doi:10.1016/B978-0-12-397035-0.00005-7 Baniassadi, M., Mortazavi, B., Hamedani, H.A., Garmestani, H., Ahzi, S., Fathi-Torbaghan, M., Ruch, D., Khaleel, M., 2012. Three-dimensional reconstruction and homogenization of heterogeneous materials using statistical correlation functions and FEM. Comput. Mater. Sci. 51, 372 – 379. doi:10.1016/j.commatsci.2011.08.001 Bredon, G.E., 1997. Sheaf Theory, Graduate Texts in Mathematics. 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