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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and Yang (2000)). For the analytical representation of this kind of numerical data, the type of the parametric distribution law should be chosen. Its parameters are determined from the solution of the system of equations connecting the parameters and moments of the random variable. Based on the distribution of fields, it is possible to obtain the value of failure probability of components for a given criterion and strength constants. In the simple case, the failure probability can be defined as [ > , ~ ⅈ ] (1) Here, is stress critical value (which is material ’ s strength parameter), ~ ⅈ denotes that stress are distributed according to ⅈ with a set of pararmeters. In the general case, when, for example, the phase properties are not isotropic, a more complex criterion (Hashin's, Tsai-Wu, Mises and others criteria) can be used. The distribution law of the expression for such criteria can be obtained in the form of a transformation of the of distribution laws of the quantities which it consists of. 3. Modeling of heterogeneous RVE Let’s c onsider a representative three-dimensional structurally inhomogeneous media with polydisperse particles. A three-dimensional geometric model of this volume is a cube (matrix) with random disjoint spheres of different sizes (inclusions). Assume that the matrix and inclusions have isotropic mechanical characteristics. The model characteristics of the matrix and inclusions were taken = 10 9 , = 0.33 and = 10 10 , = 0.33 respectively. The volume fraction of inclusions is 20%. The loading was given in the form of tensile displacements 1 = 10 −6 along the axis 1. The calculations were performed in the MSC Digimat package. An RVE and stress distributions for 11 component are shown on Fig. 1.

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Fig. 1. (a) Condsidered RVE; (b) Component 11 of stress tensor after applied load. The distributions of the 11 component for the inclusions and the matrix phases are shown on Fig. 2.