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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Fig. 4. Dependence of failure probability on tensile strength for: (a) matrix; (b) inclusions. Now let’s consider RVE of porous media with polydisperse inclusions with volume fraction 45%. As in the previous case, matrix is isotropic: = 10 9 , = 0.33 . Pores are filled with vacuum. RVE is subject to simultaneous tensile and shear load so that macroscopic strains are equal to: = ( 10 −6 10 −6 0 10 −6 0 0 0 0 0 ) (2) Distribution of 11 component of stress for such media is presented on Fig. 5a. Distribution functions for all components of stress tensor can be restored (see Fig. 5b). Normal and skew normal distributions were used as model functions.

a b Fig. 5. (a) Stress field 11 in RVE; ( б ) Probability density functions stress tensor components.

The distribution functions obtained for each component of the strain tensor make it possible to calculate the fracture probability using more complex criteria combining the strength constants of the material and the values of the components of stress or strain tensors.

4. Conclusions

The described approach allows to restore stress and strain fields distribution laws in RVE phases and calculate phase failure probabilities for phases with predetermined criteria and strength properties. Some numerical case studies were considered.