PSI - Issue 5

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

611

4

Fig. 2. Distribution of stress 11 component for matrix and inclusions.

The skew normal distribution, the Weibull distribution, and the gamma distribution were investigated as distribution models (Johnson et al. (1994)). Skew normal and Weibull distribution are parametrized by a scale, location and a shape parameter; gamma distribution has one more additional shape parameter. Plots of probability density functions for these three distributions based on numerical modeling results (Fig. 2) are presented on Fig. 3. Calculated distribution parameters are presented in table 1.

Table 1. Distribution parameters values. Matrix

Inclusions

Skew normal Weibull Gamma

Skew normal Weibull Gamma

Location parameter 735.018

251.972 -658.013

1914.33

1670.58 1546.75

Scale paramteter Shape parameter 1 Shape parameter 2

591.449 8.64909

1065.29 0.0140719 2928.37

2605.8

0.00301951

2.71031 152.57

15.0564

1.26998 26.8883

-

-

0.426703

-

-

0.245275

a

b

Fig. 3. Probability density function for 11 component of stress tensor for: (a) matrix; (b) inclusions. As an illustration, let’s obtain the graph of the failure probability function for the obtained stress distribution laws 11 in the matrix and inclusions in dependence of the variable value of the critical constant (see Fig. 4).