PSI - Issue 37

Yulia Pirogova et al. / Procedia Structural Integrity 37 (2022) 1049–1056 Yulia Pirogova / Structural Integrity Procedia 00 (2021) 000 – 000

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The analysis of spherical inclusions of various sizes was performed. The diameters of the spheres were randomly distributed within the specified limits. Several structures with different upper and lower limits of the sizes of spheres were studied. The volume fraction of samples was fixed.

Fig. 7 Correlation function of the fourth order, spherical shape of inclusions, p =0.5, r=0.25-1.5 mm

Table 2. Values of the effective Young's modulus obtained during the FE analysis.

Elastic modulus derived from FE analysis, A p E , MPa

Structure description

r =0.25-1.5 mm , N=60 r =0.25-1 mm , N=199 r =0.25-0.75 mm , N=470

1417.20

1413.81

1416.74

It was found that the fourth-order correlation function is sensitive to inclusion size (Fig. 7). However, the elastic modulus for these structures remained unchanged. This may lead to the conclusion that minor changes in the size of inclusions do not significantly affect the effective modulus of elasticity (Table 2). Another study was a comparison of structures with a fixed inclusion size, but a different size of the sample. For this study, spherical inclusions were used as a shape model.

Fig. 8 Correlation function of the second order, spherical shape of inclusions, p =0.5, r=0.25-2 mm.

The changes in sample size affected both the correlation functions (Fig. 8) and the effective modulus. Table 3 shows that as the size increases, the difference between values of the effective modulus decreases, so that the value of the modulus converges to a certain value.