PSI - Issue 80

Stanislav Buklovskyi et al. / Procedia Structural Integrity 80 (2026) 146–156 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 where q ( i l) is the heat flux in the l -th element, ( ) is the volume of the element, N is the total number of finite elements in the model. The components of the overall conductivity tensor were found as the proportionality coefficients relating the average heat flux ̅ to the applied temperature gradient as follows ̅ =− ̅ =1,2,3. (5) In the case of the considered material, the isotropic response was assumed, and the average conductivity k was calculated by averaging the responses in 3 orthogonal directions. 4. Numerical results The thermal conductivities of the CB-containing layers for composites with various wt % of CB were found utilizing formulas (1) – (3). The results are presented in Table 3. These data were used to perform numerical simulations on RVEs of the composites and extract effective thermal conductivities. 153 8

TABLE 3. Thermal conductivity of CB-containing layers for different wt % of CB in the overall composite.

CB wt%

k(W/mK)

0

0.37 0.40 0.42 0.51 0.69 1.08

0.5

1

2.5

5

10

Numerical predictions of effective thermal conductivity as functions of CB wt % in the overall composite are shown in Fig. 5. Conductivities averaged over the directions are given. The figure also provides comparison of these predictions with the experimental measurements presented in Fig.3. The numerical predictions are shown as green circles connected by a solid green line. Each numerical data point is the average of all orthogonal thermal responses for 2 RVEs (total of 6 points). In all cases, the variations in conductivity in three orthogonal directions were within 1.8%. This confirms the hypothesis of the overall material’s isotropy. The experimental data are limited by the available number of experimental measurements (see Fig. 3). These data are not sufficient to produce any statistical quantification and are shown here to illustrate the overall trend.