PSI - Issue 42

Minghua Cao et al. / Procedia Structural Integrity 42 (2022) 777–784

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Minghua Cao et al. / Structural Integrity Procedia 00 (2019) 000–000

(FFBCs) was used, constraining all the nodes on the matrix side surfaces with regard to their six degrees of freedom. PBCs or FFBCs were applied to four side surfaces of the matrix domain. The bottom surface of the matrix was restricted in plane but allowed to expand freely. The top surface was free for graphite and matrix to expand during thermal loading. The thermal loading increased linearly from 25 °C to 500 °C and decreased back to 25 °C. 3. Results of simulations 3.1. Height profile of graphite and matrix Thermal deformation of graphite and matrix under PBCs is analysed along path AB in Fig. 3b from the centre of the graphite inclusion to the matrix surface (Fig. 5). This model allows the thermal expansion of both phases. Thus, the expansion of graphite (0 μ m to 7.5 μ m of path AB) is less than that of the matrix (7.5 μ m to 15 μ m of the path) as the matrix has a larger coefficient of thermal expansion than graphite. The differences between the graphite particle and the matrix in height became more obvious when the former had a larger volume (width W ) and a greater depth ( H ). Before the loading, the height of both phases was 0 μ m. At both 500 °C and after the return to 25 °C, the difference in height between the matrix and the graphite particle increased with the applied thermal loading. The difference in height between the max and min values was 0.07 μ m (from 0.01 μ m to 0.08 μ m) at 500 °C and a pproximately 0.035 μ m at 25 °C. The shrinkage happened at the decreasing environmental temperature. Graphite Matrix (a) Graphite Matrix (b)

0.10

0.01

0.00

0.08

-0.01

0.06

W4H8 W8H8 Ver_H4 Spherical_H7.5

W4H8 W8H8 Ver_H4 Spherical_H7.5

-0.02

0.04

Height (μm)

-0.03 Height (μm)

0.02

-0.04

0.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -0.05

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Distance from centre (μm)

Distance from centre (μm)

Fig. 5. Height profile of top surface under PBCs at 500 °C (a) and after return to 25 °C (b) (see notation in Table 1).

(a)

(b)

Graphite

Matrix

Graphite

Matrix

0.30

W4H8 W8H8 Ver_H4 Spherical_H7.5

W4H8 W8H8 Ver_H4 Spherical_H7.5

0.5

0.25

0.4

0.20

0.3

0.15

0.2

0.10

Height (μm)

Height (μm)

0.1

0.05

0.0

0.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Distance from centre (μm)

Distance from centre (μm)

Fig. 6. Height profile of top surface under FFBCs at 500 °C (a) and after return to 25 °C (b) (see notation in Table 1).