PSI - Issue 42

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

780

4

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

(3)

= 4 3 � 2 � 3 , = 33 , = .

The dimensions of the 3D model are given as follows:

(4) (5)

(6) From Eqs. (1)-(3) and (4)-(6), the length of the matrix domain in the model was obtained with the following formulas: 2 = � � 2 � 2 , (7) 3 = � 4 3 � 2 � 3 3 . (8) Then, the aspect ratio of vermicular graphite was obtained according to the following equation: = , (9) = . (10) The dimensions of spherical graphite and vermicular graphite within the matrix in the developed FEA models were established. Based on the range of nodular graphite diameters, 0.29 μ m – 42.53 μ m, 15 μ m was selected as the diameter of the graphite particle in finite-element models. The maximum aspect ratio of vermicular graphite was 5; therefore, the major axis of the vermicular particle had a length of 15 μ m while the minor length was 3 μ m. The range of the cubic matrix length in 3D was 25.37 μ m – 32.23 μ m, thus, 30 μ m was selected as a representative value in this research for comparability. 2.2. Numerical model A representative volume element (RVE) was proposed by Hill (1963) and considered as a statistical representative of the material at the macroscopic scale (Seleš et al., 2021). A basic cubic 3D RVE model was created in the finite-element software package Abaqus, comprising a single graphite inclusion embedded in a matrix (Fig. 3a). However, to research the thermal-deformation mechanism of the graphite particle and the matrix more effectively, the basic model was cut in half across the XY plane. This thermal-exposure model was created to simulate the surface evolution, where the plane of cutting was considered a free top surface allowing thermal expansion of both phases. Models containing vermicular and flake graphite particles were created in a similar way. The geometric details of all numerical models were calculated according to the statistical results of microscopic images (Table 1). Flake graphite was regarded as a cuboid with different levels of width and depth, but with the fixed length of 15 μ m.

(a)

(b)

Free top surface

15 μ m

B

A

Height (H)

Z

Side surface

Y

X

Z Y

X

Bottom surface

Fig. 3. Geometry of numerical models: (a) basic model; (b) thermal-exposure model for surface-evolution analysis.