# PSI - Issue 49

Minghua Cao et al. / Procedia Structural Integrity 49 (2023) 74–80 Minghua Cao et al. / Structural Integrity Procedia 00 (2023) 000 – 000

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2. Numerical models 2.1. Geometry

HA inclusions in MMC-HA exhibit predominately spherical or ellipsoid-based shape . In this study, a set of RVE cells with dimensions 30 μm × 30 μm × 30 μm were generated in the finite-element software Abaqus. In each unit cell, an HA inclusion was embedded in a centre of a Mg domain (Fig. 2). For better assessment, the measurement path AB was chosen in a cross-section surface of the model comprising a spherical inclusion (Model A, Fig. 2b). HA inclusions were assumed to be spherical and ellipsoidal with different aspect ratios. Based on the statistical analysis of the microstructure of MMC-HA (Fig. 1), the length of diameter/major axis of HA inclusion was in the range of 0.39 μm - 22.5 μm . The magnitude of 15 μm was selected for diameter of a spherical HA inclusion. The length of the major axis of ellipsoidal HA inclusions wa s 15 μm, equal to the diameter of the spherical one. Ellipsoidal HA inclusions with aspect ratios of 3 and 5 had minor axes of 5 μm and 3 μm , respectively, for compatibility.

(a)

(b)

A

B

Z

Y

X

Fig. 2. Geometry of numerical models: (a) Model A; (b) measurement path in Model A.

2.2. Material properties Both HA and Mg were assumed to be elastoplastic in this work; the stress-strain curve of HA (Fogarassy et al., 2005) and Mg (Sandlöbes et al., 2011) were used. Other material parameters of constituents used are shown in Table 1.

Table 1. Material properties of HA and Mg.

Properties

HA

Mg

References

Density (mg/mm 3 ) Yield point (MPa)

3.16E-9

1.74E-9

(Shamami et al., 2021) (Sandlöbes et al., 2011) (Bahmani et al., 2019) (Shamami et al., 2021)

/

22.7 0.28

Poisson’s ratio

0.27

Coefficient of thermal expansion (mm/mm/°C)

1.34E-5

2.5E-5

2.3. Boundary and loading conditions Periodic boundary conditions (PBCs) and fully fixed boundary conditions (FFBCs) were applied to all boundary surfaces of the matrix domain to provide the upper and lower bounds of the results. In finite-element simulations, PBCs are commonly used to analyse the behaviour of materials with RVEs at the microscale and mesoscale (Garoz et al., 2019). By using PBCs, a small domain can be used to represent an infinitely large system, allowing simulations of distortion of boundary surfaces (Omairey et al., 2019). Nodes on the corresponding surfaces controlled with PBCs

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