# 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 have equal displacements but in opposite directions. Considering two points and + located on corresponding surfaces with a distance between them, the PBCs are expressed in the following form: ( + )= ( )+ ̅ , (1) ( + )= − ( ) , (2) where and are the displacement and traction at , respectively, and ̅ is the average infinitesimal strain over the volume (Drago and Pindera, 2007). On the other hand, FFBCs constrained all six degrees of freedom of nodes on boundary surfaces of the matrix domain. The thermal load linearly increased from 20 °C to 500 °C and decreased back to 20 °C. A summary of the numerical models with the morphology of inclusions and boundary conditions studied is shown in Table 2. 77 4

Morphology of inclusion ( μ m) ( μ m) Spherical 1 15

Table 2. Summary of numerical models.

Model

Notation

Boundary condition

A1 A2 B1 B2 C1 C2

FFBCs

A

Spherical Ellipsoidal Ellipsoidal Ellipsoidal Ellipsoidal

1 3 3 5 5

15

PBCs

5 5 3 3

FFBCs

B

15

PBCs

FFBCs

C

PBCs

3. Results of simulations 3.1. Stress distribution in Mg matrix

The distribution of von Mises stress along path AB (Fig.1) was summarised under FFBCs (Fig. 3) and PBCs (Fig. 4), respectively. Under thermal loading, the fixed boundaries restrict the thermal expansion of both HA inclusion and Mg matrix, resulting in compressive stress in the matrix with von Mises stress reaching 160 MPa at 500 °C. The trend of all curves for different aspect ratios is consistent with the stress level decreasing for the increasing aspect ratio of HA inclusion (Model A1 to C1). Along Path AB, from the interface between two phases to the boundary surface of the matrix, von Mises stress decreased in all models. After the temperature cooling down to 20 °C from 500 °C, the stress of matrix spherical inclusion (Model A1) keeps the same levels as that at 500 °C after heating up. Along path AB, the von Mises stress in Model C1 drops faster up to a distance of approx. 3 μm , but then that of Model B1 also drops to zero and then they meet at the same value at the boundary. Under PBCs (Fig.4), the distribution of von Mises stress shows a decreasing trend along path AB. The highest level of stress (82 MPa for model B2) is lower than that under FFBCs (160 MPa). Under PBCs, the unit cell is allowed to expand and does not develop excessive thermal stresses. The stress in all models under PBCs decreases when the temperature decreases from 500 °C to 20 °C. In heating (Fig. 4a), the von Mises stress of Model B2 is at the highest level (larger than 80 MPa) and that of Model C2 drops quickly to zero. In cooling (Fig. 4b), the value of the stress (67 MPa) in Model C2 is significantly higher than the other two models. The decreasing trend of von Mises stress along Path AB at 20 °C (Fig. 4b) is same as that at 500 °C (Fig. 4a). The CTE of Mg is larger than that of HA significantly. Because of the smaller volume of HA in Model C2 and the larger volume of Mg, the interaction between HA and Mg causes plasticisation resulting in constant stress in Model C2 during the cooling down process. In opposite, there is no plasticisation in Model A2 with the larger volume of HA and smaller volume of Mg under PBCs. Thus, the highest stress in Model C2 can keep at the same level but that of Model A2 and B2 decrease.

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