PSI - Issue 54

Xingling Luo et al. / Procedia Structural Integrity 54 (2024) 75–82 Xingling Luo et al. / Structural Integrity Procedia 00 (2023) 000–000

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2.2. Constitutive relations The constitutive parameters of graphite and matrix are given in Tables 3 and 4, respectively. Mechanical tests were used to derive the constitutive values for the metallic matrix, see Palkanoglou et al. (2021). An elastoplastic constitutive law and isotropic behaviour were assumed for metallic matrix and graphite particles. Generally, the behaviour of a material can be significantly influenced by microstructural features. Dynamic analysis allows for the investigation of the interaction of these microstructural elements with the applied load and the effect on the overall response. The crack growth and energy dissipation within the RVE can be studied by considering the dynamic response (Beskou and Muho, 2022).

Table 3. Constitutive parameters for graphite (room temperature) (Greenstreet et al., 1969; Palkanoglou et al., 2022). Mass density (tonne/mm³) Young’s modulus (GPa) Poisson’s ratio Yield stress (MPa) Yield strain (%) 2.26E-9 15.85 0.2 27.56 0.184

Table 4. Constitutive parameters for matrix (room temperature) (Palkanoglou et al., 2022). Mass density (tonne/mm³) Young’s modulus (GPa) Poisson’s ratio 6.8E-9 150 0.25 Plastic strain Stress (MPa) 0

323.95 376.83 404.62 460.99 532.23

0.0009 0.0018 0.0053 0.1344

Cohesive-zone elements that follow a traction-separation law were assigned to the whole domain. The traction separation law can be expressed as follows: the cohesive normal traction ( ) is a function of the relative displacement between two faces of a crack: = ( ) . � 1 � In this formulation, the cohesive element undergoes failure when the separation reaches a critical value, 0 , as shown in Fig. 2 (Naghdinasab et al., 2018). The magnitude of fracture energy, , as the area under the − curve can be obtained as = � ( ) 0 0 . � 2 � For the bilinear form of traction-separation law, the fracture energy , which controls the behaviour of the interface, can be expressed as = 1 2 . � 3 � The interface failure model assumes that the absorbed energy during the fracture of the interface is independent of the loading path. Constitutive parameters used in the cohesive model are shown in Table 5. The data for the cohesive interface were obtained from in-house nano-indentation experiments, while those for the matrix were based on in-situ experiments (Qiu et al., 2016), and the cohesive data for graphite were from Zhang et al. (2018).

Table 5. Constitutive parameters for cohesive elements (Qiu et al., 2016; Zhang et al., 2018). Phase Coheisve normal traction (MPa) Fracture energy (N/mm) Matrix 600 0.06 Interface 1.75 1.75E-04 Graphite 34 3.4E-03