PSI - Issue 42

Minghua Cao et al. / Procedia Structural Integrity 42 (2022) 777–784 Minghua Cao et al. / Structural Integrity Procedia 00 (2019) 000–000

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Contrary to the PBCs case, FFBCs restricted the thermal expansion of graphite and matrix in the XY plane. Thus, the magnitude of the out-of-plane displacement in graphite was larger than that of the matrix since the reaction force from the stiffer matrix resulted in compression to the softer inclusion. Therefore, the graphite particle was compressed in the XY plane and deformed on the free top surface (Fig. 6). In the FFBCs case, the maximum height difference between the particle and the matrix was about 0.45 μ m at 500 °C but reduced to 0.27 μ m at 25 °C . The same shrinking phenomenon happened under FFBCs as the temperature decreased. 3.2. Damage of graphite The damage distribution caused by the applied load in the graphite particle is shown in Fig. 7 (to enhance visibility, the surrounding matrix was removed). The damage under FFBCs was up to 0.23, smaller than under PBCs (up to 0.49). The difference in coefficients of thermal expansion had a more pronounced effect on the damage of graphite under PBCs. Indeed, at either 500 °C or return to 25 °C, damage in graphite under PBCs was larger than in the case of FFBCs but concentrated within a smaller area. After a completed thermal cycle, the damage in graphite accumulated during the cooling from 500 °C to 25 °C under both FFBCs (from 0.16 to 0.23) and PBCs (from 0.31 to 0.49). Damage in graphite initiated from the bottom under FFBCs, where the area with maximum damage contacted the matrix and was compressed by it. In the PBCs case, the damage in graphite started from the free top surface since the damage is mainly caused by the mismatch in the coefficients of thermal expansion between the two phases.

(a)

(b)

(c)

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0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00

Fig. 7. Damage of graphite: (a) 500 °C (FFBCs); (b) 25 °C (FFBCs); (c) 500 °C (PBCs); (d) 25 °C (PBCs).

4. Conclusion In this work, the processes of thermal deformation and damage in CGI were investigated. A three-dimensional finite-element RVE was developed consisting of a single graphite inclusion and the metallic matrix having perfect bonding. Elastoplastic constitutive behaviours were assumed for both phases. A pure thermal cycle was applied to the unit cell under FFBCs or PBCs. The morphology of the graphite particle affected the height profile of the external surface during thermal loading with regard to the volume and depth of graphite. Also, the damage of graphite was initiated from the free surface under PBCs but from the bottom of the inclusion when using FFBCs. The different thermal expansion caused the mismatch between the phases resulting in large damage under PBCs. Additionally, the damage in graphite accumulated with the application of thermal loading. In conclusion, the thermal deformation of CGI was affected by the morphology of graphite under different boundary conditions and accumulated with the applied thermal loading. References Andriollo, T., Thorborg, J., Tiedje, N., Hattel, J., 2016. A micro-mechanical analysis of thermo-elastic properties and local residual stresses in ductile iron based on a new anisotropic model for the graphite nodules. Modelling and Simulation in Materials Science and Engineering 24, 55012. Andriollo, T., Thorborg, J., Tiedje, N. S., Hattel, J., 2015. Modeling of damage in ductile cast iron - The effect of including plasticity in the graphite nodules. IOP Conference Series: Materials Science and Engineering 84, 12027. Andriollo, T., Zhang, Y., Fæster, S., Thorborg, J., Hattel, J., 2019. Impact of micro-scale residual stress on in-situ tensile testing of ductile cast