PSI - Issue 28

Evangelia Nektaria Palkanoglou et al. / Procedia Structural Integrity 28 (2020) 1286–1294 E. Palkanoglou et al./ Structural Integrity Procedia 00 (2019) 000–000

1292

7

elements in a periodic one. Further, as seen in Fig. 5 (ii), damage was localised in the circumference of the inclusion in the case of a fully fixed unit cell, compared to a more uniform response in the periodic case. The level of stiffness of damaged elements was reduced on average by 14% in both cases, although some elements exhibited a maximum reduction of 35% and 21% in the case of fully fixed and periodic BCs, respectively. Finally, no element deletion was reported in either case. Hence, both simulations correspond to early stages of decohesion, with matrix-graphite interface getting weaker, but not losing the contact yet. 3.2. Interfacial layer Debonding can be studied in more detail by incorporating an additional layer around graphite to represent the interface. Periodic boundary conditions were applied in these simulations. In Fig. 6 (i), the plastic zone created in unit cells with and without the interfacial layer, is depicted. Apparently in the latter case, plasticisation started slightly earlier at 223 °C in a thick layer around the curvilinear parts of the particle, while in the former one, a plastic zone appeared at 225 °C. Although at 500 °C the entire matrix was plasticised in both cases, plastic strains were an order of magnitude higher are reported when an interfacial layer was used. The concentration of damaged elements in the interfacial layer around the inclusion triggered the development of higher stresses in the matrix explaining the higher plastic strain found in this case.

Fig. 6: (i) Evolution of plastic zone in matrix and interface for unit cell with and without interface. (Graphite is removed since the focus is on matrix plasticisation) (ii) Average value of damage variable either in inclusion or in interface.

Analysis of damage evolution with temperature in the inclusion (without interface) or in the interface demonstrated (Fig. 6) that damage starts at around 150 °C at the interfacial layer, whereas it occurred at 215 °C inside the inclusion. The stiffness of damaged elements in the interface decreased by 28% on average at 500 °C, compared with a stiffness reduction of 14% for elements inside the inclusion. In previous case, no element was removed in the case of a unit cell without interface; however, in the case with interface exists deletion of some elements in the interface were deleted, corresponding to its partial decohesion. The evolution of average von Mises stresses with temperature for each constituent in both types of unit cell is provided (Fig. 7). The elastoplastic behaviour was found in the matrix for both cases, with a 3.5% increase in the average von Mises stress for the case of the unit cell without interface (Fig. 7 (i)). For graphite, two different responses were observed (Fig. 7 (ii)) when no interface was considered a bilinear elastoplastic behaviour was found, whereas when interface was present the obtained behaviour was linear. In the former case, damage in graphite led to such a nonlinear behaviour, while in the latter case damage took place at the interface and leading to linear behaviour in the inclusion. Finally, a nonlinear relationship between the stresses and the temperature was obtained for the interface layer (Fig. 7 (iii)), attributed mainly to the onset of damage.