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

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2.2. Microstructure-based modelling Generally, a unit cell should enclose a large number of inclusions (Hill, 1963). However, due to CGI’s complex microstructure, interfacial debonding of interacting particles is hard to study. The interaction affects the temperature, at which debonding starts, changing the effect of other parameters on development of decohesion. Therefore, generation of an RVE comprising a single inclusion was selected, assuming effective properties for the metallic matrix, to take into account the existence of the remaining particles. This assumption is justified considering the volume fraction of graphite, which is much lower compared to that of ferrite. Based on the performed microstructural characterisation and the mentioned assumptions, a two-dimensional model was generated, comprising a square domain representing the metallic matrix and an elliptical graphite inclusion. Although in CGI nodular, vermicular, and flake graphite particles coexist in different fractions, vermicular is the predominant shape as shown in Fig. 2 (nodularity values in the range from 0.20 and 0.80). Therefore, a vermicular inclusion is selected for the simulations as representative of a general graphite inclusion. The geometrical features of the model are depicted in Fig. 3 with the dimensions used for the simulations. The dimensions of inclusion were selected to be in accordance with the results of microstructural characterisation. The percentage of graphite was assumed to be 9% (see Table 1) and led to values for the dimensions of the inclusion. Debonding was investigated considering two configurations: a periodic unit cell with and without an interfacial layer. In the former case, damage was expected to occur in the outer layer of the inclusion, whereas in the latter case, it will be localised in the interface only. This interfacial layer was selected to cover about 1% of the overall volume of the unit cell, in order not to affect the quality of the numerical results.

Fig. 3 : Geometrical parameters of selected RVE.

Further, the metallic matrix was considered isotropic and ductile; hence, an elastoplastic J 2 flow theory of plasticity was used for its constitutive description. Besides, temperature-dependent data were used for the matrix, since the objective was to investigate graphite debonding under thermal loading. On the other hand, graphite is a soft and brittle material; however, there is evidence that it exhibits a limited plastic deformation and, hence, classical plasticity theory can be used for it as well (Andriollo et al., 2015; Greenstreet et al., 1973; Seldin, 1966). The selection of constitutive parameters for both constituents is given in Table 2. The values of parameters for the ferritic matrix were assumed to be the effective ones, derived from mechanical testing of CGI specimens. To consider debonding, a damage criterion was applied to either graphite or interface with deletion of corresponding elements when its critical value was met. Damage estimation in a finite-element code was performed by evaluating the magnitude of a damage variable ( D ) at all Gauss points of a finite element. This variable represents the percentage of stiffness reduction after initiation of material degradation. Therefore, an element was considered damaged after D became nonzero in one of the four Gauss points and the element was deleted after the critical value was exceeded at integration points. Element deletion corresponded to a loss of contact between matrix and inclusion, after decohesion took place. For a model of single inclusion without interface, the threshold for damage initiation was stress-based and equal to the yield stress of graphite. This selection was supported by the fact that graphite behaves mostly elastically and its plastic deformation is limited. On the other hand, when the interfacial layer was considered, its stiffness ��� , critical separation � and fracture energy were based both on the work of Zhang et al. (2018) and in-house nano-indentation experiments in the interface of CGI. These values were: ��� � ��� GPa, � � ������ nm and � ��� N/mm.