PSI - Issue 37

Evangelia Nektaria Palkanoglou et al. / Procedia Structural Integrity 37 (2022) 209–216 E. N. Palkanoglou et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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To consider and model thermal decohesion adequately, a traction-separation law was applied to the interface. This constitutive behaviour was associated with a damage criterion followed by deletion of the corresponding elements when a critical value was met. Damage was estimated by assessing the magnitude of a damage variable ( D ) at all Gauss points of a finite element. This variable corresponded to the stiffness loss, after the start of material degradation. Hence, an element was considered damaged after D exhibited nonzero values in one of the four Gauss points, whereas element deletion took place after the critical value was exceeded at all four integration points. Element deletion led to the loss of contact between the matrix and the inclusion, after debonding took place. The constitutive parameters of traction-separation law are: stiffness ( ) , critical separation ( ) , and fracture energy ( ) . Their values were based on the work of Zhang et al. (2018) and in-house nano-indentation experiments at the interface of CGI. The values used in simulations were: = 61 GPa, = 3.33 nm, and = 20 N/mm.The 2D unit cell was modelled with full-integration quadrilateral plane-stress elements (CPE4), whereas the interfacial layer was modelled with cohesive finite elements. After performing a mesh-convergence study, a total of 12336 elements was used, leading to 24720 degrees of freedom. Considering a unit cell as the smallest representative part of the microstructure, implementation of periodic boundary conditions (PBCs) at the cell’s edges is required to simulate the deformation field around it accurately (Hill, 1963). More specifically, PBCs guarantee that the edges of the unit cell remain periodic during deformation, implying that every single unit cell has the same deformation and neither overlaps nor separates from the surrounding unit cells. Considering any two points x and x + d lying on opposite edges of a unit cell with dimensions, d , the periodic boundary conditions on them are expressed as (Drago and Pindera, 2007) ( + ) = ( ) + ̅ ∙ , (1) ( + ) = − ( ) , (2) where u and t are the displacement and the surface traction, respectively. In addition, ̅ is the average infinitesimal strain over the volume element, which is mostly defined externally. Finally, pure thermal loading was applied to the unit cells, focusing on its influence on the interaction of two graphite particles as the distance between them changed. The selection of loading conditions was based on the fact that CGI is sensitive to high temperatures due to its heterogeneous nature while high-temperature conditions are generally observed at most of its industrial applications. The loading was applied as a field to the entire unit cell, in the form of a linear temperature increase throughout the domain from 50 °C to 500 °C. 3. Results 3.1. Interaction between two vermicular inclusions The effect of a neighbouring vermicular inclusion on the decohesion of a vermicular one from its surrounding matrix material is discussed in this section. The onset and propagation of decohesion for the maximum- and minimum- distance configurations is presented in Fig. 3. The onset of decohesion was defined as the temperature, at which the first cohesive element of the interfacial layer was deleted. For both configurations, debonding started at the same temperature level. However, the evolution of thermal debonding was affected by the distance between the inclusions. More specifically, the fraction of debonded areas was lower when the distance between the particles was higher. As expected, when the distance between the two vermicular inclusions increased, their interaction became less intense. Therefore, any secondary stresses induced due to this interaction were much lower, causing not only a slower propagation of the phenomenon but also a spatial localisation of this effect.