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

1290

5

Table 2: Constitutive parameters for ferritic matrix and graphite inclusions Ferritic matrix

Young’s modulus (GPa)

Poisson’s ratio

Coefficient of thermal expansion

Yield point (MPa)

Yield strain

Temperature (°C)

323.95 316.84 301.18 265.92 257.71

0.209% 0.195% 0.225% 0.178% 0.179%

50

150 300 400 500

150

0.25

1.2×10 -5

Graphite

27.56

0.184%

50

15.85

0.2

2.9×10 -6

The suggested unit cell was modelled with full-integration quadrilateral plane strain-elements (CPE4). The interfacial layer was modelled with cohesive finite elements, obeying to a traction-separation law. Following a mesh- convergence study, a total of 12218 elements was generated leading to 24456 degrees of freedom. A unit cell is a small representative part of the microstructure in terms of its features, assuming it has a regular pattern. This particular feature requires the implementation of periodic boundary conditions (PBCs) at the cell’s edges so that to simulate the deformation field around accurately (Hill, 1963). Essentially, such boundary conditions ensure that the external surfaces of the unit cell remain periodic during deformation. This implies that every single unit cell exhibits the same deformation and neither overlaps nor separates from surrounding unit cells. Considering any two points x and x + d lying on opposite edges of a unit cell of dimension 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. Further, pure thermal loading was used for all simulations in order to investigate the effect of increasing temperature on interfacial debonding. As already mentioned, CGI is vulnerable to thermal loading because of its heterogeneous nature and 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 form of a linear increase of temperature in the material from 50 °C to 500 °C. 3. Results 3.1. Fully fixed and periodic boundary conditions A comparison between unit cells with fully fixed and periodic boundary conditions (BCs) was performed, in order to study their effect on the mechanical response under thermal loading. The evolution of plastic zone for these different unit cells is presented in Fig. 4 (i). All graphs are plotted in the undeformed shape and the yield point at each temperature level is provided. It is evident that the BCs influenced the plastic zone in the unit cell. For a fully fixed unit cell, plasticisation first appeared at 102 °C at the edges of the inclusion and then propagated, eventually covering most of the unit-cell area. In the case of the unit cell with PBCs, plasticisation started at 223 °C in a thick layer around the curvilinear parts of particle, and the whole matrix area was plasticised at 500 °C. The magnitude of plastic deformation was also affected by the boundary conditions applied. Indeed, for the fully fixed unit cell, plastic strains