PSI - Issue 10

A. Hein et al. / Procedia Structural Integrity 10 (2018) 219–226 A. Hein and V. Kilikoglou / Structural Integrity Procedia 00 (2018) 000 – 000

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applied load was expected to provide an estimation of the altered elasticity of test cubes with different pore structures. In the case of the thermal simulation two different temperatures were applied on the external surfaces of the auxiliary plates (Fig.4). In this case the resulting directional heat flux through the auxiliary plates provided an estimation of the thermal conductivity of the examined test cube.

Fig. 4. (left) Mechanical model with load applied on the top surface of the upper auxiliary plate while bottom surface of lower plate is fixed; The density of the ceramics was pre-defined with 1700 kg/m 3 and the Young’s modulus with 18 GPa while for the structural steel 7850 kg/m 3 and 200 GPa were assumed; (right) Thermal model with two different temperatures applied to external surfaces of auxiliary plates; The density of the ceramics was pre-defined with 2700 kg/m 3 and the thermal conductivity with 1 W/(m·K) while for the copper 8300 kg/m 3 and 401 W/( m · K) were assumed.

3. Results and discussion

As it was expected, mechanical properties, in the present case elasticity, as well as thermal properties, in the present case thermal conductivity, decrease with increasing porosity. However, apart from the total porosity the pore shapes showed major impact on the material properties. In the case, of the Young’s modulus (Fig. 5) flat oblates (axial ratios of 1:3 and 1:4) presented a particularly rigorous decrease of elasticity relative to the solid cube without porosity, almost doubling the effect of round or even moderately flat oblates. According to the simulation also fibrous pore structures indicated an additional decrease of elasticity compared to spherical pores, even though the difference to spherical pores appears to be rather insignificant in the case of small porosities. The results were compared with approximations for isometric isolated spherical pores (Pabst and Gregorova 2014) and overlapping spherical pores (Roberts and Garboczi (2000)). It appears that pore structures with overlapping pores reduce the elasticity to a larger extent than isolated pores, which were investigated in the present case study. Mechanical strength, such as compressive, tensile or flexure strength, cannot be directly assessed from the present simulations. The FEM results provide estimations for different types of stress in particular areas of the porous ceramic cubes. Even though the maximum stress in specific areas might reach in some cases indeed levels at which crack initiation could be expected no particular relation of different types of stress to total porosity or pore shape was observed. For further investigation of strength crack propagation has to be examined for different pore structures. Nevertheless, a general relation between strength and elasticity can be assumed (Wachtman et al. 2009, p. 46) so that the collected results in terms of elasticity can be interpreted also in terms of strength. In the case of the simulated thermal conductivity structures of flat oblate shaped pores, similarly to the investigated relative elasticity, presented the largest decrease relative to the solid cube without porosity (Fig.6). It has to be noted that the moderately flat oblate shaped pores (1:2) on the other hand, presented no significant difference to the spherical pores. Both types of pores match in terms of their effect on thermal conductivity basically the expected impact of random porosity (Litovsky and Shapiro (1992)). The fibrous pore structures eventually present a clear additional decrease in terms of thermal conductivity. This confirms experimental results collected in a study of metallurgical ceramics (Hein et al. (2013)). Assuming that heat transfer was preferred to be suppressed in a furnace wall or even in a crucible, which was heated from above or inside, the observed tempering with organic