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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in a mechanical model or heat flux and temperature distribution in a thermal model, the performance of the modeled microstructure can be assessed and effective material properties can be estimated. In the present study the approach was tested focusing on pore structures. The presented models are based on observations of ceramics, which had been mixed with organic inclusions. In this context the pore shape and preferred orientation was of major interest.

2. Methodological approach

2.1. Generation of 3D model

The present digital microstructure models were generated using FreeCAD, which is an open source parametric 3D CAD modeler (https://www.freecadweb.org/) including a Python interpreter for generating complex structures (https://www.python.org/). Non-overlapping pores with defined shapes were placed at random positions within a regular cubic volume with an edge size of 10 mm. In the present case study three different pore shapes were investigated: spherical pores, oblate shaped pores and cylindrical pores. In the case of the oblate shaped pores three different ratios of minor axis against main axis were tested: 1:2, 1:3 and 1:4. The average size of the pores, which was subject to a random variation of  25%, was chosen so that pre-selected numbers of 30 to 90 pores corresponded to total porosities of c. 5 to 15 %, a porosity range relevant for example for ancient pyrotechnical ceramics (Hein et al. (2013)). The oblates and cylinders were placed with a preferred orientation perpendicular to the applied mechanical or thermal loads. Also in case of the orientation a random variation of  5° was added.

Fig. 3. (left) spherical pores; (centre) oblate shaped pores; (right) cylindrical pores.

2.2. Finite element method

The generated digital models were imported into the SpaceClaim modeler of the Ansys 18.1 workbench (Ansys Inc.). Material properties of an average ceramic material were assigned to the ceramic matrix of the porous test cubes (Fig.4). Two auxiliary rectangular plates were added to the top and bottom surfaces of the models in order to distribute the simulated loads uniformly on the ceramic surface. For the simulations material properties of structural steel in the case of the mechanical model or copper in the case of the thermal model were assigned to the auxiliary plates. For the present study in the case of the mechanical simulations the contact layers between auxiliary plates and the test cube were defined as frictional with a moderate friction coefficient of 0.2, while in the case of the thermal simulations the contacts were defined as bonded. The effect of different kinds of contacts and particularly different friction coefficients for the mechanical model will be investigated in future studies. For the meshing of the test cubes tetrahedron elements were selected and an initial element size of 1/20 of the edge size. Depending on the specific geometry and necessary refinements meshes with typically c. 100.000 up to 500.000 elements were generated. In the case of the mechanical simulation an increasing load up to 1GPa was applied on the top surface of the upper auxiliary plate, while the bottom surface of the lower auxiliary plate was fixed in the direction of the applied load (Fig.4). The average directional displacement of the external surface of the upper auxiliary plate under the