## Multiscale Investigation of Design and Reliability of Ceramics

Project manager: | Prof. Dr.-rer. nat. Gerold A. Schneider |
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Projekt worker: | M.Sc. Serkan Nohut |

Supported by: | Graduiertenkolleg „Kunst und Technik“ http://www.tuhh.de/kunstundtechnik/ |

Ceramic materials have many applications in technology. In many cases, the better mechanical properties as compared to metals become important for the material selection. Fracture experiments on series of ceramic specimens introduce two important conclusions: there appears scattering of strength and the strength decreases with increasing the volume of the specimen. The scatter of the strength is caused from the scatter of the critical flaw size in a set of specimens of the same material. Since ceramics do not have a constant strength value, design with ceramic materials can not be done with a deterministic way but with a statistical way where a failure probability of a components is calculated under prescribed conditions. In this project, the reliability of ceramics is investigated in macro- and mesoscale.

The failure probability of ceramic components is calculated in two steps: computation of stress distribution in a component with a FEM program ABAQUS, calculation of the failure probability for the given stress distribution and Weibull parameters with a FEM – Postprocessor STAU (STatistische AUswertung). Firstly, the effect of the form-optimization on the reliability of ceramic rings was studied. The reliability of ceramic components can be increased through form-optimization where the maximum stresses can be reduced or stress concentrations can be eliminated. Secondly, the reliability of ceramic springs was investigated. Demand on ceramic springs increases everyday due to its advantageous properties (e.g. corrosion resistance, high temperature strength etc.). In this project, functions were introduced for the evaluation of the failure probability of ceramic springs with different spring-and material parameters and the effect of volume- and surface flaws on the failure was reported (see Fig. 1).

Figure 1: (a) Si_{3}N_{4} ceramic spring, (b) Stress distribution in the spring

In the second part of this project, the reliability of ceramics was investigated in mesoscale with Distinct Element Method (DEM). In ceramics, the failure occurs not in atomistic scale (e.g. due to dislocations) as in metals but due to pre-existing defects (e.g. pores, cracks etc.) in the material. Therefore, DEM is a useful tool in order to simulate the fracture in ceramic materials. In Fig. 2, an example is given which is performed in order to investigate the effect of residual stresses in alumina due to anisotropic thermal expansion coefficient on the crack-tip toughness and R-curve behaviour.

Figure 2: (a) DEM model of single-edged-notched mean test, (b) Predicted effect of residual stresses on crack-tip toughness with DEM