Derivation of the effective volume of a ceramic component with a truncated cone shape under internal pressure by analytical and numerical methods

Ceramic materials are desirable in structural applications because of their strength at high temperatures, low thermal expansion, and excellent wear resistance. However, ceramic structures are generally brittle and will fail due to inherent flaws that can be introduced into the material through processing, handling, or while in service. In the strength test samples of ceramic materials, the observed strength depends on the sample volume and the test method, and the results have significant scattering. On the other hand, it is important to recognize the variability of the strength of ceramic materials for structural design, and in the design process, this variability usually requires a probability-based failure criterion, which, due to the brittle fracture of ceramics, usually uses the Weibull distribution to represent their strength. With the help of Weibull distribution, the concept of effective volume is defined and by using it, the strength of a test sample with a specific geometry and loading is predicted from another sample that has a different geometry and loading. In this research, the effective volume for a truncated cone under internal pressure has been derived analytically. With the effective volume for this configuration and a sufficient number of flexural strength tests with the help of small and low-cost flexural specimens, it is possible to predict the tensile strength of the ceramic truncated cone without conducting expensive tests. for a problem with a specific material property and dimensions, the effective volume was calculated numerically and it had a 3% error compared to the analytical value.