# Chapter 56. Evaluation of Failure Probabilities of Multiaxially Loaded Components Using the STAU Postprocessor

- John B. Wachtman Jr.

Published Online: 28 MAR 2008

DOI: 10.1002/9780470314180.ch56

Copyright © 1993 The American Ceramic Society

Book Title

## Proceedings of the 17th Annual Conference on Composites and Advanced Ceramic Materials, Part 1 of 2: Ceramic Engineering and Science Proceedings, Volume 14, Issue 7/8

Additional Information

#### How to Cite

Brückner-Foit, A., Heger, A. and Munz, D. (2008) Evaluation of Failure Probabilities of Multiaxially Loaded Components Using the STAU Postprocessor, in Proceedings of the 17th Annual Conference on Composites and Advanced Ceramic Materials, Part 1 of 2: Ceramic Engineering and Science Proceedings, Volume 14, Issue 7/8 (ed J. B. Wachtman), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470314180.ch56

#### Publication History

- Published Online: 28 MAR 2008
- Published Print: 1 JAN 1993

#### Book Series:

#### ISBN Information

Print ISBN: 9780470375266

Online ISBN: 9780470314180

- Summary
- Chapter

### Keywords:

- components;
- orientation;
- integral;
- multidimensional;
- velocity

### Summary

Failure of ceramic components is caused by the most dangerous flaw contained in the component. The risk associated with a specific flaw depends on the size of the flaw, its location in the stress field, and its orientation with respect to the principal stress axes. All of these quantities are random, and a convolution integral of the corresponding probability density functions yields the failure probability. The resulting multidimensional integral has to be evaluated numerically.

For real components, the stress field follows from a finite element analysis, and the stress tensor is only known at so-called integration points. STAU is a postprocessor that has been developed to evaluate the failure probability using the results of finite element analysis. In this computer code, special care has been taken to achieve high numerical accuracy.

Subcritical crack growth occurs under sustained loading. In a multiaxial stress field, the crack growth velocity depends not only on the size of the crack and the value of the stress tensor at a given location, but also on the orientation of the crack plane with respect to the stress axes. Hence, the lifetime distribution follows from a multidimensional integral that is very similar to the one used for the failure probability for instantaneous fracture. The postprocessor STAU can also be used to predict the lifetime distribution for components subject to sustained multiaxial loading.

Another important issue in lifetime prediction is the effect of a proof test on the reliability of a component. It is shown how the formulas for the lifetime distribution have to be modified in order to take proof testing into account. Finally, the lifetime distribution is calculated for a model component.