Chapter 39. The Numerical Evaluation of Failure Theories for Brittle Materials
- John B. Wachtman Jr.
Published Online: 28 MAR 2008
Copyright © 1993 The American Ceramic Society
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
How to Cite
Smart, J. and Fok, S. L. (2008) The Numerical Evaluation of Failure Theories for Brittle Materials, 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.ch39
- Published Online: 28 MAR 2008
- Published Print: 1 JAN 1993
Print ISBN: 9780470375266
Online ISBN: 9780470314180
- theoretical value;
In predicting the life of ceramic components there are three basic requirements: reliable material property data, an appropriate failure theory, and an accurate numerical analysis when the failure probability of a component in a complex stress state cannot be calculated analytically.
The three are not independent. For example, a numerical analysis is required to determine the deviation of the stress field within a specimen from the theoretical value during material testing. This then allows the determination of suitable corrections for the material property data identified on the basis of simple theory. Another example is the determination of the most appropriate failure theory in predicting the life of components under complex stress states. This cannot be achieved without accurate numerical analysis and the problem is best illustrated by considering two very similar failure theories: Batdorf's flow density distribution approach and Evans' multiaxial elemental strength approach. Lamon claimed that the latter approach gave better predictions, but the difference is attributed to numerical inaccuracy since it has been shown recently1 that the two theories are in fact identical, provided the same fracture criterion is assumed.
This paper will concentrate on the last problem—the numerical evaluation of failure theories. The theories can be divided into two categories: those that incorporate volume integrals and those that use surface integrals. For complex geometries and stress states, the integrals are usually calculated by postprocessing the results from a finite element analysis. A common method is to use the centroidal stresses, which are assumed uniform throughout an element. For surface-type failures, shell elements are commonly employed in the analysis. However, it will be shown in the paper that by adopting a different integration procedure, Gaussian Quadrature, results can be obtained more accurately and efficiently. This requires the sampling of stresses at various Gauss points within an element. Also, the use of shell elements to evaluate the surface integrals will be shown to be unnecessary. In both cases, the quality of the results in terms of accuracy and speed of convergence with respect to the number of elements and the number of stress-sampling points will be considered for a range of failure theories and a wide range of component shapes. It will be shown that by using the postprocessor written by the authors, the errors are generally less than those associated with finite element analysis.
Thus, the authors believe that an accurate and efficient evaluation of a particular failure theory has been achieved. This will improve the reliability of material property data and will allow a more critical examination of the various failure theories.