Chapter 55. Determination of Multimodal Defect Distributions for Use in Probabilistic Failure Theories for Load-Bearing Ceramics
- 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
Margetson, J. (1993) Determination of Multimodal Defect Distributions for Use in Probabilistic Failure Theories for Load-Bearing Ceramics, 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.ch55
- Published Online: 28 MAR 2008
- Published Print: 1 JAN 1993
Print ISBN: 9780470375266
Online ISBN: 9780470314180
- multiaxial stress;
Probabilistic failure theories have been developed for predicting the structural reliability of complex components subjected to conditions of multiaxial stress. Embodied in these theories are material failure characteristics that describe the statistical variation of defects within the volume and over the surface of the material. These strength parameters are evaluated from an analysis of the fracture data derived from suitably defined test specimens.
In this paper a general approach to the statistical characterization of material strength is adopted. It is shown, for example, that when the stress is directly proportional to the applied load (and this is the case for most strength test configurations), a standardized strength distribution can be derived. This analysis presents the possibility of characterizing the defect distributions from components of complex geometric shape. If the manufacturing routes are not the same or the magnitude of the volumes and surface areas of the component and test specimens differ significantly, then difficulties in extrapolating strength characteristics from one geometry to another may be encountered. This generalized approach could be used to resolve this problem.
The strength analysis of brittle components is usually based on a unimodal failure model where it is assumed that within a material there are surface and volume flaws that are randomly distributed, and that failure will originate from one of these defects. In practice, failure will originate from either volume or surface flaws, and within a fracture data set it may not be apparent which test specimen is associated with which failure mode. In this paper a method is presented for analyzing bimodal data and uncoupling the respective distributions from a single data set. It is also shown how the respective volume and surface defect distributions can be analyzed to yield the strength parameters required by the various probabilistic multiaxial failure stress theories.