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Conference Paper: Fracture statistics of brittle materials - parametric model validity
Title | Fracture statistics of brittle materials - parametric model validity |
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Authors | |
Issue Date | 2006 |
Publisher | International and American Associations for Dental Research. The IADR Abstract Archive is located at https://iadr.abstractarchives.com/home |
Citation | 84th General Session and Exhibition of the International Association for Dental Research & 1st Meeting of the Pan-Asian-Pacific Federation, Brisbane, Australia, 28 June-1 July 2006. In Journal of Dental Research, 2006, v. 85, n. Spec Iss B, abstract no. 1966 How to Cite? |
Abstract | For brittle materials, a parametric approach is commonly used in the estimation of the (population) strength distribution (very often simply assumed to be Weibull); validity relies implicitly on the assumed distribution being correct. A number of models leading to failure distributions have been claimed to be justifiable by the physical processes involved (i.e. as having a theoretical basis). These models have been claimed to have been developed by a consideration of aspects such as flaw characteristics, microstructure, fracture mechanics and statistics; observed data are not taken into account. Objectives: to examine critically the theoretical bases proposed for these models (and hence, of the derived distribution) and the means of selection in general. Methods: The validity of all aspects of all known models was examined in detail through a dissection of the arguments, careful identification of the underlying assumptions (both stated and unstated), and a thorough evaluation of their compatibility with materials science, fracture mechanics and statistics. Secondly, the ability to check if an assumed distribution is correct was examined. Results: No argument examined can be considered sound: continuum models violate linear elastic fracture mechanics (LEFM); the Weibull distribution does not follow extreme value theory and does not legitimately derive from LEFM; lattice-based models rely on several restrictive and unlikely requirements. The only certain information about strength distributions is that they are bounded above and below. The power of goodness-of-fit tests is limited for (typically used) small sample sizes, and thus the reverse support for the validity of an assumed distribution from experimental data is weak. Conclusions: No distribution can be assumed a priori. Consequently, in each case, the experimental data must be employed in choosing an appropriate distribution, which must therefore pass an explicit statistical goodness-of-fit test before being accepted. However, sample sizes larger than those commonly used are required. |
Description | Oral Session - Ceramics: Fatigue and Fracture Modes |
Persistent Identifier | http://hdl.handle.net/10722/53669 |
DC Field | Value | Language |
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dc.contributor.author | Yeung, C | en_HK |
dc.contributor.author | Darvell, BW | en_HK |
dc.date.accessioned | 2009-04-03T07:26:03Z | - |
dc.date.available | 2009-04-03T07:26:03Z | - |
dc.date.issued | 2006 | en_HK |
dc.identifier.citation | 84th General Session and Exhibition of the International Association for Dental Research & 1st Meeting of the Pan-Asian-Pacific Federation, Brisbane, Australia, 28 June-1 July 2006. In Journal of Dental Research, 2006, v. 85, n. Spec Iss B, abstract no. 1966 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/53669 | - |
dc.description | Oral Session - Ceramics: Fatigue and Fracture Modes | en_HK |
dc.description.abstract | For brittle materials, a parametric approach is commonly used in the estimation of the (population) strength distribution (very often simply assumed to be Weibull); validity relies implicitly on the assumed distribution being correct. A number of models leading to failure distributions have been claimed to be justifiable by the physical processes involved (i.e. as having a theoretical basis). These models have been claimed to have been developed by a consideration of aspects such as flaw characteristics, microstructure, fracture mechanics and statistics; observed data are not taken into account. Objectives: to examine critically the theoretical bases proposed for these models (and hence, of the derived distribution) and the means of selection in general. Methods: The validity of all aspects of all known models was examined in detail through a dissection of the arguments, careful identification of the underlying assumptions (both stated and unstated), and a thorough evaluation of their compatibility with materials science, fracture mechanics and statistics. Secondly, the ability to check if an assumed distribution is correct was examined. Results: No argument examined can be considered sound: continuum models violate linear elastic fracture mechanics (LEFM); the Weibull distribution does not follow extreme value theory and does not legitimately derive from LEFM; lattice-based models rely on several restrictive and unlikely requirements. The only certain information about strength distributions is that they are bounded above and below. The power of goodness-of-fit tests is limited for (typically used) small sample sizes, and thus the reverse support for the validity of an assumed distribution from experimental data is weak. Conclusions: No distribution can be assumed a priori. Consequently, in each case, the experimental data must be employed in choosing an appropriate distribution, which must therefore pass an explicit statistical goodness-of-fit test before being accepted. However, sample sizes larger than those commonly used are required. | - |
dc.language | eng | en_HK |
dc.publisher | International and American Associations for Dental Research. The IADR Abstract Archive is located at https://iadr.abstractarchives.com/home | en_HK |
dc.relation.ispartof | Journal of Dental Research | - |
dc.title | Fracture statistics of brittle materials - parametric model validity | en_HK |
dc.type | Conference_Paper | en_HK |
dc.identifier.email | Yeung, C: cyeungb@hkusua.hku.hk | en_HK |
dc.identifier.email | Darvell, BW: hrdubwd@hkucc.hku.hk | en_HK |
dc.identifier.hkuros | 119858 | - |
dc.identifier.volume | 85 | - |
dc.identifier.issue | Spec Iss B | - |