Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading
The design of various engineering structures, such as buildings, infrastructure, aircraft, ships, as well as microelectronic components and medical implants, must ensure an extremely low probability of failure during their service lifetime. Since such a low probability is beyond the means of histogr...
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crsagepubl:10.1177/1081286513505463 2024-09-09T20:07:49+00:00 Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading Le, Jia-Liang Bažant, Zdeněk P. 2013 http://dx.doi.org/10.1177/1081286513505463 http://journals.sagepub.com/doi/pdf/10.1177/1081286513505463 http://journals.sagepub.com/doi/full-xml/10.1177/1081286513505463 en eng SAGE Publications http://journals.sagepub.com/page/policies/text-and-data-mining-license Mathematics and Mechanics of Solids volume 19, issue 1, page 56-70 ISSN 1081-2865 1741-3028 journal-article 2013 crsagepubl https://doi.org/10.1177/1081286513505463 2024-08-05T04:40:20Z The design of various engineering structures, such as buildings, infrastructure, aircraft, ships, as well as microelectronic components and medical implants, must ensure an extremely low probability of failure during their service lifetime. Since such a low probability is beyond the means of histogram testing, we must rely on some physically based probabilistic model for the statistics of structural lifetime. Attention is focused on structures consisting of quasibrittle materials. These are brittle materials with inhomogeneities that are not negligible compared with the structure size, as exemplified by concrete, fiber composites, tough ceramics, rocks, sea ice, bone, wood, and many more at the micro- or nano-scale. This paper presents a finite weakest-link model of the fatigue lifetime of quasibrittle structures that fail at the fracture of one representative volume element (RVE). In this model, the probability distribution of critical stress amplitude is first derived by assuming a prescribed number of loading cycles and a fixed stress ratio. The probability distribution of fatigue lifetime is then deduced from the probability distribution of critical stress amplitude through the Paris law for fatigue crack growth. It is shown that the present theory matches well with the experimentally measured lifetime histograms of various engineering and dental ceramics, which systematically deviate from the two-parameter Weibull distribution. The theory indicates that the mean fatigue lifetime of quasibrittle structures must strongly depend on the structure size and geometry. Finally, the present model indicates that the probability distribution of fatigue lifetime can be determined from the mean size effect analysis. Article in Journal/Newspaper Sea ice SAGE Publications Mathematics and Mechanics of Solids 19 1 56 70 |
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The design of various engineering structures, such as buildings, infrastructure, aircraft, ships, as well as microelectronic components and medical implants, must ensure an extremely low probability of failure during their service lifetime. Since such a low probability is beyond the means of histogram testing, we must rely on some physically based probabilistic model for the statistics of structural lifetime. Attention is focused on structures consisting of quasibrittle materials. These are brittle materials with inhomogeneities that are not negligible compared with the structure size, as exemplified by concrete, fiber composites, tough ceramics, rocks, sea ice, bone, wood, and many more at the micro- or nano-scale. This paper presents a finite weakest-link model of the fatigue lifetime of quasibrittle structures that fail at the fracture of one representative volume element (RVE). In this model, the probability distribution of critical stress amplitude is first derived by assuming a prescribed number of loading cycles and a fixed stress ratio. The probability distribution of fatigue lifetime is then deduced from the probability distribution of critical stress amplitude through the Paris law for fatigue crack growth. It is shown that the present theory matches well with the experimentally measured lifetime histograms of various engineering and dental ceramics, which systematically deviate from the two-parameter Weibull distribution. The theory indicates that the mean fatigue lifetime of quasibrittle structures must strongly depend on the structure size and geometry. Finally, the present model indicates that the probability distribution of fatigue lifetime can be determined from the mean size effect analysis. |
format |
Article in Journal/Newspaper |
author |
Le, Jia-Liang Bažant, Zdeněk P. |
spellingShingle |
Le, Jia-Liang Bažant, Zdeněk P. Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading |
author_facet |
Le, Jia-Liang Bažant, Zdeněk P. |
author_sort |
Le, Jia-Liang |
title |
Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading |
title_short |
Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading |
title_full |
Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading |
title_fullStr |
Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading |
title_full_unstemmed |
Finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading |
title_sort |
finite weakest-link model of lifetime distribution of quasibrittle structures under fatigue loading |
publisher |
SAGE Publications |
publishDate |
2013 |
url |
http://dx.doi.org/10.1177/1081286513505463 http://journals.sagepub.com/doi/pdf/10.1177/1081286513505463 http://journals.sagepub.com/doi/full-xml/10.1177/1081286513505463 |
genre |
Sea ice |
genre_facet |
Sea ice |
op_source |
Mathematics and Mechanics of Solids volume 19, issue 1, page 56-70 ISSN 1081-2865 1741-3028 |
op_rights |
http://journals.sagepub.com/page/policies/text-and-data-mining-license |
op_doi |
https://doi.org/10.1177/1081286513505463 |
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Mathematics and Mechanics of Solids |
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19 |
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1 |
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56 |
op_container_end_page |
70 |
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1809941492552171520 |