Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures
For brittle failures, the probability distribution of structural strength and lifetime are known to be Weibullian, in which case the knowledge of the mean and standard deviation suffices to determine the loading or time corresponding to a tolerable failure probability such as 10 −6 . Unfortunately,...
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crioppubl:10.1088/0022-3727/42/21/214008 2024-09-15T18:35:30+00:00 Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures Le, Jia-Liang Bažant, Zdeněk P Bazant, Martin Z 2009 http://dx.doi.org/10.1088/0022-3727/42/21/214008 https://iopscience.iop.org/article/10.1088/0022-3727/42/21/214008 https://iopscience.iop.org/article/10.1088/0022-3727/42/21/214008/pdf http://stacks.iop.org/0022-3727/42/i=21/a=214008/pdf unknown IOP Publishing https://iopscience.iop.org/page/copyright https://iopscience.iop.org/info/page/text-and-data-mining Journal of Physics D: Applied Physics volume 42, issue 21, page 214008 ISSN 0022-3727 1361-6463 journal-article 2009 crioppubl https://doi.org/10.1088/0022-3727/42/21/214008 2024-08-26T04:19:33Z For brittle failures, the probability distribution of structural strength and lifetime are known to be Weibullian, in which case the knowledge of the mean and standard deviation suffices to determine the loading or time corresponding to a tolerable failure probability such as 10 −6 . Unfortunately, this is not so for quasibrittle structures, characterized by material inhomogeneities that are not negligible compared with the structure size (as is typical, e.g. for concrete, fibre composites, tough ceramics, rocks and sea ice). For such structures, the distribution of structural strength was shown to vary from almost Gaussian to Weibullian as a function of structure size (and also shape). Here we predict the size dependence of the distribution type for the lifetime of quasibrittle structures. To derive the lifetime statistics from the strength statistics, the subcritical crack growth law is requisite. This empirical law is shown to be justified by fracture mechanics of random crack jumps in the atomic lattice and the condition of equality of the energy dissipation rates calculated on the nano-scale and the macro-scale. The size effect on the lifetime is found to be much stronger than that on the structural strength. The theory is shown to match the experimentally observed systematic deviations of lifetime histograms from the Weibull distribution. Article in Journal/Newspaper Sea ice IOP Publishing Journal of Physics D: Applied Physics 42 21 214008 |
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For brittle failures, the probability distribution of structural strength and lifetime are known to be Weibullian, in which case the knowledge of the mean and standard deviation suffices to determine the loading or time corresponding to a tolerable failure probability such as 10 −6 . Unfortunately, this is not so for quasibrittle structures, characterized by material inhomogeneities that are not negligible compared with the structure size (as is typical, e.g. for concrete, fibre composites, tough ceramics, rocks and sea ice). For such structures, the distribution of structural strength was shown to vary from almost Gaussian to Weibullian as a function of structure size (and also shape). Here we predict the size dependence of the distribution type for the lifetime of quasibrittle structures. To derive the lifetime statistics from the strength statistics, the subcritical crack growth law is requisite. This empirical law is shown to be justified by fracture mechanics of random crack jumps in the atomic lattice and the condition of equality of the energy dissipation rates calculated on the nano-scale and the macro-scale. The size effect on the lifetime is found to be much stronger than that on the structural strength. The theory is shown to match the experimentally observed systematic deviations of lifetime histograms from the Weibull distribution. |
format |
Article in Journal/Newspaper |
author |
Le, Jia-Liang Bažant, Zdeněk P Bazant, Martin Z |
spellingShingle |
Le, Jia-Liang Bažant, Zdeněk P Bazant, Martin Z Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures |
author_facet |
Le, Jia-Liang Bažant, Zdeněk P Bazant, Martin Z |
author_sort |
Le, Jia-Liang |
title |
Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures |
title_short |
Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures |
title_full |
Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures |
title_fullStr |
Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures |
title_full_unstemmed |
Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures |
title_sort |
subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures |
publisher |
IOP Publishing |
publishDate |
2009 |
url |
http://dx.doi.org/10.1088/0022-3727/42/21/214008 https://iopscience.iop.org/article/10.1088/0022-3727/42/21/214008 https://iopscience.iop.org/article/10.1088/0022-3727/42/21/214008/pdf http://stacks.iop.org/0022-3727/42/i=21/a=214008/pdf |
genre |
Sea ice |
genre_facet |
Sea ice |
op_source |
Journal of Physics D: Applied Physics volume 42, issue 21, page 214008 ISSN 0022-3727 1361-6463 |
op_rights |
https://iopscience.iop.org/page/copyright https://iopscience.iop.org/info/page/text-and-data-mining |
op_doi |
https://doi.org/10.1088/0022-3727/42/21/214008 |
container_title |
Journal of Physics D: Applied Physics |
container_volume |
42 |
container_issue |
21 |
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214008 |
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1810478689975009280 |