The statistical size effect has generally been explained by the weakest-link model, which is valid if the failure of one representative volume element (RVE) of material, corresponding to one link, suffices to cause failure of the whole structure under the controlled load. As shown by the recent formulation of fishnet statistics, this is not the case for some architectured materials, such as nacre, for which one or several microstructural links must fail before reaching the maximum load or the structure strength limit. Such behavior was shown to bring about major safety advantages. Here, we show that it also alters the size effect on the median nominal strength of geometrically scaled rectangular specimens of a diagonally pulled fishnet. To derive the size effect relation, the geometric scaling of a rectangular fishnet is split into separate transverse and longitudinal scalings, for each of which a simple scaling rule for the median strength is established. Proportional combination of both then yields the two-dimensional geometric scaling and its size effect. Furthermore, a method to infer the material failure probability (or strength) distribution from the median size effect obtained from experiments or Monte Carlo simulations is formulated. Compared to the direct estimation of the histogram, which would require more than ten million test repetitions, the size effect method requires only a few (typically about six) tests for each of three or four structure sizes to obtain a tight upper bound on the failure probability distribution. Finally, comparisons of the model predictions and actual histograms are presented.
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August 2019
Research-Article
Fishnet Statistical Size Effect on Strength of Materials With Nacreous Microstructure
Wen Luo,
Wen Luo
Theoretical and Applied Mechanics,
Evanston, IL 60208
e-mail: wenluo2016@u.northwestern.edu
Northwestern University
, CEE/A123,Evanston, IL 60208
e-mail: wenluo2016@u.northwestern.edu
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Zdeněk P. Bažant
Zdeněk P. Bažant
1
McCormick Institute Professor,
W.P. Murphy
Professor of Civil and Mechanical
Engineering and Materials Science,
Evanston, IL 60208
e-mail: z-bazant@northwestern.edu
W.P. Murphy
Professor of Civil and Mechanical
Engineering and Materials Science,
Northwestern University
,Evanston, IL 60208
e-mail: z-bazant@northwestern.edu
1Corresponding author.
Search for other works by this author on:
Wen Luo
Theoretical and Applied Mechanics,
Evanston, IL 60208
e-mail: wenluo2016@u.northwestern.edu
Northwestern University
, CEE/A123,Evanston, IL 60208
e-mail: wenluo2016@u.northwestern.edu
Zdeněk P. Bažant
McCormick Institute Professor,
W.P. Murphy
Professor of Civil and Mechanical
Engineering and Materials Science,
Evanston, IL 60208
e-mail: z-bazant@northwestern.edu
W.P. Murphy
Professor of Civil and Mechanical
Engineering and Materials Science,
Northwestern University
,Evanston, IL 60208
e-mail: z-bazant@northwestern.edu
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received March 26, 2019; final manuscript received April 26, 2019; published online May 23, 2019. Assoc. Editor: Yonggang Huang.
J. Appl. Mech. Aug 2019, 86(8): 081006 (10 pages)
Published Online: May 23, 2019
Article history
Received:
March 26, 2019
Revision Received:
April 26, 2019
Accepted:
April 26, 2019
Citation
Luo, W., and Bažant, Z. P. (May 23, 2019). "Fishnet Statistical Size Effect on Strength of Materials With Nacreous Microstructure." ASME. J. Appl. Mech. August 2019; 86(8): 081006. https://doi.org/10.1115/1.4043663
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