Abstract
Anchored by the theory of extreme value statistics, Weibull distribution is the most widely used mathematical model for strength distribution of brittle structures. In a series of recent studies, a finite weakest-link model was developed for strength distribution of quasi-brittle structures, and the classical Weibull distribution was shown to represent the large-size asymptote of the model. By employing a length scale, the finite weakest-link model is capable of capturing correctly the size effects on both the probability distribution and the mean value of structural strength. However, the connection of this length scale with the basic material properties is still missing. This study investigates the relationship between the length scale of the finite weakest-link model and the material length scales by analyzing the size effect on the mean structural strength. The mathematical form of this relationship is derived through dimensional analysis. To validate the model, a set of mean size effect curves is obtained through stochastic simulations, which use a nonlinear constitutive model involving both the Irwin characteristic length and the crack band width. The internal length scale of the weakest-link model is determined by optimum fitting of the benchmark size effect curves in the small-size range. Furthermore, the effect of stress field on this internal length scale is studied by considering three different loading configurations. The present analysis reveals the importance of the mean size effect analysis for the calibration of finite weakest-link model.
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Acknowledgments
This work is partially supported by the Solid Mechanics Program of the U.S. Army Research Office under Grant W911NF-15-1-0197 and by the National Science Foundation under Grant NSF/CMMI-1361868. Jan Eliáš acknowledges financial support provided by the Ministry of Education, Youth and Sports of the Czech Republic under Project LO1408.
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 4 • April 2018
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©2018 American Society of Civil Engineers.
History
Received: Jul 25, 2017
Accepted: Oct 3, 2017
Published online: Feb 13, 2018
Published in print: Apr 1, 2018
Discussion open until: Jul 13, 2018
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