Statistics of strength of ceramics: finite weakest-link model and necessity of zero threshold
type: Item
instance of: scholarly article
title: Statistics of strength of ceramics: finite weakest-link model and necessity of zero threshold
zbMATH Open document ID: 1194.74013
author: S. D. Pang
author: Zdeněk P. Bažant
author: Jia-Liang Le
published in: International Journal of Fracture
publication date: 2009-09-18T00:00:00Z
review text: It is expected that the distribution of strength of quasibrittle structures changes from predominantly Gaussian to Weibullian distribution as the structure size increases. Therefore, the ratio of the safety factor to the standard deviation is nearly double when passing from small laboratory samples to quasibrittle structures much larger than the representative volume element (RVE). The present paper provides a verification of such behavior for quasibrittle ceramics. The developed finite weakest-link model is based on the fact that the rate processes (e.g. effects of temperature and activation energy) are not the only phenomena that translate from the nanoscale to the macroscale material. The tail of the cumulative distribution function (cdf) of failure probability versus strength is another such phenomenon, namely due to (i) the left tail of cdf of strength on the atomic scale is described by a power law with a zero threshold, and (ii) this power law with zero threshold is indestructible, and its exponent gets raised when passing to higher scales. The paper explores these two properties for the cdf of strength for structures consisting of touch ceramics by considering the structures of positive geometry. In this case, the derivative of stress intensity factor with respect to crack length at constant load is positive, causing failure occurring at macrocrack initiation from RVE. According to the theory, the Weibull distribution corresponds to the weakest-link chain model in which the number of links tends to infinity. When the specimen is not large enough compared to the grain size, a chain with a finite number of links must be used that leads to a distribution that differs from Weibull one. The proposed model agrees with the measured mean size effect curves for different ceramics. It is justified by energy release rate dependence of the activation energy barriers for random crack length jumps through the atomic lattice. This shows that the tail of the failure probabi…
Mathematics Subject Classification ID: 74A45
Mathematics Subject Classification ID: 74R10
Mathematics Subject Classification ID: 74S60
zbMATH DE Number: 5605034
zbMATH Keywords: size-effect
zbMATH Keywords: activation energy
zbMATH Keywords: atomic lattice
zbMATH Keywords: quasibrittle materials
zbMATH Keywords: Weibullian distribution
reviewed by: Ivan A. Parinov
MaRDI profile type: Publication
full work available at URL: s10704-009-9317-8
OpenAlex ID: W2038761580
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DOI: 10.1007/S10704-009-9317-8
description: scientific article; zbMATH DE number 5605034