Evaluation of flexural fracture toughness for
quasi-brittle structural materials using a simple
test method
M.M. Reda Taha, X. Xiao, J. Yi, and N.G. Shrive
Abstract: As new structural concepts such as partial prestressing and steel-free bridge decks are more widely accepted
and used, there is an increasing need for a reliable and reproducible fracture performance criterion that can describe re-
sistance to crack growth. The required criterion should also be easy to determine experimentally so that it can be in-
corporated in structural specifications. The nonlinear behaviour of concrete and masonry materials suggested that quasi-
brittle fracture mechanics approaches may be the most suitable for determining their fracture performance. The effec-
tive elastic crack model originally developed by Karihaloo and Nallathambi (1989) was modified to evaluate the critical
crack depth under pure flexural stresses. A computer program was developed to calculate this depth iteratively from the
experimental results. An experimental programme examining the fracture performance of four different structural mate-
rials (high performance concrete, mortar, fibre reinforced concrete, and masonry units) was carried out to examine the
applicability of the model. As no post-peak data are required for the analysis, the model allows the use of a simple test
setup to evaluate the fracture performance of quasi-brittle materials experimentally.
Key words: fracture toughness, linear elastic fracture mechanics (LEFM), elastoplastic fracture mechanics (EPFM),
quasi-brittle fracture mechanics, effective elastic crack, high performance concrete, masonry, fibre reinforced concrete.
Résumé : Car nouveau des concepts structuraux tels que la précontrainte partielle et les paquets acier-libres de passe-
relle sont reçus et plus largement répandus, il y a un besoin croissant de critère fiable et reproductible d’exécution de
rupture qui peut décrire la résistance à la progression de la fissure. Il devrait également être facile déterminer le critère
exigé expérimentalement de sorte qu’il puisse être incorporé dans des caractéristiques structurales. Le comportement
non linéaire des matériaux de béton et de maçonnerie a suggéré que les approches de mécanique de rupture quasi-
fragile puissent être les plus appropriées à déterminer leur exécution de rupture. Le modèle élastique pertinent de fente
initialement développé par Karihaloo et Nallathambi (1989) a été modifié pour évaluer la profondeur critique de fente
sous des efforts flexural purs. Un programme machine a été développé pour calculer cette profondeur itérativement à
partir des résultats expérimentaux. Un programme expérimental examinant l’exécution de rupture de quatre matériaux
structuraux différents (le béton de rendement élevé, le mortier, fibre a renforcé le béton et les unités de maçonnerie) a
été effectué pour examiner l’applicabilité du modèle. Car on n’a besoinavoir besoin d’aucun poteau-crête pour
l’analyse, le modèle permet l’utilisation d’une installation d’essai simple d’évaluer l’exécution de rupture des matériaux
quasi-fragiles expérimentalement.
Mots clés : rompez la dureté, LEFM, EPFM, mécanique de rupture de quasi-brittle, la fente élastique pertinente, le bé-
ton de rendement élevé, maçonnerie, le béton renforcé de fibres.
Reda Taha et al. 575
Introduction
Most recent design codes require that ultimate and ser-
viceability limit states be considered in the design of con-
crete and masonry structures. The ultimate limit state uti-
lizes strength-based failure criteria while serviceability limit
states use cracking criteria. Crack initiation is usually as-
sumed to occur when the modulus of rupture or cracking
strength is exceeded (CEB-FIP MC90 1993; CSA
A23.3 1994; ACI 318-02 2002; CHBDC 2000). Shah et al.
(1995) pointed out, however, that the current limit states
structural design approach neglects a number of issues that
can only be considered if fracture analysis is incorporated in
the design. These issues include the possible quasi-brittle
failure of reinforced elements designed for ductile failure
(e.g., shear failure of longitudinally reinforced concrete
beams with no shear reinforcement (Rizkalla et al. 1983));
the imprecise empirical cracking criteria of concrete and ma-
sonry that consider neither the fracture energy nor the size
of the fracture process zone; the observed debonding and
slipping of steel reinforcement in structures at crack loca-
tions, which is usually neglected but can significantly affect
Can. J. Civ. Eng. 29: 567–575 (2002) DOI: 10.1139/L02-044 © 2002 NRC Canada
567
Received 29 January 2002. Revision accepted 15 May 2002.
Published on the NRC Research Press Web site at
http://cjce.nrc.ca on 26 July 2002.
M.M. Reda Taha.
1
Stantec Consulting Ltd., 1122 4th Street
S.W., Calgary, AB T2R 1M1, Canada.
X. Xiao. Acres International Limited, 815 8th Avenue S.W.,
Calgary, AB T2P 3P2, Canada.
J. Yi and N.G. Shrive. Department of Civil Engineering,
The University of Calgary, Calgary, AB T2N 1N4, Canada.
Written discussion of this article is welcomed and will be
received by the Editor until 31 December 2002.
1
Corresponding author (e-mail: mredataha@shaw.ca).