TECHNICAL PAPERS
Jan 19, 1996

Zero-Brittleness Size-Effect Method for One-Size Fracture Test of Concrete

Publication: Journal of Engineering Mechanics
Volume 122, Issue 5

Abstract

This paper proposes a new and less laborious version of the size-effect method for measuring the fracture energy or fracture toughness of concrete as well as other nonlinear fracture characteristics, such as the effective length of fracture process zone or critical crack-tip opening displacement. The size-effect method, based on the size-effect law, is the simplest to carry out because only the maximum loads of specimens need to be measured. No measurements of postpeak deflection and unloading stiffness, nor observations of crack-tip location, are needed; the testing machine need not be very stiff, and there is no need for closed-loop displacement control. The simplicity of the method makes it suitable not only for the laboratory but also for field quality control. In the original version of the size-effect method, notched specimens of different sizes are tested. The proposed new version further simplifies testing by allowing the use of notched specimens of only one size. The idea is to supplement the one-size notched-beam tests with an evaluation of the maximum load value for specimens with a zero-brittleness number. There are two types of methods that will achieve this. In one type of method, zero-brittleness data are obtained by using plastic limit analysis based on the modulus of rupture or compression strength of concrete to calculate the limiting nominal strength for zero specimen size. In the second type of method, zero-brittleness data are obtained by testing the maximum loads of notchless specimens of the same size. The former type leads to simpler calculations but has the drawback that the material strength to calculate the maximum load for zero size depends on specimen geometry. Both types of the zero-brittleness version of the size-effect method are validated by previously reported test data. The proposed method should also be applicable to other quasibrittle materials such as rock, ice, tough ceramics, and brittle composites.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
ACI Committee 446. (1992). “State-of-art-report on fracture mechanics of concrete: Concepts, models and determination of material properties.”Fracture mechanics of concrete structure, Z. P. Bažant, ed., Elsevier Applied Science, London, U.K., 4–144.
2.
Ang, A. H-S., and Tang, W. H. (1975). Probability concepts in engineering planning and design. John Wiley & Sons, Inc., New York, N.Y.
3.
ASTM. (1994). “Practice for making and curing concrete test specimens in field.”Annual book of ASTM standards, Vol. 04.02, Concrete and Aggregates, C31-91, 7–9.
4.
Bažant, Z. P.(1984). “Size effect in blunt fracture: concrete, rock, metal.”J. Engrg. Mech., ASCE, 110, 518–535.
5.
Bažant, Z. P. (1987). “Fracture energy of heterogeneous material and similitude.” Preprints, SEM-RILEM Int. Conf. on Fracture of Concrete and Rock (Houston, Tex., June 1987), S. P. Shah and S. E. Swartz, eds., Soc. for Exper. Mech. (SEM), 390–402.
6.
Bažant, Z. P.(1994a). “Discussion of `fracture mechanics and size effect of concrete in tension,' by T. Tang, S. P. Shah, and C. Ouyang.”J. Struct. Engrg., ASCE, 120(8), 2555–2558.
7.
Bažant, Z. P. (1994b). “Is size effect caused by fractal nature of crack surfaces?”Rep. 94-10/C402i, Dept. of Civ. Engrg., Northwestern Univ., Evanston, Ill.
8.
Bažant, Z. P. (1995). “Scaling theories for quasibrittle fracture: recent advances and new directions.”Proc., 2nd Int. Conf. on Fracture Mech. of Concrete and Concrete Struct.; FraMCoS2 (ETH, Zürich, Switzerland), F. H. Wittmann, ed., Aedificatio Publishers, Freiburg, Germany, 515–534.
9.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture and damage theories, Oxford University Press, New York, N.Y.
10.
Bažant, Z. P., and Gettu, R. (1992). “Rate effects and load relaxation in static fracture of concrete.”ACI Mat. J., 89-M49, Sept., 456–467.
11.
Bažant, Z. P., Gettu, R., and Kazemi, M. T.(1991). “Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curve.”Int. J. Rock Mech. and Min. Sci., 28(1), 43–51.
12.
Bažant, Z. P., and Kazemi, M. T.(1990). “Determination of fracture energy, process zone length and brittleness number from size effect, with application to rock and concrete.”Int. J. Fracture, 44, 111–131.
13.
Bažant, Z. P., and Li, Z.(1995). “Modulus of rupture: Size effect due to fracture initiation in boundary layer.”J. Struct. Engrg., ASCE, 121(4), 739–746.
14.
Bažant, Z. P., Li, Z., and Li, Y.-N. (1994). “Brittle-plastic size effect method of measuring fracture properties of concrete or rock.”Rep., Dept. of Civ. Engrg., Northwestern Univ., Evanston, Ill.
15.
Bažant, Z. P., and Pfeiffer, P. A.(1987). “Determination of fracture energy from size effect and brittleness number.”ACI Mat. J., 84(6), 463–480.
16.
Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics, and decision for civil engineers. McGraw-Hill Book Co., New York, N.Y.
17.
Broek, D. (1988). The practical use of fracture mechanics . Kluwer Academic Publishers, Dordrecht, The Netherlands.
18.
Crow, E. L., Davis, F. A., and Maxfield, M. W. (1960). Statistics manual. Dover, New York, N.Y.
19.
Elishakoff, I. (1983). Probability method in the theory of structures . John Wiley & Sons, Inc., New York, N.Y.
20.
Gettu, R., Bažant, Z. P., and Karr, M. E. (1990). “Fracture properties and brittleness of high strength concrete.”ACI Mat. J., 87-M66, Nov., 608–618.
21.
Hillerborg, A. (1985). “Results of three comparative test series for determining the fracture energy G f of concrete.”Mat. and Struct., Paris, France, 18(107), 407–413.
22.
Jenq, Y. S., and Shah, S. P.(1985). “A two parameter fracture model for concrete.”J. Engrg. Mech., ASCE, 111(4), 1227–1241.
23.
Kanninen, M. F., and Popelar, C. H. (1985). Advanced fracture mechanics. Oxford University Press, New York, N.Y.
24.
Planas, J., and Elices, M. (1989). “Size effect in concrete structures: Mathematical approximations and experimental validation.”Cracking and damage: Strain localization and size effect, J. Mazars and Z. P. Bažant, eds., Elsevier, London, U.K., 462–476.
25.
RILEM Recommendation.(1990). “Size effect method for determining fracture energy and process zone of concrete.”Mat. and Struct., Paris, France, 23, 461–465.
26.
Tada, H., Paris, P., and Irwin, G. (1985). The stress analysis of cracks handbook, 2nd Ed., Paris Productions Inc., Mo.
27.
Tang, T., Bažant, Z., Yang, S., and Zollinger, D. (1995). “Variable-notch one-size test method for fracture energy and process zone length.”Engrg. Fracture Mech.
28.
Wells, A. A.(1961). “Unstable crack propagation in metals-cleavage and fast fracture.”Symp. on Crack Propagation, Cranfield, U.K., 1, 210–230.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 122Issue 5May 1996
Pages: 458 - 468

History

Published online: Jan 19, 1996
Published in print: May 1, 1996

Permissions

Request permissions for this article.

Authors

Affiliations

Zdeněk P. Bažant, Fellow, ASCE,
Walter P. Murphy Prof., of Civ. Engrg. and Mat. Sci., Northwestern Univ., Evanston, IL 60208.
Zhengzhi Li
Grad. Res. Asst., Northwestern Univ., Evanston, IL.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share