Nonlinear Fracture Properties from Size Effect Tests
Publication: Journal of Structural Engineering
Volume 112, Issue 2
Abstract
The previously derived size effect law for blunt fracture is exploited for determining the parameters of the R‐curve, of the crack band model, and of Hillerborg's fictitious crack model. No measurements of the crack length or of the unloading compliance are needed. It suffices to measure only the maximum load values for a set of geometrically similar specimens of different sizes. The parameters of the size effect law can then be identified by linear regression. The inverse slope of the regression line yields the fracture energy. The regression also has a twofold benefit: it smoothes statistically scattered data, and it extends the range of the data, so that one can do with fewer tests. From the experimentally calibrated size effect law, the R‐curve may then be obtained as the envelope of the family of fracture equilibrium curves for different specimen sizes. A simple algebraic formula for this envelope is presented. The size effect regression plot makes it also possible to determine crack band model parameters, particularly the fracture energy, the crack band width, and the strain‐softening modulus. The same is made possible for Hillerborg's model.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Barenblatt, G. I., “Similarity, Self‐Similarity and Intermediate Asymptotics,” Consultants Bureau, New York, NY, 1979 (translated from Russian).
2.
Bažant, Z. P., “Comment on Hillerborg's Comparison of Size Effect Law and Fictitious Crack Model,” Dei Poli Anniversary Volume, L. Cedolin, Ed., Politecnico di Milano, Milano, Italy, Oct., 1985.
3.
Bažant, Z. P., “Crack Band Model for Fracture of Geomaterials,” Proceedings of the 4th International Conference on Numerical Methods in Geomechanics, held in Edmonton, AB, Canada, June, 1982, Z. Eisenstein, Ed., Vol. 3.
4.
Bažant, Z. P., “Fracture in Concrete and Reinforced Concrete,” Mechanics of Geomaterials: Rocks, Concretes, Soils, Z. P. Bažant, Ed., John Wiley & Sons, Chichester, NY, 1985, pp. 259–304
(Proc. of IUTAM W. Prager Symposium held at Northwestern Univ., Sept., 1983).
5.
Bažant, Z. P., “Size Effect in Blunt Fracture: Concrete, Rock, Metal,” Journal of Engineering Mechanics, ASCE, Vol. 110, 1984, pp. 518–535.
6.
Bažant, Z. P., “Fracture Mechanics and Strain‐Softening of Concrete (Preprints),” U.S.‐Japan Seminar on Finite Element Analysis of Reinforced Concrete Structures, Japan Society for the Promotion of Science, Tokyo, May, 1985, pp. 71–92.
7.
Bažant, Z. P., and Cedolin, L., “Approximate Linear Analysis of Concrete Fracture by R‐Curves,” Journal of Structural Engineering, ASCE, Vol. 110, 1984, pp. 1336–1355.
8.
Bažant, Z. P., and Estenssoro, L. F., “Surface Singularity and Crack Propagation,” International Journal of Solids and Structures, Vol. 15, 1979, pp. 405–426,
and Vol. 16, 1980, pp. 479–481.
9.
Bažant, Z. P., and Kim, J. K., “Size Effect in Shear Failure of Longitudinally Reinforced Beams,” American Concrete Institute Journal, Vol. 81, No. 5, 1984, pp. 456–468.
10.
Bažant, Z. P., and Oh, B. H., “Crack Band Theory for Fracture of Concrete,” Materiaux et Constructions (Materials and Structures), RILEM, Paris, Vol. 16, 1983, pp. 155–117.
11.
Bažant, Z. P., and Oh, B. H., “Rock Fracture via Strain‐Softening Finite Elements,” Journal of Engineering Mechanics, ASCE, Vol. 110, No. 7, July, 1984, pp. 1015–1035.
12.
Broek, D., Elementary Engineering Fracture Mechanics, Noordhoff International Publishing, Leyden, The Netherlands, 1974.
13.
Hillerborg, A., Modéer, M., and Petersson, P. E., “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements,” Cement and Concrete Research, Vol. 6, 1976, pp. 773–782.
14.
Irwin, G. R., “Fracture Testing of High Strength Sheet Material,” (Report of a Special Committee), ASTM Bulletin, Jan., 1960, p. 29;
(also Irwin, G. R., “Fracture Testing of High Strength Sheet Materials under Conditions Appropriate for Stress Analysis,” Report No. 5486, Naval Research Laboratory, July, 1960).
15.
Jenq, Y. S., and Shah, S. P., “Nonlinear Fracture Parameters for Cement Based Concrete: Theory and Experiments (Preprints),” Applications of Fracture Mechanics to Cementitious Composites (NATO Advanced Research Workshop), S. P. Shah, Ed., Northwestern Univ., Evanston, IL, Sept., 1984, pp. 213–253.
16.
Krafft, J. M., Sullivan, A. M., and Boyle, R. W., “Effect of Dimensions on Fast Fracture Instability of Notched Sheets,” Cranfield Symposium 1961, Vol. 1, pp. 8–28.
17.
Mai, Y. W., “Fracture Measurements of Cementitious Composites (Preprints),” Applications of Fracture Mechanics to Cementitious Composites (NATO Advanced Research Workshop), S. P. Shah, Ed., Northwestern Univ., Evanston, IL, Sept., 1984, pp. 289–319.
18.
Petersson, P. C., “Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials,” thesis presented to the Lund Institute of Technology, at Lund, Sweden, in 1981, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
19.
Tada, H., Paris, P. C., and Irwin, G. R., The Stress Analysis of Cracks Handbook, Del Research Corp., Hellertown, PA, 1973.
20.
Tattersall, H. G., Tappin, G., “The Work of Fracture and Its Measurement in Metals, Ceramics and Other Materials,” Journal of Materials Science, Vol. 1, 1966, pp. 296–301.
21.
Velazco, G., Visalvanich, K., and Shah, S. P., “Fracture Behavior and Analysis of Fiber Reinforced Concrete Beams,” Cement and Concrete Research, Vol. 110, 1980, pp. 41–51.
22.
Wecharatana, M., and Shah, S. P., “Slow Crack Growth in Cement Composites,” Journal of the Structural Division, ASCE, Vol. 108, June, 1982, pp. 1400–1413.
23.
Wittmann, F. H., Ed., “Fracture Mechanics of Concrete,” Elsevier, The Netherlands, 1983, p. 680.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 112 • Issue 2 • February 1986
Pages: 289 - 307
Copyright
Copyright © 1986 ASCE.
History
Published online: Feb 1, 1986
Published in print: Feb 1986
Authors
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.