Comparison of the Hu-Duan Boundary Effect Model with the Size-Shape Effect Law for Quasi-Brittle Fracture Based on New Comprehensive Fracture Tests
Publication: Journal of Engineering Mechanics
Volume 140, Issue 3
Abstract
The boundary effect model (BEM) for concrete fracture and the effects of specimens size and crack length has previously been criticized on theoretical grounds, but the experimental evidence found in the literature, when taken alone, has been too limited to judge the validity of BEM conclusively. New, separately published, comprehensive fracture experiments, which were made on specimens cast from one and the same batch concrete and featured a broad ranges of both the size and the crack length (including a zero crack length), change the situation. The optimum fit of the data by Hu and Duan’s model shows major deviations from these new test results. On the other hand, the Type 1 and 2 size effect laws (SELs) and their amalgamation in the universal size effect law are found to give a far better fit of the test results. Thus, regardless of the previously expounded theoretical objections, the comparison with experimental evidence alone suffices to conclude that Hu and Duan’s model is not realistic.
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Acknowledgments
Financial support from the U.S. DOT, provided through Grant No. 20778 from the Infrastructure Technology Institute of Northwestern University, is gratefully appreciated.
References
ASTM. (1990). “Standard test method for plane-strain fracture toughness testing of high strength metallic materials.” ASTM E399-90, West Conshohocken, PA.
Bažant, Z. P. (1984). “Size effect in blunt fracture: Concrete, rock, metal.” J. Eng. Mech., 518–535.
Bažant, Z. P. (2005). Scaling of structural strength, Elsevier Butterworth-Heinemann, Burlington, MA.
Bažant, Z. P., and Kazemi, M. T. (1991). “Size dependence of concrete fracture energy determined by RILEM work-of-fracture method.” Int. J. Fract., 51(1), 121–138.
Cusatis, G., and Schauffert, E. (2009). “Cohesive crack analysis of size effect.” Eng. Fract. Mech., 76(14), 2163–2173.
Duan, K., and Hu, X. (2004). “Specimen boundary induced size effect on quasi-brittle fracture.” Strength Fract. Complexity, 2(2), 47–68.
Duan, K., Hu, X., and Wittmann, F. (2006). “Scaling of quasi-brittle fracture: Boundary and size effect.” Mech. Mater., 38(1–2), 128–141.
Hillerborg, A. (1985). “The theoretical basis of a method to determine the fracture energy of concrete.” Mater. Struct., 18(4), 291–296.
Hillerborg, A., Modeer, M., and Petersson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res., 6(6), 773–782.
Hoover, C. G., and Bažant, Z. P. (2013). “Comprehensive concrete fracture tests: Size effects of types 1 and 2, crack length effect and postpeak.” Eng. Fract. Mech., 110, 281–289.
Hoover, C. G., and Bažant, Z. P. (2014). “Universal size-shape effect law based on comprehensive concrete fracture tests.” J. Eng. Mech.., 473–479.
Hoover, C. G., Bažant, Z. P., Vorel, J., Wendner, R., and Hubler, M. H. (2013). “Comprehensive concrete fracture tests: Description and results.” Eng. Fract. Mech., 114, 92–103.
Hu, X. (2002). “An asymptotic approach to size effect on fracture toughness and fracture energy of composites.” Eng. Fract. Mech., 69(5), 555–564.
Hu, X., and Duan, K. (2007). “Size effect: Influence of proximity of fracture process zone to specimen boundary.” Eng. Fract. Mech., 74(7), 1093–1100.
Hu, X., and Duan, K. (2008). “Size effect and quasi-brittle fracture: The role of FPZ.” Int. J. Fract., 154(1–2), 3–14.
Hu, X., and Duan, K. (2010). “Mechanism behind the size effect phenomenon.” J. Eng. Mech., 60–68.
Hu, X., and Wittmann, F. (2000). “Size effect on toughness induced by crack close to free surface.” Eng. Fract. Mech., 65(2–3), 209–221.
Irwin, G. R. (1958). “Fracture.” Handbuch der physik, S. Flgge, ed., Springer, Berlin, 551–590.
RILEM. (1985). “Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams.” Mater. Struct., 18(4), 285–290.
Shah, S. P. (1990). “Size-effect method for determining fracture energy and process zone size of concrete.” Mater. Struct., 23(6), 461–465.
Tada, H., Paris, P., and Irwin, G. (1985). The stress analysis of cracks handbook, 2nd Ed., Paris Productions, Hellerton, PA.
Weibull, W. (1939). “The phenomenon of rupture in solids.” Proc. R. Swedish Inst. Eng. Res., 153, 1–55.
Weibull, W. (1951). “A statistical distribution function of wide applicability.” J. Appl. Mech., 18, 293–297.
Yu, Q., Le, J. L., Hoover, C. G., and Bažant, Z. P. (2010). “Problems with Hu-Duan boundary effect model and its comparison to size-shape effect law for quasi-brittle fracture.” J. Eng. Mech., 40–50.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 3 • March 2014
Pages: 480 - 486
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 16, 2012
Accepted: Mar 18, 2013
Published online: Feb 14, 2014
Published in print: Mar 1, 2014
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