Universal Size-Shape Effect Law Based on Comprehensive Concrete Fracture Tests
Publication: Journal of Engineering Mechanics
Volume 140, Issue 3
Abstract
The universal size-shape effect law is a law that describes the dependence of nominal strength of specimen or structure on both its size and the crack (or notch) length, over the entire range of interest, and exhibits the correct small-size and large-size asymptotic properties as required by the cohesive crack model (or crack band model). The main difficulty has been the transition of crack length from 0, in which case the size effect is Type 1, to deep cracks (or notches), in which case the size effect is Type 2 and is fundamentally different from Type 1, with different asymptotes. In this transition, the problem is not linearizable because the notch is not much larger than the fracture process zone. The previously proposed universal law could not be verified experimentally for the Type 1-Type 2 transition because sufficient test data were lacking. The current study is based on recently obtained comprehensive fracture test data for three-point bend beams cast from one batch of the same concrete and cured and tested under identical conditions. The test data reveal that the Type 1-Type 2 transition in the previous universal law has insufficient accuracy and cannot be captured by Taylor series expansion of the energy release rate function of linear elastic fracture mechanics. Instead, the size effect for a zero notch and for the transitional range is now characterized in terms of the strain gradient at the specimen surface, which is the main variable determining the degree of stress redistribution by the boundary layer of cracking. The new universal law is shown to fit the comprehensive data quite well, with a coefficient of variation of only 2.3%.
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Acknowledgments
Financial support from the U.S. DOT, provided through Grant No. 227740 from the Infrastructure Technology Institute of Northwestern University, is gratefully appreciated. Further support for theoretical study was provided by the U.S. National Science Foundation under Grant No. CMMI-1129449 to Northwestern University.
References
Bažant, Z. P. (1984). “Size effect in blunt fracture: Concrete, rock, metal.” J. Eng. Mech., 518–535.
Bažant, Z. P. (1995). “Scaling of quasibrittle fracture: I. Asymptotic analysis based on laws of thermodynamics. ii. The fractal hypothesis, its critique and weibull connection.” Bulletin 22 95-7/C402s, Dept. of Civil Engineering, Northwestern Univ., Evanston, IL.
Bažant, Z. P. (1996). “Size effect aspects of measurement of fracture characteristics of quasibrittle material.” Adv. Cem. Base. Mater., 4(3/4), 128–137.
Bažant, Z. P. (1997). “Scaling of quasibrittle fracture: Asymptotic analysis.” Int. J. Fract., 83(1), 19–40.
Bažant, Z. P. (2005). Scaling of structural strength, Elsevier Butterworth-Heinemann, Burlington, MA.
Bažant, Z. P., and Becq-Giraudon, E. (2002). “Statistical prediction of fracture parameters of concrete and implications for choice of testing standard.” Cem. Concr. Res., 32(4), 529–556.
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.
Bažant, Z. P., Kazemi, M. T., and Gettu, R. (1989). “Recent studies of size effect in concrete structures,” A. H. Hadjian, ed., Proc., Transactions, 10th Int. Conf. on Structural Mechanics in Reactor Technology, Vol. H, Los Angeles, 85–93.
Bažant, Z. P., and Li, Z. (1995). “Modulus of rupture: Size effect due to fracture initiation in boundary layer.” J. Struct. Eng., 739–746.
Bažant, Z. P., and Li, Z. (1996). “Zero-brittleness size-effect method for one-size fracture test of concrete.” J. Eng. Mech., 458–468.
Bažant, Z. P., and Pfeiffer, P. A. (1987). “Determination of fracture energy from size effect and brittleness number.” ACI Mater. J., 84(6), 463–480.
Bažant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC Press, Boca Raton, FL.
Bažant, Z. P., Vořechovský, M., and Novák, D. (2007). “Asymptotic prediction of energetic-statistical size effect from deterministic finite-element solutions.” J. Eng. Mech., 153–162.
Bažant, Z. P., and Yu, Q. (2004). “Size effect in concrete specimens and structures: New problems and progress,” Proc., 5th Int. Conf. on Fracture Mechanics of Concrete and Concrete Structures, V. C. Li, K. Y. Leung, K. J. Willam, and S. L. Billington, eds., Vol. 1, Balkema, Rotterdam, Netherlands, 153–162.
Bažant, Z. P., and Yu, Q. (2009). “Universal size effect law and effect of crack depth on quasi-brittle structure strength.” J. Eng. Mech., 78–84.
Bažant, Z. P., and Yu, Q. (2011). “Size-effect testing of cohesive fracture parameters and nonuniqueness of work-of-fracture method.” J. Eng. Mech., 580–588.
Becq-Giraudon, E. F. (2000). “Size effect on fracture and ductility of concrete and fiber composites.” Ph.D. thesis, Northwestern Univ., Evanston, IL.
Carpinteri, A., Chiaia, B., and Ferro, G. (1995). Multifractal scaling law: An extensive application to nominal strength size effect of concrete structures, No. 50, Atti del Dipartimento di Ingegneria Strutturale, Politecnico de Torino, Italy.
Coleman, T. F., and Li, Y. (1994). “On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds.” Math. Program, 67(1–3), 189–224.
Coleman, T. F., and Li, Y. (1996). “An interior, trust region approach for nonlinear minimization subject to bounds.” SIAM J. Optim., 6(2), 418–445.
Cusatis, G., and Schauffert, E. (2009). “Cohesive crack analysis of size effect.” Eng. Fract. Mech., 76(14), 2163–2173.
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). “Comparison of the Hu-Duan boundary effect model with the size-shape effect law for quasi-brittle fracture based on new comprehensive fracture tests.” J. Eng. Mech., 480–486.
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.
Irwin, G. R. (1958). “Fracture.” Handbuch der physik, S. Flgge, ed., Springer, Berlin, 551–590.
Karihaloo, B. L., Abdalla, H. M., and Xiao, Q. Z. (2003). “Size effect in concrete beams.” Eng. Fract. Mech., 70(7–8), 979–993.
Malvar, J. L., and Warren, G. E. (1988). “Fracture energy for three-point-bend tests on single-edge-notched beams.” Exp. Mech., 28(3), 266–272.
Nallathambi, P. (1986). “Fracture behaviour of plain concretes.” Ph.D. thesis, Univ. of New Castle, Callaghan, Australia.
Petersson, P. E. (1981). “Crack growth and development of fracture zone in plain concrete and similar materials.” Rep. No. tvbm-1006, Div. of Building Materials, Lund Institute of Technology, Lund, Sweden.
Rocco, C. G. (1995). “Size dependence and fracture mechanisms in the diagonal compression splitting test.” Ph.D. thesis, Dept. Ciencia de Materiales, Universidad Politecnica de Madrid, Madrid, Spain.
Sabnis, G. M., and Mirza, S. M. (1979). “Size effect in model concretes.” J. Struct. Div., 105(6), 1007–1020.
Tang, T., Bažant, Z. P., Yang, S., and Zollinger, D. (1996). “Variable-notch one-size test method for fracture energy and process zone length.” Eng. Fract. Mech., 55(3), 383–404.
Timoshenko, S. P., and Goodier, J. N. (1951). Theory of elasticity, McGraw Hill, New York.
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.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 3 • March 2014
Pages: 473 - 479
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 16, 2012
Accepted: Mar 14, 2013
Published online: Feb 14, 2014
Published in print: Mar 1, 2014
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