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Cohesive crack, size effect, crack band and work-of-fracture models compared to comprehensive concrete fracture tests

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Abstract

The simplest form of a sufficiently realistic description of the fracture of concrete as well as some other quasibrittle materials is a bilinear softening stress-separation law (or an analogous bilinear law for a crack band). This law is characterized by four independent material parameters: the tensile strength, \(f'_t\), the stress \(\sigma _k\) at the change of slope, and two independent fracture energies—the initial one, \(G_f\) and the total one, \(G_F\). Recently it was shown that all of these four parameters can be unambiguously identified neither from the standard size effects tests, nor from the tests of complete load-deflection curve of specimens of one size. A combination of both types of test is required, and is here shown to be sufficient to identify all the four parameters. This is made possible by the recent data from a comprehensive test program including tests of both types made with one and the same concrete. These data include Types 1 and 2 size effects of a rather broad size range (1:12.5), with notch depths varying from 0 to 30 % of cross section depth. Thanks to using identically cured specimens cast from one batch of one concrete, these tests have minimum scatter. While the size effect and notch length effect were examined in a separate study, this paper deals with inverse finite element analysis of these comprehensive test data. Using the crack band approach, it is demonstrated: (1) that the bilinear cohesive crack model can provide an excellent fit of these comprehensive data through their entire range, (2) that the \(G_f\) value obtained agrees with that obtained by fitting the size effect law to the data for any relative notch depth deeper than 15 % of the cross section (as required by RILEM 1990 Recommendation), (3) that the \(G_F\) value agrees with that obtained by the work-of-fracture method (based on RILEM 1985 Recommendation), and (4) that the data through their entire range cannot be fitted with linear or exponential softening laws.

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Acknowledgments

Financial support from the U.S. Department of Transportation, provided through Grant 20778 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 CMMI-1129449 to Northwestern University. The first author also wishes to thank for first year partial support under W.P. Murphy Fellowship of Northwestern University.

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  1. Christian G. Hoover

    Present address: M.I.T., Cambridge, MA, USA

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  1. Northwestern University, Evanston, IL, USA

    Christian G. Hoover

  2. Northwestern University, 2145 Sheridan Road, CEE/A135, Evanston, IL,  60208, USA

    Zdeněk P. Bažant

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Correspondence to Zdeněk P. Bažant.

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Hoover, C.G., Bažant, Z.P. Cohesive crack, size effect, crack band and work-of-fracture models compared to comprehensive concrete fracture tests. Int J Fract 187, 133–143 (2014). https://doi.org/10.1007/s10704-013-9926-0

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