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

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 σ 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 con-C. G. Hoover Northwestern University, Evanston, IL, USA Present address: C. G. Hoover M.I.T., Cambridge, MA, USA Z. P. Bažant (B) Northwestern University, 2145 Sheridan Road, CEE/A135, Evanston, IL 60208, USA e-mail: z-bazant@northwestern.edu crete, 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.

Dynamic Fracture of Concrete Compact Tension Specimen: Mesh Sensitivity Study

“…12 are plotted crack patterns with the corresponding crack velocities. They are all rather similar and agree well with the experimentally measured values [2]. Maximum crack speed of approximately 800 m/s is obtained before crack branching.…”

“…As expected, the reaction peak is in this case much higher than in the static analysis. As discussed in detail in [2,7] this is a consequence of rate sensitivity and inertia effects. At higher strain rates, larger than approximately 100/s, the effects of inertia are responsible for progressive increase of resistance and for crack branching [2].…”

“…As discussed in detail in [2,7] this is a consequence of rate sensitivity and inertia effects. At higher strain rates, larger than approximately 100/s, the effects of inertia are responsible for progressive increase of resistance and for crack branching [2]. Similar as for quasi-static analysis, reaction history response is not much dependent on the discretization.…”

“…In the here employed model ψ is chosen based on the tensile softening curves proposed by Hoover and Bažant. [2].…”

“…5. As can be seen for tension softening, bi-linear response is adopted, following the proposal from [2]. Plotted are curves for quasi-static loading and for dynamic loading (strain rate ε9 = 100/s).…”