## Abstract

The cohesive crack model has been widely accepted as the best compromise for the analysis of fracture of concrete and other quasibrittle materials. The softening stress-separation law of this model is now believed to be best described as a bilinear curve characterized by four parameters: the initial and total fracture energies G_{f} and G_{F}, the tensile strength f_{t}^{'}, and the knee-point ordinate σ_{1}. The classical work-of-fracture test of a notched beam of one size can deliver a clear result only for G_{F}. Here it is shown computationally that the same complete load-deflection curve can be closely approximated with stress-separation curves in which the f_{t}^{'} values differ by 77% and G_{f} values by 68%. It follows that the work-of-fracture test alone cannot provide an unambiguous basis for quasibrittle fracture analysis. It is found, however, that if this test is supplemented by size-effect testing, all four cohesive crack model parameters can be precisely identified and the fracture analysis of structures becomes unambiguous. It is shown computationally that size-effect tests do not suffice for determining G_{F} and f_{t}^{'}, which indicates that they provide a sufficient basis for computing neither the postpeak softening of fracturing structures nor the peak loads of a very large structure. However, if the size-effect tests are supplemented by one complete softening load-deflection curve of a notched specimen, an unambiguous calculation of peak loads and postpeak response of structures becomes possible. To this end, the notched specimen tests must be conducted in a certain size range, whose optimum is here established by extending a previous analysis. Combination of the work-of-fracture and size-effect testing could be avoided only if the ratios G_{F}/G_{f} and σ_{1}/f_{t}^{'} were known a priori, but unfortunately their estimates are far too uncertain.

Original language | English (US) |
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Pages (from-to) | 580-588 |

Number of pages | 9 |

Journal | Journal of Engineering Mechanics |

Volume | 137 |

Issue number | 8 |

DOIs | |

State | Published - Aug 3 2011 |

## Keywords

- Cracking
- Parameters
- Size effect

## ASJC Scopus subject areas

- Mechanics of Materials
- Mechanical Engineering