Size-Effect Testing of Cohesive Fracture Parameters and Nonuniqueness of Work-of-Fracture Method

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 $f_t^{\prime }$, and the knee-point ordinate ${\sigma }_1$. 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 $f_t^{\prime }$ 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 $f_t^{\prime }$, 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 ${\sigma }_1/f_t^{\prime }$ were known a priori, but unfortunately their estimates are far too uncertain.