Abstract
Fracture of concrete as well as other materials such as rocks or sea ice is preceded by progressive distributed cracking. On the macroscale, this behavior calls for a continuum model, and the crack tip blunting due to distributed cracking necessitates a nonlinear fracture mechanics approach.
The first part of this lecture gives a review of a recently formulated nonlocal continuum model which permits distributed cracking to occur in a stable manner over finite-size zones of the material, and summarizes the finite element crack band model, which is a special case of the nonlocal continuum approach. The size effect in blunt fracture is also briefly reviewed.
The second part of this lecture presents in detail a new method of identifying the material parameters for propagation of fractures blunted by a cracking zone. This method exploits the recently derived size effect law for blunt fracture for determining the parameters of the R-curve and the parameters of the finite element crack band model (as well as Hillerborg’s fictitious crack model). No measurements of the crack length or of the unloading compliance are needed, and it suffices to measure only the maximum load values for a set of geometrically similar notched specimens of different sizes. From these data, the parameters of the size effect law are identified by linear regression in certain transformed variables. The inverse slope of the regression line yields the fracture energy. The regression has further a two-fold benefit: it smoothes statistically scattered data according to a theoretically known law, and it extends the range of the data, so that fewer tests are needed than without the use of the size effect law. Using the experimentally calibrated size effect law, the R-curve may then be obtained as the envelope of family of curves representing fracture equilibrium for different specimen sizes. A simple algebraic formula for the R-curve, which closely agrees with the size effect law, is also presented. In the case of the crack band model, the size effect regression plot makes it again possible to determine all material parameters, particularly the fracture energy, the crack band width and the strain-softening modulus. Formulas for that purpose may be set up for each fracture specimen geometry, and some are presented here. The parameters of Hillerhorg’s fictitious crack model can be also easily identified from the size effect regression plot.
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© 1985 Martinus Nijhoff Publishers, Dordrecht
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Bažant, Z.P., Kim, JK., Pfeiffer, P. (1985). Continuum Model for Progressive Cracking and Identification of Nonlinear Fracture Parameters. In: Shah, S.P. (eds) Application of Fracture Mechanics to Cementitious Composites. NATO ASI Series, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5121-1_8
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