ABSTRACT
An R-curve approach for prediction of fractures of concrete and fiber reinforced concrete is presented. The R-curve is defined as an envelope of fracture energy release rate of specimens with different sizes but the same initial notch length. By assuming that an effective traction-free critical crack is a function of an initial crack length contained in a material, an expression for an R-curve with two parameters can be derived by solving a differential equation. The parameters of the R-curve can be uniquely determined according to K IC s https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315273044/bad0c98f-3085-4869-8cd8-83c29a25dfc9/content/eq95.tif"/> and CTOD c for positive geometry specimens, and according to K IC s https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315273044/bad0c98f-3085-4869-8cd8-83c29a25dfc9/content/eq96.tif"/> and dK 1/da = 0 for negative geometry specimens. Load–CMOD and load–displacement responses can be predicted based on the proposed R-curve by requiring that the crack driving force and crack growth resistance are equal at every equilibrium crack length. Toughening of matrix due to fiber bridging is taken into account by applying closing pressure on crack surfaces. The theoretical predictions are compared with the experimental results of concrete and fiber reinforced concrete containing unidirectional, continuous glass, steel or polypropylene fibers. The predicted responses indicate good agreement with the wide range of experimental results tested by various investigators.
