An r-curve approach for fracture of quasi-brittle materials

An R-curve approach for fracture of quasi-brittle materials is proposed in this paper. An 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 the function of an initial crack length contained in a material, an expression of the 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 and CTOD_c for positive geometry specimens, and according to K_IC^S and dK₁/da = 0 for negative geometry specimens. Load-CMOD and loaddisplacement response 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. The predicted curves show a good agreement with the wide range of experimental results. Pre-critical stable crack propagation of quasi-brittle materials can be well described by the present approach.