Fig. 2.
Schematics of flat and rising crack-growth resistance curves (R-curves). Unstable fracture occurs when the materials resistance to fracture ceases to increase faster than the driving force for crack propagation; this corresponds to the driving force as a function of crack size being tangent to the crack-growth resistance curve. For a material that has a flat R-curve, a single value of toughness unambiguously characterizes the material. For a material with a rising R-curve there is no single value of toughness that characterizes the material as the driving force for unstable crack propagation depends on the extent of crack growth. For materials with rising R-curves crack-growth resistance, measurements are needed to determine how the resistance to fracture evolves with crack extension. For materials with flat R-curves, there is no stable crack extension and the initial crack size (ao) is the same as the critical crack size (ac). In materials with a rising R-curve, stable crack growth occurs and the critical crack size will be larger than the initial crack size. Crack-growth resistance curves are typically plotted with crack extension (Δa) instead of crack size because the shape of the R-curve does not vary with crack size. The driving force for crack propagation can be quantified by K, G, or J.