Crack growth resistance curves (commonly referred to as K\(_{\text{R}}\) or R curves in the case of small scale yielding) are determined for various materials and are commonly used to interpret crack initiation, slow stable crack growth and the condition for crack growth instability leading to fast fracture. Slow stable crack growth is generally assumed to occur when the energy release rate \(G\) is equal to the crack growth resistance \(Y\) and when the energy release rate increases at a slower rate than the crack growth resistance. The main assumption of this paper is that the crack growth resistance in ”real” materials is not only a function of the extent of crack growth, but also the crack tip velocity since the ”real” fracture processes at the crack tip are rate dependent. Moreover, it is assumed that the nature of these rate dependent fracture processes are such that the crack tip velocity dependent portion of the resistance to crack growth is non-monotonic. Strictly speaking, the assumption of the crack growth resistance depending on the crack tip velocity, questions the basis for R curve testing. For example, in polymeric materials there is a strong crack tip velocity dependence and the R curve method is not applicable because significant crack growth occurs under constant \(G\) conditions, K. Ravi-Chandar and M. Balzano [Engng. Fracture Mech. 30, 713 (1988)]. However, in this paper the crack tip velocity dependence is considered ”weak” and it is assumed that at a constant \(G\) significant crack growth does not occur over typical loading times for the experimental determination of R curves.