Modified NASGRO equation for physically short cracks

A typical fatigue crack growth curve consists of the threshold region, the Paris region (linear in a logarithmically scaled diagram) and the transition region from the Paris region to unstable crack growth. For cracks exceeding a certain material-dependent length, this curve depends only on the load ratio R and is well described by commonly accepted crack growth models such as the Forman/Mettu (NASGRO) equation. However, cracks below this length typically grow significantly faster due to the absence of crack-closure effects, leading to an additional dependence of the crack growth curve on the crack extension Δa. In this paper, a simple analytical model for describing the crack growth behavior for any crack length and load ratio R is presented. For the QT steel 25CrMo4, the model is applied to describe the crack growth behavior for different crack length and load ratios between −3 and 0.5.