Predictions of Crack Growth Rates, R-Ratio and Overload Effects Based on Smooth Specimen LCF Data and the Moving Plastic Stress Field Ahead of the Crack Tip

The use of the stress intensity factor K to characterize the severity of crack tip stress fields is widespread throughout engineering. The relationship between K and the crack growth rate is then usually represented empirically by a straight line Paris law relationship on logarithmic axes. This study develops an analytical relationship between the two by linking crack growth to the accumulation of fatigue damage ahead of the moving crack tip. A stress-based fatigue model was used, with inputs from plastic 2D plane stress FE analyses representing an edge crack by a sharp semi-circular notch. Stress–distance profiles ahead of the crack tip were extracted at the maximum and minimum points of a range of fatigue loading cycles. These were then used with data from smooth specimen LCF tests to predict the build-up of fatigue damage at regularly spaced locations ahead of the crack tip and hence crack growth rates. Full da/dN–ΔK curves were generated for the nickel-based superalloy RR1000 at 20 °C with loading R-ratios of 0, −1 and 0.5. The R = 0 and R = −1 crack growth rate predictions agreed well with experimental data, as did the steeper growth rate slope calculated at R = 0.5. The method was then extended to predict overload behaviour.