Variable amplitude fatigue crack growth, experimental results and modeling

An incremental model was developed so as to predict the growth of fatigue cracks under complex load spectra. It contains a crack propagation law (da/dt = alpha|d rho/dt|) and a cyclic elastic plastic constitutive law for the cracked structure d rho/dt = f (phi proportional to J, phi(c)(X), phi(c)(th) phi(m)(X), phi(m)(th)). The crack growth rate da/dt is a rate of creation of cracked area per unit length of crack front. The plastic flow intensity factor rate d rho/dt is function of the loading level phi and of the thresholds for plastic deformation either within the monotonic or within the cyclic plastic zone. Two internal variables are introduced so as to define each threshold, the first one phi(X) is associated with internal stresses, while the second one, phi(th), measures the effective threshold for plastic deformation in the crack tip region. The material parameters in the equations are determined using the finite element method. This identification was performed for a 0.48%C carbon steel. Then various fatigue crack growth experiments have been performed in order to validate the model, monotonic fatigue crack growth experiments at different stress ratios from R = -1 to R = 0.4, single overloads with overloads factor between 1.5 and 1.8, and bloc loads with X overloads every Y cycles, X and Y varying from one experiment to another. The predictions of the model reproduce well experimental results. Finally the model was applied to an industrial problem: the growth of a semi elliptical crack at the surface of a train wheel. For this purpose, load spectra were measured in situ on a train wheel, it came out that the model bad to be extended to biaxial tension-compression and bending loading conditions, which was done. (C) 2007 Elsevier Ltd. All rights reserved.