Propagation Path and Fatigue Life Predictions of Branched Cracks Under Plane Strain Conditions

Abstract

Fatigue cracks can significantly deviate from their Mode I growth direction due to the influence of overloads, multi-axial stresses, micro structural inhomogeneities such as grain boundaries and interfaces, or environmental effects, generating crack kinking or branching [1]. The stress intensity factors (SIF) associated to branched fatigue cracks can be considerably smaller than that of a straight crack with the same projected length, causing crack growth retardation or even arrest. This mechanism can quantitatively explain retardation effects even when plasticity induced crack closure cannot be applied, e.g. in high R-ratio fatigue problems under plane strain conditions. Analytical solutions have been obtained for the SIF of some branched cracks, however numerical methods are the only means to predict the subsequent curved propagation behaviour. In this work, a specialized Finite Element program is used to calculate the propagation path and associated SIF of bifurcated cracks. The numerical calculations are validated through experiments on 4340 steel ESE(T) specimens. A total of 6,250 FE calculations are used to fit empirical equations to the process zone size and crack retardation factor along the curved crack branches. The bifurcation simulations include several combinations of bifurcation angles, branch asymmetry ratios, crack growth exponents, and even considers interaction between crack branching and other retardation mechanisms such as crack closure, assuming the crack opening level is well known.