A review of fatigue crack propagation modelling techniques using FEM and XFEM

Abstract

The study of the dissipation heat flow and the acoustic emission during the fatigue crack propagation in the metal A N Vshivkov, A Yu Iziumova, I A Panteleev et al. noAbstract. Fatigue is one of the main causes of failures in mechanical and structural systems. Offshore installations, in particular, are susceptible to fatigue failure due to their exposure to the combination of wind loads, wave loads and currents. In order to assess the safety of the components of these installations, the expected lifetime of the component needs to be estimated. The fatigue life is the sum of the number of loading cycles required for a fatigue crack to initiate, and the number of cycles required for the crack to propagate before sudden fracture occurs. Since analytical determination of the fatigue crack propagation life in real geometries is rarely viable, crack propagation problems are normally solved using some computational method. In this review the use of the finite element method (FEM) and the extended finite element method (XFEM) to model fatigue crack propagation is discussed. The basic techniques are presented, together with some of the recent developments. IntroductionComponents which are subjected to fluctuating loads are found virtually everywhere: Vehicles and other machinery contain rotating axles and gears, pressure vessels and piping may be subjected to pressure fluctuations (e.g. water hammer) or repeated temperature changes, structural members in bridges are subjected to traffic loads and wind loads, while those in ships and offshore structures are subjected to the combination of wind loads, wave loads and currents. If the components are subjected to a fluctuating load of a certain magnitude for a sufficient amount of time, small cracks will nucleate in the material. Over time, the cracks will propagate, up to the point where the remaining cross-section of the component is not able to carry the load, at which the component will be subjected to sudden fracture [1]. This process is called fatigue, and is one of the main causes of failures in structural and mechanical components [2]. In order to assess the safety of the component, engineers need to estimate its expected lifetime. The fatigue life is the sum of the number of loading cycles required for a fatigue crack to nucleate/initiate, and the number of cycles required for the crack to propagate until its critical size has been reached [2,3]. In this paper, computational methods to estimate the lifespan of a propagating crack whose initial geometry is known will be considered.Estimations of the fatigue crack propagation rate, da/dN, are normally based on a relation with the range of the stress intensity factor, ΔK, which is a linear elastic fracture mechanics (LEFM) parameter for quantifying the load and geometry of the crack. Paris, Gomez and Anderson [4] first proposed the existence of such a relation in 1961, and its simplest form is the Paris law [5]:

Stress intensity factors for circumferential through‐wall cracks in thin‐walled cylindrical shells subjected to tension and torsion

“…The possible errors due to the choice in extrapolation range are therefore most likely considerably lower than those mentioned above. This indicates a considerable weakness in the displacement extrapolation technique however, which is rarely emphasized in relevant reviews …”

“…This indicates a considerable weakness in the displacement extrapolation technique however, which is rarely emphasized in relevant reviews. [38][39][40][41]46,52 The accuracy of the results which are reported in this work is limited by the choices of using a shell model and the displacement extrapolation technique. Still, the accuracy for the torsional loading is judged to be higher than the two available solutions.…”

“…However, the interaction integral method is not available for shell elements in the current version of ANSYS. As an alternative, a displacement method may be used, but requires a finer mesh at the crack tip …”

“…The interaction integral method 37 is generally considered to be the best method for determining the stress intensity factor from an FE solution for the stress and displacement fields. [38][39][40][41] However, the interaction integral method is not available for shell elements in the current version of ANSYS. As an alternative, a displacement method may be used, but requires a finer mesh at the crack tip.…”

“…As an alternative, a displacement method may be used, but requires a finer mesh at the crack tip. [38][39][40][41] According to the original displacement method, which is called the displacement extrapolation technique, the following quantities should be computed for each node along the crack face 42,43 :…”