13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- FATIGUE CRACK GROWTH SIMULATION OF SURFACE CRACKS UNDER ARBITRARY CRACK FACE LOADING Xiaobin Lin HBM (nCode) United Kingdom Limited, UK Xiaobin.Lin@hbmncode.com Abstract Fatigue crack growth was simulated for a surface crack subjected to arbitrary crack face loads. The simulation was based on the step-by-step integration of a proper fatigue crack growth law along the crack front, enabling complex crack shape changes to be directly predicted. The three-dimensional finite element method with the inverse square singularity near the crack tip considered was employed to calculate the stress intensity factors along the crack front, and the contact elements were also introduced into the cracked surface to avoid the possible overlapping between the crack faces. Several typical crack face loads were analysed, and the results including crack shape development, aspect ratio changes and stress intensity factor variations were given to validate the simulation technique. The results showed that the crack shape is dependent on the applied load and non-semielliptical surface crack profiles may be adopted by fatigue cracks. The simulation is particularly useful and necessary for the fatigue crack growth analysis in a residual stress field. Keywords fatigue crack growth, stress intensity factor, surface crack, crack shape change 1. Introduction Fatigue crack growth for surface cracks in plates has been extensively investigated both theoretically and experimentally. Surface cracks are very common in many engineering components and structures, such as pressure vessels, pipeline systems, off-shore and aircraft components et al. It has been widely observed from experimental investigations [1, 2] that a surface crack under fatigue loading always changes its crack front as it grows, and the shape by the fatigue crack subjected to both tension and bending loads is close to a semi-ellipse if neglecting the possible retardation of crack growth along the free surface. Some efforts have been made to establish reasonable models to predict the fatigue crack growth of a two-dimensional surface crack, in which an experimental fatigue crack growth relation obtained from small specimen tests is employed. A typical model is that a surface crack is treated to have a semi-elliptical shape, and the change in crack aspect ratio is predicted. Newman and Raju [3] presented a two degree-of-freedom model, in which the change of crack aspect ratio is calculated by coupled integration of a Paris type of fatigue crack growth law along both crack depth and surface directions. In their model, the stress intensity factor (SIF) range at the free surface point was modified by the reducing 10% its value to consider the effect of the surface layer when the retardation of crack growth is often observed, and their own closed-form SIF equations were used. For cracks subjected to a complex stress gradient, a method similar to those mentioned above is probably suitable if SIF solutions corresponding to such a stress distribution are available. Generally, these solutions are likely to be obtained by using a weight function method, or by superposing the SIF results for a series of polynomial stress distributions. However, this method is obviously incomplete. First, it includes a semi-elliptical shape assumption which is not adequate in some situations to define the actual shape adopted by the crack. Second, crack contact is not taken into account almost in all SIF solutions reported. This may happen if there are compressive stresses acting on the crack face. Using the SIF results obtained without considering crack contact might cause a big error in fatigue crack growth calculations. In this paper, a numerical method developed
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