Crack growth behaviour in biaxial stress fields: Calculation of K-factors for cruciform specimens

The aim of this study is to propose a simplified method for calculating the Mode I stress intensity factor K for cruciform specimens under planar biaxial loading. It is assumed that two cracks have to grow with a similar crack growth rate. The straight crack paths of the two single cracks with the length a should also be similar. The calculations are carried out on an aluminum and a steel specimen, respectively. For different load cases and materials, the stresses resulting from the forces are first considered. It was found that the elastic constants E and have only a small influence of less than 3%. In addition, the coupling between the forces of the load axes, which should be minimized by slotted arms, is considered. Moreover, K-factors are calculated by finite elements (FE) for different crack lengths. These K-values together with the transmission factor allow to find a K-factor formula for cruciform specimens, which is based on the prescribed forces. Finally, the results of the FE-calculation of the exact straight crack paths were compared to experimentally determined crack paths. Furthermore, a comparison of the fatigue crack growth rates versus K-factor range for different loading is shown.