4 Curvilinear Fatigue Crack Growth Under Out-of-Phase Loading Conditions 31 4.3 Validation Experiments Experimental data in the literature for fatigue crack growth under out-of-phase loading conditions are unfortunately not complete to the extent that they can enable comparisons of predicted and measured crack path and fatigue life. As such, new validation experiments have been performed by AFRL with the participation of a master’s degree graduate student, Haywood S. Watts, from the University of South Carolina (USC). These joint AFRL-USC fatigue crack growth experiments under out-of-phase loading conditions were conducted on a special type of cruciform specimens under biaxial out-of-phase loading conditions. Due to space limitation, the description below is very brief but details of the experiments can be found in [10]. The overall shape of the cruciform specimen is similar to the one shown in Fig. 4.1 but it contains a central hole. A horizontal or inclined notch is cut on the left side of the hole. Then a fatigue pre-crack is made at the tip of the notch with the same orientation. Figure 4.2 shows the hole with an inclined notch as well as the fatigue pre-crack (the inclination or notch angle with respect to the left-ward x-axis is denoted by ¥, which is nominally 45ı but the actual value is different in the specimens). Fatigue crack growth experiments were performed on specimens made of aluminum alloy 7075-T6 or 2024-T351. Specimens made of 2024-T351 have a horizontal notch while those made of 7075-T6 have an inclined notch. 4.4 Finite Element Model and Results of Validation Simulation A finite element model has been developed for one of the experiments performed jointly by AFRL and USC. This case involves fatigue crack growth in a specimen made of aluminum alloy 7075-T6 loaded biaxially with a 180ı phase angle, a biaxiality loading ratio of 1 and R ratios of R1 DR2 D0.5. The specimen has an initial notch length of 1.10 mm, a fatigue pre-crack length of 2.14 mm, and a notch angle of 43.5ı. Two finite element meshes have been created for the model with the initial crack. The two meshes are similar except in the crack region. In the coarse mesh, there are two elements both along the length of the crack and along the crack front (i.e. through the specimen thickness), and in the fine mesh, there are four elements both along the length of the crack and along the crack front. Away from the crack region, only one element is used through the specimen thickness in both meshes. Figure 4.3 shows a global 3D view of the fine mesh, and Fig. 4.4 shows a local 3D view of the fine mesh in the crack region. Finite element simulations of the fatigue behavior of the specimen under biaxial out-of-phase loading conditions have been carried out using the in-house finite element code CRACK3D. During simulation, when crack growth is predicted along a certain direction, a local region around the crack front is automatically selected based on user input in which automatic local re-meshing will be performed by the code. Immediately around the predicted new crack front, a structured mesh will be created to enable the use of the 3D Virtual Crack Closure Technique (3D VCCT) for efficient and accurate determination of energy release rates and stress intensity factors along the crack front. In the rest of the local region, unstructured re-meshing will be performed with graded element sizes to bridge between the small elements immediately around the new crack front and usually larger elements in rest of the specimen surrounding the local region. Fig. 4.2 A schematic of the hole in the cruciform specimen, showing the notch, the fatigue pre-crack and the notch angle
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