13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- crack propagation simulation. 2.3. Crack growth process The load corresponding to the Keq,max , F(tmax) and MT(tmax) are applied to the cracked finite element model. Stress analysis is carried out in ABAQUS. The SIF solutions for the cracks are again obtained from FRANC3D based on the stress analysis. Although the solutions for KI, KII and Keq are already at hand for t= tmax , the re-evaluation of this loading case combination can now be used to let the FRANC3D software create the crack propagation increment aΔ . The ABAQUS/FRANC3D interface was implemented to perform the crack growth analysis. The finite element modeling and the stress analysis are performed in ABAQUS, FRANC3D is used to calculate crack growth parameters and updates the crack geometry and mesh. This process is continued until the crack has grown to a certain length. As referred before, on one hand the MTS criterion is used as the rule for estimating crack propagation direction in most cases, on the other hand as will be shown later that under certain loading conditions, the simulated crack growth path deviated from the experimental crack path when the length of the crack is long enough. In order to investigate the crack growth path behavior under these complicated loading cases, a modification is essentially to keep the deviation between experimental results and simulation in an acceptable extent. Due to an extremely inadequate hypothesis about the criterion which is suitable for fatigue crack growth direction prediction under non-proportional mixed mode loading, the modification is implemented manually to adjust the position of newly generated crack front in order to make the simulated crack increment direction coincident with the experimental results. As a result, although the simulated crack growth path is not perfectly identical with the experimental data, a close match is enforced. 3. Results 3.1. AlMg4.5Mn specimens In the experiment, specimen A7 (amplitude load values: F=8kN; MT=96Nm) was tested under a non-proportional loading with an out of phase angle of 90°, while specimen A8 (amplitude load values: F=6.5kN; MT=72Nm) was subjected a loading with a out of phase angle of 45°. The crack growth paths are shown in Figure 3. According to the stress analysis for the uncracked specimen, the local tangential stress along the notch root in site 1 and 3 are approximately 1.6 times larger than the stresses in site 2 and 4, therefore cracks should occur in site 1 and 3. Very curvilinear paths were displayed in specimen A7, furthermore in the experiment, crack branching appeared and then the crack growth path continues nearly perpendicularly to the previous propagation direction. The simulation algorithm at present does not contain a condition for crack branching, only the first curvilinear paths are presented. For specimen A8, the crack propagates along an angle of nearly 45° with the longitudinal axis. After the crack reaches a certain length, it has a tendency to turn into a plane, which is perpendicular to the longitudinal axis.
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