13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- crack-depth-to-width ratio increases. To estimate a corrected KI, a finite element analysis of the end conditions for the magnetic-driven fatigue apparatus was performed. The foil, which is rigidly clamped by the face-loaded grips along its ends, is under a uniform fixed-end displacement boundary condition (Figure 3c). Due to the non-uniform tensile stress �2 distribution along the specimen width, a closing moment is imposed on the specimen, which reduces the effective stress intensity at the crack tip. A summary of the results of the analysis for the loading cases examined is provided in Figure 4. The corrected stress intensity factors obtained from the FEM analysis were used in the subsequent analysis of �K versus crack growth rate presented below. Figure 4. Variation of stress intensity factor KI with the crack length. The data defined by solid squares represents KI calculated from the empirical Eq. 2; the triangular data point represents KI is determined by FEM analysis. A comparison of the data shows that the overestimation of KI by Eq. 2 increases as crack length increases. 5. Results and discussion 5.1 Results All fatigue cracks started from the root of the machined notch; cyclic crack propagation behavior, which remained perpendicular to the applied load, was similar for all specimens, indicating adequate alignment of the specimen was achieved during the experiments. Figure 5 shows typical results for crack length versus number of cycles. All specimens behaved in a similar manner, and the amount of scatter was limited for similar test parameters. Figure 6 shows crack growth rate vs. corrected stress intensity for all specimens. The double-logarithmic plot shows that the data can be fit reasonably well using a simple Paris-equation relationship between crack growth rate and applied stress intensity range (corrected with FEM analysis). The measured stress intensity factor exponent m ranged from 3.94~5.08 for the eight specimens tested (Table 2). The small change in specimen width from 12 mm to 10 mm (Group A and Group B), did not have a measurable influence on the test results. The crack growth rate data for thin foils is quite limited and the Paris “m” value for similar pure Ti foils is not available. However, the m values found in the current investigation are similar to elevated m values of around
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