curves are calculated using the equation for CR in Figure 6 and the respective tunneling curves from Figure 5. The data points in Figure 6 are the calculated correction ratio based on the area average crack length from the measured tunneling. The f term in the CR equation indicates what fraction of the tunneling magnitude represents the area average crack extension. For flat fracture the coefficient was determined from the area average crack length of Dawicke’s [2] crack front shapes and is 0.64, and for slant fracture the coefficient was determined from the average of the tunneling data as 0.5. Figure 7 compares data from Figure 2 corrected using the calibration curves for area-average crack extension with the analysis. Only data with Da > 0.2 mm were corrected. As expected, both curves shifted significantly, resulting in a better match between the FEA and experimental results near maximum load. However, the analysis now significantly over-predicts the initiation load, indicating that a lower CTOA would be required in the analysis to predict initiation. From Table 1, crack initiation in the interior occurred before 13.3 KN, but the analysis did not initiate until about 19 KN. This is similar to the result by Dawicke et al. [5]. The crack-extension values for the flat specimen were larger than the value for the slant-crack specimens at a given load. Beyond maximum load, the measured surface crack-extension values were approximately the same in Figure 2 for the flat and slant specimens. The differences in the two curves in Figure 7 indicate that the importance of the failure mechanism (tensile versus shear) between the two failure modes may be more significant than was indicated by the surface measured crack-extension data of Figure 2. CONCLUDING REMARKS The excellent match between the experimental and analysis data in Figure 3 is compelling, and led us to consider the tunneling issue more carefully. The results in Figure 7 show better correlation between the corrected test data and the analysis results near maximum load, and showed that the constant CTOA fracture criterion transfers well between the fully constrained C(T) specimen and the wide, buckling M(T) specimens. The analysis was able to accurately predict the maximum load for C(T) specimens ranging in size from 50 mm to 152 mm and for M(T) specimens ranging in size from 75 mm to 1016 mm. Optical measurement methods will likely remain the method of choice for the buckling wide panel tests. Unloading compliance measurements are difficult for buckling panels, and direct current potential difference (area average) can be somewhat difficult to set up and increases the complexity of the test procedure. However, unloading compliance is relatively straight-forward for constrained C(T) and M(T) specimens. If reliable tunneling test procedures can be developed, and if the material shows consistent tunneling behavior, then calibration procedures such as these presented here are viable. REFERENCES 1. Harris, C.E., Newman, J. C., Jr., Piascik, R. and Starnes, J. H., Jr., “Analytical Methodology for Predicting the Onset of Widespread Fatigue Damage in Fuselage Structure,” Journal of Aircraft, Vol. 35, No. 2, pp. 307-317, 1998. 2. Dawicke, D. S. and M. A. Sutton, "CTOA and Crack Tunneling Measurements in Thin Sheet 2024-T3 Aluminum Alloy," Experimental Mechanics, Volume 34 No. 4, pp. 357, 1994. 3. Wells, A.A., “Application of Fracture Mechanics at and Beyond General Yielding,” British Welding Journal, Vol. 11, 1961, pp. 563-570. 4. James, M. A. and Newman, J. C., Jr., “Three Dimensional Analysis of Crack-Tip-Opening Angles and d5-Resistance Curves for 2024-T351 Aluminum Alloy,” Fatigue and Fracture Mechanics: 32nd Volume, ASTM STP 1406, Ravinder Chona, Ed., American Society for Testing and Materials, West Conshohocken, PA, 2000 (in press). 5. Dawicke, D. S., J. C. Newman, Jr., and C. A. Bigelow, "Three-dimensional CTOA and Constraint Effects during Stable Tearing in Thin Sheet Material," ASTM STP 1256, W. G. Reuter, J. H. Underwood and J. C. Newman, Jr., Editors, American Society for Testing and Materials, pp. 223-242, 1995. 6. Ortiz, M. and Pandolfi, A., “Finite deformation irreversible cohesive elements for three-dimensional crack-propagation analysis,” Int J Num Meth Engng, n 44, pp. 1267-1282, 1999. 7. ASTM Standard E1820, Volume 03.01, American Society for Testing and Materials, 2000.
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