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A simple technique was developed using conventional finite element analysis to determine stress intensity factors (K1 and K2) for interface cracks under mixed-mode loading. This technique involves the calculation of crack-tip stresses using nonsingular finite elements. These stresses are then combined and used in a linear regression procedure to calculate K1 and K2. The technique was demonstrated by calculating K1 and K2 for three different bimaterial combinations.
For the normal loading case, the calculated K1 and K2 were within 2.6% of an exact solution. The normalized K1 and K2 under shear loading were shown to be related to the normalized K1 andK2 under normal loading. Based on these relations, a simple equation was derived for calculating K1 and K2 for mixed-mode loading from a knowledge of K1 and K2 under normal loading. Thus, for a given material combination and geometry, only one solution of K1 and K2 (under normal loading) is required to determine K1 andK2 over the full range of mixed-mode loading conditions.
The equation was verified by computing K1 and K2 for a mixed-mode case with equal normal and shear loading. The correlation between the exact and the finite element values was very good with errors of less than 3.7%.
This study provides a simple procedure to compute the K2/ K1 ratio, which can be used to characterize the stress state at the crack tip for various combinations of materials and loadings. Tests conducted over a range of K2/ K1 ratios could be used to characterize fully interface fracture toughness.
bimaterial, finite element analysis, fracture mechanics, combined loading, phase angle
Senior research scientist, Analytical Services and Materials, Inc., Hampton, VA
Senior scientist, NASA Langley Research Center, Hampton, VA