13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- method. It is envisaged that the closed-form weight function approach will provide an efficient and reliable method for calculating crack-surface displacements under arbitrary loadings. The analytical equations of the crack surface displacement can contribute to a more rapid and reliable fatigue crack growth life predictions for a radial crack emanating from a semi-circular notch in a semi-infinite plate. (a) (b) Figure.1 Crack geometry. (a) A radial crack emanating from a semi-circular notch in a semi-infinite plate. (b) Middle crack in an infinite plate 2. Theoretical procedures The weight function method [10] is a very powerful method for the determination of key fracture mechanics parameters for cracks under arbitrary load conditions, e.g. stress intensity factors and crack surface displacements. The high efficiency of this method lies in that the weight function is a property of crack geometry only, and is independent of loading. For given crack configuration, once the weight function is obtained, fracture mechanics parameters for the same crack configuration under arbitrary loadings can be easily determined through a simple quadrature. For stress intensity factors [10]:
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