13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- 5. Summary and conclusions Crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate are determined, and analytical equations have been developed. Two load cases have been treated, i.e. uniform remote tension and crack face Dugdale loading. The weight function method was used for the analysis. The following conclusions can be drawn. (1) The closed-form weight function method provides a powerful means for accurate determination of crack surface displacements under arbitrary load conditions. (2) Based on a correction of stress intensity factor ratio, highly accurate analytical equations of the crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate are developed, which fit the results from the weight function method very well. References [1] J.C. Newman, Jr., A crack-closure model for predicting fatigue crack growth under aircraft spectrum loading, ASTM STP 748 (1981) 53-84. [2] B. Budiansky, J.W. Hutchinson, Analysis of closure in fatigue crack growth, J Appl Mech 45 (1978) 267-276. [3] J.H. Kim, S.B. Lee, Fatigue crack opening stress based on the strip-yield model, Theor Appl Fract Mech 34 (2000) 73-84. [4] J.Z. liu, X.R. Wu, Study on fatigue crack closure behavior for various cracked geometries, Eng Fract Mech 57 (1997) 475-491. [5] B. Ziegler, Y. Yamada, J.C. Newman, Jr., Application of a strip-yield model to predict crack growth under variable-amplitude and spectrum loading – Part 2: Middle-crack-tension specimens, Eng Fract Mech 78 (2011) 2609-2619. [6] G.S. Wang, A.F. Blom, A strip model for fatigue crack growth predictions under general load conditions, Eng Fract Mech 40 (1991) 507-533. [7] Y. Yamada, B. Ziegler, J.C. Newman, Jr., Application of a strip-yield model to predict crack growth under variable-amplitude and spectrum loading – Part 1: Compact specimens, Eng Fract Mech 78 (2011) 2597-2608. [8] S. Mall, J.C. Newman, Jr., The Dugdale model for compact specimen, ASTM STP 868 (1985) 113-128. [9] J.C. Newman, Jr., A nonlinear fracture mechanics approach to the growth of small cracks, In: Zocher H, editor, Behaviour of short cracks in airframe materials, vol. 328, AGARD CP (1983) P: 6.1-6.26. [10] X.R. Wu and A.J. Carlsson, Weight Functions and Stress Intensity Factor Solutions, Oxford, Pergamon Press, 1991. [11] H. Tada, P.C. Paris, G.R. Irwin, The stress analysis of cracks handbook, 3rd ed, New York, ASME Press, 2000. [12] D.H. Tong and X.R. Wu, Determination of crack surface displacements for cracks emanating from a circular hole using weight function method, Fatigue Fract Eng Mater Struct 2013, in press. [13] D.H. Tong and X.R. Wu, Weight function solutions of crack surface displacements for double cracks emanating from a circular hole in an infinite plate, Acta Aeronautica et Astronautica Sinica 2013, in press, in Chinese.
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