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Boundary Weight Functions for Cracks in Three-Dimensional Finite Bodies

Published online by Cambridge University Press:  05 May 2011

Chien-Ching Ma  and
I-Kuang Shen
Chien-Ching Ma*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
I-Kuang Shen*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Professor
**Graduate student
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Abstract

An efficient boundary weight function method for the determination of mode I stress intensity factors in a three-dimensional cracked body with arbitrary shape and subjected to arbitrary loading is presented in this study. The functional form of the boundary weight functions are successfully demonstrated by using the least squares fitting procedure. Explicit boundary weight functions are presented for through cracks in rectangular finite bodies. If the stress distribution of a cut out rectangular cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple integration. Comparison of the calculated results with some solutions by other workers from the literature confirms the efficiency and accuracy of the proposed boundary weight function method.

Keywords

Stress intensity factorBoundary weight functionFinite bodyThrough crack
Type
Articles
Information
Journal of Mechanics , Volume 15 , Issue 1 , March 1999 , pp. 17 - 26
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1999

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References

REFERENCES

1.Tada, H., Paris, P. C. and Irwan, G. R., The Stress Analysis of Cracks Handbook, Del Research Corporation, Hellertown, Penna (1973).Google Scholar
2.Rooke, D. P. and Cartwright, D. J., Compendium of Stress Intensity Factors, Her Majesty's Stationery Office, London (1976).Google Scholar
3.Sih, G. C, Handbook of Stress Intensity Factors, Institute of Fracture and Solid Mechanics, Lehigh University (1973).Google Scholar
4.Bueckner, H. F., “A Novel Principle for the Computation of Stress Intensity Factor,” ZAMM, Vol. 50, pp. 529–546(1970).Google Scholar
5.Rice, J. R., “Some Remarks on Elastic Crack-tip Stress Fields,” International Journal of Solids and Structures, Vol. 8, pp. 751–758 (1972)..Google Scholar
6.Bowie, O. L. and Freese, C. E., “Cracked- Rectangular Sheet with Linerly Varying End Displacements,” Engineering Fracture Mechanics, Vol. 14, pp. 519–526(1981).Google Scholar
7.Bortman, Y. and Banks-Sills, L., “An Extended Weight Function Method for Mixed-mode Elastic Crack Analysis,” Jounral of Applied Mechanics, Vol. 50, pp. 907–909(1983).CrossRefGoogle Scholar
8.Sha, G. T., “Stiffness Derivatives Finite Element Technique to Determine Nodal Weight Functions with Singularity Elements,” Engineering Fracture Mechanics, Vol. 19, pp. 685–699 (1984).CrossRefGoogle Scholar
9.Sha, G. T. and Yang, C. T., “Weight Function Calculations for Mixed-mode Fracture Problems with the Virtual Crack Extension Technique,” Engineering Fracture Mechanics, Vol. 21, pp. 1119–1149(1985).Google Scholar
10.Parks, D. M., “A Stiffness Derivative Finite Element Technique for Determination of Crack Tip Stress Intensity Factors,” International Journal of Fracture, Vol. 10, pp. 487–501 (1974).Google Scholar
ll.Hellen, T. K.“On the Method of Virtual Crack Extensions,” International Journal of Numerical Methods in Engineering, Vol. 9, pp. 187–207 (1975).CrossRefGoogle Scholar
12.Tsai, C. H. and Ma, C. C, “Weight Functions for Cracks in Finite Rectangular Plates,” International Journal of Fracture, Vol. 40, pp. 43–63 (1989).Google Scholar
13.Ma, C. C, Chang, Z. and Tsai, C. H., “Weight Functions of Oblique Edge and Center Cracks in Finite Bodies,” Engineering Fracture Mechanics, Vol. 36, pp. 267–285(1990).Google Scholar
14.Ishikawa, H., “A Finite Element Analysis of Stress Intensity Factors for Combined Tensile and Shear Loading by Only a Virtual Crack Extension,” International Journal of Fracture, Vol. 16, pp. 243–246(1980).Google Scholar
15.Sha, G. T., “On the Virtual Crack Extension Technique for Stress Intensity Factors and Energy Release Rate Calculations for Mixed Fracture Mode,” International Journal of Fracture, Vol. 25, pp. R33–42 (1984).CrossRefGoogle Scholar
16.Banks-Sills, L. and Makevet, L., “A Numerical Mode I Weight Function for Calculating Stress Intensity Factors of Three-Dimensional Cracked Bodies,” International Journal of Fracture, Vol. 76, pp. 169–191 (1996).Google Scholar
17.Raju, I. S. and JrNewman, J. C.“Stress Intensity Factor for a Wide Range of Semi-Elliptical Surface Cracks in Finite-Thickness Plates,” Engineering Fracture Mechanics, Vol. 11, pp. 817–829 (1979).CrossRefGoogle Scholar
18.Heckmer, J. L. and Bloom, J. M., “Determination of Stress Intensity Factors for the Corner-Cracked Hole Using the Isoparametric Singularity Element,” International Journal of Fracture, Vol. 13, pp. 732–736 (1977).Google Scholar
19.Ma, C. C, Shen, I. K. and Tsai, P., “Calculation of the Stress Intensity Factor for Arbitrary Finite Cracked Body by Using the Boundary Weight Function Method,” International Journal of Fracture, Vol. 70, pp. 183–202 (1995).CrossRefGoogle Scholar
20.Labbens, R. C, Heliot, J. and Pellissier-Tanon, A., “Weight Function for Three-Dimensional Symmetrical Crack Problems,” ASTMSTP, Vol. 601, pp. 448–470 (1976).Google Scholar