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Crack tip stress intensity factors calculated by dual finite element analysis

Published online by Cambridge University Press:  04 July 2016

D. J. Allman
D. J. Allman*
Affiliation:
Royal Aerospace Establishment, Farnborough
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Extract

Stress intensity factors for centre and edge cracks in finite elastic sheets are calculated from potential energy and complementary energy release rates by dual analysis with simple compatible and equilibrium finite elements. Comparison with very accurate results of other authors who employ special singular functions to model a crack tip provides compelling numerical evidence that the calculated stress intensity factors behave respectively like lower and upper bounds to the exact values. The bound-like character of such results has been reported before in another context, though there are no known bounding principles which strictly apply to finite bodies.

Type
Research Article
Information
The Aeronautical Journal , Volume 94 , Issue 934 , April 1990 , pp. 132 - 136
Copyright
Copyright © Royal Aeronautical Society 1990 

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References

1. Fraeijs de Veubeke, B. Displacement and equilibrium models in the finite element method. In: Stress Analysis, Eds Zienkiewicz, O. C. and Hollister, G. S. Wiley, London, 1965, pp 145–197.Google Scholar
2. Argyris, J. H. Triangular elements with linearly varying strain for the matrix displacement method. Aeronaut J, 1965, 69, pp 711–713.Google Scholar
3. Allman, D. J. The linear stress triangular equilibrium model in plane elasticity. Int J Comput Struct, 1989, 31, (5), pp 673–680.Google Scholar
4. Fraeijs de Veubeke, B. Upper and lower bounds in matrix structural analysis. Matrix Methods in Structural Mechanics, Ed Fraeijs de Veubeke, B. AGARDograph, 1964, 72, 165–201, Pergamon Press, Oxford.Google Scholar
5. Parks, D. M. A stiffness derivative finite element technique for determination of elastic crack tip stress intensity factors. Int J Fract, 1974, 10, 4, pp 487–502.Google Scholar
6. Hellen, T. K. On the method of virtual crack extensions. Int J Numer Meth Eng, 1975, 9, pp 187–207.Google Scholar
7. Ranaweera, M. P. and Leckie, F. A. The use of optimisation techniques in the analysis of cracked members by the finite element displacement and stress methods. Computer Meth Appl Mech Eng, 1979, 19, 367–389.Google Scholar
8. Rice, J. R. A path-independent integral and the approximate analysis of stress concentrations by notches and cracks. J Appl Mech, 1968, 35, pp 379–386.Google Scholar
9. Haber, R. B. and Koh, H. M. Explicit expressions for energy release rates using virtual crack extensions. Int J Numer Meth Eng, 1985, 21, pp 301–315.Google Scholar
10. Lin, S.-C. and Abel, J. F. Variational approach for a new direct integration form of the virtual crack extension method. Int J Fract, 1988, 38, pp 217–235.Google Scholar
11. Bui, H. D. Dual path independent integrals in the boundary value problems of cracks. Eng Fract Mech, 1976, 6, pp 287–296.Google Scholar
12. Rooke, D. P. and Cartwright, D. J. Compendium of stress intensity factors. HMSO, 1976.Google Scholar
13. Tada, H., Paris, P. and Irwin, G. The stress analysis of cracks handbook. Del Research Corporation, Hellertown, Pennsylvania, 1973.Google Scholar
14. Allman, D. J. On compatible and equilibrium models for stretching of elastic plates. In: Energy Methods in Finite Element Analysis (Eds Glowinski, R., Rodin, E. Y. and Zienkiewicz, O. C.) John Wiley & Sons, 1979, pp 109–126.Google Scholar
15. Blackburn, W. S. Calculation of stress intensity factors at crack tips using special finite elements. In: The Mathematics of the Finite Element Method, Brunel University, 1972.Google Scholar
16. Cartwright, D. J. and Rooke, D. P. An efficient boundary element model for calculating Green's functions in fracture mechanics. Int J Fract, 1985, 27, pp R43–R50.Google Scholar
17. He, M. Y. and Hutchinson, J. W. Bounds for fully plastic crack problems for infinite bodies. In: Elastic-Plastic Fracture (Eds, Shih, C. F. and Gudas, J. P.), Vol 1 — Inelastic Crack Analysis, American Society for Testing Materials, 1983, ASTM STP 803, I-277–I-290.Google Scholar