TECHNICAL PAPERS
Aug 1, 1983

Finite Element Model to Determine KI

Publication: Journal of Engineering Mechanics
Volume 109, Issue 4

Abstract

A finite element method utilizing quadrilateral elements to obtain an efficient solution to determining the opening‐mode stress intensity factor KI is presented. Two plane stress element types are constructed: (1) “Regular” which does not contain a crack but which may be in the interior or on a boundary; and (2) “singular” or “super element” which contains the crack and is assumed to be on the boundary which is a line of symmetry. Each element utilizes as primary unknowns the displacements and strains at each node. Hermitian interpolation functions are used to describe the displacements in the regular element and Williams' stress function is used to develop the singular element. Good agreement with published results is obtained for single‐edge‐notch beams in three‐point bending and four‐point bending for relatively coarse meshes.

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References

1.
Anderson, G. P., Ruggles, V. L., and Stibor, G. S., “Use of Finite Element Computer Programs in Fracture Mechanics,” International Journal of Fracture Mechanics, No. 7, 1971, pp. 63–76.
2.
Brown, W. F., Jr., and Srawley, J. E., “Plain Strain Crack Toughness Testing of High Strength Metallic Materials,” ASTM STP 410, American Society for Testing and Materials, Philadelphia, Pa., 1966.
3.
Byskov, E., “The Calculation of Stress Intensity Factors Using the Finite Element Method with Cracked Elements,” International Journal of Fracture Mechanics, No. 6, 1970, pp. 159–167.
4.
Dixon, J. R., and Cook, L. P., “Stress Intensity Factors Calculated Generally by the Finite Element Technique,” Nature, 1969, pp. 224, 166.
5.
Hu, K. K., Kirmser, P. G., Swartz, S. E., and Huang, J. M., “On the Construction of Compatible Elements with the Use of Generalized Parameters,” Proceedings, 3rd International Conference on Finite Elements in Water Resources, Oxford, Miss., May 19–23, 1980.
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Huang, J. M., “Finite Element and Experimental Studies of Stress‐Intensity Factors for Concrete Beams,” dissertation presented to the College of Engineering, Kansas State Univ., at Manhattan, Kans., in 1981, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
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Kobayashi, O. E., Maiden, B. J., Simon and Iide, S., “Application of the Method of Finite Element Analysis to Two Dimensional Problems in Fracture Mechanics,” Report by University of Washington to Office of Naval Research, Contract No. 477 (39), TR No. 5, Oct., 1968.
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Luk, C. H., “Assumed Stress Hybrid Element Method for Fracture Mechanics and Elastic‐Plastic Analysis,” thesis presented to Massachusetts Institute of Technology, Department of Aeronautics and Astronaut, at Cambridge, Mass., in 1973, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 109Issue 4August 1983
Pages: 1103 - 1113

History

Published online: Aug 1, 1983
Published in print: Aug 1983

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Authors

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Kuo‐Kuang Hu, M. ASCE
Dept. of Civ. Engrg., Kansas State Univ., Manhattan, Kans.
Chen‐Ming J. Huang, A. M. ASCE
United Engineers and Constructors, Inc., Philadelphia, Pa.
Stuart E. Swartz, M. ASCE
Dept. of Civ. Engrg., Kansas State Univ., Manhattan, Kans.

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