An efficient analytical alternating method is developed in this paper to evaluate the mixed-mode stress intensity factors of embedded multiple cracks in a semi-infinite plane. Analytical solutions of a semi-infinite plane subjected to a point force applied on the boundary, and a finite crack in an infinite plane subjected to a pair of point forces applied on the crack faces are referred to as fundamental solutions. The Gauss integrations based on these point load fundamental solutions can precisely simulate the conditions of arbitrarily distributed loads. By using these fundamental solutions in conjunction with the analytical alternating technique, the mixed-mode stress intensity factors of embedded multiple cracks in a semi-infinite plane are evaluated. The numerical results of some reduced problems are compared with available results in the literature and excellent agreements are obtained.
Issue Section:
Technical Papers
Topics:
Fracture (Materials)
1.
Murakami, Y., et al., 1987, Stress Intensity Factor Handbook, Vols. 1 and 2, Pergamon Press, Oxford, U.K.
2.
Nowell
, D.
, and Hills
, D. A.
, 1987
, “Open Cracks at or Near Free Edges
,” J. Strain Anal.
, 22
, pp. 177
–185
.3.
Qian
, J.
, and Hasebe
, N.
, “An Oblique Edge Crack and an Internal Crack in a Semi-Infinite Plane Acted on by Concentrated Force at Arbitrary Position
,” Eng. Anal. Boundary Elem.
, 18
, pp. 155
–161
.4.
Ioakimidis
, N. I.
, and Theocaris
, P. S.
, “A System of Curvilinear Cracks in an Isotropic Elastic Half-Plane
,” Int. J. Fract.
, 15
, pp. 299
–309
.5.
Hu
, K. X.
, and Chandra
, A.
, “Interactions among Cracks and Rigid Lines Near a Free Surface
,” Int. J. Solids Struct.
, 30
, pp. 1919
–1937
.6.
Kantorovich, L. V., and Krylov, V. I., 1964, Approximate Method of Higher Analysis, transl. by C. D. Benster, John Wiley & Sons, Inc., New York and London.
7.
Hartranft, R. J., and Sih, G. C., 1973, Method of Analysis and Solutions of Crack Problems, G. C. Sih ed., Noordhoff, Holland.
8.
Shah
, R. C.
, and Kobayashi
, A. S.
, 1973
, “Stress Intensity Factor for an Elliptical Crack Approaching the Surface of a Semi-Infinite Solid
,” Int. J. Fract.
, 9
, pp. 133
–146
.9.
O’Donoghue
, P. E.
, Nishioka
, T.
, and Atluri
, S. N.
, 1985
, “Multiple Coplanar Embedded Elliptical Cracks in an Infinite Solid Subject to Arbitrary Crack Face Tractions
,” Int. J. Numer. Methods Eng.
, 21
, pp. 437
–449
.10.
Zhang
, X.
, and Hasebe
, N.
, 1993
, “Interactions between Rectilinear and Circumferential Cracks
,” Eng. Fract. Mech.
, 46
, pp. 311
–328
.11.
Raju
, I. S.
, and Fichter
, W. B.
, 1989
, “A Finite-Element Alternating Method for Dimensional Mode-I Crack Configurations
,” Eng. Fract. Mech.
, 33
, pp. 525
–540
.12.
Chen
, W.-H.
, and Chang
, C.-S.
, 1989
, “Analysis of two Dimensional Fracture Problems with Multiple Cracks under Mixed Boundary Conditions
,” Eng. Fract. Mech.
, 34
, pp. 921
–934
.13.
Krishnamurthy
, T.
, and Raju
, I. S.
, 1990
, “A Finite-Element Alternation Method for Two-Dimensional Mixed-Mode Crack Configuration
,” Eng. Fract. Mech.
, 36
, pp. 297
–311
.14.
Rajiyah
, H.
, and Atluri
, S. N.
, 1989
, “Evaluation of K-Factors and Weight Functions for 2-D Mixed-Mode Multiple Cracks by the Boundary Element Alternation Method
,” Eng. Fract. Mech.
, 32
, pp. 911
–922
.15.
Raju
, I. S.
, and Krishnamurthy
, T.
, 1992
, “A Boundary Element Alternating Method for Two-Dimensional Mixed-Mode Fracture Problems
,” Computational Mechanics
, 10
, pp. 133
–150
.16.
Isida, M., 1976, “Elastic Analysis of Cracks and Stress Intensity Factors” (in Japanese), Fracture Mechanics and Strength of Materials 2, Baifuukan, pp. 181–184.
17.
Yokobori
, T.
, Uozumi
, M.
, and Ichikawa
, M.
, 1971
, “Interaction between Overlapping Parallel Elastic Cracks
,” J. Japanese Soc. Strength Fract. Mater.
, 6
, pp. 39
–50
.18.
Kamei, A., and Yokobori, T., 1974, “Some Results on the Stress Intensity Factors of Cracks and/or Slip Bands Systems,” Reports of the Research Institute for Strength and Fracture of Materials, Tohoku University, 10, pp. 29–93.
19.
Isida
, M.
, 1969
, “Analysis of Stress Intensity Factors for Plates Containing Randomly Distributed Cracks
,” Trans. Jpn. Soc. Mech. Eng.
, 35
, pp. 1815
–1822
.20.
Rooke, D. P., and Cartwright, D. J., 1976, Compendium of Stress Intensity Factors, Hillingdon Press, Uxbridge, Middx., U.K.
21.
Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, McGraw-Hill, Inc., New York, NY.
22.
Rose
, L. R. F.
, 1986
, “Microcrack Interaction with a Main Crack
,” Int. J. Fract.
, 31
, pp. 233
–242
.23.
Lam
, K. Y.
, Wen
, C.
, and Tao
, Z.
, 1993
, “Interaction between Microcracks and a Main Crack in a Semi-Infinite Medium
,” Eng. Fract. Mech.
, 44
, pp. 753
–761
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