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TECHNICAL PAPERS

Dynamic Analysis of a Mode I Propagating Crack Subjected to a Concentrated Load

[+] Author and Article Information
Y.-L. Chung, M.-R. Chen

Department of Construction Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan

J. Appl. Mech 70(5), 668-675 (Oct 10, 2003) (8 pages) doi:10.1115/1.1600473 History: Received June 09, 1999; Revised December 17, 2002; Online October 10, 2003
Copyright © 2003 by ASME
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References

Achenbach, J. D., 1973, Wave Propagation in Elastic Solids, Elsevier, New York.
Smirov, V. I., 1964, A Course of Higher Mathematics, Addison-Wesley, London.
Thompson, J. C., and Robinson, A. R., 1969, “Exact Solution of Some Dynamic Problems of Indentation and Transient Loadings of an Elastic Half Space,” SRS 350, University of Illinois at Champaign-Urbana.
Chung,  Y. L., 1995, “The Stress Singularity of Mode-I Crack Propagating With Transonic Speed,” Eng. Fract. Mech., 52, pp. 977–985.
Chung,  Y. L., 1992, “The Transient Problem of a Mode-III Interface Crack,” Eng. Fract. Mech., 41, pp. 321–330.
Johnson, J. J., and Robinson, A. R., 1972, “Wave Propagation in Half Space Due to an Interior Point Load Parallel to the Surface,” SRS 388, University of Illinois at Champaign-Urbana.
Chung,  Y. L., 1997, “Analysis of a Running Crack Stopping Suddenly—Solution for Small Time After Stop,” Chin. J. Mech., 13, pp. 175–183.
Freund,  L. B., 1972, “Crack Propagation in an Elastic Solid Subjected to General Loading—II Non-Uniform Rate Extension,” J. Mech. Phys. Solids, 20, pp. 141–152.
Freund,  L. B., 1973, “Crack Propagation in an Elastic Solid Subjected to General Loading—III Stress Wave Loading,” J. Mech. Phys. Solids, 21, pp. 46–61.
Freund,  L. B., 1974, “Crack Propagation in an Elastic Solid Subjected to General Loading—IV Obliquely Incident Stress Pulse,” J. Mech. Phys. Solids, 22, pp. 137–146.
Eringen, A. C., and Suhubi, E. S., 1975, Elastodynamics, Vol. II, Academic Press, New York.
Freund,  L. B., 1974, “The Stress Intensity Factor Due to Normal Impact Loading of the Faces of a Crack,” Int. J. Eng. Sci., 12, pp. 179–189.
Kostrov,  B. V., 1964, “The Axisymmetric Problem of Propagation of a Tension Crack,” J. Appl. Math. Mech., 28, pp. 793–803.
Kostrov,  B. V., 1964, “Self-Similar Problems of Propagation of Shear Cracks,” J. Appl. Math. Mech., 28, pp. 1077–1087.
Chung,  Y. L., 1991, “The Transient Solutions of Mode-I, Mode-II, Mode-III Cracks Problems,” J. Chin. Inst. Civil Hydraulic Eng., 3, pp. 511–61.
Churchill, R. V., 1984, Complex Variables and Applications, McGraw-Hill, New York.
Cherepanov,  G. P., 1974, “Some Dynamic Problems of the Theory of Elasticity—A Review,” Int. J. Eng. Sci., 12, pp. 665–690.

Figures

Grahic Jump Location
The superposition scheme for a concentrated load acting on the crack surfaces
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The case B problem: (a) on the physical plane, (b) on the physical plane after shifting the origin to (x0,0), (c) on the complex θ̄ plane
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The case C problem: (a) on the physical plane, (b) on the physical plane after shifting the origin to (x0,0), (c) on the complex θ̄ plane.
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The normal surface displacement on the x axis for a=6326 m/s,b=3463 m/s,s=2770.4 m/s,t=0.01 s
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The normal surface stress σy on the x axis for a=6326 m/s,b=3463 m/s,s=2770.4 m/s,t=0.01 s
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Comparison of normalized DSIF for a central running crack subjected a concentrated load and uniform distributed load
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Normalized DSIF versus crack-tip location for a mode I running crack subjected to a concentrated load with a variation in crack-tip speed
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Normalized DSIF versus crack-tip speed for a mode I running crack subjected to a uniformly portion load with expanding speed vL/s=0.2
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Geometrical configuration of the disturbance of P and S waves
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Normalized DSIF versus crack-tip speed for a mode I running crack subjected to a uniformly portion load with expanding speed vL/s=0.5
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Normalized DSIF versus crack-tip speed for a mode I running crack subjected to a uniformly portion load with expanding speed vL/s=0.1, 0.2, 0.5, 0.7, 0.9

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