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TECHNICAL PAPERS

Scattering From an Elliptic Crack by an Integral Equation Method: Normal Loading

[+] Author and Article Information
T. K. Saha

Department of Mathematics, Surendranath College, 24/2 M. G. Road, Calcutta 700 009, Indiae-mail: tksaha@cubmb.ernet.in

A. Roy

Department of Applied Mathematics, University of Calcutta, 92 A. P. C. Road, Calcutta 700 009, Indiae-mail: aroy@cucc.ernet.in

J. Appl. Mech 69(6), 775-784 (Oct 31, 2002) (10 pages) doi:10.1115/1.1483834 History: Received November 22, 2000; Revised October 22, 2001; Online October 31, 2002
Copyright © 2002 by ASME
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References

Bond, L. J., 1990, “Numerical Technique and Their Use to Study Wave Propagation and Scattering—A Review,” Elastic Waves and Ultrasonic Nondestructive Evaluation, S. K. Datta, J. D. Achenbach, and Y. S. Rajapakse, eds., North-Holland, Amsterdam.
De Hoop, A. T., 1990, “Reciprocity, Discretization, and the Numerical Solution of Elastodynamic Propagation and Scattering Problems,” Elastic Waves and Ultrasonic Nondestructive Evaluation, S. K. Datta, J. D. Achenbach, and Y. S. Rajapakse, eds., North-Holland, Amsterdam.
Martin,  P. A., and Wickham,  G. R., 1983, “Diffraction of Elastic Waves by a Penny-Shaped Crack: Analytical and Numerical Results,” Proc. R. Soc. London, Ser. A, 390, pp. 91–129.
Roy,  A., 1984, “Diffraction of Elastic Waves by an Elliptic Crack,” Int. J. Eng. Sci., 22, pp. 729–739.
Roy,  A., 1987, “Diffraction of Elastic Waves by an Elliptic Crack—II,” Int. J. Eng. Sci., 25, pp. 155–169.
Lin,  W., and Keer,  L. M., 1987, “Scattering by a Planar Three-Dimensional Crack,” J. Acoust. Soc. Am., 82, pp. 1442–1448.
Hirose, S., 1989, “Scattering From an Elliptic Crack by the Time-Domain Boundary Integral Equation Method,” Advances in Boundary Elements, Vol 3: Stress Analysis, C. A. Brebbia, and J. J. Connor, eds, Computational Mechanics Publications, Southampton, UK, pp. 99–110.
Shifrin,  E. I., 1996, “Semi-Analytical Solution of the Problem of Elastic Wave Scattering by Elliptical Cracks,” Z. Angew. Math. Mech., 76, pp. 471–472.
Visscher,  W. M., 1983, “Theory of Scattering of Elastic Waves From Flat Cracks of Arbitrary Shape,” Wave Motion, 5, pp. 15–32.
Budreck,  D. E., and Achenbach,  J. D., 1988, “Scattering From Three-Dimensional Planar Cracks by the Boundary Integral Equation Method,” ASME J. Appl. Mech., 55, pp. 405–412.
Nishimura,  N., and Kobayashi,  S., 1989, “A Regularized Boundary Integral Equation Method for Elastodynamic Crack Problems,” Comput. Mech., 4, pp. 319–328.
Zhang, Ch., and Gross, D., 1998, On Wave Propagation in Elastic Solids With Cracks, Computational Mechanics Publications, Southampton, UK.
Alves,  C., and Duong,  T. Ha, 1995, “Numerical Resolution of the Boundary Integral Equations for Elastic Scattering by a Plane Crack,” Int. J. Numer. Methods Eng., 38, pp. 2347–2371.
Schafbuch,  P. J., Thompson,  R. B., and Rizzo,  F. J., 1990, “Application of the Boundary Element Method to Elastic Wave Scattering by Irregular Defects,” J. Nondestruct. Eval., 9, pp. 113–127.
Itou,  S., 1980, “Dynamic Stress Concentration Around a Rectangular Crack in an Infinite Elastic Medium,” Z. Angew. Math. Mech., 60, pp. 317–322.
Guan,  L., and Norris,  A., 1992, “Elastic Wave Scattering by Rectangular Cracks,” Int. J. Solids Struct., 29, pp. 1549–1565.
Glushkov,  Y. V., and Glushkova,  N. V., 1996, “Diffraction of Elastic Waves by Three-Dimensional Cracks of Arbitrary Shape in a Plane,” Appl. Math. Mech., 60, pp. 277–283.
Bostrom,  A., and Eriksson,  A. S., 1993, “Scattering by Two Penny-Shaped Cracks With Spring Boundary Conditions,” Proc. R. Soc. London, Ser. A, 443, pp. 183–201.
Roy,  A., and Chatterjee,  M., 1994, “Interaction Between Coplanar Elliptic Cracks—I. Normal Loading,” Int. J. Solids Struct., 31, pp. 127–144.
Mal,  A. K., 1968, “Dynamic Stress Intensity Factor for an Axisymmetric Loading of the Penny Shaped Crack,” Int. J. Eng. Sci., 6, pp. 623–629.
Krenk,  S., and Schmidt,  H., 1982, “Elastic Wave Scattering by a Circular Crack,” Philos. Trans. R. Soc. London, Ser. A, A308, pp. 167–198.
Mal,  A. K., 1970, “Interaction of Elastic Waves With a Penny-Shaped Crack,” Int. J. Eng. Sci., 8, pp. 381–388.
Keogh, P. S., 1983, Ph.D. thesis, University of Manchester.
Martin,  P., 1981, “Diffraction of Elastic Waves by a Penny-Shaped Crack,” Proc. R. Soc. London, Ser. A, A378, pp. 263–285.
Roy,  A., and Saha,  T. K., 2000, “Weight Function for an Elliptic Crack in an Infinite Medium. I. Normal Loading,” Int. J. Fracture, 103, pp. 227–241.
Gradshteyn, I. S., and Ryzhik, I. M., 1980, Tables of Integrals, Series and Products, Corrected and Enlarged Ed., Academic Press, San Diego, CA (English translation: A. Jeffrey, ed.).
Robertson,  I. A., 1967, “Diffraction of a Plane Longitudinal Wave by a Penny-Shaped Crack,” Proc. Cambridge Philos. Soc., 63, pp. 229–238.
Piau,  M., 1979, “Attenuation of a Plane Compressional Wave by a Random Distribution of Thin Circular Cracks,” Int. J. Eng. Sci., 17, pp. 151–167.
Martin,  P. A., 1986, “Orthogonal Polynomial Solutions for Pressurized Elliptical Cracks,” Q. J. Mech. Appl. Math., 39, pp. 269–287.
Sneddon, I. N., 1951, Fourier Transforms, McGraw-Hill, New York.
Mura, T., 1982, Micromechanics of Defects in Solids, Martinus Nijhoff, The Hague.

Figures

Grahic Jump Location
Scattering geometry of an elliptic crack. ui is the incident displacement field and usc is the scattered field.
Grahic Jump Location
Present method (lines), BIEM (triangles), and Mal (bullets) nondimensional dynamic crack-opening displacement for circular crack for k2a equal to (a) 0.0; (b) 1.4; (c) 3.2; (d) 4.4; and (e) 6.0.
Grahic Jump Location
(a) Dimensionless crack-opening displacement of an 1:1/(√2) elliptic crack with k2a equal to 4.5. (b) Dimensionless crack-opening displacement of an 1:1/(√2) elliptic crack with k2a equal to 5.5.
Grahic Jump Location
Dimensionless crack-opening displacement of an 1:1/(√2) elliptic crack with k2a equal to 5.5 (a) fourth-order system ϕ=0 deg; (b) sixth-order system ϕ=0 deg; (c) eighth-order system ϕ=0 deg; (d) fourth-order system ϕ=90 deg; (e) sixth-order system ϕ=90 deg; (f ) eighth-order system ϕ=90 deg
Grahic Jump Location
(a) Dimensionless crack-opening displacement of an 1:1/2 elliptic crack with k2a equal to 4.5. (b) Dimensionless crack-opening displacement of an 1:1/2 elliptic crack with k2a equal to 5.5.
Grahic Jump Location
Present method (lines), Zhang and Gross (bullets) and Mall (triangles) nondimensional dynamic stress intensity factor for a circular crack for ν=0.25
Grahic Jump Location
Present method (lines) and Zhang and Gross (bullets) nondimensional dynamic stress intensity factor for elliptic cracks with aspect ratio (a) 1:1/2, ϕ=90 deg; (b) 1:1/2, ϕ=0 deg; (c) 1:1/5, ϕ=90 deg; (d) 1:1/5, ϕ=0 deg. ν=0.3.
Grahic Jump Location
Scattering cross section of (a) 1:1; (b) 1:1/(√2); (c) 1:1/3, and (d) 1:1/5 elliptic cracks under normal incidence of a longitudinal wave
Grahic Jump Location
Back-scattered displacement amplitudes of (a) 1:1; (b) 1:1/(√2); (c) 1:1/2; (d) 1:1/3, and (e) 1:1/5 elliptic cracks under normal incidence of a longitudinal wave

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