Review of hypersingular integral equation method for crack scattering and application to modeling of ultrasonic nondestructive evaluation

Applied Mechanics Reviews

Volumn 56, Issue 4, 2003, Pages 383-405

  Boströ, Anders ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; AUTOMATION; BOUNDARY ELEMENT METHOD; CHEMICAL OXYGEN DEMAND; ELASTIC WAVES; FUNCTIONS; GEOPHYSICS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MECHANICAL ENGINEERING; NONDESTRUCTIVE EXAMINATION; SIGNAL PROCESSING; ULTRASONIC TESTING;

CHEBYSHEV FUNCTIONS; CRACK SCATTERING; HYPERSINGULARITY; ULTRASONIC NONDESTRUCTIVE TESTING;

CRACKS;

EID: 4344584263     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1574522     Document Type: Review

References (78)

1. Robertson IA (1967), Diffraction of a plane longitudinal wave by a penny-shaped crack, Proc. Cambridge Philos. Soc., 63, 229-238.
2. Martin PA and Wickham GR (1983), Diffraction of elastic waves by a penny-shaped crack:analytical and numerical results, Proc. R. Soc. London, Ser. A, 390, 91-129.
3. Ohyoshi T (1973), Effect of orthotropy on singular stress produced near a crack tip by incident SH-waves, Z. Angew. Math. Mech., 53, 409-411.
4. Zhang Ch (2000), Transient elastodynamic antiplane crack analysis of anisotropic solids, Int. J. Solids Struct., 37, 6107-6130.
5. Neerhoff FL (1979), Diffraction of Love waves by a stress-free crack of finite width in the plane interface of a layered composite, Appl. Sci. Res., 35, 237-249.
6. van den Berg PM (1981), Transition matrix in acoustic scattering by a strip, J. Acoust. Soc. Am., 70, 615-619.
7. Krenk S and Schmidt H (1982), Elastic wave scattering by a circular crack, Philos. Trans. R. Soc. London, Ser. A, 308, 167-198.
8. Krenk S (1979), A circular crack under asymmetric loads and some related integral equations, ASME J. Appl. Mech., 46, 821-826.
9. Itou S (1978), Three-dimensional wave propagation in a cracked elastic solid, ASME J. Appl. Mech., 45, 807-811.
10. Itou S (1980), Dynamic stress concentration around a rectangular crack in an infinite elastic medium, Z Angew. Math. Mech., 60, 317-322.
11. Martin PA and Rizzo F J (1989), On boundary integral equations for crack problems, Proc. R. Soc. London, Ser. A. 421, 341-355.
12. Martin PA and Rizzo F J (1996), Hypersingular integrals: How smooth must the density be?, Int. J. Numer. Methods Eng., 39, 687-704.
13. Martin PA, Rizzo FJ, and Cruse TA (1998), Smoothness-relaxation strategies for singular and hypersingular integral equations, Int. J. Numer. Methods Eng., 42, 885-906.
14. Martin PA (1996), Mapping flat cracks onto penny-shaped cracks, with application to somewhat circular tensile cracks, Q. Appl. Math., 54, 663-675.
15. Martin PA (1998), On potential flow past wrinkled discs, Proc. R. Soc. London. Ser. A, 454, 2209-2221.
16. Jansson P-A (1995), Rough scatterers in acoustics and elastodynamics, PhD Thesis, Chalmers Univ Tech, Göteborg.
17. Zhang Ch and Gross D (1998), On Wave Propagation in Elastic Solids with Cracks, Computational Mechanics Publ, Southampton.
18. Dundurs J (1969), Discussion, ASME J. Appl. Mech., 36, 650-652.
19. Helsing J, Jonsson A, and Peters G (2001), Evaluation of the mode I stress intensity factor for a square crack in 3D, Eng. Fract. Mech., 68, 605-612.
20. Auld BA (1990), Acoustic Fields and Waves in Solids, RE Krieger, Malabar.
21. Williams ML (1959), The stress around a fault or crack in dissimilar media, Bull. Seismol. Soc. Am., 49, 199-204.
22. Boström A (1987), Elastic wave scattering from an interface crack: Antiplane strain, ASME J. Appl. Mech., 54, 503-508.
23. van den Berg PM, and Kleinman RE (1988), The conjugate gradient spectral iterative technique for planar structures, IEEE Trans AP, 36, 1418-1423.
24. Gross D and Zhang Ch (1988), Diffraction of SH waves by a system of cracks: solution by an integral equation method, Int. J. Solids Struct., 24, 41-49.
25. Kundu T (1986), Transient response of an interface-crack in a layered plate, ASME J. Appl. Mech., 53, 579-585.
26. Chevalier Y, Louzar M, and Maugin GA (1995), Influence of interfacial slits with elastic slip on the propagation of SH waves, J. Acoust. Soc. Am., 98, 445-453.
27. Eriksson AS (1992), Elastic wave scattering by closed cracks and thin flaws-multiple scattering and resonances, PhD Thesis, Chalmers Univ Tech, Göteborg.
28. Kundu T (1987), The transient response of two cracks at the interface of a layered half-space, Int. J. Eng. Sci., 25, 1427-1439.
29. Kundu T (1988), Dynamic interaction between two interface cracks in a three layered plate, Int. J. Solids Struct., 24, 27-39.
30. Bövik P and Boström A (1997), A model of ultrasonic nondestructive testing for internal and subsurface cracks, J. Acoust. Soc. Am., 102, 2723-2733.
31. Yang Y and Norris AN (1991), Shear-wave scattering from a debonded fibre, J. Mech. Phys. Solids. 39, 273-294.
32. Norris AN and Yang Y (1991), Dynamic stress on a partially bonded fiber, ASME J. Appl. Mech., 58, 404-409.
33. Wang YS and Wang D (1996), Scattering of elastic waves by a rigid cylindrical inclusion partially debonded from its surrounding matrix 1. SH case, Int. J. Solids Struct., 33, 2789-2815.
34. Waterman PC (1969), New formulation of acoustic scattering, J. Acoust. Soc. Am., 45, 1417-1429.
35. van der Hijden JHMT and Neerhoff FL (1984), Scattering of elastic waves by a plane crack of finite width, ASME J. Appl. Mech., 51, 646-651.
36. Yang HJ and Bogy DB (1985), Elastic wave scattering from an interface crack in a layered half space, ASME J. Appl. Mech., 52, 42-49.
37. Gracewski SM and Bogy DB (1986), Elastic wave scattering from an interface crack in a layered half space submerged in water: Part I: Applied tractions at the liquid-solid interface, ASME J. Appl. Mech., 53, 326-332.
38. Gracewski SM and Bogy D B (1986). Elastic wave scattering from an interface crack in a layered half space submerged in water: Part II: Incident plane waves and bounded beams, ASME J. Appl. Mech., 53, 333-338.
39. Erdogan F and Gupta GD (1972), On the numerical solutions of singular integral equations, Q. Appl. Math., 29, 525-533.
40. Itou S (1986), Transient stresses around an interface crack. Eng. Fract. Mech., 25, 475-482.
41. Qu JM (1994), Scattering of plane-waves from an interface crack. Int. J. Eng. Sci., 33, 179-194.
42. Qu JM (1995), Interface crack loaded by a time-harmonic plane-wave, Int. J. Solids Struct., 31, 329-345.
43. Yang Y and Norris AN (1992), Longitudinal-wave scattering from a partially bonded fiber, Wave Motion, 15, 43-59.
44. Mattsson J (1996), Modeling of scattering by cracks in anisotropic solids-An application to ultrasonic detection, PhD Thesis, Chalmers Univ Tech, Göteborg.
45. Karim MR and Kundu T (1988), Transient surface response of layered isotropic and anisotropic half-spaces with interface cracks: SH case, Int. J. Fract., 37, 245-262.
46. Karim MR and Kundu T (1989), Transient response of three layered composites with two interface cracks due to a line load, Acta Mech., 76, 53-72.
47. Grahn T (2001), Ultrasonic 2D SH crack detection in a layered an-isotropic plate, J. Nondestruct. Eval., 20, 17-28.
48. Kuo AY (1984), Transient stress intensity factors of an interfacial crack between two dissimilar anisotropic half-spaces, Part 1: Orthotropic materials, ASME J. Appl. Mech., 51, 71-76.
49. Kuo AY (1984), Transient stress intensity factors of an interfacial crack between two dissimilar anisotropic half-spaces. Part 2: Fully anisotropic materials, ASME J. Appl. Mech., 51, 780-786.
50. Shen SP, Khuang ZB, and Hu S (1999), On interface crack in laminated anisotropic medium, Int. J. Solids Struct., 36, 4251-4268.
51. Boström A, Johansson M, and Svedberg T (1994), Elastic wave propagation in a radially anisotropic medium, Geophys. J. Int., 118, 401-410.
52. Payton RG and Watanabe K (1997), SH waves in cylindrical anisotropic elastic solid: A general solution for a point source, Wave Motion 25, 197-212.
53. Boström A (1999), On the importance of edge conditions in an elastodynamic crack problem, in Festskrift till Staffan Ström, A Karlsson and G Kristensson (eds), Lund.
54. Jansson P-A (1998), Elastic wave scattering from a rough strip-like crack, in Rev Progr Quant Nondestr Ev vol 17, DO Thompson and DE Chimmenti (eds). Plenum Press, New York, 65-71.
55. Boström A and Eriksson AS (1993), Scattering by two penny-shaped cracks with spring boundary conditions, Proc. R. Soc. London. Ser. A, 443, 183-201.
56. Bövik P (1992), Thin layers in elastic wave propagation-effective modelling and diffraction, PhD thesis, Chalmers Univ Tech, Göteborg.
57. Eriksson AS, Boström A, and Datta SK (1995), Ultrasonic wave propagation through a cracked solid. Wave Motion, 22, 297-310.
58. Peterson L (1989), Acoustic and elastodynamic scattering by thin three-dimensional objects, PhD Thesis, Chalmers Univ Tech, Göteborg.
59. Boström A and Wickham G R (1991), On the boundary conditions for ultrasonic transmission by partially closed cracks, J. Nondestruct. Eval., 10, 139-149.
60. Guan L and Norris A (1992), Elastic wave scattering by rectangular cracks, Int. J. Solids Struct., 29, 1549-1565.
61. Itou S (1982), Dynamic stress intensity factors around a rectangular crack in a half-space under impact load, Z. Angew. Math. Mech., 62, 301-311.
62. Jansson P-A (2000), Modeling of ultrasonic detection of a rectangular crack, in Rev Progr Quant Nondestr Ev vol 19, DO Thompson and DE Chimmenti (eds). Am Inst Physics, 57-63.
63. Matlsson J, Niklasson AJ, and Eriksson AS (2000), Modeling of ultrasonic crack detection in anisotropic materials, NDT & E Int., 33, 441-451.
64. Grahn T (2002), Scattering of elastic waves from inhomogeneities in solids-application to ultrasonic NDT, PhD Thesis, Chalmers Univ Tech, Göteborg.
65. Niklasson AJ (1997), Elastic wave propagation in anisotropic media-application to ultrasonic NDT, PhD Thesis, Chalmers Univ Tech, Göteborg.
66. Kundu T (1990), Scattering of torsional waves by a circular crack in a transversely isotropic solid, J. Acoust. Soc. Am., 88, 1975-1980.
67. Boström A and Kundu T (1991), Axisymmetric scattering of a plane longitudinal wave by a circular crack in a transversely isotropic solid, ASME J. Appl. Mech., 58, 695-702.
68. Kundu T and Boström A (1992), Elastic wave scattering by a circular crack in a transversely isotropic solid, Wave Motion, 15, 285-300.
69. Fan Y, Sinclair AN, and Honorvar F (1999), Scattering of a plane acoustic wave from a transversely isotropic cylinder enclosed in a solid clastic medium, J. Acoust. Soc. Am., 106, 1229-1236.
70. Buchwald VT (1961), Rayleigh waves in transversely isotropic media, Q. J. Mech. Appl. Math., 14, 293-317.
71. Niklasson AJ (1998), Ultrasonic three-dimensional probe modeling in anisotropic solids, J. Acoust. Soc. Am., 103, 2432-2442.
72. Auld BA (1979), General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients, Wave Motion, 1, 3-10.
73. Boström A and Wirdelius H (1995), Ultrasonic probe modeling and nondestructive crack detection, J. Acoust. Soc. Am., 97, 2836-2848.
74. Wirdelius (1995), Ultrasonic NDT in defect detection-mathematical modelling. PhD Thesis, Chalmers Univ Tech, Göteborg.
75. Boström A (1995), UTDefect - a computer program modelling ultrasonic NDT of cracks and other defects, SKI report 95:53, Swedish Nuclear Power Inspectorate, Stockholm.
76. Boström A and Jansson P-A (2000), Development of UTDefect: Rough rectangular cracks, anisotropy, etc, SKI report 00:43, Swedish Nuclear Power Inspectorate, Stockholm.
77. Lakestani F (1992), Validation of mathematical models of ultrasonic inspection of steel components, PISC III rep 6, JRC, Inst Adv Mat, Petten.
78. Becker FL, Doctor SR, Heaster PG, Morris CJ, Pitman SG, and Simonen FA (1981), Integration of NDE reliability and fracture mechanics, NURE/CR 1696. PLN-3469, VR.1, US Nuclear Regulatory Commission.