Skip to main content

Abstract

Crack depth is one of the important factors determining material strength. Hence, the accurate measurement of crack depth is essential to ensure the reliability of aged structures and manufactured products. If cracks are open, crack depth can be measured by ultrasonics because ultrasound is strongly scattered by the crack tip (Fig. 10.1a) [1]. However, if cracks are closed because of compression residual stress [2, 3] and/or oxide debris generated between the crack faces [4], ultrasonic testing can result in the underestimation (Fig. 10.1b) or nondetection (Fig. 10.1c) of cracks since ultrasound penetrates through closed cracks. Subharmonic phased array for crack evaluation (SPACE) is a novel imaging method for measuring closed-crack depths [5, 6]. SPACE uses the subharmonics generated by short-burst waves and a phased array algorithm with frequency filtering. It enables the precise measurement of closed-crack depths. This chapter starts from fundamental aspects of subharmonic generation at closed cracks. It then describes the principle of SPACE and its application to several types of closed crack.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Blitz, G. Simpson, Ultrasonic Methods of Non-Destructive Testing (Chapman & Hall, London, 1996)

    Google Scholar 

  2. W. Elber, Fatigue crack closure under cyclic tension. Eng. Fract. Mech. 2, 37–45 (1970)

    Article  Google Scholar 

  3. J.D. Frandsen, R.V. Inman, O. Buck, A comparison of acoustic and strain gauge techniques for crack closure. Int. J. Fract. 11, 345–348 (1975)

    Article  Google Scholar 

  4. S. Horinouchi, M. Ikeuchi, Y. Shintaku, Y. Ohara, K. Yamanaka, Evaluation of closed stress corrosion cracks in Ni-based alloy weld metal using subharmonic phased array. Jpn. J. Appl. Phys. 51, 07GB15-1–07GB15-5 (2012)

    Article  Google Scholar 

  5. Y. Ohara, T. Mihara, R. Sasaki, T. Ogata, S. Yamamoto, Y. Kisihimoto, K. Yamanaka, Imaging of closed cracks using nonlinear response of elastic waves at subharmonic frequency. Appl. Phys. Lett. 90, 011902-1–011902-3 (2007)

    Article  Google Scholar 

  6. Y. Ohara, S. Yamamoto, T. Mihara, K. Yamanaka, Ultrasonic evaluation of closed cracks using subharmonic phased array. Jpn. J. Appl. Phys. 47, 3908–3915 (2008)

    Article  Google Scholar 

  7. Y. Zheng, R.G. Maev, I.Y. Solodov, Nonlinear acoustic applications for material characterization: A review. Can. J. Phys. 77, 927–967 (1999)

    Article  Google Scholar 

  8. K.-Y. Jhang, Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: a review. Int. J. Precis. Eng. Manuf. 10(1), 123–135 (2009)

    Article  Google Scholar 

  9. I.Y. Solodov, C.A. Vu, Popping nonlinearity and chaos in vibrations of a contact interface between solids. Acoust. Phys. 39, 476–479 (1993)

    Google Scholar 

  10. I.Y. Solodov, Ultrasonics of non-linear contacts: propagation, reflection and NDE-applications. Ultrasonics 36, 383–390 (1998)

    Article  Google Scholar 

  11. I.Y. Solodov, N. Krohn, G. Busse, CAN: an example of nonclassical acoustic nonlinearity in solids. Ultrasonics 40, 621–625 (2002)

    Article  Google Scholar 

  12. B.A. Korshak, I.Y. Solodov, E.M. Ballad, DC effects, sub-harmonics, stochasticity and “memory” for contact acoustic non-linearity. Ultrasonics 40, 707–713 (2002)

    Article  Google Scholar 

  13. I. Solodov, J. Wackerl, K. Pfleiderer, G. Busse, Nonlinear self-modulation and subharmonic acoustic spectroscopy for damage detection and location. Appl. Phys. Lett. 84, 5386–5388 (2004)

    Article  Google Scholar 

  14. K. Yamanaka, T. Mihara, T. Tsuji, Evaluation of closed cracks by model analysis of subharmonic ultrasound. Jpn. J. Appl. Phys. 43, 3082–3087 (2004)

    Article  Google Scholar 

  15. Y. Ohara, T. Mihara, K. Yamanaka, Effect of adhesion force between crack planes on subharmonic and DC responses in nonlinear ultrasound. Ultrasonics 44, 194–199 (2006)

    Article  Google Scholar 

  16. T. Hayashi, S. Biwa, Subharmonic wave generation at interfaces of a thin layer between metal blocks. Jpn. J. Appl. Phys. 52, 07HC02-1–07HC02-6 (2013)

    Google Scholar 

  17. I. Solodov, G. Busse, Nonlinear air-coupled emission: the signature to reveal and image microdamage in solid materials. Appl. Phys. Lett. 91, 251910-1–251910-3 (2007)

    Article  Google Scholar 

  18. A. Moussatov, V. Gusev, B. Castagnede, Self-induced hysteresis for nonlinear acoustic waves in cracked material. Phys. Rev. Lett. 90(2), 124301-1–124301-4 (2003)

    Google Scholar 

  19. A.E. Ekimov, A.V. Lebedev, L.A. Ostrovskii, A.M. Sutin, Nonlinear acoustic effects due to cracks in ice cover. Acoust. Phys. 42(1), 51–54 (1996)

    Google Scholar 

  20. M. Akino, T. Mihara, K. Yamanaka, Fatigue crack closure analysis using nonlinear ultrasound. AIP Conf. Proc. 700, 1256–1263 (2004)

    Article  Google Scholar 

  21. J.M. Richardson, Harmonic generation at an unbonded interface – I. Planar Interface between semi-infinite elastic media. Int. J. Eng. Sci. 17, 73–85 (1979)

    Article  Google Scholar 

  22. B. O’Neill, R.G. Maev, F. Severin, Distortion of shear waves passing through a friction coupled interface. AIP Conf. Proc. 557, 1261–1267 (2001)

    Article  Google Scholar 

  23. P.M. Shankar, P.D. Krishna, V.L. Newhouse, Subharmonic backscattering from ultrasound contrast agents. J. Acoust. Soc. Am. 106(4), 2104–2110 (1999)

    Article  Google Scholar 

  24. P. Palanchon, A. Bouakaz, J. Klein, N.D. Jong, Subharmonic and ultraharmonic emissions for emboli detection and characterization. Ultrasound Med. Biol. 29(3), 417–425 (2003)

    Article  Google Scholar 

  25. F.M. Severin, I.Y. Solodov, Experimental observation of acoustic demodulation in reflection from a solid-solid interface. Sov. Phys. Acoust. 35(4), 447–448 (1989)

    Google Scholar 

  26. K. Yamanaka, H. Ogiso, O. Kolosov, Ultrasonic force microscopy for nanometer resolution subsurface imaging. Appl. Phys. Lett. 84(2), 178–180 (1994)

    Article  Google Scholar 

  27. O. Kolosov, K. Yamanaka, Nonlinear detection of ultrasonic vibrations in an atomic force microscope. Jpn. J. Appl. Phys. 32, L1095–L1098 (1993)

    Article  Google Scholar 

  28. N.A. Burnham, A.J. Kulik, G. Gremaud, P.-J. Gallo, F. Oulevey, Scanning local-acceleration microscopy. J. Vac. Sci. Technol. B 14(2), 794–799 (1996)

    Article  Google Scholar 

  29. E.M. Abdel-Rahman, A.H. Nayfeh, Contact force identification using the subharmonic resonance of a contact-mode atomic force microscopy. Nanotechnology 16, 199–207 (2005)

    Article  Google Scholar 

  30. V. Gusev, B. Castagnede, A. Moussatov, Hysteresis in response of nonlinear bistable interface to continuously varying acoustic loading. Ultrasonics 41, 643–654 (2003)

    Article  Google Scholar 

  31. K. Yamanaka, H. Ogiso, O. Kolosov, Analysis of subsurface imaging and effect of contact elasticity in the ultrasonic force microscope. Jpn. J. Appl. Phys. 33, 3197–3203 (1994)

    Article  Google Scholar 

  32. K. Inagaki, O. Matsuda, O.B. Wright, Hysteresis of the cantilever shift in ultrasonic force microscopy. Appl. Phys. Lett. 80(13), 2386–2388 (2003)

    Article  Google Scholar 

  33. C. Pecorari, Adhesion and nonlinear scattering by rough surfaces in contact: beyond the phenomenology of the Presisach-Mayergoyz framework. J. Acoust. Soc. Am. 116(4), 1938–1947 (2004)

    Article  Google Scholar 

  34. K. Yamanaka, Y. Ohara, S. Yamamoto, H. Endo, Analysis of subharmonic phased Array for crack evaluation (SPACE) using elastic-body-oscillator model. AIP Conf. Proc. 1022(577), 577–580 (2008)

    Article  Google Scholar 

  35. Y. Ohara, Nondestructive evaluation of closed cracks by nonlinear ultrasound, PhD Thesis, Tohoku University, Sendai, 2007

    Google Scholar 

  36. S.R. Bishop, M.G. Thompson, S. Foale, Prediction of period-1 impacts in a driven beam. Proc. R. Soc. London Sec. A 452, 2579–2592 (1996)

    Article  Google Scholar 

  37. A.B. Pippard, The Physics of Vibrations I (Cambridge University Press, Cambridge, 1978)

    MATH  Google Scholar 

  38. D. Maugis, Contact, Adhesion and Rupture of Elastic Solid (Springer, Berlin, 1999)

    MATH  Google Scholar 

  39. Y. Ohara, Y. Shintaku, S. Horinouchi, M. Ikeuchi, K. Yamanaka, Enhancement of selectivity in nonlinear ultrasonic imaging of closed cracks using amplitude difference phased array. Jpn. J. Appl. Phys. 51, 07GB18-1–07GB18-6 (2012)

    Article  Google Scholar 

  40. A. Sugawara, K. Jinno, Y. Ohara, K. Yamanaka, Closed-crack imaging and scattering behavior analysis using confocal subharmonic phased array. Jpn. J. Appl. Phys. 54, 07HC08-1–07HC08-8 (2015)

    Article  Google Scholar 

  41. Y. Ohara, H. Endo, M. Hashimoto, Y. Shintaku, K. Yamanaka, Monitoring growth of closed fatigue crack using subharmonic phased array. AIP Conf. Proc. 1211, 903–909 (2010)

    Article  Google Scholar 

  42. H. Ohara, M. Hashimoto, M. Horinouchi, Y. Shintaku, K. Yamanaka, Closed crack growth monitoring using nonlinear ultrasonic imaging method. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. J94-A(11), 800–808 (2011)

    Google Scholar 

  43. S.P. Timoshenko, J.N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970)

    MATH  Google Scholar 

  44. A. Steuwer, M. Rahman, A. Shterenlikht, M.E. Fitzpatrick, L. Edwards, P.J. Withers, The evolution of crack-tip stresses during a fatigue overload event. Acta Mater. 58, 4039–4052 (2010)

    Article  Google Scholar 

  45. Y. Ohara, K. Yamanaka, Measurement of invisible cracks by ultrasonics: development of subharmonic phased array for crack evaluation (SPACE). Inspect. Eng. 13(5), 8–14 (2008)

    Google Scholar 

  46. J.W. Goodman, Introduction to Fourier Optics (Roberts & Co, Englewood, 2004)

    Google Scholar 

  47. Y. Ohara, H. Endo, T. Mihara, K. Yamanaka, Ultrasonic measurement of closed stress corrosion crack depth using subharmonic phased array. Jpn. J. Appl. Phys. 48, 07GD01-1–07GD01-6 (2009)

    Google Scholar 

  48. M. Sato, Comparing three methods of free boundary implementation for analyzing elastodynamics using the finite-difference time-domain formulation. Acoust. Sci. Tech. 28(1), 49–52 (2007)

    Article  MathSciNet  Google Scholar 

  49. K. Yamanaka, Y. Ohara, M. Oguma, Y. Shintaku, Two-dimensional analyses of subharmonic generation at closed cracks in nonlinear ultrasonics. Appl. Phys. Express 4, 076601-1–076601-3 (2011)

    Article  Google Scholar 

  50. K. Jinno, A. Sugawara, Y. Ohara, K. Yamanaka, Analysis on nonlinear ultrasonic images of vertical closed cracks by damped double node model. Mater. Trans. 55(7), 1017–1023 (2014)

    Article  Google Scholar 

  51. A. Ouchi, A. Sugawara, Y. Ohara, K. Yamanaka, Subharmonic phased array for crack evaluation using refraction and/or mode conversion at an interface. Proc. Symp. Ultrason. Electron. 35, 259–260 (2014)

    Google Scholar 

  52. A. Ouchi, A. Sugawara, Y. Ohara, K. Yamanaka, Subharmonic phased Array for crack evaluation using surface acoustic wave. Jpn. J. Appl. Phys. 54, 07HC05-1–07HC05-6 (2015)

    Article  Google Scholar 

  53. S. Yamamoto, Y. Ohara, T. Mihara, K. Yamanaka, Application of laser interferometer to subharmonic phased array for crack evaluation (SPACE). J. Jpn. Soc. Nondestr. Insp. 57(4), 198–203 (2008)

    Google Scholar 

  54. C.-S. Park, J.-W. Kim, S. Cho, D.-C. Seo, A high resolution approach for nonlinear sub-harmonic imaging. NDT&E Int. 79, 114–122 (2016)

    Article  Google Scholar 

  55. M. Ikeuchi, K. Jinno, Y. Ohara, K. Yamanaka, Improvement of closed crack selectivity in nonlinear ultrasonic imaging using fundamental wave amplitude difference. Jpn. J. Appl. Phys. 52, 07HC08-1–07HC08-6 (2013)

    Article  Google Scholar 

  56. Y. Ohara, S. Horinouchi, M. Hashimoto, Y. Shintaku, K. Yamanaka, Nonlinear ultrasonic imaging method for closed cracks using subtraction of responses at different external loads. Ultrasonics 51, 661–666 (2011)

    Article  Google Scholar 

  57. Y. Ohara, K. Takahashi, S. Murai, K. Yamanaka, High-selectivity imaging of closed cracks using elastic waves with thermal stress induced by global preheating and local cooling. Appl. Phys. Lett. 103, 031917-1–031917-5 (2013)

    Article  Google Scholar 

  58. T. Mihara, G. Konishi, Y. Miura, H. Ishida, Accurate sizing of closed crack using nonlinear ultrasound of SPACE with high voltage transformer pulser technique. AIP Conf. Proc. 1581, 727–732 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

It is our great pleasure to thank all those who have collaborated with us in the development of SPACE. Financial support by Japan Society for the Promotion of Science (JSPS) KAKENHI (Grants-in-Aid for Scientific Research) and other various projects for part of the work described in this chapter is gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yoshikazu Ohara .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ohara, Y., Mihara, T., Yamanaka, K. (2019). Subharmonic Phased Array for Crack Evaluation (SPACE). In: Kundu, T. (eds) Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation. Springer, Cham. https://doi.org/10.1007/978-3-319-94476-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-94476-0_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94474-6

  • Online ISBN: 978-3-319-94476-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics