journal article·2009-11

Crack identification based on optimization methods using harmonic elastic waves

Y. G. Bao, X. D. Wang

International Journal of Fracture· Volume 160· Issue 1
Publisher page

Abstract

The current paper presents a theoretical study of the identification of cracks in an elastic medium based on optimization methods using harmonic elastic waves. A generalized crack model was used to determine the elastodynamic behaviour of an arbitrarily located and oriented crack subjected to a plane harmonic wave. Sensitivity analysis was conduced to evaluate the variation of stress and strain fields with various crack parameters using the direct differential method (DDM). These general results were then used to identify an unknown crack from known strain components at discrete locations. The BFGS optimization scheme based on the sensitivity analysis was used to determine the length, the orientation and the position of the crack. Numerical simulation was conducted and the results were presented to show the effectiveness of the sensitivity analysis and the optimization method. It was observed that starting from a set of arbitrarily determined initial values, the length, position and the orientation of the crack can be accurately determined.
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Research context

OpenAlex topics: Ultrasonics and Acoustic Wave Propagation · Structural Health Monitoring Techniques · Non-Destructive Testing Techniques

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (25)

Show source-provided references
1. Achenbach JD (1973) Wave propagation in elastic solids. North-Holland, Amsterdam
2. Achenbach JD (2000) Quantitative nondestructive evaluation. Int J Solids Struct 37: 13–2710.1016/S0020-7683(99)00074-8 ↗
3. Charles H, Chang FK (1995) Identifying delamination in composite beams using built-in piezoelectrics: part I experiment and analysis. J Intell Mater Syst Struct 6: 649–66310.1177/1045389X9500600506 ↗
4. Deutsch WAK, Cheng A, Achenbach JD (1997) Self-focusing of Rayleigh waves and Lamb waves with a linear phased array. Res Nondestr Eval 9: 81–9510.1080/09349849709409609 ↗
5. Eriksson AS, Bostrom A, Datta SK (1995) Ultrasonic wave propagation through a cracked solid. Wave Motion 22(3): 297–31010.1016/0165-2125(95)00036-I ↗
6. Fink M (1993) Time reversal mirrors. J Phys D Appl Phys 26: 1333–135010.1088/0022-3727/26/9/001 ↗
7. Fink M, Prada C (2001) Acoustic time-reversal mirrors. Inverse Probl 17: R1–3810.1088/0266-5611/17/1/201 ↗
8. Fu L (1987) Mechanics aspects of NDE by sound and ultrasound. Appl Mech Rev 35: 1047–1057
9. Fukunaga H, Hu N, Chang FK (2002) Structural damage identification using piezoelectric sensors. Int J Solids Struct 39: 393–41810.1016/S0020-7683(01)00149-4 ↗
10. Giurgiutiu V, Roger CA (1999) Modelling of the electro-mechanical (E/M) impedance response of a damaged composite beam. Adapt Struct Mater Syst 87: 39–46
11. Gross D, Zhang Ch (1988) Diffraction of SH waves by a system of cracks: solution by an integral equation method. Int J Solids Struct 24: 41–4910.1016/0020-7683(88)90097-2 ↗
12. Itou S (1980) Diffraction of an antiplane shear wave by two coplanar Griffith cracks in an infinite elastic medium. Int J Solids Struct 16: 1147–115310.1016/0020-7683(80)90069-4 ↗
13. Jain DL, Kanwal RP (1972) Diffraction of elastic waves by two coplanar Griffith cracks in an infinite elastic medium. Int J Solids Struct 8: 961–97510.1016/0020-7683(72)90009-1 ↗
14. Kessler SS, Spearing SM (2002) Damage detection in composite materials using Lamb wave methods. Smart Mater Struct 11(2): 269–27810.1088/0964-1726/11/2/310 ↗
15. Ludwig R, Lord W (1988) Finite element study of ultrasonic wave propagation and scattering in an aluminum block. Mater Eval 46: 108–113
16. Mal A (2001) NDE for health monitoring of aircraft and aerospace structures. In: 7th SME NDE Topical Conference, vol 20, pp 149–155
17. Marklein R, Mayer K, Hannemann R, Krylow T, Balasubramanian K, Langenberg KJ, Schmitz V (2002) Linear and nonlinear inversion algorithm applied nondestructive evaluation. Inverse Probl 18: 1733–175910.1088/0266-5611/18/6/319 ↗
18. Meguid SA, Wang XD (1995) On the dynamic interaction between a microdefect and a main crack. Proc R Soc Long A448: 449–46410.1098/rspa.1995.0027 ↗
19. Okafor AC, Chandrashekhara K, Jiang YP (1996) Delamination prediction in composite beam with built-in piezoelectric devices using modal analysis and neural network. Smart Mater Struct 5: 338–34710.1088/0964-1726/5/3/012 ↗
20. Press WH (2002) Numerical recipes in C++: the art of scientific computing, 2nd edn. Cambridge University Press, Cambridge
21. Rose JL (1999) Ultrasonic waves in solid media. Cambridge University Press, Cambridge
22. Sih GC, Loeber JF (1969) Wave propagation in an elastic solid with a line of discontinuity or finite crack. Q Appl Math 27: 193–21310.1090/qam/99830 ↗
23. Wang XD, Huang GL (2006) The coupled dynamic behavior of piezoelectric sensors bonded to elastic media. J Intell Mater Syst Struct 17: 883–89410.1177/1045389X06061130 ↗
24. Wu TT (1999) Elastic wave propagation and nondestructive evaluation of materials. Proc Natl Sci Counc ROC (A) 23(6): 703–715
25. Zhang Ch, Achenbach JD (1989) Time-domain boundary element analysis of dynamic near-tip fields for impact-loaded collinear cracks. Eng Fract Mech 32: 899–90910.1016/0013-7944(89)90006-4 ↗