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A multi-stage model of nonlinear interaction between micro-crack and ultrasound based on equivalent elastic modulus is presented in this paper. In this model, the interface characteristics of micro-cracks at a micro-level and the relative motion at a macro-level are unified into an elastic modulus of the mesoscopic element. The equivalent elastic modulus is used to characterize the stress-strain of the damage region. Then piecewise function is used to describe the nonlinear interaction between ultrasound and micro-crack. Finally, the wave equation is solved by the finite element simulation. In this manner, the nonlinear interaction law between ultrasound and micro-crack is obtained, and the validity of the model is verified. The simulation results also show that compared with bilinear stiffness model and contact surface model, the multi-stage model can well reflect the distortion of the waveform in one period of ultrasonic wave passing through the micro-crack. In addition, the influences of the crack angle, the crack length and the input amplitude on the second harmonics generation and the third harmonics generation are analyzed. In the end, the comparison and analysis of the experimental test and simulation calculations based on the proposed multi-stage model show that the proposed multi-stage model and the experimental test can well reflect the second harmonic signal produced by the nonlinear interaction of micro-crack and ultrasound, and the second harmonic amplitudes of the experimental test are basically the same as the simulation calculations based on the proposed multi-stage model. Thus, the effectiveness of the proposed multi-stage model is verified. The model provides a new simulation method to quantitatively detect the micro-crack by ultrasonic nonlinear effect.
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Keywords:
- micro-crack /
- ultrasonic /
- equivalent elastic modulus /
- multi-stage
[1] Jhang K Y 2009 Int. J. Precis Eng. Man. 10 123
[2] Chen Z J, Zhang S Y, Zheng K 2010 Acta Phys. Sin. 59 4071 (in Chinese)[陈赵江, 张淑仪, 郑凯 2010 物理学报 59 4071]
[3] Wu M, Guo F, Li M, Han Y 2016 Mater. Sci. Forum. 849 603
[4] Broda D, Staszewski W J, Martowicz A, Uhl T, Silberschmidt V V 2014 J. Sound.Vib. 333 1097
[5] Lim H J, Song B, Park B, Sohn H 2015 NDT E Int. 73 8
[6] Matlack K H, Kim J Y, Jacobs L J, Qu J 2015 J. Nondestruct Eval. 34 273
[7] Friswell M I, Penny J E T 2002 Struct Health Monit. 1 139
[8] Solodov I Y, Krohn N, Busse G 2002 Ultrasonics 40 621
[9] Williamson J B P, Greenwood J A 1966 Proc. R. Soc. London A 19 295
[10] Baltazar A, Rokhlin S I, Pecorari C 2002 J. Mech. Phys. Solids. 50 1397
[11] Nazarov V E, Sutin A M 1998 J. Acoust. Soc. Am. 102 3349
[12] Xiao Q, Wang J, Guo X S, Zhang D 2013 Acta Phys. Sin. 62 275 (in Chinese)[肖齐, 王珺, 郭霞生, 章东 2013 物理学报 62 275]
[13] Brown S R, Scholz C H 1985 J. Geophys. Res. 90 5531
[14] Cai M, Horii H 1992 Mech. Mater. 13 217
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[1] Jhang K Y 2009 Int. J. Precis Eng. Man. 10 123
[2] Chen Z J, Zhang S Y, Zheng K 2010 Acta Phys. Sin. 59 4071 (in Chinese)[陈赵江, 张淑仪, 郑凯 2010 物理学报 59 4071]
[3] Wu M, Guo F, Li M, Han Y 2016 Mater. Sci. Forum. 849 603
[4] Broda D, Staszewski W J, Martowicz A, Uhl T, Silberschmidt V V 2014 J. Sound.Vib. 333 1097
[5] Lim H J, Song B, Park B, Sohn H 2015 NDT E Int. 73 8
[6] Matlack K H, Kim J Y, Jacobs L J, Qu J 2015 J. Nondestruct Eval. 34 273
[7] Friswell M I, Penny J E T 2002 Struct Health Monit. 1 139
[8] Solodov I Y, Krohn N, Busse G 2002 Ultrasonics 40 621
[9] Williamson J B P, Greenwood J A 1966 Proc. R. Soc. London A 19 295
[10] Baltazar A, Rokhlin S I, Pecorari C 2002 J. Mech. Phys. Solids. 50 1397
[11] Nazarov V E, Sutin A M 1998 J. Acoust. Soc. Am. 102 3349
[12] Xiao Q, Wang J, Guo X S, Zhang D 2013 Acta Phys. Sin. 62 275 (in Chinese)[肖齐, 王珺, 郭霞生, 章东 2013 物理学报 62 275]
[13] Brown S R, Scholz C H 1985 J. Geophys. Res. 90 5531
[14] Cai M, Horii H 1992 Mech. Mater. 13 217
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