The stress state is critical to the reliability of structures, but existing ultrasonic methods are challenging to measure local stress. In this paper, zero-group-velocity (ZGV) Lamb mode was proposed to measure the local stress field in thin aluminum plates. The Lamb wave's dispersive characteristics under initial stress were analyzed based on the Floquet-Bloch theory with Murnaghan hyperelastic material model. The obtained dispersion curves show that higher-order Lamb wave modes near the cut-off frequencies are sensitive to applied stress across the plate, indicating that the S1-ZGV mode has a rather high sensitivity to stress. Similar to conventional ultrasonic stress measurement, it is found that the frequency of the S1-ZGV mode changes near-linearly with the amplitude of applied stress. Numerical experiments were conducted to illustrate the feasibility of local stress measurement in a thin aluminum plate based on the S1-ZGV mode. Single and multiple localized stress fields were evaluated with the S1-ZGV method, and reconstructed results matched well with actual stress fields, proving that the ZGV Lamb wave method is a sensitive stress measurement technique in thin plates.
Weiming Xuan
,
Maodan Yuan
,
Xuanrong Ji
,
Wenjin Xu
,
Yan Chen
,
Lvming Zeng
. Local Stress Measurement in Thin Aluminum Plates based on Zero-Group-Velocity Lamb mode[J]. Chinese Journal of Mechanical Engineering, 2023
, 36(2)
: 31
-31
.
DOI: 10.1186/s10033-023-00855-z
The stress state is critical to the reliability of structures, but existing ultrasonic methods are challenging to measure local stress. In this paper, zero-group-velocity (ZGV) Lamb mode was proposed to measure the local stress field in thin aluminum plates. The Lamb wave's dispersive characteristics under initial stress were analyzed based on the Floquet-Bloch theory with Murnaghan hyperelastic material model. The obtained dispersion curves show that higher-order Lamb wave modes near the cut-off frequencies are sensitive to applied stress across the plate, indicating that the S1-ZGV mode has a rather high sensitivity to stress. Similar to conventional ultrasonic stress measurement, it is found that the frequency of the S1-ZGV mode changes near-linearly with the amplitude of applied stress. Numerical experiments were conducted to illustrate the feasibility of local stress measurement in a thin aluminum plate based on the S1-ZGV mode. Single and multiple localized stress fields were evaluated with the S1-ZGV method, and reconstructed results matched well with actual stress fields, proving that the ZGV Lamb wave method is a sensitive stress measurement technique in thin plates.
[1] S Kim, Y H Park, S Park, et al. A sensor-type PC strand with an embedded FBG sensor for monitoring prestress forces. Sensors, 2015, 15(1): 1060-1070.
[2] M D Yuan, J H Zhang, S J Song, et al. Numerical simulation of Rayleigh wave interaction with surface closed cracks under external pressure. Wave Motion, 2015, 57: 143-153.
[3] D S Hughes, J L Kelly. Second-order elastic deformation of solids. Physical Review, 1953, 92(5): 1145.
[4] M D Yuan, T Kang, H J Kim, et al. A numerical model for prediction of residual stress using rayleigh waves. Journal of the KSNT, 2011, 31: 656-664.
[5] M D Yuan, T Kang, J H Zhang, et al. Numerical simulation of ultrasonic minimum reflection for residual stress evaluation in 2D case. Journal of Mechanical Science and Technology, 2013, 27(11): 3207-3214.
[6] Z H Li, J B He, D K Liu, et al. Influence of uniaxial stress on the shear-wave spectrum propagating in steel members. Sensors, 2019, 19(3): 492.
[7] W Wang, C H Xu, Y M Zhang, et al. An improved ultrasonic method for plane stress measurement using critically refracted longitudinal waves. NDT & E International, 2018, 99: 117-122.
[8] M Mohammadi, J J Fesharaki. Determination of acoustoelastic /acoustoplastic constants to measure stress in elastic/plastic limits by using LCR wave. NDT & E International, 2019, 104: 69-76.
[9] Y Javadi, H S Pirzaman, M H Raeisi, et al. Ultrasonic inspection of a welded stainless steel pipe to evaluate residual stresses through thickness. Materials & Design, 2013, 49: 591-601.
[10] Y Javadi, M Akhlaghi, M A Najafabadi. Using finite element and ultrasonic method to evaluate welding longitudinal residual stress through the thickness in austenitic stainless steel plates. Materials & Design, 2013, 45: 628-642.
[11] S Sadeghi, M A Najafabadi, Y Javadi, et al. Using ultrasonic waves and finite element method to evaluate through-thickness residual stresses distribution in the friction stir welding of aluminum plates. Materials & Design, 2013, 52: 870-880.
[12] M Mohabuth, A Kotousov, C T Ng. Effect of uniaxial stress on the propagation of higher-order Lamb wave modes. International Journal of Non-linear Mechanics, 2016, 86: 104-111.
[13] N Gandhi, J E Michaels, S J Lee. Acoustoelastic Lamb wave propagation in biaxially stressed plates. Journal of the Acoustical of Society of America, 2012, 132(3): 1284-1293.
[14] F Shi, J E Michaels, S J Lee. In situ estimation of applied biaxial loads with Lamb waves. Journal of the Acoustical of Society of America, 2013, 133(2): 677-687.
[15] N Pei, L J Bond. Comparison of acoustoelastic Lamb wave propagation in stressed plates for different measurement orientations. Journal of the Acoustical of Society of America, 2017, 142(4): EL327-EL331.
[16] N Pei, L J Bond. Higher order acoustoelastic Lamb wave propagation in stressed plates. Journal of the Acoustical of Society of America, 2016, 140(5): 3834-3843.
[17] C Prada, O Balogun, T W Murray. Laser-based ultrasonic generation and detection of zero-group velocity Lamb waves in thin plates. Applied Physics Letters, 2005, 87(19): 1066.
[18] H Bjurström, N Ryden. Detecting the thickness mode frequency in a concrete plate using backward wave propagation. Journal of the Acoustical of Society of America, 2016, 139(2): 649-657.
[19] C Grünsteidl, T Berer, M Hettich, et al. Determination of thickness and bulk sound velocities of isotropic plates using zero-group-velocity Lamb waves. Applied Physics Letters, 2018, 112(25): 251905.1-251905.5.
[20] D Clorennec, C Prada, D Royer. Local and noncontact measurements of bulk acoustic wave velocities in thin isotropic plates and shells using zero group velocity Lamb modes. Journal of Applied Physics, 2007, 101(3): 34908.
[21] M Cès, D Royer, C Prada. Characterization of mechanical properties of a hollow cylinder with zero group velocity Lamb modes. Journal of the Acoustical of Society of America, 2012, 132(1): 180-185.
[22] J Spytek, A Ziaja-Sujdak, K Dziedziech, et al. Evaluation of disbonds at various interfaces of adhesively bonded aluminum plates using all-optical excitation and detection of zero-group velocity Lamb waves. NDT & E International, 2020, 112: 102249.
[23] R. Hodé, S Raetz, J Blondeau, et al. Nondestructive evaluation of structural adhesive bonding using the attenuation of zero-group-velocity Lamb modes. Applied Physics Letters, 2020, 116(10): 104101.
[24] Y H Pao, U Gamer. Acoustoelastic waves in orthotropic media. Journal of the Acoustical of Society of America, 1985, 77(3): 806-812.
[25] M Collet, M Ouisse, M Ruzzene, et al. Floquet-Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems. International Journal of Solids and Structures, 2011, 48(20): 2837-2848.
[26] P Gómez García, J P Fernández-Álvarez. Floquet-bloch theory and its application to the dispersion curves of nonperiodic layered systems. Mathematical Problems in Engineering, 2015, 2015: 1-12.
[27] Murnaghan, D Francis. Finite deformations of an elastic solid. American Journal of Mathematics, 1937, 59: 235-260.
[28] C Prada, D Clorennec, D Royer. Local vibration of an elastic plate and zero-group velocity Lamb modes. Journal of the Acoustical of Society of America, 2008, 124(1): 203-212.
[29] A Gibson, J S Popovics. Lamb wave basis for impact-echo method analysis. Journal of Engineering Mechanics, 2005, 131(4): 438-443
