DOI QR코드

DOI QR Code

An experimental method to determine glass elastic modulus based on the fundamental frequency of the elastic support-free end beam

  • Kun Jiang (Department of Civil Engineering, University of Science and Technology Beijing) ;
  • Danguang Pan (Department of Civil Engineering, University of Science and Technology Beijing)
  • Received : 2022.09.15
  • Accepted : 2023.09.25
  • Published : 2023.10.25

Abstract

Silicate glass is usually a brittle and plate-like material, and it is difficult to measure the elastic modulus by the traditional method. This paper develops a test method for the glass elastic modulus based on the fundamental frequency of the cantilever beam with an elastic support and a free end. The method installs the beam-type specimen on a semi-rigid support to form an elastic support-free end beam. The analytic solution of the stiffness coefficients of the elastic support is developed by the fundamental frequency of the two specimens with known elastic modulus. Then, the glass elastic modulus is measured by the fundamental frequency of the specimens. The method significantly improves the measurement accuracy and is suitable for the elastic modulus with the beam-type specimen whether the glass is homogeneous or not. Several tests on the elastic modulus measurement are conducted to demonstrate the reliability and validity of the test method.

Keywords

Acknowledgement

This study was supported by the Opening Funds of State Key Laboratory of Building Safety and Built Environment & National Engineering Research Center of Building Technology (No. BSBE2022-06). The support is gratefully acknowledged.

References

  1. ASTME1876-15 (2015), Standard Test Method for Dynamic Young's Module, Shear Module, and Poisson's Ratio by Impulse Excitation of Vibration, Annual Book of ASTM Standards, Philadelphia, USA.
  2. Aydin, E. (2014), "Minimum dynamic response of cantilever beams supported by optimal elastic springs", Struct. Eng. Mech., 51(3), 377-402. https://doi.org/10.12989/sem.2014.51.3.377. 
  3. Bao, Y. and Liu, Z. (2016), "Mechanism and criterion of spontaneous breakage of tempered Glass", J. Inorg. Mater., 31(4), 401-406. https://doi.org/10.15541/jim20150444. (in Chinese) 
  4. Bedon, C., Zhang, X., Santos, F., Honfi, D., Kozlowski, M., Arrigoni, M., ... & Lange, D. (2018), "Performance of structural glass facades under extreme loads- design methods, existing research, current issues and trends", Constr. Build. Mater., 163, 921-937. https://doi.org/10.1016/j.conbuildmat.2017.12.153. 
  5. Bezerra, A.K., Melo, A.R., Freitas, I.L., Babadopulos, L.F., Carret, J.C. and Soares, J.B. (2023), "Determination of modulus of elasticity and Poisson's ratio of cementitious materials using S-wave measurements to get consistent results between static, ultrasonic and resonant testing", Constr. Build. Mater., 398, 132456. https://doi.org/10.1016/j.conbuildmat.2023.132456. 
  6. Carmen, M. and He, J. (2009), "Characterization of Young's Modulus of Nanowires on Microcantilever Beams", J. Appl. Mech., 76(6), 064502. https://doi.org/10.1115/1.3130443. 
  7. Carolina, A., Antonio, O., Giuseppe, M. and Antonio, B. (2018), "Experimental and numerical investigation of cyclic response of a glass curtain wall for seismic performance assessment", Constr. Build. Mater., 187, 596-609. https://doi.org/10.1016/j.conbuildmat.2018.07.237. 
  8. Chang, Y., Wang, N., Wang, B., Li, X., Wang, C., Zhao, K. and Dong, H. (2021), ''Prediction of bending spring back of the medium-Mn steel considering elastic modulus attenuation'', J. Manuf. Proc., 67, 345-355. https://doi.org/10.1016/j.jmapro.2021.04.074. 
  9. Chen, Y., Sullivan, M., Zhang, A. and Prorok, B.C. (2018), "A new method to extract elastic module of brittle materials from Berkovich indentation", J. Eur. Ceram. Soc., 38(1), 349-353. https://doi.org/10.1016/j.jeurceramsoc.2017.08.029. 
  10. Clough, R.W. and Penzien, J. (2003), Dynamics of Structural, Computers and Structures, 2nd Edition, Berkeley, CA, USA.
  11. GB/T 37788-2019 (2019), Test Method for Elastic Moduli of Ultra-Thin Glass, State Administration of Market Regulation of the People's Republic of China, Beijing, China. (in Chinese) 
  12. Giaccu, G.F., Meloni, D., Concu, G., Valdes, M. and Fragiacomo, M. (2019), "Use of the cantilever beam vibration method for determining the elastic properties of maritime pine cross-laminated panels", Eng. Struct., 200, 109623. https://doi.org/10.1016/j.engstruct.2019.109623 
  13. Huang, H., Winchester, K.J., Suvorova, A., Lawn, B.R., Liu, Y., Hu, X.Z., ... & Faraone, L. (2006), "Effect of deposition conditions on mechanical properties of low-temperature PECVD silicon nitride films", Mater. Sci. Eng.: A, 435, 443-459. https://doi.org/10.1016/j.msea.2006.07.015. 
  14. Jiang, K., Pan, D.G., Zhang, X.C. and Hu, N.D. (2021), "Test study on damage identification of structural sealant based on boundary modal", Eng. Mech., 39(S1), 350-355. https://doi.org/10.6052/j.issn.1000-4750.2021.05.S046. (in Chinese) 
  15. Jiang, Y., Liu, Y., Zeng, J., Wang, Y., Xie, Q. and Hu, N. (2023), "Equivalent elastic modulus measurement of cross-ply composite plates using Lamb waves", Compos. Struct., 321, 117230. https://doi.org/10.1016/j.compstruct.2023.117230. 
  16. Kim, H., Lim, Y., Million, M., Tafesse, M. and Yang, B. (2022), ''Micromechanics-integrated machine learning approaches to predict the mechanical behaviors of concrete containing crushed clay brick aggregates'', Constr. Build. Mater., 317(24), 125840. https://doi.org/10.1016/j.conbuildmat.2021.125840. 
  17. Kim, Y.Y. (2018), "Young's modulus measurement of a silicon nitride thin-film using an ultrasonically actuated microcantilever", Measure., 115, 133-138. https://doi.org/10.1016/j.measurement.2017.10.029. 
  18. Klyuchnyk, R., Kmit, I. and Recke, L. (2017), "Exponential dichotomy for hyperbolic systems with periodic boundary conditions", J. Diff. Equ., 262(3), 2493-2520. https://doi.org/10.1016/j.jde.2016.11.003. 
  19. Konrad, R., Marcin, T. and Kazimierz, F. (2019), "Contactless optical measurement methods for glass beams and composite timber-glass I-beams", Measure., 134(3), 662-672. https://doi.org/10.1016/j.measurement. 2018.09.061. 
  20. Konstantiniuk, F., Krobath, M., Ecker, W., Czettl, C., Schalk, N. and Tkadletz, M. (2023), "Influence of the aspect ratio of the micro-cantilever on the determined Young's modulus using the Euler-Bernoulli equation", Mater. Today Commun., 35, 106225. https://doi.org/10.1016/j.mtcomm.2023.106225. 
  21. Li, H., Huang, X., Jin, S., Jiang, Z. and Wang, B. (2022), "Reliability and sensitivity analysis of cold-bent curtain wall glass", J. Build. Eng., 49, 104116. https://doi.org/10.1016/j.jobe.2022.104116. 
  22. Liu, Y., Li, W. and Yang, F. (2013), "Vibration modal analysis of cantilever beams with complicated elasticity boundary constraint", 6th International Conference on Nonlinear Mechanics (ICNM), Shanghai. 
  23. Ma, S., Huang, H., Lu, M. and Veidt, M. (2012), "A simple resonant method that can simultaneously measure elastic modulus and density of thin films", Surf. Coating. Technol., 209, 208-211. https://doi.org/10.1016/j.surfcoat.2012.08.072. 
  24. Natsuki, T. and Natsuki, J. (2019), "Measurement of the elastic modulus of nanowires based on resonant frequency and boundary condition effects", Physica E: Low Dimens. Syst. Nanostruct., 105, 207-211. https://doi.org/10.1016/j.physe.2018.09.003. 
  25. Nielsen, J.A., Thiele, K., Schneider, J. and Meyland, M. (2021), "Compressive zone depth of thermally tempered glass", Constr. Build. Mater., 310(6), 12538. https://doi.org/10.1016/j.conbuildmat.2021.125238. 
  26. Oliver, W. and Pharr, G. (1992), "An improved technique for determining hardness arm elastic modulus using load and displacement sensing indentation experiments", J. Mater. Res., 7(6), 1564-1583. https://doi.org/10.1557/JMR.1992.1564. 
  27. Oliver, W. and Pharr, G. (2004), "Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology", J. Mater. Res., 19(1), 3-20. https://doi.org/10.1557/jmr.2004.19.1.3. 
  28. Pan, D.G., Jiang, K., Zhang, X.C. and Huang, Y. (2020), "Sealants delamination detection of structural sealant glazing systems based on driving-point accelerance", Shock Vib., 5(18), 7260438. https://doi.org/10.1155/2020/7260438. 
  29. Periyannan, S. and Balasubramaniam, K. (2015), "Simultaneous moduli measurement of elastic materials at elevated temperatures using an ultrasonic waveguide method", Rev. Scientif. Instrum., 86(11), 114903. https://doi.org/10.1063/1.4935556. 
  30. Quaglio, O., Silva, J., Rodovalho, E. and Costa, L. (2020), "Determination of Young's module by specific vibration of basalt and diabase", Adv. Mater. Sci. Eng., 2020, Article ID 4706384. https://doi.org/10.1155/2020/4706384. 
  31. Roebben, G., Bollen, B., Brebels, A. and Humbeeck, J. (1997), "Impulse excitation apparatus to measure resonant frequencies, elastic moduli, and internal friction at room and high temperature", Rev. Scientif. Instrum., 68(12), 4511-4515. https://doi.org/10.1063/1.1148422. 
  32. Rose, J. (2000), "Ultrasonic waves in solid media", J. Acoust. Soc. Am., 107(4), 1807-1808. https://doi.org/10.1121/1.428552. 
  33. Salvadori, M., Brown, I., Vaz, A., Melo, L. and Cattani, M. (2003), ''Measurement of the elastic modulus of nanostructured gold and platinum thin films'', Phys. Rev. B, 67(15), 153404. https://doi.org/10.1103/PhysRevB.67.153404. 
  34. Tang, J., Liu, L., Jiang, L., Huang, H. and Wang, Q. (2021). "A harmless thin film elastic module measurement method through bending the nonlinear sliding cantilever beam", Measure., 175, 108984. https://doi.org/10.1016/j.measurement.2021.108984. 
  35. Trung, T. and Lee, N. (2016), "Flexible and stretchable physical sensor integrated platforms for wearable human-activity monitoring and personal healthcare", Adv. Mater., 28(22), 4338-4372. https://doi.org/10.1002/adma.201504244. 
  36. Uheida, K., Deng, Y., Zhang, H., Laura, G., Gao, J., Xie, L., Huang, S., Qin, X., Wong, S., Guo, J., Zhang, G. and Ahmed, M. (2021), "Determining equivalent-sectional shear modulus in torsion tests for laminated glass beams using photogrammetry method", Compos. Struct., 276, 114572. https://doi.org/10.1016/j.compstruct.2021.114572. 
  37. Vasiliki, G. (2021), "Soil-structure-interaction effects on the flexural vibrations of a cantilever beam", Appl. Math. Model., 97, 138-181. https://doi.org/10.1016/j.apm.2021.03.045. 
  38. Wang, S., Zhao, W., Fu, X., Zhang, Z., Wang, T. and Ge, J. (2020), ''A universal method for quantitatively evaluating rock brittle-ductile transition behaviors'', J. Petrol. Sci. Eng., 195, 107774. https://doi.org/10.1016/j.petrol.2020.107774. 
  39. Wang, T. and Li, H. (2016), ''Effects of deformation of elastic constraints on free vibration characteristics of cantilever Bernoulli-Euler beams", Struct. Eng. Mech., 59(6), 1139-1153. https://doi.org /10.12989/sem.2016.59.6.1139. 
  40. Yang, J., Lei, Y., Pan, S. and Huang, N. (2003), "System identification of linear structures based on Hilbert-Huang spectral analysis. Part 2: Complex modes", Earthq. Eng. Struct. Dyn., 32(10), 1533-1554. https://doi.org 10.1002/eqe.288. 
  41. Yuan, Y., Zhou, Y., Wang, L. and Wu, Z. (2021), "Coupled deformation behavior analysis for the glass panel in unitized hidden-frame supported glass curtain wall system", Eng. Struct., 244(10), 112782. https://doi.org/10.1016/j.engstruct.2021.112782. 
  42. Zgheib, E., Alhussein, A., Slim, M., Khalil, K. and Francois, M. (2019), "Multilayered models for determining the Young's modulus of thin films by means of impulse excitation technique", Mech. Mater., 137, 103143. https://doi.org/10.1016/j.mechmat.2019.103143. 
  43. Zhu, F., Bai, P., Gong, Y., Lei, D. and He, X. (2018), "Accurate measurement of elastic module of specimen with initial bending using two-dimensional DIC and dual-reflector imaging technique", Measure., 119(4), 18-27. https://doi.org/10.1016/j.measurement.2018.01.043.