Interlaminar shear modulus of cardboard obtained by torsional and flexural vibration tests

Hiroshi Yoshihara; Masahiro Yoshinobu; Makoto Maruta

doi:10.1515/npprj-2023-0022

Enjoy 40% off

academic books on De Gruyter Brill *

Article

Interlaminar shear modulus of cardboard obtained by torsional and flexural vibration tests

Hiroshi Yoshihara , Masahiro Yoshinobu and Makoto Maruta

Published/Copyright: May 16, 2023

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information

From the journal Nordic Pulp & Paper Research Journal Volume 38 Issue 3

Abstract

The interlaminar shear modulus of cardboards was measured using torsional vibration (TV) and flexural vibration (FV) methods. In the TV method, the sample widths were decreased during the tests, and the interlaminar and in-plane shear moduli were determined using the data obtained based on the different widths. By contrast, in the FV method, the resonance frequencies from the first to third FV modes were measured using samples of various lengths, and the interlaminar shear modulus and Young’s modulus in the length direction were calculated using Timoshenko’s vibration theory. In addition to the experiment, modal analyses based on the finite element (FE) method were performed, and the sample configurations used to accurately obtain the interlaminar shear modulus were experimentally and numerically investigated. The TV method did not allow the interlaminar shear modulus to be obtained appropriately because the vibration behavior often deviated from that theoretically derived by the TV equation. By contrast, the FV method allowed the interlaminar shear modulus to be obtained appropriately for a wide range of sample lengths.

Keywords: cardboard; flexural vibration test; interlaminar shear modulus; sample configuration; torsional vibration test

Corresponding author: Hiroshi Yoshihara, Faculty of Science and Engineering, Shimane University, Nishikawazu-cho 1060, Matsue, Shimane 690-8504, Japan, E-mail: yosihara@riko.shimane-u.ac.jp

Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

Brancheriau, L. and Bailleres, H. (2002). Natural vibration analysis of clear wooden beams: a theoretical review. Wood Sci. Technol. 36: 347–365, https://doi.org/10.1007/s00226-002-0143-7.Search in Google Scholar

Eekhout, M., Verheijen, F., and Visser, R. (Eds.) (2008). Cardboard in architecture. New York: IOS Press.Search in Google Scholar

Goens, E. (1931). Über die Bestimmung des Elastizitätsmodulus von Stäben mit Hilfe von Biegungsschwingungen. Ann. Phys. Ser. 403: 649–678, https://doi.org/10.1002/andp.19314030602.Search in Google Scholar

Guitard, D. (1987). Mécanique du matériau bois et composites. Toulouse: Editions Cépaduès.Search in Google Scholar

Hearmon, R.F.S. (1948). Elasticity of wood and plywood. London: HM Stationary Office.Search in Google Scholar

Hearmon, R.F.S. (1958). The influence of shear and rotatory inertia on the free flexural vibration of wooden beams. Br. J. Appl. Phys. 9: 381–388, https://doi.org/10.1088/0508-3443/9/10/301.Search in Google Scholar

Huang, H. and Nygårds, M. (2010). A simplified material model for finite element analysis of paperboard creasing. Nord. Pulp Pap. Res. J. 25: 502–509, https://doi.org/10.3183/npprj-2010-25-04-p502-509.Search in Google Scholar

Huang, H. and Nygårds, M. (2012). Numerical investigation of paperboard forming. Nord. Pulp Pap. Res. J. 27: 211–225, https://doi.org/10.3183/npprj-2012-27-02-p211-225.Search in Google Scholar

Kitahara, K. (1967). Wood physics. Tokyo: Morikita Shuppan.Search in Google Scholar

Kubojima, Y., Yoshihara, H., Ohta, M., and Okano, T. (1997). Accuracy of the shear modulus of wood obtained by the Timoshenko’s theory of bending. Mokuzai Gakkaishi 43: 439–443.Search in Google Scholar

Love, A.E.H. (1944). A treatise on the mathematical theory of elasticity. New York: Dover.Search in Google Scholar

Nygårds, M. (2008). Experimental techniques for characterization of elastic-plastic material properties in paperboard. Nord. Pulp Pap. Res. J. 23: 432–437, https://doi.org/10.3183/npprj-2008-23-04-p432-437.Search in Google Scholar

Nygårds, M., Fellers, C., and Östlund, S. (2007). Measuring out-of-plane shear properties of paperboard. J. Pulp Pap. Sci. 33: 105–109.Search in Google Scholar

Nygårds, M., Fellers, C., and Östlund, S. (2009). Development of the notched shear test. In: Trans. 14th fund. res. symp.. Oxford, UK.Search in Google Scholar

Srinivasa, P., Nygårds, M., Hagman, A., Pendergraph, S.A., and Sundström, P.J. (2019). On the torsion method for measurement of out-of-plane shear properties. In: Proc. 2019 int. paper phys. confer. Indianapolis, USA.Search in Google Scholar

Takami, I. (1964). Poisson’s ratio of plywood. Bull. Gov. For. Exp. Stn. Jpn 188: 122–174.Search in Google Scholar

Timoshenko, S.P. (1921). On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Phil. Mag. 41: 744–746, https://doi.org/10.1080/14786442108636264.Search in Google Scholar

Uesaka, T. (1983). Specimen design for measurement of interlaminar and in-plane shear moduli by the torsion pendulum method. In: Mark, R.E. (Ed.), Handbook of physical and mechanical testing of paper and paperboard, Vol. 1. New York: Marcel Dekker, Inc., pp. 89–99.Search in Google Scholar

Wang, Z., Zhang, D., Wang, Z., Liang, X., Yang, X., and Wang, J. (2023). Research progress on dynamic testing methods of wood shear modulus: a review. Bioresources 18: 2262–2270, https://doi.org/10.15376/biores.18.1.wang.Search in Google Scholar

Yoshihara, H. (2010). Poisson’s ratio of plywood measured by tension test. Holzforschung 63: 603–608, https://doi.org/10.1515/hf.2009.092.Search in Google Scholar

Yoshihara, H. and Maruta, M. (2020). Effect of the specimen configuration on the accuracy in measuring the shear modulus of western hemlock by torsional vibration test. Wood Sci. Technol. 56: 1479–1496, https://doi.org/10.1007/s00226-020-01234-w.Search in Google Scholar

Yoshihara, H., Yoshinobu, M., and Maruta, M. (2021). Comparing Young’s modulus values of paperboard obtained by four methods. Mokuzai Gakkaishi 67: 208–216, https://doi.org/10.2488/jwrs.67.208.Search in Google Scholar

Yoshihara, H., Yoshinobu, M., and Maruta, M. (2022). Evaluation of the shear modulus of paperboard measured from a torsional vibration test. J. Soc. Mater. Sci. 71: 585–590, https://doi.org/10.2472/jsms.71.585.Search in Google Scholar

Yoshihara, H., Yoshinobu, M., and Maruta, M. (2023a). Buckling test of flat cardboard and examination of critical load for buckling. Mokuzai Gakkaishi 68: 165–171, https://doi.org/10.2488/jwrs.68.165.Search in Google Scholar

Yoshihara, H., Yoshinobu, M., and Maruta, M. (2023b). Bending stiffness and moment capacity of cardboard obtained from three-point and elastica bending tests. Nord. Pulp Pap. Res. J. 38: 73–85, https://doi.org/10.1515/npprj-2022-0087.Search in Google Scholar

Received: 2023-04-16

Accepted: 2023-05-04

Published Online: 2023-05-16

Published in Print: 2023-09-26

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/npprj-2023-0022

Keywords for this article

cardboard; flexural vibration test; interlaminar shear modulus; sample configuration; torsional vibration test