Effect of sample length and width on Young’s modulus value of paperboard obtained from flexural vibration test
Source abstract
Abstract
Abstract The Young’s moduli in the machine (M) and cross-machine (C) directions, denoted as E md and E cd , respectively, were determined for two flat paperboard samples with a thickness of 1 mm using a flexural vibration (FV) test. During the tests, the length ( L ) and width ( B ) of the samples were varied in the ranges of 60 ≤ L ≤ 140 mm and 10 ≤ B ≤ 50 mm, respectively, and their effects on E M and E C were examined. Before the FV tests, finite element calculations were performed, and the results were compared with those obtained from the subsequent FV tests. The sample configurations had a greater effect on E md than on E cd . When the sample length was aligned in the M direction, saddle-shaped deformation increased with the increasing B value, reducing the accuracy of E md . However, statistical analyses revealed that sample configurations affected E md and E cd , and the optimal ranges of L and B were 80 ≤ L ≤ 120 mm and 10 ≤ B ≤ 30 mm, respectively.
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Research context
OpenAlex topics: Material Properties and Processing · Wood Treatment and Properties · Advanced Cellulose Research Studies
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Faculty of Science and Engineering , 12938 Shimane University , Matsue , Japan
Faculty of Science and Engineering , Shizuoka Institute of Science and Technology , Fukuroi , Japan
References (47)
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1. ASTM standard C623-21. (2021). Standard test method for Young’s modulus, shear modulus, and Poisson’s ratio for glass and glass-ceramics by resonance.
2. ASTM standard C1548-02. (2020). Standard test method for dynamic Young’s modulus, shear modulus, and Poisson’s ratio of refractory materials by impulse excitation of vibration.
3. ASTM standard D828-22. (2022). Standard test method for tensile properties of paper and paperboard using constant-rate-of-elongation apparatus.
4. ASTM standard D4065-20. (2020). Standard practice for plastics: dynamic mechanical properties: determination and report of procedures.
5. ASTM standard D6874-12. (2012). Standard test methods for nondestructive evaluation of wood-based flexural members using transverse vibration.
6. ASTM standard E756-05. (2017). Standard test method for measuring vibration-damping properties of materials.
7. ASTM standard E1876-21. (2021). Standard test method for dynamic Young’s modulus, shear modulus, and Poisson’s ratio by impulse excitation of vibration.
8. Bahari, A.R., Fudzi, M.S.M., Ahmad, N.U., and Rahman, H.A. (2013). Material properties characterization of coir cardboard. ARPN Journal of Engineering and Applied Sciences 10: 9521–9526.
9. Baum, G.A., Brennan, D.C., and Habeger, C.C. (1981a). Orthotropic elastic constants of paper. Tappi J. 64: 97–101.
10. Baum, G.A., Habeger, C.C., and Fleischman, E.H. (1981b). Measurement of the orthotropic elastic constants of paper. The Institute of Paper Chemistry, Appleton, Wisconsin 26: 453–478, https://doi.org/10.15376/frc.1981.1.453.10.15376/frc.1981.1.453 ↗
11. 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/s00226-002-0143-7.10.1007/s00226-002-0143-7 ↗
12. DIN standard 53121. (2008). Testing of paper and board – Determination of the bending stiffness by the beam method.
13. Eekhout, M., Verheijen, F., and Visser, R. (Eds.) (2008). Cardboard in architecture. IOS Press, New York.
14. Hagman, A. and Nygårds, M. (2012). Investigation of sample-size effects on in -plane tensile testing of paperboard. Nord. Pulp Paper Res. J. 27: 295–304, https://doi.org/10.3183/npprj-2012-27-02-p295-304.10.3183/npprj-2012-27-02-p295-304 ↗
15. Horio, M. and Onogi, S. (1951a). Dynamic measurement of physical properties of pulp and paper by audiofrequency sound. J. Appl. Phys. 22: 971–977, https://doi.org/10.1063/1.1700081.10.1063/1.1700081 ↗
16. Horio, M. and Onogi, S. (1951b). Forced vibration of reed as a method of determining viscoelasticity. J. Appl. Phys. 22: 977–981, https://doi.org/10.1063/1.1700082.10.1063/1.1700082 ↗
17. Huang, H. and Nygårds, M. (2010). A simplified material model for finite element analysis of paperboard creasing. Nord. Pulp. Paper Res. J. 25: 502–509, https://doi.org/10.3183/npprj-2010-25-04-p505-512.10.3183/npprj-2010-25-04-p502-509 ↗
18. Huang, H. and Nygårds, M. (2012). Numerical investigation of paperboard forming. Nord. Pulp Paper Res. J. 27: 211–225, https://doi.org/10.3183/npprj-2012-27-02-p211-225.10.3183/npprj-2012-27-02-p211-225 ↗
19. ISO standard 1924-2:2008. (2008). Paper and board – Determination of tensile properties – Part 2: Constant rate of elongation method (20 mm/min).
20. ISO standard 1924-3:2005. (2005). Paper and board – Determination of tensile properties – Part 3: Constant rate of elongation method (100 mm/min).
21. ISO standard 5628:2019. (2019). Paper and board – Determination of bending stiffness – General principles for two-point, three-point and four-point methods.
22. ISO standard 5629:2017. (2017). Paper and board – Determination of bending stiffness – Resonance method.
23. ISO standard 6721-1:2019. (2019). Plastics – Determination of dynamic mechanical properties.
24. ISO standard 17561:2016. (2016). Fine ceramics (advanced ceramics, advanced technical ceramics) − Test method for elastic moduli of monolithic ceramics at room temperature by sonic resonance.
25. ISO standard 22605:2020. (2020). Refractories − Determination of dynamic Young’s modulus (MOE) at elevated temperatures by impulse excitation of vibration.
26. JIS standard A 1127:2010. (2010). Methods of test for dynamic modulus of elasticity, rigidity and Poisson’s ratio of concrete by resonance vibration.
27. JIS standard G 0602:1993. (1993). Test methods for vibration-damping properties in laminated damping steel sheets of constrained type.
28. JIS standard K 7244-1:1998. (1998). Plastics − Determination of dynamic mechanical properties − Part 1: General principles.
29. JIS standard P 8113:2006. (2006). Paper and board − Determination of tensile properties − Part 2: Constant rate of elongation method.
30. JIS standard R 1602:1995. (1995). Testing methods for elastic modulus of fine ceramics.
31. JIS standard Z 2280. (1993). Test method for Young’s modulus of metallic materials at elevated temperature.
32. Kitahara, K. (1967). Wood physics. Morikita Shuppan, Tokyo.
33. Martin, G., Srinivasa, P., Nygårds, M., and Östlund, S. (2021). Experimental and finite element simulated box compression tests on paperboard packages at different moisture levels. Packag. Technol. Sci. 34: 229–243, https://doi.org/10.1002/pts.2554.10.1002/pts.2554 ↗
34. Martin, G., Hagman, A., Östlund, S., and Nygårds, M. (2023). Torsional and compression loading of paperboard packages: experimental and FE analysis. Packag. Technol. Sci. 36: 31–44, https://doi.org/10.1002/pts.2693.10.1002/pts.2693 ↗
35. Matsumoto, T. (1962). Studies on the dynamic modulus E and the logarithmic decrement of wood by transverse vibration. Bull. Kyushu Univ. Forest 36: 1–86.
36. Nakao, T. and Kimura, M. (1986). Measurement of dynamic Young’s modulus of paperboard. TAPPI J. 69: 129–133.
37. Riemen, W.P. and Kurath, S.F. (1964). The dynamic mechanical properties of paper. TAPPI J. 47: 629–633.
38. Sato, J., Hutchings, I.M., and Woodhouse, J. (2007). Measurement of the elastic modulus of paperboard from the low-frequency vibration modes of rectangular plates. Jpn. TAPPI 61: 837–851, https://doi.org/10.2524/jtappij.61.837.10.2524/jtappij.61.837 ↗
39. Sato, J., Hutchings, I.M., and Woodhouse, J. (2008). Determination of the dynamic elastic properties of paper and paperboard from the low-frequency vibration modes of rectangular plate. Appita 61: 291–296.10.2524/jtappij.61.837 ↗
40. Shah, A. and Hirpara, S. (2017). Paper-tubes as a building material. J. Sustain. Construct. Mater. Technol. 2: 79–82, https://doi.org/10.29187/jscmt.2018.10.10.29187/jscmt.2018.10 ↗
41. TAPPI standard T 404 cm-92. (1992). Tensile breaking strength and elongation of paper and paperboard (using pendulum-type tester).
42. TAPPI standard T 494 om-06. (2006). Tensile properties of paper and paperboard (using constant rate of elongation apparatus).
43. Venkatesan, S., Afroz, M., Navaratnam, S., and Gravina, R. (2023). Circular-economy-based approach to utilizing cardboard in sustainable building construction. Buildings 13: 181, https://doi.org/10.3390/buildings13010181.10.3390/buildings13010181 ↗
44. Yoshihara, H., Yoshinobu, M., and Maruta, M. (2021). Comparing Young’s modulus values of paperboard obtained by four methods. Mokkuzai Gakkaishi 67: 208–216, https://doi.org/10.2488/jwrs.67.208.10.2488/jwrs.67.208 ↗
45. Yoshihara, H., Yoshinobu, M., and Maruta, M. (2023). Interlaminar shear modulus of cardboard obtained by torsional and flexural vibration tests. Nord. Pulp Paper Res. J. 38: 399–411, https://doi.org/10.1515/npprj-2023-0022.10.1515/npprj-2023-0022 ↗
46. Yoshihara, H., Yoshinobu, M., and Maruta, M. (2024). Comparing the in-plane shear moduli of cardboard measured by flexural vibration, torsional vibration, static torsion, off-axis vibration, and off-axis tension tests. Nord. Pulp Paper Res. J. 39: 359–373, https://doi.org/10.1515/npprj-2023-0087.10.1515/npprj-2023-0087 ↗
47. Yoshihara, H., Yoshinobu, M., and Maruta, M. (2025). Effect of attached weight on the measurement of the Young’s modulus and loss tangent of solid wood via the free and forced flexural vibration methods. Wood Sci. Technol. 59: 41, https://doi.org/10.1007/s00226-025-01646-6.10.1007/s00226-025-01646-6 ↗