Normal and shear delamination of paperboards
Source abstract
Abstract
Abstract In packaging, the structural integrity of paperboard under complex stresses is essential. This study examines the delamination behavior of paperboard under normal and shear loading modes, which are the base for developing mixed-mode models. Four commercial paperboard grades, sourced from fibers across three geographical regions, are investigated using Double Cantilever Beam (DCB) and Split Double Cantilever Beam (SDCB) tests, which are used to calibrate a cohesive zone model from the literature. This model introduces a shape parameter that governs the cohesive traction-separation relationship, consistent across both normal and shear modes. Experimental findings support this approach, demonstrating that, while the shape parameter remains mode-independent, its numerical value varies uniquely for each paperboard quality.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Material Properties and Processing · Industrial Vision Systems and Defect Detection · Wood Treatment and Properties
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
4209 Karlstad University , Karlstad , Sweden
Tetra Pak , Lund , Sweden
Lund University , Lund , Sweden
Billerud , Gävle , Sweden
KTH Royal Institute of Technology , Stockholm , Sweden
Funding
Stiftelsen för Kunskaps- och Kompetensutveckling
References (24)
Show source-provided references
1. Alzweighi, M., Tryding, J., Mansour, R., Borgqvist, E., and Kulachenko, A. (2023). Anisotropic damage behavior in fiber-based materials – modeling and experimental validation. J. Mech. Phys. Solid. 181: 105430, https://doi.org/10.1016/j.jmps.2023.105430.10.1016/j.jmps.2023.105430 ↗
2. Benzeggagh, M. L. and Kenane, M. (1996). Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Compos. Sci. Technol. 56: 439–449, https://doi.org/10.1016/0266-3538(96)00005-x.10.1016/0266-3538(96)00005-X ↗
3. Biel, A., Tryding, J., Ristinmaa, M., Johansson-Näslund, M., Tuvesson, O., and Stigh, U. (2022). Experimental evaluation of normal and shear delamination in cellulose-based materials using a cohesive zone model. Int. J. Solids Struct. 252: 111755, https://doi.org/10.1016/j.ijsolstr.2022.111755.10.1016/j.ijsolstr.2022.111755 ↗
4. Carpinteri, A., Corrado, M., and Paggi, M. (2011). An analytical model based on strain localisation for the study of size-scale and slenderness effects in uniaxial compression tests. Strain 47: 351–362, https://doi.org/10.1111/j.1475-1305.2009.00715.x.10.1111/j.1475-1305.2009.00715.x ↗
5. Ebrahimijamal, M., Biel, A., Tryding, J., and Nygårds, M. (2025). Optimized specimen for paperboard shear delamination testing. Exp. Mech., https://doi.org/10.1007/s11340-025-01204-y.10.1007/s11340-025-01204-y ↗
6. Fellers, C. (1977). Procedure for measuring the interlaminar shear properties of paper. Sven. Papperstidning 80: 89–93.
7. Fellers, C. and Andersson, C. (2012). Evaluation of the stress-strain properties in the thickness direction — particularly for thin and strong papers. Nord. Pulp Pap Res. J. 27: 287–294, https://doi.org/10.3183/npprj-2012-27-02-p287-294.10.3183/npprj-2012-27-02-p287-294 ↗
8. Fellers, C., Östlund, S., and Mäkelä, P. (2012). Evaluation of the Scott bond test method. Nord. Pulp Pap Res. J. 27: 231–236.10.3183/npprj-2012-27-02-p231-236 ↗
9. Hutchinson, J. W. and Suo, Z. (1991). Mixed mode cracking in layered materials. In: Hutchinson, J. W. and Wu, T. Y. (Eds.), Advances in applied mechanics, Vol. 29. Elsevier, Amsterdam, pp. 63–191.10.1016/S0065-2156(08)70164-9 ↗
10. Isaksson, P., Gradin, P. A., and Östlund, S. (2010). A simplified treatise of the scott bond testing method. Exp. Mech. 50: 745–751, https://doi.org/10.1007/s11340-009-9269-y.10.1007/s11340-009-9269-y ↗
11. Jina, W. and Nagasawa, S. (2018). Finite element analysis of the folding process of creased white-coated paperboard using a combined fluffing resistance and shear yield glue model. J. Adv. Mech. Des., Syst., Manuf. 12: 1–15, https://doi.org/10.1299/jamdsm.2018jamdsm0063.10.1299/jamdsm.2018jamdsm0063 ↗
12. Li, Y., Stapleton, S., Simon, J., and Reese, S. (2016). Experimental and numerical study of paperboard interface properties. Exp. Mech. 56: 1477–1488, https://doi.org/10.1007/s11340-016-0184-8.10.1007/s11340-016-0184-8 ↗
13. Li, Y., Stapleton, S. E., Reese, S., and Simon, J.-W. (2018). Anisotropic elastic-plastic deformation of paper: out-of-plane model. Int. J. Solids Struct. 130-131: 172–182, https://doi.org/10.1016/j.ijsolstr.2017.10.003.10.1016/j.ijsolstr.2017.10.003 ↗
14. Lundh, A. and Fellers, C. (2001). The Z-toughness method for measuring the delamination resistance of paper. Nord. Pulp Pap Res. J. 16: 298–305, https://doi.org/10.3183/npprj-2001-16-04-p298-305.10.3183/npprj-2001-16-04-p298-305 ↗
15. 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-p432-437.10.3183/npprj-2008-23-04-p432-437 ↗
16. Nygårds, M. and Malnory, J. (2010). Measuring the out-of-plane shear strength profiles in different paper qualities. Nord. Pulp Pap Res. J. 25: 366–371.10.3183/npprj-2010-25-03-p366-371 ↗
17. Nygårds, M., Fellers, C., and Östlund, S. (2007). Measuring out-of-plane shear properties of paperboard. J. Pulp Pap. Sci. 33: 105–109.
18. Olsson, P. and Stigh, U. (1989). On the determination of the constitutive properties of thin interphase layers – an exact inverse solution. Int. J. Fract. 41: R71–R76, https://doi.org/10.1007/bf00018870.10.1007/BF00018870 ↗
19. Rice, J. R. (1968). A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35: 379–386, https://doi.org/10.1115/1.3601206.10.1115/1.3601206 ↗
20. Sørensen, B. F. (2016). Modeling damage, fatigue and failure of composite materials; materials. In: Talreja, R. and Varna, J. (Eds.), Woodhead publishing Series in composites Science and engineering. Woodhead Publishing, Amsterdam, pp. 213–240.
21. Tryding, J. and Ristinmaa, M. (2017). Normalization of cohesive laws for quasi-brittle materials. Eng. Fract. Mech. 178: 333–345, https://doi.org/10.1016/j.engfracmech.2017.03.020.10.1016/j.engfracmech.2017.03.020 ↗
22. Tryding, J., Johansson-Näslund, M., Biel, A., Stigh, U., Tuvesson, O., and Ristinmaa, M. (2023). Delamination of cellulose-based materials during loading–unloading conditions: interface model and experimental observations. Int. J. Solids Struct. 279: 112365, https://doi.org/10.1016/j.ijsolstr.2023.112365.10.1016/j.ijsolstr.2023.112365 ↗
23. Xia, Q. S. (2002). Mechanics of inelastic deformation and delamination in paperboard, Ph.D. thesis. Massachusetts Institute of Technology, United States of America.
24. Xu, X.-P. and Needleman, A. (1994). Numerical simulations of fast crack growth in brittle solids. J. Mech. Phy. Solids 42: 1397–1434, https://doi.org/10.1016/0022-5096(94)90003-5.10.1016/0022-5096(94)90003-5 ↗