Stress Relaxation of a Paper Sheet under Cyclic Load: An Experimental and Theoretical Model
Sharon Kao-Walter, Etienne Mfoumou, Efraim Laksman
DOI: 10.4236/msa.2010.16046   PDF   HTML     6,413 Downloads   11,447 Views   Citations


Mechanical experiments have been performed to study the dynamic stress relaxation of a paper sheet material mainly used in food packaging industry. The material was cyclically tensile-loaded with a strain range between 2.4% and 4%. The time period for each cycle was 400 seconds. It was found that stress will decrease when the number of cycles increases in the case of upper load and vice versa in the case of lower load. At the same time, the stress to strain curves followed the same pattern as the one from the previous cycle. The stress relaxation behavior of each cycle has been analyzed and the dynamic relaxation modulus was derived. An improved model is proposed to describe the dynamic relaxation behavior of the paper sheet. This model shows a very good fit to the experimental results and trends of prediction are observed. Furthermore, the physical description of this model and the variation by the cycles is discussed.

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S. Kao-Walter, E. Mfoumou and E. Laksman, "Stress Relaxation of a Paper Sheet under Cyclic Load: An Experimental and Theoretical Model," Materials Sciences and Applications, Vol. 1 No. 6, 2010, pp. 317-322. doi: 10.4236/msa.2010.16046.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. Tryding, “In-Plane Fracture of Paper,” Ph.D. Thesis, Lund University, Lund, 1996.
[2] Q. S. Xia, M. C. Boyce and D. M. Parks, “A Constitutive Model for the Anisotropic Elastic-Plastic Deformation of a Paper and Paperboard,” International Journal of Solids and Structures, Vol. 39, No. 15, 2002, pp. 4053-4071.
[3] M. K. Ramasubramanian, Y. Y. Wang, “Constitutive Models for Paper and Other Ribbon-Like Nonwovens—A Literature Review,” In: R. Perkins, Ed., Mechanics of Cellulosic Materials, The American Society of Mechanical Engineers, New York, 1999, pp. 31-42.
[4] G. A. Baum, D. C. Brennan and C. C. Habeger, “Orthotropic Elastic Constants of Paper,” Tappi Journal, Vol. 64, No. 8, 1981, pp. 97-101.
[5] P. M?kel? and S. ?stlund, “Orthotropic Elastic-Plastic Material Model for Paper Materials,” International Jour-nal of Solids and Structures, Vol. 40, No. 21, 2003, pp. 5599-5620.
[6] A. DeMaio and T. Patterson, “Similarities in Bonding Influence between Pre-Failure Tensile Creep and Stress-Strain Behavior of Paper,” Mechanics of Materials, Vol. 40, 2008, pp. 133-149.
[7] L. O. Nordin and J. Varna, “Nonlinear Viscoelastic Behavior of Paper Fiber Composites,” Composites Science and Technology, Vol. 65, 2005, pp. 1609-1625.
[8] R. M. Guedes, A. T. Marwues and A. Cardon, “Analytical and Experimental Evaluation of Nonlinear Viscoelastic-Viscoplastic Composite Laminates under Creep, Creep-Recovery, Relaxation and Ramp Loading” Mechanics of Time-Depend Materials, Vol. 2, 1998, pp. 113-128.
[9] M. Megnis and J. Varna, “Micromechanics Based Modeling of Nonlinear Viscoplastic Response of Unidirectional Composite,” Composites Science and Technology, Vol. 63, 2003, pp. 19-31.
[10] J. A. TenCate and T. J. Shankland, “Slow Dynamics in the Nonlinear Response of Berea Sandstone,” Geophysics Research Letters, Vol. 23, 1996, pp. 3019-3022.
[11] J. A. TenCate, E. Smith and R. A. Guyer, “Universal Slow Dynamics in Granular Solids,” Geophysical Research Letters, Vol. 85, No. 5, 2000, pp. 1020-1023.
[12] P. A. Johnson, B. Zinszer and P. N. J. Rasolofosaon, “Resonance and Elastic Nonlinear Phenomena in Rock,” Journal of Geophysical Research, Vol. 101, 1995, pp. 11553-11564.
[13] K. Trachenko, “Slow Dynamics and Stress Relaxation in a Liquid as an Elastic Medium,” Physical Review B, Vol. 75, 2007, pp. 212-201.
[14] E. Mfoumou, K. Haller, C. Hedberg and S. Kao-Walter, “Slow Dynamics Experiments on Thin Sheets,” Proceedings of the V Iberian Congress of Acoustics, XXXIX Spanish Congress of Acoustics TECNICACUSTICA 2008, and the European Symposium of Acoustics, Coimbra, 2008, ID-197.
[15] L. Vangheluwe, “Relaxation and Inverse Relaxation of Yarns after Dynamic Loading,” Textile Research journal, Vol. 63, No. 9, 1993, pp. 552-556.
[16] R. Milasius, D. Milasiene and V. Jankauskaite, “Investigation of Stress Relaxation of Breathable-Coated Fabric for Clothing and Footwear,” Fibres & Textiles in Eastern Europe, Vol. 11, No. 2, 2003, p. 41.
[17] A. G. Makarov and A. M. Stalevich, “Prediction of Reverse Relaxation and Deformation-Recovery Processes in Synthetic Fibres,” Fibre Chemistry, Vol. 34, No. 6, 2002, 448-451.
[18] R. Rajdip and Q. Lu, “Stress Relaxation Study of Paper and Plastic Film Based Packaging Material,” Master’s Thesis, Blekinge Institute of Technology, Karlskrona 2009.
[19] E. Mfoumou, “Low Frequency Acoustic Excitation and Laser Sensing of Vibration as a Tool for Remote Characterization of Thin Sheets,” Ph.D. Thesis, Blekinge Institute of Technology, Karlskrona, 2008.
[20] P. Sherman, “Industrial Rheology,” Academic Press, New York, 1970.
[21] N. N. Mohsenin, “Physical Properties of Plant and Animal Materials,” Breach Science Publishers 1, New York, 1970.
[22] P. Kolseth and A. de Ruvo, “Swedish Forest Products Research Laboratory,” Unpublished results.
[23] R. E. Mark, “Handbook of Physical and Mechanical Testing of Paper and Paperboard,” Dekker, New York, 1983.
[24] E. N. Laowrence and R. F. Landel, “Mechanical Properties of Polymers and Composites,” 2nd Edition, Marcel Dekker, New York, 1994.
[25] Wikipedia, “Viscoelasticity,” 2010. http://en.wikipedia. org/wiki/Viscoelasticity.

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