Stress Relaxation of a Paper Sheet under Cyclic Load: An Experimental and Theoretical Model
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Abstract
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.
- J. Tryding, “In-Plane Fracture of Paper,” Ph.D. Thesis, Lund University, Lund, 1996.
- 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.
- 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.
- 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.
- 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.
- 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.
- L. O. Nordin and J. Varna, “Nonlinear Viscoelastic Behavior of Paper Fiber Composites,” Composites Science and Technology, Vol. 65, 2005, pp. 1609-1625.
- 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.
- 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.
- 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.
- 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.
- 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.
- K. Trachenko, “Slow Dynamics and Stress Relaxation in a Liquid as an Elastic Medium,” Physical Review B, Vol. 75, 2007, pp. 212-201.
- 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.