A Poisson Model of Nonwoven Fiber Assemblies in Compression at High Stress

Abstract

A new model has been developed that predicts the compression behavior of thick. nonwoven fiber assemblies at high stress levels. The model uses the Poisson distribution to describe how fibers are stacked on top of one another during web formation. The stress/thickness relationships developed are based solely on the compression properties of the stacked fiber mass. Effects predicted by the model include greater packing uni formity for increasing web weight, decreasing fiber diameter. and decreasing fiber transverse compression modulus. An expression for the fractional area of a compressed web that is actually under stress is also given. The stress/thickness behavior predicted by the model is compared to the measured compression characteristics of nylon. Spec tra®, Kevlar®, and fiberglass needled batts. The measured and predicted behavior agree well enough in most cases to validate both the Poisson distribution approach to the placement of fiber mass in randomly formed nonwoven materials and the simple com pressive stress relationships developed from it.

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References

Camaby, G.A. , and Pan, N. , Theory of the Compression Hysteresis of Fibrous Assemblies, Textile Res. J. 59, 275-284 (1989).

Dunlop, J.I. , The Dynamic Bulk Modulus of Fibre Masses, J. Textile Inst. 72, 154-161 (1981).

Jones, R.L. , The Effect of Fiber Structural Properties on Compression Response of Fiber Beds. Tappi 46, 20-28 (1963).

Kallmes, O. , and Corte, H. , The Structure of Paper, Part 1: The Statistical Geometry of an Ideal Two Dimensional Fiber Network , Tappi 43, 737-752 (1960).

Kawabata, S. , Measurement of the Transverse Mechanical Properties of High-performance Fibres, J. Textile Inst. 81, 432-447 (1990).

Komori, T. , and Makishima, K. , Numbers of Fiber-to-Fiber Contacts in General Fiber Assembles, Textile Res. J. 47, 13-17 (1977).

Komori, T. , and Itoh, M. , A. New Approach to the Theory of the Compression of Fiber Assemblies, Textile Res. J. 61, 420-428 (1991).

Komori, T. , and Itoh, M. , Theory of the General Deformation of Fiber Assemblies. Textile Res. J. 61, 588-594 (1991).

Komori, T. , Itoh, M. , and Takaku. A. , A Model Analysis of the Compressibility of Fiber Assemblies, Textile Res. J. 62, 567-574 (1992).

10.

Lee, D.H. , and Lee. J.K. , Initial Compressional Behavior of a Fibre Assembly, in "Objective Measurement Applications to Product Design and Process Control," S. Kawabata , R. Postle , and M. Niwa , Eds., The Textile Machinery Society of Japan, Osaka, 1985, pp. 613-622.

11.

Lee, D.H. , Camaby, G.A. , Carr, A.J. , and Moss, P.J. , A Review of Current Micromechanical Models of the Unit Fibrous Cell, WRONZ Communications no. C113, 1990.

12.

Lee, D.H. , and Camaby, G.A. , Compressional Energy of the Random Fiber Assembly, Part I: Theory , Textile Res. J. 62, 185-191 (1992).

13.

Lee, D.H. , Carnaby, G.A. , and Tandon, S.K. , Compressional Energy of the Random Fiber Assembly, Part II: Evaluation , Textile Res. J. 62, 258-265 (1992).

14.

Meyer, Stuart L. , "Data Analysis for Scientists and Engineers ," J. Wiley & Sons, Inc., NY , 1975, pp. 181-182, 207-208.

15.

Oliver, J.F. , and Wiseman, N. , Water Removal in Wet Pressing: The Effect of Felt Roughness, in "Trans. of the Technical Section, Canadian Pulp & Paper Assoc.," Montreal, Jan. 30-Feb. 3, 1978, vol. 4, 1978, pp. TR104-109.

16.

Österberg. L.B. , Compression of Press Felts, Nordic Pulp Paper Res. J. ( special Issue) (3), 36-39 ( 1988).

17.

Phoenix, S.L. , and Skelton, J. , Transverse Compressive Moduli and Yield Behavior of Some Orthotropic, High-Modulus Filaments, Textile Res. J. 44,934-940 ( 1974).

18.

van Wyk, C.M. , Note on the Compressibility of Wool, J. Textile Inst. 37, T285-292 (1946 ).