Deformation of a Single Helix Under Simultaneous Application of Extension,Compression,and Bending

Abstract

An idealized model for a twisted yarn structure assumes that each fiber or filament follows a helical path and the yarn has a circular cross section in the undeformed state. An investigation of the behavior of a single helix can therefore be considered as a first step toward the mechanical analysis of yarn deformation under simultaneous extension, compression, and bending, which is the kind of deformation that occurs in many textile processes and applications. This paper presents a theoretical model of the large-scale deformation of a single helix subjected to bending, compression, and extension. The work studies the effects of varying the ratio of the flexural rigidity to the torsional rigidity of the helix material and of varying the helix angle together with the variation of the deformation forces. The cross section of a deformed helix is discussed in relation to the position of the neutral axis and strain energy. Also, some experimental data are presented to show the relevance of the theoretical results to the experimental findings.

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References

Gegauff, C. , Bull. Soc. Ind. Mulhouse 77, 153 (1907).

Goktepe, F. , The Effect of Yam Structure on the Deformation of the Yam Cross-section, Doctoral thesis, The University of Leeds, 1997.

Hearle, J.W.S. , Grosberg, P. , and Backer, S. , "Structural Mechanics of Fibres, Yams and Fabrics," vol. 1, Wiley-Interscience , U.K., 1969, p. 65.

Konopasek, M. , and Hearle, J.W.S. , Computational Theory of Bending Curves , Fibre Sci. Technol. 5(1), 1-28 ( 1972).

Leaf, G.A.V. , The Bending Behaviour of a Helical Filament, Part I: The Rigidity of the Helix , J. Textile Inst. 70, 323-329 (1979).

Leaf, G.A.V. , The Bending Behaviour of a Helical Filament, Part II: Curvature, Twist and Strain Energy, J. Textile Inst. 70, 330-336 (1979).

Leaf, G.A.V. , and Oxenham, W. , The Compression of Yams, Part I: The Compression-Energy Function, J. Textile Inst. 72, 168-175 (1981).

Leaf, G.A.V. , and Oxenham, W. , The Compression of Yams, Part II: The Load-Compression Function, J. Textile Inst. 72, 176-182 (1981).

Leaf, G.A.V. , and Tandon, S.K. , Compression of a Helical Fibre Under Distributed Forces, J. Textile Inst. 86, 218-231 (1995).

10.

Love, A.E.H. , "A Treatise on the Mathematical Theory of Elasticity ," 4th ed., Dover Publications , NY, 1944.

11.

Oxenham, W. , The Thickness and Compression of Yams, Doctoral thesis, The University of Leeds, U.K., 1974.

12.

Tandon, S.K. , Deformations of Helical Fibres Under Uniformly and Nonuniformly Distributed Compressive Forces, Doctoral thesis, The University of Leeds, U.K., 1988.