Influence of Slipping Friction on Stress Concentration in Blended Yarns

Abstract

We report the effect of a variable frictional shear force distribution along a slipping broken fiber on the stress concentration (SCF) in blended yarns. Our micromechanical model leads to a system of second order differential equations, which we solve using a convenient eigenvector expansion approach. The results for an exponential variation of frictional shear on a slipping fiber, starting from zero at the broken end, are compared to those for a constant friction force. While the extent of the slip region increases by as much as 50% for the exponential variation compared to the constant friction case, the SCF changes only slightly, generally decreasing less than 6%. Decreases are smaller when a high elongation fiber is broken than when a low elongation fiber is broken. The hybrid effect in blended yarns, established in previous work, continues to be supported by these new results.

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References

Daniels, H. E. , The Statistical Theory of Strength of Bundles of Threads , Proc. R. Soc. London A 183, 405-435 (1945).

Godfrey, T. A. , and Rossettos, J. N. , A Constitutive Model for the Extension of Blended Yarns with Fragmented Low-Elongation Fibers , Textile Res. J. 71, 845-854 (2001).

Hearle, J. W. S. , Grosberg, P. , and Backer, S. , “Structural Mechanics of Fibers, Yarns, and Fabrics,” Wiley-Interscience, NY , 1969.

Hedgepeth, J. M. , and Van Dyke, P. , Local Stress Concentrations in Imperfect Filamentary Composite Materials , J. Compos. Mater. 1, 294-309 (1967).

Kilby, W. F. , The Mechanical Properties of Twisted Continuous-Filament Yarns , J. Textile Inst. 55, T589-T632 (1964).

Phoenix, S. L. , Statistical Theory for the Strength of Twisted Fiber Bundles with Applications to Yarns , Textile Res. J. 49, 407-423 (1979).

Pitt, R. E. , and Phoenix, S. L. , On Modelling the Statistical Strength of Yarns and Cables Under Localized Load-Sharing Among Fibers , Textile Res. J. 51, 408-425 (1981).

Realff, M. L. , Pan, N. , Seo, M. , Boyce, M. C. , and Backer, S. , A Stochastic Simulation of the Failure Process and Ultimate Strength of Blended Continuous Yarns , Textile Res. J. 70(5), 415-430 (2000).

Rossettos, J. N. , and Godfrey, T. A. , Hybrid Effect at Fiber Breaks in Twisted Blended Yarns , Textile Res. J. 72, 313-319 (2002).

10.

Thwaites, J. J. , The Elastic Deformation of a Rod with Helical Anisotropy , Int. J. Mech. Sci. 19, 161-168 (1976).

11.

Thwaites, J. J. , “Mechanics of Flexible Fibre Assemblies,” Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands , 1980, pp. 87-112