Strength of Unidirectional Short Fiber Structures as a Function of Fiber Length

Abstract

The strength of super-oriented polymer fibers or unidirectional short fiber composites strongly depends on the length of the molecule chains or the reinforcing fibers, respectively. A simple statistical model is developed based on the theory of fiber flows and the strength of the structure and its dependence on fiber length are determined in case of fibers broken or damaged owing to parting rigidly from the environment simultaneously. Later, two new special and modified versions of the so-called ES-bundle and one of the idealized statistical fiber-bundle-cells developed earlier, are introduced and applied to model the breaking process of the fibrous structure at different damage modes and its dependence on the fiber length is analyzed. In case of constant fiber length, a simple analytical relationship between the mean tensile strength and the fiber length is obtained which is valid for all the cases discussed. On the basis of the results, formulas are developed to estimate the strength of short fiber composites as a function of fiber length and fiber content, as well as to model the effect of the reduction in the fiber adhesion in case of a very small matrix content. The practical applicability of the results is demonstrated by identifying the relationship between tensile strength and molecule mass of PP fibers.

Keywords

fibrous structure highly oriented unidirectional fiber bundle short fiber composite tensile strength fiber breakage fiber slippage

Get full access to this article

View all access options for this article.

References

Zilahi, M. (1951). Theory of Drafting Fibrous Materials (in Hungarian), Akademiai Kiado, Budapest .

Zilahi, M. (1953). Raw Materials of the Textile Industry (in Hungarian), Tankonyvkiado, Budapest .

Morton, W. E. and Hearle, J. W. S. (1962). Physical Properties of Textile Fibres, The Textile Institute, Butterworth, Manchester & London .

Merenyi, G. (1964). Theory of the Basic Operations of the Spinning Technology (in Hungarian), Vol. I-II, Tankonyvkiado Budapest .

Renyi, A. (1966). Probability Theory (in Hungarian), Tankonyvkiado, Budapest .

Hearle, J. W. S. , Grosberg, P. and Backer, S. (1969). Structural Mechanics of Fibers, Yarns and Fabrics, Wiley-Interscience, New York .

Geleji, F. (1970). Properties of Fibers (in Hungarian), Tankonyvkiado, Budapest .

Phoenix, S. L. (1974). Probabilistic Concept in Modeling the Tensile Test Behavior of Fiber Bundles and Unidirectional Fiber/matrix Composites , In: Composite Materials: Testing and Design, 3rd Conference, Technical Publication 546, ASTM, Vol. 30, pp. 130-151 .

Vincze, I. (1975). Mathematical Statistics with Technical Applications (in Hungarian), Muszaki Konyvkiado, Budapest .

10.

Zurek, W. (1975). The Structure of Yarn, 2nd revised edn, Warsaw, Poland, 1971, Springfield, Virginia, USA .

11.

Harlow, D. G. and Phoenix, S. L. (1978). The Chain-of-Bundles Probability Model For the Strength of Fibrous Materials I: Analysis and Conjectures , Journal of Composite Materials, 12(4): 195-214 .

12.

Harlow, D. G. and Phoenix, S. L. (1978). The Chain-of-Bundles Probability Model For the Strength of Fibrous Materials II: A Numerical Study of Convergence , Journal of Composite Materials, 12(7): 314-334 .

13.

Phoenix, S. L. (1979). Statistical Aspect of Failure of Fibrous Materials , In: Tsai, S. W. (ed.), Composite Materials: Testing and Design (Fifth Conference), American Society for Testing and Materials, ASTM STP 674, pp. 455-483 .

14.

Phoenix, S. L. (1979). Statistical Theory for Strength of Twisted Fibre Bundles with Applications to Yarns and Cables , Textile Research Journal, 49(7): 407-423 .

15.

Kovacs, L. (ed.) (1979) Pocket Book of Plastics (in Hungarian), Muszaki Konyvkiado, Budapest .

16.

Hearle, J. W. S. , Thwaites, J. J. and Amirbayat, J. (1980). Mechanics of Flexible Fibre Assemblies, In: NATO Advanced Study Institutes Series E: Applied Sciences - No. 38, Sijthoff and Noordhoff, Germantown, Maryland, USA .

17.

Retting, W. (1991). Mechanik der Kunststoffe. Carl Hanser Verlag, Munchen, Wien, (ISBN 3- 446-16101-5).

18.

Vas, L. M. (1990). Statistical Fiber Bundle Strength and its Application to Testing Fibers and Yarns (in Hungarian) , Magyar Textiltechnika, 43(4): 165-185 .

19.

Wisnom, M. R. (1991). Relationship between Strength Variability and Size Effect in Unidirectional Carbon Fibre/Epoxy , Composites, 22(1): 47-52 .

20.

Part III: (7-8), 187-191 .

21.

Bobeth, W. (Hrsg) (1993). Textile Faserstoffe -Beschaffenheit und Eigenschaften, Springer-Verlag, Berlin .

22.

Vas, L. M. and Csaszi, F. (1993). Use of Composite-bundle Theory to Predict Tensile Properties of Yarns , Journal of the Textile Institute, 84(3): 448-463 .

23.

Vas, L. M. and Halasz, G. (1994). Modelling the Breaking Process of Twisted Fibre Bundles and Yarns , Periodica Polytechnica Mech. Eng., 38(4): 325-350 .

24.

Gibson, R. F. (1994). Principles of Composite Material Mechanics, McGraw-Hill, New York .

25.

Sutherland, L. S. and Guedes Soares, C. (1997). Review of Probabilistic Models of the Strength of Composite Materials , Reliability Engineering and System Safety, 56(3): 183-196 .

26.

Phoenix, S. L. (2000). Modeling the Statistical Lifetime of Glass Fiber/Polymer Matrix Composites in Tension , Composite Structures, 48(1-3): 19-29 .

27.

Czvikovszky, T. , Nagy, P. and Gaal, J. (2000). Fundamentals of Polymer Engineering (in Hungarian), Muegyetemi Kiado, Budapest .

28.

Desrumaux, F. , Meraghni, F. and Benzeggagh, M. L. (2000). Generalised Mori-Tanaka Scheme to Model Anisotropic Damage Using Numerical Eshelby Tensor , Journal of Composite Materials, 35(7): 603-624 .

29.

Schjodt-Thomsen, J. and Pyrz, R. (2000). Stress-Strain Modelling of Micro Cellular Materials , In: Proceedings of the 3rd Nordic Meeting on Materials and Mechanics, 8-11 May, Rebild Bakker Conference Center, Institute of Mechanical Engineering, Aalborg University, Denmark, pp. 1-12 .

30.

Srikanath, N. , Saravanaranganathan, D. , Gupta, M. , Lu, L. and Lai, M. O. (2000). Modelling and Determination of Dynamic Elastic Modulus of Magnesium Based Metal Matrix Composites , Materials Science and Technology, 16(3): 309-314 .

31.

Cotterell, B. (2002). The Past , Present, and Future of Fracture Mechanics, Engineering Fracture Mechanics, 69(5): 533-553 .

32.

Vas, L. M. and Racz, Zs. (2004). Modeling and Testing the Fracture Process of Impregnated Carbon Fiber Roving Specimens During Bending. Part I: Fiber Bundle Model , Journal of Composite Materials, 38(20): 1757-1785 .

33.

Vas, L. M. , Racz, Zs. and Nagy, P. (2004). Modeling and Testing the Fracture Process of Impregnated Carbon Fiber Roving Specimens During Bending. Part II: Experimental Studies , Journal of Composite Materials, 38(20): 1787-1801 .

34.

Jao Jules, E. , Tsujikami, T. , Lomov, S. V. and Verpoest, I. (2004). Effect of Fibres Length and Fibres Orientation on the Predicted Elastic Properties of Long Fibre Composites (10 pages). Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm

35.

de Miranda Boari, Z. , Monteiro, W. A. and de Jesus Miranda, C. A. (2005). Mathemathical Model Predicts the Elastic Behavior of Composite Materials , Materials Research, 8(1): 1516-1439 , Sao Carlos, January/March (13 pages). Downloaded from http://www.scielo.br/

36.

Valavala, P. K. and Odegard, G. M. (2005). Modeling Techniques for Determination of Mechanical Properties of Polymer Nanocomposites , Review on Advanced Materials Science (RAMS), 9(1): 34-44 .