Determination of Complex Compliances of Fibrous Polymeric Composites

Abstract

The paper presents a method for determining the complex compliances of a composite consisting of a viscoelastic isotropic matrix and unidirectional elastic monotropic fibres. These compliances represent the viscoelastic nature of a given composite material system. Elastic compliances of the composite have been derived fully analytically. Generating functions of shear/bulk viscoelasticity of the matrix have been defined by the Mittag-Leffler fractional exponential functions. This approach presents possibilities for modelling realistic shear/bulk creep of a polymer matrix. Complex compliances of the composite have been determined using the principle of elastic-viscoelastic analogy. A computer algorithm for calculating elastic and viscoelastic compliances of the composite has been formulated, programmed and tested on the selected composite material.

Keywords

unidirectional fibre-polymer matrix composite monotropic fibre viscoelasticity of polymers viscoelasticity of composites theory of reinforcement elastic compliances complex compliances

References

1. Wilczyński, A. P. , 1990. A Basic Theory of Reinforcement for Unidirectional Fibrous Composites, Composites Science & Technology, 38, pp. 327-337.

2. Wilczyński, A. P. , and Lewinski, J. , 1995. Predicting the Properties of Unidirectional Fibrous Composites with Monotropic Reinforcement, Composites Science & Technology, 55, pp. 139-143.

3. Wilczyński, A. P. , 1996. Viscoelasticity of Fibrous Polymeric Composites: A Theoretical Approach, Proc. 3rd Int. Conf on Composites Eng. ICCE/3, pp. 927-928, New Orleans, 1996.

4. Wilczyński, A. P. , 1997. Fibrous Polymeric Composites. Numerical Methods in Modelling Material (in Polish), Proc. 36th Polish Symp. on Modelling in Mechanics, pp. 293-297, Wisla (Poland) 1997.

5. Rabotnov, Ju.N. , 1966. Creep of Elements of Structures (in Russian), Moscow, Nauka Press.

6. Hill, R. , 1965. Theory of Mechanical Properties of Fibrestrengthened Materials. Self-consistent Model, J. Mech. Phys. Solids, 189.

7. Wilczyński, A. P. , 1968. Selected Problems of Testing of Mechanical Properties of Linearly Elastic Solids (in Polish), Warsaw, Publ. House of Warsaw Univ. Technol.

8. Wilczyński, A. P. , 1996. Polymeric Fibrous Composites (in Polish), Warsaw, WNT Press.

9. Ferry, J.D. , 1970. Viscoelastic Properties of Polymers, New York, John Wiley & Sons, Inc.

10.

10. Wilczyński, A. P. , 1978. The Fractional Exponential Function as a Master Function for Mechanical Behavior of Plastics, Proc. SPE 3-th ANTEC, pp. 220-221, Washington, 1978.

11.

11. Bland, D.R. , 1960. The Theory of Linear Viscoelasticity, Oxford, Pergamon Press.

12.

12. Jones, R.M. , 1975. Mechanics of Composite Materials, New York, McGraw-Hill, B.C.

13.

13. Daniel, I.M. and Ishai, O. , 1994. Engineering Mechanics of Composite Materials, New York-Oxford, Oxford Univ. Press.