Constitutive Equations of Viscoelasticity and Estimation of Viscoelastic Parameters of Unidirectional Fibrous Polymeric Composites

Abstract

A method for modelling viscoelastic properties of fibre reinforced polymeric composites, based on the original reinforcement theory as well as original description of viscoelasticity of the matrix [4}, is developed in the paper. The composite material consists of a viscoelastic isotropic polymer matrix and elastic monotropic fibres. In order to model arbitrary shear/bulk creep in the matrix, the Mittag-Leffler fractional exponential functions are used as the generating functions. Hence, the viscoelastic model of the polymer matrix is described with 2 elastic constants and 6 viscoelastic constants, while the elastic properties of the fibres are described with 5 well-known elastic constants. Both groups of the material constants can be estimated experimentally relatively easy. Coupled constitutive equations of linear viscoelasticity of a unidirectional fibrous polymeric composite, modeled as a homogeneous monotropic material are formulated in the study. The viscoelastic model of the composite is described using 5 elastic constants and 27 viscoelastic constants, i.e., 9 long-lasting compliance ratios, 9 retardation times, and 9 fractions defining an order of the fractional exponential functions. The elastic-viscoelastic analogy is used to predict theoretically the complex compliances of the composite [4]. An iterative optimization procedure for theoretical prediction of the viscoelastic constants of the composite is formulated, computerised and positively tested on the selected composite materials.

Keywords

unidirectional fibrous composite isotropic viscoelastic matrix monotropic elastic fibres homogenization constitutive equations of linear viscoelasticity viscoelastic parameters optimisation procedure

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References

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