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.