A Semi-Analytical Resolution of a Generalized Unidirectional Self-Consistent Model: Theoretical Bases and Experiment in Viscoelasticity

Abstract

In recent articles [1], [2] we presented a finite element computation based on the homogenization theory of periodic media [3] or on the effective moduli approach to predict the complex moduli for unidirectional multiply coated continuous fiber composites via the correspondence principle [4], [5]. To have a method to compare with those approaches, we present first a semi-analytical resolution for a generalized unidirectional self-consistent model which predicts all the five independent elastic moduli and their complex counterparts [6], [7]. The resolution of this model is obtained by extending the general solution to the displacement and stress field within the constituents, proposed by Pagano-Tandon [8] and Carman et al. [9] for the problem "n concentric cylinders" of Hashin-Rosen's type [10]. Our direct resolution provides a new evaluation for the transverse shear modulus. The four other coefficients are proved to be coincident with the ones obtained by the n-phase "Composite Cylinder Assemblage," noted CCA model [10]. In the second part, this semi-analytical solution is compared with some experimental results that we obtained on the dynamic mechanical spectrometer METRA VIB and with other available predicting methods, for a unidirectional coated continuous fiber composite glass/epoxy. In order to obtain a better prediction for the loss tangent factor tan r1tE of the complex transverse Young's modulus ET in the main mechanical relaxation zone, two temperature-dependent evaluations for the complex Poisson's ratio of the viscoelastic polymer matrix are presented.