Andrzej Wilczyński

A basic theory of reinforcement for unidirectional fibrous composites

Abstract This paper proposes algorithms to obtain analytical results for a simple theory of reinforcement suitable for polymeric fibrous composites. Although the assumptions used in this theory are quite realistic, the obtained results are simple enough to be processed by a pocket computer. Comparison with experimental data shows that the proposed theory predicts rigidity constants of the material with sufficient accuracy for both practical and theoretical applications. This leads to a supposition that stress concentration predictions may be of the same value, giving together a useful tool for dimensioning structures or for optimising the material itself.

Determination of Complex Compliances of Fibrous Polymeric Composites

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.

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

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.

Predicting the properties of unidirectional fibrous composites with monotropic reinforcement

This paper presents an extention of an algorithm for obtaining numerical values of elastic constants of a unidirectional fibrous composite with monotropic reinforcement. This extension permits the prediction of properties not only for isotropic reinforcement, such as glass fibres, but also for the more complicated case of monotropic reinforcement with carbon or polyethylene fibres. Comparison with some experimental data shows that the proposed theory predicts elastic constants with good accuracy.

Some relationships and limitations of tensorial polynomials strength theories

Abstract The most general and convenient form of strength theory for orthotropic materials was first proposed by Malmeister, who also introduced the strength tensors into his model. Other strength theories, the most popular of which were those of Goldenblat and Kopnov and Tsai and Wu have firmly established this proposal in both theory and application. On the basis of these publications a general form of strength theory may be given as Φ = Π ik σ ik + Π iklm σ ik σ lm + ⋯ ⩽ 1 . A considerable amount of work has been carried out on this theory but better understanding is still needed in some cases. This paper presents new possibilities of using approximate relationships for partial replacement of experimental data. Comparison between the proposed relationships and experimental results for isotropic and anisotropic cases is favourable.