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2 Composites Theory and Practice

2 2022

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Modelling of linear elasticity and viscoelasticity of thermosets and unidirectional glass fibre-reinforced thermoset-matrix composites. Part 1, Theory of modelling

Klasztorny Marian, Nycz Daniel B.

Composites Theory and Practice

2022

R. 22, nr 1

3--15

The paper presents advanced analytical modelling of the linear elasticity and viscoelasticity of thermosets and unidirectional long glass fibre-reinforced thermoset-matrix (UFRT) composites. New non-aging materials fully relaxed after the curing and post-curing processes are considered. Quasi-static long-term isothermal reversible viscoelastic processes under normal conditions are modelled. The thermosets are isotropic materials with viscoelastic shear strains and elastic bulk strains, and the fibres are isotropic and elastic. New rheological models for thermosets and UFRT composites, described by the smallest possible number of material constants, are developed. The viscoelastic generic function for shear/quasi-shear stresses is assumed as the Mittag-Leffler fractional exponential function in an integral form. The thermoset is described by two elastic and three viscoelastic parameters. The homogenized UFRT composite is described by five elastic and five viscoelastic parameters. Conjugated/unconjugated standard/inverse constitutive equations of the linear elasticity/elasticity-viscoelasticity governing thermosets and UFRT composites are formulated. The equations are mutually analytically transformable.

Modelling of linear elasticity and viscoelasticity of thermosets and unidirectional glass fibre-reinforced thermoset-matrix composites. Part 2, Homogenization and numerical analysis

Klasztorny Marian, Nycz Daniel B.

Composites Theory and Practice

2022

R. 22, nr 1

25--39

The study continues the advanced analytical modelling of the linear elasticity and viscoelasticity of thermosets and unidirectional glass fibre-reinforced thermoset-matrix (UFRT) composites. The thermosets are isotropic materials with viscoelastic shear strains and elastic bulk strains, and the fibres are isotropic and elastic. The modified homogenization theory for UFRT composites, based on the selected tasks of the linear theory of elasticity, is developed. The modifications include a volumetrically equivalent cylindrical representative volume cell, solutions determined for an isotropic fibre based on the solutions for a monotropic (transversely isotropic) fibre, and certain modifications in the third task of the theory of elasticity. The viscoelastic constants of the thermoset are derived analytically and validated by fitting of the simulation and experimental shear strains on a logarithmic time scale in the unidirectional tension creep test. The viscoelastic constants of the UFRT composite are derived analytically and validated by fitting of the storage compliances corresponding to the new viscoelastic model and one obtained from the viscoelastic-elastic correspondence principle. The tension creep experiment is performed on the selected structural unsaturated polyester resin. Identification and validation are carried out for that thermoset and the corresponding UFRT composite with long E-glass fibres. All the modelling hypotheses are confirmed.