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Novel rheological modelling of thermosets and unidirectional monotropic fibre-reinforced thermoset matrix composites

Klasztorny Marian, Nycz Daniel B.

Composites Theory and Practice

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2023

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R. 23, nr 1

3--21

EN

A refined, fully analytical rheological modelling of thermosetting polymers and unidirectional monotropic fibre-reinforced thermoset matrix (UFRT) composites is presented. New polymers and composites under normal conditions, fully relaxed from curing and post-curing stresses, are modelled. The theory includes quasi-static short-term/medium-term/long-term reversible rheological processes. Thermosets are isotropic materials exhibiting linearly viscoelastic shear strains and linearly elastic bulk strains. Fibres are monotropic (transversely isotropic) and linearly elastic materials. A generic function well reproducing the viscoelastic characteristics of thermosets and UFRT composites is a Mittag-Leffler fractional exponential function in an integral form. Coupled/uncoupled standard/inverse constitutive equations of linear rheology are formulated for thermosets and UFRT composites. The equations are mutually analytically transformable. New rheological models (coded H-R/H) for thermosets and UFRT composites are described by the smallest possible number of material constants. The thermoset is described by two independent elastic constants and three independent viscoelastic constants. The homogenized UFRT composite is described by five independent elastic constants and four independent viscoelastic constants, whereby two visco-elastic constants are common to the matrix and the composite. An improved homogenization theory of UFRT composites, based on analytical solutions of the selected tasks of the theory of linear elasticity, is formulated for monotropic fibres and positively validated experimentally. The viscoelastic constants of the thermoset are calculated analytically in an iterative loop using a long-term unidirectional tension creep experimental test. The viscoelastic constants of the UFRT composite are calculated analytically employing H-R/H shear/quasi-shear storage compliances and VECP (the viscoelastic-elastic correspondence principle) shear/quasi-shear storage compliances. The H-R/H rheological model was validated numerically for selected UFRT composites. The validation tests were performed on the enhanced reliability UFRT composites reported by Soden, Hinton, and Kaddour (Composites Science and Technology, 1998, 2002).

2

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

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2022

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R. 22, nr 1

3--15

EN

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.

3

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

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2022

|

R. 22, nr 1

25--39

EN

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.