Jan Schjødt-Thomsen

The Mori–Tanaka stiffness tensor: diagonal symmetry, complex fibre orientations and non-dilute volume fractions

Abstract This paper considers the diagonal symmetry of the stiffness tensors predicted using the Mori-Tanaka (MT) approach. Since the MT approach may yield asymmetric stiffness tensors this paper considers an alternative approach to ensure the diagonal symmetry. Furthermore, an extension of the MT approach to non-dilute volume fractions is considered. It is shown that the MT approach by Benveniste [Mech. Mater. 6 (1987) 147], may not yield diagonally symmetric stiffness tensors in situations when a statistical fibre orientation function is incorporated. Only when the inclusions are spherical and randomly distributed or fully aligned will the MT predicted stiffness tensor be diagonally symmetric. The extension to non-dilute volume fractions is seen to lie within the Hashin–Shtrikman–Walpole (HSW) bounds and comparison to other approaches and experiments found in the literature shows very good agreement.

Overall creep modelling of short fibre reinforced composites with weakened interfaces and complex fibre orientation distributions

Abstract This paper deals with the overall creep response of a short fibre reinforced composite. The fibres are oriented differently in the matrix through a distribution function of the Euler angles. No fibre length distribution function is used, i.e. the fibres are of the same length. The approach is based upon the Mori–Tanaka mean field theory in which the fibres are considered as inhomogeneities containing equivalent eigenstrains. Furthermore, the effect of an imperfect interface is considered through a modified Eshelby tensor. It is shown that for UD composites the interfacial parameter does not influence the elastic stiffness in the fibre direction. For various fibre distributions the weakened interface has the largest influence when applying shear loading to a nearly unidirectional composite.

Non-linear creep modelling of single-fibre model composites

This paper describes a method for determining the stress/strain fields in a single-fibre model composite subjected to creep loading conditions. The method is based upon Eshelbys thought experiment and the integration of interfacial tractions. The non-linear viscoelastic behaviour is modelled through an incremental stress/strain formulation based on the Schapery model. Comparisons have been made between the predictions from the model, a non-linear finite-element model, and experimental fibre strains measured by micro-Raman spectroscopy and good qualitative agreement is observed. The nature of the interfacial tractions controls the form of the interfacial shear stress which govern the shape of the longitudinal fibre stress profile. As a consequence the rates at which the strain is building up in the fibre are different when comparing calculations and experiments. However, the characteristics of the experiments are reflected in the theoretical predictions. Generally, it is seen that the initial residual stress in the fibre is restricting the level of the fibre strain during subsequent creep loading and can be beneficial in delaying tensile fibre fractures.

Influence of Statistical Cell Dispersion on the Local Strain and Overall Properties of Cellular Materials

A model which is capable of taking higher order interaction into account was recently proposed. The model is based on Eshelbys equivalent eigenstrains, which enables the calculation of both local and overall properties of the considered heterogeneous material. This model was used for the analysis of the influence of different statistical cell dispersions on variations in local strains and overall properties of the generated cellular material. Preliminary results indicate that for 3D random dispersions the influence of the cell distribution on the cell eigenstrains is rather weak. This suggest that using traditional approaches for modelling stress/strain fields or effective properties of cellular materials may lead to reasonably accurate results despite the fact that direct interaction is neglected. However, as is shown, this may not be the case for dispersions which are not trivial.

The influence of stochastic interfacial parameter distribution on the stiffness of composites with complex fibre orientation

Abstract This paper deals with the overall stiffness determination of a short-fibre-reinforced composite with complex fibre orientation and soft interfaces. The fibres are oriented differently in the matrix through a distribution function of the Euler angles. No fibre length distribution function is used, i.e. the fibres are of the same length. The approach is based upon the Mori–Tanaka mean-field theory. Furthermore, the effects of an interface with stiffness differing from those of the matrix and fibre are considered through a modified Eshelby tensor. The parameter describing the interfacial stiffness is considered as a stochastic variable described by a statistical distribution function. It is shown that when the fibres are oriented mainly towards the directions of the principal stresses the effects of the soft interface is diminishing. Furthermore, it is shown that when the interfacial stiffness parameter is described by a β distribution the resulting composite stiffness distribution resembles a uniform distribution.

Synthesis and characterization of montmorillonite-carbon nanotubes hybrid fillers for nanocomposites

Montmorillonite-carbon nanotubes hybrids were prepared by growth of carbon nanotubes (CNT) on five different types of iron-montmorillonite clays using the chemical vapour deposition (CVD) method. Microscopy studies revealed the presence of carbon nanotubes protruding from clay surfaces and linking the clay layers in a network structure. X-ray diffraction results showed changes in the clay interlayer spacing induced by growth of carbon nanotubes within the layers of iron-montmorillonites. The quality of the resulting carbon nanotubes was evaluated by Raman spectroscopy and thermogravimetric analyzes were used to evaluate the amount of carbon nanotubes and its thermal stability. The method used for the preparation of the iron-montmorillonites appeared to be critical for the quality and quantity of carbon nanotubes obtained in each hybrid. In a preliminary study the hybrids were used to reinforce polyurethane nanocomposite foams.