Ryszard Pyrz

Quantitative description of the microstructure of composites. Part I: Morphology of unidirectional composite systems

Abstract For the purpose of micromechanical modeling the behavior of unidirectional composite materials it is necessary to identify the descriptors that in the best way characterize the spatial dispersion of fibers. By introducing a second-order intensity function and the Dirichlet tessellation, the statistical analysis of fiber distribution has been carried out. The analysis has been performed for three distributions obtained experimentally and for several simulated distributions. It is shown that customary assumptions about complete randomness or perfect regularity of the dispersion may be in error, compared with real situations. A simple micro-mechanical model illustrates the influence of distribution statistics on the calculated stress field.

Prediction of the overall moduli of layered silicate-reinforced nanocomposites—part I: basic theory and formulas

Abstract This part of the two-part paper presents the basic theory and formulas for the prediction of the overall moduli of layered silicate-reinforced polymeric nanocomposites. In view of the morphology of the composites and the anisotropic nature of layered silicate, formulas for the overall moduli of composite materials reinforced with transversely isotropic spheroids are derived in this part using the Mori–Tanaka method. These formulas are then used to examine the influences of the anisotropy and aspect ratio of the transversely isotropic spheroids on the overall moduli of the composite materials. It is found that the overall moduli of the composite materials reinforced with transversely isotropic spheroids are predominated by the stiffness of the spheroids in the direction of their major axis, especially for the cases of small and large aspect ratios. The predictions based upon the Mori–Tanaka method are also compared with approximate formulas in the literature for isotropic thin oblate spheroids. It is found that these approximate formulas agree well with the Mori–Tanaka predictions at low volume fractions of the reinforcement.

Correlation of microstructure variability and local stress field in two-phase materials

Abstract Improved characterization of present-day materials that are manufactured to obtain optimal property values by microstructure effects necessitates a more thorough knowledge of the microstructure pattern. Methods of spatial statistics have been used to analyse patterns of second-phase inclusions as observed on planar sections. Several parameters and functions that discriminate between different dispersions of inclusions have been investigated. The effects of inclusion patterns on the interface stresses in unidirectional fibre reinforced composite material are discussed. The range of a local geometrical disorder and a physical range of interaction between stresses and positions of inclusions are obtained for investigated patterns.

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.

Prediction of the overall moduli of layered silicate-reinforced nanocomposites—part II: analyses

In this part of the two-part paper, the basic theory and formulas presented in Part I are applied to various montmorillonite silicate-reinforced polymeric nanocomposites. Considering the microstructural characteristics of composites containing intercalated silicate stacks, a hierarchical model is also proposed in this part to predict the overall moduli of these composites. Theoretical predictions are compared with experimental data for isotropic composites. It is found that for the chosen elastic constants of montmorillonite silicate, all the experimental results fall within the Hashin-Shtrikman bounds for two-phase isotropic composite materials, as does the theoretical prediction of the hierarchical model. The theoretical predictions for the intercalated and exfoliated nanocomposites are close to the experimental data for the considered cases. This paper also points to the need for further examinations of the so-called constrained region that has been widely mentioned in the literature. A simple model for calculating the overall moduli of composites containing constrained regions around the reinforcements is proposed. This simple model shows that the thickness of platelet-like inhomogeneities plays a very important role in stiffening composites containing constrained regions.

Synthesis of unsaturated polyesters for improved interfacial strength in carbon fibre composites

Carbon fibres are gaining use as reinforcement in glass fibre/polyester composites for increased stiffness as a hybrid composite. The mechanics and chemistry of the carbon fibre-polyester interface should be addressed to achieve an improvement also in fatigue performance and off-axis strength. To make better use of the versatility of unsaturated polyesters in a carbon fibre composite, a set of unsaturated polyester resins have been synthesized with different ratios of maleic anhydride, o-phthalic anhydride and 1,2-propylene glycol as precursors. The effective interfacial strength was determined by micro-Raman spectroscopy of a single-fibre composite tested in tension. The interfacial shear strength with untreated carbon fibres increased with increasing degree of unsaturation of the polyester, which is controlled by the relative amount of maleic anhydride. This can be explained by a contribution of chemical bonding of the double bonds in the polymer to the functional groups of the carbon fibre surface.

Viscoelastic Properties of Polyethylene Syntactic Foam with Polymer Microballoons

Syntactic foam products are most often made from glass microballoons embedded in a thermosetting polymer matrix, and they have good mechanical and thermal properties. However, the glass microballoons easily break in shear and are therefore very difficult to use for manufacturing methods that cause shearing of the material. Polymer microballoons are an alternative by which it is possible to produce a foamed product using unmodified commercial extruders or injection moulding machines. The present study deals with the viscoelastic properties of extruded polyethylene (PE) and a foam made from PE and approximately 40 volume percent of polymer microballoons. Results are shown from creep tests carried out at three temperatures and with three force levels, and from stress relaxation tests carried out at room temperature and with five deformation levels. The overall conclusion was that for some applications the foam will be the best choice, whereas for others it is more advantageous to use bulk polyethylene.

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.

Creep of Carbon/Polypropylene Model Composites: a Raman Spectroscopic Investigation

Abstract The paper considers the load-transfer mechanisms in carbon-fibre/polypropylene matrix model composites subjected to creep loading and subsequent recovery. The fibre strains are measured in situ by micro Raman spectroscopy. The coefficient of friction is calculated on the basis of the measured initial residual strains and the initial interfacial pressure on the fibre obtained from the Lame solution. A theoretical approach is utilised to describe the creep strain in the matrix material. The analysis shows that the load transfer between the fibre and the matrix is of a mechanical nature governed by the radial pressure on the fibre and the coefficient of friction. The calculations indicate that this load transfer mechanism will—for longer loading times—cause the composite to behave as a pure matrix with holes.

Statistical Model of Fracture in Materials with Disordered Microstructure

The discrete fracture model of disordered materials is presented. The disorder of materials is characterized by the second-order intensity function that is able to discriminate between different dispersion patterns. The truss-like model is constructed based upon the geometry of inclusions dispersion and the stress field imposed on the system. Correlation between the load carrying capacity as predicted by the model and the underlying microstructure has been established. The model simulates development of microcracks in a damaging regime and is able to mirror development of a single crack, as well. A morphology of the percolating crack is compared with respective descriptors of fracture obtained from experimental results.