Fibre-reinforced composites, theory

Several recent papers have maintained interest in crystalline deformation processes. Shinozaki and Groves suggest that a theory proposed for fibre reinforced composites by Kelly and Davies is helpful in describing the tensile yield behaviour of oriented polypropylene. Three distinct failure mechanisms are proposed, as depicted in Fig. 8. 

Characteristic material properties for fibre reinforced composites cannot be so rigorously defined as for most other structural materials. Standard data are either not generally available or cannot be relied upon except for preliminary design. Because of its nonhomogeneity and anisotropy, up to 21 elastic constants may, in theory, be required for a full analysis of a complex laminate. In practice though, due to symmetry, these reduce to ... 

Abstract This chapter describes the elastic qualities of advanced fibre-reinforced composites, in terms of characterization, measurement and prediction from the basic constituents, i.e. the fibre and matrix. The elastic analysis comprises applying micromechanics approaches to predict the lamina elastic properties from the basic constituents, and using classical lamination theory to predict the elastic properties of composite materials composed of several laminae stacked at different orientations. Examples are given to illustrate the theoretical analysis and give a full apprehension of its prediction capability. The last section provides an overview on identification methods for elastic proprieties based on full-field measurements. It is shown that these methodologies are very convenient for elastic characterization of anisotropic and heterogeneous materials. 

Pindera, J. M., Aboudi, J., Arnold, S. M. (1998) Higher-order micro-macrostructural theory for the analysis of functionally graded materials , in Advanced Multilayered and Fibre-Reinforced Composites, Y. M. Haddad ed. London Kluwer Academic Publishers, pp. 111-32. 

The fibre-reinforced composites, namely asbestos cements and glass fibre-reinforced polymers, were analyzed as a two-phase material already by Krenchel (1964). He proposed two different theories to calculate Young s modulus and in the second the Poisson ratio is also given ... 

Both presented theories lead to similar conclusions concerning the cracking strain of reinforced matrices however, both exaggerate the influence of fibres. After the crack opening, the ACK theory may be used to calculate the probable crack spacing and the composite s Young s modulus. Furthermore, in that theory, a few of the parameters used are taken from the testing of relevant composite elements and therefore it is to some extent more appropriate for verification and calibration than other proposed theories for fibre-reinforced composites. 

Earlier authors proposed theories which predict the speed of viscoelastic crack propagation, by assigning a detailed structure to the crack tip, both under unstable and subcritical or fatigue failure. We mention Knauss (1970, 1974), Knauss and Dietmann (1970), Mueller and Knauss (1971) and a review by Knauss (1973) also the work of Wnuk (1971-73b). Later, there was the work of Schapery (1974-79), McCartney (1977-79) and Golden and Graham (1984). See also Kanninen and Popelar (1985). Majidzadeh et al. (1976) discuss various models in the context of application to pavement design. McCartney (1987) is concerned with crack extension criteria for fibre-reinforced composites. 

H. Ichikawa and T. Ishikawa, Silicon carbide fibres, in Comprehensive Composite Materials, A. Kelly and C. Zweben (eds), Vol. 1 Fibre Reinforcements and Theory of Composites, Elsevier Science, Amsterdam, 2000, p. 107. 

In-plane alignment of the fibres Due to the very nature of the technique used for processing the NW composites, inplane alignment of the NWs is a realistic possibility. From the Krenchel theory of short-fibre reinforcements [20], the orientation and length effects can be incorporated using an efficiency factor to evaluate E,... 

Recently, much attention is being placed on fibres-reinforced/polymer systems as subjects of study. It was caused by increasing emphasis on high performance reinforced polymer composites. The concept of acid/base interactions across the fibre/polymer interface was noted particularly and the relevance of acid/base theories to the behaviour of po-... 

Two concepts from fibre-reinforcement theory are of general use in polymer mechanics. The first is the effect of inclusion shape on the anisotropic elastic moduli of a composite. Two rules control the effects of fibre reinforcement ... 

The analytical approach to the problem of multiple cracking in fibre-reinforced brittle matrix composites was examined by many authors and a few papers by Aveston, Kelly and their co-workers are particularly important (e.g. Aveston et al. 1971). That approach, called the ACK theory is one of the well-known theories of fibrous composites. It was later described in several books, (e.g. Hannant 1978 Bentur and Mindess 2006) and that is why it is only briefly mentioned in Section 10.1.2. 

A composite with equal amounts of fibre in the longitudinal and transverse directions has equal strength and stiffness in the two directions. However, neither would be as high as in the uni-directional case. In theory, if that same amount of fibre was randomly laid in-plane (isotropically), then the resulting composite would have equal strength and stiffness in all in-plane directions but less than in the bi-directional case (in the axes of the fibres). The directionality of the reinforcement has a significant effect on the amount of reinforcement which can be packed into a composite. 

This is Volume 2 of Natural Rubber Materials and it covers natural rubber-based composites and nanocomposites in 27 chapters. It focuses on the different types of fillers, the filler matrix reinforcement mechanisms, manufacturing techniques, and applications of natural rubber-based composites and nanocomposites. The first 4 chapters deal with the present state of art and manufacturing methods of natural rubber materials. Two of these chapters explain the theory of reinforcement and the various reinforcing nanofillers in natural rubber. Chapters 5 to 19 detail the natural rubber composites and nanocomposites with various fillers sueh as siliea, glass fibre, metal oxides, carbon black, clay, POSS and natural fibres ete. Chapters 20-26 discuss the major characterisation techniques and the final ehapter covers the applications of natural rubber composites and nanoeomposites. By covering recent developments as well as the future uses of rubber, this volume will be a standard reference for scientists and researchers in the field of polymer chemistry for many years to come. 

A more realistic model is that proposed by P.E.Chen. Using the finite elements theory, the author takes into consideration the interactions between fibres. He found a plateau for the fracture effort of the unidirectional composites. The maximal effort supported for a epoxy/glass fibres composite does not overtake 60% from that one corresponding to the same matrix, but reinforced with continuous fibres. 

The fibres in short fibre composites are not usually fiilly aligned. An early attempt to deal with such systems was made by Brody and Ward [12], who applied the aggregate model of Section 7.5 above assuming that the elastic constants of a representative unit of structure could be predicted by Equations (8.7a)-(8.7e). It was found that this simple theory fitted the results for composites reinforced with short fibres of carbon or glass reasonably well, with the moduli lying close to the lower Reuss bounds. Recent studies by Ward and co-workers [13] have shown that this approach is viable provided that the elastic constants of the representative unit are calculated more exactly. 

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