Plasticity and fracture of composites

If the fibres are uniaxial, there is still some symmetry in the material, and the number of parameters needed to describe the elastic behaviour is smaller than 21, the value for a triclinic lattice. If the fibres are directed, but their positions in space are irregular or arranged on a hexagonal lattice, the material is transversally isotropic i. e., its properties are the same in all directions perpendicular to the fibre direction. In this case, there are five independent elastic constants (see section 2.4.6). If the fibres are uniaxial and arranged on a rectangular lattice, the material is orthotropic, and the number of independent elastic components is nine (see section 2.4.5). 

To determine the elastic constants, empiric equations are frequently used that provide a useful approximation, often even in the case of non-continuous fibres. One example are the so-called Halpin-Tsai equations [29]. 

It was already discussed that one of the advantages of composites is the fact that the strengthening phase cannot contain defects larger than its extension. For fibre composites, which are our focus here, the crucial dimension is the fibre diameter. Carbon fibres are used with diameters of less than 5 pm if the objective is to increase the strength as much as possible. 

We saw in the previous section that the elastic properties of a composite can be described using a rule of mixtures. This, however, is usually not the case for the plastic and the failure behaviour. 

In this section, we start by discussing the behaviour of fibre composites under tensile loads, at first for the simplest case of continuous fibres. Subsequently, we will discuss the load transfer between the matrix and non-continuous fibres and see how this determines the failure properties and the fracture toughness of the material. For this, we also have to consider that fibre properties are statistically distributed. Finally, we will discuss the behaviour under compressive loads, loads perpendicular to fibre direction, and arbitrarily oriented loads. 

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Gaymans R.J., Oostenbrink A.J., A.C.M. van Bennekom, Klaren J.E., Plastic Institute of London, Conf. Preprints on deformation and fracture of composites, April 1991, paper 23... 

Boniface L, Ogin SL, Smith PA. Damage development in woven glass/epoxy laminates under tensile load. In Proceedings second international conference on deformation and fracture of composites, Manchester, UK. London Plastics and Rubber Institute 1993. 

Plastic Forming and Fracture of Metals and Alloys and of Composites 358... 

PLASTIC FORMING AND FRACTURE OF METALS AND ALLOYS AND OF COMPOSITES... 

Two approaches have been taken to produce metal-matrix composites (qv) incorporation of fibers into a matrix by mechanical means and in situ preparation of a two-phase fibrous or lamellar material by controlled solidification or heat treatment. The principles of strengthening for alloys prepared by the former technique are well estabUshed (24), primarily because yielding and even fracture of these materials occurs while the reinforcing phase is elastically deformed. Under these conditions both strength and modulus increase linearly with volume fraction of reinforcement. However, the deformation of in situ, ie, eutectic, eutectoid, peritectic, or peritectoid, composites usually involves some plastic deformation of the reinforcing phase, and this presents many complexities in analysis and prediction of properties. 

Such soft-touch materials are usually TP Vs or thermoplastic elastomers (TPEs) which combine the moldability of thermoplastics in the melt state with elasticity, lower hardness, fracture resistance, and surface characteristics of elastomers. However, plastics and elastomers respond differently to mechanical stress. Hence, both rheological behavior and mechanical strength will to a large extent depend on the morphology of the blend which may change with change in the composition. 

Fig. 6.7. A model for plastic bending of fiber and fragmentation of matrix during fracture of randomly oriented fiber composites. After Helfet and Harris (1972) and Hing and Groves (1972).

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