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The behaviour of composite materials is often sensitive to changes in temperature. This arises for two main reasons. Firstly, the response of the matrix to an applied load is temperature-dependent and, secondly, changes in temperature can cause internal stresses to be set up as a result of differential thermal contraction and expansion of the two constituents. These stresses affect the thermal expansivity (expansion coefficient) of the composite. Furthermore, significant stresses are normally present in the material at ambient temperatures, since it has in most cases been cooled at the end of the fabrication process. Changes in internal stress state on altering the temperature can be substantial and may strongly influence the response of the material to an applied load. Creep behaviour is affected by this, particularly under thermal cycling conditions. Finally, the thermal conductivity of composite materials is of interest, since many applications and processing procedures involve heat flow of some type. This property can be predicted from the conductivities of the constituents, although the situation may be complicated by poor thermal contact across the interfaces.
Thermal expansion and thermal stresses
Thermal stresses and strains
Data for the thermal expansion coefficients (a) of matrices and reinforcements, as a function of temperature, are shown in Fig. 10.1. Polymers and metals generally expand more than ceramics. It can be seen that the differences in expansivity between fibre and matrix are large in many cases.
Composites make up a very broad and important class of engineering materials. World annual production is over 10 million tonnes and the market has in recent years been growing at 5–10% per annum. Composites are used in a wide variety of applications. Furthermore, there is considerable scope for tailoring their structure to suit the service conditions. This concept is well illustrated by biological materials such as wood, bone, teeth and hide; these are all composites with complex internal structures designed to give mechanical properties well suited to the performance requirements. Adaptation of manufactured composite structures for different engineering purposes requires input from several branches of science. In this introductory chapter, an overview is given of the types of composite that have been developed.
Types of composite material
Many materials are effectively composites. This is particularly true of natural biological materials, which are often made up of at least two constituents. In many cases, a strong and stiff component is present, often in elongated form, embedded in a softer constituent forming the matrix. For example, wood is made up of fibrous chains of cellulose molecules in a matrix of lignin, while bone and teeth are both essentially composed of hard inorganic crystals (hydroxyapatite or osteones) in a matrix of a tough organic constituent called collagen (Currey 1983). Commonly, such composite materials show marked anisotropy – that is to say, their properties vary significantly when measured in different directions.
The previous chapter covered factors affecting strength, which is related to the stresses at which damage and failure occur in composites. In many situations, the energy absorbed by the material under load is equally important. A tough material is one for which large amounts of energy are required to cause failure. In many loading configurations, such as when a component is struck by a projectile, only a finite amount of energy is available to cause failure. In other cases, such as with loads arising from temperature changes, only a finite degree of strain needs to be accommodated in order for the stresses to become small. In such situations, toughness, rather than strength, is the hey property determining whether the material is suitable. In this chapter, a brief outline is given of the basics of fracture mechanics, with particular reference to the energetics of interfacial damage. This is followed by an appraisal of the sources of energy absorption in composites. Finally, slow crack growth in composites is examined for conditions where fast fracture is not energetically favoured.
Fracture mechanics
The reader is referred to sources such as Gordon (1978), Ashby and Jones (1980) and Ewalds and Wanhill (1984) for introductions to fracture mechanics. In this section, the treatment is abbreviated and oriented towards effects in composites.
In the previous two chapters, some background was given about the various types of reinforcement and the ways in which they may be distributed within different matrices. In this chapter, attention is turned to the problem of predicting the behaviour of the resulting composites. Prime concern is with the mechanical properties. The incorporation of the reinforcement is usually aimed at enhancing the stiffness and strength of the matrix. The details of this enhancement can be rather complex and difficult to describe with complete rigour. The simplest starting point is to consider the elastic behaviour of a composite with continuous fibres, all aligned in the same direction. Aligned composites are normally used to exploit the stiffness (and strength) parallel to the fibres. However, it is also important to understand the way they behave when loaded in other directions. The treatment therefore includes the behaviour under transverse loading. In this chapter and in the following one, the assumption is made that there is perfect bonding between fibre and matrix across the interface between them. The detailed nature of the interfacial region, and the consequences of imperfect bonding, are considered in Chapter 7.
Axial stiffness
The simplest treatment of the elastic behaviour of aligned long-fibre composites is based on the premise that the material can be treated as if it were composed of parallel slabs of the two constituents bonded together, with relative thicknesses in proportion to the volume fractions of matrix and fibre.
The previous two chapters are concerned with the elastic behaviour of composites containing fibres which are, in effect, infinitely long. The preparation of composites containing short fibres (or equiaxed particles) allows scope for using a wider range of reinforcements and more versatile processing and forming routes (see Chapter 11). Thus, there is interest in understanding the distribution of stresses within such a composite, and the consequences of this for the stiffness and other mechanical properties. In this chapter, brief outlines are given of two analytical approaches to this problem. In the shear lag model, a cylindrical shape of reinforcements is assumed, and the stress fields in fibre and matrix are simplified so as to allow derivation of straightforward analytical expressions for the composite stiffness. The Eshelby method, on the other hand, is based on the assumption that the reinforcement has an ellipsoidal shape (which could range from a sphere to a cylinder or a plate). This allows derivation of an analytical solution which is more rigorous than that of the shear lag model, but with the penalty of greater mathematical complexity. In the treatment given here, attention is concentrated on the principle of the Eshelby approach; sources are suggested for readers needing more mathematical details.
The shear lag model
The most widely used model describing the effect of loading an aligned short-fibre composite is the shear lag model, originally proposed by Cox (1952) and subsequently developed by others (Outwater 1956, Rosen 1960, Dow 1963), which centres on the transfer of tensile stress from matrix to fibre by means of interfacial shear stresses.
The elastic behaviour of long- and short-fibre composites was described in Chapters 4 to 6. The stresses in the individual plies of a laminate under an external load and the stress distributions along short fibres were examined. This information is used to explore the ways in which a material suffers microstructural damage, leading to the ultimate failure of a component. There are two important aspects to this behaviour. Firstly, there is the deflection, degree of damage and ultimate failure of a component as a function of applied load. Secondly, there are the processes which cause absorption of energy within a composite material as it is strained. The latter determine the toughness of the material and are treated in Chapter 9. In the present chapter, attention is concentrated on predicting the applied stress at which damage and failure occur. The treatment is oriented towards long-fibre materials and laminates, and, in particular, towards polymer-based composites. Most of the principles apply equally to discontinuous reinforcement and other types of matrix. Some specific points concerning failure of such systems are dealt with in Chapter 9.
Failure modes of long-fibre composites
The application of an arbitrary stress state to a unidirectional lamina can lead to failure by one or more basic failure processes. The three most important types of failure are illustrated in Fig. 8.1. Large tensile stresses parallel to the fibres, σ1 lead to fibre and matrix fracture, with the fracture path normal to the fibre direction.
The preceding three chapters have dealt with the elastic behaviour of composites. Among the assumptions made in most of these treatments is that the interfacial bond is ‘perfect’. This means that there is no debonding, cracking or sliding – in fact, no elastic or inelastic processes of any description. In practice, many important phenomena may take place at the interface, depending on its structure and the stresses generated there. These processes tend to promote plastic deformation of the matrix and can also influence the onset and nature of failure. Before treating the strength and fracture behaviour of composites (Chapters 8 and 9), it is necessary to consider the interface and examine how its response can be characterised and influenced. In the present chapter, the meaning and measurement of bond strength are described. This is followed by an outline of the formation of interfacial bonds in various systems and a summary of the techniques used to influence the bonding characteristics.
Bonding mechanisms
Adsorption and wetting
If the surfaces of two bodies spontaneously come into intimate (atomic scale) contact when they are brought close to each other (commonly with one of the bodies in liquid form), then ‘wetting’ is said to have taken place. Adhesion is primarily caused by van der Waals forces, although other types of bonding may reinforce these. The occurrence of wetting can be treated using simple thermodynamics, but in practice there may be chemical changes taking place which are time-dependent. Fig. 7.1 illustrates solid/solid and solid/liquid interfaces.
Composite materials are used in a very wide range of industrial applications. In this chapter, the objective is to identify some of the considerations involved in commercial exploitation of composites. This is done by means of a few case studies and there is no attempt to present a systematic survey. The examples given cover a range of composite type, engineering complexity, manufacturing route, market size and competitive position relative to conventional materials. At the beginning of each case study, a list is given identifying the reasons for preferring a composite to more conventional engineering materials. Although the examples are spread over the full range of matrix types, the bulk of the annual composite production of around 10 million tonnes is currently in the form of PMCs. At the start of each example, a list is given of the requirements of the application.
Minesweeper hull
low density
ease of moulding to complex shape
non-magnetic
good resistance to corrosion and marine fouling
good resistance to fatigue and stress corrosion cracking
Glass-reinforced plastic (GRP) is now very popular for various land and sea transport applications. While large ships are usually constructed in steel, over 80% of marine hulls less than about 40 m in length are made of GRP (Smith 1990). This is partly because fabrication in GRP is more economic for relatively small craft.
In this chapter, the underlying science of fibres and matrices is described. Some specific examples are given to illustrate the key factors involved. A wide range of reinforcements, mostly in the form of fibres, is now available commercially. Their properties can be related directly to the atomic arrangement and the defect content of the reinforcement, which must be controlled in the manufacturing processes. Matrices may be based on polymers, metals or ceramics. The choice of matrix is related to the required properties, the intended applications of the composite and the method of manufacture. The properties of the matrix depend on microstructure which, in turn, depends on manufacturing route and subsequent thermal and mechanical treatments. Certain properties of the composite may be sensitive to the nature of the reinforcementi/matrix interface; this topic is covered in detail in Chapter 7.
Reinforcements
Many reinforcements are now available, some designed for a particular matrix system. A selection is listed in Table 2.1. Typical properties of fibres are given in Table 2.2. All have high stiffness and relatively low density. Carbon, glass and aramid fibres are now used extensively in polymer matrix composites. Carbon fibres are also important for carbon/ carbon composites. Ceramic fibres, whiskers and particles can be used to reinforce metal and ceramic matrices.
Electrons reflected from a crystal surface are generated by two scattering mechanisms. Bragg reflection, which is purely an elastic scattering process, is responsible for producing sharp peaks governed by Bragg's law. Inelastic scattering, which is dominated by valence-loss and thermal diffuse scattering (TDS), contributes a Kikuchi pattern background in the electron angular distribution and results in electron energy losses and momentum transfers. The excitation of Bragg reflections critically depends on the diffracting conditions, and the intensity distribution in a RHEED pattern is the result of dynamical scattering of electrons by the crystal surface. It is thus important to understand how electrons are reflected from the surface in order to illustrate the surface sensitivity of REM.
In this chapter, the physics of surface resonance in RHEED are systematically illustrated. Experimental results will be shown to exhibit the nature of surface resonance. It will be demonstrated that the surface sensitivity of RHEED will be dramatically enhanced by resonance. Finally, the effect of inelastic scattering on resonance reflection will be discussed.
The phenomenon
Surface resonance is one of the most important scattering processes in RHEED and REM. The surface resonance effect was first observed by Kikuchi and Nakagawa (1933); the reflected-electron intensity suddenly increases when the diffraction spot crosses an oblique Kikuchi line. This is illustrated by the RHEED pattern shown in Figure 4.1. When the resonance condition is not satisfied, there is no strongly reflected beam (Figure 4.1 (a)). The intensity is increased by almost an order of magnitude if the surface resonance is excited (Figure 4.1(b)).
Image calculations for REM are usually difficult because it is necessary to incorporate surface defects, such as steps and dislocations. This, in principle, can be done with the PeTSM theory; but, in practice, the huge amount of computation required and the sensitivity of REM image contrast to focus, beam convergence and diffracting conditions make the calculations rather involved and difficult compared with experimental observations. Attempts have been made to simulate surface step images (Peng and Cowley, 1986; Ma and Marks, 1990), but the results are still not very satisfactory. For this reason, in this chapter, the contrast mechanisms of REM imaging are described based on simplified models, in order to illustrate the physical concepts.
There are four basic contrast mechanisms in REM. Phase contrast (or Fresnel contrast) is produced by the path-length difference (or phase shift) of electron waves due to the change in surface morphology. This contrast dominates the images of atom-high surface steps. High-resolution information can be obtained from the phase contrast mechanism. Diffraction contrast (or Bragg contrast) is produced by the variation of local Bragg reflection angles due to lattice distortion from dislocations, local strain and crystal boundaries. Compositional contrast is produced by a variation in scattering power of different elements. This type of contrast appears on different surface domains or regions, depending on the local composition, and usually has relatively lower resolution. Finally, geometrical (or morphology) contrast is produced by variation in surface geometry, such as large surface steps and facets.