EARLY HISTORY AND GENERAL INTRODUCTION

The first discussions in the literature concerning the applications of SR in protein crystallography were given by Harrison (1973), Wyckoff (1973) and Holmes (1974). The first experimental tests were made on SPEAR by Webb et al (1976, 1977) and reported by Phillips et al (1976, 1977); precession photographs of protein crystals were obtained with a 60-fold reduction in exposure times over a home laboratory X-ray source (in this case a conventional fine focus Cu Kα tube running at 1200W) and test data were collected about the iron K edge for rubredoxin and the copper K edge for azurin. The azurin crystal suffered much less from radiation damage in the intense beam than during a longer equivalent exposure on a conventional source. This was the first indication that radiation damage to a protein crystal was less with a more intense X-ray source (figure 10.1). The anomalous dispersion effects using the Fe K edge enabled phases to be determined for rubredoxin with a mean figure of merit of 0.5 (mean phase error of 60°). The anomalous dispersion effects using the Cu K edge were used to confirm the copper sites in azurin utilising phases determined from conventional source data (Adman, Stenkemp, Sieker and Jensen 1978).

X-rays are used to probe the atomic or molecular structure of matter because the wavelength of the radiation is of approximately the same dimension as an atom. Similarly longer wavelength visible light is appropriate for studying larger structures, e.g. cell organelles. However, since there is no known X-ray lens the equivalent function of a glass lens for visible light in a conventional microscope has to be performed by computational transformation of X-ray diffraction patterns.

The basic steps in a macromolecular crystal structure analysis involve:

1. (i) crystallisation;

2. (ii) space group and cell parameter determination;

3. (iii) data collection;

4. (iv) phase determination;

5. (v) electron density map interpretation;

6. (vi) refinement of the molecular model.

Figure 2.1 (a)—(f) illustrates some of these steps showing, as an example, the structure determination of human erythrocyte purine nucleoside phosphorylase (PNP) (Ealick et al (1990)). A list of general texts on crystallography is given in the bibliography, section 1.

CRYSTALLISATION, CRYSTALS AND CRYSTAL PERFECTION, SYMMETRY

Crystallisation is a process involving precipitation of the dissolved protein from solution. This is achieved by decreasing the protein solubility, decreasing any repulsive forces between individual protein molecules and/or increasing the attractive forces. The crystals that might be produced need to be of ‘X-ray diffraction quality’.

The use of focussed, monochromatised radiation at the synchrotron has so far yielded the most results in terms of biological molecular structure compared with the other methods being developed. This is readily explained because of the ease with which the monochromatic diffraction data measured at the synchrotron have been processed with existing computer programs for data from monochromatic, emission line, laboratory X-ray sources. In contrast, the Laue method, although it is being very actively developed at the synchrotron (chapter 7), had been abandoned in the home laboratory. Hence, the monochromatic method is covered first in this book. In appendix 1 details are given of the various monochromatic diffraction geometries. These geometries are:

1. (a) monochromatic still exposure;

2. (b) rotation/oscillation geometry;

3. (c) Weissenberg geometry;

4. (d) precession geometry;

5. (e) diffractometry.

Quantitative X-ray crystal structure analysis usually involved methods (b), (c) and (e) although (d) has certainly been used. Photographic film is being replaced by use of electronic area detectors or, even more recently, the IP.

At the various synchrotrons all these geometries have been exploited for macromolecular crystal data collection as they have also on conventional X-ray sources. Once the polychromatic synchrotron X-ray beam has been rendered monochromatic the single crystal data can be measured and processed as for a conventional X-ray source.

Introduction

The term ‘flexible composites’ is used hereinafter to identify composites based upon elastomeric polymers of which the usable range of deformation is much larger than those of the conventional thermosetting or thermoplastic polymer-based composites (Chou and Takahashi 1987). The ability of flexible composites to sustain large deformation and fatigue loading and still provide high load-carrying capacity has been mainly analyzed in pneumatic tire and conveyor belt constructions. However, the unique capability of flexible composites is yet to be explored and investigated. This chapter examines the fundamental characteristics of flexible composites.

Besides tires and conveyor belts, flexible composites can be found in a wide range of applications. Coated (with PVC, Teflon, rubber, etc.) fabrics have been used for air- or cable-supported building structures, tents, parachutes, decelerators in high speed airplanes, bullet-proof vests, tarpaulin inflated structures such as boats and escape slides, safety nets, and other inexpensive products. Hoses, flexible diaphragms, racket strings, surgical replacements, geotextiles, and reinforced membrane structures in general are examples of flexible composites.

Following Chou (1989, 1990), the nonlinear elastic behavior of three categories of materials is examined: pneumatic tires, coated fabrics, and flexible composites containing wavy fibers. These materials provide the model systems of analysis with elastic behaviors ranging from small to large deformations.

The performance characteristics of pneumatic tires are primarily controlled by the anisotropic properties of the cord/rubber composite. The low modulus, high elongation rubber contains the air and provides abrasion resistance and road grip. The high modulus, low elongation cords carry most of the loads applied to the tire in service.

The science and technology of composite materials are based on a design concept which is fundamentally different from that of conventional structural materials. Metallic alloys, for instance, generally exhibit a uniform field of material properties; hence, they can be treated as homogeneous and isotropic. Fiber composites, on the other hand, show a high degree of spacial variation in their microstructures, resulting in non-uniform and anisotropic properties. Furthermore, metallic materials can be shaped into desired geometries through secondary work (e.g. rolling, extrusion, etc.); the macroscopic configuration and the microscopic structure of a metallic component are related through the processing route it undergoes. With fiber composites, the co-relationship between microstructure and macroscopic configuration and their dependence on processing technique are even stronger. As a result, composites technology offers tremendous potential to design materials for specific end uses at various levels of scale.

First, at the microscopic level, the internal structure of a component can be controlled through processing. A classical example is the molding of short-fiber composites, where fiber orientation, fiber length and fiber distribution may be controlled to yield the desired local properties. Other examples can be found in the filament winding of continuous fibers, hybridization of fibers, and textile structural forms based upon weaving, braiding, knitting, etc. In all these cases, the desired local stiffness, strength, toughness and other prespecified properties may be achieved by controlling the fiber type, orientation, and volume fraction throughout the structural component.

Evolution of engineering materials

Compared to the evolution of metals, polymers and ceramics, the advancement of fiber composite materials is relatively recent. Ashby (1987) presented a perspective on advanced materials and described the evolution of materials for mechanical and civil engineering. The relative importance of four classes of materials (metal, polymer, ceramic and composite) is shown in Fig. 1.1 as a function of time. Before 2000 BC, metals played almost no role as engineering materials; engineering (housing, boats, weapons, utensils) was dominated by polymers (wood, straw, skins), composites (like straw bricks) and ceramics (stone, flint, pottery and, later, glass). Around 1500 BC, the consumption of bronze might reflect the dominance in world power and, still later, iron. Steel gained its prominence around 1850, and metals have dominated engineering design ever since. However, in the past two decades, other classes of materials, including high strength polymers, ceramics, and structural composites, have been gaining increasing technological importance. The growth rate of carbon-fiber composites is at about 30% per year – the sort of growth rate enjoyed by steel at the peak of the Industrial Revolution. According to Ashby the new materials offer new and exciting possibilities for the designer and the potential for new products.

Fiber composite materials

Fiber composites are hybrid materials of which the composition and internal architecture are varied in a controlled manner in order to match their performance to the most demanding structural or non-structural roles.

Introduction

Three-dimensional textile preforms are fully integrated continuous-fiber assemblies with multi-axial in-plane and out-of-plane fiber orientations (Chou, McCullough and Pipes 1986; Ko 1989a). Composites reinforced with three-dimensional preforms exhibit several distinct advantages which are not realized in traditional laminates. First, because of the out-of-plane orientation of some fibers, three-dimensional preforms provide enhanced stiffness and strength in the thickness direction. Second, the fully integrated nature of fiber arrangement in three-dimensional preforms eliminates the inter-laminar surfaces characteristic of laminated composites. The superior damage tolerance of three-dimensional textile composites based upon polymer, metal and ceramic matrices has been demonstrated in impact and fracture resistance. Third, the technology of textile preforming provides the unique opportunity of near-net-shape design and manufacturing of composite components and, hence, minimizes the need for cutting and joining the parts. The potential of reducing manufacturing costs for special applications is high. The overall challenges and opportunities in three-dimensional textile structural composites are very fascinating.

Three-dimensional textile preforms can be categorized according to their manufacturing techniques. These include braiding, weaving, knitting and stitching, as shown in Fig. 7.1.

There are three basic braiding techniques for forming three-dimensional preforms, namely 2-step, 4-step and solid braidings. In the case of 2-step braiding, the axial yarns are stationary and the braider yarns move among the axials. Thus, the axial yarns are responsible for the high stiffness and strength in the longitudinal direction and relatively low Poisson contraction. A high degree of flexibility in manufacturing can be achieved in 2-step braiding by varying the material and geometric parameters of the axial and braider yarns.

Introduction

Laminated composites are made by bonding unidirectional laminae together in predetermined orientations. The basis for analysis of thin laminated composites is the classical plate theory. When the thickness direction properties significantly contribute to the response of the laminate to an externally applied elastic field, the classical plate theory breaks down.

Fundamental to the treatment of thin laminates is the knowledge of the thermoelastic properties of a unidirectional lamina. These properties are predictable from the corresponding properties of constituent fiber and matrix materials as well as the fiber volume fraction. Having established the elastic response of a unidirectional lamina, the behavior of laminated composites is then analyzed from the strain and curvature of the mid-plane of the laminate as well as the force and moment resultants acting on its boundary edges. Because of the complexity of the constitutive equations for a general anisotropic laminated plate, simplifications of the stress–strain relations are accomplished through the manipulation of the geometric arrangement of the laminae. The lamination theory is a relatively mature subject; its treatment can be found in text books of, for instance, Ashton, Halpin and Petit (1969), Jones (1975), Vinson and Chou (1975), Christensen (1979), Tsai and Hahn (1980), Carlsson and Pipes (1987), and Chawla (1987), and in the review articles of Chou (1989a and b). A modification of the classical plate theory is in the inclusion of higher order terms in the displacement field expansion to account for the transverse shear deformation. An outline of such modifications adopted by various researchers is presented.

Introduction

Composites reinforced with discontinuous fibers are categorized here as short-fiber composites. The fiber aspect ratio (length/diameter = l/d) is often used as a measurement of fiber relative length. Depending upon the dispersion of fibers in the matrix, the relevant d values may include those of the filaments, strands, rovings, as well as other forms of fiber bundles. Although discontinuous fibers such as whiskers have been used to reinforce metals and ceramics, the majority of short-fiber composites are based upon polymeric matrices. Discontinuous fiber-reinforced plastics are attractive in their versatility in properties and relatively low fabrication costs. The concern of the rapid depletion of world resources in metals and the search for energy-efficient materials has contributed to the increasing interest in composite materials. Discontinuous fiber-reinforced plastics will constitute a major portion of the demand of composites in automotive, marine and aeronautic applications.

A discontinuous fiber composite usually consists of relatively short, variable length, and imperfectly aligned fibers distributed in a continuous-phase matrix. In polymeric composites the fibers are mostly glass, although carbon and aramid are also used; non-fibrous fillers are often added. The orientation of the fibers depends upon the processing conditions employed and may vary from random in-plane and partially aligned to approximately uniaxial.

The understanding of the behavior of short-fiber composites is complicated by the non-uniformity in fiber length and orientation as well as the interaction between the fiber and matrix at fiber ends (Chou and Kelly 1976, 1980).

Introduction

Fiber-reinforced composites are a valuable class of engineering materials because they can exhibit both high stiffness and strength simultaneously, in contrast to more homogeneous materials which are generally brittle and defect sensitive. In fiber composites, the inherent lack of toughness of the reinforcing fiber, or its sensitivity to microstructural defects, is overcome by the local redundancy of the composite structure, so that its strength may be utilized effectively. Individual fibers are relatively weakly coupled by the matrix so that failure of one fiber does not generally precipitate immediate failure of the composite as a whole, allowing high strength and stiffness to be achieved in the fiber direction.

The tensile failure of a fiber-reinforced material is a complex process which involves an accumulation of microstructural damage. Unlike homogeneous brittle materials, fiber composites do not contain a population of observable pre-existing defects, one of which ultimately precipitates failure. Instead, an accumulation of fiber or matrix fractures develops as the material is loaded and this constitutes a ‘critical defect’ in a macroscopic view of the fracture. Fracture mechanics may successfully account for the strength of single fibers, but it is inadequate to extend its application to unidirectional fiber composites when the overall behavior is dominated by the probability of defects in fibers propagating under the stress concentrations surrounding previous fiber fractures as well as the probability of defects in the matrix which are responsible for the multiplication of transverse cracks. Consequently, the statistical process of damage development in composites needs to be emphasized (Manders, Bader and Chou 1982).

Introduction

The term ‘hybrid composites’ is used to describe composites containing more than one type of fiber materials. Hybrid composites are attractive structural materials for the following reasons. First, they provide designers with the new freedom of tailoring composites and achieving properties that cannot be realized in binary systems containing one type of fiber dispersed in a matrix. Second, a more cost-effective utilization of expensive fibers such as carbon and boron can be obtained by replacing them partially with less expensive fibers such as glass and aramid. Third, hybrid composites provide the potential of achieving a balanced pursuit of stiffness, strength and ductility, as well as bending and membrane related mechanical properties. Hybrid composites have also demonstrated weight savings, reduced notch sensitivity, improved fracture toughness, longer fatigue life and excellent impact resistance (Chou and Kelly 1980a). Some of the pioneering studies on this topic can be found in the work of Wells and Hancox (1971), Hayashi (1972), Kalnin (1972), Hancox and Wells (1973), Bunsell and Harris (1974), Harris and Bunsell (1975), Walton and Majumdar (1975), Aveston and Sillwood (1976), Bunsell (1976), Harris and Bradley (1976), Zweben (1977), Arrington and Harris (1978), Badar and Manders (1978, 1981a,b), Marom, Fischer, Tuler and Wagner (1978), Rybicki and Kanninen (1978), Summerscales and Short (1978), Aveston and Kelly (1980), Wagner and Marom (1982), Fukuda (1983a–c), and Harlow (1983).

Depending upon the arrangements of fibers and pre-preg layers, hybrids can be categorized into the following types. In the first type the different fiber materials are intimately mixed together and infiltrated with a matrix simultaneously.

Introduction

Flexible composites, which are described in Chapter 8, behave very differently from conventional rigid polymer composites in the following ways:

1. (1) Flexible composites are highly anisotropic (i.e. longitudinal elastic modulus/transverse elastic modulus » 1). Figure 9.1 compares the normalized effective Young's modulus (Exx/E22) vs. fiber orientation for two types of unidirectional composites. The upper curve obtained from Kevlar- 49/silicone elastomer shows that the stiffness of the elastomeric composite lamina is very sensitive to the fiber orientation. At a 5δ off-axis fiber orientation, for example, a 1° change in fiber angle causes the effective stiffness to change by 53%. The lower curve obtained from Kevlar- 49/epoxy shows less than 7% change at the same off-axis angle.

2. (2) Flexible composites show low shear modulus and hence large shear distortion, which allows the fibers to change their orientations under loading.

3. (3) Flexible composites have a much larger elastic deformation range than that of conventional rigid polymer composites. Thus, the geometric changes of the configuration (i.e. area, direction, etc.) need to be taken into consideration.

4. (4) The nonlinear elastic behavior with stretching–shear coupling, due to material and geometrical effects, is pronounced in flexible composites under finite deformation.

Therefore, the conventional linear elastic theory, based on the infinitesimal strain assumption for rigid matrix composites, may no longer be applicable to elastomeric composites under finite deformation.

The theories of non-linear and finite elasticity made a major advancement during the Second World War, in response to the development of the rubber industry. M. Mooney, in 1940, advanced his well-known strain–energy function.