All structures are three-dimensional, and the exact analysis of stresses in them presents formidable difficulties. However, such precision is seldom needed, nor indeed justified, for the magnitude and distribution of the applied loading and the strength and stiffness of the structural material are not known accurately. For this reason it is adequate to analyse certain structures as if they are one- or two-dimensional. Thus the engineer's theory of beams is one-dimensional: the distribution of direct and shearing stresses across any section is assumed to depend only on the moment and shear at that section. By the same token, a plate, which is characterized by the fact that its thickness is small compared with its other linear dimensions, may be analysed in a two-dimensional manner. The simplest and most widely used plate theory is the classical small-deflexion theory which we will now consider.

The classical small-deflexion theory of plates, developed by Lagrange (1811), is based on the following assumptions:

1. (i) points which lie on a normal to the mid-plane of the undeflected plate lie on a normal to the mid-plane of the deflected plate;

2. (ii) the stresses normal to the mid-plane of the plate, arising from the applied loading, are negligible in comparison with the stresses in the plane of the plate;

3. (iii) the slope of the deflected plate in any direction is small so that its square may be neglected in comparison with unity;

4. […]

The exact large-deflexion analysis of plates generally presents considerable difficulties, but there are three classes of plate problems for which simplified theories are available for describing their behaviour under relatively high loading. These ‘asymptotic’ theories are membrane theory, tension field theory (sometimes called wrinkled membrane theory) and inextensional theory. All are described below. For a plate of perfectly elastic material, the error involved in using these theories tends to zero as the loading is increased or as the thickness is reduced. In any practical material, however, there is a limit to the elastic strain that may be developed, and this in turn limits the range of validity of these asymptotic theories to plates which are very thin. For steel and aluminium alloys, a typical limit to the elastic strain is 0.004, and this restricts the range of validity of the asymptotic theories as follows. For membrane theory and tension field theory the thickness must be less than about 0.001 of a typical planar dimension, while for inextensional theory the thickness must be less than about 0.01 of a typical planar dimension.

Membrane theory (considered by Föppl 1907)

When a thin plate is continuously supported along the boundaries in such a manner that restraint is afforded against movement in the plane of the plate, the load tends to be resisted to an increasing extent by middle-surface forces.

In the first edition of this book, I attempted to present a concise and unified introduction to elastic plate theory. Wherever possible, the approach was to give a clear physical picture of plate behaviour. The presentation was thus geared more towards engineers than towards mathematicians, particularly to structural engineers in aeronautical, civil and mechanical engineering and to structural research workers. These comments apply equally to this second edition. The main difference here is that I have included thermal stress effects, the behaviour of multi-layered composite plates and much additional material on plates in the largedeflexion régime. The objective throughout is to derive ‘continuum’ or analytical solutions rather than solutions based on numerical techniques such as finite elements which give little direct information on the significance of the structural design parameters; indeed, such solutions can become simply number-crunching exercises that mask the true physical behaviour.

Polymers have existed since the advent of life on earth. Natural rubber is still obtained from the rubber plant, and deposits of natural bitumen are also familiar. However, for present day engineering applications, very few natural polymers are likely to be specified, so attention must be focused on the synthetic variety, the earliest of which was a crude form of phenolic resin originating over 100 years ago. Since that time, development of polymers has posed a continual challenge to the suppliers of chemicals; the challenge also extends to designers who are perhaps not, as a group, as familiar with the ramifications of polymer technology as they are with more traditional materials. Any such difficulties as exist should be laid at the door of our educational system, despite the existence of many texts on the subject.

Polymers, as a class and in the present context, are chemical compounds based on carbon atoms; the compounds are complex, so cannot be defined as precisely as, for example, common table salt. A single polymer molecule might typically comprise many thousands of carbon atoms joined one to another, with the remaining available chemical bonds attached to other atoms such as oxygen, hydrogen, chlorine, nitrogen and sulphur, to mention just a few possibilities. To make a crude analogy, an assemblage of polymer molecules can be likened to a plate of spaghetti which has been well stirred ready for consumption.

It would be impertinent for the writer, who is after all a materials technologist and not a designer, to attempt to specify, even in general terms, the whole range of skills which a successful designer needs to employ in his profession. However, the hypothesis is still held that a designer is likely to focus his skills primarily upon the mechanical, aesthetic and functional requirements of products, and would not be expected to possess a general knowledge of all other aspects of the design process which would be available to him in a perfect world. When arriving at design decisions, experience makes a vital contribution, as it must seldom be possible to analyse in depth all aspects of an engineering problem by reducing every parameter to a numerical value. In our real world these decisions must be supported by an intuitive feel for their consequences, being in many cases arrived at from inadequate supporting data.

The following sections emphasise those aspects of the designer's work which are closely linked to the process of materials selection. The cataloguing of unfamiliar topics throughout this chapter should remind the reader of his need for expert advice from time to time; here, as in the rest of the book, the content of this chapter is designed to make the reader sufficiently familiar with the materials aspects of his problem that he can formulate questions properly and have some hope of understanding the expert's response.

This book does not aspire to discuss pure materials science topics, nor to offer comprehensive numerical design data for each material, although reference is made to underlying materials science concepts wherever opportune. It does, however, seek to identify those parameters which must be considered when selecting materials for use in engineering applications. Emphasis is put on the needs of manufacturing industry, which is defined for present purposes as involved in production of prefabricated parts and components intended for civil, domestic, marine, military, aerospace and chemical processing applications. The decision has been taken to omit all aspects of the building and construction industry, so no reference is made to concrete, timber, bitumens, soil and masonry.

The chapter on the impact of design on manufacturing industry is intended to demonstrate how correct selection of materials in terms of their performance, availability and cost, together with exploitation of available production capability, will enhance the profitability of a commercial operation.

Having embarked upon a design study, it is necessary for the expertise and judgement of the design engineer to be coordinated with those of other experts to produce the most effective result. The chapter on the design process draws attention to the variety of knowledge and advice which the designer needs to draw upon to make materials choices with a high level of confidence.

We have now arrived at the core of the book, the purpose of which is to introduce the designer to the main areas of materials technology. We first consider aspects of the design process which should point up the differences between the performance of classes of materials in practice; and then in later chapters we make a brief review of the main materials properties available. This done, we then consider the ‘envelope of properties’ of individual materials, which must be defined in order to demonstrate suitability for exploitation in particular designs.

The design process must take into consideration the many aspects of materials behaviour, so that there is never too great a mismatch between the materials actually selected and the realistic performance demanded of the final product. Table 3.1 (Judd 1983) identifies mechanical, thermal, electrical and other performance aspects of materials which have to be considered as a whole or in part during the initial design and materials selection processes. Many of these properties and responses to outside influences are functions of all materials used for engineering designs, although some specifically refer only to metals or only to non-metals.

The properties of materials selected control to a considerable degree, the fabrication methods that can be employed on the ultimate product. Aspects of production, apart from consideration of manufacturing volumes, include the weight of material needed, shapes and sizes of preformed components such as sheet metal and rod, part-size tolerances, and the surface finishes to be adopted.

For any company and its products to be successful in the market-place, most products must have a worthwhile lifetime and reliability in service to match the expectations of the purchaser. In order to achieve this the designer, among others, must have some feel for the ways in which the useful life in service of a material can be estimated, and must reflect these factors in his design. The purpose of this chapter is to discuss briefly some aspects of prediction of service life and the design needed to ensure that this life and a safe product results. Consideration of the design decisions for correct materials choice and the mechanisms of failure of materials in service is focused on metals and plastics as examples of the whole field of materials.

Predicting service life

Materials respond to their environments in a time-dependent manner, which is usually forecast from accelerated laboratory experiments; results of experiments are compared with what has been seen under real service conditions to prove and extend their validity. Provided that accelerating factors for laboratory tests are correctly chosen, and that the tests themselves are correctly representative of real life service, it is reasonable to expect that results can be used to calculate what must be done to achieve a predetermined life in service. Laboratory tests which attempt to simulate, in an accelerated way, real life exposures must of course be truly representative in a mechanistic way.

Metals pervade industrial life and are the obvious first choice for making industrial, professional or consumer durables of small to enormous dimensions. Products of metal range in size from a pin to a major suspension bridge or an ocean-going liner. Having said this, it is useful to understand the realities of sources of metals and their general supply characteristics, both in terms of world raw material availability and in terms of stock materials obtainable from a metals supplier. Varjian & Hall (1984) review the modern situation in some detail. A combination of high metal stocks in the London Metal Exchange warehouses, and a slow economic growth worldwide has conspired to put down the pressure on prices and hence to depress the staffing levels and profitability of mining and mining-related jobs in many countries. The authors then consider the mid-1980s situation for several metals.

In 1983, world production of aluminium was about 14 million tons of which half originated in the Americas, prices being around $0.8 per pound. Chromium is largely produced as chemical compounds, the amount of chromium-based alloys and basis metal being relatively small in the light of an annual South African chromium ore production of 2.4 million metric tons. The copper industry in 1983 continued to suffer from world oversupply of the metal, of which almost eight million tons were produced in the year, at prices of the order of $0.75 per pound.

When selecting materials the designer must be aware of those quasi-legal parameters against which his choice will be evaluated. He will initially generate a specification for his product: this will list comprehensively the technical and environmental requirements of the product for which materials must be found. Standards are then usually set up, defining technical performance limitations of candidate materials, processes and engineering practices, and will be used to validate final choices.

Specifications and standards are vital to successful industrial activity at all stages between product design and point of sale, where the customer's view of and expectations from his purchase have been moulded by what standards led him to expect.

Types of standards

Value standards are those which society expects to apply to the community as a whole: they include, for example, standards for clean water, regulation of emitted toxic gases and of radioactivity from industry. Davis (1984) has produced a review of UK environmental specifications in the last 25 years.

Regulatory standards may be developed by an industry to serve its own needs or image, or they may be imposed as mandatory by a Government Department. Examples are Health and Safety practices, and the control of industrial liquid effluent compositions.

Our present interest is specifically with materials and methods standards, which define achievable, and hence expected, performance parameters and the associated testing methods.