D. Designing with metals, ceramics, polymers and composites

288



Engineering Materials 2



Design with materials



289



Chapter 27

Design with materials



Introduction

Design is an iterative process. You start with the definition of a function (a pen, a

hairdryer, a fuel pin for a nuclear reactor) and draw on your knowledge (the contents of

this book, for instance) and experience (your successes and failures) in formulating a

tentative design. You then refine this by a systematic process that we shall look at later.

Materials selection is an integral part of design. And because the principles of mechanics, dynamics and so forth are all well established and not changing much, whereas

new materials are appearing all the time, innovation in design is frequently made

possible by the use of new materials. Designers have at their disposal the range of

materials that we have discussed in this book: metals, ceramics, polymers, and combinations of them to form composites. Each class of material has its own strengths and

limitations, which the designer must be fully aware of. Table 27.1 summarises these.

Table 27.1. Design-limiting properties of materials



Material



Good



Poor



Metals

High E, KIC

Low sy



Stiff (E ≈ 100 GPa)

Ductile (ef ≈ 20%) – formable

Tough (KIC > 50 MPa m1/2)

High MP (Tm ≈ 1000°C)

T-shock (DT > 500°C)



Yield (pure, sy ≈ 1 MPa) → alloy

Hardness (H ≈ 3sy) → alloy

1

Fatigue strength (se = – sy)

2

Corrosion resistance → coatings



Ceramics

High E, sy

Low KIC



Stiff (E ≈ 200 GPa)

Very high yield, hardness (sy > 3 GPa)

High MP (Tm ≈ 2000°C)

Corrosion resistant

Moderate density



Very low toughness (KIC ≈ 2 MPa m1/2)

T-shock (DT ≈ 200°C)

Formability → powder methods



Polymers

Adequate sy , KIC

Low E



Ductile and formable

Corrosion resistant

Low density



Low stiffness (E ≈ 2 GPa)

Yield (sy = 2–100 MPa)

Low glass temp (Tg ≈ 100°C) → creep

Toughness often low (1 MPa m1/2)



Composites

High E, sy , KIC

but cost



Stiff (E > 50 GPa)

Strong (sy ≈ 200 MPa)

Tough (KIC > 20 MPa m1/2)

Fatigue resistant

Corrosion resistant

Low density



Formability

Cost

Creep (polymer matrices)



290



Engineering Materials 2



At and near room temperature, metals have well-defined, almost constant, moduli

and yield strengths (in contrast to polymers, which do not). And most metallic alloys

have a ductility of 20% or better. Certain high-strength alloys (spring steel, for instance) and components made by powder methods, have less – as little as 2%. But

even this is enough to ensure that an unnotched component yields before it fractures,

and that fracture, when it occurs, is of a tough, ductile, type. But – partly because of

their ductility – metals are prey to cyclic fatigue and, of all the classes of materials,

they are the least resistant to corrosion and oxidation.

Historically, design with ceramics has been empirical. The great gothic cathedrals,

still the most impressive of all ceramic designs, have an aura of stable permanence. But

many collapsed during construction; the designs we know evolved from these failures.

Most ceramic design is like that. Only recently, and because of more demanding structural applications, have design methods evolved.

In designing with ductile materials, a safety-factor approach is used. Metals can be

used under static loads within a small margin of their ultimate strength with confidence that they will not fail prematurely. Ceramics cannot. As we saw earlier, brittle

materials always have a wide scatter in strength, and the strength itself depends on

the time of loading and the volume of material under stress. The use of a single,

constant, safety factor is no longer adequate, and the statistical approach of Chapter 18

must be used instead.

We have seen that the “strength” of a ceramic means, almost always, the fracture or

crushing strength. Then (unlike metals) the compressive strength is 10 to 20 times larger

than the tensile strength. And because ceramics have no ductility, they have a low

tolerance for stress concentrations (such as holes and flaws) or for high contact stresses

(at clamping or loading points, for instance). If the pin of a pin-jointed frame, made of

metal, fits poorly, then the metal deforms locally, and the pin beds down, redistributing the load. But if the pin and frame are made of a brittle material, the local contact

stresses nucleate cracks which then propagate, causing sudden collapse. Obviously,

the process of design with ceramics differs in detail from that of design with metals.

That for polymers is different again. When polymers first became available to the

engineer, it was common to find them misused. A “cheap plastic” product was one

which, more than likely, would break the first time you picked it up. Almost always

this happened because the designer used a polymer to replace a metal component,

without redesign to allow for the totally different properties of the polymer. Briefly,

there are three:

(a) Polymers have much lower moduli than metals – roughly 100 times lower. So

elastic deflections may be large.

(b) The deflection of polymers depends on the time of loading: they creep at room

temperature. A polymer component under load may, with time, acquire a permanent set.

(c) The strengths of polymers change rapidly with temperature near room temperature. A polymer which is tough and flexible at 20°C may be brittle at the temperature of a household refrigerator, 4°C.

With all these problems, why use polymers at all? Well, complicated parts performing several functions can be moulded in a single operation. Polymer components can



Design with materials



291



be designed to snap together, making assembly fast and cheap. And by accurately

sizing the mould, and using pre-coloured polymer, no finishing operations are necessary. So great economies of manufacture are possible: polymer parts really can be

cheap. But are they inferior? Not necessarily. Polymer densities are low (all are near

1 Mg m−3); they are corrosion-resistant; they have abnormally low coefficients of friction; and the low modulus and high strength allows very large elastic deformations.

Because of these special properties, polymer parts may be distinctly superior.

Composites overcome many of the remaining deficiencies. They are stiff, strong and

tough. Their problem lies in their cost: composite components are usually expensive,

and they are difficult and expensive to form and join. So, despite their attractive

properties, the designer will use them only when the added performance offsets the

added expense.

New materials are appearing all the time. New polymers with greater stiffness and

toughness appear every year; composites are becoming cheaper as the volume of their

production increases. Ceramics with enough toughness to be used in conventional

design are becoming available, and even in the metals field, which is a slowly developing one, better quality control, and better understanding of alloying, leads to

materials with reliably better properties. All of these offer new opportunities to the

designer who can frequently redesign an established product, making use of the properties of new materials, to reduce its cost or its size and improve its performance and

appearance.



Design methodology

Books on design often strike the reader as vague and qualitative; there is an implication that the ability to design is like the ability to write music: a gift given to few. And

it is true that there is an element of creative thinking (as opposed to logical reasoning

or analysis) in good design. But a design methodology can be formulated, and when

followed, it will lead to a practical solution to the design problem.

Figure 27.1 summarises the methodology for designing a component which must

carry load. At the start there are two parallel streams: materials selection and component design. A tentative material is chosen and data for it are assembled from data

sheets like the ones given in this book or from data books (referred to at the end of this

chapter). At the same time, a tentative component design is drawn up, able to fill the

function (which must be carefully defined at the start); and an approximate stress

analysis is carried out to assess the stresses, moments, and stress concentrations to

which it will be subjected.

The two streams merge in an assessment of the material performance in the tentative design. If the material can bear the loads, moments, concentrated stresses (etc.)

without deflecting too much, collapsing or failing in some other way, then the design

can proceed. If the material cannot perform adequately, the first iteration takes place:

either a new material is chosen, or the component design is changed (or both) to

overcome the failing.

The next step is a detailed specification of the design and of the material. This may

require a detailed stress analysis, analysis of the dynamics of the system, its response



292



Engineering Materials 2



Fig. 27.1. Design methodology.



Design with materials



293



to temperature and environment, and a detailed consideration of the appearance and

feel (the aesthetics of the product). And it will require better material data: at this point

it may be necessary to get detailed material properties from possible suppliers, or to

conduct tests yourself.

The design is viable only if it can be produced economically. The choice of production and fabrication method is largely determined by the choice of material. But the

production route will also be influenced by the size of the production run, and how

the component will be finished and joined to other components; each class of material

has its own special problems here; they were discussed in Chapters 14, 19, 24 and 25.

The choice of material and production route will, ultimately, determine the price of the

product, so a second major iteration may be required if the costing shows the price to

be too high. Then a new choice of material or component design, allowing an alternative production path, may have to be considered.

At this stage a prototype product is produced, and its performance in the market is

assessed. If this is satisfactory, full-scale production is established. But the designer’s

role does not end at this point. Continuous analysis of the performance of a component usually reveals weaknesses or ways in which it could be improved or made more

cheaply. And there is always scope for further innovation: for a radically new design,

or for a radical change in the material which the component is made from. Successful

designs evolve continuously, and only in this way does the product retain a competitive position in the market place.



Further reading

(a) Design

G. Pahl and W. Beitz, Engineering Design, The Design Council, 1984.

V. Papanek, Design for the Real World, Random House, 1971.

(b) Metals

ASM Metals Handbook, 8th edition, American Society for Metals, 1973.

Smithells’ Metals Reference Book, 7th edition, Butterworth-Heinemann, 1992.

(c) Ceramics

W. E. C. Creyke, I. E. J. Sainsbury, and R. Morrell, Design with Non-Ductile Materials, Applied

Science Publishers, 1982.

D. W. Richardson, Modern Ceramic Engineering, Marcel Dekker, 1982.

(d) Polymers

DuPont Design Handbooks, DuPont de Nemours and Co., Polymer Products Department,

Wilmington, Delaware 19898, USA, 1981.

ICI Technical Services Notes, ICI Plastics Division, Engineering Plastics Group, Welwyn Garden

City, Herts., England, 1981.



294



Engineering Materials 2



(e) Materials selection

J. A. Charles and F. A. A. Crane, Selection and Use of Engineering Materials, 2nd edition, ButterworthHeinemann, 1989.

M. F. Ashby, Materials Selection in Mechanical Design, Pergamon, 1992.

M. F. Ashby and D. Cebon, Case Studies in Materials Selection, Granta Design, 1996.



Problems

27.1 You have been asked to prepare an outline design for the pressure hull of a deepsea submersible vehicle capable of descending to the bottom of the Mariana Trench

in the Pacific Ocean. The external pressure at this depth is approximately 100 MPa,

and the design pressure is to be taken as 200 MPa. The pressure hull is to have

the form of a thin-walled sphere with a specified radius r of 1 m and a uniform

thickness t. The sphere can fail in one of two ways:

external-pressure buckling at a pressure p b given by

2



 t

pb = 0.3E   ,

 r

where E is Young’s modulus; yield or compressive failure at a pressure p f given

by

 t

pf = 2σ f   ,

 r



where σ f is the yield stress or the compressive failure stress as appropriate.

The basic design requirement is that the pressure hull shall have the minimum possible mass compatible with surviving the design pressure.

By eliminating t from the equations, show that the minimum mass of the hull is

given by the expressions

 ρ 

mb = 22.9r 3 p 0.5  0.5  ,

b

E 



for external-pressure buckling, and



 ρ

mf = 2πr 3 pf   ,

σf 

for yield or brittle compressive failure. Hence obtain a merit index to meet the

design requirement for each of the two failure mechanisms. [You may assume

that the surface area of the sphere is 4π r 2.]

Answers: E 0.5/ρ for external-pressure buckling; σ f/ρ for yield or brittle compressive

failure.

27.2 For each material listed in the following table, calculate the minimum mass and

wall thickness of the pressure hull of Problem 27.1 for both failure mechanisms at

the design pressure.



Design with materials



E (GPa)



Material

Alumina

Glass

Alloy steel

Titanium alloy

Aluminium alloy



s f (MPa)



Density, r (kg m−3)



390

70

210

120

70



5000

2000

2000

1200

500



295



3900

2600

7800

4700

2700



Hence determine the limiting failure mechanism for each material. [Hint: this is

the failure mechanism which gives the larger of the two values of t.]

What is the optimum material for the pressure hull? What are the mass, wall

thickness and limiting failure mechanism of the optimum pressure hull?

Answers:

Material

Alumina

Glass

Alloy steel

Titanium alloy

Aluminium alloy



mb (tonne)



tb (mm)



mf (tonne)



tf (mm)



Limiting failure mechanism



2.02

3.18

5.51

4.39

3.30



41

97

56

74

97



0.98

1.63

4.90

4.92

6.79



20

50

50

83

200



Buckling

Buckling

Buckling

Yielding

Yielding



The optimum material is alumina, with a mass of 2.02 tonne, a wall thickness of

41 mm and a limiting failure mechanism of external-pressure buckling.

27.3 Briefly describe the processing route which you would specify for making the

pressure hull of Problem 27.2 from each of the materials listed in the table. Comment on any particular problems which might be encountered. [You may assume

that the detailed design will call for a number of apertures in the wall of the

pressure hull.]



296



Engineering Materials 2



Chapter 28

Case studies in design



1. DESIGNING



WITH METALS: CONVEYOR DRUMS FOR AN IRON ORE TERINAL



Introduction

The conveyor belt is one of the most efficient devices available for moving goods over

short distances. Billions of tons of minerals, foodstuffs and consumer goods are

handled in this way every year. Figure 28.1 shows the essentials of a typical conveyor

system. The following data are typical of the largest conveyors, which are used for

handling coal, iron ore and other heavy minerals.

Capacity:

Belt speed:

Belt tension:

Motor rating:

Belt section:

Distance between centres of tail drum and drive drum:



5000 tonne h−1

4 m s−1

5 tonne

250 k W

1.5 m wide × 11 mm thick

200 m



Fig. 28.1. Schematic of a typical conveyor system. Because the belt tends to sag between the support rollers

it must be kept under a constant tension T. This is done by hanging a large weight on the tension drum. The

drive is supplied by coupling a large electric motor to the shaft of the drive drum via a suitable gearbox and

overload clutch.



Case studies in design



297



It is important that conveyor systems of this size are designed to operate continuously

for long periods with minimum “down-time” for routine maintenance: the unscheduled breakdown of a single unit in an integrated plant could lead to a total loss of

production. Large conveyors include a number of critical components which are

designed and built essentially as “one-offs” for a particular installation: it is doubly

important to check these at the design stage because a failure here could lead to a

damagingly long down-time while a harassed technical manager phones the length

of the country looking for fabrication shops with manoeuvrable capacity, and steel

merchants with the right sections in stock.



Tail drum design

The tail drum (Fig. 28.1) is a good example of a critical component. Figure 28.2 shows

the general arrangement of the drum in its working environment and Fig. 28.3 shows

a detailed design proposal. We begin our design check by looking at the stresses in the

shaft. The maximum stress comes at the surface of the shaft next to the shaft-plate

weld (Fig. 28.4). We can calculate the maximum stress from the standard formula



σmax =



Mc

I



(28.1)



where the bending moment M is given by

M = Fx



(28.2)



and the second moment of area of the shaft is given by



I =



π c4

.

4



(28.3)



Using values of F = 5000 × 9.81 N, x = 380 mm, and c = 75 mm, we get a value for σmax

of 56 MPa.

This stress is only a quarter of the yield stress of a typical structural steel, and the

shaft therefore has an ample factor of safety against failure by plastic overload.



Fig. 28.2. Close-up of the tail drum. The belt tension applies a uniformly distributed sideways loading

to the drum.



298



Engineering Materials 2



Fig. 28.3. Cross-section through the tail drum. All dimensions are in mm. We have assumed a belt tension

of 5 tonnes, giving a total loading of 10 tonnes.



Fig. 28.4. Shaft-plate detail.



The second failure mode to consider is fatigue. The drum will revolve about once

every second, and each part of the shaft surface will go alternately into tension and

compression. The maximum fatigue stress range (of 2 × 56 = 112 MPa) is, however,

only a quarter of the fatigue limit for structural steel (Fig. 28.5); and the shaft should

therefore last indefinitely. But what about the welds? There are in fact a number of

reasons for expecting them to have fatigue properties that are poorer than those of the

parent steel (see Table 28.1).

Figure 28.6 shows the fatigue properties of structural steel welds. The fatigue limit

stress range of 120 MPa for the best class of weld is a good deal less than the limiting

range of 440 MPa for the parent steel (Fig. 28.5). And the worst class of weld has a

limiting range of only 32 MPa!