The 1994 Edward DeMille Campbell Memorial Lecture ASM INTERNATIONAL

Materials, Bicycles, and Design

M.F. ASHBY

If the selection of materials is to be integrated into engineering design, a procedure is needed to identify, from among the enormous range of materials, the subset which most closely meets the design requirements. The elements of such a procedure are here described and illustrated by using it to select materials for bicycle frames. I.

INTRODUCTION

THE starting point of this article can be put in four short sentences. Materials and processes underpin all engineering design31~1 The computer (by which we mean "information technology") has revolutionized the way the geometric, thermomechanical, and manufacturing aspects of design are tackled. [5,6] But the selection of material and process is poorly integrated into this new technology. What can we do about it?

M.F. ASHBY received his Bachelors degree and Doctorate in Natural Sciences at the University of Cambridge and then joined the Institute for Metal Physics at the University of Grttingen, Germany, working with Professor P. Haasen from 1962 to 1965. From 1966 to 1973, he held the post of Professor of Applied Physics in the Division of Engineering and Applied Physics at Harvard University. Since 1973, he has been a member of the Cambridge University Engineering Department, where he holds the post of Royal Society Research Professor. Professor Ashby has been the editor of Aeta Metallurgica since 1974. His research interests include mechanisms of plasticity and fracture, methodologies for materials selection and their integration into an integrated design framework, and the modeling of material-shaping processes. The Edward DeMille Campbell Memorial Lecture was established in 1926 as an annual lecture in memory of and in recognition of the outstanding scientific contributions to the metallurgical profession by a distinguished educator who was blind for all but two years of his professional life. It recognizes demonstrated ability in metallurgical science and engineering. METALLURGICAL AND MATERIALS TRANSACTIONS B

II.

M A T E R I A L S AND THE DESIGN PROCESS

Figure 1 helps clarify the problem. The central column shows, much simplified, the stages of the design process. A market need is identified. Concepts which might meet the need are devised. The functional units of each concept are identified and their viability is examined (left-hand columns). Potentially practical concepts are selected and the design proceeds to the embodiment stage in which a layout is developed and approximate estimates of its overall performance are made. If successful, the design passes to the detail stage in which analysis and optimization lead to a set of working drawings giving the size and layout of each component; critical components are subjected to finite-element analysis; and the performance of assemblies is optimized using modeling or simulation tools, until the design is finally frozen. The output is a product specification: a set of instructions for shape, material, and technology of manufacture.t5,6] An example may help. A need is perceived for a manpowered ground transportation system. Concepts are devised, allowing the imagination to range as freely as possible; a small subset is sketched in Figure 2. The concepts' viability is examined. The first (Figure 2(a)) might be thought in the 1990s to be socially unacceptable. The most trivial of analyses reveals that the second (Figure 2(b)) is physically impractical. The third (Figure 2(c)) requires unusual human skills. The fourth--if refined--might just work. VOLUME 26B, DECEMBER 1995--110l

/ /

.j,.-

-

j

.

9

ii

f

-\r"

//I

-

~, ?

Fig. 1 The design process, with design tools on the left and material and process selection on the right. In the early stages, the emphasis is on breadth; in the later stages, it is on precision.

\

Fig. 4

Detailed design: the arrows signify dimensions and angles.

(Concept modeler) Function modeler

Material

1I 3-D solid modeler FEM ... Simulate ...Optimize

8

DFA ... DFM ...

"t"

and Process

=

Product Specification

Selector

Rapid prototyp~ng

Fig. 5 l)evclopnlcnts ill computer-aided design. Many of the developments can be interfaced, allowing concurrent design; materials and process selection are poorly integrated, at present. / : Fig. 2

.... ~

7

_

. _

1 _ =

(a) through (d) Concepts for man-powered transport.

Fig. 3 - - A n embodiment of the concept in Fig. 2(d).

Analysis and development of a function structure (mode of propulsion and mechanisms of motion, steering, braking, etc.) lead to a sophisticated embodiment (Figure 3). Optimization of frame shape and section, bearings, gearing, and other critical components leads ultimately to a three-dimensional geometric model, fully dimensioned, for each component; in total, a detailed specification (Figure 4). Sophisticated tools are available to the designer to help with these tasks (extreme left column of Figure 1, and Figure 5). Shape is captured by 3-dimensional solid-modeling tools which allow perspectives, projections, elevations, and sections to be explored and which interface directly with finite element, optimization, and simulation codes; the op1102--VOLUME 26B, DECEMBER 1995

timized geometry can be passed to numerically controlled machining, pattern-making, or prototyping equipment. Under development are function modelers which exploit intbrmation about thc function of a component or assembly (rather than merely its shape) to generate and scale geometric models and suggest assemblies. On the horizon are concept modelers, using associative logic to suggest new conceptual solutions to problems. Increasingly, these tools are interfaced to allow concurrent rather than sequential design, minimizing development time and allowing the designer to make changes in shape or configuration and to watch the consequences of the changes cascade through the chain of linked tools. Material and process selection (Figure 1, right-hand columns) have failed to keep pace with these developments. They appear in the "sequential" position of the second box of Figure 5. New designs generally make use of materials and processes already familiar to the designer. Could not their selection be integrated into the design framework? To answer this, it is valuable to examine first the causes of their separation. Look for a moment, then, at the design history of the bicycle.

IlL

THE DESIGN HISTORY OF THE BICYCLE

You could fill a small library with writings about the bicycle (a selection is listed as References 7 through 13). As an example of design, the bicycle is a happy choice: today the bicycle is almost exactly 200 years old and enjoying its second great peak of popularity. The hobby METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 6 - - T h e history of the bicycle: there was a period of intense technical development around 1890; today we are currently experiencing an intense period of material development.

horse---our concept in Figure 2(d)--was first in general use around 1795. By 1815, it had acquired steering, the invention of a German--the Count von Draise--with the quite unexpected additional benefit that one could now balance on a moving bicycle. By 1838, pedals--
to ask: can all these materials be equally good for making bicycles? But before delving into that, we should examine what can be learned from this history. The most obvious lesson is this: technical development comes first and innovation in the use of materials follows later. Understandable. If you are a designer struggling to devise concepts, develop embodiments, analyze detail, and plan product manufacture, you choose materials you know. Unfamiliar materials carry risks: a program to develop a new material carries heavy risks. But the sequence we see here, though understandable, is undesirable. A design, once frozen, constrains the use of materials; the potential of a new material may never then be realized. An example is as follows. The standard bicycle frame is made of 1-in. tubing. An accessory industry has grown tip around this dimension: all the things you clip, clamp, or screw onto bicycle frames are designed for 1-in. tubes. An innovative designer seeking to employ a new material is under pressure to retain this tube diameter: failure to do so divorces the new design from all the accessories available to the old one. Yet the constraint of 1-in. tubing m a y - indeed does--prevent the most effective use of many alternative materials, as we shall see subsequently. So we return to the question: can materials selection be integrated into the design process? We need a design-led materials selection procedure. IV.

DESIGN-LED M A T E R I A L S S E L E C T I O N

The essentials of a design-led materials selection system E~4,I5~are sketched in Figure 7. Its inputs are design requirements: function, constraints, and objectives. Function defines the purpose of the component: to carry bending moments, to transmit heat, etc. Constraints are conditions that must be met in performing the function: first, functional constraints such as a limit on elastic deflection or the requirement that the component does not fail; and second, geometric constraints which prescribe certain dimensions. The objective describes the quantity to be minimized or maximized: the weight, the cost, the life, etc. VOLUME 26B, DECEMBER 1995--1103

I

Function (Carry bending ~ ] moment)

ICons,ra' o,sI I Objective (Limitdeflection, ],_-~] ( Minimizewt.

.,-"-3 IMPACT / , ~

n RIDER 'k"J ~WEIGHT

minimizecost) iMPACT

Translator (materialindices)

[

Bending

Material Selector

Torsion

Fig. 9 - - T h e loading on the bicycle frame: (a) bending and (h) torsionJ TM

M

I

Short list of materials

-'-t

t Fig. I0

Iterate

t-'--

Fig. 7 Design-led materials selection: lhe inpuls are function and shape: and the output is a short list of possible materials and processes.

Compound Properties

ProDerties

Modulus E~ E / p Strength ae/

Function

Fixed radius [ Fixed shape

'Density p ._._

~..a e/P

E1/2/ p

Stiffness

Oe2/3/p

Strength

Fig. 8---Simple and compound properties.

The first step is to translate these requirements into a specification for material selection. This we do by deriving "material indices," combinations of material properties which, if maximized, optimally meet the design requirements. These become the inputs to the materials selector, the output of which is a short list of candidate materials and data describing them. Figure 8 gives an idea of what they look like. Materialperformance is described by simple properties (left-hand column): the lightest unit cube of a material is that with the lowest density p, and the stiffest is that with the highest modulus E. Component performance is measured by compound properties or indices (central columns): combinations like specific stiffness E/p or a specific endurance limit ~flp. These indices look simple but they are remarkably powerful: they capture function, constraints, and objective. One example is a lightweight frame for a competition bicycle. It must bear service loads safely (that is without failure), be as light as possible, and at the same time be 1104--VOLUME 26B, DECEMBER 1995

M

A tube, loaded in bending.

adequately stiff--a frame which flexes too much dissipates the rider's energy. Figure 9 shows the important loads. The forks, for obvious reasons, are loaded in bending. The frame, less obviously, carries bending and torsional loads created by impact and by out-of-plane pedaling forces, and it is these which are most important in choosing its strength and stiffness. We take bending as an example; the results of torsion are the same. And here we need a model. The simplest model which just captures the essentials is laid out below. A. Translation: Design Requirements to Material Indices Most bicycles have tubular frames. The tube diameter, for an ordinary "street" bike, is standard (roughly 1 in.; 25 mm), allowing standardization of accessories. Consider this first. The design requirements can now be stated formally: a material is sought for a light, strong, tubular beam of fixed outer diameter (Figure 10). The function is to carry bending moments. The objective is to minimize the mass m of the frame. Expressed per unit length L of tube, the mass is m -- = 2 ~ r t p L

[1]

where r is the outer radius of the tube, t is the wall thickness, and p is the density of the material of which it is made. This is the objective function, the quantity to be minimized. The first constraint is that of strength: the tube must not fail. Mechanical failure could be by plastic collapse, by fast fracture, by buckling, or by fatigue caused by repeated cyclic loads. Take fatigue as an example. The cyclic bending moment Ms the tube can withstand with infinite life is Ms -

r

[2]

where % is the endurance limit and I is the second moment METALLURGICAL AND MATERIALS TRANSACTIONS B

El/2

Planar slice

M4 =

[8] P We need these results subsequently. For now, note that indices capture function, constraints, and objectives; they translate design requirements into prescriptions for selecting material.

B. Material Property Space

0

Q.

E if)

Simple property P2 Fig. 11--A planar slice throughmaterialpropertyspace. of area, given, for a thin-walled tube, by

I = "rrr3t

[3]

There is a second constraint, this time one of geometry: the tube radius, r, is as fixed. The wall thickness is free; we choose it so that it will just support MB. Substituting Eqs. [3] and [2] into Eq. [1] gives the mass per unit length in terms of design parameters and material properties:

E --=

C

P or taking logs, log E = log p + log C

m =

L

Property combinations like those of Eqs. [5] through [8] suggest the idea of plotting one property--E, say--against another--p, for instance--such that combinations such as E/p and EVZp can be examined. More generally, one can think of a "material property s p a c e " - - a hyperspace with values of material properties as coordinates. The space is populated with blobs, each describing a class of materials: metals, woods, composites, etc. Each contains a large number of smaller blobs, each describing one member of the class. Figure 11 is a schematic slice through this space. One material property PI (the modulus, for instance) is plotted against another P2 (the density, perhaps) on logarithmic scales. The slice intersects the blobs, as shown. Indices divide the space and allow the part of it containing materials well suited to a given application to be isolated. Think, for a moment, of P1 as E and P2 as p. The condition

O

r

[41

The lightest tube which performs the function and meets the constraints is therefore that made from the material with the greatest value of the compound property or "index." M~ = - P

[5]

A change of function, objective, or constraints changes the index. If the function were transmission of heat rather than mechanical load, thermal conductivity would appear in place of endurance limit. If the objective were to minimize cost rather than weight, the density p would be replaced by Cmp, where C~, is the cost per kilogram of the material. More relevant here, if the first constraint is that of stiffness rather than strength, is that the index (derived in a similar way) becomes E M2 = P

[6]

And if the second constraint--that of fixed tube radius--is relaxed and replaced by that of fixed tube shape (r/t fixed) then--reiterating the derivation--the index for strength becomes Ore2/3

M3 -

P

and that for stiffness becomes METALLURGICAL AND MATERIALS TRANSACTIONS B

[7]

[9]

defines a family of straight parallel lines of slope 1, one line for each value of the constant C. The condition EI/2

=C P defines another set with slope 2. We want the subset of materials with the largest values of C; the appropriate family of lines identifies these. The indices give a method for optimal selection. Any one of the indices given previously (and there are many more) can be used in this way, plotting it on the appropriate slice through property space. We shall call these slices "material selection charts." Figure 11 is a planar slice. We learn more if we examine nonplanar slices. Figure 12 shows the idea. If each of the axes of the chart is not made up of simple properties but instead functions of two or more of them, then the chart projects a curved surface through the space, again intersecting the material blobs, as shown. And if the functions we choose are themselves indices, the procedure allows selection of materials which maximize two different indices at the same time. As an example, if the two indices M 3 and M4 (Eqs. [7] and [8]) are chosen, then the materials which lie near the top right of Figure 12 are those which have large values of both. In the examples which follow, we have used curved sections to make the selections.

C. Selection of Materials for Bicycle Frames The method is best illustrated by example. The standard bike made of the standard material (steel) has 1-in. tubes. VOLUME 26B, DECEMBER 1995--1105

Non-planar slice

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V

e,) o -O E 0

Q.

E 0 o

Compound property g(P3,P4 ...) Fig. 12 500

A curved slice through material property space.

FRAME MATERIALS:

7"

,2

s

E

o~200

WOODS GFRP.s

ri

ALLOYS~.~,,~ L

100 r

aO

o.

6O

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40

M9A,Lt OYS

F

ELS B265

AZ6I

(ALLOYS

753

707

531

6

"-7

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Mg ALLOYS

g ~ 2o POLYMERS

A[ALLOYS-~"~ I

1 I

At ALLOYS

U

~I STEELS

L_J

J3

2~

lo.

t

111

I0

-EL

), ' 6 8 lo z PROPERTY GROUP E/#

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i I I

2"

~o 60 80 too (GPo/Mg.m "3)

2.~

2'6 2.7

[

zoo

Fig. 13 A selection chart for strength and stiffness, with fixed tube radius, r, but tube wall thickness free.

Accessories fit this frame size, so there is an incentive--as already mentioned--to retain it. With this constraint, what gain in performance, in the sense of strength and stiffness per unit weight, do alternative materials offer? Figure 8 tabulates the indices. The second column gives those for fixed tube radius--they are the indices MI and M2 derived in Section A. Imagine, now, a database of material properties containing information about the materials that are, or could be, used for bicycle frames. From it, we call the simple properties E, O-e, and p. With these, we form the compound properties in the second column of Figure 8 and plot them as a material selection chart. Figure 13 shows the result. The horizontal axis shows specific stiffness, and the vertical one gives specific fatigue strength. Polymers and short-fiber composites lie to the lower left; they are poor by both criteria. Continuous carbon-fiber composites (CFRPs) lie toward the upper right, good by both criteria. Metals-1106--VOLUME 26B, DECEMBER 1995

steels, the alloys of aluminum, magnesium, and titanium-lie almost on top of each other; to separate them, the box in which they lie has been expanded horizontally to the right. It contains the alloys commonly used for bicycle frames: the low alloy steels 531 and 753; the aluminum alloys 7075, 2024, and 6061 in the T4 or T6 condition; the relatively low-strength B265 titanium; and the magnesium alloy AZ61. All have almost identical values of M, and M2; at fixed tube radius, there is almost nothing to choose between them. Even CFRPs offer very little if fabricated as 1-in. tubing; the additional weight of the nodes needed to connect the tubes offsets the weight savings offered by the material itself. The potential of light alloys and composites is unlocked, so to speak, when the constraint on tube radius is relaxed; fat-tube bikes can exploit their advantages more fully. Indices for tubing of constant shape (r/t) rather than constant size (r) were derived earlier; they are listed in the third column of Figure 8. Calling the database again and forming these new compound properties gives the slice through property space shown in Figure 14. And this time things have changed, if we take 531 (it lies near the lower left) as the benchmark, we find that all the other metals offer gains, both in stiflhess and in strength. The designer now has an option: i f - as in a mountain bike--strength is more important than stiffness, the best choice might be those metals which lie highest on the strength axis: high-strength titanium and metal-matrix composites. If, instead, stiffness is the over-riding consideration (as in a track bicycle), then it is the metals lying furthest to the right which are most attractive: magnesium alloys and, above all, beryllium. The CFRPs (and wood, too) are outstanding by both criteria; only the problem of joining has to be overcome to exploit them fully.

V.

COMPUTER-AIDED MATERIAL SELECTION

All this is perfectly practical.tt~J,,} Focus for a moment on Figure 14 (the materials charts for fixed shape) and the light alloys it contains. Figure 15 is the output of a computer-based selection system [a6] which implements the procedure I have described here. The figure shows the same curved slice through property space. Data, in this instance, were drawn from a database for light alloys, so steel wood and CFRP are not there, but otherwise, it looks very much like the previous figure. The large ovals span the range of properties of each alloy class: aluminum, magnesium, titanium, and beryllium. The smaller bubbles within them describe individual alloys, in specified states of heat treatment; some of those relevant to the bicycle frame are labeled. The software allows selection lines to be constructed, isolating subsets of materials with attractive values of both indices, and weighted, if desired, in the direction of strength or the direction of stiffness. This subset can then be passed to further selection stages in which other constraints (adequate toughness, availability in tubular form, weldability, etc.) can be applied, identifying the small set of materials which satisfy all the design requirements. More important, the method can be integrated into the design framework. The inputs, as we have seen, are design specifications: function, constraints, and objectives. The output is a short list of candidate materials, with property data M E T A L L U R G I C A L AND MATERIALS TRANSACTIONS B

Fig. 16--The output of a computer-aided selection system for a fixed tube shape when material cost is to be minimized. Fig. 1 4 ~ A selection chart for strength and stiffness, with shape, r/t, fixed but radius, r, free.

M5 =

Ore2/3 Gp

[10]

where Cm is the cost of the material per kilogram; M5 measures the strength per unit cost, for fixed tube shape. The horizontal axis is

E~/2

M6 = - -

Cmp

[11]

It measures stiffness per unit cost. And now, steels decisively win: although not shown here, they are better than any of the light alloys (531 lies just off the top right comer of the figure). The light alloys themselves form a clear ranking; aluminum alloys offer the best value for the money, so to speak, in this application; they are followed by magnesium and, then far behind, by titanium and beryllium. All this can be done very quickly, offering the designer the same sort of flexibility that he expects from the design tools already at his disposal. gI. Fig. 15--The output of a computer-aided selection system for a fixed tube shape when weight is to be minimized.

which can be passed to downstream tools for simulation, finite element analysis, etc. Properly integrated for other design tools, the designer could select any one of these candidates and watch the consequence of the choice cascade through the linked chain of design tools and, if the results are unsatisfactory, could pick an alternative candidate and follow the consequences again. We have limited ourselves thus far to the performancerelated objective of minimizing weight. Suppose, as a final example, material cost rather than weight was the objective, then, drawn from the same database, the appropriate slice through property space is created, as shown in Figure 16. The vertical axis is METALLURGICAL AND MATERIALS TRANSACTIONS B

CONCLUSIONS

There is evidence that in mechanical design, technical innovation precedes innovation in material and process. While this is understandable, it is undesirable; when a new material is introduced into an already detailed design, its potential may never be fully realized. The computer has greatly changed the design world. Sophisticated tools exist to capture function and geometry; to simulate, model, and analyze; to optimize, both for mechanical performance and manufacturability; and more. No such tools exist for the selection of materials and processes, with the result that their selection is poorly integrated into the design stream. There is, today, a sense that the achievements of material science have outstripped the ability o f the engineer to apply them; and this divergence relates, at least in part, to the problem we have just defined: the inability of the designer to explore the potential of altemative materials in his design. A strategy is needed to deal with it. The outlines of a design-led materials selection system VOLUME 26B, DECEMBER 1995--1107

have been developed in this article. The scheme takes, as input, design requirements: function, constraints, and objectives. It delivers, as outputs, a subset of viable materials with data for their properties. This input/output scheme has the features necessary for integration into the larger design framework, allowing the designer to explore, early in the design process, the selection of material and its consequences. And although we have not discussed it here, it appears possible that a parallel scheme could be developed for selecting manufacturing processes. A full implementation poses many challenges. The resources required are considerable; but so they were before the development of the solid modeling software which, today, is in general use. And the rewards are considerable. Above all, it is the route to a convergence of two of the main streams of engineering: materials science and mechanical design. ACKNOWLEDGMENTS The author wishes to acknowledge the financial support of the Engineering and Physical Sciences Research Council of the United Kingdom through a rolling grant to the Engineering Design Centre of the Cambridge University Engineering Department, and to thank Dr. D. Cebon, Professor C.A. McMahon and Drs. H.R. Shercliff and M.P.F. Sutcliffe for stimulating discussions and documents which have helped to shape this article.

1108--VOLUME 26B, DECEMBER 1995

REFERENCES 1. G.E. Dieter: Engineering Design, a Materials and Processing Approach, McGraw-Hill, London, 1983. 2. F.A. Crane and J.A. Charles: Selection and Use of Engineering Materials, ButterwortAa and Co., London, 1984. 3. M.M. Farag: Selection of Materials and Manufacturing Processes for Engineering Design, Prentice-Hall, London, 1990. 4. G. Lewis: Selection of Engineering Materials, Prentice-Hall, London, 1990. 5. G. Pah| and W. Beitz: Engineering Design, The Design Council, London, 1984. 6. D.G. Ullman: The Mechanical Design Process, McGraw-Hill, New York, NY, 1992. 7. A. Sharp: Bicycles and Tricycles, an Elementary Treatise on their Design and Construction, The MIT Press, Cambridge, MA, 1993. 8. R. Watson and M. Gray: The Penguin Book ~[ the Bicycle, Penguin Books, Harmondesworth, United Kingdom, 1978. 9. F.R. Whitt and D.G. Wilson: Bic3,cfing Science, 2nd ed., The MIT Press, Cambridge, MA, 1985. 10. K. Kobayashi: Histoire du Vg'loeipbde de Drais h Michaux, Bicycle Culture Centre, Tokyo, 1903. I I. W. Ulrich: f'ahrrad ~k'g/Zeit, The Technical Museum, Vienna, 1990. 12. C.J. McMahon, Jr. and C.D. Graham, Jr.: Introduction to Engineering Materials; The Bi~Tele and the Walkman, University of Pennsylvania, Philadelphia, PA, USA, 1993. 13. Engineering Materials: An lntr~duction, Unit I I, Bike Frames, The ()pen University, Mihon Keynes, UK, 1982. 14. M.F. Ashby: Materials Selection in Mechanical Design, Pergamon Press, Oxlbrd, United Kingdom, 1992. 15. D. Cebon and M.F. Ashby: Met. Mater., 1992, Jan., pp. 25-3(I. 16. CMS Materials Selection Sr (iranta Design Ltd., 20 Trumpington Street, Cambridge CB2 IQA, United Kingdom.

METALLURGICALAND MATERIALSTRANSACTIONSB