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ashby_paper - Indian Journal of Technology Vol. 28,...

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Unformatted text preview: Indian Journal of Technology Vol. 28, June-August 1990. pp. 217-225 Materials selection in engineering design Michael F Ashby Engineering Department. University of Cambridge, Cambridge C32 1P2, UK. New materials enable advances in engineering design. But the advances are possible only if data for appropriate properties are available and a procedure exists for using the data to make a rational choice. This paper describes a procedure for materials selection in mechanical design which allows the identification, from among the full range of materials available to the engineer, of the subset most likely to perform best in a given application. The number of materials available to the engineer is enormous: estimates range between fifty thousand and eighty thousand*. They are drawn from the six broad classes shown in Fig. lwmetals, polymers, ela- stomers, ceramics, glasses and composites. Within a class, there is some commonality in properties, proce- ssing and use-pattern. Ceramics, for instance, have high moduli, polymers havelow; metals can be sha- ped by casting and forging, composites require lay— up or special moulding techniques. But this com- partmentalisation has its dangers: it can lead to speci- alisation (the metallurgist who knows nothing ofce— ramics) and to conservative thinking (“we use steel because that is what we have always used”). There was a time when metals so dominated me chanical design that ignorance of the potential of other materials was hardly a handicap. But that has dramatically changed. The range ofmaterials avail- able to the engineer is larger, and is growing faster, than ever before. New materials create opportunities for innovation: for new products, and for the evolu— tionary advance ofexisting products to give greater performance at lower cost. Markets are captured by the innovative use of new materials, and lost by the failure to perceive the opportunities they present. But how is one to find one’s way through the enormous catalogue, narrowing it down to a single, sensible, choice? Can one devise a rational procedure for mate- ’“Materials enter all engineering design, from the most integrated of microelectronics to the most massive of civil engineering struc— tures. The cost ofrnaterials in microelectronics is a small fraction (5 % or less) of the cost of the product. By contrast, in mechanical and civil engineering, material costs often exceed 50% of the pro- duct cost, and the volume of material used is very large. So we will restrict ourselves to the materials of mechanical and civil engineer~ ing. It is here that the competition between materials is greatest, and opportunities for innovation are most marked. rial selection? To answer that, we must first look brie‘ fly at the design process. The Design Process, and the Role of Materials in It Fig. 2 shows, much simplified, the stages ofthe de— sign process "3. A market need is identified. A concept for a product which meets that need is devised. If appr- oximate calculations (left hand columns) show that, in principle, the concept will work, the design proce- eds to the embodiment stage: a more detailed analysis, leading to a set of working drawings giving the size and layout of each component of the product, and esti— mates ofits performance and cost. if the outcome is successful, the designer proceeds to the detailed de— sign stage: a full analysis (usingcomputer methodsif l " -CEHAM|CS POLYMERS</- LASTOMERS GLASSES Fig. I —The menu of engineering materials. Each class has proper- ties which occupy a particular part (or “held”; of each of the materials selection charts, shown later. to .i lNDlAN J. TECHNOL, JUNE-AUGUST 1990 necessary) of critical components, preparation of de— tailed production drawings, specification oftoleran- cc, precision, joining methods, finishing and so forth. Materials selection3'4 enters at every stage of the design process. But the nature of the data fer material properties needed at each‘stage differs greatly in its level of precision and breadth (Fig. 2, right hand co- lumns}. At the conceptual design stage, the designer requires approximate data for the widest possible range ofmaterials. All options are open: a polymer may be the best choice for one concept, a metal for another, even though the function is the same. That sort ofdata is found in low-precision tables such as those of the Fulmer Materials Optimisers, the Mater— ials Selector‘S or in materials selection charts of the sort shown later in this article”. The low level of precision is not a problem; it is perfectly adequate for this task. The problem is access. how can the data be presented to give the designer the greatest freedom in considering alternatives? The charts help here. Exa— mples will be given in a moment. Embodiment design needs data at the second level of precisiOn and detail. The calculations involved in de- ciding on the scale and lay-out of the design require the use ofmore detailed compilations: multi—volume handbooks like The ASM Metals Handbook9.- Smit— hells1 0, The Handbook ofPlastics and Elastomers' ‘, The Handbook of Properties of Technical and Engine— ering Ceramics‘ 2, or computer data-bases which contain the same information. They list, plot and ANALYSIS: lVlABILlT‘f) ENGIhEflMS SCIENCE STATISTICS DY NAMICS STRESS ANALYSES FLUIDS HEAT COMPUTER SCIENCE MODELLING {PERFORMANCE} METHODS IEFFJEHC‘N DETAILED ANALYSIS lNC FINITE ' ELEMENTSETC [SAFETYl compare properties ofa single class ofmaterials, and allow choice at a level ofdetail not possible from the broader compilations which include all materials. The final stage ofderniled design requires a still higher level ofprecision and detail. This is best found in the data-sheets issued by the material producers themselves. A given material (polyethylene, for ins- tance) has a range of prOperties, which derive from differences in the way different producers make it. At the detailed—design stage, a'supplier should be identi- fied. and the properties of his product used in the design calculation. But sometimes even this is not good enough. Ifthe component is a critical one (mea- ning that its failure could, in some sense or another, be disastrous) then it may be prudent to conduct inhouse tests, measuring the critical property on a sample of the batch of material that will be used to make the product itself. This paper concerns the first level of data—the broad, low precision compilation—and ways of presenting it which simplify the task of selecti- on. Materials Seiection in Conceptual Design It is important, as we have said, to start the design process with the full menu of materials in mind; fail— ure to do so may mean a missed opportunity. The immensely wide choice is narrowed, first. by primary constraints dictated by the design, and then by seekin g the subset of materials which maximise the perfor- mance of the components. One way of doing this quic- kly and effectively is with materials selection charts. MATERlALE SELECTION ALL MATERI - lLCW PRECISIoN I MATERIALS SCI N E STRUCTURE SUBSE T OF MATERFALS [HIGHER PRECTSION FlNlSHlNG ONE MATERIAL ECONOMICS IBEST AVJMLABLE PRECISIDNl 218 PRODUCT Fig, 2—The design process, much simplified (central column). showing how engineering science and materials science interface with each stage. The breadth and precision of the materials data required at each stage differ greatly. ASHBY: MATERIALS SELECTION IN ENGINEERING DESIGN The idea behind the charts is illustrated by Fig. 3. Dire material property (the modulus in this case) is Jlotted against another (the density) on logarithmic iC’dlCS. When this is done. it is found that data for a given class of materials (engineering polymers, for :xample) cluster together; they can be enclosed in a single envelope. The envelope is constructed to en- close all members of the class—even those not explici— tly listed on the chart. The result displays. in a conven- iently accessible way. data for E and p for all materi- als, Prr‘nmry constraints in materials selection are im- posed by characteristics of the design of a component which are non-negotiable: the temperature and envi- ronment to which it is exposed, its density, its cost and so forth. If these are specified, all but a subset of mate» rials which satisfy these constraints can be eliminat- ed. A primary constraint corresponds to a horizontal or vertical line On the diagram: all materials to one side of the line can be rejected. Further narrowing is achieved by seeking the com— bination of properties which maximise the performa- ace of the component. For most common load-bear- ing components, performance is limited, not by a sin- gle property, but by a combination ofthem, The ligh— test tie rod which will carry a given axial load is that with the greatest value ofoyl'p, (where cry is the yield strength and p is the density of the material). The lightestcolumn which will support a given compres- sive load without buckling is that with the greatest value of Evin: (where E is Young‘s modulus). The best material for a spring, regardless of its shape or the 1000 MODULUS- DENSITY 6 o g ' Easimssam'. in 535;. YOUNG‘S MODULUS. E ,GPG or U in“ 10 DENSITY, p , mg/m3 Fig. 3—A schematic ofa materials selection Chara—Young's mo- dulus. E. is plotted against the density. p. on log scales. Each class of material (Fig. 1) occupies a characteristic part of the chart. The log scales allow performance criteria (such as E; p or EV‘g‘p) to be examined in an easy way way it is loaded, is that with the greatest value of oi/E. Ceramics with the best thermal shock resistance are those with the largest value of crfilEcr (where oris the fracture stress and or is the thermal cocflicient of ex- pansion); and so forth. There are numerous Such combinations, depending on the application. Those for some simple loading geometries are listed in Fig.4; there are many more. The charts can be used to select materials which maximise any one of these combinations. Look again at Fig. 3: it shows modulus, E, plotted against density. p, on log scales. The condition Ellp = C or; taking logs; 10g E=log p-l-log C is a family ofstraight parallel lines ofslope 1. one line for each value of the constant C. The condition Elam = C gives another set, this time with a slope of 2; and Eysfp 3‘: C gives yet another set with slope 3. It is now easy to identify a subset of materials which are optimal for each loading geometry; further crite— ria can subsequently be applied to this subset to meet other design requirements (corrosion resistance. for instance) matters. Ila straight—edge is laid parallel to the EVsz = C line; all the materials which lie on the line will perform equally well as a light column loaded- in compression; those above the line are better. those below worse. lithe straight-edge is translated tow- ards the top left corner of the diagram; the choice narrows. At any given position of the ed ge, two mate- rials which lie on its edge are equally good. and only the subsets which remain above are better. The same procedure. applied to the tie (Efp) or plate in bending (Eyifp), lead to different equivalences and optimal subsets of materials. In mechanical design; there are twelve properties which. singly or incombination, usually limit perfor- mance. They are listed in Table 1; they include densi- ty, cost, stifiness, strength. thermal properties. wear properties and creep resistance. Charts exist for all ' ofthem, combined in the ways which occur most fre- M quentlyi's. We now introduce four ofthe charts through brief examples ofthe way each allows materials to be selec— ted for particular applications. The Materials Selection Charts and Their Uses Materiafsfbr table legswLuigi Tavolino, fu rniture designer. conceives ofa light-weight table of daring simplicity: a flat sheet of toughened glass supported 219 INDIAN .I. TECHNOL, JUNE-AUGUST 1990 MINIMISE WEIGHT FOR GIVEN T. I SPECIFIED r FREE TORSION TUBE T..!,r SPECIFIED AND TUBES F. 1 SPECIFlED COLUMN DR TUBE F. I SPECIFIED SENDING OF PLATE Elm SF‘ECIFIED I FREE EUCKLINEI OF PLATE F, 1.0: SPECIFIED I FREE W W p,r SPECIFIED 1 FREE RDTATING CYLINDER w, r SPECIFIED I FREE §PH§RE WITH INTERNAL PWE p, r SPECIFIED t FREE ELASTIC DESIGN seal—~65 . SPRING UF MIN VOLUME SPRING 0F MIN. WEIGHT ELASTIC HINGES HINGE WITH NO RXIAL LOAD HINGE WITH AXIAL LOAD KNIFE EDGESt PIVOTS r-\ I . . ll POINT DR LINE CONTACT WITH MIN. FRICTION LOSS PLASTIC AND FRACTURE- SAFE DESIGN LOAD-CONTROLLED DESIGN MAX Km AND 0', DISPLACEMENT-CONTROLLED DESIGN YIELD BEFORE BREAK MAX KK/E AND ql/E MAX elm/(Tr LEAK BEFORE BREAK MAX Itfc/oy THERMAL DESIGN THERMAL FLUX w, leo m THERM AL STRESS, SHOCK 1 MIN. THERMAL STFISSS Tl MIN. HEAT FLUX AT STEADT STATE MIN TEMP RISE AFTER TIME I HA)!- THERMAL SHOCK Fig. 4—Some property-combinations which determine performance Table l—Basic subset of material properties- Relative cost, CR (m) Density. 0 (Mslm’) Young‘s modulus, E (GPa) Strength, oy (MPa) Fracture toughness, ch (MPa 111%) Damping coefficient, tan (5) (-) Thermal conductivity, DI. (W/mK) Thermal difi'usivity, a (ml/s} Thermal diffusivity, a (UK) Strength at temperature, UT (MP3,) Wear rate, WM {—) Corrosion resistance (—J on slender, unbraced, cylindrical legs (Fig. 5). The legs must be solid (to make them thin) and as light as possible (to make the table easier to move). They must suppon: the load imposed on them by the table top and whatever is placed upon it without buckling. What materials could one recommend? 229 Fig. 5-—A light-weight table with slender cylindrical legs. The legs must be slender and must not buckle elastically when the table is loaded. That requires a material with high values of both E and Ham. Slenderness imposes a primary constraint: slender columns must be stilt, that is, they must be made of a material with a high modulus, E. Lightness, while still supporting the design load, puts a further restriction on the material choice: Fi g. 4 (and the discussion of the last section) suggest that the choice should focus on materials with high values ofEV’/p. The appropri- ate chart is shown in Fig. 6. On it, Young‘s modulus, E, is plotted against density, p; it is the chart of which Fi g. 3 is a schematic. Materials of a given class cluster ASHBY: MATERIALS SELECTION IN ENGINEERING DESIGN 1000 W YOUNGS MODULUS E {G=3E/8‘. KeEi) F . L I G is / I’ENGINEERING % [ [%]'Lm/SI ,d canpcsnes L1J _ 10 if} 3 ._J D C} C) E ti!) o 1.0 2 3 LCW‘ER e LIMIT 0 - For: muescuos >- LDPE i LAMINATE I ‘ GFRP i KFRP 4., Ms ALLcrs — z ._m f, H :0 PLAQCISED TIN GT:me 4‘ / ENGLNEERINE/ AL.L Y5 YLON ENGlNEERiNG POLYMERS LY 557V , P‘iFE x 0.3 DENSlTY, P,mg/'m3 3O 3 Fig. oiMaterials selection chart lr‘r'oung's modulus against density. The balloons enclose data for a given class ot‘n-iateriai. Materials for light. slender columns: wood is a good choice: so is a composite such as CFRP. which (having a higher modulus) gives a column which is both light and slender. together: metals in the top right, composites near the middle. polymers near the bOttom. and so Forth. Fig. 6 shows the selection procedure. A line ol'slope 2 is drawn on the diagram: it links materials with equal values of E Vii’p. Materials above the line are better choices For this application than materials on the line; materials below are worse. The line is displaced up— wards until a reasonably Small selection ofmaterials is left above it. They are identified on Fig. 6 (b): smarts, (-oiiipas'ims (particularly CFRP) and certain special (digit/taming ceramics. Metals are out: they are far too heavy: polymers too: they are not nearly stiff enough. The choice is further narrowed by the primary cons~ traint that, for slenderness= E must be large. A horizo— ntal line on the diagram links materials with equal values of E; those above are stiffer. Fig. 6(b) shows that this now eiiminates woods. CFRP is the best cho— ice: it gives legs which weigh the same as the wooden ones but are much thinner. At this stage, other aspects ol‘the design must he examined: strength. cost and so forth. Other charts help with this. but that requires more space than is available here. Malariafsfor thejbrks Ufa racing biC}-’Ci€"——The first consideration in bicycle design (Fig. 7) is strength. Fig. TiThe bicycle. The forks are loaded in bending. The lightest forks which will not collapse plasticallv are those made with the material with the greatest value of Gym/i0. Stianess matters, ol‘course; but the initial design cri; terion is that the i‘rarne and l‘orks should not vicid or fracture in normal use. The loading on the l‘rame is not obvious; in practice it is a combination ofaxial load— ing, torsion and bending. That on the forks is simpler: it is predominantly bending. if the bicycle is for racing then the v eight is a primary consideration: the forks should he as light as possible. Then (see Fig. 4] one should choose a material with the greatest value of erg/W). y i' INDIAN J. TECHNOL, JUNE-AUGUST 1990 10m 2. STRENGTH-DENSITY METAL AND POLYMERS= HELD STRENGTH CERAMICS AND GLASSESICOHPRESSWESVPEVGTH ELASTOMER52TEN51LE TEnR SmENGTH . COMPOSITES: TENSILE FAILURE STRENGTH o3r , MF’CI ENGINEERING POLTMERS GUICE LINES FDR HlNIMLIM WEFGHT DESIGN DENSITY p , rng/rnJ Fig. 8-Matcrials selection chart 2‘. Strength (the yield strength for ductile materials, the compressive crushing strength for brittle solids) plotted against density. p. Materials for the forks of a racing bicycle: forks made of a titanium alloy or of 7075 aluminium alloy perform better than steel; CF RF is better still. But other aSpects of the design (stillness, resistance to fracture, fabrication costs, etc.) must be examined before a final choice is made. The appropriate chart is shown in Fig. 8: strength {yield strength for ductile materials, crushing strength f or brittle) plotted against density. As befo- re, members of one class of material cluster together in one area of the chart: metals near the top right, poly- mers in the middle, structural foams in the bottom left. Fig. 8 shows the selection procedure. A line of slope 372 is drawn on the chart; it links materials with the same value of of” / p, that is, materials which (as far as strength is concerned) are equally good for making the forks of a racing bicycle. All materials above the line are better; those below are worse. Four materials are singled out. High strength alu- minium (7075, T6) and titanium alloys are equally go- od; Reynold 531 (a high strength steel popular for bicycle frames) is a little less good; CF RP is definitely better. At this stage it is necessary to examine other aspects of the material choice: stiffness, resistance to fracture and so forth (charts exist which help with this), and to examine the cost of fabrication (though, to the committed racing cyclist, cost is irrelevant). CFRP emerges from such an analysis as an attractive, though expensive, choice; and, ofco urse, it is used in exactly this application. 222 SPRINGS éF-S % 119 l +95 i Fig. 9—Springs. The best materia] for a Spring, regardless of its shape or the way in which it is loaded, is that with the highest value of (ti/E. Materials for SpringSmSprin gs come in many sha- pes (Fig. 9), and have many purposes. Regardless of their shape or use, the best material for a spring of minimum volume (for a watch, for instance) is that with the greatest value of oyE. We will not go into that not», but simply use the. result as a way of introdu- cing the. chart shown in Fig. it): modulus, E, plotted ASHBY: MATERIALS SELECTION IN ENGINEERING DESIGN 1000 1.. MODULUS- STRENGTH METALS AND POLYMERSHHELD STRENGTH CERAMICS AND GLASSES:COHFRESSVE STYEN ELASTDMERS . TEAR STRENGTH COMPOSITES - TENSILE STRENGTH 100 MIN. ENERGY STORAGE PER um VOLUME 'YIELD BEFOE BUCKLING 5 le II 5: \ :- rouNes MODULUS, E, spa \ \ / 2" g_ ‘3 ts"0 0-1 . Poimsss \ FCAMS / ENGINEERING ALLOYS Eucrnssnms i F‘UL‘IMERS I ‘i g I F; / MAX ENERGY 988E ' STORAGE PEP UNIT VOLUME —l I BUCKLING a EJSTOMERE BErOFlE HELD f . . , IOO STRENGTH e, , MPG Fig. Ill—Materials selection chart 4: Young’s modulus, E, plotted against strength 0:, (the yield strength for ductile materials, the compressive crushing strength for brittle solids]. Materials for springs: rubber1 of course, is good; high strength (“spring”) steel is good; but glass and CFRP both, under the right circumstances, make excellent springs. against strength, cry. As always, materials group toge- ther by class, though with some overlap. This diagram has many uses; one is the identification of good mate— rials for springs. The procedure is shown in Fig. 10. A line ofslope 1,52 links materials with the same value of Gilli". As the line is moved to the right (to increasing values ot‘oi/E) a smaller selection of materials is left exposed. The result is shown in the figure, where candidate mate- rials are identified. The best choices are a high-str- ength steel (spring steel, in fact) and, at the other end of the line. rubber. But certain other materials are sugge— sted too: CFRP (now used for truck springs), titanium (1110 ys {good but expensive), glass (used in galvanom— eters) and nylon (children’s toys often have nylon springs). Note how the procedure has identified the best candidates from almost every class: metals, glas- ses, polymers, elastomers and composites. Safe pressure vessels—Pressure vessels, from the simplest aerosol can to the biggest boiler, are design— ed, for safety, to yield before they break. The details of this design method vary. Small pressure vessels are usually designed to allow general yield at a pressure still too low to propagate any crack the vessel may Fig. l l-—A pressure vessel containing'a flaw. Safe design req uires that pressure vessels shOuld leak before they break. The best mate- rial is then that with the greatest value of chfoy. contain (“yield before break”); then materials with the largest possible value of K1405, are the best choice ~—they will tolerate the biggest flaw. With large pres— sure vessels this may not be possible; instead, safe design is achieved by ensuring that the smallest crack that will propagate unstably has a length greater than the thickness of the vessel wall (“leak before break”), and the best choice of material is one with a large value oszlc/oy. 'Ihat covers safety; the actual pressure that the vessel-can hold is proportional to cry itself, so the designer seeks to maximise this too (Fig. 1 1). 223 INDIAN J. TECHNOL, JUNE-AUGUST 1990 1000 6. FRACTU RE TOUGHNESS-STRENGTH “HALE AND POLYMERSLYIED STRENGTH CERAMICS AND GLASSE5£0MPRESSNE STRENGTH CDMFO$T65:TEN$LESTRENGTH PROCESS zone DIAMETER a; it; fire; GUIDE LINES FOR SAFE DESIGN 10 ENQiN-‘fifimg COMFOSJTES l-O J POLYMERS \- Asrsns B n z 0.1 I __.. 0.01 ' ' ‘ 0.1 l ll) 0 l NCRETE I ® ark/'3 DIIMDND _.—.-- Euewesnme QEEAMICS MO 1000 10.000 STRENGTH 0;,mPo Fig. 12—Materials selection chart 6: fracture toughness, Kn, plotted against strength cry. Materials for pressure vessels: steel, copper alloys and aluminium alloys best satisfy the “yield before break” criterion. In addition, a high yield strength allows a high working pressure. The materials in the remaining triangle are the best choice. These selection criteria are most easily applied by using the chart shown in Fig. l2. On it, the fracture toughness, Km, is plotted against strength, oy. Strong, tough, materials lie towards the top right; hard, brittle materials in the bottom right, and so on. The three criteria appear as lines of slope I, IE2 and as lines that are vertical. Take “yield before break” as an example (Fig. 12). A diagonal line corresponding to Kine, = C links materials with equal performance; those above the line are better. The line shown on Fig. 12( b) excludes everything but the toughest steels, cop- per and aluminium alloys, though some polymers nea- rly make it (pressurised lemonade and beer contain- ers are made of these polymers). The pressure which the vessel can hold depends also on the magnitude of o’y itself. The vertical line excludes 3111 materials with a yield strength below 100 MPa, leaving only tough steels and copper alloys. Large pressure vessels are always made of steel. Those for models—a model steam traction engine, for ins~ tance—are copper; it is favoured, in the small scaie application, because of its greater resistance to corro— 31021. 224 Conclusions Materials are evolving faster than ever before. New and improved materials create opportunities for in— novation. The opportunities can be missed unless a rational procedure for» material selection is followed. At the conceptual stage, while the design is still fluid, the designer must consider the full menu ofmat— erials: metals, polymers, elastomers, ceramics, glas- ses and numerous composites. Material data for a single class or sub-group of materials (suitable for the embodiment stage) are available in handbooks and computeriscd data bases; and the precise, full, data for a single material (needed at the detailed—deSign stage) are available from the supplier of the material, or can be generated by in-house tests. The difficult step is the first: choosing from the vast range of engineering materials an initial subset on which design calculations can be based. One appro— ach to this problem is described here. Data for the mechanical and thermal properties of all materials are presented as a set of materials selection Charts. ASHBY: NIATERIALS SELECTION IN ENGINEERING DESIGN The axes are chosen to display the common perfor- mance~limiting properties: modulus, strength, tou— ghness, density, thermal conductivity, wear—rate and so forth. The logarithmic scales allow performance— limiting combinations of properties (like EV‘fp or (Ii/E) to be examined and compared. The examples given in the text show how the charts give a broad overview of material performance in a given application, and allow a subset of materials (of- ten drawn from several classes) to be identified quic- kly and easily. The uses are much wider than those shown here; charts exist which help with problems of dynamics, heat transfer, thermal stress, wear and cost. They help, too, in finding a niche for new materi- als: plotted on to the charts, the applications in which the new material offers superior performance become apparent. At present, the charts exist as hand-drawn diagrams like those shown here. But it is an attractive (and attain- able) goal to store the data from which they are const— ructed in a data base coupled to an appropriate graph— ics display to allow charts with any combination of axes to be presented; and to construct on them lines which isolate materials with attractive values ol'perfw orrnance—limiting properties (j List as in the examples) leading to a printmout of candidate materials with their properties. A micro-computer based system of this sort is at present under development in the Engin- eering Department at Cambridge. References 1 Pahl G St. Beitz W, Engineering design (The Design Council, London and Springer, Berlin), 1984. 2 French M .1, Conceptual design for engineers (The Design Council. London and Springer, Berlin), 1985. 3 Dieter G E, Engineering design, A material: and processing approach (McGraw-Hill, London), I983. 4 Crane F A A & Charles J A, Selection (endure of'engineering materials (Butterworths, London}, 1984. 5 demer materials Optimism (Palmer Research Institute, Stoke Poges, Bucks, UK), 1974. 6 .Mareriais seiectbr, iMaterials engineering, Special issue (Rein- hold, Stamford, Conn, USA), 1976. 7 Ashby M F, .Maieriaiy seiecrion in design, Internal Report, CUED, Cambridge [to be published]. 8 AshbyM F, Acid M’etail, 37* (1989} in press. 9 A534 [Metals Handbook, 8th edn (American Society for Metals, Columbus, Ohio, USA), 1973. l0 Smithells C J. Metals re 'erence book, 6th edn (Butterworths, London), 1984. ll Handbook ql'piaszics and drummers, edited by C A Harper (McGraW—Hill, New York), 1975. 12 Nlorrel R, Handbook nfproperties oftecfmicai and engineering ceramic-s, Parts I and U (National Physical Laboratory, HMSO, London), 1985. 1987. ...
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