Modern Physical Metallurgy and Materials Engineering Part 15 doc

Materials for sports 411 Composite ‘woods’ have been made from CFRP. These heads, which emphasize lightness and strength, are similar in shape and style to classic wooden heads and have a similar placing of the centre of gravity. Typ- ically, they have wear-resistant alloy sole plates and a foam-filled core. Compression moulding or injection moulding are used in their manufacture. 14.4.4 Iron-type club heads The relatively narrow heads for ‘irons’ are usually made from steels and copper alloys which are shaped by either hot forging or investment casting. Stainless materials include 17Cr–4Ni and AISI Types 431 and 304. As an alternative to the traditional blade-type head, ‘cavity-back irons’ provide peripheral weighting. In a recent innovation, a non-crystalline zirconium- based alloy 2 containing Cu, Ti, Ni and Be has been used for the heads of irons (and putters). This alloy has high specific strength and good damping capacity and can be successfully vacuum cast in a glassy state without the need for ultra-fast freezing rates. 14.4.5 Putting heads Although a set of golf clubs may only contain one putter, it is typically used for 40–50% of the strokes in a game. The dynamic demands are less than those for ‘woods’ and ‘irons’, consequently putter designs have tended to be less innovative. Design parameters include ‘sweet spot’, weight distribution, bending stiff- ness, etc., as previously. Alloys used include stainless steel (17Cr–4Ni), manganese ‘bronze’ (Cu–Zn–Mn) and beryllium–copper (Cu–2Be). 14.5 Archery bows and arrows 14.5.1 The longbow For centuries, archery bows have combined design skill with knowledge of material properties. From the evidence of many well-preserved yew longbows retrieved in 1982 from the wreck of the Tudor war- ship ‘Mary Rose’, which sank in Portsmouth harbour (1545), we know that the original seasoned stave was shaped in such a way as to locate sapwood on the outer convex ‘back’ of the bow and darker heartwood at the concave ‘belly’ surface. When the bow was braced and drawn, this natural composite arrangement gave the greatest resistance to the corresponding tensile and compressive stresses. Considerable force, estimated to be in the order of 36–72 kgf (80–160 lbf), was needed 2 Vitreloy or Liquidmetal, developed at Caltech, now produced by Howmet Corp. Greenwich, CT-06830, USA. to draw a heavy longbow. 3 The mystique of the long- bow and its near-optimum design have intrigued engi- neers and scientists; their studies have greatly helped in providing a theoretical basis for modern designs of bows and arrows (Blyth & Pratt, 1976). 14.5.2 Bow design A bow and its arrows should be matched to the strength and length of the archer’s arm. A well-designed bow acts as a powerful spring and transfers stored strain energy smoothly and efficiently to the arrow. As the archer applies force and draws the bowstring from the braced condition (which already stores energy) through a draw distance of about 35 cm, additional energy is stored in the two limbs (arms) of the bow. In general, increasing the length of the bow reduces stress and increases the potential for energy storage. Upon release of the bowstring, stored energy accelerates the arrow as well as the string and the two limbs of the bow. The efficiency (Á) of the bow at the moment of loose may be taken simply as the kinetic energy of the arrow divided by work expended in drawing the bow. Alternatively, allowance can be made for the energy-absorbing movement of the two limbs, as in the Klopsteg formula: Á D m/k C m14.1 where m is the weight of the arrow and k is the ‘virtual weight’ of the particular bow. The constant term k treats energy losses in the bow as an extra burden on the driven arrow, travelling with the same velocity. For a given bow and draw force, Á increases with arrow mass. Thus, for a certain yew bow k D 23.5g, increasing the arrow weight from 23.5 g to 70.5 g increased the efficiency of the bow from 50% to 75%. Bow materials are often compared in terms of spe- cific modulus of rupture and specific modulus of elas- ticity. Thus, for wooden bows, timbers which combine ahighMoR/ with a comparatively low E/ are gen- erally preferred as they provide lightness, the necessary resistance to bending stresses and a capacity to store energy. The fine-grained hardwoods ash and wych elm meet these criteria. Although nominally a softwood, yew was favoured for longbows, its very fine grain giving remarkable bending strength. Strain energy per unit volume can be derived from the stress v. strain diagram and expressed as 0.5ε 2 E. It follows that max- imizing strain ε (below the elastic limit) is an effective way of maximizing stored energy. There are two main types of modern bow, the stan- dard recurve (Olympic) bow and the more complex compound bow. In contrast to the D-section of the 3 Skeletal remains of an archer, taken from the same shipwreck, indicate that a lifetime of drawing the longbow produced permanent physical deformation. This powerful weapon was developed in conflicts in the Welsh Marches; its ability to penetrate plate armour had both military and social significance. 412 Modern Physical Metallurgy and Materials Engineering Figure 14.4 Modern competition bow, compound-type: laminated upper limb (wood, gfrp, cfrp) and CNC-machined central riser (Al–Mg–Si alloy 6082) (courtesy of Merlin Bows, Loughborough, U.K.). Tudor longbow, limb sections of a recurve bow are wide, flat and thin, giving resistance to twisting. The energy efficiency of a compound bow (Figure 14.4) is twice that of the longbow and, as a consequence, can propel an arrow much faster, at velocities of 90 m s 1 or more. Pulley cams at the ends of the two limbs sus- tain the load at full draw during the sighting period of 10 s or more. The most powerful compound bows use light alloys for the mid-section (‘riser’ or grip) e.g. forged Al alloy, diecast Mg alloy. Laminated wood is used for some bow grips, e.g. maple plus rosewood. The two limbs are very often laminated in construction and are much less susceptible to temperature change and humidity than wood alone. Many different material combinations are used for laminae, e.g. CFRP, wood, GRP, foam, etc. For instance, in one type of compos- ite bow limb, facing and backing strips of GRP are joined to each side of a thin core strip of maple with epoxy adhesive. Tubular alloy steel limbs have been superseded as they were prone to internal aqueous cor- rosion: sudden fracture of a drawn bow (or its string) can be extremely dangerous. 14.5.3 Arrow design Successful discharge of an arrow from a bow involves a careful balancing of three arrow characteristics; namely, length, mass and stiffness (‘spine’). Subse- quent flight depends on the aerodynamic qualities of the design of head, shaft and fletching. The length of the arrow is determined by the geometry of the human body; typically, lengths range from 71 to 76 cm. The mass chosen depends initially upon the type of archery, e.g. maximum range, target shooting, etc. The prod- uct of efficiency (Á) and stored energy E s  gives the kinetic energy of the arrow, hence: ÁE s D 0.5 mv 2 o 14.2 where m D mass of the arrow and v o D its initial velocity. Thus velocity increases with bow efficiency and decreasing arrow mass. Finally, an arrow must possess an optimum, rather than maximum, stiffness (‘spine’) which must be matched to the bow. Bending stiffness of an arrowshaft is measured in a three-point bend test (Figure 7.6). Central to the design of an arrow is the phenomenon known as the Archer’s Paradox (Figure 14.5). At the loose, with the arrow pointing slightly away from the target, the arrow is subjected to a sudden compressive force along its length which, together with the deflect- ing action of the archer’s fingers, generates lateral vibrations in the moving arrow. Correct matching of the dimensions, stiffness and vibration characteristics (frequency, amplitude) of the arrow enables the arrow to clear the bow cleanly. In addition to dependence on the arrow’s dimensions, the frequency of flexu- ral vibration is proportional to the square root of the specific stiffness E/. Frequencies are in the order of 60 Hz. Reasonable agreement has been obtained between theory and high-speed cin ´ ephotographic stud- ies. 4 Of the 15 kinds of wood used as arrows for long- bows in medieval times, ash was generally regarded as the best. Nowadays, arrowshafts are tubular and made from (i) drawn and anodized aluminium alloy (7075- T9, 7178-T9), (ii) similar alloys bonded to a smooth outer wrap of unidirectional CFRP and (iii) pultruded CFRP. (Early CFRP arrows were unpopular because they tended to develop splintering damage.) Most arrowshafts are constant in diameter along their length but have the disadvantage that their bending moment varies, increasing from zero at the ends to a maximum at the centre. Tapering (‘barrelling’) the tubular shaft from the middle to the ends reduces this undesirable flexing characteristic: barrelled arrows are used by top professionals. Feathers are the traditional fletching material and still used but are fragile and suffer from the weather. They rotate the arrow and give stability during flight 4 At the Royal Armaments Research & Development Establishment (RARDE), UK. Materials for sports 413 Figure 14.5 The Archer’s Paradox (after Pratt, 1976). but consume kinetic energy. Smooth polymeric vanes made from polyethylene terephthalate (Mylar)are strong, weather resistant and, because of their lower aerodynamic drag, give greater range; the same poly- mer is also commonly used in stranded form (Dacron) for bowstrings. 14.6 Bicycles for sport 14.6.1 Frame design The modern bicycle is a remarkable device for con- verting human energy into propulsion. The familiar diamond frame, with its head, top, seat and down tubes, evolved in the late nineteenth century. When in use, it distorts elastically; this compliance provides rider comfort. Compliance absorbs energy and frame stiffness is accordingly maximized in racing machines. The stress distribution in a working frame is complex, being in-plane as well as out-of-plane. Sudden impact stresses must be withstood. Poor design, workman- ship and/or maintenance can lead to component failure which, because of the fluctuating nature of stressing, often has fatigue characteristics. McMahon & Graham (1992) have provided a detailed comparison of typical tube materials for frames. Beam theory is used to identify the key design parameters. The basic linking formula which expresses the stresses and strains at points along a beam deflecting under load is: M/I D /y D E/r 14.3 where M D bending moment, I D moment of inertia of beam section,  D stress at a point, y D distance of point from neutral axis of beam, E D modulus of elasticity and r D radius of curvature of loaded beam. In particular, we are concerned with (i) the maximum tensile stress  max in the convex surface of a tube subjected to a nominal bending moment and (ii) the corresponding radius r of bending. Obviously,  max should bear a good relation to the yield strength of the material and r should be maximized. A tubular cross-section offers special advantages. Within a bent beam, it locates as much material as possible in the highly stressed regions which lie distant from the neutral axis: this axis lies in the plane mark- ing the transition from tension to compression. Being symmetrical in section, a tube can be loaded trans- versely in any direction and can withstand torsion. Its moment of inertia is D 4  d 4 /64, where D and d are the outside and inside diameters of the tube, respec- tively. From relation (14.3) it can be seen that, for a given bending moment, increasing the moment of iner- tia reduces stress and increases the radius of curvature. In similar fashion, it can be reasoned that reducing the tube wall thickness increases the surface stress  max . Sometimes it is beneficial to raise the moment of iner- tia by changing from a circular cross-section to a more expensive elliptical cross-section. Thus, in front wheel forks, which are subjected to severe bending stresses, an increase in the major diameter of the ellipse reduces stress in the crucial plane. Table 14.1 compares the bending characteristics of tubes made from four typical materials used for cycle frames; that is, from plain carbon steel, 0.3C–Cr–Mo alloy steel (AlSl 4130), 6061 (T6) aluminium alloy and Ti–3Al –2.5V alloy. Calculated values for bend curvature and maximum stress, which are the crite- ria of stiffness and permissible loading, are compared. The frames of mountain bicycles must sustain sudden impact shocks; accordingly, larger-diameter (D) and/or thicker-walled tubing is used for certain frame mem- bers in order to reduce stress levels. The specific elastic moduli E/ for the four materials are similar. Alu- minium alloy offers weight saving but, because of its relatively low E value (70 GN m 2 ), at the expense of greater flexure of the frame. Titanium alloy allows reductions in tube diameter and wall thickness; its spe- cific yield strength  y / is about two and a half times greater than that of Cr–Mo steel. Although not included in Table 14.1, cold-drawn seamless Mn–Mo tube steels have a special place in the history of competitive cycling. e.g. Reynolds 531. Their nominal composition is 0.25C–1.4Mn –0.2Mo. Introduced in the 1930s, they have been used for the frames of many Tour de France winners and are still 414 Modern Physical Metallurgy and Materials Engineering Table 14.1 Comparison of weight and bending characteristics of four metallic frame materials: r and  max calculated for tubes subjected to a bending moment of 100 N m (from McMahon & Graham, 1992) Material DdMoment Mass per Radius of Maximum  max / y (mm) (mm) of inertia I unit length curvature r stress  max (cm 4 )(gm 1 ) (mm) (MN m 2 ) Racing cycles C steel 28.70 26.16 1.041 860 48 138 0.58 Cr–Mo steel 28.78 26.93 0.750 601 67 190 0.39 Al alloy 28.80 25.91 1.124 332 127 128 0.50 (6061-T6) Mountain cycles (Top tube) Al alloy 38.10 35.56 2.50 397 57 76 0.30 (6061-T6) Ditto 34.93 30.81 2.87 575 49 61 0.24 Ti–3Al–2.5V 31.75 29.47 1.41 549 64 45 0.18 widely used for racing cycles. 5 14.6.2 Joining techniques for metallic frames The above guidelines provide a general perspective but do not allow for the potentially weakening effect of the thermal processes used for joining the ends of individual frame tubes. Such joints often coincide with the highest bending moments. In mass produc- tion, the cold-drawn low-carbon steel tubes of standard bicycle frames are joined by brazing. Shaped rein- forcing sockets (lugs) of low–carbon steel, together with thin inserts of solid brazing alloy, are placed around the tube ends, suitably supported, and heated. A 60Cu–40Zn alloy such as CZ7A (British Stan- dard 1845) freezes over the approximate temperature range of 900–870 ° C as the frame cools and forms a strong, sufficiently ductile mixture of ˛ and ˇ phases (Figure 3.20). Butted tubes are commonly used to counteract softening of the steel in the heat-affected zones (HAZ); they have a smaller inside diameter (d) toward the tube ends. For limited production runs of specialized racing frames made from butted alloy tubes, fillet brazing with an oxy-acetylene torch at a lower temperature is more appropriate, using a silver brazing alloy selected from the AG series of British Standard 1845, such as 50Ag–15Cu–16Zn –19Cd (melting range 620–640 ° C). Cadmium-free alloys are advocated if efficient fume-extraction facilities are not available because CdO fumes are dangerous to health. Tungsten-inert gas (TIG) welding 6 is widely used and has tended to replace brazing, e.g. lugless Cr–Mo steel frames for mountain bicycles. Unlike oxyacety- lene flames, heating is intense and very localized. The hardenability of Cr–Mo steels is such that a strong 5 ‘531’ tubes were used for the chassis of the jet-powered Thrust 2 vehicle in which Richard Noble broke the one-mile land speed record (1983), achieving a speed of 1019 km h 1 6 Patented in the 1930s in the USA., where argon and helium were available, this fluxless arc process is widely used for stainless steels and alloys of Al, Ti, Mg, Ni and Zr. mixture of dispersed alloy carbides, pearlite and possi- bly bainite forms in the weld fillet as they air cool from temperatures above 850 ° C. The latest type of low- alloy steel for frames, available in either cold-drawn or heat-treated condition (Reynolds 631 and 853), is air hardening. Although inherently very hard (400 VPN), TIG-welding increases its hardness in the HAZ. It pos- sesses better fatigue resistance than other alloy steels and its strength/weight ratio makes it competitive with Ti–3Al–2.5V alloy and composites. Aluminium alloy tubes, which are solution treated and artificially aged (T6 condition), present a problem because heating during joining overages and softens the structure, e.g. 6061, 7005. The high thermal con- ductivity of aluminium worsens the problem. Titanium alloys, such as the frame alloy Ti–3Al –2.5V, absorb gases and become embrittled when heated in air, e.g. oxygen, nitrogen, hydrogen. Again, it is essential to prevent this absorption by shrouding the weld pool with a flowing atmosphere of inert gas (argon). 14.6.3 Frame assembly using epoxy adhesives These joining problems encouraged a move toward the use of epoxy adhesives with sleeved tube joints. 7 As well as helping to eliminate the HAZ problem, adhesives make it possible to construct hybrid frames from various combinations of dissimilar materials (adherends), including composites. Brake assemblies can be glued to CFRP forks. Adhesive bonds also damp vibrations, save weight, reduce assembly costs and are durable. Extremes of humidity and tempera- ture can cause problems and care is essential during adhesive selection. Adhesives technology meets the 7 Adhesive-bonded racing cycles, sponsored by Raleigh Cycles of America, were highly successful in the 1984 Olympic Games. Subsequently, Raleigh made mountain cycles from aluminium alloy tubes (6061-T8) bonded with Permabond single-part ESP-311 epoxy adhesive. Materials for sports 415 stringent demands of modern aircraft manufacturers 8 and makes a vital contribution throughout the world of sport. The structural adhesives most widely used in gen- eral engineering are the epoxy resins; their ther- mosetting character has been described previously (Section 2.7.3). Normally they are water resistant. They form strong bonds but, being in a glassy state, are brittle. Accordingly, thermoplastic and/or elastomeric constituents are sometimes included with the ther- mosetting component. When using the two-part ver- sion of a thermosetting adhesive, it is important to control the proportions of basic resinous binder and catalytic agent (hardener) exactly, to mix thoroughly and to allow adequate time for curing. In single-part epoxy adhesives the resin and hardener are pre-mixed: rapid curing is initiated by raising the temperature above 100 ° C. Thermoplastic adhesives, used alone, are weaker, more heat sensitive and less creep resistant. Elastomeric adhesives, based on synthetic rubbers, are inherently weak. Meticulous preparation of the adherend surfaces is essential for all types of adhesive. 14.6.4 Composite frames Epoxy resins are also used to provide the matrix phase in the hollow, composite frames of high-performance bicycles. Carbon fibre reinforced polymers (Section 11.3.2.1) combine high strength and stiffness; their introduction facilitated the construction of monocoque (single shell) frames and led to the appearance of a remarkable generation of record- breaking machines. 9 Typically, they feature a daring cantilevered seat, a disc rear wheel and three-spoke open front wheels, all of which are made from CFRP. An example is depicted in Figure 14.6. 14.6.5 Bicycle wheels The familiar array of wire spokes between axle and rim normally uses hard-drawn wire of either plain 0.4% carbon steel (AISI 1040) or austenitic 18Cr–8Ni stain- less steel (McMahon & Graham, 1992). Each spoke is tangential to the axle, thus preventing ‘wind-up’ displacement between axle and rim, and is elastically pretensioned (e.g. 440 MN m 2 )sothatitisalwaysin tension during service. During each wheel revolution, the stress on a given spoke is mostly above the preten- sion stress, falling once below it. Under these cyclic conditions, carbon steel has a greater nominal fatigue endurance than the corrosion-resistant 18/8 steel but 8 Urea-formaldehyde resins (Beetle cements) revolutionized aircraft building in the 1940s when they were used for bonding and gap-filling functions with birchwood/balsa composites and spruce airframes e.g. De Havilland Mosquito, Airspeed Horsa gliders. 9 The prototype was the Lotus bicycle on which Chris Boardman won the 4000 m individual pursuit in the 1992 Olympic Games at Barcelona. Figure 14.6 High-performance Zipp bicycle with monocoque frame (courtesy of Julian Ormandy, School of Metallurgy and Materials, University of Birmingham, UK). has a smaller resistance to corrosion fatigue. The latter property is boosted by plating the carbon steel with a sacrificial layer of zinc or cadmium. Both types of steel respond well to the strain-hardening action of wire drawing through tungsten carbide dies. Wheel rims should be strong, stiff, light and corrosion resistant. They are often formed by bending strips of extruded, precipitation-hardenable aluminium alloy to shape and joining e.g. 6061-T6. Conventional multi-spoked wheels generate energy- absorbing turbulence during rotation. The distinctive CFRP front and rear wheels of highly specialized time- trial machines, made by such firms as Lotus, Zipp, RMIT-AIS and Ultimate Bike, have a much lower aerodynamic coefficient of drag. They are the prod- ucts of extensive computer-aided design programmes, wind tunnel simulations and instrumented performance testing. 14.7 Fencing foils A typical steel foil is about 0.9 m long and tapers to a rectangular cross-section of 4 mm ð 3 mm. This design gives a low resistance to buckling under the large axial stress produced when an opponent is struck directly, an action which can bend the foil forcibly into a radius as small as 20 cm. Traditionally, sword- makers use medium-carbon alloy steels of the type employed in engineering for springs. The extensive range of elastic behaviour that is associated with a high yield strength is obviously desirable. The foil is formed by hot working 10 mm square bar stock and then oil quenching and tempering to develop a marten- sitic structure with a yield strength in the order of 1500–1700 MN m 2 . On occasion, during a fencing bout, the applied stress exceeds the yield strength and the foil deforms plastically: provided that the foil is defect free, the fencer can restore straightness by care- ful reverse bending. In practice, however, used foils are not defect free. During bouts, repeated blows from the opposing blade produce small nicks in the surface 416 Modern Physical Metallurgy and Materials Engineering of a foil. In time, it is possible for one of these stress- raising notches to reach a critical size and to initiate fatigue cracking within the tempered martensite. Final failure occurs without warning and the buttoned foil instantly becomes a deadly weapon. One research response to this problem was to con- centrate upon improving fracture toughness and resis- tance to fatigue failure, thus eliminating instantaneity of failure. 10 In this alternative material, a steel–steel composite, lightly tempered fibres of martensite are aligned within a continuous matrix phase of tough austenite. 10 mm square feedstock of duplex steel for the blade-forging machine is produced by diffusion annealing packs of nickel-electroplated bars of spring steel at a temperature of 1000 ° C, extruding and hot working. While the bars are at elevated temperatures, nickel interdiffuses with the underlying steel. Nickel is a notable austenite ()-forming element, as indicated previously in Figure 9.2. The optimum volume frac- tion of tough austenite is about 5%. This duplex mate- rial has the same specific stiffness as the conventional steel and has greater fracture toughness. In the event of a surface nick initiating a crack in a longitudinal filament of brittle martensite, the crack passes rapidly across the filament and, upon encountering the tough interfilamentary austenite, abruptly changes direction and spreads parallel to the foil axis, absorbing energy as the austenite deforms plastically and new surfaces are formed. In practical terms, if the fencer should fail to notice marked changes in the handling character- istics of a deteriorating foil, the prolonged nature of final fracture is less likely to be dangerous and life threatening. Although safer, the duplex foil involves increased material-processing costs and has a yield strength about 5–10% lower than that of heat-treated spring steel. Highly alloyed maraging steels (Section 9.2.3) are used nowadays for top-level competition fencing. By combining solid solution strengthening with fine pre- cipitation in low-carbon martensite, they provide the desired high yield strength and fracture toughness. A typical composition is 0.03C (max)–18 Ni–9 Co –5 Mo –0.7 Ti–0.1 Al. 14.8 Materials for snow sports 14.8.1 General requirements The previously quoted examples of equipment fre- quently share common material requirements and prop- erties, such as bending stiffness, yield strength, tough- ness, fatigue resistance, density and comfort. However, each sport makes its own unique demands on materials. In snowboarding and skiing equipment, for instance, additional requirements include toughness at sub zero temperatures (say down to 30 ° C), low frictional drag 10 Materials research conducted at Imperial College, London, on behalf of the fencing sword manufacturers, Paul Leon Equipment Co. Ltd, London (Baker, 1989). and resistance to prolonged contact with snow and moisture. More specifically, in cross-country (Nordic) skiing, lightness is very important as it makes striding less tiring. From a commercial aspect, it is desirable that materials for individual items of equipment should be able to display vivid, durable colours and designer logos. 14.8.2 Snowboarding equipment The bindings which secure a snowboarder’s boots to the top surface of the board are highly stressed dur- ing a downhill run. Good binding design provides a sensitive interaction between the board and the snow- boarder’s feet, facilitating jumps and turns. Modern designs are complex and usually employ a variety of polymers. Thus, the recent snowboard design shown in Figure 14.7 includes components made from an acetal homopolar (Delrin), a nylon-based polymer (Zytel) and a thermoplastic polyester elastomer (Hytrel). 11 Highly crystalline Delrin is tough, having a low glass- transition temperature T g , and strong and fatigue resistant. It is also suitably UV resistant and moisture resistant. Zytel is tough at low temperatures, can be moulded into complex shapes and can be stiffened by glass-fibre reinforcement. The third polymer, Hytrel, has properties intermediate to those of thermoplas- tics and elastomers, combining flexibility, strength and fatigue resistance. Both Hytrel and the nylon Zytrel can be fibre reinforced. Thus, some snowboard blades are made from Zytrel reinforced with fibres of either glass or aramid (Kevlar). Colourants mixed with the resins give attractive moulded-in colours. Figure 14.7 Snowboard binding utilizing: thermoplastic elastomer (Hytrel)—ankle strap A, spoiler B, ratchet strap G, nylon (Zytrel)—side frames D and H, base and disc F, top frame J; acetal homopolar (Delrin)—strap buckles C1 and C2 (courtesy of Fritschi Swiss Bindings AG and Du Pont UK Ltd). 11 Delrin, Hytrel and Zytel are registered trademarks of DuPont. Materials for sports 417 Figure 14.8 Transverse section showing multi-component structure of a downhill ski (from Easterling, 1990 by permission of the Institute of Materials). 14.8.3 Skiing equipment In the older sport of skiing, the principal items of equipment are the boots, bindings, skis and poles. External Hytrel–Kevlar components have been used to enhance the stiffness of ski boots; this feature gives the boots a firmer grip on the skier’s ankles and leads to better control of the skis. Polymers feature promi- nently in many design of ski bindings. For instance, in the Fritschi Diamir touring binding, 12 acetal poly- mer (Delrin) is used for the locking bar, heel release lever, heel block and front swivel plate while glass- reinforced nylon (Zytel) is used for the front block and the two base plates. Modern ski designs aim at solving the conflicting requirements of (i) longitudinal and torsional stiffness that will distribute the skier’s weight correctly and (ii) flexibility that will enable the ski to conform to irregularities in the snow contour (Easterling, 1993). Originally, each ski runner was made from a single piece of wood, e.g. hickory. Laminated wood skis appeared in the 1930s. The adoption of polymers for ski components in the 1950s, combining lightness and resistance to degradation, was followed by the introduction of metal frames for downhill skis, e.g. alloy steel, aluminium alloy. By the 1960s, GRP and CFRP were coming into prominence. The internal structure of a ski is determined by the type of skiing and, as Figure 14.8 shows, often uses a surprising number of different materials. Skis usually have a shock-absorbing, cellular core that is natural (ash, hickory) and/or synthetic (aramid, aluminium, titanium 12 Used by Hans Kammerlander in his 1996 ski descent of Mount Everest. or paper honeycomb). Polyethylene and polyurethane have been used for the soles of skis. Modern ski poles are tubular and designed to give high specific stiffness and good resistance to impacts. Nowadays, CFRP–GRP hybrids are favoured. The pointed tips are sometimes made of wear-resistant carbide. 14.9 Safety helmets 14.9.1 Function and form of safety helmets Most sports entail an element of personal risk. The main function of a safety helmet is to protect the human skull and its fragile contents by absorbing as much as possible of the kinetic energy that is vio- lently transferred during a collision. The three principal damaging consequences of sudden impact are fracture of the skull, linear acceleration of the brain relative to the skull, and rotational acceleration of the brain. Although linear and rotational acceleration may occur at the same time, many mechanical testing procedures for helmets concentrate upon linear acceleration and use it as a criterion of protection in specifications. A typical helmet consists of an outer shell and a foam liner. The shell is usually made from a strong, durable and rigid material that is capable of spreading and redistributing the impacting forces without suffer- ing brittle fracture. This reduction in pressure lessens the risk of skull fracture. The foam liner has a cel- lular structure that absorbs energy when crushed by impact. Specialized designs of helmets are used in cycling, horse riding, canoeing, mountaineering, ski- ing, skate boarding, ice hockey, etc. Some designs are quite rudimentary and offer minimal protection. 418 Modern Physical Metallurgy and Materials Engineering In general, the wearer expects the helmet to be com- fortable to wear, lightweight, not restrict peripheral vision unduly and be reasonably compact and/or aero- dynamic. Production costs should be low. Increasing the liner thickness is beneficial but, if the use of hel- mets is to be promoted, there are size constraints. Thus, for a cricket helmet, acceptable shell and liner thick- nesses are about 2–3 mm and 15 mm, respectively (Knowles et al., 1998). Strong and tough helmet shells have been produced from ABS and GRP. The great majority of shock- absorbent foam linings are made from polystyrene (Figure 14.9): polypropylene and polyurethane are also used. 14.9.2 Mechanical behaviour of foams Polymeric foams provide an extremely useful class of engineering materials (Gibson & Ashby, 1988; Dyson, 1990). They can be readily produced in many different structural forms by a wide variety of methods using either physical or chemical blowing agents. Most thermoplastic and thermosetting resins can be foamed. The properties of a foam are a function of (i) the solid polymer’s characteristics, (ii) the relative density of the foam; that is, the ratio of the foam density to the density of the solid polymer forming the cell walls / s , and (iii) the shape and size of the cells. Relative density is particularly important; a wide range is achievable (typically 0.05–0.2). Polymer foams are often anisotropic. Broadly speaking, two main types of structure are available: open-cell foams and closed- cell foams. Between these two structural extremes lies a host of intermediate forms. In the case of safety helmets, the ability of a liner foam to mitigate shock loading depends essen- tially upon its compression behaviour. Initially, under compressive stress, polymer foams deform in a lin- ear–elastic manner as cell walls bend and/or stretch. Figure 14.9 Cell structure of polystyrene foam, as used for shock-absorbent packaging: average cell diameter 100 µm (courtesy of Chris Hardy, School of Metallurgy and Materials, University of Birmingham, UK). With further increase in stress, cell walls buckle and collapse like overloaded struts; in this second stage, energy absorption is much more pronounced and defor- mation can be elastic or plastic, depending upon the particular polymer. If the cells are of the closed type, compression of the contained air makes an addi- tional and significant contribution to energy absorp- tion. Eventually the cell walls touch and stress rises sharply as the foam densifies. This condition occurs when a liner of inadequate thickness ‘bottoms out’ against the helmet shell. The design of a helmet liner should provide the desired energy absorption with- out ‘bottoming out’ and at the same time keep peak stresses below a prescribed limit. Some polymeric structures can recover their origi- nal form viscoelastically and withstand a number of heavy impacts; with others, a single impact can cause permanent damage to the cell structure, e.g. expanded PS. After serious impact, helmets with this type of liner should be destroyed. Although this requirement is impracticable in some sporting activities, there are cases where single-impact PS liners are considered to be adequate. 14.9.3 Mechanical testing of safety helmets Various British Standards apply to protective helmets and caps for sports such as climbing (BS 4423), horse- and pony riding (BS EN 1384) and pedal cycling, skateboarding and rollerskating (BS EN 1078). These activities involve different hazards and accordingly the testing procedures and requirements for shock absorp- tion and resistance to penetration differ. In one typical form of test, a headform (simulating the mass and shape of the human head) is encased in a helmet and allowed to fall freely through a certain distance against a rigid anvil. Specified headform materials (BS EN 960) depend on the nature of the impact test and extend from laminated hardwood (beech) to alloys with a low resonance frequency (Mg–0.5Zr). A tri- axial accelerometer is affixed to the headform/helmet assembly in the zone of impact. The area beneath the curve of a continuous graphical record of striking force v. local deformation taken during the test provides a useful measure of the kinetic energy absorbed as the helmet structure is crushed. Specified values for permissible peak acceleration at impact which appear in test procedures vary but generally extend up to about 300 g,whereg (acceleration due to gravity) D 9.81 m s 2 . Drop heights range from about 1 to 2.5 m, depending upon the striking force required. Test spec- ifications often include requirements for helmets to be mechanically tested after exposure to extremes of tem- perature, ultraviolet radiation and water. On occasions, unsafe and/or inadequate helmets are marketed: natu- rally, closer international collaboration and regulation is being sought. Materials for sports 419 Further reading Baker, T. J. (1989). Fencing blades—a materials challenge. Metals and Materials, Dec., 715–718, Institute of Materials. Blyth, P. H. and Pratt, P. L. (1992). The design and materials of the bow/the arrow, Appendices to Longbow: A Social and Military History, 3rd edn. by Robert Hardy. Patrick Stephens Ltd, Cambridge. Cochran, A. (ed.) (1994). Golf: the Scientific Way.Aston Publ. Group, Hemel Hempstead, Herts. UK. Easterling, K. E. (1993). Advanced Materials for Sports Equipment. Chapman & Hall Ltd, London. Gibson, L. J. and Ashby, M. J. (1988). Cellular Solids–Stru- cture and Properties. Pergamon Press. Knowles, S., Fletcher, G., Brooks, R. and Mather, J. S. B. (1998). Development of a superior performance cricket helmet, in The Engineering of Sport (ed. S. J. Haake). Blackwell Science, Oxford. Lees, A. W. (ed.) (1989). Adhesives and the Engineer. Mechanical Engineering Publications Ltd, London. McMahon, C. J. and Graham, C. D. (1992). Introduction to Materials: the Bicycle and the Walkman. Merion Books, Philadelphia. Pearson, R. G. (1990). Engineering Polymers (ed. R. W. Dyson), Chapter 4 on foams, pp. 76–100, Blackie & Son Ltd, Glasgow and London. Shields, J. (1984). Adhesives Handbook. 3rd edn. Butter- worths, Oxford. Appendix 1 SI units The Syst ` eme Internationale d’Unit ´ es (SI) was intro- duced in the UK in the late 1960s. Historically, the SI can be traced from the metric enthusiasms of Napoleonic times, through a centimetre–gram (c.g.) system, a centimetre–gram–second (c.g.s.) system, a metre–kilogram–second (MKS) system in 1900 and a metre–kilogram–second–ampere (MKSA Giorgi) system in 1950. Table A1 lists the seven basic units and Table A2 lists the prefixes. The SI is ‘rational, comprehensive and coherent’. Coherency means that the product or quotient of basic units gives an appropriate derived unit of the resultant quantity. A coherent system facilitates manipulation of units, checking the dimensions of equations and, most importantly, the correlation of different disciplines. Some of the more frequently-used derived units are given in Table A3. The force unit, the newton, is the cornerstone of the SI. Appropriately, the gravitational attraction for an apple is roughly one newton. The SI unit of stress is Nm 2 : the pascal (Pa) is an orphan, being non-SI and non-coherent. Energy is defined in mechanical terms, being the work done when the point of application of a force of 1 N is displaced through a distance of 1 m in the direction of the force. Table A1 Quantity Unit Symbol Length metre m Mass kilogram kg Time second s Electric current ampere A Temperature degree Kelvin K Luminous intensity candela cd Amount of substance mole mol Table A2 Factor Prefix Symbol 10 12 tera T 10 9 giga G 10 6 mega M 10 3 kilo k 10 2a hecto a h a 10 1a deca a da a 10 1a deci a d a 10 2a centi a c a 10 3 milli m 10 6 micro  10 9 nano n 10 12 pico p 10 15 femto f 10 18 atto a a Discouraged Table A3 Physical quantity SI unit Definition of unit Volume cubic metre m 3 Force newton (N) kg m s 2 Pressure, stress newton per N m 2 square metre Energy joule (J) N m Power watt (W) J s 1 Electric charge coulomb (C) A s Electric potential volt (V) W A 1 Electric resistance ohm ()VA 1 Electric capacitance farad (F) A s V 1 Frequency hertz (Hz) s 1 [...]... 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Materials Vincent, J (1990) Metals and Materials, June, 395, Institute of Materials Walker, P S and Sathasiwan, S (1999), J Biomat 32, 28 Chapter 14 Butterfield, B G and Meylan, B A (1980) ThreeDimensional Structure of Wood: an Ultrastructural Approach, 2nd Edn Chapman and Hall, London Easterling, K E (1990) Tomorrow’s Materials Institute of Metals, London Haines, R C., Curtis, M E., Mullaney, F M and. .. 894.76 N m 2 1 rad 27 GN m 2 83 GN m 2 74 GN m 2 45 GN m 2 30 GN m 2 9.964 02 kN 15. 444 3 MN m 2 103 kg 133.322 N m 2 2.997 925 ð 108 m s 1 Figure references Chapter 1 Rice, R W (1983) Chemtech 230 Chapter 2 Askeland, D R (1990) The Science and Engineering of Materials, 2nd (SI) edn Chapman and Hall, London Chapter 3 Brandes, E A and Brook, G B (1992) Smithells Metals Reference Book Butterworth-Heinemann,... contours, 156 bright -and dark-field imaging, 147, 161 convergent beam diffraction pattern (CBDP), 149 diffraction contrast, 147 dynamical theory, 158 –60 electron channelling, 145–6 first-order Laue zones (FOLZ), 150 g-vector, 156 –8 higher-order Laue zones (HOLZ), 149 higher-voltage electron microscopy (HVEM), 149–50 imaging of dislocations, 147, 157 –8, 159 , 166 Kikuchi lines, 148 kinematical theory, 156 scanning... and Suzuki, T (1981) Metall Trans 12A, 1647 Sidjanin, L and Smallman, R E (1992) Mat Science and Technology, 8, 105 Smithells, C J., Smithells Metals Reference Book, 7th edn Butterworth-Heinemann Woodfield, A P., Postans, P J., Loretto, M H and Smallman, R E (1988) Acta Metall., 36, 507 Chapter 10 Bovenkerk, H P et al (1959) Nature, 184, 1094–1098 Green, D J (1984) Industrial Materials Science and Engineering, ... 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The design and materials of the bow/the arrow,