Sports materials

12.3 Sports materials

12.3.1 Introduction

Formula 1 motor racing and ocean-going yacht racing have always attracted large sums of money for the latest materials development in the search for lighter, faster and more energy-efficient progress. However, in the last two decades there has been an enormous growth in the application of advanced materials to sports equipment for individual use, i.e. tennis rackets, golf clubs, bicycles, etc. The application of these high-performance materials is again high cost, but the competitive nature of both the professional sportsman and amateur has driven a growth in the sports equipment market which is quite remarkable. Golf clubs and tennis rackets which used to cost a few tens of pounds now cost several hundreds, but the incurred benefits in terms of performance and achievement justifies the extra financial outlay.

In this section, a case examination is made of the materials specifically developed for golf, tennis, cycling, skiing, archery and fencing, together with a consideration of the materials developed for protection when participating in these sports.

12.3.2 Golf equipment

A golf club consists essentially of two parts, the shaft and the head. Design considerations for the shaft include its weight, bending stiffness and torsional stiffness. During the drive the shaft tends to bend and twist a few degrees. Torsional stiffness keeps the club head face ‘square’ to the direction of flight on impact and is therefore desirable. However, off-center impact is often related more to the non-planar nature of the swing than torsional stiffness, off-center impact causing the ball either to hook or to slice. Bending of the shaft in a typical swing is shown in Figure 12.10. Stiff shafts tend to reduce the bending moment. The bend point of the shaft (or shaft region with the minimum radius of curvature during bending) is also important. A bend point higher up the shaft is favored by the big hitters.

A variety of materials have been used to make the shaft, which is usually hollow to minimize the weight. These include alloy steel, (7XXX) aluminum alloys, Ti–6Al–4V and more recently compos- ites. Epoxy matrices with carbon, Kevlar, glass or boron are used for reinforcement in composite shafts. The so-called ‘graphite’ shafts are CFRP hollow shafts and are extremely light with a high damping capacity for the impact vibrations which travel along the shaft to the grip. They are made by wrapping pre-preg sheets of carbon fiber around a tapered mandrel, by filament winding around a mandrel or resin transfer molding (see Chapter 11). Composite manufacture allows some manipula- tion of the torsional stiffness and bend point. The balance point of the shaft can also be manipulated to meet the demands of the variety of club heads being designed.

Early driver heads were traditionally made of persimmon with a plastic face insert, sole plate and incorporating a head plug to adjust the center of gravity and weight to around 200 g. Such a small head required great skill and accuracy to strike the ‘sweet spot’ on the club face. A revolution in driver head design has been made with the introduction of a larger hollow metal volume, which enables the larger sweet spot to be located easily. Metal processing can produce these large-headed ‘woods’ in stainless steel, maraging steels, aluminum alloys, Ti–6Al–4V and other titanium alloys (Ti–15Cr–6Zr). A zirconium-based alloy, Zr–13.2 Cu–11 Ti–9.8 Ni–3.4 Be, in the amorphous state

Case examination of biomaterials, sports materials and nanomaterials 599 18

16 Impact with ball

6 Start

Shaft bent forwards

4 of downswing

Planar bending moment (Nm) ⫺ 6 Shaft bent backwards ⫺ 8 Oscillations due to backswing

⫻ 10 ⫺ 1 Figure 12.10 Shaft bending in typical swing of golf club (after Horwood, 1994).

Time (seconds)

has also been developed – a glassy metallic club surface can increase the coefficient of restitution at the impact with the golf ball. Most ‘oversized’ driver heads are now made with titanium alloys, metastable β-Ti alloys or (α + β) Ti alloys, incorporating a crown, face and sole plate. An integrated design can be investment cast and the precision casting may be welded by tungsten inert gas (TIG) or electron beam welding (EBW) to form a thin-walled hollow shell, which may be filled with low-density foam. With hollow cavity heads the moment of inertia is greater and the center of gravity is located closer to the strike face. Some designs still use separate inserts, e.g. TriMetal clubs, which have a maraging steel face and Cu/W sole plate to lower the center of gravity. Such innovative features confer a more forgiving club head with regard to inaccurate striking. A greater moment of inertia reduces head twisting when the impact is off the sweet spot, thereby reducing ball spin.

Generally, the components should be as thin as possible, have a high yield stress and low elastic modulus. Such a σ y /

E index minimizes any plastic deformation by impact and maximizes elastic deformation. It therefore follows that components fabricated by forging or rolling will be superior to cast because of their finer microstructure coupled with finer precipitates, resulting in high yield strength. Welding of the high-strength alloys may require post-weld heat treatment.

The club heads of ‘irons’ are also undergoing development. Commonly made of stainless steels, 17Cr–14Ni, AISI Types 431 and 304 by either forging or investment casting, the traditional blade is hollowed out at the back to produce ‘cavity-back’ iron heads. This produces peripheral weighting, which is more ‘forgiving’ for off-center shots. Putters have less dynamic demands than woods and irons, and most design features are for weight distribution, balance and sweet spot. The traditional flat-faced, hollow-backed ‘ping putter’ made with cast manganese bronze (Cu–Zn–Mn) is still fashionable but more putters are now large flat-bottomed made of stainless steel.

With modern materials golf balls have developed into a three-layer composite. The inner core is generally made of solid or liquid filled rubber which is covered with a polybutediene layer. The outer coating is made of an ionomer (surlyn) or polyurethane and is dimpled. These dimples ( ∼400) are either round or hexagonal in shape and cover more than three-quarters of the ball surface. The dimples alter the aerodynamic drag on the ball by producing a boundary layer on the ball which is turbulent

600 Physical Metallurgy and Advanced Materials at a lower velocity than on a smooth ball. This leads to a reduced pressure drag which remains fairly

constant with increased speed.

12.3.3 Tennis equipment

Tennis racket frames have, over the years, developed from wood through aluminum to graphite com- posite materials. Frames of wood and aluminum are now out of favor and are almost exclusively graphite. Graphite composite frames are stronger and stiffer than other frames and can be manu- factured with a larger head. Impact and vibration decrease with frame stiffness, favoring graphite frames and, because they are lighter, may be swung somewhat faster. Almost all the top graphite rackets are manufactured from thermoset carbon fiber composites with extra glass fiber reinforce- ment and the racket tip for high impact resistance. Basic carbon pre-preg sheets are cut at different angles and widths to produce layers (Figure 12.11). In the lay-up, zero degree pre-preg is used for bending stiffness and 45 ◦ pre-preg for torsional stiffness. The tube for the racket frame is formed by folding around a polyamide thermoplastic nylon 66 foil tube. The throat piece is made by wrapping pre-preg around expandable foam. All the pieces, frame, pre-preg layer handle and throat, are then assembled inside the mold, closed and given the appropriate temperature-curing cycle. Finishing includes removing excess resin, sanding, drilling the grommet holes for the strings, lacquering and hardening.

Natural gut from the intestines of cows is probably the top choice of professionals for strings, but is less readily available and extremely expensive. Strings made from nylon are by far the most used, but Kevlar and polyester are also used. The strings must be resistant to UV radiation, abrasion, moisture, creep and any chemical agents such as sweat, oils, etc. However, the major requirement is to reduce the impact force on the hand and arm, and provide ball control and impact power. Strings are typically 1.3 mm in diameter, made from a braid composed of plaited and inter- twined bundles of strong fibers. After immersion in an elastomeric solution, the string is given a polymeric coating to protect it from abrasion and wear. They are strung at a tension typically of 250–300 N, when high tension leads to improved ball control and lower tension to increased power. Being viscoelastic, the strings lose tension with time from stringing, which has to be allowed for in manufacture.

Tennis balls intended for fast courts such as grass consist of a hollow rubber compound core covered by a felt fabric. The core is made by gluing segments together with an adhesive, which is subsequently cured. The ball is slightly pressurized with a gas which gradually leaks after removal from the pressurized container. Thus, the balls lose bounce and have to be replaced after a number of games. Pressureless balls having a thicker core are used by amateurs and weekend players. All balls must conform to standards of size and bounce. Tennis balls have a relatively high drag coef- ficient, as a result of the ‘fuzz’ on the felt covering, which decreases as the fuzz wears with games played.

12.3.4 Bicycles

Almost everybody has grown up having owned a bicycle. They are probably the most energy-efficient means of travel and have rarely failed us. Nevertheless, the stress distribution in the frame is both in-plane and out-of-plane and, being quite complex, can lead to failure. For most bikes the failure is likely to be a fatigue type, originating at the usual places of high stress. Low-carbon steel is the most common material for bike frames, being cheap, tough, weldable and easy to paint, but the relative merits of other materials are shown in Table 12.3 based on simple deflecting beam

Case examination of biomaterials, sports materials and nanomaterials 601

Pre-preg layers

Parts

Material Fiber angle 1 PA foil

Direction 2 Glass

⫾ 20⬚ 3 Carbon

⫾ 30⬚ 4 Carbon 5 Glass 6 Carbon

⫾ 30⬚ 7 Carbon 8 Carbon

⫾ 30⬚ 9 Carbon 10 Glass

⫾ 30⬚ The main tube

11 Carbon ⫾ 30⬚ 12 Carbon

The throat piece and reinforcements

Figure 12.11

A typical lay-up for a composite racket (Jenkins, 2003, courtesy of CRC Press). equations. 1 It is desirable to lower the tensile stress σ max in the convex surface of the tube and

maximize the radius of bending r. Reducing the tube wall thickness (D − d) increases the surface stress σ max but cold drawing to reduce thickness increases the strength and reduces weight. In many bikes the front wheel forks, which experience severe bending stresses, are elliptical in shape, giving a higher moment of inertia but with the major ellipse diameter able to reduce the stress in the appropriate

1 M/I = σ/y = E/r, where M = bending moment, I = moment of inertia of beam section, σ = stress at a point, y = distance of point from neutral axis of beam, E = modulus of elasticity and r = the radius of curvature of the beam

shape.

602 Physical Metallurgy and Advanced Materials Table 12.3 Comparison of weight and bending characteristics of four metallic frame materials: r

and σ max calculated for tubes subjected to a bending moment of 100 N m ( from McMahon and Graham, 1992).

Material

D (mm)

d (mm) Moment

Mass per Radius of Maximum σ max /σ y

of inertia I unit

curvature stress

(cm 4 )

length

r(mm)

σ max

(MN m −2 ) Racing cycles

(g m −1 )

0.58 Cr–Mo steel

C steel

0.50 Mountain cycles (top tube)

Al alloy (6061-T6) 28.80 25.91 1.124

Al alloy (6061-T6) 38.10 35.56 2.50 397

49 61 0.24 Ti–3Al–2.5V

plane. Of the alloys listed, the titanium alloy has a high strength-to-weight ratio and with excellent corrosion resistance is now competing with alloy steels for mountain bikes, which have to be tough enough to withstand sudden impact shock on the rough terrain.

Joining the tubes to form the frame requires particular attention as the joints often coincide with the highest bending moments. The cold-drawn, low-carbon steel tubes of mass-produced standard bicycles are joined by brazing. Reinforcing lugs together with (α + β) brass brazing alloy are inserted in the tube ends and heated to around 875 ◦

C. For more specialized racing frames butted alloy tubes are fillet brazed with a silver brazing alloy with an oxyacetylene torch at a lower temperature to reduce any heat-affected zones (HAZ). However, TIG welding has tended to replace brazing for alloy steel frames. The hardenability of the Cr–Mo steels is such that a strong mixture of alloy carbides form in the weld fillet on cooling after welding, increasing the hardness in the HAZ. The resultant structure has a better fatigue resistance than other steels and its favorable strength/weight ratio makes it competitive with the titanium alloy. When joining the titanium alloy tubes the weld pool has to

be shrouded with flowing argon to prevent the pick-up of embrittling gases, e.g. oxygen, nitrogen, hydrogen. Similarly, aluminum alloy tubes have to be guarded against overageing and softening. Carbon fiber-reinforced polymers may also be used for high-performance bicycles. The monocoque (single shell) frame, shown in Figure 12.12, is one such construction and features a cantilever seat,

a disk rear wheel and three-spoke front wheel, all made from CFRP. 2 Joining problems may be overcome by the use of epoxy adhesives, which are well established in the aircraft industry. These structural adhesives produce bonds which are strong and durable, damp vibrations, save weight and reduce assembly costs. Normally, thermoplastic and/or elastomeric constituents are added to the thermosetting component to improve the toughness. The CFRP wheels clearly have a much lower aerodynamic drag than multi-spoke wheels. They are basically a contoured sandwich structure consisting of two carbon/epoxy facings, possibly with a polystyrene foam core, bonded onto a light aluminum alloy hub and to a carbon/epoxy rim. With the more conventional wheel the spokes are pre- tensioned ( ∼400 MN m −2 ) plain carbon steel, sometimes coated with sacrificial zinc for corrosion protection. The fatigue endurance of the carbon steel is acceptable for the cyclic stress conditions. The

2 Chris Boardman won the 400 m individual pursuit at the 1992 Olympic Games in Barcelona with a Lotus prototype.

Case examination of biomaterials, sports materials and nanomaterials 603

Figure 12.12 High-performance Zipp bicycle with monocoque frame (courtesy of Julian Ormandy, School of Metallurgy and Materials, University of Birmingham, UK).

rim is usually made of extruded precipitation-hardened aluminum alloy, bent to shape and joined. With the spokes, the aluminum (6001-T6) is sufficiently strong and light with good corrosion resistance.

12.3.5 Skiing materials

Skis that were originally made from a single piece of hickory wood have now developed into a rather complex multi-component, multi-material piece of equipment. The main requirements of the ski are good strength and flexibility along the length with torsional stiffness, so that the skier’s weight is properly distributed while traversing the irregular snow contours. In addition, it is necessary to dampen the ski structure to absorb dynamic impact loading. To meet these demands a multi-layer structure has evolved consisting of a base, usually polyurethane, a shock-absorbing core, usually natural ash or hickory wood, fiberglass and an elastomeric secondary core, steel or high-strength aluminum alloy edges, side walls of glass materials, top layer and reinforcing damping layers. An early design is shown in Figure 12.13, but this has evolved with the exact design and processing commercially guarded in a very competitive industry. In parallel with material development, modern skis have been reduced in length from around 200 cm in 1990 to around 160 cm.

The ski is only part of the equipment necessary for skiing. Boots, bindings and ski poles are also needed. Ski boots must provide a firm grip on the skier’s ankles to allow proper control of the ski. External Hytrel–Kevlar components have been used to stiffen the ski boot for this purpose (Hytrel is a thermoplastic polyester elastomer). Binding, i.e. the attachment between boot and ski, has also devel- oped significantly, with sophisticated release mechanisms. These release instantly under too severe twisting, while providing foot stability and control. An acetal (highly crystalline) polymer, which is

tough, has a low glass transition temperature T g and good fatigue resistance, is used for the locking bar, heel release lever, heel block and front swivel plate, while glass-reinforced nylon is used for the front block and two base plates. These polymers are tough at low temperatures and both UV and mois- ture resistant. Other release bindings employ titanium and plastic components. Figure 12.14 shows the variety of different materials used in the binding for snowboards. Finally, ski poles are tubular with high specific stiffness and toughness. They are usually made of CFRP or CFRP–GRP hybrids.

12.3.6 Archery

Every schoolboy having read, or watched, Robin Hood is familiar with the longbow, probably knows it was made from yew and that considerable force (35–70 kgf) was needed to draw it. When drawn,

604 Physical Metallurgy and Advanced Materials

Wood composites of hickory or ash

Aluminum honeycomb or acrylic foam also used

ABS, phenolics Glass fiber/polyester laminates

Graphite or Kevlar or ceramic fiber stiffeners

Ferritic stainless steel (or high-strength aluminum alloy)

Grooved low-friction material, e.g. polyurethane (PU)

Figure 12.13 Transverse section showing multi-component structure of a downhill ski ( from Easterling, 1990, by permission of the Institute of Materials, Minerals and Mining).

Figure 12.14 Snowboard binding utilizing: thermoplastic elastomer (Hytrel) – ankle strap A, spoiler B, ratchet strap G; nylon (Zytrel) – side frames D and H, base and disk F, top frame J; acetal homopolar (Delrin) – strap buckles C1 and C2 (courtesy of Fritschi Swiss Bindings AG and Du Pont UK Ltd).

the strain energy stored in the ‘string’ and the two (upper and lower) limbs of the bow is trans- ferred to the arrow, which accelerates up to a velocity of 50 m s −1 . Yew was favored for longbows, from the various woods around, because of its excellent bending strength and capacity to store energy.

Case examination of biomaterials, sports materials and nanomaterials 605

Figure 12.15 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, UK).

Modern bows are either the standard recurve (Olympic) bow or the multi-material compound bow. The recurve bow has limb sections which are wide, flat and thin, and has a particular resistance to

any twisting during use. The compound bow is shown in Figure 12.15. The mid-section (riser or grip) is usually made of a light, strong forged aluminum alloy, while laminated wood, GFRP or CFRP is used for the upper and lower limbs. The release of an arrow from the bow involves a combination of three arrow characteristics, namely length, mass and stiffness. Correct matching of these features is necessary for the arrow to clear the bow properly. Arrow shafts are usually made of tubular, drawn and anodized aluminum (7079-T9, 7178-T9) or similar alloys bonded to a smooth outer wrap of CFRP. Barreling from the middle to the end of the shaft removes any undesirable flexing introduced by the variable bending moment of the constant-diameter shafts. Finally, the feathers or fletching are nowadays made from polyethylene terephthalate (Mylar) and provide the arrows with stability during flight. In smooth polymeric form they are durable and weather resistant, with low aerodynamic drag.

The same material in stranded form (Dacron) is used for the bow string.

12.3.7 Fencing foils

It is evident that sports materials are very much influenced by the developments of the newer com- posites, based on polymers. However, one area where old-fashioned metallurgy comes into its own is the sport of fencing, at which the UK has often excelled. Traditionally, the foils are made from medium-carbon alloy spring steels, hot worked, then oil quenched and tempered to develop a marten- sitic structure with a yield strength around 1600 MN m −2 . The foil is just less than a meter long, tapering to a rectangular section of 4 mm × 3 mm. With this type of spring steel the foil is able to bend quite easily when parried during a match. Unfortunately, continual striking by an opponent’s foil leads to surface notches, which can result in fatigue failure, producing a rather dangerous broken blade. Nowadays, highly alloyed maraging steels (see Chapter 8) are used for competition fencing.

These very-low-carbon steels were developed for their exceptional high strength and toughness, and

are based on Fe–18% Ni with additions of 5% Mo and 8% Co. They are solution treated at 815 ◦

C, air cooled to produce low-carbon martensite and aged at 485 ◦

C to produce precipitates of intermetallic compounds. These steels are expensive but well established and reliable, so there is little incentive for development in metal–matrix composites.

The fencing mask is one area where polymer materials outperform metals. Mask design has been revolutionized by the application of the polycarbonate thermoplastic (Lexan). It is transparent and has high impact strength, resisting local deformation under conditions where metal masks deform.

606 Physical Metallurgy and Advanced Materials

Cell edge bending

Cell edge

Figure 12.16 Deformation of an open-cell foam structure ( from M. F. Ashby, 2005).

Densification σ Onset of plasticity,

buckling or crushing

Plateau stress σ pl

Stress Absorbed Densification

energy U

strain ε d

Modulus E Strain, ε

Figure 12.17 Compressive stress–strain behavior of foam materials ( from M. F. Ashby, 2005).

12.3.8 Sports protection

The development of the science and manufacture of polymeric foams has revolutionized the field of protection equipment for sport. Cycle and motor cycle crash helmets, body protection, football shin pads, etc. have all quickly improved. Most thermoplastic and thermosetting resins can be formed as foams with physical or chemical blowing agents. The mechanical behavior of the foam depends on the basic polymer properties, the relative density of the foam (e.g. 0.1 means the cell walls occupy 10% of the total volume) and the shape of the cell. Foams are, however, very much bending-dominated structures, as shown in Figure 12.16. Under a compressive stress the foam is linear elastic, as shown in Figure 12.17, up to the elastic limit, after which the cell walls start to buckle and collapse at almost constant stress until the cell walls impinge on one another, when the stress rises rapidly. The

‘constant’ stress collapse stage is important for energy absorption and is given by U ≈σε d , where σ is the plateau stress (yield, buckling or fracture stress of the foam) and ε d is the densification strain. Some foams collapse by elastic buckling, while brittle foams collapse by fracture of the cell walls. The densification strain is important since the energy absorption behavior has effectively ‘bottomed

out’. This situation is undesirable for protective gear and indicates an inadequate thickness of foam protection.

For football shin and ankle guards the foam is covered with a plastic shell and energy is absorbed by compression of the foam between the shell and the leg. The currently used foam is ethylene vinyl

Case examination of biomaterials, sports materials and nanomaterials 607

Figure 12.18 Cell structure of polystyrene foam, as used for shock-absorbent packaging: average cell diameter 100 μm (courtesy of Chris Hardy, Department of Metallurgy and Materials,

University of Birmingham, UK).

acetate (EVA) or ethylene–styrene interpolymers (ESI). The shell is usually polycarbonate (PC), since LDPE tends to buckle, causing the foam to ‘bottom out’. For crash helmets the outer shell is made of a strong, durable polymer, e.g. ABS or GRP, which has a reasonably high fracture toughness to resist shattering on impact. Some newer helmet designs have an additional inner microshell of PVC shaped to the inner foam. Glassy polymers having a high bulk compressive yield stress are used for the foam liners with glassy polypropylene (EPP) or glassy polystyrene (EPS) liners most favored. Figure 12.18 shows a micrograph of a polystyrene foam. Some liners can recover after not too violent impact, while others undergo permanent structural damage. EPP, for example is less brittle than EPS and recovers better. Whether the helmet should be discarded after an impact depends on the nature of the impact. In some sports the player is more liable to experience a number of minor impacts, e.g. cricket helmets, while for cycling the impact is likely to be more serious, when the helmet should be replaced.