Engineering Design with Natural Rubber [4 ed.]

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engineering design with natural rubber

NR TECHNICAL BULLETINS

This NR Technical Bulletin is published by the Malaysian Rubber Producers’ Research Association, an organization of the Malaysian Rubber Research and Development Board. Additional copies of this bulletin may be obtained from The Librarian The Malaysian Rubber Producers’ Research Association Tun Abdul Razak Laboratory Brickendonbury Hertford SG138NL England

or any of the MRRDB Offices listed on the inside back cover. In addition to NR Technical Bulletins, the MRPRA publishes two free quarterly journals – Rubber Developments and NR Technology – specimen copies of which may also be obtained from any MRRDB Office.

The information given in this bulletin is believed to be reliable; however, in view of variations in conditions we do not guarantee that identical results will be obtained. Users should satisfy themselves that any method which they desire to employ is not restricted by patents in the names of other parties.

NR TECHNICAL BULLETINS

ENGINEERING DESIGN WITH NATURAL RUBBER by T. B. Lindley PhD, B.Eng, D.I.C, CEng, MIMechE, MInstP, FIRI The Malaysian Rubber Producers' Research Association

CONTENTS . . . . . . . . . . . 2

Shear Mounting . . . . . . . . . . 26

The SI System . . . . . . . . . . . 3

Inclined Shear Mounting . . . . . . 28

The Nature of Rubber . . . . . . . . 4 Cis-polyisoprene, raw rubber, vulcanization, crosslinking

Torsion Disk . . . . . . . . . . . 30

Introduction

Bush Mounting . . . . . . . . . . 31 Compression Вlock . . . . . . . . 33

Physical Properties . . . . . . . . 8 Young's modulus, incompressibility, strength, hardness, tensile stressstrain characteristics, crystallization, creep and stress relaxation, fillers, hysteresis, dynamic modulus

Compression Strip . . . . . . . . 35 Bridge Bearings . . . . . . . . . . 36 Compression of Rollers . . . . . . . 38 Solid rubber rollers, hollow rubber rollers, rubber covered rollers, rubber spheres, solid rubber tyres

Effects of Environment . . . . . . . 15 Effect of temperature on stiffness, glass hardening at low temperatures, low temperature crystallization, high temperature effects, oxygen, sunlight, ozone, swelling in liquids, chemical degradation

Compression of Solid Rubber Rings . . 41 Circular section, rectangular section Tension . . . . . . . . . . . . . 42 Testing and Specification . . . . . . 43 Rubber, spring, note on bond testing

Fatigue and other Failure Phenomena . 21 Bonding Rubber to Metal . . . . . . 23 Friction

Appendix: Theoretical Derivation of the Compression Characteristics of Bonded Rubber Blocks . . . . . 45

Natural Rubber as a Spring Material . . 24 Natural frequency, transmissibility

Bibliography . . . . . . . . . . . 46

Stiffness Characteristics . . . . . . . 26

1

Introduction Natural rubber is a very versatile and adaptable materia1 which has been successfully used in engineering for over a hundred years. A major application which employs its outstanding physical properties to best advantage is as a spring. Good weathering resistance, achieved by means of modern protective agents, ensures that natural rubber springs last for many years. Unlike metal, rubber possesses some inherent damping, which is particularly beneficial when resonant vibrations are encountered, and it can store more clastic energy than steel. In rubber-metal units, natural rubber is chemically bonded to the metal, which provides the means for location and fixing. Installation is simplified by tire flexibility of rubber springs, and subsequently no maintenance is required. This book describes the effect of various external conditions on natural rubber and gives the stiffness formulae for the more usual forms of rubber spring. This information enables the suitability of natural rubber as a material to be assessed, and preliminary design to be carried out. Once this stage is reached a manufacturer should be approached as he may already produce a suitable standard component, and if not he will be able to advise on the manufacturing aspects of a new design.

Rubber springs giving a 10 cm deflection for loads of 50N - 500 kN. All are drawn to the same scale. (From Hirst, A. J. 'Rubber Suspension Systems' in Use of Rubber in Engineering. Bibliography Ref. 12)

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The SI System The basic SI units used for the quantities length, mass and time, are, metre (m) kilogramme (kg) second (s) Expressions for derived SI units based on these are: force 1 newton (N) = 1 kg m/s2 energy 1 joule (J) = 1 Nm power 1 watt (W) = 1 J/s frequency 1 Hertz (Hz) = 1/s Other SI units, with the names of other units which may be used, include: N/m2 stress and modulus (In some countries 1 N/m2 is called a Pascal.) 2 Ns/m dynamic viscosity 1 cP (centipoise) = 10-3 Ns/m2 N/m surface energy K (kelvin) thermodynamic temperature. The interval 1 К = 1ºC (degree Celsius) W/mK thermal conductivity The main units used in this book are: MN/m2 for stress and modulus 1 lbf/in2 = 0·00689 MN/m2 1 tonf/in2 = 15·4 MN/m2 1 kgf/cm2 = 0·0981 MN/m2

1 MN/m2 = 145 lbf/in2 1 MN/m2 = 0·065 tonf/in2 1 MN/m2 = 10·2 kgf/cm2

and N and kN for load and force 1 N = 0·225 lbf 1 kN = 0·1 tonf 1 N = 0·102 kgf

1 lbf = 4·45 N 1 tonf = 10 kN 1 kgf = 9·81 N

Prefixes for decimal multip1es and sub-multiples оf SI units: Factor prefix 1012 109 106 103 102 10 10-1

tera giga mega kilo hecto deca deci

symbol T G M k h da d 3

factor

prefix

symbol

10-2 10-3 10-6 10-9 10-12 10-15 10-18

centi milli micro nano pico femto atto

c m μ n p f a

The Nature of Rubber Natural rubber is a member of the class of substances known as high polymers. Many other natural products (silk, cellulose, wool, proteins, etc.) and synthetic plastics, resins and rubbers belong to this class of which the distinguishing feature is the long length of the molecular chain. Rubbers are a subdivision of this class, having flexible molecular chains and the ability to deform elastically when crosslinked.

Fig. 1. Alternative configurations of the isoprene monomer; left - cis (natural rubber), right - trans (guttapercha).

Cis-polyisoprene The chemical formula of natural rubber is (C5H8)n where n is about 10 000 and C5H8 is the monomer isoprene. The configuration of each isoprene unit is in accord with a definite and unique geometrical pattern (Fig. 1). Any other arrangement would give a material of quite different properties. In natural rubber the arrangement is designated cis, hence the chemical name for natural rubber - cis-polyisoprene. A different geometrical arrangement of the isoprene unit is the trans configuration found in gutta percha (i.e. transpolyisoprene).

Raw Rubber Rubber latex occurs beneath the bark of certain trees, notably 'Hevea brasiliensis' , which is cultivated in the plantations of Malaysia and other tropical countries. Rubber trees are tapped for the latex every other day, producing nearly three million tons of rubber each year. The latex is coagulated then processed into blocks, sheets or crepe for shipping in compressed bales. At this stage it is still raw rubber and, with the possible exception of crepe soles, has little practical use; it flows under load as the long molecules slide over each other, thus preventing recovery when the load is removed, it crystallizes readily at temperatures around 0ºC and below, and it becomes soft and sticky in hot weather.

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Table 1 A B C D

NATURAL RUBBER FORMULATIONS

Conventional accelerated-sulphur gum compound Bridge bearing compound Compound for flexible couplings and mountings for use at high temperatures Fully-soluble EV compound for components requiring low creep and reproducible stiffness (EV, efficient-vulcanization, refers to the efficient use of sulphur in forming crosslinks.) A

B

C

D

parts by weight per hundred rubber Natural Rubber SMR5 Natural Rubber SMR5 CV

100 -

100 -

100 -

100

Vulcanizing System Sulphur Stearic acid CBS Zinc oxide Dicumyl peroxide Zinc 2-ethyl hexanoate MOR TBTD

2·5 2 0·6 5 -

2·5 1 0·7 5 -

2·5 -

0·6 5 2 1·44 0·6

Protective Agents PBN antioxidant Flectol H antioxidant DOPPD antioxidant

1 -

1 4

2 -

2 -

Filler SRF black

-

45

50

25

Processing Oil Dutrex R

-

2

-

-

Vulcanizing Conditions Time, minutes Temperature, ºC

40 140

30 140

60 153

30 153

Physical Properties Hardness, IRHD Tensile strength, MN/m2 Tensile strength, lbf/in2 Elongation at break, %

47 26 3750 730

62 24 3550 540

57 22 3200 330

47 27 3900 610

Trade names and abbreviations of compounding ingredients: SMR 5 top grade of Standard Malaysian Rubber SMR 5 CV constant viscosity version of SMR 5, for easier processing CBS n-cyclohexyl benzothiazole-2-sulphenamide MGR 2-morpholinothio-benzothiazole TBTD tetrabutylthiuram disulphide PBN phenyl-β-naphthylamine Fiectol H poly-2, 2, 4-trimethyl-l,2-dihydroquinoline DOPPD nn'-dioctyl-paraphenylene diamine (eg UOP 88) SRF semi reinforcing furnace (black)

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Vulcanization To make it of practical use raw rubber has to undergo a chemical reaction known as vulcanization, a process discovered by Charles Goodyear in 1839. He found that when raw rubber was masticated, mixed with sulphur and then heated, the doughlike mixture was converted into an elastic material, becoming stable over a much wider temperature range and resistant to how under load. Vulcanized rubber is generally referred to simply as 'rubber'. Nowadays many diverse chemicals are used in producing a rubber; some are necessary for the vulcanization process while others assist or accelerate it; some chemicals protect, stiffen, soften, cheapen, colour the vulcanizate, and a processing oil may be added to facilitate mixing these chemicals with the raw rubber. Some examples of rubber mixes (compounds) are given in Table 1. The vulcanization (or curing) process is generally carried out under pressure in metal moulds at a temperature of at least 140ºC, and takes from a few minutes to several hours depending upon the type of vulcanizing system being used.

Crosslinking During vulcanization, the long chain molecules of rubber are chemically linked, usually by sulphur, at intervals along their lengths with adjacent rubber chains. The kind of crosslink produced depends upon the curing conditions - time and temperature - as well as the amount and type of vulcanizing ingredients in the compound and this, in turn, will affect the properties of the vulcanizate (Fig. 2).

polysulphidic crosslinks (x ≥ 2) conventional acceleratedsulphur vulcanizate

mono- and disulphidic crosslinks

carbon-carbon crosslinks

eg fully-soluble EV vulcanizate

eg dicumyl peroxide vulcanizate

increasing high-temperature resistance increasing strength Fig. 2. - The chemical nature of the various types of crosslinks influences the properties of the rubber.

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Table 2 PHYSICAL CONSTANTS OF VULCANIZED NATURAL RUBBER Comparison of a soft gum rubber, a harder black-filled rubber, mild steel and water.

Hardness* Tensile strength (TS) Elongation at break (EB) Young’s modulus (E0) Shear modulus (G) Bulk modulus (E∞ ) Poisson’s ratio Resilience Velocity of sound transmission Specific gravity Specific heat Thermal conductivity relative to water Coefficient of cubical expansion/deg C Electrical resistivity † Dielectric constant Power factor

IRHD MN/m2 % MN/m2 MN/m2 MN/m2 % m/s

ohms/cm cube

Gum rubber

Filled rubber

Mild steel

Water

45 28 680 1·9 0·54 1000‡ 0·4997 80 37 0·93 0·45 0·25 67×10-5 1·7× 1016 3 0·002

65 21 420 5·9 1·37 1200 0·4997 60 37 1·16 0·41 0·31 56 × 10-5 3× 1010 15 0·1

100 420 40 210 000 81 000 176 000 0·29 100 5000 7·7 0·116 73 3·5× 10-5

0

2100

1430 1 1 1 -5 21 × 10 9× 10-6 80

* hardness scale range is 0 to 100 (IRHD = International Rubber Hardness degrees) † but specially-compounded conductive rubbers 1-107 ohms/cm cube ‡ This value for bulk modulus is based on the compression of pads of high diameter/thickness ratios. The most accurate published value of the bulk modulus of gum natural rubber appears to be about 2000 MN/m2 (Compressibility of natural rubber at pressures below 500 kg/cm2, L. A. Wood and G. M. Martin (of National Bureau of Standards, Washington DC) Rubber Chemistry and Technology 1964. 37. 850-856). If this value is preferred for design purposes then the values for bulk modulus E∞ given in Table 3 should be doubled before being used in the determination of compression modulus at high shape factors, pages 33 -34.

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Physical Properties Young’s Modulus Vulcanized rubber is a solid, three-dimensional network. The more crosslinks there are in the network the greater is the resistance to deformation when a force is applied. Certain fillers, notably the reinforcing blacks, create a structure within the rubber which further resists deformation. The load-deflexion curves for rubber in tension and compression are approximately linear for strains of the order of a few per cent, and values of Young’s modulus E0 can be obtained from these linear regions. (Shear modulus G can be obtained in a similar manner.) As the curves are continuous through the origin the values of Young’s modulus in tension and compression are approximately equal. The shear modulus, G, is about one-third to one-quarter of Young's modulus (see Table 3). Table 3 HARDNESS AND ELASTIC MODULI Based on experiments on natural rubber spring vulcanizates similar to A in Table 1 and containing (above 48 IRHD) SRF black as filler. Note that hardness is subject to an uncertainty of about ±2 degrees. Hard ness IRHD ± 2

Young’s modulus E0 MN/m2

Shear modulus G MN/m2

k

Bulk modulus* E∞ MN/m2

30 35 40 45 50 55 60 65 70 75

0·92 1·18 1·50 1·80 2·20 3·25 4·45 5·85 7·35 9·40

0·30 0·37 0·45 0·54 0·64 0·81 1·06 1·37 1·73 2·22

0·93 0·89 0·85 0·80 0·73 0·64 0·57 0·54 0·53 0·52

1000 1000 1000 1000 1030 1090 1150 1210 1270 1330

Shore A (approx.)

lbf/in2

lbf/in2

35 45 55 65 75

168 256 460 830 1340

53 76 115 195 317

lbf/in2 0·89 0·80 0·64 0·54 0·52

142 000 142 000 154 000 171 000 189 000

k is used in the calculation of compression characteristics (pages 33 and 36). The majority of springs are in the hardness range 40-60 IRHD. Average design limits: 15% compression, 50%, shear. * See footnote ‡ to Table 2 on previous page.

Note. - Theoretically, with a Poisson’s ratio of ½, should equal 3G. This is so for soft gum rubbers, but for harder rubbers containing a fair proportion of non-rubber constituents, thixotropic and other effects increase E0 to about 4G.

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Incompressibility The bulk modulus of rubber E∞ (1000 - 2000 MN/m2) is many times larger than its Young’s modulus E0, and Poisson's ratio can be taken as ½. The very high bulk modulus means that rubber hardly changes in volume even under high loads, so that for most types of deformation there must be space into which the rubber can deform. The more restriction that is made on its freedom to deform the stiffer it will become, a feature used in the design of compression springs.

Strength The breaking stress of rubber in tension is about 14-28 MN/m2 when calculated on the original cross-sectional area. When calculated on the cross-section at break, the breaking stress may be as high as 200 MN/m2 which is only a factor of five or so below the corresponding value for steel. A stress well in excess of 160 MN/m2 is required to cause the failure of rubber in compression.

Hardness Hardness measurements are generally used to characterize vulcanized rubbers (see Table 3). For rubber, hardness is essentially a measurement of the reversible, elastic deformation produced by a specially-shaped indentor under a specified load and is therefore related to the Young’s modulus of the rubber, unlike metal hardness which is a measure of an irreversible, plastic indentation. Readings in International Rubber Hardness degrees (IRHD), British Standard Hardness degrees (ºBS) and on the Shore Durometer A Scale are approximately the same. This is in contrast to the measurements of metal indentation hardness, where the scales of Brinell and Rockwell В (steel ball). Rockwell A and C (diamond cone) and Vickers (diamond pyramid) are widely different. Hardness is relatively simple and easy to obtain but is subject to some uncertainty, hence the ±2 degrees tolerance given in Table 3. Shear modulus values are considerably more accurate, but are less easily obtained.

Tensile Stress-Strain Characteristics Some typical stress-strain curves for natural rubber are shown in Fig. 3. Two features lead to the increased stiffness of high strains: one is due to the sections of molecules between adjacent crosslinks approaching their limiting extension; the other is strain-induced crystallization which occurs in only a few rubbers, notably natural rubber. Rubber is frequently specified, and its quality controlled during manufacture, by its hardness and its tensile stress-strain properties, ie tensile strength, elongation at break and stress at 100%, 300% (etc) strain. 9

Fig. 3. - Tensile stress-strain curves for four natural rubber compounds of different hardnesses: 73 IRHD contains 50 parts of a reinforcing black; 59 1RHD contains 50 parts of a non-reinforcing block, and different vulcanising systems account for the different curves of the two gum compounds (47 and 33 IRHD).

Crystallization At moderate strains, of about 200% natural rubber begins to crystallize, and more and more crystallites are formed as the strain increases. This straininduced crystallization differs slightly from low temperature crystallization (due to the freezing of unstretched rubber which is discussed later) in that it occurs extremely rapidly and the crystallites are oriented in the direction of the extension. The crystalline structure produced in natural rubber on straining is primarily responsible for its high tensile strength, long fatigue life and excellent tear resistance. The structure disappears on removal of the strain.

Creep and Stress Relaxation When vulcanized rubber is held at constant deformation the stresses set up gradually decrease with time as the crosslinked network approaches an equilibrium condition. This is stress relaxation. The same process occurs in creep, when the rubber continues to deform under a given load. A similar relaxation process occurs when the imposed deformation or load is removed. Although all but a few per cent of the original deformation is recovered immediately, further recovery takes much longer and may never be complete. The amount of deformation not recovered is known as set or permanent set. Where chemical effects are absent (see page 12), the longer the relaxation processes continue the slower they become. For most gum and filled vulcanizates stress relaxation and creep vary approximately linearly with the logarithm of time under load. For example, the amount of creep occurring 10

Fig. 4. - Typical creep curves obtained in shear using conventional accelerated-sulphur vulcanizates.

in the decade of time from one minute to ten minutes after loading is the same as the amount in the much longer decade from one week to ten weeks after loading. Rates for rubbers, therefore, are usually measured as the change of stress or strain in one decade of time divided by the stress or strain one minute after the deformation is imposed (Fig. 4 and Table 4). The relaxation rate of all natural rubber vulcanizates is generally lower than that of other rubbers. Thus conventional accelerated-sulphur vulcanizates of natural rubber show stress relaxation rates from about 1·5% per decade (gum) to about 6% per decade (when containing a fair proportion of filler). Two other types - dicumyl peroxide and fully- soluble EV vulcanizates— are available where lower rates are required. Stress relaxation rates are substantially independent of the type or amount of deformation, but creep rates depend both on the rate of stress Table 4 TYPICAL STRESS RELAXATION RATES Hardness IRHD

Type of rubber

Conventional accelerated sulphur vulcanizates (polysulphidic crosslinks) gum with 40 parts non-reinforcing black with 40 parts reinforcing black Dicumyl peroxide vulcanizate (carboncarbon crosslinks) gum with 40 parts non-reinforcing black with 40 parts reinforcing black Fully-soluble EV vulcanizates (mono- and disulphidic crosslinks) gum with 25 parts semi-reinforcing black

11

Stress relaxation rate % per decade Unworked After rubber scragging

48 68 73

1·6 4·3 5·6

— 3·1 4·2

— 65 66

0·9 3·0 3·5

— 2·1 2·6

42 47

0·65 2·5

0·65 2·3

relaxation and the load-deflexion characteristics. In tension the creep rate may reach double the rate of stress relaxation; in shear it is about the same and in compression it is lower. For unfilled rubbers having the same type of vulcanizing system the relaxation rales decrease with increasing hardness. Over the usual range of hardness possible with gum rubbers ( ~ 33-48 IRHD) this will not alter the rate by more than about a third (although very high relaxation rates may be found with very soft rubbers). In filled rubbers the relaxation rates increase with the amount of filler. Stress relaxation and creep rates vary considerably with the composition and type of rubber and also depend on whether the rubber is new and unworked or has been pre-loaded (scragged) to the working deformation at some time before the test. The process of scragging reduces the stress relaxation rate, as can be seen from Table 4, but is usually of importance only for filled rubbers. At long times at normal temperatures, chemical effects may cause the relaxation processes to occur more rapidly than short term tests predict. Similar chemical effects occur in short times at elevated temperatures often due to oxidative scission of the rubber network. Protection against oxygen attack by antioxidants can greatly reduce these effects and is discussed later. Large rubber engineering components are protected from oxidation simply because their bulk prevents easy diffusion of oxygen to the interior. High humidity can increase the relaxation rate by a factor of as much as two as compared with dry conditions. Again, however, this is usually only of importance for thin components and the normal type of thin sheets used in testing. The effect is less marked for dicumyl peroxide and fully-soluble EV vulcanizates. In engineering applications creep is most rapid during the first few weeks under load but should not exceed 20% (for 70 IRHD) of the initial deflexion in this period. Allowance can be made for this in the design. Thereafter, in correctly compounded rubbers, only a further 5-10% increase in deflexion should occur over a period of many years.

Fillers Rubbers containing only processing aids and chemicals for protection, colouring and effecting vulcanization are known as gum, or unfilled, rubbers. The majority of rubbers used for engineering applications contain a filler, generally one of the many kinds of carbon black, which may comprise up to one-third of the total volume of the vulcanizate. These black fillers fall into two groups (i) 'reinforcing' blacks which improve the tear and abrasion properties of the unfilled gum rubber as well as increasing the Young's modulus, hysteresis and creep; and (ii) 'non- reinforcing' blacks which have little effect on tear and abrasion and give only moderate increases in modulus, 12

hysteresis and creep. They can, however, be added in greater volumes than reinforcing blacks. Fig. 5. — Hysteresis loops after 10 cycles (full lines) for vulcanizates containing 50 parts reinforcing black (left) and 50 parts non- reinforcing black (right). The broken lines represent the first cycle of each test. Stress and strain are calculated on the dimensions at the start of the first cycle. The shift of the start of the final cycle loops away from the origin is due to set.

Fig. 6. — First cycle hysteresis loops for a natural rubber gum vulcanizate extended to various strains. At low strains (enlarged top left) there is little hysteresis, but it is very much greater at high strains owing to crystallization.

Hysteresis Hysteresis, ie the work represented by the area between the loading and unloading curves (loop area) in a load-deformation cycle, occurs with all 13

Fig. 7. — The effect of amplitude of deformation on the shear modulus of natural rubber vulcanizates. The figures on the curves are parts by weight of SRF black per hundred rubber. Hardnesses are approximately 45, 55, 65 and 75 IRHD reading upwards from the bottom curve.

Fig. 8. — The first, second and tenth tensile stress-strain loops on a vulcanizate containing 50 parts reinforcing black. Most of the structure breakdown (and also set) occurs on the first cycle. Compare with the initial hysteresis loop on a gum vulcanizate also strained to 200% (Fig. 6) and the same black-filled vulcanizate. only strained to 50% (Fig. 5).

14

rubbers (Fig. 5). For natural rubber containing no filler there is very little hysteresis up to moderate extensions (see inset Fig. 6); fillers increase hysteresis. At high extensions, not normally used in practical applications, the hysteresis is much greater (Fig. 6). This is associated with the crystallization taking place on extension and is responsible for the high strength of natural rubber. Rapidly repeated deformations can cause considerable hysteresis energy to be created which must be dissipated as heat. The rise in temperature ('heat build-up') may result in thermal degradation. Natural rubber, with its low hysteresis, is the preferred material for vibration applications where the hysteresis provides a small but desirable measure of damping without the danger of serious heat build-up, Hysteresis is a measure of the energy lost; the converse is resilience, which is a measure of the energy returned. Both depend not only upon the type of polymer but also on the filler and other compounding ingredients.

Dynamic Modulus The modulus of natural rubber under dynamic conditions is substantially independent of the frequency below 1000 Hz and at ambient temperatures (0ºC - 50ºC). The dynamic force-deflexion curves of tilled rubbers are amplitude dependent. If the curves are assumed to be linear then the effective moduli decrease as the amplitude increases (Fug. 7). Весаuse dynamic strain amplitudes are normally much less than the static ones on which they are superposed the ratio of dynamic stillness to static stiffness may be quite high. This effect is additional to, and generally more pronounced than, any direct effect of frequency. The modulus may also be altered by structure breakdown. During the first loading of a black-filled rubber some of the black structure is broken down so that on subsequent loadings the rubber will appear softer. Almost all the breakdown occurs within a few load cycles, being most marked in rubbers containing reinforcing fillers (Fig. 5). The amount of breakdown increases as the strain increases (Fig. 8). It is common practice to preload to the maximum load a few times (ie to scrag) before testing rubber engineering components, even on static tests.

Effects of Environment Various changes can occur in a rubber component as a result of the conditions under which it is used or stored. If the conditions are too severe the rubber may rapidly become unserviceable; conversely it could last indefinitely under less arduous conditions. The ways in which different conditions can affect natural rubber are described briefly below; in many cases the effects of the changes can be eliminated, or at least minimized, by suitable 15

compounding. It is emphasized that many of the deleterious conditions referred to are not encountered in general engineering applications.

Effect of Temperature on Stiffness From -20ºC to above 70ºC the stiffness of unfilled rubber is approximately proportional to the absolute temperature. Rubber, in this respect, is not dissimilar to a gas, but the effect is the opposite of that observed in metals where the variation of observed in metals where the variation of stiffness with increase in temperature is small but negative. The addition of high levels of reinforcing black can modify this behaviour considerably, so that stiffness may fall with increasing temperature.

Fig. 9. — Effect of temperature on the stiffness of a filled natural rubber vulcanizate at 0·5 Hz (full line) and 16 Hz (broken line).

Glass Hardening at Low Temperatures Below -20ºC the stiffness gradually increases as the temperature is lowered until at about -40ºC it is double that at +20ºC. Further cooling results in a rapid stiffening and hardening until at about -60ºC natural rubber is glasslike and brittle. This variation in stiffness, illustrated in Fig. 9, is reversible with temperature, the vulcanizate becoming rubbery again when warmed. The figure also shows how the rate of deformation affects the stiffness at low temperatures. 16

Low Temperature Crystallization When maintained at low temperatures certain rubbers may crystallize, and this results in a progressive stiffening and loss of elasticity. Natural rubber takes many days to crystallize at around -25ºC, and increasingly longer at higher or tower temperatures. Like glass-hardening, crystallization disappears rapidly as the temperature is increased. Low temperature crystallization is not generally a serious practical problem in natural rubber (unlike comparable synthetic rubbers which stiffen more rapidly or at higher temperatures).

High Temperature Effects The physical properties of rubbers are generally temperature dependent, and are also reversible with temperature provided no chemical changes occur in the rubber. However, like many other organic materials, rubber is prone to degradation by oxygen particularly at high temperatures. At service temperatures approaching those used for vulcanization (about 140ºC), further vulcanization may occur resulting in increased hardness and decreased mechanical strength. Conventional rubber compounds can be used at the maximum ground temperatures (60ºC) likely to be encountered in practice, but with special compounding natural rubber can be used for many months up to 100ºC and intermittently even higher. At very high temperatures (350ºC and above) rubber first softens as molecular breakdown occurs then resinifies, becoming hard and brittle.

Oxygen Where natural rubber compounds are used for engineering purposes chemicals known as antioxidants are invariably included to protect them from attack by oxygen. This oxygen attack gives long term creep and stress relaxation, processes which are accelerated by increase in temperature. Oxidative attack also varies with the detailed composition of the vulcanizate and results in a general deterioration of physical properties. Antioxidants arc extremely efficient at stopping this degradation.

Sunlight Rubber springs are generally situated in positions where they are shielded from direct sunlight, but additional and effective protection is given by the carbon black filler which is incorporated in most engineering rubbers and which acts by shutting out the ultra-violet radiation. Light coloured rubbers, when exposed to sunlight, arc susceptible to the oxidation initiated by the UV radiation, and their surfaces are rapidly degraded to give a crazed resinous skin. Although the need for light coloured rubbers is rare in engineering applications, a reasonable measure of protection can be achieved with a UV absorber and suitable antioxidant. 17

Fig. 10. — Left: a strip of unprotected natural rubber freely exposed at 100% tensile strain on a London roof for 3 months. Centre: the same conditions but the rubber now contains antiozonant and is fully protected. Right: the same rubber as in the left- hand photograph was exposed at 100% tensile strain for 3 months down a London railway tube. As no ozone was present the unprotected rubber did not crack.

Ozone The surface degradation of rubber, variously described as perished, checked, cracked, crazed or weathered, can normally be attributed to attack by atmospheric ozone, oxygen and sunlight. Minute concentrations of ozone in the atmosphere, (a few parts per hundred million at ground level), can cause cracking within a few weeks in unprotected rubber components subjected to tensile deformation. The cracks form perpendicular to the direction of tensile strain in the rubber surface - a feature which distinguishes them from light crazing. A characteristic of ozone attack is that a minimum ('critical') tensile strain is required for cracks to form, which is about 6% for unprotected gum natural rubber. Protection is obtained by the inclusion of waxes or chemical antiozonants in the vulcanizate. These act by increasing the critical strain through the formation of an inert layer on the rubber surface, and may give complete protection for static exposure to ozone up to strains of 100% and more (Fig. 10). The layer is less extensible than the rubber and may be broken by movement of the surface thus permitting ozone attack to occur. Specific chemical antiozonants ('antiflex agents') reduce the rate of crack growth, as well as increasing critical strain, and so are preferred in dynamic applications. Fig. 11. A 6 mm thick by 44 mm diameter disk of transparent natural rubber which has been compressed between metal plates and subjected to high concentration ozone for a period of exposure equivalent to 50+ years outside. The depth of penetration of the ozone is about 1 mm, ie the width of the thin dark ring around the disk which has been photographed through its thickness.

18

In compression the rale of ozone attack is reduced to negligible proportions, of the order of a hundred times slower than in tension (Fig. 11). By designing compression springs so that surface stresses are compressive, cracks cannot open and complete protection can be achieved. As ozone attack is a surface problem thin sections of rubber, notably weather strips and seals, must be adequately protected. Chemical antiozonants may cause staining of paintwork (this is not generally a problem with rubber springs) but waxes, which are non-staining, are satisfactory for low strain static exposure. In the majority of large rubber springs the relatively small exposed surface of rubber ensures a reasonable measure of protection for the bulk of the rubber and experience has shown that the weathering of large components made from natural rubber is not a serious practical problem. However, in particular circumstances where conditions are likely to be unduly severe, a flexible protective coating of a more resistant material can be given to the component.

Fig. 12. — The effect of volume on ageing. Both pieces of rubber have been aged for the same time: the thicker piece is still flexible but the thinner one has become hard and brittle.

Swelling in Liquids If a rubber absorbs a large volume of liquid it will become very weak and useless for almost every conceivable engineering application. There is, however, a limit to the amount of liquid that can be absorbed by different rubbers, and it is this equilibrium swelling which is the conventional measure of swelling resistance. There is no one rubber which is resistant to swelling by all liquids, but all rubbers are resistant to some. Natural rubber is swollen to a negligible extent by water and is swollen very little, for example, by acetone, alcohol, and vegetable oils such as castor oil. Most rubbers are swollen by degreasing solvents but the 'oil-resistant' rubbers, as the name implies, are only slightly swollen by lubricating oils. The swelling of rubber by liquids is a diffusion controlled process and, up to the equilibrium swelling ratio, the volume of liquid absorbed is proportional to the square root of the time for which the rubber has been immersed in the liquid. 19

For most organic liquids the rate of penetration depends upon the viscosity of the swelling liquid rather than on its chemical nature. Thus the time to penetrate 5 mm is about four days for a mobile liquid like benzene, one to two years for an engine lubricating oil, and about thirty years for a thick grease such as Vaseline. As it is unusual for springs to be used completely immersed in oil, adequate protection for natural rubber against oil splashes can normally be obtained by a suitable shield or by coating with an oil resistant paint. Occasional splashing is not serious, and the bulk of large components is generally a sufficient safeguard in itself.

Fig. 13. — The lime taken by a liquid to penetrate a given distance into rubber depends on its viscosity. The curve shows the time taken to penetrate 5 mm into natural rubber; it would take four times as long to penetrate 1 cm. (1 centipoise = 1 mNs/m2)

Chemical Degradation Degradation by chemicals other than oxygen and ozone is unlikely to be a serious consideration in most engineering applications of rubber. Swelling agents may cause rubber to become unserviceable before any chemical attack by the swelling liquid can take place. Natural rubber is resistant to most inorganic acids, salts and alkalies (with the exception of concentrated sulphuric acid, the halogens and strong oxidizing agents such as nitric and chromic acids) and is widely used for the linings of tanks and chemical baths, especially those containing caustic solutions.

20

Fatigue and Other Failure Phenomena Rubber, like metal, may fail by fatigue if subjected to repeated deformations, even though these are much less than the breaking strain. Fatigue failure in rubber is caused by the growth of cuts through a component, although the component may have become unserviceable before this if the cuts are large enough to seriously affect the stiffness. All surfaces contain imperfections which give rise to tensile strain concentrations when the component is deformed and in rubber these imperfections correspond to very small cuts, flaws or cracks at which the cut growth process of fatigue may commence. The magnitude of the strain at the tip of a cut depends upon the tensile strain in the surface and the size of the cut. For the usual working conditions the tip strain is below the breaking strain of the rubber, and growth is due predominantly to ozone attack, the rate of growth being proportional to the ozone concentration. Provided antiozonants are present, ozone cut growth occurs only under dynamic conditions, the antiozonants protecting against static attack in the periods of rest. Indoors, at low ozone concentrations, cut growth is slow; outdoors, ozone attack of rubber does not appear to be a serious problem in the majority of applications, eg vehicle springs, bridge bearings, etc, although tyres, possibly because of their exposed position, seem to be rather more prone. As a cut grows by ozone attack the strain at the tip increases and when it is sufficiently high physical tearing occurs. Antioxidant, which is present in all rubber springs, prevents additional cut growth due to oxygen during this physical tearing. In non-crystallizing synthetic rubbers cuts may continue to grow under a steady load until failure occurs, or the strain is removed. In contrast, natural rubber requires repeated loading to cause cut growth, and even this must involve passing the rubber through the unstrained state for the growth to be substantial. These beneficial effects, which are probably due to hysteresis resulting from crystallization at the tip of the cut, are partially responsible for natural rubber’s superiority in spring applications. In the majority of rubber springs the cyclic deformation is imposed on a larger static deformation so that the strain in the rubber does not relax during cycling. This considerably improves the fatigue life of natural rubber springs; a similar improvement in the fatigue life of metal when undergoing non-zero strain cycles is well known. Once the physical tearing stage has been reached, growth is relatively rapid, the rate of growth increasing with length of the cut. When the strain at the tip is very great the cut may propagate in a similar manner to a sudden fracture in brittle materials. It may occur when the cut is large (tear test) or when the bulk strain is large (tensile test). 21

Abrasion has certain characteristics which suggest that it also consists of one or more of the above tearing processes, but it is an extremely complex phenomenon and is not yet fully understood. One of the most frequent causes of rubber components becoming unserviceable is excessive creep or stress relaxation. This has been referred to earlier. Proper compounding of the rubber and allowing for initial creep can extend the useful life considerably. Embrittlement and crystallization at low temperatures are generally rare occurrences. So too is thermal degradation at high temperatures, which may be the result of excessive heat build-up caused by hysteresis when a component is subjected to rapid deformation. Blow-out in truck tyres, a typical example of this type of failure, is sometimes described as fatigue failure. The low hysteresis of natural rubber at low and moderate strains precludes the excessive temperature rise which in other more hysteretic rubbers can result in failure. It is mainly for this reason that natural rubber has proved so satisfactory for heavy duty truck tyres. In some applications the life of the rubber is considerably longer than that of the metal parts. To prevent rusting, metal parts can be covered with rubber as, for example, in certain types of bridge bearings (Fig. 32). This eliminates the need for periodic painting; the rubber does not require maintenance.

Fig. 14. — The fatigue life of natural rubber test pieces subjected to tensile deformations at 2 Hz (Left-hand side, minimum strain 0%, maximum varying.) Increasing the minimum strain can considerably increase the fatigue life. (Right-hand side, minimum strain varies, maximum 250%.)

22

Most rubber springs are designed to 'fail safe'. In the event of rubber failure some compression loading remains as a 'built-in' emergency measure to prevent far more serious damage, hence the widespread use of inclined shear units, compression mountings and rubber bushes. 'Fail safe' features can also be achieved by appropriate design of the metal parts.

Bonding Rubber to Metal In a large number of rubber springs the rubber, which is the spring medium, is bonded to metal. Metal parts are generally required for fixing purposes, but may also be a necessary part of the design - for example the horizontal metal plates which increase the vertical stiffness of bridge bearings. Bonding prevents the rubber from slipping at the load carrying surfaces thus ensuring reliable load-deflexion characteristics. Most modern bonding is carried out by the brass plating method or by the use of proprietary bonding cements. The former, in which the metal is first coated with a layer of brass, is gradually being superseded by the much simpler method of painting cement onto sand-blasted metal surfaces. The coated metal parts when placed in the mould are bonded to the rubber during the vulcanization process. Excellent bond strengths can be obtained by both methods; more often than not the bond is stronger than the rubber. As well as steel many non-ferrous metals and non-metallic materials can be satisfactorily bonded to rubber by the use of suitable cements. In the design of bonded rubber components the avoidance of sharp corners and stress concentrations is just as important as in the design of metal components (Fig. 15). Generous fillets, having radii at least 10-20% of the smallest overall dimension of the component, should prove beneficial.

Fig. 15. — Effect of reducing stress concentrations on the fatigue life of 25 ·4 mm square × 6·3 mm thick test pieces of natural rubber subjected to cyclic shear deformations of ±100% strain at 2 Hz. Large flaws visible at the number of cycles shown.

23

Friction Bonding, or one of the various forms of mechanical keying, is not always essential as the friction of rubber against a mating surface may be adequate to prevent slip. Plain, unbonded blocks can slip (and thus become softer) under a direct compressive loading. This slippage may not necessarily occur at short times. To avoid the possibility of slip the shape factor (see page 33) of unbonded blocks should be less than half the coefficient of friction. The coefficient of friction against most dry surfaces is generally about unity, but for design purposes it is usually assumed that slip due to a shear force will not occur if the ratio of maximum shear force to minimum compressive force is less than rubber-steel 0·2, rubber-concrete 0·33. If water, which is a lubricant for rubber, is present it will normally be squeezed out under load, but the presence of other lubricants and greases should be avoided.

Natural Rubber as a Spring Material Natural rubber occupies a similar position with regard to rubber springs as spring steel does with metal springs. These two materials are not the sole choices in their respective groups, but they are the obvious and most widely used ones, particularly where long life and arduous duty are involved. The principle reasons for natural rubber’s outstanding success as a spring rubber can be summarized as follows: It has excellent resistance to fatigue, cut growth and tearing. It is highly resilient. It has low heat build-up. It bonds very efficiently to metals. It is inexpensive and easy to manufacture. It has a wider range of operating temperatures than moss other rubbers. Compared with metal springs: Natural rubber springs require no maintenance. They have a high energy storage capacity. They can easily be designed to give different stiffnesses in different directions, or non-linear load-deflexion characteristics. They can accommodate a certain amount of misalignment and are easier to install. Although natural rubber is highly resilient, the small amount, of inherent hysteresis serves to dampen dangerous resonant vibrations (see Fig. 17). The various conditions mentioned earlier, which appear unfavourable to natural rubber, need not unduly limit its applications. For example, in many old cars natural rubber mountings are still giving satisfactory service after many years exposure to heat, draught, grease and petrol fumes. 24

Natural Frequency The natural frequency (nf ) in Hz of a mounted body on a spring is �� = ⁄√�

where x is the effective deflexion of the spring in centimetres. The effective deflexion is affected (and usually decreases) by the amplitude effect and by non-linear springs (Fig. 16). Fig. 16. - ОAB is a 'static' load deformation, curve. Its exact position and shape will depend on the amount of structure breakdown. The static stiffness at A is the slope, of the tangent AС. When a dynamic, small amplitude, deformation ED is superimposed on the static deformation at A its stiffness is the slope of AF. Tints the effective dynamic deformation FG is smaller than CG or OG, and the natural frequency will be higher than that predicted from static behaviour. C and F are generally closer to О than illustrated, especially with gnat and lightly-filled natural rubber vulcanizates.

Fig. 17. - The transmissibility of a natural rubber containing 40 parts by weight of carbon black. Temperature 19ºC. Experimental data of Snowdon, J. C., Brit. J. Appl. Phys, 1958, 9, 461-9. The full line is the theoretical relationship for no damping.

25

Transmissibility Transmissibility (T) is the ratio of the amplitude of the vibration on the ‘protected’ side of the spring to that of the disturbing vibration or, when the spring is on a rigid base, the ratio of the corresponding forces. T depends on the ratio of the disturbing frequency n to the natural frequency nf of the mounted system (see above). Under normal operating conditions when n > 3nf natural rubber gives attenuation comparable with materials having no damping (Fig. 17). At resonance, when n = nf the small amount of damping in natural rubber prevents the peak value of T becoming excessive.

Stiffness Characteristics A mathematical theory of rubber-like elasticity has been developed for elastic deformations of up to several hundred per cent. The theory applies strictly only to ideal rubbers, which are completely reversible, incompressible and isotropic, but in practice actual rubbers have been shown to conform quite well. The behaviour of certain kinds of rubber spring may therefore be calculated for deformations of any practicable amount. However, when the deformation is complex, an exact solution may be unattainable. In some of these cases approximate relationships can be derived from the classical theory of elasticity. This theory, which is the basis of standard engineering practice, only applies to materials in which the strains are very small (a few per cent), but the errors introduced by extrapolation to strains of the order of 10-20% are not excessive. In the stiffness equations which follow, terms beyond the first have only been given where their contribution is likely to exceed the variability of the elastic constants. Calculated stiffnesses should be within ±15% of the actual stiffness in most cases; small adjustments can he obtained by slight changes of rubber hardness. In general, stiffness is particular to a given direction, the stiffnesses in other directions may sometimes be an order of magnitude different as, for example, in bridge bearings. By the suitable selection and location of two or more units the stiffness of a composite spring in three different directions can be varied independently. The design of such springs, of which the inclined shear mounting is a typical example, requires only a knowledge of mechanics and the principal stiffnesses of the units.

SHEAR MOUNTING

Fig. 18. Shear mourning.

26

Shear stiffness =

Shear strain � � A = cross sectional area =

�

=

�

Shear stress �=

G = shear modulus (from Table 3)

x = shear deflexion

K = shear stiffness

e = shear strain

q = shear stress

F = shearing force

t = thickness of rubber

Metal plates can be inserted in the rubber without affecting the shear stiffness (see Fig. 31). but their thickness must not be included in 't' the thickness of the rubber. The maximum working strain depends upon the operating conditions and the type of rubber used. It rarely exceeds 100% and is generally less than 50%. When the ratio of thickness to length exceeds about 0·25 the deflexion xb due to bending should be allowed for. It is given by �

� =

�

where kr is the radius of gyration of the cross-section about the neutral axis. For a rectangular section kr 2 = L2/12, where L is the dimension in the direction of the force F . For a circular section kr 2 = D 2/16, where D is the diameter.

Fig. 19.—Laboratory test to determine shear modulus and bond strength. On the right the rubber is sheared over 300% and shows no sign of bond failure. Second from left, the rubber is sheared to about the maximum occurring in many practical applications.

27

Bending can be allowed for by replacing G by an apparent shear modulus G' , given by ′

=

+� /

�

(See Reference 22 for more detailed information.)

Fig. 20. — The stress-strain curves of rubber in shear are substantially linear over the normal working ranges.

INCLINED SHEAR MOUNTING If the left-hand unit alone is considered, a horizontal force H will be necessary to maintain equilibrium under a vertical load F . The system of forces is shown in Fig. 22.

Fig. 21. — Inclined shear mounting.

28

Fig. 22. — Force and deflexion diagram.

½ F = F c cosα + F s sinα xc = x cosα yc = y sinα F c = Kc xc F s = Ks xs

⸫ ½ F = Kc x cos2α + Ks x sin2α Ky = F/x = 2(Kc cos2α + Ks sin2α)

where α = inclination of bearing from horizontal F = total load x = deflexion Кy = overall vertical stiffness Kc = compression stiffness of each unit (see page 35) Ks = shear stiffness of each unit (see page 27) Kx = overall horizontal stiffness (in plane of paper) Kz = overall horizontal stiffness (perpendicular to plane of paper)

This type of mounting enables different stiffnesses in the vertical and in each of the two horizontal directions to be obtained. In the horizontal direction perpendicular to the plane of the paper the stiffness Kz will be that of the two units in shear, ie Kz = 2 Ks There are two limiting values for the horizontal stiffness in the plane of the paper Kx. The upper one, when a couple prevents rotation under the action of the horizontal load, is given by a similar expression to Ky, α being replaced by 90° — α, ie Kx = 2(Kc sin2α + Ks cos2α) The lower value is obtained when there is no restraining couple, ie =

cos

+

29

sin

=

Example: A mine car suspension consists of two bonded rubber blocks 10 cm square by 2·5 cm thick each inclined at 75° to the horizontal. The rubber is 55 IRHD, ie G = 0·81 MN/m2, E0 = 3·25 MN/m2, k = 0·64. For each block Ks = GA / t = 0·81 × 0·1 × 0·1 / 0·025 = 324 kN/m

the shape factor S = 10 / (4 × 2.5) = 1 Kc = E0 (1 + 2kS2) A / t = 3·25 (l + 2 × 0·64 × 12) 0·01 / 0·025 =

= 2960 kN/m sin2α = 0·93

cos2α = 0·067

vertical stiffness Ky = 2 (2960 × 0·067 + 324 × 0·93) = 1000 kN/m

transverse stiffness Kz = 2 × 324 = 648 kN/m

longitudinal stiffness (two values) Kx = 2 (2960 × 0·93 + 324 × 0·067) = 5540 kN/m

and Kz = 2 × 2960 × 648 / 1000

= 3830 kN/m

(1 kgf/cm = 1 kN/m)

TORSION DISK �

=

�

=

�

�

−

(θ in radians)

� − (θ in degrees) � � 9 � К = torsional stiffness t = thickness T = torque D = outer diameter θ = angular rotation d = inner diameter G = shear modulus (from Table 3) =

=

If one end plate of the disk (Fig. 23) is rotated through θ radians relative to the other plate with the thickness remaining unchanged, a compressive force proportional to θ2 is exerted on the end plates by the rubber. For a solid rubber disk this force is approximately πGθ2D 4/64t2.

30

Fig. 23. — Torsion disk comprising an annulus of rubber bonded to metal end plates.

The maximum shear strain ( = tan ϕ = Dθ/2t) occurs at the outer surface. (For more detailed information see Reference 23)

BUSH MOUNTING

Fig. 24. — Bush mounting in torsion.

Torsional stiffness Kθ �

� = = ⁄ − ⁄ � (θ in radians)

or

where T = torque θ = rotation of inner shaft relative to outer G = shear modulus (from Table 3) L = length of bush d = inner diameter of rubber D = outer diameter of rubber 31

�

=

.

= ⁄ − ⁄ � (θ in degrees)

Axial stiffness Ka

The axial deflexion x of a bush arises primarily from shearing of the rubber, although there may be some contribution from bending. The axial stiffness, Ka , of a bush which is at least as long as its diameter (ie L ≥ T), is given by =

�

=

log

.

⁄

where x = axial deflexion F = axial force

Fig. 25. — Axial deformation of a bush.

For shorter bushes (ie D > L) the axial stiffness (Ka ) given above should be divided by the factor 1 + α(D/L)2 where α has the following values: d/D 0·1 x

0·2

0·4

0·6

0·8

0·03 0·03 0·02 0·01 0·0025

Radial stiffness Kr

The radial stiffness Kr has been solved mathematically for only two cases — very long bushes and very short bushes

=

�

= Fig. 26. — Radial deformation of a bush.

The two values of β given below correspond to long (βL) and short (βS) bushes. The stiffness of intermediate length bushes will lie between, the extremes given by βL and βS for the appropriate ratio of d/D . d/D βL βS

0·1 9·5 5·2

0·2 18·3 7·9

0·3 34 11·1

0·4 66 15·3

0·5 135 21

0·6 310 30

0·7 900 44

0·8 0·9 3400 32 000 70 150

For more detailed information on bushes see Reference 24, on which the above is based. 32

COMPRESSION BLOCK

Fig. 27. — Effect of shape factor: Experimental stress-strain curves for 6.3 mm thick disks of rubber (47 IRHD) in compression. The shape factor is shown alongside each curve; the diameter in mm is 25.4 times the shape factor.

The stillness of rubber in compression, when the loaded surfaces arc prevented from slipping (by bonding or by mechanical location), depends upon the shape factor S (see Fig. 27), defined as the ratio of one loaded area to the total force-free area, as shown in Fig. 28. =

�

S = shape factor t = thickness L = length B = breadth

+

For a block of square section (ie L = B) or circular section (diameter = L)

=

�

The compression modulus Ec depends upon the shape factor S (for derivation see Appendix). Ec = E0 (1 + 2kS2)* Ec = compression modulus S = shape factor

E0 = Young’s modulus (from Table 3) k = a numerical factor (from Table 3) *See footnote on following page.

33

Fig. 28. — Variation of compression modulus Еc with shape factor S for natural rubbers of differing hardnesses (SRF black filler used for 55 1RHD and above). * Although deformation due to bulk compression can normally be ignored, it can cause a noticeable reduction in Ec when the ratio Ec/E∞ exceeds about 10%. (E∞ is the modulus of bulk compression, from Table 3.) To allow for this reduction, use a modified compression modulus obtained by dividing Еc by 1 + (Ec/E∞). If Wood and Martin’s value for bulk modulus is preferred (see footnote to Table 2) then the E∞ value in Table 3 should be doubled.

34

When S > 3 it may be more convenient to use Ec ≈ 5GS2

where G is the shear modulus (from Table 3).

Fig. 29. — Rubber block in compression.

The compression stiffness, Kc, is given by =

�

=

� where F = compressive load Ec = compression modulus (corrected, if necessary, for the effect of bulk compression) A = cross-sectional area t = thickness x = deflexion It is not advisable to rely on friction alone to prevent slip under a compressive load when using unbonded rubber parts, because slip may occur if S > μ/2, where S is the shape factor and μ the coefficient of friction. The load (F ) - deflexion (x) curve of rubber in compression is nonlinear. With no slip it has the approximate form F = E cAe(1 + e)

where e, the compressive strain, equals x/t. The non-linearity is usually ignored for strains up to about 10%. There is as yet no method of calculating that a block will be stable but experience has shown that provided the thickness is less than one- quarter of the least plan dimension there should be no instability.

COMPRESSION STRIP When a long strip of rubber is compressed the strain in the direction of its length will be negligible. Shape factor � = �

Fig. 30. — Compression strip.

35

Compression modulus Ec Ec = 4E0 (l + kS2)/3

The compression stiffness per unit length, Kc, is given by =

=

� where F = load per unit length

�

�

=

�

+� �

Ea = compression modulus (corrected, if necessary, for the effect of bulk compression) E0 = Young's modulus (from Table 3) b = width of strip t = thickness of strip x = deflexion k = a numerical factor (from Table 3) S = shape factor

The load per unit length (F ) - deflexion (x) curve for a compressed strip is non-linear. It has the approximate form F = Ec be(l + 3e/2)

where e, the compressive strain, equals x/t. As in the case of blocks, the non-linearity is usually ignored for strains up to about 10%.

BRIDGE BEARINGS The principle requirements of a bridge bearing are: (i) A high vertical stiffness to prevent appreciable changes in height of the bridge deck under changing load and (ii) A relatively low horizontal stiffness to prevent excessive loads on the supporting piers due to thermal expansion and contraction of the bridge deck. The cross-sectional area of a bearing will depend upon the allowable pressure on the support. Knowing this area, the thickness of rubber necessary to limit the horizontal stiffness can be readily determined. The required vertical stiffness is then obtained by insertion of a sufficient number of metal spacer plates. This is the basis of the design of rubber bridge bearings. The design procedure will depend upon the data provided. As an example suppose a square-sectioned bearing in 60 IRHD rubber has to be designed with the following approximate values:

36

Fig. 31. — The vertical stiffness of a rubber bock can be increased by inserting into the block horizontal metal spacer plates which reduce the freedom of the rubber to bulge. The shear stiffness is not altered by the presence of these horizontal plates.

Vertical stiffness Horizontal stiffness Ratio of side L to total rubber thickness T Shear modulus

Kc = 200 MN/m Ks = 3 MN/m L = 5T (for stability) G = 1·06 MN/m2 (from Table 3)

Thickness of one layer Number of layers Area Shape factor (of one layer)

t = T/n. n A = L2 S = L/4t

S = L/4t = 5Tn/4T = 5n/4

Shear stiffness =

Approximate compression stiffness =

=

=

= �

� � from which n, which must be integral, is 3. Ks = GA/T = 5GL T = L/ 5 = 0·6 / 5 = 0·12 m

=

=

= (

�

⸫ L = Ks / 5G = 0·57 m (say 0·6 m) t = T/n = 0·12/3 = 0·04 m

The bearing consists of three layers each 60 cm × 60 cm × 4 cm. From these values the calculated stiffnesses are: Ks = 3·18 MN/m Kc = 224 MN/m (approximate equation for S > 3) Kc = 227 MN/m (from page 35, without bulk modulus effects) Kc = 213 MN/m (from page 35, including bulk modulus effects) 37

)

Fig. 32. — Sketch showing part section of a three layer bearing. The thin layer of rubber encasing the 3 rubber layer / 4 metal plate unit protects the metal and accommodates irregularities in the contact surfaces. It does not materially affect the stiffness. Note that the edges of the plates have been rounded off.

COMPRESSION OF ROLLERS When a curved surface of a rubber component is compressed against a rigid plane the stiffness generally increases as the area of contact increases during the deformation. Thus the load deformation characteristics tend to be markedly non-linear. These are described for various shapes. For the rollers (solid, hollow and rubber covered) the relationships apply for plane strain conditions, ie for length ≫ rubber thickness. For more detailed information see Reference 26.

Solid Rubber Rollers (Fig. 33)

F = load per unit length

=

.

�

⁄

+

�

6

x = compression E0 = Young’s modulus

d = cross-sectional diameter

Hollow Rubber Rollers For hollow rollers with thin rubber walls there is a sharp increase in stiffness at a compression equal to the inner diameter (d1). The initial stiffness is given by classical elasticity theory; the stiffness after the turn up is approximately that of a compression strip of width d/2 and thickness d-d1.

Rubber Covered Rollers (Fig. 34) The relationships between the compression x of the rubber covering (thickness t) of rubber covered rollers of overall diameter d are shown in Fig. 34 for rollers of differing t/d ratios.

38

Fig. 33. — Compression characteristics of solid and hollow rubber rollers. That for the solid rubber corresponds to the quoted equation; ignoring the last (sixth power) term, as shown by the broken line, is sufficiently accurate for most purposes. F is the load per unit length.

Fig. 34. — Compression of rubber covered rollers of differing cover thickness/overall diameter ratios. F is the load per unit length.

39

Rubber Sphere (Fig. 35) Some rubber components (eg bump stops) have hemispherical caps. The compression is approximately half that of the sphere shown in Fig. 35.

Fig. 35. — Compression of a rubber sphere.

Fig. 36. — Compression of wheels with solid rubber tyres. (Experimental data for wheels with a diameter d five times the tread width.)

40

Solid Rubber Tyres The stiffness per unit width of tyre is less than that for a roller of the same cross-section because the rubber can deform sideways (ie the effective shape factor is less). Some typical experimental results are shown in Fig. 36. F = load per unit width of tyre

x = compression of tyre

E0 = Young's modulus

t = thickness of tyre

b = width of tyre

d = outer diameter of tyre

COMPRESSION OF SOLID RUBBER RINGS Circular section The force per unit length F for a solid rubber cylinder should he multiplied by πD where D is the mean diameter of the ring. The width of the flattened surface of rubber increases during the compression, and is approximately 2·4x, where a is the diametral compression. From this the average contact stress can be determined.

Rectangular section

Fig. 37. – Rubber annulus of rectangular section.

=

�

=

� =

�

K = stiffness F = load x = deflexion E0 = Young's modulus (Table 3) k = a numerical factor (Table 3)

�

−

{ +�(

�� � + { } � � �

− ) } �

D = external diameter d = internal diameter D m = mean diameter = ½ (D + d) b = radial width of section = ½ (D - d) t = thickness

(This expression arises from the compression stiffness of a rubber strip.) 41

TENSION Rubber is not normally used in springs in tension. When it is the following points should be noted. 1. Failure in tension is not normally of the 'fail safe' kind. 2. Extra care must be given to the design of the bond, and there must be no chance of serious overload. 3. Creep and set are higher than with shear and compression. 4. The stiffness in tension depends upon the shape of the unit (as in compression) and is approximately the same as the compression stiffness. 5. In short bonded units internal cracking occurs at quite a low strain and may then drastically affect the stiffness.

Fig. 35. — Bonded rubber disk under tension.

Fig. 39. — Tensile force-extension curves of a bonded rubber disk 20 mm diameter, 3.2mm thick. The discontinuity at C on site first cycle is due to internal cracking and not hysteresis. The low hysteresis of this rubber is shown by the second cycle (to 150%) and is similar to the low strain first cycle tests on this rubber shown in Fig. 6.

Rubbers with very poor tear strength may rapture catastrophically at low load; otherwise these internal cracks do not appear to affect the strength of the component, but dynamic fatigue has not been investigated. Tensile forces (F ) satisfying the following are insufficient to cause internal flaws to be formed. F < ½AE0 (1 - 1/S)

for S > 2

F < ½AE0

where F = tensile force S = shape factor

for S < 2

A = cross-sectional area E0 = Young’s modulus 42

Testing and Specification To ensure that a suitable rubber compound is used in the manufacture of the component, that the bond between the rubber and metal is adequate, and that the spring conforms to the required stiffness, tire engineer could use a specification based on the following information:

Rubber The rubber should conform to one of the specifications in Table 5. These are based on the physical requirements of British Standard Specification 1154: 1970, with, the addition of a bond test where applicable. There is no need for a low temperature flexibility test (except in rare circumstances) when a natural rubber compound is used. The tests should be as described in the relevant part of BS 903 'Methods of Testing Vulcanized Rubber' or in the corresponding International Standard (ISO) or other national standard (eg ASTM), viz: Determination of hardness: BS 903; Part A26; ISO 48; ASTM D1415. Determination of tensile strength and elongation at break: BS 903 Part A2; ISO 37; ASTM D412. Determination of compression set: BS 903 Part A6 Method A; ISO 815; ASTM D395 Method B. (Note that set is given as a percentage of the imposed compression.) Accelerated ageing tests: BS 903 Part A19; ISO 188; ASTM D573. Determination of rubber-to-metal bond strength: BS 903 Part A21; ISO 813; ASTM D429. Table 5 PHYSICAL PROPERTIES OF VULCANIZED NATURAL RUBBER COMPOUNDS From Table 2 of BS 1154 : 1970 Vulcanized Natural Rubber (High Quality) Z15

Z16

IRHD

Compound number Z11 Z12 Z13 Z14 As received condition 31-40 41-50 51-60 61-70

71-80

81-89

MN/m2 lbf/in2 %

19·5 (2800) 700

17·0 (2500) 600

17·0 (2500) 500

14·0 (2000) 400

10·5 (1500) 250

8·5 (1200) 150

30

30

30

30

35

45

Property

Hardness (inclusive) Tensile strength (minimum) Elongation at break (minimum) Compression set (maximum) Tensile strength Elongation at break

%

After ageing 7 days at 70ºC Not less than 90% of the unaged value. Not less than 85% of the imaged value.

43

Only in exceptional cases will there be any need for a weathering test. Alternatively an ozone resistance test (BS 903 Part A23; ISO 1431; ASTM D1149) may be employed. The preferred test conditions are: tensile strain 20%; ozone concentration 25 parts per hundred million; temperature similar to service (but 30ºC is often used); time of exposure 2 days. No cracks should be visible on the rubber surface when examined with a lens of X7 magnification.

Spring One spring should be tested to 1½ times the maximum design load. The stiffness should be within ±20% of the required stiffness although where necessary a smaller tolerance can be achieved. No surface flaws should become apparent during the test and there should be no irregularities in the deflected shape. It may also be desirable to carry out dynamic stiffness and damping tests at the service conditions of frequency, temperature and amplitude. The engineer may waive any or all of the tests where evidence can be produced that satisfactory test results are already available for materials and components identical with those to be used. This is particularly the case with standard lines, which have been designed for specific applications and in which the rubber may not be to the above general specification but to one more appropriate to its service requirements.

Note on Bond Testing Some so-called bond tests are primarily tests of the tear strength of the rubber since the bonding would be considered unsatisfactory if failure occurred at the bond. The 90-degree stripping test, illustrated in Fig. 40 is such a test. In an alternative test. Fig. 38, a bonded rubber sandwich is pulled apart and, in general, bond failure occurs due to the high strain concentrations created at the edge of the bonds. An unusual feature of this type of test is that the deformation results in a hydrostatic tension in the centre of the rubber causing internal cracks to form there at a small fraction of the ultimate load. Rubbers of poor tear strength can fail prematurely on this test. The test is not suitable as a non-destructive, production-control test of the bond, a simple shear test (Fig. 19) is more satisfactory. Fig. 40. — 90-degree stripping test.

44

APPENDIX* THEORETICAL DERIVATION OF THE COMPRESSION CHARACTERISTICS OF BONDED RUBBER BLOCKS Approximate load-deformation relations are derived below for small compressions of rubber blocks, between rigid plates to which they adhere or are bonded. The total displacements are considered to arise from the superposition of simple displacements, namely, (1) the pure homogeneous deformation defined by the displacement of one rigid bonding plate towards the other, and (2) the subsequent displacements necessary to cause points in the planes of the bonded surfaces to be restored to their original positions in these planes. Two extreme cases are considered, infinitely long rectangular blocks, the infinite dimension being at right angles to the direction of compression, and circular disks, loaded axially. Rectangular Blocks of Infinite Length The pure homogeneous deformation consists of a compressive strain e in the vertical direction, zero strain in the length direction, and an expansion in the width direction given, since tire rubber is virtually incompressible in volume, by e also. The rubber is placed in a state of pure shear and the force F 1 which has to be applied to the bonded surfaces to maintain such a deformation is given by† F 1 = 4E0be/3

(1)

per unit length, where E0 is the Young's modulus of the rubber and b is the width of the block. The second displacement system is that causing points in the planes of the bonded surfaces to be restored to their original positions in these planes. In order to calculate the corresponding system of forces which has to be applied to the bonded surfaces, it is necessary to make the simplifying assumption that horizontal planes remain plane during the deformation, as seems probable when the width b is much greater than the thickness t. Vertical sections consequently take up parabolic forms,‡ as represented diagrammatically in Fig. 41. The maximum outward displacement of any originally vertical section is dictated by the requirement that the volume contained between it and the central plane in the undeformed state shall

equal file volume contained between it and the central plane when it takes up the parabolic form and the bonded surfaces approach by an amount δ ( = et). For a plane at a distance x from the central vertical plane, considering unit length, we have xt = x(t — δ) + 2ut/3 where 2ut/3 is the approximate volume contained between the parabolic front of maximum displacement u and the vertical plane at x, when the compression δ is small. Hence,

u = 3xδ/2t In an elementary section of width dx the small displacement u may be maintained by the action of an excess hydrostatic pressure dp acting on one curved face, where dp is given by the classical theory of elasticity in the form dp = — (8E0u/3t2)dx

Since the curved surface at x = b/2 is force free. p may be obtained by integrating both sides of equation (2) between the limits x = x and x = b/2, yielding p = 2E 0δ(b2/4-x2)/t3

The pressure p acts on the rigid bonded plates also. The corresponding force F2 acting on each of these surfaces may be obtained by integrating such terms as p dx between the limits x = b/2 and x = — b/2, to give F 2 = E0δb2/3t2

(3)

The apparent value of Young’s modulus for the rubber block is given by E = (F/b)(1/e) where F is the total force which has to be applied to the bonded surfaces per unit length to maintain the deformation, and is given by F 1 + F 2 where F 1 and F 2 are given by equations (1) and (3) respectively. Hence, E = 4E0/3 + E0b2/3t2 = 4E0(1 + S2)/3 (4) where the shape factor S, the ratio cd one loaded surface to the force-free surface, is equal to b/2t

Fig. 41. - Initial and deformed stales for an infinitely long block subjected to a small compression. *From Appendix 1 of Tire Compression of Bounded Blocks, by A. N. Gent and P. B. Lindley, Proceedings of the Institution of Mechanical Engineers, 1959, Vol. 173, No. 3, pages 111-122. † Southwell, R. V. 1941 'An introduction to the Theory of Elasticity', p. 126 (Clarendon Press Oxford). ‡Adkins, J. E. 1954 Proc. Camb. phil. Soc., vol. 50, p. 334.

45

(2)

Circular Disks The apparent Young’s modulus may be derived similarly for а circular disk. The force F 1 which must be applied to maintain the first deformation, a simple compression of amount e, is given by F 1 = E0πa2e

where a is the radius of the disk. The force F 2 which has to be applied to maintain the second displacement system may be calculated by a similar procedure to that used in the previous example. Initially, vertical cylindrical surfaces are assumed to take up parabolic forms such that the volume contained within them, is unchanged. When the compressive displacement δ is small, and the radius r is much greater than the maximum radial displacement u, then u = 3rδ/4t where t is the thickness of the disk. Tire pressure p acting at a distance r from the centre is found to be p = E0δ(a2-r 2)/t3

and hence the force F 2 is obtained as F 2 = πE0δa4/2t3

An analogous relation lias been derived by Dienes and Klemm* for the rate of approach of two parallel circular plates separated by a viscous liquid. The apparent Young’s modulus E for a circular disc is obtained finally in the form E = E0(1+ a 2/2t2) = E0(1+2S2)

where S, the ratio of one loaded surface to the force-free surface, is equal to a/2t. As the thickness of the block is increased, the terms in equations (4) and (5) representing the contribution F 2 to the total force decrease, so that when the condition on which the calculation for F 2 is based - that the width or radius is much greater than the thickness - becomes quite inapplicable, the contribution F 2 to the total force becomes relatively small. Equations (4) and (5) may therefore be expected to apply over a considerable range of thicknesses. Note: In practice it is necessary to multiply the S2 term by the factor k, given in Table 3.

*DIENES, G. J. and KLEMM, H. F. 1946 J. Appl. Phys., vol. 17, p. 458.

BIBLIOGRAPHY A selection of books, papers and periodicals for reference and further reading.

Books 1. Treloar, L. R. G., The Physics of Rubber Elasticity. Oxford University Press, 2nd ed., 1958. 2. Green, A. E. and Adkins, J. E., Large Elastic Deformations. Oxford University Press, 1960. 3. Bateman, L. (Ed.), Chemistry and Physics of Rubber-like Substances. London, Maсlaren, 1963. 4. Davey, A. B. and Payne, A. R., Rubber in Engineering Practice. London, Maclaren, 1965. 5. Payne, A. R. and Scott, J. R., Engineering Design with Rubber . London, Maclaren, 1960. 6. Naunton, W. J. S. (Ed.), The Applied Science of Rubber . London, Edward Arnold, 1961. 7. McPherson, A. T. and Klemin, A. (Eds.), Engineering Uses of Rubber . New York, Reinhold, 1956. 8. Buchan, S., Rubber to Metal Bonding. London, Grosby Lockwood, 2nd ed., 1959. 9. Scott, J. R., Physical Testing of Rubbers. London, Maclaren, 1965. 10. Mclellan, J. (Ed.), Rubber in Transport Engineering. London, NRPRA, 1970. 11. Mernagh, L. R. (Ed.), Rubber Handbook (Design Engineering Series), London, Morgan-Grampian, I969. 12. Allen, P. W., Lindley, P. B. and Payne, A. R. (Eds.), Use of Rubber in Engineering. London, Maclaren, 1967. 13. Lindley, P. B. and Rodway, H. G. (Eds.), Rubber in Engineering 1973. London, NRPRA, 1973.

46

(5)

Papers 14. Gent, A. N., “On the relation between indentation hardness and Young's modulus." Trans. Instn Rubb. Ind.. 1958, 34, 46 - 57. 15. Mullins, L., “Aspects of physical basis of reinforcement.'' Trans. Instn. Rubb. Ind., 1956, 32, 231 - 241. 16. Gent, A. N., Relaxation processes in vulcanized rubber. 1. Relation between stress relaxation, creep, recovery and hysteresis. J. appl. Polym. Sci., 1962, 6, 433 - 441. 17. Braden, M. and Gent, A. N., Ozone cracking. Rroc. Instn Rubb. Iid., 1961, 8, 88-97. 18. Lake, G. J. and Lindley, P. B., Ozone cracking, flex cracking and fatigue of rubber, Rubb. J., 1964, 146 (10), 24 - 30, 79: (11), 30 - 36, 39. 19. Southern, E. and Thomas, A. G., Diffusion of liquids in crosslinked rubbers, I. Trans. Faraday Soc., 1967, 63, 1913—1921. 20. Cadwell, S. M., Merrill, R. A., Sloman, C. M. and Yost, F. L., Dynamic fatigue life of rubber, Ind. Engng Chem. Analyt. Edn, 1940, 12, 19 - 23. 21. Scha1lamach. A., Recent, advances in knowledge of rubber friction and tire wear. Rubb. Chem. Technol., 1968, 41, 209 - 244. 22. Rivlin, R. S. and Saunders, D. W., Cylindrical shear mountings. Trans. Instn Rubb. Ind., 1949, 24, 296 - 306. 23. Rivlin, R. S., Torsion of a rubber cylinder. J. appl. Phys., 1947, 18, 444449. 24. Adkins, J. E. and Gent, A. N., Load-deflexion relations of rubber bush mountings. Br. J. appl. Phys., 1954, 5, 354 - 358. 25. Gent, A. N. and Lindley, P. B., The compression of bonded rubber blocks. Proc. Instn mech. Engrs, 1959, 173, 111 - 122. 26. Lindley, P. B., Load-compression relationships of rubber units. J. Strain Anal., 1966, 1, 190-196. 27. Gent, A. N. and Lindley, P. B., Internal rupture of bonded rubber cylinders in tension. Proc. R. Soc. A, 1958, 249, 195 - 205. 28. Lindley, P. B., Design and use of natural rubber bridge bearings, NR Technical Bulletin, NRFRA, 1962. 29. Derham, C. J. and Lindley, P. B., Factors affecting the design and compounding of rubber O-rings for low-pressure underground pipelines. Proc. 5th Intl Conf. on Fluid Sealing, Paper CI, BHRA, England, 1971. 30. Flexible shaft couplings, Engrs' Dig., 1967, 28, (4), 93. 31. Anti-vibration mountings, Engrs' Dig. Technical Survey (reprint), 1961. 32. Horovitz, M., Suspension of internal-combustion engines in vehicles. Proc. Auto Div. Instn mech. Engrs, 1957/58, (1), 17 - 35. 33. Moulton, A.. E. and Tursicr, P. W., Rubber springs for vehicle suspension, Proc. Auto. Div. Instn mech. Engrs, 1956/57, (1), 17 - 42. 34. Lindley, P. B. and Payne, A. R. Rubber mountings for large structures. Consult. Engr , 1966, 30, (9), 40-42, 45. 35. Derham, C. J., Lake, G. J. and Thomas, A. G. Some factors affecting the service life of natural rubber articles, Proc. Nat. Rubb. Conf., Kuala Lumpur , 1968.

47

36. Lindley, P. В., Plane stress analysis of rubber at high strains using finite elements. J. Strain Anal., 1971, 6, 45 - 52. 37. Lindley, P. B., Strain concentrations at the corners of stretched rubber sheets. J. Strain Anal., 1971, 6, 279 - 285. 38. Bakirzis, E. A., Stiffness characteristics of rubber impact absorbers, J. Strain Anal., 1972, 7, 33 - 40. 39. Eiliott, D. J., Natural rubber formulations for engineering applications. NR Technology, 1972, No. 8. (Describes soluble compounding as docs paper G by J. F. Smith in Ref. 13.)

Periodicals Journal of the IRI. Theoretical and technological papers. Published by the Institution of the Rubber Industry, Bi-monthly. Journal of Applied Polymer Science. Highly theoretical patters, Interscience Publishers, New York, Monthly. Rubber Chemistry and Technology. Wide variety of theoretical to technological papers. Reprints articles from many sources and includes specialty commissioned translations and reviews. Published by the Rubber Division of the American Chemical Society. Five issues per annum. Rubber World. Practical technological papers plus business news. Bill Brothers, New York, Monthly. Rubber Age. Technological articles and news features. Palmerton Publishing Co. Inc., New- York, Monthly. Soviet Rubber Technology. English cover-to-cover translation of Russian Kauchuk I Rezina. Maclaren & Sons Ltd., London. Monthly. Rubber and Plastic Age. News and short features. Rubber and Technical Press Ltd., London. Monthly. Rubber Journal. News, short features and technological articles, Maclaren &. Sons Ltd., London, Monthly. Plastic and Rubber Weekly. News items. Controlled circulation. Maclaren & Sons Ltd. Rubber Developments. Feature magazine on the uses of natural rubber. MRPRA. Quarterly, free. NR Technology. Papers on the technology of natural rubber. MRPRA. Quarterly, free.

ACKNOWLEDGEMENTS Most of the work reported here has been carried out as part of the research programme of the Malaysian Rubber Producers' Research Association. I thank my colleague Mr A. G. Thomas for his helpful advice and suggestions during the preparation of the book. I would also like to thank Mr C. J. Derham and Dr J. F. Smith for their advice on some of the revisions made in the later editions.

48

Malaysian Rubber Research and Development Board Malaysia Head Office Malaysian Rubber Research and Development Board, Natural Rubber Building, PO Box 508, Kuala Lumpur

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Published by The Malaysian Rubber Producers Research Association Tun Abdul Razak Laboratory, Brickendonbury, Bertford. Printed in Great Britain by Hertford Offset Ltd Hertford SG13 7LS First edition 1964 Second edition 1966 Third edition 1970 Fourth edition 1974 Reprinted 1978