Modern Physical Metallurgy and Materials Engineering Part 13 pps

Itindicates that acrylics are relatively difficult to extrude Figure 11.7 Typical plot of apparent shear viscosity versus shear stress for LDPE at 210°C and atmospheric pressure: effects

In Chapter 2 the basic chemistry and structural

arrangements of long-chain molecules were described

and it was shown how polymers can be broadly

classified as thermoplastics, elastomers and thermosets

Certain aspects of their practical utilization will now

be examined, with special attention to processing;

this stage plays a decisive role in deciding if a

particular polymeric material can be produced as a

marketable commodity The final section (11.3) will

concern composites, extending from the well-known

glass-reinforced polymers to those based upon ceramic

and metallic matrices

11.1.2 Mechanical aspects of Tg

As indicated in Chapter 2, it is customary to quote a

glass-transition temperature Tgfor a polymer because

it separates two very different r´egimes of mechanical

behaviour (The value of Tgis nominal, being subject

to the physical method and procedure used in its

deter-mination) Below Tg, the mass of entangled molecules

is rigid Above Tg, viscoelastic effects come into play

and it is therefore the lower temperature limit for

pro-cessing thermoplastics The structural effect of raising

the temperature of a glassy polymer is to provide an

input of thermal energy and to increase the vibrations

of constituent atoms and molecules Molecular mobilty

increases significantly as Tg is approached: rotation

about C– C bonds in the chain molecules begins, the

free volume of the structure increases and

intermolecu-lar forces weaken It becomes easier for applied forces

to deform the structure and elastic moduli to fall

The mechanical properties of polymers are highly

dependent upon time and temperature, the response

to stress being partly viscous and partly elastic For

instance, ‘natural’ time periods are associated with the

various molecular relaxation processes associated withthe glass transition In linear viscoelastic behaviour,total strain comprises a linear elastic (Hookean) com-ponent and a linear viscous (Newtonian) component.The stress – strain ratios depend upon time alone In themore complex non-linear case, which usually applies

to polymers, strain is a function of time and stressbecause molecular movements are involved

The phenomenon of stress relaxation can be used

to chart the way in which the behaviour of a givenpolymer changes from glassy to rubbery Figure 11.1shows the non-linear response of a polymer that issubjected to constant strain ε0 Stress  relaxes withtime t The relaxation modulus Er at time t is given

Figure 11.2 Time–temperature dependence of elastic modulus in thermoplastic polymeric solid: (a) change in relaxation

modulus Ert as function of time; (b) change in tensile modulus as function of temperature (from Hertzberg, 1989; by permission of John Wiley and Sons).

polymer changes in character from a glassy solid,

where the relaxation modulus is a maximum, to a

rubbery solid In the complementary Figure 11.2b,

data from standard tensile tests on the same polymer

at different temperatures are used to provide values

of elastic moduli E The similarity of profiles in

Figures 11.2a and 11.2b illustrates the equivalence of

time and temperature (Theoretically, the modulus for

a short time and a high temperature may be taken to

equate to that for a combination of a long time and a

low temperature; this concept is used in the preparation

of relaxation modulus versus time graphs.) The glass

transition temperature Tghas been superimposed upon

Figures 11.2a and 11.2b

Although single values of Tg are usually quoted,

the process of molecular rearrangement is complex

and minor transitions are sometimes detectable Thus,

for PVC, the main glass transition occurs at

tem-peratures above 80°C but there is a minor transition

at 40°C Consequently, at room temperature, PVC

exhibits some rigidity yet can elongate slightly before

fracture Addition of a plasticizer liquid, which has a

very low Tg, lowers the Tg value of a polymer

Sim-ilarly, Tgfor a copolymer lies between the Tgvalues

of the original monomers; its value will depend upon

monomer proportions

In elastomeric structures, as the temperature is

increased, the relatively few crosslinks begin to vibrate

vigorously at Tg and the elastomer becomes

increas-ingly rubbery As one would anticipate, Tg values

for rubbers lie well below room temperature

Increas-ing the degree of crosslinkIncreas-ing in a given polymer

has the effect of raising the entire level of the lower

‘rubbery’ plateau of the modulus versus temperature

plot upwards as the polymer becomes more glassy

in nature The thermosets PMMA (Perspex, Lucite)

and PS have Tg values of 105°C and 81°C,

respec-tively, and are accordingly hard and brittle at room

temperature

11.1.3 The role of additives

Industrially, the term ‘plastic’ is applied to a polymer

to which one or more property-modifying agents have

been added Numerous types of additive are used bymanufacturers and fabricators; in fact, virgin polymersare rarely used An additive has a specific function.Typical functions are to provide (1) protection fromthe service environment (anti-oxidants, anti-ozonants,anti-static agents, flame-retardants, ultraviolet radia-tion absorbers), (2) identification (dyes, pigments),(3) easier processability (plasticizers), (4) toughness,and (5) filler

In many instances the required amount of additiveranges from 0.1% to a few per cent Although ultra-violet (UV) components of sunlight can structurallyalter and degrade polymers, the effect is particularlymarked in electric light fittings (e.g yellowing) Stabi-lizing additives are advisable as some artificial lightsources emit considerable amounts of UV radiationwith wavelengths in the range 280 – 400 nm For anypolymer, there is a critical wavelength which will havethe most damaging effect For instance, a wavelength

of 318.5 nm will degrade PS, which is a commonchoice of material for diffusers and refractors, by eithercausing cross-linking or by producing free radicals thatreact with oxygen

The action of a plasticizer (3) is to weaken molecular bonding by increasing the separation of thechain molecules The plasticizer may take the form of

inter-a liquid phinter-ase thinter-at is inter-added inter-after polymerizinter-ation inter-andbefore processing Additions of a particulate toughener(4) such as rubber may approach 50% and the material

is then normally regarded as a composite

A wide variety of fillers (5) is used for polymers Inthe case of thermosets, substances such as mica, glassfibre and fine sawdust are used to improve engineeringproperties and to reduce the cost of moulded prod-ucts PTFE has been used as a filler (15%) to improvethe wear resistance of nylon components Althoughusually electrically non-conductive, polymers can bemade conductive by loading them with an appropriatefiller (e.g electromagnetic shielding, specimen mounts

in SEM analysis) Fillers and other additives play animportant role in the production of vulcanized rubbers.Inert fillers facilitate handling of the material beforevulcanization (e.g clay, barium sulphate) Reinforcing

Figure 11.3 (a) World consumption of plastics, (b) plastics consumption by market sector, Western Europe, and (c) destination

of post-consumer plastic waste, Western Europe (courtesy of Shell Briefing Services, London).

fillers restrict the movement of segments between the

branching points shown in Figure 2.24 For instance,

carbon black has long been used as a filler for car tyres,

giving substantial improvements in shear modulus, tear

strength, hardness and resistance to abrasion by road

surfaces Tyres are subject to fluctuating stresses

dur-ing their workdur-ing life and it has been found useful

to express their stress – strain behaviour in terms of

a dynamic shear modulus (determined under cyclic

stressing conditions at a specified frequency) Time is

required for molecular rearrangements to take place

in an elastomer; for this reason the dynamic

modu-lus increases with the frequency used in the modumodu-lus

test The dynamic modulus at a given frequency is

significantly enhanced by the crosslinking action of

vulcanization and by the presence of carbon black

These carbon particles are extremely small, typically

20 – 50 nm diameter Small amounts of anti-oxidants1

and anti-ozonants are often beneficial The principal

agents of degradation under service conditions are

extreme temperatures, oxygen and ozone, various

liq-uids In the last case a particular liquid may penetrate

between the chains and cause swelling

11.1.4 Some applications of important

plastics

Figures 11.3a and 11.3b summarize 1990 data on

world and West European consumption of plastics The

survey included high-volume, low-price commodity

plastics as well as engineering and advanced plastics

Thermoplastics dominate the market (i.e PE, PVC and

PP) Development of an entirely new type of plastic is

extremely expensive and research in this direction is

1In the 1930s, concern with oxidation led the Continental

Rubber Works, Hannover, to experiment with

nitrogen-inflation of tyres intended for use on Mercedes

‘Silver Arrows’, Grand Prix racing cars capable of 300

km/h This practice was not adopted by Mercedes-Benz for

track events

limited Research is mainly concerned with ing and reducing the cost of established materials(e.g improved polymerization catalysts, composites,thermoplastic rubbers, waste recycling)

improv-The low- and high-density forms of polyethylene,LDPE and HDPE, were developed in the 1940s and1950s, respectively Extruded LDPE is widely used asthin films and coatings (e.g packaging) HDPE is usedfor blow-moulded containers, injection-moulded cratesand extruded pipes An intermediate form of adjustabledensity known as linear low-density polyethylene,LLDPE, became available in the 1980s Althoughmore difficult to process than LDPE and HDPE, film-extruded LLDPE is now used widely in agriculture,horticulture and the construction industry (e.g heavy-duty sacks, silage sheets, tunnel houses, cloches, damp-proof membranes, reservoir linings) Its tear strengthand toughness have enabled the gauge of PE film to bereduced A further variant of PE is ultra-high molecu-lar weight polyethylene, UHMPE, which is virtuallydevoid of residual traces of catalyst from polymer-ization Because of its high molecular mass, it needs

to processed by sintering UHMPE provides the wearresistance and toughness required in artificial joints ofsurgical prostheses

Polyvinyl chloride (PVC) is the dominant plastic inthe building and construction industries and has effec-tively replaced many traditional materials such as steel,cast iron, copper, lead and ceramics For example,the unplasticized version (UPVC) is used for win-dow frames and external cladding panels because ofits stiffness, hardness, low thermal conductivity andweather resistance PVC is the standard material forpiping in underground distribution systems for potablewater (blue) and natural gas (yellow), being corrosion-resistant and offering small resistance to fluid flow.Although sizes of PVC pipes tend to be restricted, PVClinings are used to protect the bore of large-diameterpipes (e.g concrete) The relatively low softening tem-perature of PVC has stimulated interest in alternativepiping materials for underfloor heating systems Poly-butylene (PB) has been used for this application; being

supported, it can operate continuously at a temperature

of 80°C and can tolerate occasional excursions to

110°C However, hot water with a high chlorine

con-tent can cause failure Other important building plastics

are PP, ABS and polycarbonates Transparent roofing

sheets of twin-walled polycarbonate or PVC provide

thermal insulation and diffuse illumination: both

mate-rials need to be stabilized with additives to prevent UV

degradation

The thermoplastic polypropylene, PP (Propathene)

became available in the early 1960s Its stiffness,

tough-ness at low temperatures and resistance to chemicals,

heat and creep TmD165 – 170°C are exceptional PP

has been of particular interest to car designers in their

quest for weight-saving and fuel efficiency In a

typi-cal modern saloon car, at least 10% of the total weight

is plastic (i.e approximately 100 kg) PP, the

lowest-density thermoplastic (approximately 900 kg m 3), is

increasingly used for interior and exterior automotive

components (e.g heating and ventilation ducts, radiator

fans, body panels, bumpers (fenders)) It is amenable

to filament-reinforcement, electroplating, blending as a

copolymer (with ethylene or nylon), and can be

pro-duced as mouldings (injection- or blow-), films and

filaments

Polystyrene (PS) is intrinsically brittle Engineering

polymers such as PS, PP, nylon and polycarbonates

are toughened by dispersing small rubber spheroids

throughout the polymeric matrix; these particles

con-centrate applied stresses and act as energy-absorbing

sites of crazing The toughened high-impact form of

polystyrene is referred to as HIPS PS, like PP, is

nat-urally transparent but easily coloured When supplied

as expandable beads charged with a blowing agent,

such as pentane, PS can be produced as a rigid

heat-insulating foam

Some of the elastomers introduced in Chapter 2 will

now be considered Polyisoprene is natural rubber;

unfortunately, because of reactive C– C links in the

chains it does not have a high resistance to chemical

attack and is prone to surface cracking and degradation

(‘perishing’) Styrene-butadiene rubber (SBR),

intro-duced in 1930, is still one of the principal synthetic

rubbers (e.g car tyres).1 In this copolymer, repeat

units of butadiene2are combined randomly with those

of styrene Polychloroprene (Neoprene), introduced in

1932, is noted for its resistance to oil and heat and

is used for automotive components (e.g seals, water

circuit pipes)

As indicated previously, additives play a vital role in

rubber technology The availability of a large family of

1Synthetic (methyl) rubber was first produced in Germany

during World War I as a result of the materials blockade;

when used for tyres, vehicles had to be jacked-up overnight

to prevent flat areas developing where they contacted the

ground

2Butadiene, or but-2-ene, is an unsaturated derivative of

butane C4H10; the central digit indicates that the original

butene monomer CH contains two double bonds

rubbers has encouraged innovative engineering design(e.g motorway bridge bearings, mounts for oil-rigsand earthquake-proof buildings, vehicle suspensionsystems)

Silicone rubbers may be regarded as being mediate in character to polymers and ceramics FromTable 2.7 it can be seen that the long chains con-sist of alternating silicon and oxygen atoms Althoughweaker than organic polymers based upon carbonchains, they retain important engineering properties,such as resilience, chemical stability and electricalinsulation, over the very useful temperature range of

inter-100°C to 300°C These outstanding characteristics,combined with their cost-effectiveness, have led to theadoption of silicone rubbers by virtually every industry(e.g medical implants, gaskets, seals, coatings)

11.1.5 Management of waste plastics

Concern for the world’s environment and future energysupplies has focused attention on the fate of wasteplastics, particularly those from the packaging, carand electrical/electronics sectors Although recovery

of values from metallic wastes has long been tised, the diversity and often complex chemical nature

prac-of plastics raise some difficult problems Nevertheless,despite the difficulties of re-use and recycling, it must

be recognized that plastics offer remarkable propertiesand are frequently more cost- and energy-effective thantraditional alternatives such as metals, ceramics andglasses Worldwide, production of plastics accounts forabout 4% of the demand for oil: transport accountsfor about 54% Enlightened designers now considerthe whole life-cycle and environmental impact of apolymeric product, from manufacture to disposal, andendeavour to economize on mass (e.g thinner thick-nesses for PE film and PET containers (‘lightweight-ing’)) Resort to plastics that ultimately decompose

in sunlight (photodegradation) or by microbial action(biodegradation) represents a loss of material resource

as they cannot be recycled; accordingly, their use tends

to be restricted to specialized markets (e.g agriculture,medicine)

Figure 11.3c portrays the general pattern of tics disposal in Western Europe Landfilling is themain method but sites are being rapidly exhausted insome countries The principal routes of waste man-agement are material recycling, energy recycling andchemical recycling The first opportunity for materialrecycling occurs during manufacture, when uncontam-inated waste may be re-used However, as in the case

plas-of recycled paper, there is a limit to the number plas-oftimes that this is possible Recycling of post-consumerwaste is costly, involving problems of contamination,collection, identification and separation.3 Co-extruded

3German legislation requires that, by 1995, 80% of allpackaging (including plastics) must be collected separatelyfrom other waste and 64% of total waste recycled asmaterial

blow-moulded containers are being produced with a

three-layer wall in which recycled material is

sand-wiched between layers of virgin polymer In the

Ger-man car industry efforts are being made to recycle

flexible polyurethane foam, ABS and polyamides New

ABS radiator grilles can incorporate 30% from old

recycled grilles

Plastics have a high content of carbon and hydrogen

and can be regarded as fuels of useful calorific value

Incinerating furnaces act as energy-recycling devices,

converting the chemical energy of plastics into

ther-mal/electrical energy and recovering part of the energy

originally expended in manufacture Noxious fumes

and vapours can be evolved (e.g halogens); control

and cleaning of flue gases are essential

Chemical recycling is of special interest because

direct material recycling is not possible with some

wastes Furthermore, according to some estimates,

only 20 – 30% of plastic waste can be re-used after

material recycling Chemical treatment, which is an

indirect material recycling route, recovers monomers

and polymer-based products that can be passed on as

feedstocks to chemical and petrochemical industries

Hydrogenation of waste shows promise and is used to

produce synthetic oil

11.2 Behaviour of plastics during

processing

11.2.1 Cold-drawing and crazing

A polymeric structure is often envisaged as an

entan-gled mass of chain molecules As the Tg values

for many commercial polymers are fairly low, one

assumes that thermal agitation causes molecules to

wriggle at ambient temperatures Raising the

tempera-ture increases the violence of molecular agitation and,

under the action of stress, molecules become more

likely to slide past each other, uncoil as they rotate

about their carbon – carbon bonds, and extend in length

We will first concentrate upon mechanistic aspects

of two important modes of deformation; namely, the

development of highly-preferred molecular

orienta-tions in semi-crystalline polymers by cold-drawing and

the occurrence of crazing in glassy polymers

Cold-drawing can be observed when a

semi-crystalline structure containing spherulites is subjected

to a tensile test at room temperature A neck appears in

the central portion of the test-piece As the test-piece

extends, this neck remains constant in cross-section

but increases considerably in length This process

forms a necked length that is stronger and stiffer

than material beyond the neck At first, the effect of

applied tensile stress is to produce relative movement

between the crystalline lamellae and the interlamellar

regions of disordered molecules Lamellae that are

normal to the direction of principal stress rotate in a

manner reminiscent of slip-plane rotation in metallic

single crystals, and break down into smaller blocks

These blocks are then drawn into tandem sequencesknown as microfibrils (Figure 11.4) The individualblocks retain their chain-folding conformation and arelinked together by the numerous tie molecules whichform as the original lamellae unfold A bundle ofthese highly-oriented microfibrils forms a fibril (smallfibre) The microfibrils in a bundle are separated

by amorphous material and are joined by survivinginterlamellar tie molecules The pronounced molecularorientation of this type of fibrous structure maximizesthe contribution of strong covalent bonds to strengthand stiffness while minimizing the effect of weakintermolecular forces

Industrially, cold-drawing techniques which takeadvantage of the anisotropic nature of polymer crys-tallites are widely used in the production of synthetic

fibres and filaments (e.g Terylene) (Similarly,

biax-ial stretching is used to induce exceptional strength in

film and sheet and bottles e.g Melinex )

Crystalliza-tion in certain polymers can be very protracted For

instance, because nylon 6,6 has a Tg value slightlybelow ambient temperature, it can continue to crystal-lize and densify over a long period of time during nor-mal service, causing undesirable after-shrinkage Thismetastability is obviated by ‘annealing’ nylon briefly

at a temperature of 120°C, which is below Tm: less fect crystals melt while the more stable crystals grow

per-Stretching nylon 6,6 at room temperature during the

actual freezing process also encourages crystallizationand develops a strengthening preferred orientation ofcrystallites

Let us now turn from the bulk effect of cold-drawing

to a form of localized inhomogeneous deformation, oryielding In crazing, thin bands of expanded materialform in the polymer at a stress much lower than thebulk yield stress for the polymer Crazes are usuallyassociated with glassy polymers (PMMA and PS) butmay occur in semi-crystalline polymers (PP) They are

Figure 11.4 Persistence of crystalline block structure in

three microfibrils during deformation.

several microns wide and fairly constant in width: they

can scatter incident light and are visible to the unaided

eye (e.g transparent glassy polymers) As in the

stress-corrosion of metals, crazing of regions in tension

may be induced by a chemical agent (e.g ethanol on

PMMA) The plane of a craze is always at right angles

to the principal tensile stress Structurally, each craze

consists of interconnected microvoids, 10 – 20 nm in

size, and is bridged by large numbers of

molecule-orientated fibrils, 10 – 40 nm in diameter The voidage

is about 40 – 50% As a craze widens, bridging fibrils

extend by drawing in molecules from the side walls

Unlike the type of craze found in glazes on pottery, it is

not a true crack, being capable of sustaining some load

Nevertheless, it is a zone of weakness and can initiate

brittle fracture Each craze has a stress-intensifying

tip which can propagate through the bulk polymer

Crazing can take a variety of forms and may even

be beneficial For instance, when impact causes crazes

to form around rubber globules in ABS polymers,

the myriad newly-created surfaces absorb energy and

toughen the material Various theoretical models of

craze formation have been proposed One suggestion

is that triaxial stresses effectively lower Tgand, when

tensile strain has exceeded a critical value, induce a

glass-to-rubber transition in the vicinity of a flaw, or

similar heterogeneity Hydrostatic stresses then cause

microcavities to nucleate within this rubbery zone

As Figure 11.5 shows, it is possible to portray the

strength/temperature relations for a polymeric material

on a deformation map This diagram refers to PMMA

and shows the fields for cold-drawing, crazing, viscous

flow and brittle fracture, together with superimposed

contours of strain rate over a range of 10
6to 1 s
1

11.2.2 Processing methods for thermoplastics

Processing technology has a special place in the

remarkable history of the polymer industry: polymer

Figure 11.5 Deformation map for PMMA showing

deformation regions as a function of normalized stress

versus normalized temperature (from Ashby and Jones,

1986; permission of Elsevier Science Ltd, UK).

chemistry decides the character of individual moleculesbut it is the processing stage which enables them to bearranged to maximum advantage Despite the variety

of methods available for converting feedstock ders and granules of thermoplastics into useful shapes,these methods usually share up to four common stages

pow-of production; that is, (1) mixing, melting and enization, (2) transport and shaping of a melt, (3)drawing or blowing, and (4) finishing

homog-Processing brings about physical, and often cal, changes In comparison with energy requirementsfor processing other materials, those for polymers arerelatively low Temperature control is vital because

chemi-it decides melt fluidchemi-ity There is also a risk of mal degradation because, in addition to having limitedthermal stability, polymers have a low thermal con-ductivity and readily overheat Processing is usuallyrapid, involving high rates of shear The main methodsthat will be used to illustrate technological aspects ofprocessing thermoplastics are depicted in Figure 11.6.Injection-moulding of thermoplastics, such as PEand PS, is broadly similar in principle to the pressuredie-casting of light metals, being capable of produc-ing mouldings of engineering components rapidly withrepeatable precision (Figure 11.6a) In each cycle, ametered amount (shot) of polymer melt is forciblyinjected by the reciprocating screw into a ‘cold’ cavity(cooled by oil or water channels) When solidifica-tion is complete, the two-part mould opens and themoulded shape is ejected Cooling rates are fasterthan with parison moulds in blow-moulding becauseheat is removed from two surfaces The capital out-lay for injection-moulding tends to be high because ofthe high pressures involved and machining costs formulti-impression moulding dies In die design, specialattention is given to the location of weld lines, wheredifferent flows coalesce, and of feeding gates Com-puter modelling can be used to simulate the melt flowand distributions of temperature and pressure withinthe mould cavity This prior simulation helps to lessendependence upon traditional moulding trials, which arecostly Microprocessors are used to monitor and con-trol pressure and feed rates continuously during themoulding process; for example, the flow rates into acomplex cavity can be rapid initially and then reduced

ther-to ensure that flow-dividing obstructions do not duce weakening weld lines

pro-Extrusion is widely used to shape thermoplasticsinto continuous lengths of sheet, tube, bar, filament,etc with a constant and exact cross-sectional profile(Figure 11.6b) A long Archimedean screw (auger)rotates and conveys feedstock through carefully pro-portioned feed, compression and metering sections.The polymer is electrically heated in each of the threebarrel sections and frictionally heated as it is ‘shear-thinned’ by the screw Finally, it is forced through adie orifice Microprocessor control systems are avail-able to measure pressure at the die inlet and to keep

it constant by ‘trimming’ the rotational speed of thescrew Dimensional control of the product benefits

Figure 11.6 (a) Injection-moulding machine, (b) production

of plastic pipe by extrusion and (c) thermoforming of plastic

sheet (from Mills, 1986; by permission of Edward Arnold).

from this device On leaving the die, the

continuously-formed extrudate enters cooling and haul-off sections

Frequently, the extrudate provides the preform for a

second operation For example, in a continuous

melt-inflation technique, tubular sheet of LDPE or HDPE

from an annular die is drawn upwards and inflatedwith air to form thin film: stretching and thinningcease when crystallization is complete at about 120°C.Similarly, in the blow-moulding of bottles and air-ducting, etc., tubular extrudate (parison) moves ver-tically downwards into an open split-mould As themould closes, the parison is inflated with air at a pres-sure of about 5 atmospheres and assumes the shape ofthe cooled mould surfaces Relatively inexpensive alu-minium moulds can be used because stresses are low.Thermoforming (Figure 11.6c) is another secondarymethod for processing extruded thermoplastic sheet,being particularly suitable for large thin-walled hol-low shapes such as baths, boat hulls and car bodies(e.g ABS, PS, PVC, PMMA) In the basic version ofthe thermoforming, a frame-held sheet is located abovethe mould, heated by infrared radiation until rubberyand then drawn by vacuum into close contact with themould surface The hot sheet is deformed and thinned

by biaxial stresses In a high-pressure version of moforming, air at a pressure of several atmospheresacts on the opposite side of the sheet to the vacuumand improves the ability of the sheet to register finemould detail The draw ratio, which is the ratio ofmould depth to mould width, is a useful control param-eter For a given polymer, it is possible to construct

ther-a plot of drther-aw rther-atio versus temperther-ature which cther-an beused as a ‘map’ to show various regions where thereare risks of incomplete corner filling, bursts and pin-holes Unfortunately, thinning is most pronounced atvulnerable corners Thermoforming offers an econom-ical alternative to moulding but cycle times are ratherlong and the final shape needs trimming

11.2.3 Production of thermosets

Development of methods for shaping thermosettingmaterials is restricted by the need to accommodate acuring reaction and the absence of a stable viscoelas-tic state Until fairly recently, these restrictions tended

to limit the size of thermoset products

Compres-sion moulding of a thermosetting P-F resin (Bakelite)

within a simple cylindrical steel mould is a well-knownlaboratory method for mounting metallurgical samples.Resin granules, sometimes mixed with hardening orelectrically-conducting additives, are loaded into themould, then heated and compressed until crosslinkingreactions are complete In transfer moulding, whichcan produce more intricate shapes, resin is melted in

a primary chamber and then transferred to a ventedmoulding chamber for final curing In the car indus-try, body panels with good bending stiffness are pro-duced from thermosetting sheet-moulding compounds(SMC) A composite sheet is prepared by laying downlayers of randomly-oriented, chopped glass fibres, cal-cium carbonate powder and polyester resin The sheet

is placed in a moulding press and subjected to heat andpressure Energy requirements are attractively low.Greater exploitation of thermosets for large car partshas been made possible by reaction injection-moulding

(RIM) In this process, polymerization takes place

dur-ing formdur-ing Two or more streams of very fluid

chemi-cal reactants are pumped at high velocity into a mixing

chamber The mixture bottom-feeds a closed chamber

where polymerization is completed and a solid forms

Mouldings intended for high-temperature service are

stabilized, or post-cured, by heating at a temperature

of 100°C for about 30 min The reactive system in RIM

can be polyurethyane-, nylon- or polyurea-forming

The basic chemical criterion is that polymerization in

the mould should be virtually complete after about

30 s Foaming agents can be used to form

compo-nents with a dense skin and a cellular core When glass

fibres are added to one of the reactants, the process is

called reinforced reaction injection-moulding (RRIM)

RIM now competes with the injection-moulding of

thermoplastics Capital costs, energy requirements and

moulding pressures are lower and, unlike

injection-mouldings, thick sections are not subject to shrinkage

problems (‘sinks’ and voids) Cycle times for

RIM-thermosets are becoming comparable with those for

injection-moulded thermoplastics and mouldings of

SMC Stringent control is necessary during the RIM

process Temperature, composition and viscosity are

rapidly changing in the fluid stream and there is a

chal-lenging need to develop appropriate dynamic models

of mass transport and reaction kinetics

11.2.4 Viscous aspects of melt behaviour

Melts of thermoplastic polymers behave in a highly

viscous manner when subjected to stress during

pro-cessing Flow through die orifices and mould

chan-nels is streamline (laminar), rather than turbulent,

with shear conditions usually predominating Let us

now adopt a fluid mechanics approach and consider

the effects of shear stress, temperature and

hydro-static pressure on melt behaviour Typical rates of

strain (shear rates) range from 10 – 103s
1(extrusion)

to 103– 105s
1(injection-moulding) When a melt is

being forced through a die, the shear rate at the die

wall is calculable as a function of the volumetric flow

rate and the geometry of the orifice At the necessarily

high levels of stress required, the classic Newtonian

relation between shear stress and shear (strain) rate

is not obeyed: an increase in shear stress produces

a disproportionately large increase in shear rate In

other words, the shear stress/shear rate ratio, which is

now referred to as the ‘apparent shear viscosity’, falls

Terms such as ‘pseudo-plastic’ and ‘shear-thinning’ are

applied to this non-Newtonian flow behaviour.1 The

general working range of apparent shear viscosity for

extrusion, injection-moulding, etc is 10 – 104Ns m
2

(Shear viscosities at low and high stress levels are

measured by cone-and-plate and capillary extrusion

techniques, respectively.)

1In thixotropic behaviour, viscosity decreases with increase

in the duration of shear (rather than the shear rate).

Figure 11.7 shows the typical fall in apparent shearviscosity which occurs as the shear stress is increased

If Newtonian flow prevailed, the plotted line would

be horizontal This type of diagram is plotted forfixed values of temperature and hydrostatic pressure Achange in either of these two conditions will displacethe flow curve significantly Thus, either raising thetemperature or decreasing the hydrostatic (bulk) pres-sure will lower the apparent shear viscosity The latterincreases with average molecular mass For instance,fluidity at a low stress, as determined by the standardmelt flow index (MFI) test,1 is inversely proportional

to molecular mass At low stress and for a givenmolecular mass, a polymer with a broad distribution ofmolecular mass tends to become more pseudo-plasticthan one with a narrow distribution However, at highstress, a reverse tendency is possible and the versionwith a broader distribution may be less pseudo-plastic.Figure 11.8 provides a comparison of the flowbehaviour of five different thermoplastics and is usefulfor comparing the suitability of different processes Itindicates that acrylics are relatively difficult to extrude

Figure 11.7 Typical plot of apparent shear viscosity versus

shear stress for LDPE at 210°C and atmospheric pressure: effects of increasing temperature T and hydrostatic pressure

P shown (after Powell, 1974; courtesy of Plastics Division, Imperial Chemical Industries Plc).

1This important test, which originated in ICI laboratoriesduring the development of PE, is used for mostthermoplastics by polymer manufacturers and processors.The MFI is the mass of melt extruded through a standardcylindrical die in a prescribed period under conditions ofconstant temperature and compression load

Figure 11.8 Typical curves of apparent shear viscosity

versus shear stress for five thermoplastics at atmospheric

pressure A Extrusion-grade LDPE at 170°C; B

extrusion-grade PP at 230°C; C moulding-grade acrylic at

230°C; D moulding-grade acetal copolymer at 200°C; E

moulding-grade nylon at 285°C (after Powell, 1974;

courtesy of Plastics Division, Imperial Chemical Industries

Plc.).

and that PP is suited to the much faster deformation

process of injection-moulding In all cases, Newtonian

flow is evident at relatively low levels of shear stress

The following type of power law equation has been

found to provide a reasonable fit with practical data and

has enabled pseudo-plastic behaviour to be quantified

in a convenient form:

where C and n are constants Now  D , hence the

viscosity D Cn
1 The characteristic term n
1

can be derived from the line gradient of a graphical

plot of log viscosity versus log shear rate In practice,

the power law index n ranges from unity (Newtonian

flow) to <0.2, depending upon the polymer This index

decreases in magnitude as the shear rate increases

and the thermoplastic melt behaves in an increasingly

pseudo-plastic manner

So far, attention has been concentrated on the

vis-cous aspects of melt behaviour during extrusion and

injection-moulding, with emphasis on shear processes

In forming operations such as blow-moulding and

filament-drawing, extensional flow predominates and

tensile stresses become crucial; for these conditions,

it is appropriate to define tensile viscosity, the

coun-terpart of shear viscosity, as the ratio of tensile stress

to tensile strain rate At low stresses, tensile viscosity

is independent of tensile stress As the level of tensilestress rises, tensile viscosity either remains constant

(nylon 6,6), rises (LDPE) or falls (PP, HDPE) This

characteristic is relevant to the stability of dimensionsand form For example, during blow-moulding, thin-ning walls should have a tolerance for local weak spots

or stress concentrations PP and HDPE lack this erance and there is a risk that ‘tension-thinning’ willlead to rupture On the other hand, the tensile viscos-ity of LDPE rises with tensile stress and failure duringwall-thinning is less likely

tol-11.2.5 Elastic aspects of melt behaviour

While being deformed and forced through an sion die, the melt stores elastic strain energy Asextrudate emerges from the die, stresses are released,some elastic recovery takes place and the extrudateswells Dimensionally, the degree of swell is typicallyexpressed by the ratio of extrudate diameter to diediameter; the elastic implications of the shear processare expressed by the following modulus:

where is the elastic shear modulus,  is the shearstress at die wall, and Ris the recoverable shear strain.The magnitude of modulus depends upon the poly-mer, molecular mass distribution and the level of shearstress (Unlike viscosity, dependency of elasticity upontemperature, hydrostatic pressure and average molec-ular mass is slight.) If the molecular mass distribution

is wide, the elastic shear modulus is low and elasticrecovery is appreciable but slow For a narrow distribu-tion, with its greater similarities in molecular lengths,recovery is less but faster With regard to stress level,the modulus remains constant at low shear stresses butusually increases at the high stresses used commer-cially, giving appreciable recovery

The balance between elastic to viscous behaviourduring deformation can be gauged by comparing thedeformation time with the relaxation time or ‘naturalviscosity to elastic shear modulus  /, and derivesfrom the Maxwell model of deformation The term vis-coelasticity originated from the development of suchmodels (e.g Maxwell, Voigt, standard linear solid(SLS)) The Maxwell model is a mechanical analoguethat provides a useful, albeit imperfect, simulation ofviscoelasticity and stress relaxation in linear polymersabove Tg (Figure 11.9) It is based upon conditions

of constant strain A viscously damped ‘Newtonian’dashpot, representing the viscous component of defor-mation, and a spring, representing the elastic compo-nent, are combined in series At time t, the stress  isexponentially related to the initial stress 0, as follows:

is sufficient time for viscous movement of chain

Figure 11.9 Representation of stress relaxation under

constant strain conditions (Maxwell model).

molecules to take place and stress will fall rapidly

rubbery behaviour, to zero at the start of viscous

behaviour A real polymer contains different lengths of

molecules and therefore features a spectrum of

relax-ation times Nevertheless, although best suited to

poly-mers of low molecular mass, the Maxwell model offers

a reasonable first approximation for melts

Let us now apply the relaxation time concept to

an injection-moulding process in which a

thermo-plastic acrylic at a temperature of 230°C is sheared

rapidly at a rate of 105s
1 Assume that the injection

(deformation) time is 2 s For the shear rate given,

Figure 11.8 indicates that the apparent shear viscosity

is 9 Ns m
2 and the corresponding maximum shear

stress is 0.9 MN m
2 At this shear stress, the elastic

shear modulus for acrylic is 0.21 MN m
2 The value

µs, which is very small compared

to the injection time of 2 s, hence viscous behaviour

will predominate A similar procedure can be applied

to deformation by extrusion For instance, PP with a

relaxation time of 0.5 s might pass though the

extru-sion die in 20 s The time difference is smaller than

the previous example of injection-moulding, indicating

that although deformation is mainly viscous,

elastic-ity will play a greater part than in injection-moulding

The previously-mentioned phenomenon of die swell

then becomes understandable (Swelling is equivalent

to the spring action in the Maxwell model.) Although

the degree of elastic behaviour may be relatively

small during injection-moulding and extrusion, it can,

nevertheless, sometimes cause serious flow defects

Relaxation times for extensional flow, as employed

in blow-moulding, can be derived from the ratio of

apparent tensile viscosity to elastic tensile modulus

E D /εR Suppose that a PP parison at a

temper-ature of 230°C hangs for 5 s before inflation with

air If the tensile viscosity and tensile modulus are

36 kN s m
2and 4.6 kN m
2, respectively, the ation time is roughly 8 s Hence sagging of the parisonunder its own weight will be predominantly elastic

relax-11.2.6 Flow defects

The complex nature of possible flow defects lines the need for careful product design (sections,shapes, tools) and close control of raw materials andoperational variables (temperatures, shear rates, cool-ing arrangements) The quality of processing makes avital contribution to the engineering performance of apolymer

under-Ideally, melt flow should be streamlined throughoutthe shaping process If the entry angle of an extru-sion die causes an abrupt change in flow direction, themelt assumes a natural angle as it converges upon thedie entry and a relatively stagnant ‘dead zone’ is cre-ated at the back of the die In this region, the meltwill have a different thermal history In addition to itsdominant shear component, the convergent flow con-tains an extensional component that increases rapidlyduring convergence If the extensional stress reaches acritical value, localized ‘melt fracture’ will occur at afrequency depending upon conditions The fragmentsproduced recover some of the extensional strain Theeffect upon the emerging extrudate can range from amatt finish to gross helical distortions The associatedflow condition is often termed ‘non-laminar’ despitethe fact that the calculated value of the dimensionlessReynolds number is very low The choice of entryangle for the die is crucial and depends partly uponthe polymer

As a melt passes through the die, velocity gradientsdevelop, with the melt near the die surface movingslower than the central melt Upon leaving the die,the outer layers of extrudate accelerate, eliminating thevelocity gradient Above a critical velocity, the resul-tant stresses rupture the surface to give a ‘sharkskin’effect which can range in severity from a matt finish

to regular ridging perpendicular to the extrusion tion ‘Sharkskin’ is most likely when the polymer has

direc-a high direc-averdirec-age moleculdirec-ar mdirec-ass (i.e highly viscous)and a narrow molecular mass distribution (i.e highlyelastic); these factors cause surface stress to build uprapidly and to relax slowly Fast extrusion at a lowtemperature favours this defect Heating of the tip ofthe die lowers viscosity and reduces its likelihood

An inhomogeneous melt will produce a non-uniformrecovery of elastic strain at the cooling surface andinfluence its final texture Thorough mixing beforeshaping is essential However, inhomogeneity mayexist on a molecular scale For instance, in bothinjection-moulding and extrusion, a broad distribution

of molecular mass gives a more matt finish than a row distribution Thus, extrusion of a polymer with

nar-a nnar-arrow mnar-ass distribution nar-at nar-a rnar-ate slow enough toprevent the development of ‘sharkskin’ will favour ahigh-gloss finish

Volatile constituents tend to vaporize, or ‘boil off’,

from the melt if processing temperatures are high For

instance, water vapour may derive from hygroscopic

raw materials Sometimes, a polymer degrades and

releases a volatile monomer Hydrostatic pressure

usu-ally keeps the volatiles in solution; as the hot polymer

leaves the die, this pressure is released and the

escap-ing volatiles form internal bubbles and may pit the

surface

When a polymer is heated to the processing

temper-ature, the weak intermolecular forces are readily

over-come by thermal vibrations Its density may decrease

by as much as 25% The subsequent cooling can

produce shrinkage defects, particularly in crystalline

polymers, which assume more closely packed

con-formations than amorphous polymers, and in thick

sections Polymers have a low thermal conductivity

and the hot core can contract to produce depressions

or ‘sink marks’ in the surface If the surface layer

cools rapidly, its rigidity can encourage internal voids

to form Careful product design can minimize

shrink-age problems Cooling under pressure after

injection-moulding is beneficial

Orientation effects, which are common in shaped

polymers, have a special significance when the

poly-mer is ‘reinforced’ with short lengths of glass fibre (It

has been estimated that roughly half of the

engineer-ing thermoplastics are fibre-filled.) In extruded pipes,

fibres will tend to be aligned parallel to the extrusion

direction and improve longitudinal strength However,

this orientation weakens the pipe transversely and the

burst strength will suffer In addition, the tubular form

necessitates use of a ‘spider’ to support a central die,

or mandrel, which causes the melt to split and

coa-lesce before entering the die The resultant weld lines

introduce weakening interfaces A die system is now

available in which one or both dies are rotated Their

shearing action has the beneficial effect of inclining

fibres at an angle to the extrusion direction Weld lines

are also reoriented so that they are placed in shear

rather than tension when in service

11.3 Fibre-reinforced composite

materials

11.3.1 Introduction to basic structural

principles

11.3.1.1 The functions of filaments and matrix

In engineering practice, where considerations of

mec-hanical strength and stiffness are usually paramount,

the term ‘composite’ is generally understood to refer

to a material which combines a matrix phase with

admixed filaments of a reinforcing (strengthening)

phase A composite derives from the essentially simple

and practical idea of bonding together two or more

homogeneous materials which have very different

properties Thus, in the glass-reinforced polymer

(GRP) known generally as Fibreglass, large numbers

of short, strong and stiff fibres of glass are randomlydispersed in a weaker but tougher matrix of thermosetresin In general, the diameter of reinforcing filamentsfor composites is in the order of 10
m They may becontinuous, extending the full length of a component,

or short (discontinuous) and may share a commonorientation, be randomly oriented or even woven intocloth There is a statistical distribution of strengthvalues among filaments made from brittle materialssuch as glass, boron and carbon

The term ‘composite’ is sometimes taken to includematerials in which the second phase is in the form

of particles or laminae In such cases the compositestructure may offer special advantages, other thanstrength, such as economy and corrosion-resistance(e.g filler in plastics, plastic-coated steel sheet) Therecorded history of technology contains numerousaccounts of innovative, often remarkable, ideas forcomposites.1 The present account primarily concernsthe reinforcement of polymeric, metallic and ceramicmatrices with fibres and ‘whisker’ crystals Finally, on

an even finer scale, we will consider application ofthe composite principle to microstructural constituents(i.e nanocomposites) Relatively simple mechanicalmodels will be used because they provide sufficientintroduction to the ground rules of composite designand behaviour

Although fibres are a striking feature of a composite,

it is initially helpful to examine the functions of thematrix Ideally, it should be able to (1) infiltrate thefibres and solidify rapidly at a reasonable temperatureand pressure, (2) form a coherent bond, usuallychemical in nature, at all matrix/fibre interfaces,(3) envelop the fibres, which are usually very notch-sensitive, protecting them from mutual damage byabrasion and from the environment (chemical attack,moisture), (4) transfer working stresses to the fibres,(5) separate fibres so that failure of individual fibresremains localized and does not jeopardize the integrity

of the whole component, (6) debond from individualfibres, with absorption of significant amounts ofstrain energy, whenever a propagating crack in thematrix chances to impinge upon them, and (7) remainphysically and chemically stable after manufacture.11.3.1.2 Continuous-fibre composites

In mechanical terms, the prime function of the matrix

is to transfer stresses to the fibres (item (4) above)because these are stronger and of higher elasticmodulus than the matrix The response of a composite

to applied stress depends upon the respective properties

of the fibre and matrix phases, their relative volumefractions, fibre length and the orientation of fibresrelative to the direction of applied stress

1During the Battle of the Atlantic in World War II, GeoffreyPyke proposed the construction of ocean-going aircraft

carriers from paper pulp/frozen sea water (Pykecrete) In

1985, ice/wood fibres (Icecrete) was proposed for wharf and

off-shore oil platform construction in Norwegian waters

Figure 11.10 ‘Parallel’ (a) and ‘series’ (b) models of unidirectional filament alignment in composites.

Some basic principles of the elastic response to

stress can be obtained from mechanical models in

which continuous fibres are set unidirectionally in

an isotropic, void-free matrix (Figures 11.10a and

11.10b) It will be assumed that the Poisson ratio

for the fibre material is similar to that of the matrix

Using subscript letters c, f, m, l and t we can signify

where property values refer respectively to composite,

fibre, matrix, longitudinal and transverse directions

Thus Vf/Vm is the ratio of volume fractions of fibre

and matrix, where 1
Vf D Vm Certain longitudinal

properties for a composite can be obtained by using the

‘parallel’ model shown in Figure 11.10a and applying

the Rule of Mixtures For this condition of isostrain,

stresses are additive and the equations for stress

(strength) and elastic modulus are:

clDflVfCmVm 11.5

EclDEflVfCEmVm 11.6

It is now possible to derive the following relation:

fl/m D Vf/VmEfl/Em 11.7

Figure 11.11 illustrates this relation, showing that

as the modulus ratio and/or the volume fraction of

fibres increase, more and more stress is transferred to

the fibres If the modulus ratio is unity, the composite

must contain at least 50% v/v fibres if the fibres are

to carry the same load as the matrix Three typical

composites A, B and C with 50% v/v reinforcement

are superimposed on the graph to show the extent to

which two increases in modulus ratio raise the stress

ratio

An alternative arrangement of fibres relative to

applied tensile stress is shown in Figure 11.10b The

transverse elastic modulus for the composite is given

by the equation:

1/Ect D Vf/Eft C Vm/Em 11.8

This ‘series’ version of the Rule assumes a condition

of isostress and is derived by adding strains: it is less

accurate than the ‘parallel’ version Both versions can

be used to calculate shear moduli and conductivities

(thermal, electrical) More refined mathematical

treatments are available: they are particularly helpful

for transverse properties Sometimes fibre properties

are highly anisotropic and this feature influences the

corresponding value for the composite; for instance,

Eft−Efl for aramid (Kevlar, Nomex ) and carbon

fibres In general,  × , E ×E and E > E ,

Figure 11.11 Relation between modulus ratio and stress

ratio (continuous parallel fibres).

so that the equations for the ‘parallel’ and ‘series’models express, in mathematical form, the dominanteffect of fibres on longitudinal properties and thedominant effect of the matrix on transverse properties

If typical tensile stress versus strain curves for fibreand matrix materials (Figure 11.12a) are compared,

it can be seen that the critical strain, beyond whichthe composite loses its effectiveness, is determined bythe strain at fracture of the fibres, εf At this strainvalue, when the matrix has usually begun to deformplastically and to strain-harden, the correspondingstress on the matrix is 0

m Thus, in the relatedFigure 11.12b, it follows that the strength of thecomposite lies between the limits 0

mand f, dependingupon the volume fraction of fibres When a few widely-spaced fibres are present, the matrix carries more loadthan the fibres Furthermore, in accordance with theRule of Mixtures, the strength of the composite falls

as the volume fraction of fibres deceases Constructionlines representing these two effects meet at a minimumpoint, Vmin Obviously, Vf must exceed Vcrit if thetensile strength of the matrix is to benefit from the

Figure 11.12 (a) Stress–strain curves for filament and matrix and (b) dependence of composite strength on volume fraction of

continuous filaments.

presence of fibres In practical terms, the upper limit

for Vf is about 0.7 – 0.8 At higher values, fibres

are likely to damage each other The Rule is only

applicable when Vf> Vmin

At the critical volume for fibres, mDcand VfD

Vcrit From the Rule equation we derive:

VcritDm
0

m/f
0

In general, a low Vcrit is sought in order to minimize

problems of dispersal and to economize on the amount

of reinforcement Very strong fibres will maximize

the denominator and are clearly helpful

Strain-hardening of the matrix (Figure 11.12a) is represented

approximately by the numerator of the above ratio

Thus, a matrix with a strong tendency to strain-harden

will require a relatively large volume fraction of fibres,

a feature that is likely to be very significant for metallic

matrices For example, an fcc matrix of austenitic

stainless steel (Fe-18Cr-8Ni) will tend to raise Vcrit

more than a cph matrix of zinc

11.3.1.3 Short-fibre composites

So far, attention has been focused on the behaviour

of continuous fibres under stress Fabrication of

these composites by processes such as

filament-winding is exacting and costly On the other hand,

composites made from short (discontinuous) fibres

enable designers to use cheaper, faster and more

versatile methods (e.g injection-moulding,

transfer-moulding) Furthermore, some reinforcements are only

available as short fibres At this point, it is appropriate

to consider an isolated short fibre under axial tensile

stress and to introduce the idea of an aspect ratio

length/diameter D l/d It is usually in the order of

10 to 103 for short fibres: many types of fibre and

whisker crystal with aspect ratios greater than 500 are

available For a given diameter of fibre, an increase

in length will increase the extent of bonding at the

fibre/matrix interface and favour the desired transfer

of working stresses As will be shown, it is necessary

for the length of short fibres to exceed a certain critical

length1 if efficient transfer of stress is to take place.With respect to diameter, fibre strength increases as thediameter of a brittle fibre is reduced This effect occursbecause a smaller surface area makes it less likely thatweakening flaws will be present

For the model, in which a matrix containing a shortfibre is subjected to a tensile stress (Figure 11.13a),

it is assumed that the strain to failure of the matrix

is greater than the strain to failure of the fibre Thedifferences in displacement between matrix and fibrethus cause shear stress, , to develop at the cylindricalinterfaces toward each fibre end A correspondingtensile stress, , builds up within the fibre At eachend of the fibre, these stresses change over a distance

known as the stress transfer length (l/2); that is,

the tensile stress increases as the interfacial shearstress decreases In Figure 11.13a, for simplicity, weassume that the gradient of tensile stress is linear Ifthe length of the fibre is increased, the peak tensilestress coincides with fracture stress for the filament(Figure 11.13b) The total length of fibre now has acritical value of lc and the transfer length becomes

lc/2 If the length is sub-critical, fibre failure cannot

occur At the critical condition, the average tensilestress on the fibre is only f/2 With any further

increase in fibre length, a plateau develops in the stressprofile (Figure 11.13c) The average tensile stress

on the fibre, which is stated beneath Figure 11.13c,approaches the fracture strength f as the fibre lengthincreases beyond its critical value In effect, the load-carrying efficiency of the fibre is approaching that ofits direct-loaded continuous counterpart Provided thatthe shear stresses do not cause ‘pull-out’ of the fibre,fracture will eventually occur in the mid-region ofthe fibre

The condition of critical fibre length can bequantified Suppose that an increment of tensile force,

υ, is applied to an element of fibre, υl The balance

1A Kelly introduced the concept of ‘critical fibre length’

Figure 11.13 Distribution of tensile stress in a short fibre fDfracture stress of fibre in tension,  D mean tensile stress.

between tensile force and interfacial shear force is:

υd2/4 D d.υl 11.10

Hence the gradient υ/υl for the build-up of

tensile stress is 4/d For the critical condition

(Figure 11.13b), the gradient is f divided by the

critical transfer length lc/2 The critical length lc is

therefore fd/2 Expressed in terms of the critical

aspect ratio, the criterion for efficient stress transfer

takes the form:

This relation provides an insight into the capabilities

of short-fibre composites For instance, for a given

diameter of fibre, if the interfacial shear strength of

the fibres is lowered, then longer fibres are needed

in order to grip the matrix and receive stress When

the operating temperature is raised and the shear

strength decreases faster than the fracture strength

of the fibres, the critical aspect ratio increases The

presence of tensile and shear terms in the relation

highlights the indirect nature of short-fibre loading:

matrix strength and interfacial shear strength are

much more crucial factors than in continuous-fibre

composites where loading is direct Interfacial shear

strength depends upon the quality of bonding and

can have an important effect upon the overall impact

resistance of the composite Ideally, the bond strength

should be such that it can absorb energy by debonding,

thus helping to inhibit crack propagation Interfacial

adhesion is particularly good in glass fibre/polyester

resin and carbon fibre/epoxy resin systems Coupling

agents are used to promote chemical bonding at the

interfaces For example, glass fibres are coated with

silane (size) which reacts with the enveloping resin

Sometimes these treatments also improve resistance to

aqueous environments However, if interfacial bonding

is extremely strong, there is an attendant risk that an

impinging crack will pass into and through fibres withlittle hindrance

Provided that Vf> Vcrit, the tensile strength atfracture of a short-fibre reinforced composite can becalculated from the previous Rule of Mixtures equation

by substituting the mean tensile stress term for thefracture stress, as follows:

cD1
lc/2lVfC0

It is assumed that the shear strength  remains constantand that fibres are perfectly aligned First, the equationshows that short fibres strengthen less than continuousones For example, if all fibres are ten times thecritical length, they carry 95% of the stress carried bycontinuous fibres On the other hand, if their lengthfalls below the critical value, the strength suffersseriously For instance, if the working load on thecomposite should cause some of the weaker fibres

to fail, so that the load is then carried by a largernumber of fibres, the effective aspect ratio and thestrength of the composite tend to fall The same type

of equation can also be applied to the elastic modulus

of a short-fibre composite; again the value will be lessthan that obtainable with its continuous counterpart.The equation also shows that matrix properties becomemore prominent as fibres are shortened

11.3.1.4 Effect of fibre orientation on strengthLet us reconsider composites in which continuousfibres are aligned in the same direction as thedirection of applied stress The strength of this highlyanisotropic type of composite varies with the volumefraction of fibres in a linear manner, as shown inFigure 11.12b If the fibres are now oriented at anangle  to the direction of applied tensile stress, thegeneral effect is to reduce the gradient of the strengthcurve for values of Vf greater than Vmin, as shown inFigure 11.14 This weakening effect is represented by

Figure 11.14 Effect of fibre orientation on strength of

unidirectional composite (continuous fibres

inserting an orientation factor  in the basic strength

equation to give:

cDfVfC0mVm 11.13

As  increases from zero,  falls below unity

In order to provide a more detailed analysis of the

variation of composite strength with fibre orientation,

it is customary to apply a ‘maximum stress’ theory

based on the premise that there are three possible

modes of composite failure Apart from the angle of

fibre orientation , three properties of the composite

are invoked: the strength parallel to the fibres fl, the

shear strength of the matrix parallel to the fibres m,

and the strength normal to the fibres ft Each mode

of failure is represented by an equation which relates

the composite strength clto a resolved stress

For the first mode of failure, which is controlled by

tensile fracture of the fibres, the equation is

The equation for failure controlled by shear on a plane

parallel to the fibres is:

As the temperature is raised, this mode of failure

becomes more likely in off-axis composites because

the shear strength mfalls more rapidly than fl

In the third mode of failure, transverse rupture

occurs, either in the matrix or at the fibre/matrix

interface (debonding) The relevant equation is:

Figure 11.15 shows the characteristic form of the

relation between composite strength and fibre

orienta-tion While illustrating the highly anisotropic character

of the unidirectional continuous reinforcement, it also

shows the merit of achieving low values of 

Predic-tions, using the maximum stress theory, and

experi-mental results are in good agreement and confirm the

general validity of this curve (Measured values of fl,

 and  are required for these calculations.) The

Figure 11.15 Relation between failure mode, strength and

fibre orientation (schematic diagram for unidirectional continuous-fibre composite).

mode of failure is decided by the equation which givesthe lowest value of composite strength cl Thus, trans-verse rupture becomes dominant when  is large Atrelatively low values of , there is a rapid fall in com-posite strength which is associated with the transitionfrom tensile failure in fibres to failure by shear Combi-nation of the first two of the three equations eliminates

cl and gives the critical angle for this transition:

critDtan
1m/fl 11.17

If the longitudinal strength is about ten times the shearstrength of the matrix, then the angle is about 6°.When an application involves applied stressesthat are not confined to one direction, the problem

of anisotropy can often be effectively solved orminimized by using continuous fibres in the form ofwoven cloth or laminates Although these forms aremore isotropic than unidirectional composites, there isinevitably a slight but usually tolerable loss in strengthand stiffness Glass, carbon and aramid fibres are used;sometimes two or more different types of fibre are used

in combination (hybrid composites) Fibre cloth in avariety of weave patterns is available In a nominallytwo-dimensional sheet of woven cloth there is a certainamount of fibre oriented in the third dimension A moretruly three-dimensional reinforcement, with improvedthrough-thickness properties, can be obtained byplacing woven cloths on top of each other and stitchingthem together with continuous fibre

Laminates based on carbon and aramid fibres arecommonly used for high-performance applicationsthat involve complex stress systems (e.g twisting,bending) The unit of construction is a thin ply

of unidirectional composite, 50 – 130µm thick Pliesare carefully stacked and oriented with respect toorthogonal reference axes (0° and 90°) The simplestlay-up sequence is (0/90/90/0) Other more isotropicsequences are 0/ C 45/
45/
45/ C 45/0 and