Principles of Polymer Engineering

Contents

0. Introduction 0.1. The past 0.2. Engineering plastics

1. Structure of the molecule 1 . 1 . Introduction 1.2. Addition polymers 1.3. Condensation polymers 1.4. Copolymers 1.5. Cross-linked polymers 1.6. Molecular symmetry and the tendency to form crystals 1.7. Distribution of relative molecular mass Problems Notes Structure of polymeric solids 2.1. Introduction 2.2. Structure of the crystal 2.3. Crystal shape 2.4. Crystallinity 2.5. Crystallization and melting 2.6. The glass transition temperature 2.7. Molecular conformation in the amorphous polymer 2.8. The freely jointed chain 2.9. The Gaussian chain 2.10. Molecular orientation Problems Notes

3.

The 3.1. 3.2. 3.3. 3.4. 3.5. 3.6.

elastic properties of rubber

Introduction Structure of an ideal rubber Entropy elasticity Elasticity of a network Stress-strain relationship ~ n ~ i n e e r rubbers in~

Contents

x

Problems Notes 4.

Viscoelasticity 4.1. Introduction 4.2. The nature of viscoelasticity 4.2.1. Creep 4.2.2. Stress relaxation 4.2.3. Dynamic properties 4.3. Theory of linear viscoelasticity 4.3.1. The Zener model 4.3.2. Distribution of relaxation times 4.3.3. Origin of temperature dependence 4.4. Polymer selection: stiffness 4.4.1. Temperature dependence 4.4.2. Stress analysis Problems Notes

5.

Yield and fracture 5.1. Introduction 5.2. Yielding 5.2.1. Considhe's construction 5.2.2. Eyring's model of the flow of solids 5.2.3. Yielding under multiaxial stresses 5.3. Crazing 5.4. Fracture mechanics 5.4.1. Measurement and application of KIc 5.5. Fracture properties of polymers Problems Notes

6.

Reinforced polymers 6.1. Introduction 6.2. Reinforced plastics 6.2.1. Polymer matrices 6.2.2. Fibrous reinforcement 6.2.3. Platelet reinforcement 6.3. Forming of reinforced plastics 6.3.1. Pultrusion 6.3.2. Filament winding 6.3.3. Hand lay-up 6.3.4. Hand spray-up

Contents

6.3.5. Compression moulding 6.3.6. Reinforced reaction injection moulding ( R R I M ) 6.3.7. Reinforced thermoplastics 6.4. The mechanics of fibre reinforcement 6.4.1. Continuousfibres 6.4.2. Discontinuous fibres 6.5. Reinforced rubbers Problems Notes 7.

8.

Forming 7.1. Introduction 7.2. The flow properties of polymer melts 7.2.1. Bulk deformation 7.2.2. Elongational~ow 7.2.3. Shear flow 7.3. Extrusion 7.3.1. Extruder barrel 7.3.2. Extruder screw 7.3.3. Die and calibration equipment 7.4. Injection moulding 7.4.1. Hot runner moulds 7.4.2. The gate 7.4.3. Control of pressure, temperature, and time 7.4.4. Thermosets 7.4.5. Reaction injection moulding ( R I M ) 7.5. Thermoforming 7.6. Blow moulding 7.7. Compression and transfer moulding 7.7.1. Compression moulding 7.7.2. Transfer moulding Problems Notes Design

8.1. Introduction 8.2. Materials selection 8.2.1. The selection procedure 8.2.2. The 'big four' commodity thermoplastics 8.2.3. The engineering thermoplastics 8.2.4. Thermosets and composites 8.2.5. Rubbers

xi

xii

Contents

8.3. Designing for manufacture 8.3.1. Injection moulding 8.3.2. Joining and fbstening 8.3.3. Thermosetting polymers 8.4. Designing for stiffness 8.4.1. PIastics 8.4.2. Fibre composites 8.4.3. Rubbers 8.5. Designing for strength 8.6. Case histories 8.6.1. Optical memory devices (compact discs) 8.6.2. Motorcycle drive sprocket 8.6.3. Cross-country ski bindings 8.6.4. Glass fibre -epoxy composite leaf spring 8.6.5. Helicopter blade 8.6.6. Cautionary tale no. I 8.6.7. Cautionary tale no. 2 Problems Notes Further reading Answers t o problems Index

Index

Note: the letter P after a page number indicates that the reference is to one of the set problems.

acrylic polymers 31 acrylonitrile 28P acrylonitrile-butadiene-styrene polymer (ABS) 183, 206, 31 1, 31 7P, 327, 328 activation enthalpy 134, 172 activation volume 173-6, 205 addition polymers 1 1, 12 affine deformation 80 ageing chemical 30, 358 physical 137, 142-5 aircraft 5, 6, 183, 367 alloys (metal) 1, 8, 16 . amorphous fraction 19, 41, 48-50, 62 anisotropy 38, 60, 200, 208, 221, 350 apparent viscosity 273 applications of polymers aircraft 5, 183, 355, 367 boats 209, 225 building and construction 283 cars and vehicles 1, 6, 96, 21 1, 227, 323, 324, 329 chemical 323 domestic 30 electrical 70, 329. 364 fibres 70 films 30, 70, 321 medical 1, 30 optical 6 1, 364 packaging 30, 70, 321 pipes 30, 159, 183 aramid fibre ( ~ e v l a r ~5,) 209, 2 17, 2 18, 22 1 Arrhenius equation 134, 163, 164, 172, 280 aspect ratio of filler 2 12, 2 13, 245 atactic polymer 19, 20 automobiles see cars Avogadro's number 62P, 93P

Baekeland 373 Bagley correction 279 Bakelite 373 barrier flight extryder screw 290

biaxial orientation 62, 70, 179. 200. 312 birefringence 60, 61, 66P blends 23, 24 block copolymer 16, 29P, 92, 160 blow moulding 70, 3 1 1 -1 3 Boltzmann equation 76 Boltzmann superposition principle (BSP) 148-54. 348. 349 branching 9, 13. 19. 31, 271 Brownian motion 101 bulk deformation of melt 267 butadiene 33 butyl rubber 330 capillary flow 273-9 car tyres (reinforcement) 210, 21 1 carbon black in rubbers 89, 21 1, 2 5 2 4 carbon fibre 100. 209. 217-22, 242. 255P Carothers 3 cars, use of polymers in 1, 6. 7. 227, 323 cellulose nitrate (Celluloid) 2, 3 centrally-cracked plate 183-5 Charpy impact strength 358, 359 chlorine (in PVC) 63P chloroprene rubbers 92, 93 chopped strand mat (CSM) 225. 256P Clausius-Clapeyron equation 64P coextrusion 321. 322 compact disc (polymer application) 61. 364-7 compact tension (CT) test 192, 193 compliance 102, 106, 114, 148 composite materials 209-63 cost 215 density 214 failure criteria 236, 242 manufacture 223-7 matrices 215, 216, 329 modulus continuous fibres 229-33 discontinuous fibres 247 short-fibre 244-52 thermal expansion 234, 235, 256

compression moulding 224. 226, 3 13-14 computer-aided design (CAD) in moulding 333-6 condensation polymers 1 1, 14. 15. 19 conformation of molecules 50-2, 55, 56, 62 Considere construction 169-7 1 contour length of chain 51, 53, 54 copolymerization 15, 32, 90 copolymers 15, 16, 32, 33, 64P. 90 costs 215, 327 covalent bond 60, 221 Cox theory 261 -3 crack propagation speed 208 crankshaft rotation of molecule 164. 165 crazing 167-9, 180-3, 202P under biaxial stress 181 environmental 182, 206, 368 under internal stress 18 1 in rubber-modified plastics 182 creep 101 -8, 126, 145, 148. 345-50 critical length of fibres 250-2. 263 crosslinking 10, 16-18, 29P, 73, 75, 88, 138, 165 crystallinity 18, 40-2, 46, 63P, 86 crystallization 34, 42-7 modulus, effect on 140, 142 of rubber 86, 254 temperature dependence 4 4 yield stress. effect on 179 crystals 18, 34-42, 61, 62, 64P, 73 damping 1 12 debonding of fibres 248-50 Debye 129, 162 deflection-limited design 347 degradation 9. 30. 32. 138. 199 degree of polymerization 20, 21 density 214. 327 density gradient column 41 design of polymer products 323-74 die swell 281, 293 dielectric properties 162, 325 dipole relaxation 162 distribution Gaussian 57, 58, 69, 70 o f Kelvin elements 131, 156P of Maxwell elements 133. 156P. 157P of stress along fibre 245, 246. 249 divinyl benzene 17 dough moulding compound (DMC) 226 Dow Chemical Company 3 1 draft angle in injection mould 332 drawing 169. 171 Du Pont Company 3. 21 7 ductile-brittle transition 196 ductility 167

dynamic fatigue 197-9. 357-61 of composites 222, 361 dynamic properties 1 12-22 use of Boltzmann superposition principle 151, 152

ebonite 165 elastic constraint a t crack tip 189 elastomer 96. 97 electron (unpaired) 12 elongation at break 327 elongational flow 268-72 elongational viscosity 269-72 end groups 9, 13, 30, 42 end-to-end separation of polymer chain 51 6, 68, 69, 73-8 1, 96P energy content 7, 8 entanglements 73, 167, 281 enthalpy of thermal activation 134-6. 164. 172 entropy elasticity 75-8. 97P, 98P epoxy resins 216, 255P, 258, 329, 330 ethylene 9-12. 15 ethylene oxide 32 I ethylene-propylene rubber (EPR) 64, 91, 330 ethylene-vinyl acetate copolymer 321 ethylene-vinyl alcohol copolymer (EVAL) 321 expansion, thermal 234, 256, 260, 327 extension ratio 79, 170 extruder barrel 283, 284 extruder die 2 9 0 4 drawdown 291 -3 extruder screw 284-90 extrusion 264, 283-94 extrusion-blow moulding 3 1 1 Eyring theory 172-7

failure envelope 181 failure of composites 236-44, 361 4 Faraday 3 fatigue see dynamic fatigue or static fatigue fibre composites. design with 350-3 fibre reinforcement 2 12-22 fibres (polymer) 70 fibrils 61, 167, 172, 180 filament winding 224, 225, 343 film blowing 264, 265 films (polymer) 70, 321 flexural modulus test 344 flow elongational 268-72 Newtonian 272, 275, 276

,,

Index

non-Newtonian 270, 2 7 2 4 , 277, 278, 316P rate 276, 278, 315P. 316P shear 272-83 fluorinated rubbers 93 fluorine 36 folding of molecules 67 formaldehyde 30P, 32 forming processes 264-322 for composites 223-7 fracture energy see GIC fracture mechanics, linear elastic (LEFM) 183-95, 207 fracture toughness see KIc free radical 12, 13, 29P freely jointed chain 53 -5 frequency response 120 of Zener model 128-30 fringed micelle 38, 39 functionality 16, 17

gauche conformation 65P Gaussian chain 54-8, 68, 96 GI,, G, 186-9 gel permeation chromatography (GPC) 24, 25 Gibbs free energy 35, 163, 164 glass fibre 217-19, 222, 255P glass-fibre reinforced plastic (GRP) 209, 229, 234, 330 glass-mat reinforced thermoplastics (GMT) 227 glass transition 47-50, 64P, 91, 1 12, 120, 121, 138, 139 Goodyear 2, 3 graft copolymer 16, 29P, 160 graphite 220 Griffith fracture theory 183-7, 207

Hancock 2 hand lay-up 224, 225 hand spray-up 224, 226 heat distortion temperature data 327 helicopter rotor blade 367, 368 helix conformation 36-8 Helmholtz free energy 75, 81, 93P hexene 27P high-impact polystyrene (HIPS) 3 1, 33, 182, 183, 328, 329 Hyatt 3 hydrocarbon 90, 93 hydrogen 35, 63P hydrogen bonding 38, 179, 221 hydrolysis 199 .,

387

hydrostatic pressure, effect on yield 177-9 hysteresis see damping ICI plc 4 ideal gas 76, 97, 98 ideal rubber 73-88, 94-6P impact tests 177, 359 injection blow moulding 3 1 1 injection moulding 26, 266, 294-308 clamping 320, 321 control 302 feed hopper 3 19 gating 299-301, 333 machine 266, 295 mould filling 300, 301, 332 mould shrinkage 296, 318P packing 297, 298, 303 reinforced thermoplastics 226, 332, 334 RIM 307, 308 runner 296 sprue 296 temperatures 305 thermosets 305-8 weld lines 300, 301, 333, 335-7 insert moulding 338 interfacial shear strength 248-50 interfacial shear stress in composites 2 4 4 4 , 248 -50 interlaminar shear strength (ILSS) 363, 364 internal stress 18 1 isochronal curves 103, 104, 1 1 1, 345, 346 isometric curves 345, 346 isoprene 27P isotactic polymer 19, 20, 48 Izod impact strength 327, 3 5 8 4 0 jump frequency 164, 173 kayaks, use of composites in 209, 210 Kelvin model 125, 156P generalized 131 ~ e v l a see r ~ aramid fibre KIC, Kc 187-95, 208 lamellae 18, 39, 44, 64P, 172 laminate analysis 350-3, 361 latent heat of melting 64P Leadermann 136 leaf spring, use of composites 367 limiting oxygen index (LOI) data 327 definition 374 linear density 216

388 Index linear elastic fracture mechanics (LEFM) 183-95, 207 linear low-density polyethylene (LLDPE) 30 linear viscoelasticity 103, 122-37 logarithmic decrement 1 16-1 8, 120-22 Macintosh 2 macromolecules 3 materials selection 323 -3 1 Maxwell model 125, 156P mechanics of fibre reinforcement 227-52 melamine-formaldehyde resin (MF) 329, 330 melt elasticity 31, 281 -3, 31 1 melt flow index (MFI) 26, 279, 280 melting 44-6, 64P melting point 43-6, 48, 63P, 64P metals (comparison with polymers) 1, 2, 8, 16, 26, 48, 101, 108, 115, 167, 209, 217, 229 metering zone of extruder 283, 285-9 mica 222, 223, 227 Michelin 2 modified poly(pheny1ene oxide) (MPPO) 293, 329 modulus 62 complex 1 14-2 1, 129, 151 of composites 229-33, 247 creep 345-8 of plastics 209, 327 of polymer crystals 38 of rubbers 83, 84, 94P, 95P measurement of flexural 344 relaxed and unrelaxed (definition) 109, 110 stress relaxation 109-12, 158P variation with angle 256P Mohr's circle, applied to composites 232, 233, 242, 243 molar mass 22-4 molecular weight see Relative molecular mass monomer 9, 1 1-1 7, 27-9P Mooney equation 88, 96P, 98, 99 motorcycle drive sprocket, nylon 367 multiaxial stress 177

natural rubber (NR) 4, 62, 72, 86-90, 94, 137-9, 330, 331 carbon black reinforced 210, 21 1, 253, 254 necking 95P, 168-71 in polymer melt 271, 272 network elasticity 78-84 neutron scattering 50

nitrile rubber (NBR) 89, 90 nucleation 46, 47 nuclei 42 number average molar mass 23-5 nylon see polyamide orientation (molecular) 58-62, 70, 172, 180, 200, 312, 332 orientation factor 59-61, 66P orientation of fibres in injection mouldings 332, 334 in laminates 343 packaging 70, 321 paraffin 21, 23, 24, 34 Paris equation 198 Parkes, Parkesine 2, 3 pellets, production of 319 phase angle 6 113, 115, 118, 129 phenolic resin 329, 373 photo-oxidation 89, 358 pipe manufacture 291, 292 plane strain fracture 189, 194 plane stress fracture 188 plasticizer 165, 166 platelet reinforcement 212, 213, 222, 223 Plunkett 67 Poisson's ratio of composites 230, 231, 260 of plastics and rubbers 347 polyacrylonitrile (PAN) 90, 100, 219 polyamide 6 (PA6) 3 1, 63P, 137-9, 327, 329 polyamide 1 I (PA 11) 31 polyamide 12 (PA 12) 32 polyamide 6.6 (PA6.6) 4, 14, 15, 45, 63P, 140, 141, 179, 327, 329, 347 polybutadiene (BR) 33 38, 67 polybutene poly(buty1ene erephthalate) (PBT) 327, 329 polycarbonat (PC) 175, 196, 324, 329, 373 polychloroprdne 92 polyester 15, '32, 70 *I polyester resins 215, 255P, 258, 330 poly(ether ether ketone) (PEEK) 330, 374 poly(ether sulphone) (PES) 373 polyethylene (PE) branched (LDPE) 9, 30, 45, 46, 122, 123, 270, 271, 280, 282 chemistry 9, 12, 13, 21, 50 crystallinity 35, 40, 42, 44, 45, 46, 62P, 63P linear (HDPE) 10, 14, 21, 27P, 30, 45, 46, 108, 122, 123, 270 linear low-density (LLDPE) 30

371,

k

Index

properties 21, 122, 123, 169, 171, 179, 326-8 poly(ethy1ene terephthalate) (PET) 15, 32, 45, 62, 63P, 140, 142, 329 polyisobutylene 49, 1 1 1, 112, 119, 120 polyisoprene 72, 89 polymer 2, 9, 34, 44 polymerization 9-18, 33 poly(methy1 methacrylate) (PMMA) 12, 31 37, 121, 141, 165, 181, 200, 280, 281, 323. 329. 358 poly(parapheny1ene terephthalamide) 221 poly(pheny1ene oxide) (PPO) 292, 293, 329, 373 poly@henylene sulphide) (PPS) 327, 374 polypropylene (PP) 7, 12, 30, 37, 45, 48, 49, 63P, 91, 326-8 polystyrene (PS) 12, 3 1, 167. 182, 183, 31 7P, 328 poly(styrene-co-acrylonitrile) (SAN) 100, 182 polysulphone (PSF) 327, 373 polytetrafluoroethylene (PTFE) 36, 42, 67, 255P, 323, 331 . polyurethane (PU) 1414 , 308, 331 poly(viny1 chloride) (PVC) 12, 31, 62, 63P, 1 3 7 4 0 , 145, 198, 326-8, 331, 358 plasticized 33 1 poly(viny1 fluoride) (PVF) 62P poly(viny1idene fluoride) (PVDF) 62P power-law fluid 277, 278 press fitting 341, 342 pressure in capillary flow 279 melting, effect on 64P in polymerization 9 in yielding 177-9 prices of plastics (data) 327 profiles (extruded) 293 propylene 15, 19 pseudoelastic design method 346-50 pseudoplasticity of melts 273 pultrusion 223-5

Rabinowitsch equation 278 radiation crosslinking 10 random copolymer 16, 160 random walk 68 reaction injection moulding (RIM) 226, 307, 308, 326 recovery 101, 149, 167 Regnault 31

389

reinforced reaction injection moulding (RRIM) 224, 226 relative molecular mass (RMM) 9, 20-6, 44, 48, 199, 280 relaxation time 125, 130 relaxations 122 residual stress in composites 260, 261 in mouldings 304, 305 ribs, stiffening and strengthening with 353 Rohm and Haas 3 1 rubbers 2 4 , 72-93, 252-4, 330, 331, 354-7 rubber-toughening 180, 182, 200 rule of mixtures 214, 229, 230

second moment of area of beam 147, 158 polar, of shaft 146 secondary transitions 121, 122, 138, 165 shape factor 355, 356 shear failure in composites 241, 242, 248, 363 shear flow 272-83 shear lag theory 245, 261 -3 shear modulus of composites 232 of rubber 83, 84, 94P, 95P shear thinning 273 sheet moulding compound (SMC) 226. 326 shift factor 134-7 shrinkage 62, 71, 297, 337, 338, 343 side group motion 122 single edge notch (SEN) test 192 sink marks 337, 338 size coatings 2 16 ski bindings 367 snap fitting 341, 343 solubility 100 solvent crazing 182, 358 solvent, polymers in 26 specific gravity data 327 specific stress 2 17, 259 specific volume 41, 46, 48 Spencer-Gilmore equation 298 spherulites 18, 39, 40, 4 2 4 , 47 spring-dashpot models 123-5 springs use of composites 367 use of rubber 354-6 staking, joining method 339, 340, 342 static fatigue 197, 359 Staudinger 3, 30 stereoregularity 19, 20 strain hardening 171

390

Index

strain limits 345, 347 strain rate effects in yielding 171, 174-7 strength of composites 2 3 6 4 4 , 250, 257P stress analysis of polymers 143-54 stress concentration factor 184, 337 stress intensity factor (K) 188, 189, 207 critical (K,,) 187-97 stress relaxation 109-1 2, 127, 128 in a bolt 159 of Zener model 127, 128 stress-strain curve rubbers 85 viscoelastic polymers 153, 167 Zener model 156 stretch-blow moulding 3 12 styrene 17, 31 styrene-butadiene rubber (SBR) 33, 89, 91, 330, 331 sub-critical crack growth 197, 198, 357, 358 sulphur crosslinking of rubbers 3, 4, 88, 138, 139 surface-to-volume ratio of reinforcements 212, 2 13 swell ratio 281 -3, 292, 293 swelling in liquids 88, 90, 96, 100 symmetry in laminates 350 in molecules 18 syndiotactic polymer 19, 20 talc 222, 223 tan 6 115 temperature dependence of compliance 134-6 of fracture behaviour 199 of modulus 83, 1 3 7 4 3 of relaxation times 134, 165 of viscosity 280, 28 1 of yield stress 174 tennis racquet, use of composites 209-1 1 tensile strength of composites 2 3 6 4 4 , 250-2, 257P data for plastics 327 of oriented fibres 62 tex (unit) 216 Tg see Glass transition thermal expansion coefficient 47, 48 of composites 234, 235 data for plastics 327 thermal stability 32 thermoforming 308-1 1, 332 thermoplastic (definition) 5, 10 thermoplastic polyester 32, 70 thermoplastic rubber (TR) 33, 90, 91 thermoset polyester see polyester resins thermosets (definition) 5, 11

three-point bend (3PB) test 192 time-temperature superposition 135-6 torsion of shaft 105, 145 torsion pendulum 116-18, 121 toughening 180, 182, 200, 329 toughness effect of degradation 199 effect of orientation 200, 201 effect of RMM 199, 200 trans conformation 65P transfer moulding 3 13 transient stress, in oscillation 152 true stress 86, 170 twin screw extruder 290

ultrasonic welding 339, 341 urea-formaldehyde resin (UF) 329, 330, 374

vacuum forming 308 van der Waals bonds 60, 99 vented screw in extruder 286-9 vinyl polymer 12, 19, 20, 16, 37 viscoelasticity 101-66 linear 103-37, 146-58P non-linear 104, 106, 111, 346 of polymer liquids 281 -3, 31 1 viscosity, apparent definition 273 determination 273 RMM dependence 280, 282 stress dependence 280-2 temperature dependence 280, 281 voids 42, 215, 343, 357 von Mises yield criterion 177 vulcanization 2, 3, 18, 88 ,.'

1

i

i

wall shear ate 276, 278, 316P wall thick ess of mouldings 337, 338 warping 71, 337, 353 water absorption 32, 141, 144, 345, 347 formation in polymerization 14, 15 weathering 358 weight average molar mass 23-5 weld lines 300, 333, 335-7, 357 welding 3 3 8 4 1 wire coating 294 WLF theory 205, 280, 319 X-ray diffraction 34, 38

r:

Index

Y (geometrical factor in fracture mechanics) 193, 194, 196, 203, 207 yielding 168-80 under multiaxial stress 177-80 of net section in cracked bar 196 yield stress 171, 174 data for plastics 327 lowering by rubber particles 180

pressure dependence 177-9 strain-rate dependence 174-7 temperature dependence 174, 175 yield zone at crack tip 177, 194 Zener model 124-34 Ziegler-Natta catalysts 10, 14, 19, 30

391