MM3 POE Solution Sheet Polymer Engineering. Q1. (a) CREEP RECOVERY STRESS RELAXATION

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1 Q1. () CREEP RECOVERY STRESS RELAXATION Mxwell ε σ Kelvin ε σ Sndrd Liner Solid ε σ Mxwell: Kelvin: SLS: Creep poor represenion of reep nd no ime dependen reovery Resonble relxion behviour, bu no residul sress Creep + reovery resonble bu no elsi deformion/reovery No sress relxion Creep, reep reovery & relxion behviour re ll good (quliively) BUT reep ours over nrrow ime rnge [] 1

2 Q1. (b) Lod se (i): Bolzmnn Superposiion Priniple ) J( ) ( i i Therefore (180) 15 x 10 [J(80) + J(0) + J(40)] 15 x 10 [ exp(-) exp(-1.5) exp(-1)].5 x % Lod se (ii): d ( ) For rmped loding ( ) J ( ) d d 0 [5] For 0 0s: d d 4510 d d d For 0 80s: 0 d For Kelvin elemen: 1 J( ) 1 exp E ( 100) exp d exp 40 0 x 10-4 [0 40 exp(-0.5) exp(-)] 1.% [10] () The shif for ( T ) defines he rio beween imes wih equl reep omplines wo differen emperures (log T represens he horizonl shif in ompline versus log urves beween he wo emperures). The shif for is funion of he wo emperures of ineres, wih pproprie equions differing for differen merils. WLF relionship n work well for morphous polymers in he rubbery se, ie. emperure rnge T g o T g o C (where T g is he glss rnsiion emperure). Arrhenius relionship n work well for semi-ryslline polymers nd for morphous polymers in he glssy se (ie. emperures below T g ).

3 Q. () The min sges in ll polymer proessing operions re: (i) (ii) (iii) (iv) (v) (vi) Meling Mixing nd Homogenision Mel Trnspor Above hree sges re ypilly hieved by n rhimedin srew whih involves mixing of sbilisers, pigmens e nd rnsformion of grnule feedsok ino uniform mel. Primry Shping - my be hieved in wo dimensions by flow hrough n exrusion die, or hree dimensions by flow ino spli mould/ pressing ino n open mould. Seondry Shping - my involve drwing of polymer mss s in he produion of fibres, films or blow moulding. Sbilision of Shpe - for hermoplsis his is he ooling (nd hene solidifiion) operion whils for hermoses nd elsomers i is he uring (ross-linking) proess. (vii) Finishing Operions - my inlude mhining, oing, de-flshing. [8] (b) Blow moulding: See figure below: n exruded ube (prison) is enlosed in n open mould. Mould is losed nd he prison is infled o onform o he mould surfe Mould is old relive o he polymer mel, so h he moulding is ooled quikly s i ons he mould surfe. Proess is used o produe hollow omponens suh s boles (PC/PET/PP), r perol nks (LDPE), lrge oniners. [4] [5]

4 () (d) An inrese in emperure llows he moleules o disenngle more redily resuling in reduion in he sher visosiy. A reduion in pressure hs similr effe ie. redued visosiy. Visosiy vs re urves re usully displed verilly bu remin prllel o eh oher s emperure or pressure hnges. Cone nd Ple Rheomeer (k Drg Flow) Polymer pled beween heed fl ple nd one (ngle <5 o ), wih ip of one lowered so h i jus ouhes ple. Cone roed relive o ple nd orque T o minin vrious roionl res is mesured, from whih he visosiy n be luled. Pressure Flow Rheomeer (k Rm Exruder) Polymer is heed in brrel nd fored by pison under pressure hrough pillry (ylindril) die. Pressure drop, P, ross he die is mesured using pressure rnsduer, nd flow re Q is onrolled by movemen of pison. Assuming meril is Newonin (hene ppren visosiy ), he visosiy n hen be luled. [5] Limiions: Cone nd Ple low sher srin res (up o 10s -1 roionl or 100 s -1 osillory) possibly high enough for exrusion bu no for injeion moulding. Pressure Flow Newonin ssumpion resuls in error ompred o rue sher visosiy (up o 15% higher); lso mesured pressure drop dees pressure losses enry o die, requiring muliple mesuremens wih differen die lenghs o deermine enry loss. [4] [4] 4

5 Q. () FLOW RATE: Cviy fill ime 0.5s Cviy volume 100 x 0 x 000 mm x 10 - m Therefore volume flow re Q 1. x 10-5 m /s This pplies o eh hlf of he runner (eiher side of he sprue exi) & eh viy MINIMUM PRESSURE: Runner L 0mm, R mm Try low re power lw onsns & hek sher srin re: C 500, n 0.8 -(n +1)Q w n R 5 -( 0.8+1) (10 ) 09 s -1 - wrong region for flow urve Try high re power lw onsns & hek sher srin re: C 4000, n 0.5 -(n +1)Q w n R 5 -( 0.5+1) ( 10 ) 87 s -1 - orre region for flow urve Clule sher sress wll from power lw: Pressure drop: n w C ( ) P w L P w R.91 MP Cviy L 100mm, T 0 mm, h mm Try low re power lw onsns & hek sher srin re: C 500, n 0.8 -(n+1) Q w n Th 5 -( ) ( 10 ) 50 s -1 - orre region for flow urve Clule sher sress wll from power lw: Pressure drop: n w C ( ) P w L P w 8.90 MP h Minimum pressure o fill viies & runners ol pressure drop 1.81 MP [18] 5

6 CLAMPING FORCE: Pressure sprue exi 5.1 MP ( x minimum pressure from bove) A end of runner 1.71 MP A end of viy 1.81 MP Men pressure (P) Projeed re (m ) Clmping fore (N) Runner (x). x 10 x 8 x x 10 Cviy (x) 17. x 10 x x x 10 5 TOTAL FORCE 107. kn (b) Differenes beween bove nd rel injeion moulding proess: - Above ssumes isoherml behviour. Rel proess is NON-ISOTHERMAL, so h ooling of mel during flow is modelled. This ffes visosiy, hene injeion pressure nd lmping fore (pressure would be higher hn from bove lulion). - In exreme ses polymer my FREEZE (ool o below mel emperure) before mould is filled bove nno pure suh behviour. - Above does no model flow proess urely wihin eh region - eg. for problem in pr (), flow in plque would iniilly be rdil he sprue exi.

7 Q4. () [5] (i) (ii) (iii) High visosiy (eg. PP): deompression srew, ype B bove, o void over-heing high oupu res. Meering seion spli ino wih vening seion in beween. Amorphous PVC: ype C bove, long ompression zone for grdul sofening hrough glss rnsiion emperure. Semi-ryslline Nylon: ype D bove, rpid ompression zone for shrp meling poin of ryslline sruure. [] 7

8 (b) Exruder hrerisi - from formul shee, ignoring lekge flow nd pplying superposiion: This n be wrien s: where: Q Q D Q P P Q C1N C (1) 1 C1 D H sin os 0.5 x π x (0.1) x ( x 10 - ) x sin 17 o x os 17 o 5.91 x 10-5 DH sin C 1l π x 0.1 x ( x 10 - ) x (sin 17 o ) / (1 x 0.) 1.08 x Die hrerisi from formul shee (n1): Th P P Q C () 1 L Therefore C 0.0 x (4 x 10 - ) / (1 x 0.0) x 10-9 Opering pressure: C1N P C C 5.1 MP Flow re from eqn 1: () Opering pressure: P Q C x 10-5 m /s C1N P C C [1] C1N Re-rrnging: C C P.4 x 10-9 From definiion of die hrerisi: 1C L h T ie. h 4.mm 8

9 Q5. () (b) Sress Brile sress Yield sress Temperure Brile frure & plsi flow (ie. yielding) re onsidered s sepre proesses whih hve differen dependene on emperure (solid lines in figure). A priulr emperure, filure ours by whihever proess hs he lower sress. The inerseion of he urves defines he brile-duile rnsiion. Temperure < rnsiion, filure by brile frure Temperure > rnsiion, filure by yielding Effe of inresing srin re is o shif eh urve o higher sress levels (doed lines in figure). Yield sress is ffeed more hn brile sress, hus he brile-duile rnsiion shifs o higher emperures higher srin res. [7 + 5 for digrm] 9

10 (b) PMMA: Expression for riil rk-lengh n be obined by re-rrnging equion for sress inensiy for nd subsiuing riil inensiy for for K I. Thus: 1 K Y mx IC x 10 - m Time for brile frure his lod level n be luled from expression in speil hndou: 1 n o ( n ) C Y 1 1n n 1 / 1 / (7x10 ) (8.15x10 ) ( ) xx x10 upvc: Criil rk-lengh: 1 K Y mx IC 1.90 x 10 4 seonds (5.9 hours) x 10 - m [5] Time for brile frure: 1 n o ( n ) C Y 1 1n n 14 / 1 4/ (15 x10 ) (1.8 x10 ) (4 ) x1x x x 10 seonds (1.9 hours) [4] Shor erm srengh n be obined from sress inensiy for equion: PMMA: upvc: K IC x 10 8 N/m (10 Mp) Y K IC x 10 7 N/m (88.5 Mp) Y [] () Sress, upvc Unsble nek PP Sble nek upvc ypilly forms n unsble nek sie of nek ges hinner unil filure ours. PP ypilly forms sble nek sedy lod suppored s nek rvels long he smple, hen srin hrdening prior o filure. Srin, 10