Special Topics in Relaxation in Glass and Polymers. Lecture 7: Viscoelasticity III Dynamic Testing

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1 Spcal Topcs n Rlaxaon n Glass and Polymrs Lcur 7: Vscolascy III Dynamc Tsn Dr. Ulrch Fohrnham Rsarch and Tchnoloy Dvlopmn SCHOTT AG

2 In h follown, rlaxaon xprmns on lass wll dscussd. Dsclamr: As all lcurs n hs cours, h manuscrp may conan rrors dsp s carful prparaon. In nral, no laly s assumd concrnn any scnfc or chncal us of any lcur of hs cours. In parcular, any xprmnal work nsprd y hs nos has o n accordanc wh safy and ohr ruls whch ar no vn hr. Any chncal work such as producon of oods whch may nsprd y hs nos has o n accordanc wh safy and ohr ruls whch apply for manufacur and lar us. Ths ruls ar no vn hr hr. Thy may dffr snfcanly from on locaon o anohr, as hy do, for xampl, n cas of fr-procon lazns. Conac your local nsrucor for furhr nformaon. Dr. Ulrch Fohrnham

3 Dynamc sn va slf-oscllaons (a h nfrquncy) xampl: Flxur pndulum, afr Rör, rvalsd n h 99s y Bark-Zollmann al. Clamp fxn sampl o rack Rack Glass sampl Har Th flxur pndulum monors slf oscllaons n a ndn mod. From h oscllaon prod, Youn s modulus s drmnd. From h loarhmc dcrmn, rlaxaon m s drmnd. Clamp fxn sampl and xnson Mal xnson of sampl Fron vw wh Bflar suspnson o counralanc wh Sd vw Th flar suspnson counralancs h wh a h oom n ordr o prvn ohr rsorn forcs han hos comn from ndn h sampl and s mal xnson. Th mal xnson works as analou amplfr of h dsplacmn snal.

4 Analyss of h flxur pndulum Sarn pon: Bndn (of hn plas) and lonaon ar quvaln: h l d s For hn plas, ndn s quvaln o comprsson of on sd and dlaaon of h ohr sd. So h vscolasc havour of oh ndn and lonaon s drmnd y Youn s modulus and h xnsonal vscosy η. Th xnsonal vscosy dscrs h crp of,.., a lass rod whch s sujc o connuous lonaon. s ds d 3 F 4 d h 3 3 F 4 η d h 3 η lasc dformaon (ndn) Crp (ndn) l For ncomprssl*) Nwonan (η ndpndn from dformaon ra) fluds on can drv η 3η ( shar ) so ha wh on has 3G 9K 3G lasc dformaon (lonaon) Crp (lonaon) h frs n Maxwll s rlaxaon m and h lar masural y h rlaxomr. *) Cours approxmaon. In raly w do no hav K and should no nlc ulk vscolascy. d d F A F A l η η η ( shar ) η G

5 Analyss of h flxur pndulum (connud) 3η ( ) m l f l, lass ( ) l η lass lass mal m m z m l vs cos,lass m m l,, A A m A lass lass l, ml 6η A ml m lasc,lass vs cos,lass ± 3η m Th las quaons hold for small anuaons only. m Th ovrall oscllaon wll hav h sam m dpndnc as l,., lass l, A lasc,lass m lass A l mal mal l, l A z mal mal m A lm A mal m In a frs approach, on may ra h s-up of h flxur pndulum as an oscllan srs of a smpl Maxwllmodl rprsnn h lass, an nd sprn rprsnn h mal, and a load. Of cours, a mor sophscad lass modl (Burr c.) would possl also. If xcd onc, hs sysm wll carry ou dampd oscllaons.

6 Analyss of h flxur pndulum (furhr connud) If on nroducs h loarhmc dcrmn L as h anuaon afr on oscllaon: and h nfrquncy of h sysm wh mal only (no lass): Maxwll s rlaxaon m: η τ G 3η Λ Ln( ( ) m m Λ m m π z ( π ) z m and ( ) m lm A m m... ) Ln( ml 6η m A π m, on s: No: τ s ndpndn from omry and hrfor h sam for h flxur pndulum and s lnar rprsnaon. For, h rsul on would hr would vald for h lnar rprsnaon only. ) Comparson of vscosy masurmns flxur pndulum no rlal for T < annaln pon. Cops from Glaschn. Br. wh frndly prmsson of Dusch Glaschnsch Gsllschaf

7 Furhr xprmns wh h flxur pndulum (No aan ha mor sophscad modls and daa rducons would possl also.) No ha many of hs lasss hav n rplacd wh so-calld N-yps n h manm (no P, no As).

8 Som xrcss:. Consdr 3-pon ndn wh consan load. How s h rlaon of vscosy o h consan vlocy a whch h mddl of h sampl movs downward?. Consdr h smpl rprsnaon of h flxur pndulum. Dos h nfrquncy ncras or dcras f h lass sampl s rmovd and h mal srp s sd alon? 3. Cos() can wrn as a lnar comnaon of xp() and xp(-). How? 4. Consdr aan h flxur pndulum. Th m dpndnc s xp(-/s)*cos(*p*hz*). Calcula h loarhmc dcrmn.

9 Dynamc sn va forcd oscllaons Norh pol Souh pol xampl: Torsonal dvc, afr d Bas and Glard Prmann man Col wh alrnan currn (adjusal frquncy!) Mrror Glass sampl Boom fxur Har An alrnan anular momnum s appld whch s causd y alrnan currn runnn hrouh h col n h prmann manc fld. Th rlaon wn anular momn and currn s known from calraon. Ths anular momnum causs orsonal srss*) n h sampl. Th rsuln orson s rcordd va h cours of a lh am whch s rflcd a h mrror fasnd o h uppr sampl holdr. Th sz of h orsonal anl as wll as s phas shf o h anular momnum s rcordd. From hs phas shf δ, h rlaxaon kncs may drmnd. *) No ha n conras o h flxur pndulum, w hav pur shar hr. Bulk vscolascy dos no xs hr and nd no nlcd hrfor.

10 MITT Ulrch Fohrnham, SCHOTT AG: Rlaxaon Procsss n Glass and Polymrs, Lcur 7 MITT Analyss of h orsonal dvc ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) / / sn ) ( an ) ( G í ) ( lm G of valus hh for d lm G d lm G G G G* d G, or cos, d d ) ( d G ) ( / τ π Γ δ τ Γ τ γ Γ λ λ τ τ υ π σ π γ γ γ γ τ γ τ τ

11 Rsuls y d Bas and Glard 964 Soda-lm-lass wh h composon: 7% SO, 4.5% NaO KO, % CaO MO,.5% rs Cops from Glaschn. Br. wh frndly prmsson of Dusch Glaschnsch Gsllschaf

and ulk vscolascy s ack. Wh ypcal valus for lass,.. 6 GPa and ν.

12 Forcd oscllaons / alrnav o orson: ndn Frs approach: oscllaory 3-pon ndn (prload plus oscllan load) h d l s s 3 F 4 d h 3 Howvr: h prolm of mxn shar and ulk vscolascy s ack. Wh ypcal valus for lass,.. 6 GPa and ν., and on arrvs a aou 8% of h lonaon n du o shar and h rmann % n du o comprsson/dlaaon. 3G 9K

13 Forcd oscllaons / alrnav o orson: ndn (connud) Scond approach: asymmrc 4-pon ndn I ACrS-GOMD-Mn, Grnvll, May 6h-9h, 6 Ida for mplmnaon of shar mod n DMA Incras sampl hh Bsd ndn whch s a compos mod conssn of shar and dlaaon/comprsson (whch wll calld ndrc shar and ndrc dlaaon/comprsson from hr on), hr s an addonal drc shar whch may nlcd for hn sampls u no for hck sampls. Asymmrc 4-pon-ndn cor of sampl: shall sujc o shar Analyss of asymmrc 4-pon-ndn: Sz of ndn par? Sz of drc shar par? Sz of ndnaon du o Hrzan prssn (of sampl holdr n sampl)?

14 Forcd oscllaons / alrnav o orson: ndn (connud) Scond approach: asymmrc 4-pon ndn II ACrS-GOMD-Mn, Grnvll, May 6h-9h, 6 Balanc of shar- and comprsson/dlaaon-conruons w w ndn drc shar wlonaon a F dh 3 6 5Gdh a ( a ) a du o ndnaon ( a ) ( a ) F a ( a ) P h ν ln π ab G 3G 3G 9K 9K w oal shar par comprsson / dlaaon par Opmum omry undr condon (a, >.5c) and for ypcal lass moduls ( 6GPa, ν.) shar par 87.7% Allown also for handln ssus & manufacurn olrancs of sampl holdrs a mm mm c 4mm h 7mm, shar par 86% h a c

Forcd oscllaons / alrnav o orson: ndn (connud) Scond approach: asymmrc 4-pon ndn III ACrS-GOMD-Mn, Grnvll, May 6h-9h, 6 Chck of Analycal Opmzaon y Fn lmn Smulaon Basc Assumpon: lonaon oal lonaon du o

15 Forcd oscllaons / alrnav o orson: ndn (connud) Scond approach: asymmrc 4-pon ndn III ACrS-GOMD-Mn, Grnvll, May 6h-9h, 6 Chck of Analycal Opmzaon y Fn lmn Smulaon Basc Assumpon: lonaon oal lonaon du o shar lonaon du o comprsson/dlaaon /G /K ypcal valus from aov: 6GPa, ν. G 5GPa, K GPa Now: mak F smulaon wh G 5GPa, K GPa lonaon oal and wh G 5GPa, K GPa lonaon du o shar shar par lonaon du o shar / lonaon oal Chck of h omry from aov: mm mm 7mm mm mm 7mm 4mm 4mm 4mm F-analyss of a lass wh 6GPa, ν. G5GPa, K33.33GPa. lonaon µm load 9383N,.. lonaon/load.6575µm/n vrcal dsplacmn 4mm F-analyss of a lass wh 75GPa, ν.5 G5GPa, K. lonaon µm load 444N,.. lonaon/load.8738µm/n vrcal dsplacmn.8738/ > shar par s only 8%

Forcd oscllaons / alrnav o orson: ndn (connud) Scond approach: asymmrc 4-pon ndn IV ACrS-GOMD-Mn, Grnvll, May 6h-9h, 6 Opmum omry accordn o Fn lmn Smulaon 8mm 6mm 4mm 4mm 8mm 6mm 4mm 4mm 6mm

16 Forcd oscllaons / alrnav o orson: ndn (connud) Scond approach: asymmrc 4-pon ndn IV ACrS-GOMD-Mn, Grnvll, May 6h-9h, 6 Opmum omry accordn o Fn lmn Smulaon 8mm 6mm 4mm 4mm 8mm 6mm 4mm 4mm 6mm F-analyss of a lass wh 6GPa, ν. G5GPa, K33.33GPa. lonaon µm load 874.4N,.. lonaon/load.9959µm/n vrcal dsplacmn 6mm F-analyss of a lass wh 75GPa, ν.5 G5GPa, K. lonaon µm load 64.4N,.. lonaon/load.79989µm/n vrcal dsplacmn.79989/ > shar par s 86%. F-analyss of a lass wh 6GPa, ν. G5GPa, K33.33GPa. lonaon µm load 874.4N,.. lonaon/load.9959µm/n man srsss (plan srss smulaon) Almos homonous shar n h mddl.

17 Forcd oscllaons / alrnav o orson: ndn (connud) Scond approach: asymmrc 4-pon ndn IV Masurmn on Borofloa33 ACrS-GOMD-Mn, Grnvll, May 6h-9h, 6 Paramrs: sac load 4N, dynamc load N dynamc lonaon masurd: µm dynamc lonaon calculad: drc shar.7µm ndn.6µm ndnaon.78µm 4.µm Dynamc-Mchancal Analyss on Borofloa33 wh an asymmrc four-pon-ndn load and h frquncs Hz (op curv),.8hz, 3.3Hz, 6Hz (oom curv) Tanns [Loss Anl],35,3,5,,5, Tanns [Loss Anl du o shar] Masurmn on Borofloa33 Hz.87Hz 3.393Hz 6 Hz Tmpraur C Plus f of Γ an( δ ) wh ( ) ( τ ).3347 H/R 5.4 K τ π sn s,5 -, T mpraur [ C]

MITT MITT Ulrch Fohrnham, SCHOTT AG: Rlaxaon Procsss n Glass and Polymrs, Lcur 7 Dynamc mhods / nral prolm: Masurmn of sampl or conac wn sampl and samplholdr?

18 MITT MITT Ulrch Fohrnham, SCHOTT AG: Rlaxaon Procsss n Glass and Polymrs, Lcur 7 Dynamc mhods / nral prolm: Masurmn of sampl or conac wn sampl and samplholdr? Masurmn on sl: f prload and oscllan load xcd cran valus, h valus found for Youn s modulus and h loss anl com ralsc: Br omrcal f of sampl and samplholdr; sampl s hammrd no h rh shap. prload oscllan load

19 Som xrcss:. Consdr forcd oscllaons dynamc sn. Wha s h formula for an(δ) n cas?. Consdr aan forcd oscllaons dynamc sn. Assum ha a snl smpl Maxwllmodl dscrs h shar vscolascy of lass wll. A h mpraur of h xprmn, η Pa s holds. Th shar moduls s 5GPa. Wha s Maxwll s rlaxaon m? Whch valus wll masurd for an(δ) y h d Bas and Glard apparaus f h frquncy s, s, Hz, and, nd, Hz? 3. Consdr <. By h d Bas and Glard apparaus, you hav masurd an(δ) as a funcon of. You mak a plo Lo(an(δ)) vs. Lo(). How can you oan from ha?

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