Proceedings of the SEM Annual Conference June 1-4, 2009 Albuquerque New Mexico USA ©2009 Society for Experimental Mechanics Inc.
Effect of Cure Temperature on Dynamic Mechanical Behavior of Rigid Polyurethane Foam
Sriram Mohan, Mrinal C Saha School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma 73019
[email protected]
ABSTRACT Viscoelastic properties of rigid polyurethane foams have been evaluated using dynamic mechanical analysis. The foam samples were cured at different temperatures such as 30oC, 60oC, and 80oC, and samples were tested at temperatures between 25°C-150°C and at frequencies between 1-2000 cpm using a torsional rheometer. The dynamic shear tests were carried out in two phases. In the first phase, temperature sweeps were performed at different temperatures with 0.05o angle of strain. In the second phase, logarithmic frequency sweeps were carried out at each temperature with 0.05o angle of strain. Viscoelastic properties were found to be dependent on the cure temperature, and irrespective of the cure temperature, a decrease in dynamic complex modulus was observed with increase in temperature. The frequency data were used to obtain a master curve based on the principle of frequency-temperature superposition at a reference temperature of 100°C. The shift factors were found to follow an Arrhenius relationship and the activation energies of the sample cured at different temperature were compared. INTRODUCTION Polyurethane (PU) foams are found in many applications as structure and non-structure in aerospace, marine, space shuttle, transportation, packaging, electronics, and sport industries. One of great advantages of the PU foam is that the material can be produced with different amount of degree of rigidity (open-cell structure to be flexible or a closed-cell structure to be more rigid) depending on the applications. Rigid PU foams are of interests as core of the sandwich structure in improving the structural performance such as stiffness and strength. In sandwich applications, the foam core provides additional functional requirements in mitigating harsh thermal and mechanical shock. Rigid PU foams are becoming common encapsulation materials in many application including electronics and stockpile of nuclear weapon. A wide range of thermal shock necessitates the characterization of viscoelastic properties of foams. Although the formation of polyurethane foams follows the general reaction of multifunctional isocyanate and polyols coupled with a foaming reaction, the chemical composition of structural cross-links and microstructures within this system depends on the processing temperature. Hatchett et al. [1] have reported that the composition of chemical cross-links, the density, and the modulus all decrease as a function of increasing processing temperature. They have shown through FT-IR studies that such decrease in density and modulus is due to the decomposition of uretoneimine cross-links at higher processing temperature beyond 40oC. Dynamic Mechanical Analysis (DMA) is one of the most widely used techniques in studying the viscoelatic properties of polymeric materials. The temperature dependent analyses can provide information on material transitions such as glass transition, while the frequency dependent analyses can give information on molecular structure of polymers. Another aspect of the frequency dependent material behavior is that one can move polymer materials through transition by varying the frequency. This is another reason why we need to know
both frequencies to which the material will be exposed to in practice and the frequency dependence of the material. Although the temperature range of the DMA allows us to investigate the transition behavior of most polymers, the low frequency range of the DMA may not be sufficient to investigate the material’s behavior at higher frequency in practical use. Many investigators have been manipulating the low frequency data in various ways to extend the polymer behavior at practical frequency range of interest. Superposition technique can be used in constructing a master curve utilizing low frequency data in estimating material’s behavior outside the range of the instrument. One of the most familiar superposition techniques is based on the Williams-Landel-Ferry (WLF) model [2] and has been used by many researchers in predicting material’s behavior at higher frequency [3]. Although a significant amount of literatures is available on the temperature and frequency dependent behavior of polymeric materials, a relatively less research data is available for polymeric foam materials, especially in shear loading. Li-Chung Chang et al. [4], have investigated the dynamic storage modulus of water blown polyurethane foam with and without soy flour as a function of temperature while varying frequency in compression. Using the time-temperature superposition principle (tTSp), they have demonstrated that the foams with biomasses in them have a wider relaxation distribution. Some researchers have studied impact behavior of rigid polyurethane foams with a focus on strain rate and temperature effect. They also have modeled the dynamic crash loading of polyurethane foam and have found that the foam behavior is extremely strain rate and temperature dependent [5]. H. Lu et al. [6] have investigated dynamic behavior of polyurethane pads used for industrial polishing before and after their use. They have tested the pads on a DMA in tension mode from -125°C to 200°C at a frequency of 1 Hz. In another study it has been observed that the recycled polyurethane foams showed a steep decline in the shear modulus at a temperature of 250°C subjected to dynamic torsion [7]. The frequency-temperature superposition (fTSp) concept has been extensively used in studying polymeric materials with and without additives. J.K. Newman [8] and Dickinson and Witt [9] showed that asphalt and polymer-modified asphalts followed the Williams-Landel-Ferry type of superposition model. Researchers have also used tTSp to study the dense polymer films. The tTSp was applied to study the creep behavior of PMMA by obtaining a master curve and predicting the creep behavior over a long period of time [10]. K.Schroter and E. Donth [11] have studied the shear response of different glass formers at glass transition temperature. They have used a rheometric dynamical analyzer to observe the storage and loss modulus as a function of frequency. Other polymers like polystyrene melt [12], polyurea [13], colloidal suspensions [14], polyester resin networks [15], carbon black [16] have been being studied using dynamic mechanical analysis and analyzed using superposition theorem. Recently fTSp was applied in obtaining the complex shear modulus of PU foam by testing foams at a temperature range of 0-20°C and a frequency range of 0.16-16Hz to predict the foam behavior in acoustic range (3000 Hz) [17]. The objective of this paper is to understand the effect of processing temperature on the viscoelastic behavior of rigid PU foams as a function of temperature and frequency. A master curve based on WLF model is to be constructed using the temperature and frequency data to predict the dynamic shear modulus over a wide range of frequencies as well as different cure temperature. Frequency-Temperature Superposition Frequency-temperature superposition (fTSp) is based on the concept, applicable to viscoelastic materials that the property at increased temperature is equivalent to reduced frequency and the property at decreased temperature is equivalent to increased frequency. Then, a master curve can be constructed by translating horizontally and vertically the frequency dependent viscoelastic properties generated at different temperatures with respect to a reference temperature. The concept is schematically shown in Fig. 1. If we assume that the material undergoes a sinusoidal shear strain of amplitude γo at angular frequency then its response is also sinusoidal with the same frequency and amplitude but with phase shift.δ The relationship between the dynamic shear stress and strain ′ " is then given through the complex modulus G*( ) as with where ′ and " are respectively, the storage and loss modulus. At a given temperature, these moduli are only frequency dependent and are directly related to the amplitude of stress, strain, and phase angles as ′ / cos and
"
/
sin
The damping factor can be calculated as
tan
" "
Based on the viscoelastic
data, a master curve is then generated from translating the complex modulus G*(ω) versus frequency curves horizontally and vertically with reference to the reference temperature as follows: , , , .....(1) | where G*(Ti, ω) represents the dynamic rigidity modulus in kPa at temperature Ti in Kelvin, ref ρ represents the density of the material at the reference temperature in g/cc, Tref is the reference temperature in Kelvin, G*(Tref,ω)
rrepresents the dynamic rigidity modulus in kPa at temperature e Tref in Ke elvin, at and bTi |Tref reprresent the h horizontal and d the vertical shift factors at temperature Ti. It is oftten considere ed that the ve ertical shift is negligible d to the mild variation in due n density and d hence bTi |T Tref is assume ed to be 1. The T horizontal shifting factor aTi |Tref d depends on temperature range used d. In the neighborhood of o glass tran nsition tempe erature the frequency f d dependent shift factor can be written as [2]: .....(2)
Fig. 1: Principle of o frequency temperature t s superposition ; Tref represen nts reference temperature;; T1< Tref and T2 > Tref where C1 and C2 are materrial constants depends on the reference w e temperature e. For temperratures below w the glass transition tem mperatures, shift s factor iss related to the activatio on energy and a follows the t Arrheniuss type of r relationship:
where E is th w he activation energy e in J/m mol, R is the gas constantt which is equal to 8.314 JK-1mol-1 and d T is the a absolute temp perature in K [17, 18, 19, 20, 2 21]. E EXPERIMENT TAL M Material The foam ma T aterial consistts of two-partt polyurethan ne foam precu ursors in the form of liquiid having a theoretical d density of 0.24 4 g/cc. The fo oam materialss were purchased from Uttah Foam [22 2] under a trad de name of Aquathane A 4 415. The part--A is a 4-4’-m methylenediph henyl diisocya anate (MDI) and a part-B is polyols p mixed d with water as a blowing a agent and am mines as a curring agent. Th he mix ratio fo or part A to pa art B is 52.4:4 47.6. F Fabrication o foam samp of ple Individual parrts (part-A and part-B) were w measure ed and subje ected to high h shear agita ation using a digitally c controlled reversible mecha anical stirrer operating o at 1800 1 rpm for about 15 min nutes to enhan nce nucleatio on. Any air b bubbles produ uced due to agitation a were e allowed to degas for seve eral minutes. Then 104.8g of part-A and d 95.2g of p part-B were ta aken in a bea aker maintaining a ratio of 52.4:47.6 an nd mixed veryy slowly using g the same mechanical m s stirrer but at a very low spe eed (200 rpm m) for about 1 minute. Extra a care is take en during low speed mixing g to avoid a air bubbles to trap du any uring mixing. The entire contents c of th he beaker we ere then transsferred to a preheated p
rrectangular siilicone mould d maintained at cure temp perature (30°C, 60°C, 80°°C) in an ove en and was allowed a to c cure for 12 ho ours. The den nsity of the cu ured sample was w measure ed. Several th hin slices of 5mm 5 were cut from the c cured polyure ethane foam block using a band saw and a then the samples in the t form of disk d of 30mm diameter w were cut usin ng a circular drill cutter. The samples were w then sa anded down using a 120 grit sand pap per to the r required thickkness of abou ut 2.7mm requ uired for the shear s testing. Any debris associated a w sample prreparation with w removed by using an air was a blower. T Test Equipment Dynamic shea D ar tests are performed p using the advan nced polymer analyzer (AP PA) model AT TD-CSS 1000 0 obtained f from Alpha te echnologies Inc I [23]. The e instrument has two para allel circular plate dies with several grooves to p provide additional grip and d to prevent slippage. The e sample cavvity is about 40mm diame eter and 2.7 mm high. T Typically, o-rin ngs are used to test liquidss and prepreg gs, to preventt the escape of o materials out o of the die. Since we s start out with a solid test material, m all our o tests are being conducted without the o-ring. The sample ch hamber is m maintained se ealed and pre essurized during the test. The instrum ment is capab ble of applying both isothe ermal and n non-isotherma al cure tests, temperature sweeps, stra ain sweeps and a frequencyy sweeps in measuring m visscoelastic p properties of polymer matterials. The bottom b die prrovides oscilla atory motion at controlled d strain and frequency f w while the top die d remains stationary s during the test. The T top die is fixed with a torque t transducer which re ecords the to orque develo oped in the sample. s Both h dies have built-in b thermocouple whicch control the e dies at a given g test temperature within w a varia ation of 0.1°C C. The APA instrument i ha as the following features: maximum to orque 220 d dNm, oscillatiion frequency y: 0.1 – 200 00 cpm (0.00 017 – 33.33 Hz), tempera ature: RT – 200°C, strain n: 0.28%1 1250%. The instrument is i fully contrrolled by a computer c witth the capab bility of prog gramming sevveral test s sequences in any order. Th he raw torque e values were e used to com mpute the dyn namic comple ex shear modulus G* in k kPa from the following f expression
where S* is th w he dynamic complex torqu ue converted from f dNm to N-mm, l refe ers to the thickkness of the sample in m J refers to mm, t the polar moment m of ine ertia of the sa ample in mm4 and θ referss to the strain n angle in rad dians. The tests were con nducted unde er two testing modes as disscussed below w: T Temperature Sweep Testting The APA instrrument was run T r under tem mperature swe eep mode fro om 25°C to 15 50°C with a ra amp rate of 5°C/min 5 to d determine the e viscoelastic properties off materials ass a function of o temperaturre. The glass transition tem mperature o the polyure of ethane foam was measurred by monito oring the dam mping factor as a function of tempera ature. The temperature sweep s was performed at a fixed strain angle of 0.05° and the frrequency of te esting was co onstant at 1 100cpm (1.67 7 Hz). F Frequency Sw weep Testing The frequenccy sweep te T est was conducted with constant a amplitude sine wave oscillation at vario ous frequenccies in the r range of 1 – 2000cpm (0.017 –33.333 3 Hz) on a lo ogarithmic s scale. All freq quency swee ep tests were e performed at a a fixed s strain angle of 0.05° and at a various tem mperatures in the range o 25°C–100°C of C. R RESULTS AN ND DISCUSS SION D Density The density of the foam T m samples was w measurred using g gravimetric m method. Thre ee samples with dimen nsions of 2 25.4mm x 25.4mm x 12.7m mm were pre epared and th he density Fig. 2: Polyure F ethane foam density d as a fu unction v values were determined. d Fig.2 F shows the t variation of o density of cure temperrature
of PU foams as a function o n of cure tem mperature. Th he scatter in density value es are also shown s in the plot. The d density of PU U foam is high hest with valu ues of 0.26 gm/cc g when processed p at 30oC. A sign nificant drop (~22%) ( in d density is obsserved when processing te emperature iss 45oC and further increase in processing temperatu ure results in n slow decrea ase in density y. The densityy of PU foam processed at 80oC resultss in about 27% % decrease in density. T decrease The e in density du ue to increase e in processin ng temperatu ure is attribute es to the incre ease in therm mal activity o the PU foam of m at higher te emperature. Similar S observvations were reported r by Hatchett H et al. [1]. T Temperature Sweep The temperatture dependent variation of T o the comple ex shear m modulus and damping facttor (tan δ) hass been shown n in Fig. 3 Although at 3. a room temp perature the PU foam sho ows the lo owest comple ex shear mod dulus processed at 30oC and the h highest shear modulus processed p att 60oC the modulus m v values decre ease sharply y with increa ase in temp perature in ndicating thatt the thermal stability of these PU foam ms is low a compared to the foam processed att 80oC. The PU as P foam c cured at 80oC shows a go ood retention of shear modulus at h higher temperrature which is i very eviden nt from the tan δ plot. T The slow rate e of transforrmation (glassy to rubberry state) r results in highest glass trransition tem mperature for the PU fo foam processsed at 80oC.. For all the foam samp ples, the g glass transitio on initiated at around 80°C C and continue ed up to 1 140°C. The peak p of the ta an δ curve ind dicates full trransition f from a glasssy phase to a highly visscous phase with a Fig g. 3: Complex shear modulus and tan δ)) as a m maximum losss componentt. The temperrature corresponding fun nction of temp perature to o the peak of the tan δ is s the glass tra ansition temp perature. F the foam cured For c at 30°C C, the glass trransition was found to be 135°C. 1 Where eas for the foa ams cured at 60°C, the g glass transitio on temperaturre was 131°C C and in the case c of the 80 0°C cured foa am the glass transition tem mperature w found to be was b 139°C. Frequency Sweep S All the frequency sweep data were gen A nerated at diffferent f frequencies w within the ran nge of 0.016 – 33.33 Hz. The s sample was excited with h low shearr angle of 0.05°. 0 S Several comp plex shear mo odulus data were w generate ed as a function of frequency fo or a wide range of temperrature e exceeding the e glass trans sition tempera ature of the foam. f V Variations of complex shear modulus as a functio on of lo ogarithmic fre equency for selected temp perature are shown s in n Fig. 4a-b. It I is clear tha at the PU foa ams cured at 80°C s showed the highest she ear modulus over the entire e f frequency ran nge. Table 1 summarizes s t initial and the d final m modulus at each e frequenc cy sweep. It can be seen n that the initial and final modulus s decrease with w increase in test With temperature irrespective i of o the cure temperature. t in ncrease in cu ure temperatu ure the initial and final mo odulus in ncreases.
T Table 1: Summ mary of the frrequency swe eep data Cure e Temp (oC) 30
60
80
est Temp Te (oC) 25 45 60 80 100 25 45 60 80 100 25 45 60 80 100
Go (MPa)
Gf (MPa)
49.7 48.7 42.2 33.5 24.4 52.6 45.4 42.7 37.9 29.0 54.8 43.9 42.1 36.5 23.6
56.4 57.8 50.0 44.4 38.4 61.6 55.0 53.5 48.2 40.4 67.7 55.0 52.2 48.7 39.0
b a Fig. 4: Complex shear s modulus as a functio on of frequenccy for PU foam m cured at diffferent tempe erature (a) 25°C 2 and (b) 100°C
Fig. 5: Co omplex shear mdulus and tan t δ) as a function of temperrature
Fig g. 6: Master curve c obtained d from fTSp for f different cured foams
emperature Superpositio F Frequency-T on Frequency-tem F mperature su uperposition plot (fTSp) was generated from the e frequency data by superposing h horizontal shiifted datasets s gathered at a different te emperatures with respect to a referen nce temperatture. This p provides a me eans to predic ct data over several s decad des of time/fre equency. Fig.. 5 shows the e methodologyy adopted to o build a superposed mas ster curve the very same way w it is expla ained in Fig.1. The master curve was pllotted at a r reference tem mperature (Treff) of 100°C; all a datasets ga athered at tem mperatures le ess than Tref were w shifted to o the right a all the da and atasets gathered at temperatures greatter than Tref were w shifted to the left. The master currve for the d dynamic shea ar modulus is s shown in Fiig. 6 for PU foams f cured at different te emperatures.. The master curve for s shear modulu us constructed d from the da ata generated d at low frequency range (0.0167 – 33.33 Hz) can be b used to p predict the dyynamics comp plex modulus of PU foam for f several de ecades which is not actually possible to o measure u using the insttruments ava ailable. It can be seen tha at at higher frrequency the e effect of cure temperatu ure on the c complex shea ar modulus is very predominant; 80oC cu ured foam showing the hig ghest and 60oC cured foam m showing the lowest she ear modulus. The shift facctors arising from f the laterral superposittion are plotte ed against T-T Tref, and it hat there is a linear relatio on between th he shift factorrs and the tesst temperaturre, which indiccates that iss observed th the superposition was succ cessful. We also a attempted d to compute the energy of o activation re equired to rela ax the PU
a
foam cross links. This was done through an fo n A Arrhenius fit of o the shift fa actors as a fu unction of testt temperature. A linear cu urve fit wass applied to o ln n(aT/Tref) with h respect to 1/T for temperratures below w the reference temperature es as shown in Fig. 7. Forr the calculattion of activation a e energy, the e temperatures less than the e reference te emperature iss c considered, fo or the 60°C and the 80°C cure sampless the tests were e conducted up u to 100°C. It is observed d that the activation energ gy of the fo oam sampless ncrease with h increase in n cure temp perature. The e in a activation ene ergy at 80oC cured foam is about 38.5 5 K KJ/mole which h is about 35% % higher activvation energyy that was obse erved for 30oC cure temperrature. Fig g.7: Arrheniuss plot of shift factor for foam m cured at 30oC. D Dynamic shea ar properties of PU foams cured at diffe erent tempera ature have be een investiga ated under tem mperature a and frequency sweep modes. The gla ass transition temperature e of the mate erial was increased from 135°C to 1 oC as the temperature of cure varied 139 d from 30°C to t 80°C. Subssequent frequ uency sweep testing was performed p to o construct a master curve c using the frequenccy-temperature superposition principle with the reference temperature of o 100°C. The shift factor for all tempe eratures wass used to determine the activation a ene ergy using A Arrhenius rela ationship and was found to o be compara able with othe er published data. d An incre ease of 35% was w found in n the activatio on energy as the cure temperature incre eased from 30°C to 80°C. CONCLUSIONS C
A ACKNOWLEG GMENTS We would like W e to thank Dr.. Henry Pawlo owski of Alph ha Technolgie es, Akron, OH H for his sugg gestions in ru unning our e experiments. R References [1] Hatchett, D. W., Kinya anjui, J. M., Sapochak, L., 2005, “FTIR Analysis of o Chemical Gradients G in Thermally T P Processed Mo olded Polyure ethane Foam””, Polymer De egradation an nd Stability, 87 7(3), pp. 555--561M.L. [2 2] Williams, R.F. R Landel, J.D. J Ferry, J. Amer. Chem m, Soc., 77, 37 701,1955 [3] W.K. Goertzen and M.R R. Kessler, Mater. M Sci. Eng g.: A, 421 (1-2 2), 217,2006. [4 4] Li-Chung Chang, Yu Y Xue, Fu-H Hung Hseih, 2000, “Dyn namic-mecha anical study of water blo own rigid p polyurethane foams with an nd without so oy flour,” Journ rnal of Applied d Polymer Sciiences, Vol. 81, 8 pp.2027-2 2035 [5] Jun Zhan ng, Noboru Kikuchi, K Victorr Li, Albert Ye ee, Guy Nussholtz, 1998,“Constitutive modelling m of polymeric fo foam material subjected to t dynamic crash c loading,” Internation nal Journal off Impact Eng gineering, Vo ol.21,No.5, p pp.369-386. [6] H. Lu, Y. Obeng, O K. A. Richardson, 2003, “Appliccability of dyn namic mechan nical analysis for CMP polyyurethane p studies,” Materials Cha pad aracterization n, Vol.49, No.2 2, pp.177-186 6. [7] K. Bledzkii, J. Zicans, R. R Merjis Meri, D. Kardasz,, 2008, “Some e physical and mechanical properties of o recycled p polyurethane foam blends,” Mechanics of Composite e Materials, Vol.44, No.5, pp.515-522. p [8] J.K. Newm man, 1998, “Dynamic she ear rheologica al properties of o polymer modified m aspha alt binders,” Journal J of E Elastomers an nd Plastics, Vol.30, V No.3, pp.245-263. p
[9] E.J. Dickinson, H. P. Witt, 1974, “The dynamic and shear modulus of paving asphalts as a funciton of frequency,” Transactions of The Society of Rheology, Vol.18, No.4, pp.591-606. [10] A. Balakrishnan, 2005, “Mechanical and Gas Transport behaviour of Poly(Methyl Methacrylate) Dense Films at Elevated Temperatures, Masters Thesis, University of Colorado, Boulder, Colorado, United States of America. [11] K. Schroter, E. Donth, 2002, “Comparison of shear response with other properties at the dynamic glass transition of different glassformers,” Journal of Non-Crystalline Solids, Vol.307-310, pp.270-280. [12] W. Pfandl, G. Link, F. R. Schwarzl, 1984, “Dynamic shear properties of a technical polystyrene melt,” Rheologica Acta, Vol.23, pp.277-290. [13] Yu. S. Urzhumtsev, 1975, “Time-temperature superposition, review,”Mechanics of Composite Materials, Vol.11, No.1, pp.57-72. [14] Young Sil Lee, Norman J. Wagner, 2003, “Dynamic properties of shear thickening colloidal suspensions,” Rheologica Acta, Vol. 42, pp.199-208. [15] Taheri Qazvini, N. Mohammadi, 2005, “Dynamic mechanical analysis of segmental relaxation in unsaturated polyester resin networks: effect of styrene content,” 2005, Polymer, Vol.45, pp.9088-9096. [16] K. C. Guriya, D. K. Tripathy, 1996, “Dynamic viscoelastic properties of carbon black loaded closed-cell microcellular ethylene-propylene-diene rubber vulcanizates: effect of blowing agent, temperature, frequency and strain,” Journal of Applied Polymer Science, Vol. 61, No.5, pp.805-813. [17] N.M. Etchessahar, S. Sahraoui, 2005, “Frequency dependence of elastic properties of acoustic foams,” Journal of Acoustical Society of America,Vol.117, No.3, pp.1114-1121. [18] J.D. Ferry, 1970, Viscoelastic Properties of Polymers, John Wiley and Sons. [19] Kevin. P. Menard, 2008, Dynamic Mechanical Analysis, CRC Press. [20] E. Catsiff, A. V. Tobolsky, 1955, “Stress relaxation of polyisobutylene in the stress relaxation region,” Journal of Colloidal science, Vol.10, pp.375-392 [21] A.V. Tobolsky, E. Carsiff, 1956, “Elastoviscous properties of polyisobutylene (and other amorphous polymers) from stress relaxation studies IX: summary of results,” Journal of Polymer Science, Vol.19,pp.111-121. [22] Material Data Sheet: AT-415, Utah Foam Products, Inc., Salt Lake City,UT 84119. [23] Alpha technologies, Akron, OH, USA
