The relationship between dynamic mechanical behavior, transverse curvature, and wear of magnetic tapes

WEAR ELSEVIER

we~r202 (t996) 17-29

The relationship between dynamic mechanical behavior, transverse curvature, and wear of magnetic tapes Brian L. Weick, Bharat Bhushan ComputerMicrotribologyand ContaminationLaboratory.Departmentof Mechaniea!Engineering.206 W. 18thAvenue. The OhioSlate Oni~rsily, Columbus.OH43210.IIOZ USA

Received8 August1995;accepted27 November1995

Abstract Dynamic mechanicalmeasurementsof the viscoelasticbehaviorof mag,etic tapes and substratesare presented.Hve types of tapes were analyzed including three polyethyleneterephthalate (PET) tapes with metal particulate,barium fertile particulate,and metal-evaporated coatings.A polyethylenenaphthalate(PEN) tapewitha bariumferriteparticulatecoatingwas alsoanalyzedalongwithan aromaticpolyamide (ARAMID) tape with a metal..evaporatedcoating.Fromthe dynamicmechanicalanalysis(DMA), the storage (or elastic) modulus,E', was obtainedas a functionof temperatureand frequencyalongwith the loss tangent,tan ,~,whichis a measurementof viscousenergydissipation. Frequency-temperaturesuperpositionwas used to predictthe dynamicmechanicalbehaviorof the tapes and substratesover a 10.-12decatde frequencyrange. Results show that the advancedPEN and ARAMIDtapes tend to have higher storage modulithan the PEr tapes, and the PET tapes are mere susceptibleto non.recoverabledeformationat higherfrequenciesdue to their higher loss tangems.Also, storagemodali for the tapesare typicallyhigherthan those forthe substrates,due to the rolethat the particulateor meta|-evaporatedcoatingsplayin increasing the overallmodulusof the tapes.Tapeswith particulatecoatingshavesomewhathighertosstangentsthantheirconstitutivesabstrates,whereas ultra-thin metal-evaporatedcoatings contributelittle to the loss tangentbehaviorof a tape. The DMA data is used in a model to predictthe resistanceof a tape to transversecurvaturewhentensionis applied,Transversecurvatureof a magnetictape is relatedto higheredge wearof a head.To facilitatethe predictionof edge wearand enablethe designof better magnetictapes, a techniqueis presentedwhichcan be usedto predict transversecurvaturefrom the elastic moduli,substrateorthotropyratios, and thicknessesof the subs~tes and coatings. Keyword~: Tdbology;Polymer;Viscoelasticity;Composite:DMA;Modulus

1, Introduction The magnetic storage industry has progressed to a point where a variety of substrates and magnetic coatings are avail. able for magnetic tapes. In the past, these tapes were fabricated using relatively thick polyethyleneterephthalate (PET) films with thicknesses ranging from ! 2-36 ~m. The magnetic coatings ranged in thickness from 2 to 5 ~m and were typically comprised of magnetic particles suspended in an alas. tomeric binder. Ceramic particles used for these coatings included gamma iron oxide, chromium dioxide, and cobaltmodified iron oxide. More recently, iron metal particles (MP) and barium ferritc (BaO. 6Fe20~ or BaFe) particles have been used in the paniculate magnetic coatings. The microscopic acicular MP particles and plate-like BaFe particles and thinner magnetic coatings allow for an increase in the amount of information which can be magnetically stored in a tape area, In other words, the areal density is increased. In addition to the thinner particulate coatings, magnetic tapes

with high coercivity ultra-thin metal.evaporated or ME coat. ings on the order of 200-300 nm have also been produced, The extremely thin and continuous ME coatings with a high magnetic moment density are attractive because of their ability to store magnetically even more information per unit area than an MP or B ~ c tape. When theadvanced MP, B~e, or M E coatings are applied to thinner substrates to obtain higher areal densities (track density x linear density), higher volumetric densities can also be achieved, The properties of these thinner substratcs to some extent control the properties of the tape as a whole. Therefore, extensive characterization studies have been performed for PET, and alternative substrates such as polyethylene naphthalat¢ (PEN), an aromatic polyamide (ARAMID), a polyamide (Pl), and a polybenzoxazole (PBO) [ 1-4]. The significance of the mechanical, thermal, and hygroscopic characteristics of these substrates was assessed in this research. Such properties are also important for the magnetic tapes, For instance, to achieve high areal

0043-1648196/$15,00Copyright© 1996ElsevierScienceS.A. All dghts reserved

P!1S0043-1648(95)06887.2

18

8.1. Weick, B. Bhashanl Wear 20"2(1996) 17-29

densities, tapes and substrates with high mechanical andenvironmental stability and high surface smoothness are required. Since high track densities correspond with a low track pitch, lateral contraction of the tape and substrate due to thermal, pi ...... minimal during storage on a reel and use in a drive. Furthermore, a substrate for an advanced magnetic tape should have a high elastic modulus, yield strength, and breaking strength to minimize stretching and damage, and these characteristics should not be significantly altered when the magnetic coating is applied. In addition, since high coercivity magnetic films on ME tapes are deposited and/or heat treated at elevated temperatures, a substrate with stable mechanical properties up to a temperature of 100-150 °C or even higher is desirable. Current industrial requirements call for a magnetic tape with a one terabyte per cubic inch volumetric density an~ the following characteristics: a 4 itm thick tape substrate, a magnetic medium with a track density of about 90(30 tracks per inch, and a linear density of about I60 kbits in -t with a 64 head array and 8 bead positions. Because of limitations in fabrication of narrow track heads, data stored on such adevice will be read from only 236 tracks while scanning in a data recovery mode [2]. Therefore, for a 12.7 mm wide tape, ifa 10% track mismatch is tolerable, shrinkage of less than about 5.0 ttm in the transverse direction is desirable provided that the head can be recentered. For this reason, extensive research has been performed to characterize the shrinkage and viscoelastic behavior of PET and alternative substrates [ 1--4]. This research included some measurements of the shrinkage and viscoelastic 'creep' characteristics of actual magnetic tapes. Viscoelasticity refers to the combined elastic and viscous deformation of a substrate when external forces are applied, and shrinkage occurs when residual stresses present in the substrate are relieved at elevated temperatures [ 1]. Since shrinkage is a non-recoverable deformation process, if the substrate of a magnetic storage tape shrinks, the head will not be able to read back information on that tape. Similarly, if a subswate deforms viscoelastically, information stored on the tape could also be lost. Various long-term reliability problems including uneven tape-stack profiles (or hardbands), mechanical print-through, instantaneous speed variations, and tape stagger problems can all be related to the substrate's viscoelastic characteristics [ 1]. To minimize these reliability problems, it is not only important to minimize creep strain, but the rate of increase of total strain needs to be kept to a minimum to prevent stress relaxation in a wound reel. The elastic and viscoelastic behavior of the substrate is also important to determine how the tape responds as it is unwound from the reel and travels over the head. This elastic / viscoelastic recovery and subsequent conformity of the tape with the head occurs in just a few milliseconds and req~ires optimization of the substrate's dynamic properties. The properties are measured using dynamic mechanical analysis (or DMA), and the information acquired from this analysis includes E' which is the storage or elastic modulus, and tan 6 which is a measure of the amount of viscous or non-recov-

erable deformation with respect m the elastic d ffermation. Both E' and tan 6 are measured as a function of temperatme and deformation frequency, and results can be used to predict the dynamic response of tapes over several orde~ of magniI~UlUI~. OUlk, n IIJIg.'4gDIUIIClclltIT*wJtl~Ill[It Vl~, O J I I . . , a U ~ ~ l l

U U g . O ~ll~, ~t il.Ol • ~ •

and alternative subswates [5], but no comparative measurements have been made for the tapes themselves. The dynamic mechanical data for the subslrates were used to determine the frequency-dependent strain on the substrate as it travels over the head [ 5]. However, DMA data can also be used to predict tape-to-bead conformity. A lack of tape-to-head conformity can lead to an increa~ in wear of the head as demonstrated by Hahn [ 6]. Hahn showed that magnetic tapes and substrates with higher bending stiffnesses fail to conform to the head, and therefore contact the head at distinct points leading to exc~s~.v~ we.%-of ~e head surface. Wear of the. subsuate is not a concern because the magnetic coating is in contact with the head [7-9]. Tape stiffness has also been shown to be related to edge wear of a head [9]. Since the tape is a muttitayer composite, it is likely that the individual moduli of the layers interact to cause transverse curvature of the tape which leads to the edge wear phenomenon. The primary objective of this research was to obtain DMA measurements for representative magnetic tapes a~d use these measurements to predict which tapes are more resistant to transverse curvature. Tapes which are more resistance to transverse curvature are less likely to cause edge wear of a head. A technique is presented which can be used to predict transverse curvature from the elastic moduli, substrate orthotropy ratios, and thicknesses of the substrates and coatings. It was also desirable to obtain DMA measurements for the substrates used in these magnetic tapes. These substrates were obtained by dissolving the magnetic coatings using suitable solvents, and DMA experiments were therefore performed for the actual substrates used in the magnetic tape~. A discussion of the DMA measurements is presented which shows how different magnetic coatings and subswates affect the frequency and temperature-dependent modulus of magnetic tapes, and a rule of mixtures approach is used to predict the dynamic modulus of a magnetic coating from tape and substrate moduli.

2. Experimental technique

2. I. Test equipment A Rheometrics RSA-II Dynamic Mechanical Analyzer was used to measure the dynamic mechanical properties of the magnetic tape substrates. The analyzer was used in a tension/compression mode, and 22.5 mm long sections of the tapes and substrates were used. In this mode, rectangular s~mples are fastened vertically between the grips and a sinusoidal so'ain is applied to the specimen. Frequency/ temperature sweep experiments were performed for a 0.1100 tad s- t (0.016-16 Hz) range, and 30 data points were

19

B.L Weic/~B. BhushanlWear202 0996) 17. 29

Tab~ l of,_apesamples

Magneticcoating

Thickness (txm)

Substrate'

Thickness (~,m)

Manufacturer and tape name

MP-PET BaFe-PET

M e ~ paniculate Barium fertilepazticulate

3.0 4.0

Poly(ethyleaeterephtham ) Poly(ethylenetereph~'~~te)

7,5 6.6

Sony HiS MP-120 ToshibaHi8 BaFe-120

ME,-PET BaFe-PEN

Mclal.cvaporatcd Bariumferritepa.,liculale

0.2 2.4

Poly(ethyleneIcn~phtheh.~.} Poly(ethylenenaphthalale)

7.4 4.5

SonyHiSME-IS0 3M DC2120XL

MP.,--ARAMID

Metal-evaporated

0.2

Aromaticpoly(amide}

4.5

Sony NTC-90

• Includingthe thicknessof the back.coatingfor the metal-evaporatedtapes(thicknessesare approximate). taken for each frequency sweep at eleven different temperature levels ranging from - 5 0 to 50 °C. The temperature increment was 10 °C, and the soak dine for each ~mperature level was 10 s. The analyzer was operated in 'autotcnsion' mode with a strain offset of 0.25%. This autotension mode of operation maintained a static force on the samples, and prevented buckling of the thin films by applying the peak dynamic forces (corresponding to a strain of 0.0025) while using the static force as a mean [ 10]. Equations used to calculate the storage modulus, E', and loss tangent, tan & are as follows:

the complex modulus which is in-phase with the applied strain, and the loss (or viscous) modulus, W~'*is , a measure of the component which is out-of-phase with the applied strain. The in-phase stress and strain results in elastically stored energy which is completely recoverable, whereas out-ofphase stress and strain results in the dissipation of energy which is non-recoverable and is lost to the system [ t0]. The loss tangent, tan 8, is simply the ratio of the loss (or viscous) modulus to the storage (or elastic) modulus.

E' =cus ( ~ ]

Table I provides a list of the magnetic tapes examined in this research. The approximate thicknesses of the substrates and coatings are also listed along with the manufacturer and tape name. The Hi8 tapes arc used in helical-scan stereo video recorders of the same name, and three varieties of PET-based tapes have been tested. One PET tape has a metal particulate coating consisting of iron particles in an elastomeric matrix. The Toshiba tape uses barium ferrite particles in an elastomerit matrix, and the Hi8 tape with the metal-evaporated coating is an advanced long-play tape. The 3M DC2120XL is a quarter-inch cartridge (or QIC) digital tape used in PCbased tape drives to back up hard disks. Although the majority of QIC tapes use a PET substrate, the tape tested in this research uses an ultra-thin PEN substrate to increase the storage capacity of the tape to 170 Mbytes. (Typical 13(22120 tapes have a storage capacity of 120Mbytes.) The Sony NTC-90 Digital Micro Tape is used in the Scoopman Digital Microrecorders and consists of a metal-evaporated coating on an advanced ARAMID substrate. Note that the thicknesses of the PEN and AILAMID substrates are only 4.5 Fro, and are therefore used in the more advanced tapes to increase volumetric density. The Scoopman tape (which uses the ARAMID substrate) has a 90 minute storage -.'apacity and is less than half the size of standard micro cassettes used in answering machines. Note that PET and PEN can be manufactured using a relatively inexpensive drawing process whereas ARAMID is manufactured using a relatively expensive casting process. To test the substrates themselves, suitable solvents were used to dissolve the magnetic coatings on some ofth~ sampies. The substrates for the ME tapes were obtained by dipping the tapes in a 10% (col.) HCI solution for one to two

g'=sin 8 ~ ]

(la)

tE*I -- ~/(E')2 + (E") ~"

(lb)

tan (5=-E'

(Ic)

~-~D

(ld)

o'=Fgg~

where E' = storage (or elastic) modulus E~ = viscous (or loss) modulus IE* I = magnitude of the complex modulus e = applied strain cr = measured stress 8 = phase angle shift between stress and strain L = length of the sample D=displacement from the strain transducer K~,= a stress constant equal to ! 00/(w) (t) [ 10 ] w = width of the sample t = thickness of the sample g = gravitational constant (9.81 m s-:) F= measured force on the sample from the load cell. In simple terms, at each temperature level the analyzer operates by applying a strain on the sample in a sinusoidal fashion for each of the 0.1 to 100tad s -t frequencies. The strain is measured by a displacement transducer, and the corresponding sinusoidal load on the sample is measured by a load cell. Since the polymeric tapes are viscoelastic there will be a phase lag between the applied strain and the measured load (or stress) on the specimen. The storage (or elastic) modulus, E', is therefore a measure of the component ef

2.2. Test specirnens

20

R L Weick. 8. Bhushan/ Wear202 [1996) 17-29

minutes until the metal coating flaked off. A scrubbing process was used to obtain the substrates for the MP and Bale particulate tapes. In this process a cotton swab soaked in methyl ethyl ketone was rubbed against the magnetic layer for approximately half an hour or until the coating was removed.

3. Results and discus~on 3.1. D M A measurements

Results from the dynamic mechanical analysis are shown in Fig. 1 and Fig. 2 for MP-PET, Bale-PET, ME-PET, Bale-PEN, and ME-ARAMID. Storage moduli, E', are plotted in Fig. 1, and the loss tangents, tan 8, are plotted in Fig. 2. h addition to the two dimensional representations of E' and tan 8 as functions of temperature and frequency, a threedimensional ~presentation of these parameters is also shown for each material. (The two-dimensional graphs arc actually views of the three-dimensional surface from the appropriate side.) Each three-dimensional surface was generated from the raw data, and the -,n-by-ten element surface is indicative of the temperature levels at which frequency, sweep experiments were performed. In other words, the temperature was increased from - 50 °C to 50 °C in increments of 10 °C, and at each temperature level a frequency sweep was performed in which 30 data points were acquired logarithmically from 0.016 to 16Hz (0.1 to 100 tad). From the raw data in Fig. I and Fig. 2 a technique known as frequency-temperature superposition can be used to predict the storage i'noduli and loss tangents over a wider frequency range at a specific reference temperature [l 1,12]. This superposition is performed using DMA data taken over a relatively narrow frequency range at different temperature levels. For instance, the E' versus frequency curves in Fig. 1 are used as the starting point, and a reference temperature of 20 °C is selected. Curves at temperatures higher than 20 °C are shifted to the left until they fit together smoothly, and curves corresponding with temperatures lower than 20 °C are shifted to the right. The shift direction corresponds with the viscoelastic nature of the polymer composite tapes. Storage moduli measured for a polymer at high frequencies under ambient conditions will be equivalent to those measured at lower frequencies and colder temperatures. This means that there is a correspondence between frequency (or rate of deformation) and temperature, Fig. I indicates this correspondence for the tapes. From the three-dimensional surfaces it can be seen that higher elastic moduli correspond with higher deformation frequencies and lower temperatures, whereas lower elastic moduli correspond with lower deformation frequencies and higher temperatures. This can also be seen from the two-dimensional representations of the data; lower deformation frequencies and higher temperatures always correspond with lower elastic moduli, and vice versa.

Master curves for the tapes obtained from the frequencytemperature superposition analysis arc shown in Fig. 3 and Fig. 4 for the storage modulus and loss tangent, respectively. Storage moduli and loss tangent characteristics for the tapes are compared with those measured for the substrates in Fig. 5 and Fig. 6. A 20 °C reference temperature was used for the frequency--temperature superposition analyses, and the amount by which each temperature-dependent data set was shifted is shown in Table 2. The shift f.~zto~ shown in this table indicate how much etch curve was shifted to enable a smooth fit to be obtained. A negative shift factor indicates that the curves were shifted to the left, and a positive shift factor indicates shifting to the right. Some ,,erfical shiPdng was also necessary to accommodate "~h~inherent temperature dependence of the elastic modulus a.~.dmass per unit volume of the polymer [ i3], but these vertical shift factors never exceeded t1~¢¢ tenths of a decade. As expected from previous research, the storage moduli for the PET tapes are in general lower than those measured for the PEN and ARAMID tapes. Previous rese.arch has shown that the more advanced PEN and ARAMID substrates have higher storage moduli than the PET substrates [5], and the tape data presented in.Fig. I and Fig. 3 are consistent with this trend. However, there arc clear and me~lsurable difference.s between the tape and substrate E' dam as shown in Fig. 5. The only possible exception to this is the MP-PET tape which has a somewhat higher modulus than the BalePEN tap. Tl',is could be due to the relatively thick MP film on the PET substrate which when applied to the substrate could cause amore substantial increase in the modulus of the tape as a whole. Results shown in Fig. 5 appear to substantiate this argument since the increase in modulus for the MP-PET tape versus the MP-PET substrate is more than the increase measured for the Bale-PEN tape and substrate. The presence of the relatively thick MP film on the PET substrate could also explain the discontinuities in the raw modulus data shown in the first set of graphs in Fig. 1. At the lower frequency of 0.016 Hz there is a substantial decrease in modulus along with discontinuities at various temperatures. However, the lower modulus at the 0.016 Hz frequency could also be due to the fact that this is the first frequency for acquiring each set of temperature data, and the DMA apparatus automatically readjusts the tension from the previous frequency sweep. Similar but less discontinuous differences between data at 0.016 Hz and the next highest frequency can be seen in Fig. t for the other PET tapes. Another apparent difference in the master curve data is in the length of the curves. This is especially true for the ARAMID tape when compared to the other tapes, and is merely a manifestation of the frequency-temperature superposition technique. The modulus-frequency-tempemt,~e data for the ME,-ARAMID experiments are simply superimposed or 'fit together' over a wider frequency range. Note that this tendency was observed for both the ME-ARAMID tape and substrate.

B.L Weick, B. Bttushan / Wear 202 (1996) 17-29

21

11

o.ol

- --0~.1 . . . . .

i

~o

g,°

o.ot

1

lo

o,oi

o.t

1

~.

Ten.endure (IC)

(a)

o.1

Ten~iqnum ('C)

MP - PET

Tempiq(¢w ('C)

BaFe - PET

ME - PET

II

lJ

T.'e

tu t41

O.Q1

FreQuency(Hz)

O.t t Fmque~w O.Iz)

t0

"liiilk~-

"J,,, .N •~

Tw~mae

¢C)

(b) B a F e - P E N

.25 •~

0

;~ fC)

l0

ME - ARAMID

Fig. I. Slmage modulus (E') as a function of frequency and temperatu~ for maSnetic tapes.

1o

22

B.L Weiclc 9. ahush~IWear 202 (1996) 17-2~

_o.o,,.,,~:.

~.o.o,].~

o,oi

o.i

1 Frequency 0,1ll

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• -~o

o.oi

o.1 I FmCluO~y (Hz)

o.o!

o.1 l FnKluency (Hz)

-~5

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~

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-so

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(a)

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~~-a-~I: oo!

: "~o.o,l...f-rbr..-rpid..~.,o

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~,

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.so

-~s

Temperllmrll (~C)

MP - PET

BaFe - PET

°"' !"[%. °"°ib~?>-~

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0.~}®: ~°°41,

°o2i' 0.O1

o

.

0.1 t F~llquency(Hz)

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; I i " i ] ,

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....:~:-: :: ;i.-.~:,:-.'-. ~ ,~ o.o,,,,'__.

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(b)

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- PEN

~

Templralu~ll (~:)

0.061

i

,,

,'r~:I !i~~:~

0 . 0 0 ~ . -50 .25 0 26 Templlra~m ('C)

ME - A R A M I D

big.2. Tan 8 as a functionof ticquencyand tcmpcmt.~ formagnetic m p ~

50

so

B.L Weick, B. Bhushan/Wear 202 (1996) 17-29

23

Ref~'wce Tem;~'atum. 20 "C 15

MP- PET T/~:'E

10

SI.SS1RATE

nl

sl 10'; 104 10-3 10.2 10"1 1 10 102 103 104 10s 10s 107 FrequenCy(Hz)

Fig. 3. Storage modulus (E') master curves for five magnedc tapes.

0.12]

~

Refererce TemDers~m - 20 *C

°'°t1 \ , ,%

ii 15 IO

ME -

....

TAPE

1114104 10¢ 10~ ID'I 1 10 ~lOz 10=' 104 10s 101 107 F~q,M,CV(HZ)

1

81FI- PEN

10 -s 104 10"3 10"2 10"~ 1 10 102 10s 104 105 10a 107 Freq.e~;y (Hz) Rg, 4. Tan 8 mastercurvesfor five magnetictapes,

With the exception of Bale-PET, the storage moduli for the tapes are all higher than the moduli measured for the substrates. This is clearly shown in Fig. 5, and is not surprising since the magnetic coatings are comprised of either rigid ceramic or metal particles in an elastomeric film, or a continuous metal film. Since these magnetic films are likely to have a higher modulus than the polymeric substrates, when they are applied to the substrate the overall modulus of the composite magnetic tape is higher than the substrate alone. Only Bale.-PET has a subsuat¢ with a higher modulus than the whole tape. At first this was thought to be due to the use of a Bale coating versus other coatings. However, the BaFe-PEN tape has a higher modulus than its substrate. An alternative explanation could be related to the relative thickness of the BaFe coating and the manner in which it is applied. Recall from Table i that Bale-PET is a Toshiba Hi8 120 rain. video tape used for helical scan recording. Therefore, it is plausible that the plate-like BaFe particles are kept in a relatively unorientexl state during manufacture of the tape [ 14]. In comparison, the Bale-PEN tape is used in a linear tape drive and the Bale particles in it are likely to be oriented in the direction of tape travel. As a result, the oriented Bale particles contribute to an increase in E' for the Bale-PEN tape, whereas the unoriented particles in the BaFe-PET tape do not cause an increase in E'. TherefoR, the elastomeric binder for the Bale coating on the PET substt~tes contributes to a decrease

8QI

ME- AR,t.MID

',O4 104 10.3 10~ 10"1 1 10 ~01 tO~ 104 |0$ 106 10I' F~Kluency~t£

Fig. 5. Storagemodulus (E') .;aster curves for magnetictapescompared

withmastercurvesfortheirsubstrates.

in E' for the tape as a whole. The role of orientedand unoriented fibers in controllingthe modulus of composite materials such as magnetic tapes is a well-documented phenomenon thatallowsengineersand scientiststo 'design' composite materialsto have a certainmodulus [ 14,15]. Another observationwhich can be made from the comparison of tape and modulus data shown in Fig.5 relatesto the shape of the curves.The E' curves for the PET tapesappear to be flatterthan the curves for their substrates,This is believedto be due to the factthatthe tapesam in factmultilayer composites comprised of a magnetic film and a substrafe.Note thatthe magnetic filmalonecan be consideredto be a composite. The upward change in slope for the PET subs~tes was also observed in previousresearch in which subsu'atesobtaineddirectlyfrom polymeric filmmanufactur-

24

B.L W¢ick.B. Bhushan/Wear 20"2(1996) 17-29 0-12]

:l

M~'-Fx'r

0,L .o 0.04

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.

,

,

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0.12.

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ME

-PL~I"

101 104 10"1 10'1 10"1 1 10 10~ 103 104 105 70li 101' FrlKf~rcy {HI) 0.12 ~

OJ9 0.04

•o

B~-o-PEN

8UBSTRATE

0

~ 6.12' J ~

,

ME- A R A M I D

o'. ..................................................

10~1lO4 10''I 10..2 104 t $0 102 10:1 104 105 106 10 ;r Fnlqulncy 04=,t

recoverable deformation. From Fig. 4 it can be seen that the loss tangents for BaFe--PEN and IvIE-.ARAMID tapes show a decreasing trend with increasing frequency. In other words, at higher frequencies the PEN and ARAMID tapes do not dissipate as much non-recoverable energy as the PET tapes. Therefore, the PET tapes are more likely to be deformed and stretched when they experience high frequency transient strains in a tape drive. The characteristic tan 8 curves shown in Fig. 4 for the relatively thin (6.6-7.5 v.m thick) PET tapes have also been observed for thicker (14.4 ~m) PET submates [5]. Loss tangentcurves for the actualsubstratesused in the magnetic tapes are shown in Fig. 6 and are compared with the curves obtained for the tapes. For the three PET tapes,the losstangems are typicallyhigher than for the substrafes,which means thatthe tapes are more susceptibleto non.recoverabiedeformation than the substratesthemselves. However, when compared to the PET tape data,the rateof increase in loss tangent is higher for the PET subswates at higherfrequencies.In otherwords, the frequencydependence of the loss tangent is less for the PET tapes than for the substrates,theonly exceptionbeing ME-PET which has tan 8 valuesforthe substrateand tape which are virtuallyindistinguishable.This could be due to the factthatthe ME coating is extremely thinand the loss tangentdata is thereforedominatedby the PET substrate.A similarobservationwas made for the ME-ARAMID tape, although the substrate has a loss tangent which is slightly higher than that measured for the tape at lower frequencies. Bale-PEN has a tape tan 8 which is also higher than that measured for the substrate itself, but once again this difference is only large at the lower frequencies. It should also be noted that the loss tangent data for the ARAMtD and PEN substrates in Fig. 6 compare favorably with previous independent measurements for the substrates [5]. 3.2. The use of DMA measurements to predict transverse curvature and edge wear ofa head

Fig. 6. Tan/~ master curves for maglmtictapes compared with master curves

fortheirsubstrates. ers were tested independently [5]. The substrate data for the Bale-PEN and ME-ARAMID tapes also agree remarkably well with what was measured previously [5]. Loss tangent master curves shown in Fig. 4 and Fig. 6 depict the relative amount of non-recoverable, viscous deformation experienced by each tape or substrate. Fig. 4 is a comparison of loss tangent curves for the tapes, and Fig. 6 shows the loss tangent curves for each tape compared with their respective substrate. Recall from Section 2 that the loss tangent, tan 8, is the ratio of the loss modulus, £', to the storage modulus, E'. The storage modulus, E', is the elastic component of the modulus which responds in-phase with the applied strain, and ~ is the viscous component which lags the applied strain. Therefore, tan ~ is the phase lag between the two components, and is a relative measurement of non-

The stiffness of a magnetic tape can be directly related to head wear [6,9]. As shown in Fig. 7, stiffer tapes do not conform to the hem and therefore contact the Mad at discrete contact points which can lead to increased wear [6]. Recent studies have also shown that the relative amount of head wear tends to be higher at the edges of the head when compared to the center [9]. This higher relative edge wear has also been shown to be related to tape stiffness, and could correspond with the edges of the tape contacting the head. Furthermore, due to the multilayer 'composite' structure of the tape, it is likely that the tape will show transverse curvature when an axial load is applied. This transverse curvature results in a lack of transverse conformity,as shown in Fig. g. The amount of this curvature depends on the relative thickness of the layers as well as the material properties of each layer. To evaluate the extent of this transverse curvature, classical lamination theory (CLT) can be used to determine s~'ess~strain

B.L Weirk B+Bhushan/WeorZM

(J996JJ3-29

25

T&e 2 ShiftfactMEfiomfrequutEy-cemperatusuyerpositionanalysis lieferencetempemture=20°C) Temperature

L.og(shitifxto~~Hz)

(w M&PET Tape

we-PET substnte

Tape

BtlR-PEN

ME-PET SUbstRIte

Substrate

Tape

Tape

ME-ARAMlD Sub-

Tape

Sdstmte

-50

3.20

3.36

3.85

3.34

2.92

4.05

2.45

3.19

-40

2.83

2.71

3.34

2.89

2.41

3.45

2.35

3.33

5.81 5.15

5.86 5.28

-30

2.32

2.22

2.X9

2.32

I.90

2.71

2.06

2.83

4.36

4.56

-20

1.90

1.64

2.35

1.87

I.48

2.11

1.66

2.44

3.57

3.79

-10

1.41

1.23

1.70

I.49

1.20

I.51

1.27

1.81

2.76

3.02

0

0.88

0.76

1.05

0.81

0.97

1.23

1.88

2.02

IO 20 30

0.44 0.00 -0.35

0.35 0.00 -0.28

0.48 0.00 -0.42

0.00 -0.34

0.30 0.00 -0.35

0.44 0.00 -0.43

0.00 -o.si

0.67 0.00 -0.65

0.96 0.00 -1.11

1.09 0.00 -1.06

40

-0.87

-0.51

-0.91

-0.62

-0.79

-0.94

-1.12

-1.41

-2.08

-1.90

SO

- 1.47

-0.88

-1.56

-0.99

-1.37

-1.41

-2.02

-2.27

-3.00

-2.49

0.99 0.48

0.98

0.54

Fig.9.Cross-xctionalview ofamagnetictapcshwingnomencl&ture.

tape-to-head conformity.

Fig.7.Lackof

Fig.8.LPckoftape-to-beadtransverse ccmforntity.

relationshipsfor each layerandthe compositemagnetictape asawhole [16]. To develop an analytical expression for predicting transverse curvature,the nature of the individuallayers which comprise a magnetic tape must first be examinedmore closely.The substrateor base film is of coursea polymer. Thereforeit does not necessarily have a modulus of elasticity whichis uniform.PET for exampletypicallyhas a different modulusalong its majorand minoropticalaxes, whichare definedas thoseax;tswhichtransmitlightwhenviewedunder crosspolarizersheets[ I] , Themajoraxiscanhavea modulus as muchas I .5 timeshigherthanthe modulusfor the minor axis [ 51. A materialwith suchpropertiesas PETis usually referredtoas anorthotropicmaterial,andtheorthotropyratio, a, is definedas the rnoduh~salongthe major(or stiff) axis withrespectto the modulusalongthe minor (or compliant} axis.PENalso has a tendencyto haveorthotropiccharacteristics, whereasABAMIDtends to have isotropiccharacteristicsforwhichthe modulusis thesameregardlessof material orientation.As alreadydemonstratedin this paper,the magnetic layer wili have different modulus characteristics dei~~din~on whetherit is a metaLevaporated (ME) filmor a particulatecoating (BaFe or MP). The ME film can be consideredas a continuousfilmwithisotropiccharacteristics. Althoughthe particulateMPor BaFecoatingsarethemselves

compositescomprisedof an elastomericbinder with hard metalor ceramicparticles,theycanbe consideredto be macroscopicallyisotropicto simplifythe followinganalysis.But first,the modulusof the magneticfilmsmust be determined from the frequencyand temperaturemodulusdata for the tapesand substratesshownin Fig. 3 and Fig. 5. Fig. 9 showsthe simplenomenclatureused in the ‘Nileof mixtures’approachto determiningthe modulusof the magneticlayerfrom the modulus measured for the substrate and tape as a whole [ 161,Fromthe rule of mixturesapproachit can be shownthat E

=

(I

E,(h)- E,(b) a

(2)

whereE,,s the modulusof the magneticlayernf thicknessa; E,= the modulusof the wholetape of thicknessh; Eb= the modulusof the substrateof thicknessb. To apply this equationusing the DMA data shown in Fig. 5, one must first choose a frequencyand temperature. Ambient temperatureconditions will be assumed, and a 6OkHzfrequencywill be chosen. This is consistent with previous research where tape deformation frequencies approaching60 kHz were shownto occurwhen a magnetic tape encounters and travelsover a head [5]. Table3 shows the E, and Eb values obtained ftom Fig. 5 for a 60 kHz frequency, (Some extrapolationwas used since not ail of the mastercurvesin Rg - .5 exceed 60 kIk) Using Eq. (21, Ea values can be calculatedas shown in Table3. Not surprisingly,thehighestmoduliwerecalculatedfor themetakvaporated tapes, The magneticcoating on the MISARAMID tape was shown to have a modulusof 84.5GPa, and the coatingon the ME-PETtape was shownto have a modulus

B,L W¢ick.R Bhusi'.an/Wear 202(1996)17-29

26

Tabte3 Thicknesses,moduli,andtransversestiffnessvaluesformagneticlapes (modulusvaluesare fora 60 kHzfu~lUencyat 20'~C:Poisson'sratiosassumedto be 0.3)

MP-FEI" BaFe-PET ME-PET BaFc-I~N ME--ARAMID

h (~m)

b {gm)

a (p.m)

Et (GPa)

E), ' (GPa)

E. (GPa)

B,JBo(a= I)

10.5 10.6 7.6 6.9 4.7

7.5 6.6 7.4 4.5 4.5

3.0 4.0 0.2 2.4 0.2

1I.I 8.8 8.4 10.9 t7.0

9.4 10.4 6.8 9.9 14.0

15.4 6.2 67.6 12.8 84.5

0.738 0.781 0.993 0.632 0.988

"Eb, is assumedto be equalto Ebz.thereforethe ortholropy~io. a. equals1.

of 67.6 GPa. This is due m the fact that these coatings are metallic and continuous, and therefore they should have moduli substantially higher when compared to their substrates. In comparison, moduli for the particulate tapes are substantially lower than those for the ME coatings, but typically higher than the moduli for their subsa'ates due to the synergistic effect of the hard particles embedded in a compliant (elastomeric) matrix. BaFe coatings have moduli of 12.8 GPa for BaFe-PEN and only 6.2 GPa for BaFe-PET. The MP coating on the MP-PET tape has a somewhat higher modulus of 15.4 GPa. Note that the substrate and magnetic film moduti summarized in Table 3 are used to determine the transverse curvature stiffness, B,z, which is a measure of the tape's resistance to curvature when an applied load per unit width Nx, is applied to the tape. From classical lamination theory, N~causes axial and transverse strain as well as curvature as defined in the following equation:

Nx= AHex + AIzey + BHK~+ Bt2Ky

(3)

where N~- axial force per unit width; Art and A t : - stiffness terms for the axial and transverse strains, respectively; Btl and BI2-=stiffness terms for the axial and transverse curvatures, respectively; ~xand Ey- strains in thex andydirections; Kxand ~cy-curvatures in the x and y directions. It is not plausible to solve Eq. (3) for K:, and determine explicit numbers for the amount of transverse curvature a tape is subjected to under an axial load. This would require the determination of all the stiffnesses, and a knowledge of the other strains and curvatures. Therefore, the simple approach is to calculate B12 from equations defined by the classical lamination theory for a two-layer composite (i.e. magnetic tape). From Eq. (3) it should be clear that higher Bt2 values correspond with lower curvatures, Ky. Therefore, 812 as calculated using the equation below can be thought of as a measure of the tape's resistance to transverse curvature. Or, stated another way, tapes with higher BI2 valuos will transversely conform to the head, and the edge wear phenomenon observed by Bhushan and Lowry [9] will be minimal. Using the equations presented by Jones [ 16], the transverse curvatule is given as

B

lr,,,,,,Eb,b'

':~ L-~-:-~,~

"oEd'! l-,,~j

where v,, and Ub,2--Poisson's ratios for the coating and substrate, respectively; Eb~and Eb2- elastic moduli for the major and minor axes of the substrate, respectively; E,~-elastic modulus for the magnetic coating; a and b-thicknesses of the magnetic coatings and substrates, respectively; a-- orthotropy ratio for the subswate, (Ebt/Eb2). Since it is desirable to develop a non-dimensionalized measurement of a tape*s resistance to transverse curvature, BI2 will be divided by Be. which is defined as the Bt2 value for the tape when the magnetic film thickness is zero. The quantity B,z/Bo is shown below. B,2=I Be

,'.(--1,~,,2) ~,(~)2 vb,2( 1 - l,2) ebt

(5)

From Eq. (5), as the thickness ratio alb increases, the value of Bt2/Bo decreases. Similarly, Bt2/Bo will also decrease with an increasing modulus ratio EJEb~, or an increasing orthotropy ratio a. Note that even if e = 1, there will still be some curvature which will increase as a/b increases. Also, Be itself is a function of the orthotropy ratio. Therefore, a substrate with a high a will have a low Be value, and will therefore experience some transverse curvature when an axial tension per unit width is applied. Fig. t0 and Fig. ! 1 show the transverse stiffness trends for magnetic tapes in a non-dimensional, graphical form. In Fig. 10, BI:/Bo is shown as a function of the thickness ratio for various values of the modulus ratio. A higher thickness

o,I

0

\

0.1

0.2

\

0.3

\

\

0.4

0.5

0.6

o/b

(4)

Fig. I0.Transversestiffnessofmagnetictapesasa functionofthethickness ratio (Pobson'sratiosareassumedto he equalto 0.3).

B.L W&k B. Bhuhon / Wear 202 (1996) 17-29

a/b

27

magneticlayerin determiningtransversestiffness.Asdeterminedfromthegraphicalrepresentationof the data,thetapes with metal-evaporated coatingsare goingto haveless transversecurvaturethan tapes with particulatecoatings.Thisis due to their BIJBo valueswhich approach1. Afthoughthe MEcoatingshavemoduliwhicharesubstantiallyhigherthan thosedeterminedfortheMP andBaFecoatings,the factthat the ME coatingsare only 0.2 pm meansthat the transverse stiffness characteristicsof the substratewill dominate.In comparison,the particulatecoatingsare an order of magnitudethickerthanthe MEcoatings;thereforeparticulatecoatings will play a more active role in determiningthe 8&, values.In fact, the transverse stiffnessof theparticulatetapes is somewhatlower than that measuredfor the ME tapes, whichmeensthatthe transversecurvature(and edgegrooving type head wear 191) will be higher for the particulate

R6

tapeS.

J3,2/80valuesinTable 4weredeterminedusingortbotropy ratioscalculatedfrom the substrateDMAdata presentedby WeickandBhushan[ 51for themachineandtransversedirections (majorand minoroptical axes for PET). PEThas the highest ortbotropy ratio of I.4 whereas PEN has an LYratio

oo+...

,.

1

1.2

,’

....!.

.

1.A

.

..‘..I...,.

a

/

1.6

in

2

Fig. I I. Transversestiffness of magnehctapes as a functionof substrate orthotropy,a (Poisson’sratiosm assun- to be equalto 0,31.

or modulus ratio will cause the transverse stiffness to decrease.In otherwords,as the tbicknwsand/or modulusof the magneticcoating increasesrelativeto the thicknessor modulusof the substrate,the transversecurvatureof the tape will increase.Notethatthe effectof orthotropyis notconsidered in Fig, 10sincethe orthotropyratio forthe substrate,IY, is assumedto be I. Fig. 11showstheeffect of orthotropyon transversestiffnessfortwomodulusratios.TheEalEbl ratio of IOwas used to generatethe top graphin Fig. 11and is a typicalvaluefor metal-evaporated(ME) tapes;whereasthe modulusratioof I.5 used for the bottom graph is indicative of particulate tapes such as the MP and BaFe tapes. As expected. Fig. I 1shows that as the orthotropy of the substrate increases, the transverse curvature of the tape will increase.

The extent of this curvaturewill be greaterfor particulate tapes than ME tapes since the thicknessratiosare typic&y largerforparticulatetapes.Thicknessratiosfortheparticulate tapesused in this studytypicallyrangefrom 0.4 to 0.6, and a/b ratiosfor the ME tapes are substantiallysmaller,ranging from 0.02 to 0.04. Therefore,from Fig. 11,ME tapes with modulusratios on the order of 10 will have BlzlBovalues approaching1. In comparison,particulatetapes will have lowertransversestiffnessvaluesrangingfromanly0.2to0.6. ExplicitBI,/Bo valuesare shown in Table3 for the magnetictapesexaminedin thisresearch. Inthistable,theorthotropyratio is assumedto be 1 to emphasizethe role of the

which is somewhatreduced,namely 1.24.The ARAMID substrateis essentiallyan isotropicmaterialsince its orthotropy ratio is 1. Therefore, the Blz/BOvalues for MEARAMIDare the samein Table3 and Table4. An increase in orthotropycausesthe Bll/BOv&s to IXrcduccd.Thisis the case for the PETandPENtapes.MP-PET,forexample, has a &/BO valueof 0.738whenorthotropyis not considered.However,whentheorthotropyratioof 1.4 is considered, the B,J& valueforMP-PETdropsto 0.623.Similartrends canbe observedfortheotherPET tapeswhenorthotropyis considered,and the BaFe-PENtapealso shows a reduction in transversestiffnesswhenthe orthotropyof its substrate is considered. Qearly ME-ARAMTD has the highest transverse stiffness with aB,,lB, value of 0.988,whichdoesnotchange

whenorthotropy is considered becauseARAMIDis a relatively isotropic substrate. As a result, ME-ARAMID will

haveminimaltransversecurvature,andit wiflthereforetransverselyconform totheheadresulting inminimaledge~KKWingof thehead,suchasthatobservedby BhushanandLowry 191. Table 4 Transverse stiffiws

of magnetictapes accountingfor orthotqy (modUIus aad thichess values are shownin Table3: Poisson’sratios assumed10be 0.3) aa

BdBo

MP-PET

1.40

0.623

BaFe-PFT

1.40

0.685

ME-PET

I .4O

0.990

Balk-PEN ME-ARAMID

1.24

0.535

1.00

0.988

@Substrate orthotmpy ratio, a calculated from the data shown in (51.

28

8.L. Weick B. Bhushun/WearZM

As shown by t.!~eE’ master curves, PEN and ARAMID tapes tend to have higher storage moduli than the PET tapes, although the MP-PET tape appears to have a somewhat higher modulus than the BaFe-PEN tape due to the relatively thick MP coating. In particular, the MB-ARAMID tape has a substantially higher modulus due to its advanced ARAMID substrate. Overall, the application of a particulate or metalevaporated coating appears to increase the storage modulus, the onfy exception being BaFe-PET where the substrate appears to have a higher modulus. (This was attributed to the nature of the BaPe coating, which is likely to have unoriented particles since the BaFe-PET tape is used in a helical scan recording system.) E?”master curves for the PET tapes also appear to be flatter (i.e. less frequency dependent) than those for their substrates. This is not true for BaFe-PEN and MEARAMID since the storage moduli for their tapes and substrates show similar curvatures. At frequencies above approximately 100 Hz. the PEN and ARAMID tapes appear to be less susceptible to non-recoverable deformations than PET tapes. This is shown by the lower tan 6 curves for PEN and ARA!!ID in the higher frequency ranges. The tan S data also sho +hat the particulate tapes may be more susceptible to non-recoverable deformation than their individual substrates since the tan S data for the tapes are higher. However, the frequency dependence of the tan S curves is less for the particulate tapes than the sub strates. Unlike the particulate tapes, the metal-evaporated tapes appear to have tan S characteristics which are dominated by their substrates. This is due to the fact that the ME coatings are relatively thin (and stiff), and therefore do not contribute negative attributes to the loss tangent behavior of the tape as a whole. (Recall that the loss tangent is a measurement of viscous energy dissipation relative to the elastic storage capacity of amaterial.) In fact, for the ME-AR.%llD material the loss tangent is slightly lower for the tape than the substrate, suggesting that the stiffer metal-evaporated coating does play some role in lowering the loss tangent for the composite tape. Magnetic tapes with particulate coatings such as MP or BaFe were shown to be more susceptible to transverse curvature under applied tension than tapes with metal-evaporated (ME) coatings. Therefore, since transverse curvature can lead to a lack of tape-to-head transverse conformity, heads placed in contact with particulate tapes would be more susceptible to wear from contact with the edges of the magnetic tape. The extent of the transverse curvature was also shown to he related to the orthotropy of the substrate. As a result, tapes utilizingmore orthotropic substrates such as PET or PEN are more likely to show a lack of tape-to-head transverse conformity than tapes which utilize an isotropic substrate such as ARAMID. In fact, transverse curvature for the ME-ARAMID tape was predicted to be minimal due to the combined use of an ultra-thin ME coating and an isotropic ARAMID substrate.

(1996) 17-29

In previous research on tape substrates the emphasis was on determining which substrate is the best for an advanced magnetic tape I2-51. ARAlMIDand PEN were the two substrates chosen due to their enhanced properties. The results for the ME-ARAMID and BaFe-PBN tapes support this choice since their storage moduli tend to be higher, and their tan S curves tend to be lower than those for the PET tapes. This is especially true at frequencies greater than 100 Hz. Deformationofthetapescanoccuratthesehigherfrequencies when they encounter a head or vibrate as they come off a roll [5J. Therefore, the ARAMID and PEN tapes would be less susceptible to damage in advanced tape drives due to their enhanced dynamic mechanical properties.

Acknowlcdgcments This research was sponsored by the National Storage Industry Consortium/Advanced Research Projects Agency (Grant MDA 972-93-l-0009), and we would like to thank Dr. Jim Baton at NSIC for his support. We are also grateful to the National Media Lab at 3M for allowing us to use their Rheometrics (RSA-II) Dynamic Mechanical Analyzer. In particular, we would like to thank Ed Goettert and Dr. John Van Bogart at NML/3M.

References [ I] B. Bhushan, Mechanics nnd Reliubilirjr

of Flexible

Moglteric Media,

Springer, New York, 1992. [2] B.L. Weick and B. Bhushan. Chamcteritition

of magnetic tapes and

substrates, EEE Trans. hfogn.. in press. Weick and B. Bhushan. Shrinkage and viscoetvtic behavior of

[31 B.L.

alternative subsbates for magnetic tapes, l/XE Tram Magfi, 31 2931-2939. [a] B.L. Weick and B. Bhnshan. Viscoelntic and shrinkage behavior of ultra-thin polymeric t?!n~, J. Appt. Polym. Sci., 58 ( 1995) 2381-2398.

(1995)

[Sl B.L. Weick and B, Bhushan.The tibologica! and dynamic behavior of alternative magnetic tape substrates. Weur. 190 ( 1995) 28-49. [6] F.W. Hahn. Wear of recording he& by magnetic tape, inB. Bhushan et at. (eds.t, 7ri&ofuSy and Mechanics 0~Afugnefic Srorqe Sysrems, Vol. I, ASf.E, Park Ridge. fL, 1984. pp. 41-48. [71 S.T.PattonandB.Bhushan,Frictionandwearofmetalparticle.barium ferrite, and ME tapes in rotary bead recorders, ASME J. Tribal., 118 (1996) 21-32. [S] B. Bhushan and J.A. Monahan, Accelerated friction and wear studies of various particulate and thin film magnetic tapes against tape path materials in pure sliding and romry/sliding modes, ‘liibol.

Trans.,38

(1995) 329-341. [9] B. Bhushaa and &A. Lowry. Friction and wear studies ofvarious head materiats and magnetic tapes in a linear mode accelerated test using a new nano-scratch wear meGsufements technique, Wear.f%J(1995) l-15. I101 Owners’ Muau~~lfor rhe Rheumerrics RSA-II Dynamic Mechanical Anobrer. Rheometrics, Piscataway, NJ.

B.L Weick,B. BhushanlWear 202 [1996) 17-29 [ 11] ML. Williams. R.F. Laadel, aad J.D. Feny, J. Amer. Chem. Soc., 77 (1955) 3701-370"/. | 12] J.D. Fen~,Viscoelasticfrope~es of Polymers,Wiley,New York, 3rd edn., 1980. [13]JJ. Aklonis and WJ. MacKnigh[, Introduction to Polymer Viscodaslicity, Wiley, New York, 1983.

29

[14j F. Jorgensen,Tb,e Complete Handbook of Magnetic Recording,Tab Profession~d~ l~fc~e, Pennsylvania,3~Iedn.,1988. [15] K.K. Chawla, Composite Mo~.rials Science and Engineering, S~nger, New York, 1987. [16] R.M. Jones, Mechanics o/Composite Materials, Hemisphere, New York, 1975.