AD-755 695

POLYMER SOUND SPEEDS AND ELASTICCONSTANTS

Bruce Hartmann, et al

Naval Ordnance LaboratoryWhite Oak, Maryland

22 December 1972

DISTRIBUTED BY:

5 TM

National Technical Information ServiceU. S. DEPARTMENT OF COMMERCE5285 Port Royal Road, Springfield Va. 22151

HOLT' 72-269

Jack Jaznk

el POYMR SOND PEES AN ELSTI

-D D

APPROVED FOR PUBLIC RELEASE;DiSTRIBUTION UNLIMITED

NATIONAL TECHNICALINFOPMATION SERVICE

-A .15

UNCLASSIFI LUSevunty) Ca .aation

DOCUMENT CONTROL DATA. R & )Seu.tury Classii~gti on of title, bndy of absttarat e d , ndexirtt.,nnotelricn niut be entered when rise overall report f esn6itiedj

I ORIGINATING ACTIVITY (Clrporett sUthor) 28. REPORT SECURITY CLASSIFICATION

Naval Ordnance Laboratory UNCLASSIFIEDSilver Spring, Maryland 20910 2b. GROUP

3 REPOAT TITLE

"Polymer Sound Speeds and Elastic Constants"

4. DESCRIPTIVE NOTES (Ty)rp of repolt and inclusive dates)

S. AU Ti.ORIUS (Fi.8t n&me. middle initial, lost name)

Bruce Hartmann & Jacek Jarzynski

G. REPORT DATE 7. TOTAL NO. OF PAGES 7b. NO. Or REFS

22 December 1972 1 1211. CON TRACT OR GRANT NO. 68. ORIGINATOS REPORT NUMNERISI

ORD 333 0C4/092-I/UF 51-543-301 72-269b. PROJECT No.

€. lb. OTHER REPORT NOtS) (Any ash*, niuber tht81 may be asleaijd

thia epoti)ti r

None

10. OISTRIBUTION STATEMENT

Approved for public release; distribution unlimited.

It. SUPPLEMENTARY NOTES S SPONSORING MILITARY ACTIVITY

Naval Ordnance Systems CommandI Washington, D. C.

IS. ABSTRACT

Sound speed measurements were made on 25 polymers atroom temperature and on five of these polymers as a functionof temperature. On 15 of the polymers, both longitudinaland shear sound speeds were measured. Using these soundspeeds and measured densities, the elastic constants of thepolymers were calculated.'

DDF3 (PAGE ,) .UNCIASSIFIEDS/N 0101. 607. 6801 |sectity cilassifiestlon

UNCLASS TRIEDSecurity Classificalon

,E' LINK A LIN '-0 LIN CRO tOLI WT AOLg WT ROLE WT

Sound speedElastic constantsPolymer properties

DD ;":'..1473 (,AC,) UNCLASSIFIED(PAGE' 2) l1(.kCUtity ClaSfication

NOL.TR 72-269

NOLTR 72-269 22 December 1972

POLYMER SOUND SPEEDS AND ELASTIC CONSTANTS

This report describes experimental work done in measuring longitudinaland shear sound speeds in polymers and using these measurements tocalculate the elastic constants of the polymers. These measurementsare needed for acoustic design purposes and for determining elasticconstants for equation of state calculations.

This work was conducted in part under Task NOL 278/ONR and in partunder Task ORD 333 004/092-1/UF 51-543-301. The materials used inthis report were obtained from commercial sources. Their evaluationby the Laboratory in no way implies Navy endorsement of thesematerials.

ROBERT WILLIAMSON IICaptain, USNCommander

ALBERT LI(.HODYBy directi

ib

U- -~ -IMF,

NOLTR 72-269

CONTENTS

Page

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 1

CALCULATION OF ELASTIC CONSTANTS.... . . . . . . . ..

EXPERIMENTAL RESULTS ................... 2

CONCLUSIONS AND RECOMMENDATIONS ."... . . . . . . . . 4

REFERENCES . . . . . . . . . ......... . . . . . . 5

APPENDIX A - MATERIALS USED . . . . . . . . . . . . . . . A-I

ILLUSTRATIONS

Figure Title

1 Elastic Constants vs Temperature for Polvpropvlene

TABLES

Table Title

I Sound Speeds and Density for Rigid Polymers

II Longitudinal Sound Speed for Rubbers

III Temperature Dependence of Sound Speeds and Elastic Constants

IV Elastic Constants of Rigid Polymers

iii

NOLTR 72-269

INTRODUCTION

This report presents the results of sound speed measurements on25 polymers. This data is needed not only for various acousticapplications, where the sound speeds are used directly, but also forequation of state calculations, where sound speed measurements areused to determine elastic constants.

All the measurements reported here were made at a frequency of0.6 MHz using the immersion apparatus previously described.1 Bothlongitudinal and shear sound speed measurements were made on most ofthe polymers. On five of the polymers, measurements were made as afunction of temperature. For the sake of completeness, all of thedata obtained in the immersion apparatus is reported here, includingthe results previously reported in checking out the equipment.1

The principal conclusions of this work are that sound speedmeasurements are relatively easy to make in the immersion apparatus,are of sufficient accuracy for most applications, and are usefulboth in acoustics and equation of state calculations.

CALCULATION OF ELASTIC CONSTANTS

One of the uses of sound speed measurements is to determineelastic constants. This determination reauires both longitudinalsound speed:

vI =/(B + 4G/3)/p (1)

and shear sound speed:

vs W (2)

where B = bulk modulus, G = shear modulus, ana p = density. Theshear modulus can be calculated from Eauation (2), knowing vs and p.The bulk modulus can then be calculated from Equation (1) knowing vl,G, and p.

For an isotropic solid, such as the polymers studied here, thereare only two independent elastic constants. 2" These two can be takento be G and B, but it is sometimes convenient to use other elasticconstants, such as Young's modulus, Y, and Poisson's ratio, a.

1

4

---- r

NOLTR 72-269

These constants can be calculated using the standard relations2

Y ~3G(3= + G/3B

1 Y (4)

The four constants G, B, Y, and 0 are referred to as engineeringconstants. Other constants are also used, and they can be calculatedfrom the engineering constants. For example the Lam6 constants p andX are given by

=G (5)2

;= B- (6)

The elastic constants can also be expressed using the elasticstiffness matrix. In generalized form, Hooke's law is given 2 by

6ai = Z cij Cj (7)

i=l

where the ai are the stress components, the ei are the straincomponents, and the cji are the isothermal elastic stiffness coeffi-cients. For an isotrojic solid

c44 = c55 = c66 = G (8)

cll = c22 = c33 = B + 4G/3 (9)

C12 = C13 = 23 = c2l = c3l = C32 = B - 2G/3 (10)

All other coefficients are zero.

In this report, all the engineering elastic constants will becalculated. If any other elastic constants are desired, they canbe calculated using Equations (5) to (10).

EXPERIMENTAL RESULTS

All of the experimental results will be given in this section.A description of the materials used is given in the appendix.

In Table I are a list of measured sound speeds and densities atroom temperature for various rigid polymers. They are listed inorder of decreasing longitudinal sound speed. About half of theseresults were given in the previous reportI and compared withliterature values. The sound speeds were found to be accurate toabout ±2%. In some cases, no shear wave measurements were possiblebecause the absorption was too high.

2

.. W

NOLTR 72-269

In Table II are a list of measured longitudinal sound speedsat room temperature for various compounded rubbers. The values forbutyl and natural rubber are in reasonable agreement with literaturevalues. 3 In no case was it possible to measure a shear sound speed.

Sound speed measurements as a function of temperature weremade on five polymers. Results for nolymethylmethacrylate,polyethylene, and polypropylene were reported previously. 1 Measure-ments on polyethylene oxide (longitudinal sound speed only) havealso been published elsewhere. 4 In addition, measurements were madeon polyacrylonitrile-butadiene-styrene. The temperature derivativesof the sound speeds are given in the first two columns of Table III.

For those polymers on which both longitudinal and sheer soundspeed measurements are available, the engineering elastic constantsat room temperature have been calculated and are given in Table IV,using data from Table I.

Since the sound speeds are accurate to about ±2% and the elasticconstants depend on the square of the sound speed, the elasticconstants are expected to be accurate to about ±4%. In comparingthese results with other values, two points need to be considered.First, high frequency measurements (such as those reported here)yield higher modulus values than low frequency measurements becauseof relaxation effects. Pastine5 has pointed out that the frequencydependence of B is small but the frequency dependence of G and Y canbe considerable. For example, recent measurements of the lowfrequency elastic constants of high density polyethylene6 gaveB = 4.5 x 1010 dyne/cm2 compared with our value of 4.54 x 1010 dyne/cm2and Y = 0.7 x 1010 dyne/cm2 compared with our value of2.55 x 1010 dyne/cm2 . Schuyer7 has pointed out that the Young'smodulus of polyethylene can vary by a factor of ten depending on thefrequency.

There is another source of difference between high frequencyand low frequency measurements of elastic constants. Low frequencymeasurements are, generally, isothermal while high frequency measure-ments are adiabatic. For rigid polymers at room temperature, theadiabatic bulk modulus is about 10% greater than the isothermalbulk modulus8 while the adiabatic and isothermal shear moduli areidentical. 9 For many purposes, the difference between adiabatic andisothermal elastic constants can be ignored, especially when comparedwith relaxation effects.

Having both sound speeds as functions of temperature, theelastic constants can be calculated as a function of temperature.Illustrative results for polypropylene are shown in Figure 1. Thetemperature dependence of the bulk modulus is an important parameterfor the Gruneisen equation of state, which is widely used forreentry calculations. In particular, the Anderson-Gruneisen

3

NOLTR 72-269

parameter, 6, is given by10

1 dlnB (12)a dT

where a is the cubic coefficient of thermal expansion and T is the

absolute temperature. Values of - d are also given in Table III.

For polymethylmethacrylate, our value of 0.0020 deg -1 is in excellentagreement with the value of 0.0022 deg -I found by Asay, Lamerson, andGuenther.11 For high density polyethylene, our value of 0.0051 deg"is in good agreement with the value of 0.0041 deg -I found by Asay,Urzendowski, and Guenther. 12

There is an additional source of error in these calculations ofelastic constants as a function of temperature. In these calcula-tions, it was assumed that the density of the polymer is constant atits room temperature value. There are two ways in which this causesan error. First, the sound speeds are calculated using the roomtemperature thickness of the specimen. Second, the elastic constantsare calculated using the room temperature density. These effects mayadd another 10% to the error in the temperature dependence of theelastic constants.

CONCLUSIONS AND RECOMMENDATIONS

The immersion apparatus gives a convenient way to determine thesound speeds and elastic constants of polymers. These values are ofsufficient accuracy for the majority of cases in acoustics andequation of state calculations.

Further work should be done to make shear wave measurements onthose polymers for which only longitudinal values are now available.Some improvement in the electronics will be recuired to accomplishthis.

As a useful adjunct to the sound speed measurements, thermalexpansion measurements should be made on all the polymers examined.The expansion coefficient is necessary not only in order to makeaccurate calculations of the elastic constants as a function oftemperature, but also in determining the Anderson-Gruneisenparameter, 6.

Finally, more polymers should be examined in order to build upa sufficient amount of data to make possible the determination ofrelations between polymer structure and bulk properties.

4

NOLTR 72-269

REFERENCES

1. B. Hartmann and J. Jarzynski, NOLTR 72-73, 1972.

2. W. P. Mason, Physical Acoustics and the Properties of Solids,Van Nostrand, New Jersey, 1958.

3. D. G. Ivey, B. A. Mrowca, and E. Guth, J. Appl. Phys. 20, 486(1949).

4. B. Hartmann and J. Jarzynski, NOLTR 72-187, 1972.

5. D. J. Pastine, J. Chem. Phys. 49, 3012 (1968).

6. R. W. Warfield, J. E.. Cuevas, and F. R. Barnet, Rheol. Acta 9,439 (1970).

7. J. Schuyer, J. Polym. Sci. 36, 475 (1959).

8. R. W. Warfield, D. J. Pastine, and M. C. Petree, NOLTR 69-98,1969.

9. G. Bradfield, Use in Industry of Elasticity Measurements inMetals with the Help of Mechanical Vibrations, Her Majesty'sStationery Office, London, 1964, p 146.

10. Y. A. Chang, J. Phys. Chem. Solids 28, 697 (1967).

11. J. R. Asay, D. L. Lamberson, and A. H. Guenther, J. Appl. Phys.40, 1768 (1969).

12. J. R. Asay, S. R. Urzendowski, and A. H. Guenther, Air ForceWeapons Laboratory, Kirtland Air Force Base, New Mexico,AFWL-TR-67-91, 1968.

5

NOLTIR 72-269

W

$4E

CA to r-4 -4 F' C) 4 r4

r-

U) C

m ILI

0.: a.

Or) t - 0 w 1 r ') m sm 0- c') col f- M 00 N N- 0' .z 1 -.- 00 o0 4' w' m' 4 N Ln .-4 0 0 Ch - 01 0- f r

.- 4 *.' N 4 N -N N N N' NrN4 N N N N - 0 N r4 ,d -4

~~z4

0 0 >'0 4 N ~ f - 0 4 1 N >1' F

0 .b4 >

-r4 -4 4-i

0o v1 -4

to 93 w "

'44

V 41 0 -1 w1 j 41

0 0 V4 4 4 #-.- P4 4 4 -4 0 41Q mm r 41 04 -4 %-% 4 0 1.,

+1 4 + 01 + 43+41 04 3 04 c.U0 0 4) V4 "-4 :1

4) Of 4)00 0 0 8 " + -

r4~~~ ~ o-4 V-4# 0 0 0 4) -4 %w-r40 0 4 > -4 V P 4 04 - 14 -1 4 -414 c

41 0 a14 C 0 c 4

CL~P 0- r4 0 Q >U . 0' 0 'U0 0 0 - 0 "41 40- " r 4 -i r V-4..q P 4 -P4 '4V4 .- d P4 0-1 "1d 14 .4

00 0 E 00 0 0 01 0 064 0U 4) 0 04 0 0

040ad4 #404I04 , 44. 034040C 4 a, 04 4 40 0 0 A.*.JA L r - r

NOLTR 72-269

TABLE II. LONGITUDINAL SOUND SPEED FOR RUBBERS

LongitudinalRubber speed*, m/sec

Butyl 1990

Neoprene - 0

Polybutadiene 1570

Natural rubber 1550

Polycarboranes i loxane 1450

Polydimethylsiloxane 1020

*At room temperature and a frequency of 0.6 MHz

4

NOLTR 72-269

TABLE III. TEMPERATURE DEPENDENCE OF SOUNDSPEEDS AND ELASTIC CONSTANTS

dvI dv - dlnB3" _ 3-f " dT

Polymer m/sec deg m/sec deg 1/deg

Polymethylmethacrylate 2.5 2.0 0.0020

Polypropylene 15. 6.7 0.0101

Polyethylene, high deitsity 9.6 6.8 0.0051

Polyethylene oxide 7.2

Polyacrylonitrile-butadiene-styrene 3.5 0.7 0.0039

-4-

- ~mr - - -__ __ __ __ __ __Imp-__ __

NOLTR 72-269

Mr-4 LA 1 -0 cn Hq Lin to '0 a1 tA 00~ 0 01 0 N H- a Ln t- o ' N co 0 N

0 .n M .w c. r, 4 4 4 c

'0 ra 0 CA C N H Cm o t- w w c4 4 v4 4 (c

zf)

>f 0,- *n en m m v M ON c . a .n f . .00 O 0 ' ' 0 co -w w en Nl Nm en r4N w A w A o

0 .ctl

w U) H H H N0 H H H 0 00 9

to)

U) V>1

o 0o

o 0 0 0 0 0 0 0U 0 0 0

04 x s .0> 0 $

0 H0 0

0o 0H 0 o o o o1, 0 H

NOLTR-72-269

OIIVN SANOSSIOdOD (a 41

in) F4z

0 0

0C.

22

IL

0 (1)

0

00

00

0~ Cww

In 0) j 0 I-a~~ ~ ~ wo3Cooisno

NOLTR 72-269

APPENDIX A

MATERIALS

All of the materials used in this work will be described inthis section. Trade names are given for identification purposes only.

Polyepoxide: a reaction product of bisphenol-A withepichlorohydrin crosslinked with metaphenylene diamine. The resinwas made by the Shell Chemical Company, New York, New York, underthe trade name Epon 828.

Polyhexamethylene adipamide (Nylon 6-6): a highly crystallinepolymer made by the Dupont Company, Wilmington, Delaware, under thetrade name Zytel 101.

Polycaprolactam (Nylon 6): a highly crystalline polymer madeby the Allied Chemical Corporation, Morristown, New Jersey, underthe trade name Plaskon 8200.

Polymethylmethacrylate: an amorphous polymer made by theRohm and Haas Company, Philadelphia, Pennsylvania, under the tradename Plexiglas II UVA.

Polypropylene: a highly crystalline polymer made by theAvisun Corporation, Marcus Hook, Pennsylvpnia, under the trade name.Avisun 1010.

Polyethylene, high density: a highly crystalline polymer madeby the Allied Chemical Corporation, Morristown, New Jersey, underthe trade name FF-001.

Polyoxymethylene: a highly crystalline polymer made by theDupont Company, Wilmington, Delaware, under the trade name Delrin.

Polystyrene: an amorphous polymer made by the Dow ChemicalCompany, Midland, Michigan, under the trade name Styron 666.

Polyepoxide + glass spheres II: a syntactic foam made ofhollow glass spheres in an epoxy resin made by the Hysol Corporation,Olean, New York, under the trade name C8-5388 with H2-3551 hardener.

Polyvinylbutyral: an amorphous polymer made by the DupontCompany, Wilmington, Delaware, under the trade name Butacite.

A-1

j , . S l ! Mim--

1W - -- - -

NOLTR 72-269

Polyethylene oxide: a highly crystalline polymer supplied inpowder form by the Union Carbide Corporation, New York, New York,under the trade name WSR-301. The powder was compression molded at1000 atm and 180 0C for one hour and allowed to cool to room temperaturebefore the pressure was released.

Polyepoxide + glass spheres I: a syntactic foam made of hollowglass spheres in an epoxy resin made by the 3M Company,St. Paul, Minnesota, under the trade name Scotchcast XR-5090.

Polyacrylonitrile-butadiene-styrene I: a terpolymer made by theMarbon Chemical Company, Washington, West Virginia, under the tradename Cycolac T-1000.

Polyepoxide + glass spheres III: a syntactic foam made ofhollow glass spheres in an epoxy resin made by the Hysol Corporation,Olean, New York, under the trade name C8-5388 with H-3737 hardener.

Polyacrylonitrile-butadiene-styrene II: a terpolymer made bythe Marbon Chemical Company, Washington, West Virginia, under thetrade name Cycolac H-1000.

Polyethylene, low &nsity: a highly crystalline polymer made bythe Columbian Carbon Company, New York, New York, under the tradename EF403.

Polyvinylidene fluoride: a highly crystalline polymer made bythe Pennsalt Chemicals Corporation, Philadelphia, Pennsylvania, underthe trade name Kynar.

Polyester + water: an unsaturated polyester (from isoph-halicand maleic acids with propyl and dipropyl glycol) and styrene whichhas been emulsified with water, trapping the encapsulated water.The polymer used here was 50% water and was made by theAshland Chemical Company, Columbus, Ohio, under the trade nameWEP661P.

Polytetrafluoroethylene: a highly crystalline polymer made bythe Dupont Company, Wilmington, Delaware, under the trade name Teflon.

The next six materials ara rubbers. Except as noted, thesematerials were all compounded with carbon black and various otherfillers., and were obtained as a commercial product. Only the rubberitself will be described below.

Butyl rubber: a copolymer of isobutylene with a small amountof isoprene added in order to make it vulcanizable.

Neoprene: generic name denoting rubberlike polymers ofchloroprene (2 chloro-l,3 butadiene).

A-2

K

NOLTR 72-269

Polybutadiene: a research sample with a 1,2 polybutadienecontent of 65% kindly supplied by the Firestone Tire andRubber Company, Akron, Ohio.

Natural rubber: a high molecular weight polymer of isolorene, inwhich essentially all the isoprenes have the cis-1,4 confiquration.

Polycarboranesiloxane: a cross-linked siloxane Polymer withmetacarborane incorporated into the backbone after every two siloxanegroups. Supplied by the Olin Company, Stamford, Connecticut, underthe trade name Dexsil 200.

Polydimethylsiloxane: an unfilled silicone rubber.

A-3