7ADA114 239 AKRON UNIV OH INST OF POLYMER SCIENCE F/G 1/QTHRESHOLD TEAR STRENGTH OF ELASTOMERS.dU)

APR 82 A N GENT. R H TOBIAS N010114-76-C-l4og

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Technical Report No. 15

THRESHOLD TEAR STRENGTH OF ELASTOMERS

by

A. N. Gent and R. H. Tobias

Institute of Polymer ScienceThe University of Akron

Akron, Ohio 44325

April, 1982

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15. KEY *ORO$ (CdmtN. ON F*eW@. Oid it n@40Y -' AdmUt by WMh anb-)I

CrosslInking, Elastomers, Fracture', Molecular Net .work, Poly-butadiene, Polydimethylsiloxane, Polyisoprene poplyphosphazene,Rubber, Strength, Tearing.

20. AeSTR4ZT (Gan.,w on vee" side H I600 e..nd t~ Iff NO@ 00068fbi)Tear strengths have been measured for a wide variety of

molecular networks under threshold conditions; i.Ie., at hightemperatures, low rates of tearing, and with swo 1 len samples.For all of the polymers examined, the threshold tear strengthwas found to be proportional to the square root of the averagemolecular weight Oc of network strands, in agreement with theorHowever, for the tame Mc and hence for similar values of elasti-

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S20. (continued)

modulus, different polymers showed major differences in thres-hold tear strength. The tear strength of polydimethylsiloxanenetworks was only about one-third as large as that for networksof polybutadiene and cis-polyisoprene and the values obtainedfor polyphospb~azene neworks were only about one-fifth as large,at the same !U. These striking differences are attributed todifferences inh network strand length and extensibility for thesame molecular weight. The threshold tear strengths are shownto be in satisfactory quantitative agreement with theoretically-predicted values on this basis.

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THRESHOLD TEAR STRENGTH OF ELASTOMERS

by

A. N. Gent and R. H. Tobias

Institute of Polymer Science

The University of Akron, Akron, Ohio 44325

Introduction

The tear strength of an elastomeric material has been

shown to reach a lower limit, termed here the threshold

strength, when dissipative processes are minimized (1,2).

The threshold value can be determined experimentally at low

rates of tearing, at high temperatures, and when the

material is highly swollen with a low-viscosity liquid.

Under these near equilibrium conditions, experimental tear

strengths are found to reach minimum values of 40-80 J/m2

(1,2). Lake and Thomas (3) have developed a simple theoret-

ical treatment to predict the magnitude of the threshold

tear strength for elastomers from the length of the molecu-

lar strands comprising a network and the dissociation energy

of the chemical bonds comprising each strand. Expressed as

the energy T0 required to tear through a unit area of

the material, their theoretical result is

T o M KMc1/2 (1)

where Mc is the mean molecular weight of the network

2

strands and K is a constant involving the effective mass,

length and flexibility of a single main-chain bond, the den-

sity of the polymer and the dissociation energy of the

weakest bond. For C-C molecular strands K is predicted to

2 1/2be about 0.3 J/m /(molecular weight unit) . Experimen-

tal values of T0 for randomly crosslinked networks of

polybutadiene were found to be consistent with equation 1

when K was given a somewhat higher value, about 1.0

J/m2/(molecular weight unit) /2 . Apart from this

numerical discrepancy, the threshold strength of polybuta-

diene networks seems to be reasonably well accounted for (2).

Measurements have now been carried out on a number of

elastomers, of widely differing chemical constitution. They

are: cis-polyisoprene (cis-PI), trans-polyisoprene

(trans-PI), polydimethylsiloxane (PDMS) and a fluoroalkoxy-

substituted polyphosphazene (PNF). In each case, networks

were made of a wide range of strand lengths, by a random

crosslinking process, and the threshold tear strengths deter-

mined by careful measurements at high temperatures and low

rates of tearing. Tear strengths were also measured for sam-

ples swollen highly with low-viscosity fluids, for compari-

son with the results obtained with unswollen materials. The

results are given in the following sections of this paper

and compared with the predictions of the Lake-Thomas theory.

3

A brief outline of the Lake-Thomas theory is now given,

in order to draw attention to the main molecular parameters

which appear in the coefficient K relating the threshold

tear strength to Mc in equation 1. It is assumed that a

number N' of network strands pass through a randomly-chosen

fracture plane of unit area and that this number must be

broken for the fracture to propagate. The work required to

break them is TO. Each strand is regarded as of uniform

length, composed of n main-chain atoms, each with an associated

average molecular weight of Mo . Thus, the malecular weight Mc of a strand

is given by nMo , and its dissociation energy by nU where U is

the dissociation energy of a main-chain bond. Hence,

T N' MoU (2)

In order to determine the number N' of strands crossing

the fracture plane Li terms of the number N of network strands

per unit volume, it is assumed that only those strands lying

within a volume element defined by the fracture plane itself

and a perpendicular distance R, equal to the r.m.s. distance

between strand ends in the undeformed state, need to be

considered. Furthermore, only about one-third of these strands

will actually cross the fracture plane. The other two-thirds

will lie generally parallel to the plane and hence escape

fracture. Thus,

N' ( - NR/3) - 1/3 (p A/Mc)R

where P is the density of the polymer and A is Avogadro's number.

A more precise computation of N' yields a numerical factor of

(3/8) 1/2 in place of 1/3 (3).

4

The distance R is given by nr /21 r' where nr is the

number of links in a hypothetical chain of freely-jointed

links chosen to have the same value of R and fully-stretched

length L as the "real" chain of n main-chain bonds, each of

projected length 1 (4). Typically, the length 1r of an

equivalent freely-jointed link is several main-chain bonds and,

correspondingly, the number nr of random links in the equiva-

lent chain is several times smaller than the number n of bonds.

The parameter q - 1 r/1 - n/nr is a measure of chain stiffness.

Estimates of ! can be obtained from measurements of the stress-

optical coefficient (4); they range from 5-10 main-chain

bonds for various elastomer polymers.

On substituting in equation 2 for NJ, T0 is finally

obtained as

- (3/8)1/2 1 Auql2 1 /2 /Mo3 /2.

The coefficient K in equation 1 is thus given by

K- (3/8)1/2 P AUq l/Mo 3 / 2 (3)

Values of K calculated from equation 3 are compared with

experimentally-determined values in the final section of this

paper.

5

2. Experimental details

(a) Materials

(1) Cis-polyisoprene (cis-PI) and trans-polyisoprene

(trans-PI)

Samples of 96% cis-l,4 - polyisoprene (Natsyn 2200,

Goodyear Tire and Rubber Company) and trans 1,4 - polyisoprene

(Trans-Pip, Polysar Inc.) were mixed with various amounts of

dicumyl peroxide (DiCup R, Hercules Chemical Company). They

were then pressed into sheets, about 1.5 mm thick, and cross-

linked by heating them for 2 hr at 1500 C. Similar samples

were also prepared from 100% cis 1,4 - polyisoprene(natural

rubber, SMR-5L) but, as described later, it was not found

possible to determine the threshold tear strength for these

samples with comparable precision when the degree of cross-

linking was low.

(ii) Polybutadienes

Samples of cis 1,4 - polybutadiene (Cis - 4, Phillips

Petroleum Company) and a cis: trans: vinyl copolymer (36:54:10,

Diene 35 NFA, Firestone Tire and Rubber Company) have been

examined previously (2). The results are included here for

comparison with those obtained for other elastomeric materials.

(iii) Polydimethylsiloxane (PDMS)

This polymer was supplied by General Electric Company.

The number-average molecular weight Mn was 430,000 g/g-mole.

6

It was also mixed with various amounts of dicumyl peroxide

and crosslinked by heating for 2 h at 1500 C.

(iv) Fluoroalkoxy-substituted polyphosphazene (PNF)

Polyphosphazene (Phosphonitrilic Fluoroelastomer PNF-200,

Firestone Tire and Rubber Company) was mixed with various

amounts of dicumyl peroxide (DiCup R, Hercules Chemical Com-

pany) and crosslinked by heating for 2 h at 1500C.

(i Measurement of network strand molecular weight Mc

Values of the Mooney-Rivlin elastic coefficients C1

and C2 were determined from stress-strain relations in tension

(4), determined at ambient temperature. The values obtained

are given in Table 1, together with corresponding values of

the small-strain elastic modulus (Young's modulus)

E = 6 (C1 + C2). The extensibility of the PNF materials was

too small to permit an accurate determination of C1 and C2.

Values of E were obtained in these cases from the initial

slopes of the stress-strain relations.

According to the statistical theory of rubberlike elastic-

ity, E is directly related to the average network strand

molecular weight Mc (4)01

E - 3e RT/M c (4)

where is the density of the elastomer, R is the gas constant

and T is absolute temperature. Values of Mc calculated by

means of equation 4 are given in Table 1.

The exact relationship between the chemical structure

of the network and the elastically-effective strand population

is still subject to debate. It has been assumed here that

7

those network strands that govern the small-strain elastic

behavior are also responsible for the tear strength under

threshold conditions, so that values of Mc calculated from

equation 4 are appropriately employed in equation 1. This

assumption ignores the non-Gaussian behavior of rubber materials.

It has been claimed that the C1 term is directly proportional

to the density of network strands and that the non-Gaussian

C2 term arises from constraints on their elastic response

which become less important at high strains. From this point

of view, it would be more appropriate to calculate Mc from C1 ,

C PRT/2MCC1 : R c

for comparison with tear strengths, which are inevitably

associated with high strains. Had the elastic coefficient

C1 been used instead of E for calculating Mc the values

obtained would have been generally about twice as large and

values of the constant K from equation 1 would then have been

about 30% lower than those discussed below. The general form

of the results and the relative rankings of the different

elastomers would not have been altered, however.

(vi) Measurement of threshold tear strength

Rectangular strips, about 60 mm long, 10 m wide and

1.4 mm thick were scored along a central line to a depth of

about 0.7 m, leaving about one-half of the original thick-

ness to be torn through. Tearing was generally found to

take place at an angle of approximately 450 to the sheet

8

thickness, as shown schematically in Figure 1. The tear

energy T was calculated from the measured tear force F by

the relation (1, 2)2

T = 2 x F/t (5)

where X is the linear swelling ratio of the sample and t is

the width of the tear path, measured on the torn strip after2

tearing was completed. The term As in equation 5 accounts

for the reduced number of network strands crossing the tear

plane in a swollen specimen. For unswollen samples, X,= 1

The swelling liquids used were m-xylene or paraffin oil

with PI and PB networks, m-xylene or silicone oil with PDMS

networks, and dibutyl sebacate with PNF networks. Samples

were torn while immersed in a water bath, at temperatures

between 700C and 900C. The water effectively prevented

evaporation of the swelling liquid during tearing.

For natural rubber samples swollen with paraffin oil

it was found necessary to use much higher test temperatures,

in the range 90°C - 1800C, in order to approach a lower

limit in tear strength. For the lightly-crosslinked materials

the tear strength did not reach a lower limit even at temp-

eratures of 150 0 C, Figure 2, and at temperatures much above

this, rapid deterioration occurred. It is thought that

strain-induced crystallization was present, even at high

temperatures and in the swollen state, strengthening these

materials in comparison with wholly-amorphous elastomers.

9

Swollen samples of cis-PI containing about 96% cis units

were found to reach well-defined threshold values at approxi-

mately 1400 C. Presumably the somewhat smaller cis content

reduced the tendency to crystallize on stretching, so that

these materials were completely amorphous during tearing

at 1400C and above.

Good agreement was obtained between values of T determined

with swollen and unswollen samples, provided that sufficiently

high test temperatures were used. Some representative results

for PDMS materials are given in Table 2. Mean values of T

for swollen and unswollen materials have been taken as measures

of the threshold tear strength T0 . They are given in Table 1

for all of the materials examined.

'In

10

3. Experimental results and discussion

Experimentally-determined values of the threshold tear

strength TO are plotted against the elastic modulus E in

Figure 3 and against corresponding values of Mc in Figure 4,

using logarithmic scales for both axes. The results are in

reasonably good agreement with linear relations in all cases,

with slopes of -1/2 when plotted against E and +1/2 when

plotted against Mc. Thus, the general form of the results

is in good agreement with the theory of Lake and Thomas (3).

It is noteworthy that at similar values of E, the thresh-

old tear strength of the hydrocarbon elastomers are all rather

similar in magnitude but they are much larger than for PDMS

and PNF, by a factor of about three. Marked differences are

also shown at similar values of Mc , Figure 4, by a factor of

about three for PDMS and about five for PNF. These differ-

ences are attributed to differences in the molecular constants

which govern the coefficient K relating the threshold tear

strength to Mc. Estimated values of the various molecular

constants are listed in Table 3, together with the values of

K calculated from them by means of equation 3. Experimentally-

determined values of K, taken from the linear relations for

each elastomer shown in Figure 4, are included in Table 3 for

comparison with theoretically-derived results.

The agreement is reasonably good, both in absolute

magnitude and in the relative ranking of the various elastomers.

1i

As there are no fitting constants in the theory, this agree-

ment must be regarded as quite satisfactory and indicates

that the main molecular parameters governing the tear strength

of elastomers under threshold conditions have been taken

into account.

The large effect of the mass per main-chain atom is

particularly noteworthy. It appears to be the principal factor

responsible for the striking differences between the tear

strengths of the hydrocarbon elastomers, PI and PB, and those

of the inorganic elastomers, PDMS and PNF.

Acknowledgements

This work was supported by research grants from the Office of

Naval Research (Contract ONR NOOO14-76-C-0408) and Lord Kinematics

Division of Lord Corporation. The authors are also indebted to

Dr. C. T. R. Pulford of The Goodyear Tire and Rubber Company for

helpful discussions, to Dr. L. J. Kuzma of The Goodyear Tire and

Rubber Company for samples of cis 1,4-polyisoprene (Natsyn 2200),

to Polysar Corporation for samples of trans 1,4-polyisoprene (Trans-

Pip), to Dr. D. F. Lohr of The Firestone Tire and Rubber Company for

samples of phosphonitrilic fluoroelastomer (PNF 200), and to the

General Electric Company for samples of polydimethylsiloxane (SE-30

Silicone elastomer).

'3

References

1. H. K. Mueller and W. G. Knauss, Trans. Soc. Rheol. 15,

217-233 (1971).

2. A. Ahagon and A. N. Gent, J. Polymer Sci. Polymer Phys.

Ed. 13, 1903-1911 (1975).

3. G. J. Lake and A. G. Thomas, Proc. Royal Soc. (London)

A300, 108-119 (1967).

4. L. R. G. Treloar, Physics of Rubber Elasticity, 2nd ed.,

Clarendon Press, Oxford, 1958.

Table 1. Threshold tear strength T0 of molecular networks

with varying Mc

Dicumyl C1 C2 E Mcl03 (a) To 0 jm2peroxide

(%) (kPa) (kPa) (kPa) (g/g-mole)NR

1 95 73 1010 6.7 ca 1502 182 63 1470 4.6 Ea 903 254 83 2020 3.3 62 ± 74 337 68 2430 2.8 52 ± 55 424 122 3275 2.1 43 ± 3

cis-PI1 121 1150 5.8 108± 92 197 78 1650 4.1 63 ± 44 387 48 2610 2.6 51 5 5

trans-PI2 155 132 1720 4.8 60 ± 53 228 91 1915 4.3 48 ± 44 384 63 2680 3.1 38 ± 5

cis-PB (b)0.5 182 174 2135 3.1 81 ± 82.0 455 160 3690 1.8 58 ± 8

PB (b)0.025 44 110 1150 5.8 78 ± 80.05 110 148 1550 4.3 71 ± 90.2 332 148 2880 2.3 45 ± 50.4 570 145 4290 1.6 40 ± 6

PDMS1.0 9 20 175 41.0 78 ± 61.2 14 23 220 32.2 74 ± 31.5 19 29 290 24.8 62 ± 31.75 21 30 305 23.3 56 ± 32.0 26 31 340 20.9 48 ± 32.5 31 31 370 19.2 46 ± 22.75 32 35 400 17.8 44 ± 33.0 36 33 415 17.2 42 ± 34.0 45 25 420 17.0 39 t 2

PNF0.5 225 56 55 ± 81.0 340 37 45 ± 51.5 365 34 41 ± 52.0 (C) 395 32 40 ± 43.2 435 29 38 ± 4

aCalculated from E using equation 4.bTaken from reference 2.

2% Vul-Cup R (Hercules, Inc.), equivalent to 3.2% dicumyl peroxide.

Table 2. Effect of swelling with m-xylene on the threshold tear

strength of POMS networks

Dicunyl To (Unswollen) 's T (Swollen) N 2 T (Swollen)peroxide (J/m2 ) (J/m2) (J/m2 )

1.0 89 + 8 2.22 17.2 + 1.7 85 + 10

1.2 79 + 5 1.94 19.8 + 2.0 75 + 8

1.5 62 + 5 1.91 17.3 + 1.6 63 + 7

1.75 55 + 3 1.88 17.0 + 2.3 60 + 9

2.0 49 + 4 1.82 16.1 + 2.2 53 + 8

2.5 46 + 4 1.80 15.2 + 1.7 49 + 6

2.75 44 + 3 1.78 14.9 + 2.0 47 + 7

3.0 43 + 3 1.77 14.0 + 2.3 44 + 8

4.0 40 + 3 1.75 13.4 + 1.5 41 + 5

16

Table 3. Theoretical and experimental values of the coefficient K

(J/m 2/(molecular weight) 1/2) in equation 1

K

E t r t(calc.UxI19 (a o from

(k3/ 3 ) (J) 1/2 1 (g/g- equa- KElastomer (nm) mole) tion 3) (expt.)

PB 910 5.75 1. 6 3 (b) 0.115 13.5 0.73 1.15

trans-PI 940 5.75 1 .8 4 (b) 0.127 17 0.67 0.78

cis-PI 920 5.75 1 . 3 2 (b) 0.115 17 0.43 1.05

PDMS 970 6.10 2.5 (c) 0.143 37 0.31 0.35

PNF 1,700 3.50 ca S (c) 0.160 185 0.07 0.22

a From R. T. Sanderson, "Chemical Bonds and Bond Energy,"

Academic Press, Inc., New York, 1971

b From reference 4.

c Estimated values.

FIG=R LEDS

. ethd of measuring tear strength.

2. Tear strength T of natural rubber samples crosslinked with various

wfmts of dicumyl peroxide and swllen with paraffin oil.

3. Threshold tear strength T0 of various elastaurs vs Young's modulus

E. 1, PB (6); 2, cis-PI (0) and NR (0); 3, trans-PI (S); 4,

4. Threshold tear strength To of various elastaers vs molecular weight

Mc of netwrk strands calculated from Young's ndulus E by means of

equation 4. Symbols as for Figure 3: 1, PB (a); 2, cis-PI (0) and

NR (0); 3, trans-PI (0); 4, PDMS (D); 5, PNF (U).

18

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0DY 122

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