Journal of Non-Newtonian Fluid Mechanics, 28 (1988) 183-212 183 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

RHEOLOGICAL BEHAVIOR OF RUBBER CARBON BLACK COMPOUNDS IN VARIOUS SHEAR FLOW HISTORIES

SERGIO MONTES, JAMES L. WHITE, NOBUYUKI NAKAJIMA Polymer Engineering Center, The University of Akron, Akron, Ohio 44325 (U.S.A.)

(Received January 11, 1988)

Summary

The rheological properties of rubber carbon black compounds are studied in various shear flow histories. In particular we studied (i) stress relaxation, (ii) transient and steady state shear flow, (iii) stress relaxation after steady flow, (iv) sequential shear flow history, (v) storage effects, (vi) programmed step shear histories. At low carbon black concentrations, the rheological response is similar in character to that of unfilled elastomers. For carbon black concentrations of 20 percent by volume and above, the compounds exhibit yield values which increase with carbon black concentration and decreasing particle size. The rubber carbon black compounds exhibit 'hys- teresis loops' in programmed step shear histories and rheological property growth in storage experiments.

1. Introduction

Rubber-carbon black compounds have long played an important role in industry especially in the manufacture of tires. Investigations of the rheo- logical properties of rubber-carbon black compounds would appear to reach back half a century. In 1933, Dillon and Johnston [1] (of Firestone) published a study of flow of rubber-carbon black compounds in a capillary rheometer and characterized their shear flow viscosity. They suggested that these materials exhibited yield values and followed a Power-law asymptote at high shear rates. Dillon and Johnston also reported flow marker experi- ments. Studies of the flow behavior of elastomers in rotational rheometers

184

q~

~U

r~

J~

r~

r~

~ ~ i ~ ~ ~ ~ ~o ~

r~

185

date to the same period with the development of the Mooney shearing disk viscometer [2]. The first reported study of transient stress development in elastomers in this instrument was by Dillon and Cooper [3] for different types of natural rubber. In 1950, Mullins and Whorlow [4] presented an extensive study on the shear flow behavior of natural rubber-carbon black compounds, noting the distinctive time dependent character relative to the unfilled rubber. They contrasted the behavior with similar phenomena found in vulcanized rubber-carbon black compounds and associated it with the formation of carbon black network structures. The striking hysteretic char- acteristics of carbon black filled vulcanDed rubber are called 'Mullins effects' after this work.

The studies of Dillon et al. [1,3] and Mullins and Whorlow [4] were the forerunners of a second period of research. In the 1960s and early 1970s, Bartenev and his co-workers [5] and Vinogradov et al. [6] (compare Vinogradov and Malkin [7]) carried out extensive investigations of the shear flow behavior of rubber-carbon black compounds, establishing clearly the occurrence of yield values. Extensive studies of extrusion behavior of these materials was given by White and Crowder [8]. Nakajima, Bowerman and Collins [9] described the flow characteristics of rubber compounds in a range of experiments. From 1979, papers by White and his co-workers [10-15] have established the occurrence of yield values of carbon black compounds of thermoplastics such as polystyrene [10,11] and polyethylene [14] and elastomers including butadiene-styrene copolymer [11,15,16] and polyiso- prene [13,15]. Yield values were found in uniaxial extension [10,11] as well as shear flow. Earlier rheological studies are summarized in Table 1. Flow marker studies of the extrusion of carbon black filled thermoplastics [14] and elastomers [15,17,18-20] have been reported. The problem of boundary conditions on rubber compound-steel surfaces has been investigated by Turner and Moore [21] and the present authors [22].

It is our purpose in the present paper to present a critical experimental study of the rheological behavior of rubber-carbon black compounds in shear flow. In previous studies we have largely emphasized steady state behavior of the systems, showing the occurrence of a yield value and modeling the steady state shear viscosity. A key early study of transient effects in these materials was by Mullins and Whorlow [4]. Some transient studies were reported by Lobe and White [10] on carbon black-polystyrene compounds, and by Suetsugu and White [23] on calcium carbonate-poly- styrene compounds. Our ambitions are greater here. Extensive studies of shear transients during the startup of the flow and following flow will be studied. We will also look at step transients, programmed histories and storage effects. These will be contrasted with steady state data.

186

2. Exi~rlmentni

2.1 Materials

Two elastomers were involved in this study. These were a natural rubber (SMR 5), designated NR, and a styrene-butadiene copolymer (Firestone, Duradene 706), designated SBR. Carbon black compounds at 10, 20 and 30 volume percent carbon black were prepared on a two-roU mill. Three different carbon blacks Nl10, N326 and N990 of varying particle size and structure were used. Table 2 summarizes the characteristics of the carbon blacks. An antioxidant, American Cyanamid 2246 for N R and Flectol flakes for SBR, was used at a concentration of 0.5%.

After mixing the samples were compression molded into sheets of 6 mm in thickness and allowed to relax for 24 h at room temperature. After this period they were kept in a freezer in an effort to minimize storage harden- ing.

2.2 Measurements

For low shear rates, a sandwich viscometer was used in the creep mode. This is the same apparatus (Fig. la) used in various earlier studies by the authors as described in earlier studies [12-16].

For intermediate shear rates a rebuilt Monsanto Mooney-viscometer with variable rotation rate and the capability of varying imposed pressures was used with a grooved biconical rotor of 2.4 cm in radius (R). This instrument is shown schematically in Fig. l b and described elsewhere [22]. The design was suggested by an earlier instrument built by Turner [21]. The shear stress was determined by [24]

o12 = 3 M / 4 ~ ' R 3, (1)

where M is the torque. The shear rate was calculated through

V = a / f l , (2)

TABLE 2 Characteristics of the carbon blacks used

Supplier Grade Average particle B.E.T. surface size (/~m) area (m2/g)

Huber N990 0.450 8 Phillips N326 0.027 80 Cabot Nll0 0.020 140

OVeR

187

I

I-

~ I I plunger

- - trans

• • rotor

i i = ~ I !

dtsp|acement gauge

7 weight

cylinder

cav i t y ducer

Fig. la. Rheological instruments used in this study. Sandwich rheomcter.

Fig. lb. Rheolosical instruments used in this study. Mooney viscometer with biconical rotor.

Fig. lc. Rheological instruments used in this study. Capillary rheomcter.

where fl is the rotor rotation rate and 13 is the rotor angle. Two 25 × 25 x 6 mm samples were placed in the top and bottom parts of the rotor and the cavity was closed as in the conventional Mooney viscosity procedure.The system was then pressurized through the injection port at the top of the cavity. A 30 minute period, after pressurization, was allowed in all measure-

188

merits in order to assure thermal and hydrostatic equilibrium. All the measurements were carried out at 100°C and 3.2-6.4 MPa. These condi- tions are satisfactory for preventing slippage in the range of shear rates investigated, as shown in our previous studies [22].

In the high shear rate region, a Monsanto Processability Tester (Fig. lc) was used with a set of three dies of 5, 10 and 20 L / D ratios and a diameter of 1.5 ram. The shear stress was calculated through

A p = Ape + 4(o12)wL/D, (3)

Where Ap is the total pressure drop and Ape is the ends pressure loss. The die wall shear rate was determined from [25]

32Q [ 3n' + 1] (4a) 7. = ~rD3 4n ' '

d In(o12)w n' = (4b)

d In 32Q/~rD 3 "

Transient experiments were carried out with the pressurized multispeed Mooney viscometer. The sandwich viscometer and the capillary rheometer were used only in the steady state shear flow experiments.

3. Results

3.1 Stress relaxation

A shear strain (70) w a s imposed on the material in the shortest time possible using the pressurized Mooney viscometer with a biconical rotor. The torque was monitored as a function of t ime until no appreciable change in the relaxation rate was observed, a period that often was of the order of 24 h. A stress relaxation modulus was calculated from

c(t) =o12(t)lvo. (5) Figures 2a -d present the results for N R and Figs. 3a and b for SBR and their N326 carbon black compounds. The pure elastomers and the 10 percent compounds show continued relaxation at all times whereas the 20 and 30 percent compounds show a stress that does not decay to zero but to a finite value. Values of G(oo) are sumrtmrized in Table 3.

The relaxation rates seem to be independent of strain. The addition of carbon black increases the level of the modulus regardless of the strain value. This is also shown in Fig. 4 where the relaxation modulus at 100 s is plotted as a function of shear strain for three different loading levels. An

189

increase of two orders of magnitude is observed for the highest concentra- tion. Figure 4 also shows that the relaxation modulus decreases with strain amplitude.

1o' ,~ ~ i NR ,oo°o

D.

¢ 1.2 o ~ . 6

'% , ,;o 1o' ,o" ,o' ,o ~ t(a)

Fig. 2a. Relaxation modulus from small instantaneous strains. Experiments on biconical Mooney viscometer. NR, T = 100 o C.

,05 , ~ ! ~ ~ ~ lo' ~..~.... I "--...,"~,~-'-.,.,, loo o .

"~',~ I " ~ . - " ~ -

,o, I i0 i ~

t(a) Fig. 2b. Relaxation modulus from smal] instantaneous strains. Experiments on biconical Mooney viscometer. NR+0 .1 volume fraction N326 black, T = 100 o C.

190

Io~ I i I NR ~=o.2 N326 : °o:°P I

5' - % : ::o ,I , o _ _ . _ _ , : ~o~:, ' "1

' i , I 1

t ls) Fig. 2c. Relaxation modulus from small Ln_stantaneous strains. Experiments on biconica] Mooney viscometer. NR + 0.2 volume fraction N326 black, T = 100 o C.

,d

ca ft.

O

,o'

l v ! '

o 0.676 v 1.91 O 3.83

NR ~=0.3 N326 I00 °C

I010 o ' , ,o' t d ,o ~ lo' lo ~ t (s)

Fig. 2d. Relaxation modulus from small instantaneous strains. Experiments on biconical Mooney viscometer. NR + 0.3 volume fraction N326 black, T- - 100 o C.

The long time asymptote of the shear modulus G(oo) increases with carbon black concentration as shown in Fig. 5. G(oo) decreases with strain amplitude.

191

sd

id

0 id

i i i

I°~o° Io' Id lo ~ t ( s )

0 0.138 O 0 3 6 3 0 0.88 a 0.875 • 1.79 n 3.83 • 7.66 v 15.3 • 30.7

SBR

IOO "c

I I

io'

Fig. 3a. Relaxation modulus G(t) from small instantaneous strains. SBR, T = 100 o C.

A t~ mio 4 0

io ~

i01

SBR qb'=0.2 N326 I00 °C

"~ 0.138 A 3.83 • 0.345 o 7.66 v 0.622 o IS.3 O 1.2| 030.6 4 1.91

I I

Io 2 ao 3 to' Io 5 t(s)

Fig. 3b. Relaxation modulus G(t) from small instantaneous strains. SBR+0.2 volume fraction black T = 100 o C.

W e n o w tu rn to par t ic le size effects. T h e s t ress r e l a x a t i o n m o d u l u s increases wi th dec reas ing par t i c le size as s h o w n in Fig. 6 fo r a c a r b o n b l a c k v o l u m e f r ac t ion of 0.2. G(t) for the N 9 9 0 c o m p o u n d s dec reases to zero.

192

TABLE 3

Relaxation modulus asymptotes G(oo)

Compound

NR, ~ = 0.2 N326 NR, ~ = 0.3 N326 SBR, ~ = 0.2 N326

Strain Strain Strain 3'0 G(oo), Pa 3'0 G(oo), Pa 3'0 G(oo), Pa

0.24 6.74x 103 0.057 1.56 X 105 1.0 2.48 X 103 0.282 6.0 x 104 1.9 1.92 X 103 0.576 3.8 x 104 7.6 6.92 x 102 1.91 1.65 X 104

30.6 1.73 X 102 3.83 8.8 x 103

0.138 2.3 x 104 0.345 1.2 x 104 0.622 9.5 × 104 1.21 5.2 × 103 1.91 4.0 × 103 3.83 1.9 × 103 7.66 1.28 X 103

15.3 6.0 × 102 30.6 3.0 × 102

However G(oo) for the Nl10 and N326 has a finite value, which is larger for the smaller particle size N l l 0 compounds.

3.2 Transient viscosities

The transient shear viscosity ~/('i',t) is shown in Figs. 7a,b and c for the N R N326 rubber-carbon black compounds. The behavior of the SBR and

0

10

i o__l, ,oo s

0.3

0.2 o. ~

0.1 o - ~

~ - 0 o-

NR N326 I00 °C

\

~ 0 z %

Fig. 4. Relaxation modulus G(3'0, t) as a function of shear strains 3'0 for NR - N320 carbon black compounds of varying loading. T -- 100 ° C.

193

io =

,,=¢ S Jd (9

id

i .o.a

~.o.~

i0 "=' lO-i I0 ° I01 I0 = %

NR IO0°C

\

\

Fig. 5. Long time asymptote relaxation modulus G (7o, ao) as a function of strain for N R - N326 carbon black compounds. T = 100 ° C.

its N326 compounds are shown in Figs. 8 a and b. At low shear rates the viscosity increases monotonically while at higher shear rates an overshoot appears before the viscosity reaches a steady state value. The response

io'

io'

O.

(9

I0"

N~JO

NR ~ = 0 , 2 I 0 0 ° 0

I00 S

~ m

\ I

I0 "2 1(3-1 I0 ° I0 ! I0 2 %

Fig. 6. Relaxation Modulus G(Y0, t ) for N R and with Nl10 , N326 and N990 as a function of strain. T = 1 0 0 ° C .

194

appears to be similar in character for all the samples although some differences can be noted. At high shear rates, the shape of the curves is different for N R and SBR, with the latter showing a well defined overshoot whereas N R instead exhibits a temporary plateau which later in time decays to the steady state value. The magnitude of the overshoot, as measured by the ratio of the maximum to the steady state viscosities is dependent upon

|0G1 , w

i NR 100°0 ~ -'°''-'°---° O'02TF

[ I

IJL I '~'o ~, ,0o ,o, ,o ' ,o ~

t (s)

Fig. 7a. Transient shear viscosity ~(~, t ) for NR-carbon black compounds of varying loading level. NR.

io"

O'%

v

L i .R ~--o.i . s2e

I 0 s " ~ ~ ~ 1 4 °'°3°4 se

10 5 .

ioo °c

~°~d' io ° io' io ~ io ~ d t (s)

Fig. 7b. Transient shear viscosity ~(~,, t) for NR-carbon black compounds of varying loading level. NR + 0.1 N326 black, T ffi 100 o C.

195

107 NR ~)=0.2 N326 IO0°C I

,~ l# ~"

i 0 ~ •

=°'io" 1o 0 io' io = lo' tls) 10'

Fig. 7c. Transient shear viscosity ~l('t, t) for NR-carbon black compounds of varying loading level. NR+0.2 N326 black, T = 100 o C.

i o ~

~ s .o38 3

. ~ 0.114 S "l e~

K-

0~!o NR (~=0.3 N i26

I i01 I0 = tls)

too °o

io ~ io'

Fig. 7d. Transient shear viscosity 71('~, t) for NR-carbon black compounds of varying loading level. NR + 0.3 N326 black, T = 100 o C.

carbon black loading and shear rate. This ratio increases with shear rate and black loading as shown in Table 4. The ratio also increases with decreasing black particle size as summarized in Table 5.

3.3 Steady state shear viscosity

The steady state shear viscosity results for N R and SBR with N326 black are presented in Figs. 9 and 10 as a function of shear stress. The effect of

196

DO ~

|o ~

m a.

SBR (~=0 IO0°G

I '

L57 S - I

I°=o" Io 0 Io' tls) I°= D°~ =°~

Fig. 8a. Transient shear viscosity 7/(7, t) for SBR, T=100°C.

lo' m n

iO s . ~

I ] ~ ~ ""-=-° ' -~ ,~ o.o.

I O' I 0"* I0 ° 10 4

I SBR (~=0.2 N326 I00 °O I

I I ! I

Io' Io' =o ~ f i e )

Fig. 8b. Transient shear viscosity ~/(7, t) for SBR+0.2 N326 black, T=100°C.

particle size on the N R compounds is shown in Fig. 11. Decreasing particle size increases steady state viscosity and the overshoot/steady state ratio.The shear viscosity of the pure melt is constant at low stresses and decreases with increasing stress. The compounds, however, show a viscosity that at the 0.2 and 0.3 volume loading appears to increase towards inf'mity at finite shear stress. Yield values appear to exist. These values increase with black loading and with decreasing particle size. They are summarized in Table 6.

TABLE 4

Overshoot/steady state viscosity ratio concentration effects (N326 compounds)

197

Material ~t(s -1) ~ln~/11~o

N R ~ = 0.0 0.01277 1.00 0.133 1.11 0.768 1.17 1.54 1.19

N R ~ = 0.1 0.0384 1.00 0.140 1.06 0.768 1.12 1.54 1.13

N R ~ -- 0.2 0.277 1.11 0.135 1.21 0.768 1.29 1.54 1.28

N R ~ = 0.3 020318 1.77 0.0563 1.65 0.114 1.78

SBR ~ -- 0.0 0.033 1.40 0.246 1.71 0.763 1.78 1.57 1.77

SBR ~b = 0.2 0.033 1.23 0.245 1.46 0.754 1.60 1.55 1.66

3. 4 Stress relaxation after steady state flow

After steady state shear flow is achieved the rotor can be stopped and the torque monitored as a function of time. The results, plotted in the form of

TABLE 5

Overshoot/steady state viscosity ratio particle size effects

N990 N326 Nl10

~,(s -~) n.~/n® "~(s -~) n, ,~, /n~ "?(s -~) nn., , /n~ 0.0307 1.04 0.0277 1.11 0.0307 1.17 0.138 1.05 0.135 1.21 0.141 1.39 0.522 1.13 0.768 1.29 0.512 1.47 1.54 1.13 1.54 1.28 1.54 1.47

198

O m

2 3 4 5 6

log 0

Fig. 9. Steady state shear viscosity ~ as a function of shear stress for NR and its N326 black compounds, T ffi 100 o C, Creep (o), Mooney (o), Capillary (e).

i

C ' ,

0 0

I0 . 2 N 3 2 6

%,

0 i

2 3 4 5

log o

Fig. 10. Steady state shear viscosity ~ as a function of shear stress for SBR and its 0.2 N326 black compounds. T ffi 100 o C.

12

I0

i 3 2 6

199

9 9 0

o

• I -"=.

N R I00 °0

0 2 3 4 5 6

l o g o

Fig. 11. Steady state shear viscosity )! as a function of shear stress for NR with three carbon blacks (Nl l0 , N326, N990).

the ratio of shear stress/shear rate are presented in Figs. 12a-d for the N R compounds and in Figs. 13a and b for the SBR. After steady state shear flow the stress in the gums and 10-percent compounds relaxes continuously with time to zero. For the 20- and 30-percent loading materials, the relaxation rate not only is increasingly reduced but also the stress does not relax to zero but to a finite value. This value ~/t(-Loo ) decreases with

TABLE 6

Yield values in steady shear flow for natural rubber

volume ~ fraction/ Particle size Ys (Pa) carbon black (urn) estimated

0.2 N326 27 4.4× 103 0.3 N326 27 1.7 × 105 0.2 N990 450 - 0.2 N326 27 4.4× 103 0.2 Nl10 20 1.4 x l0 s

200

increasing shear rate and increases with carbon black loading as shown in Table 7.

3.5 Sequential steady shear histories

In this experiment a material is sheared at a constant shear rate until the steady state is reached. At this moment the rotor is stopped and the sample is allowed to relax for varying periods of time. At the end of the period a

' I

. - - ~4 "00 .768 _ _

10 5 " - -

~ 10 4 C'

,o • NR I00 °C

i o 2 ~ I0 -I IO 0 I0' IO 2 I ~ I0 4

t ( s )

Fig. 12a. Shear viscosity relaxation following flow for NR, T : 100 o C.

)d

io'

i~.10 5

io'

0.038

0.14

0,768

1.54 g-!

NR <~=0.1 N326 I i o o °o

io ° lo' lo ~ io 3 )o" t ( s )

Fig. 12b. Shear viscosity relaxation following flow for NR+0 .1 N326 black, T = 100 ° C.

id ,

Oi t I ~ NR qb=0.2 N326 106 ~ I00 *O ~ o.o~ s-'

' ° '

I°io° io' Io' Io ~ d Io ~ t(s)

Fig. 12c. Shear viscosity relaxation following flow for N R + 0 . 2 N326 black, T = 1 0 0 ° C .

201

id

~ t o s

c '

NR ~=0,3' N326 i I00 °O I

~ _ o o..s-' I

jo' ic Io ~ id Io 4 Io 6

t(s)

Fig. 12d. Shear viscosity relaxation following flow for N R + 0.3 N326 black, T = 100 ° C.

second steady shearing deformation is imposed. The results for NR com- pounds are shown in Figs. 14a, b and c, and those for SBR in Figs. 15a and b. For short periods the viscosity for the second deformation period is lower than the original.When the rest period increases the differences for gum elastomers becomes smaller until the viscosities match. The compounds do not follow this pattern. For long rest periods the stresses exhibit much larger values than did the initial sample.

202

id

~td 03 co

c"

0.0384 " j

0.161

0.3114

SBR tz7 !

,o3 I i i

id' Io 0 to' lo' i@ Id t ( s )

Fig. 13a. Shear viscosity relaxation following flow for SBR, T = 100 * C.

"G ~J a. Io 5

i d

id io o

Ii•SBR (:I:)-0.2 N326 ioo *c

. i ,

I01 I0 2 10 3 10 4 10 5 t(s)

Fig. 13b. Shear viscosity relaxation fonowing flow for SBR + 0.2 N326 black, T = 100 ° C.

3.6 Storage effect on shear viscosity and relaxation modulus

The results described in the previous section suggested a series of experi- ments in which a sample was allowed to relax, after insertion into a rotational rheometer for various periods of time (At0) before a constant shear rate or constant strain was imposed. The magnitude of the overshoot in shear flow increases with storage period for the c.~rbon black compounds with ~ of 0.2 or 0.3. The steady state values are, however, the same. This is

203

0.%5

NR I00 °0 o.TS S "1

O. o.lo atts~

• INITIAL

0 2 1 0

a 3 0

0.05

0 ~ L ~ ~ l - ~p_ 4 6 B o ~- t(min)

Fig. 14a. ~ucn t i~ tr~si¢m she~ viscosity ~itc~ v~-ious periods o(~est [or I~I~, T =- 100 o C.

0.2

C/)

0. ~, 0.15 NR ~)=O.l N326

I00 °0 o.Tss s -~

At(sl • INITIAL

o E, O00

o le, O

a t |

4 | .~

0.1

o 2 t(min) Fig. 14b. Sequ~tial t~s~si~t sh~r viscosity sftef various p~riods of rest for N g . NI~ +0.1

N326 black, T = 100 ° C.

204

0,l ,-, 0.3 I1.

0.2

O.I

NR ~=0.2 N326 I00 °(3

- - ~ At(s) 53 g4o

¢ 6 SO0

°-I o

• INITIAL o 13 o 3.4

I

2 3 log t(s)

Fig. 14c. Sequential transient shear viscosity after various periods of rest for. NR+0.2 N326 black, T = 100 o C.

shown in Figs. 16 and 17a, b. Concentrat ion effects are shown in Fig. 16 where it is found that after 24 h at the testing conditions the pure elastomer shows no change in viscosity. This is also the case for the ten percent compounds, but not for the 20-percent compounds which show a substantial increase in the transient viscosity values and no change in the steady state. The overshoot grows with time, apparently leveling off at about 20 h.

These effects are also particle size dependent. N990 shows no change in transient viscosity with rest period whereas N l l 0 show an accentuated response (Fig. 18). Similar effects occur for the relaxation modulus at 100 s. as may be seen in Fig. 19.

TABLE 7

Shear viscosity 11(~,, co) after after steady flow

NR, #, = 0.2 NR, c/, = 0.3 SBR, # = 0.2

~, n(~,, co) ~ ,(~,, co) ~ n(~, co) (s - ] ) (Pa s) (s - ] ) (Pa s) (s - l ) (Pa s)

0.0277 2.06 × 105 0.0318 9.33 x 105 0.0266 - 0.135 3.04 x 10 4 0.0563 4.77-105 0.141 4.50 x 104 0.768 2.60 × 103 0.114 2.43 × 105 0.379 1.28 × 104 1.54 1.49 × 103 - - 1.59 3.0 × 103

205

10' SBR 100%

0 .=6 S "t

a. Id &t(h) 0 INITIAL A 5.3

o 0.53

o 0.05

Jd Io ° Io' Io 2 Io 3 t(8)

Fig. 15a. Sequential transient shear viscosity after various periods of rest for SBR. SBR, T = 1 0 0 ° C .

Io'

¢0

i 8.R e=o.2 '.s26 ioo°o [ 0.28 S "1 I

t .6 c~s At(h) (108 INITIAL

J°loO io I io ~ io • io 4 t ( s )

Fig. 15b. Sequential transient shear viscosity after various periods of rest for SBR_ SBR +0.2 N326 black, T = 100 o C.

3. 7 Programmed step shear rate histories

The shear stress responses to programmed shear rate histories imposed on the samples in the form of an always increasing or decreasing shear rate are shown in Figs. 20a-d, and 21a and b. The gums and 10-percent compounds

206

Dd

Ate(h) o 0.5 • 24.0

0.768 S "1

too °c

f~o' / o.o I0" . ~ ~ , .~6~, . -0 _

i

! ,

'do~ ,o ° to' ,o 2 td tla)

to'/Id

11. I 0 ~

Fig. 16. Transient shear viscosity after half hour and 24 hour storage periods within the rheometer with ~, = 0.768 s -1 for NR with 0, 0.1 and 0.2 volume fractions.

exhibit the same shear viscosities on the upside and downside. The dis- crepancy between the curves increases with carbon black loading. N990 compounds show no hysteresis (Fig. 21a) unlike Nl10 compounds, which exhibit a striking hysteresis (Fig. 21b). Again decreasing carbon black particle size acts in a manner similar to increasing loading level.

4. Discussion

From the above discussion, it is clear that rubber-carbon black filled compounds at high concentrations show remarkably different rheological responses in shear flow in contrast to unfilled, low volume fraction com- pounds or compounds containing large particles. They exhibit not only yield values as noted by various earlier investigations [5-7,12,13,15,16] but strik- ing time dependent effects. Stresses relax to a finite value rather than zero and there are strong storage and hysteresis effects on the transient shear viscosity. The former effect had been noted by Lobe and White [10] and the latter noted in the manuscript by Mullins and Whorlow [4].

207

o.81 0.6

~ 0 . 4

Ato(h) o t 3

0 =1

a I I

NR ~=0.2 N 326 = 5 • O.S

ioo °o

0.2

0 0 I 2

log t ( G ~

Fig. 17a. Storage time effects on transient shear viscosity of NR with 0.2 volume fraction N326 black. T -- 100 o C.

C~3

~.0.2

0.1

A :h) A 22~

¢ 15.3

0 7.1

o 1.9

o 0 . 6 3

N 326

~00 %

I I I

0 0 I 2 3

log t $ )

0.37 S " I

Fig. 17b. Storage time effects on transient shear viscosity of SBR with 0.2 volume fraction N326 black. T = 1 0 0 ° C .

208

t~

CO m o. to e C"

NR ~-02 Nggo ioo °c

0.7S8 S -I

6t~h) • Z4.3 D 20.7

o 4.2

• 0 .6

Jd io-' i°° t(s) io' io z

Fig. 18a. Influence of carbon black particle size on storage effect effects on transient shear viscosity. NR + 0.2 N990 black.

io'

~,o"-

tO-' I0 °

A l o ( h ) o 13

NR~)=02 NIIO a s A I

I00 °O 0.6, s" • 0 .5

I I ! !

Io' tg t ( 8 1

I#

Fig. 18b. Influence of carbon black particle size on storage effect effects on transient shear viscosity. NR + 0.2 N l l 0 black.

This study also shows the importance of the experimental procedures during the testing of carbon black compounds. Any deformation given in the sample prior to nominal testing, (as occurs during the squeezing type insertion of the sample in the Mooney viscometer), must be taken into consideration in the interpretation of the rheological response of these systems. The occurrence of non-zero long time relaxation moduli G(oo) and

209

to'

l o ~ . m

" ~ l O 4 O1

io'

i i NR

O O.5

~=0.2

~X~ qb=O. I

, °o

I 01 ; i0 -2 i0 -0 10 ° I0 t I0 z

%

Fig. 19. Storage effect on step relaxation modulus.

shear viscosity decay functions T/(?,oo) seems associated with the occurrence of a yield value Y.

The overall response of the carbon black compounds considered in this study is very similar to other thixotropic systems studied and reported in the literature, such as suspensions of carbon black in oils [26].

io" I

NR iOO °(3 l I

to "2 to-' )o ° )o ) (8 -~ )

Fig. 20a. Programmed shear rate history effect on shear stress response: effect of black loading. NR, T = 100 o C.

210

o I

NR ~=0.1 N326 I I00 °O I

i

tO "z iO-I i0 o I0 I ( s -~ )

Fig. 20b. Programmed shear rate history effect on shear stress response: effect of black loading. NR+0.1 N326, T = 1 0 0 ° C .

i NR (~=0.2 N326 I

too % I 0

Io "= IO-' Io0 to ~

~/(s-~)

Fig. 20c. PrOgrammed shear rate history effect on shear stress response: effect of black loading. NR+0 .2 N326, T = 1 0 0 ° C .

NR d#=O.3 N326 i oo %

o.

o

,o' Io "2 Io-' Io 0 Io'

~(s -1)

Fig. 20d. Programmed shear rate history effect on shear stress response: effect of black loading. NR+0.3 N326, T = 1 0 0 ° C .

211

io ~

o. v lO s o

NR ~ = 0 2 N990 ioo °c

.-.--8

i0~_~ u la'~ ~(s_~) Io ° io'

Fig. 21a. Programmed shear rate history effect on shear stress response: effect of black particle size. NR+0.2 N990 black T = 1 0 0 ° C .

i d

NR ~==0.2 NIIO I00 °0

Y 10-2 i0-= I0 ° I0 =

• ~ (s-~)

Fig. 21b. Programmed shear rate history effect on shear stress response: effect of black particle size. NR + 0.2 N990 black, T = 100 ° C.

The complex rheological behavior of these materials is demonstrated, as viscoelastic, plastic and thixotropic effects appear together. Rheological modeling, therefore, has to include these three aspects. Based on the success in the modeling of similar materials [23], the description of the rheological properties of rubber carbon black compounds in terms of a plastic, viscoe- lastic, and thixotropic constitutive model seems at first encouraging.

The time constants associated with our storage experiments as well as those of Nullin.~ and Whorlow [4] suggest values of order of 1 to 20 h.

212

However steady state is achieved in shear flow in apparently a matter of minutes. Perhaps all is explicable in terms of deformation rate dependent relaxation times.

Acknowledgement

This research was supported in part by the National Science Foundation under NSF Grant MSM - 8514952.

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