Testing of viscoelastic materials

In a method of testing a sample of viscoelastic material held under pressure between two opposing, temperature-controlled dies, the sample is subjected to an oscillatory, rotary shearing force which has a predetermined amplitude and a frequency within the range 0.001 to 2 Hz, and a torque which is indicative of the response of the sample to the shearing force is measured, at least one measurement of the torque being made when the predetermined amplitude is at least .+-.10.degree. but not greater than .+-.360.degree..

This invention relates to a method and apparatus for measuring the 
properties of viscoelastic materials. 
The relevant prior art includes the plastometer of Mooney described in U.S. 
Pat. No. 2,037,529, and the rheometer described in U.S. Pat. No. 
1,036,904. In each of these instruments, a sample of the material to be 
tested is enclosed in a cavity formed between two opposing dies, 
rotational shear is applied to the sample by means of a rotor embedded in 
the sample, and the torque required to apply the shear is measured. In the 
former instrument, the rotation of the rotor is continuous; in the latter 
the rotation is oscillatory. 
Other instruments in which an oscillatory, rotary shearing force is applied 
to a sample of viscoelastic material held between two opposing dies are 
those described in U.S. Pat. No. 3,479,858, U.S. Pat. No. 3,488,992, U.S. 
Pat. No. 4,343,190, and U.S. Pat. No. 4,552,025. In these instruments, the 
force is applied by rotation of one die relative to the other, and the 
measurements made are of the torque required to apply the shearing force 
or of the torque induced in the second die (reaction torque) when the 
first (driven) die is rotated. 
For the operation of prior art instruments involving an oscillatory 
shearing force, relatively small angles of oscillation are envisaged. This 
is because such instruments have been primarily intended to obtain 
information about the behaviour of compounded rubber stocks immediately 
prior to and during vulcanisation. For example, U.S. Pat. No. 1,036,904 
mentions oscillation through a small angle, for example 2.degree.; U.S. 
Pat. No. 3,479,858 refers to reciprocal rotation through a given angle 
(usually not more than 15.degree.); and U.S. Pat. No. 4,343,190 and U.S. 
Pat. No. 4,552,025 state that the rotation is preferably sinusoidal and is 
preferably performed through an angle of from 0.1.degree. to 10.degree.. 
As regards the frequency of oscillation in the prior art methods, U.S. Pat. 
No. 3,681,980 mentions frequencies of up to 3,600 cycles per minute (60 
Hz), with an example at 852 cycles per minute (14.2 Hz), and U.S. Pat. No. 
4,343,190 and U.S. Pat. No. 4,552,025 mention frequencies of from 1 to 
2000 cycles per minute (0.0167 to 33.33 Hz) and from 1 to 10000 cycles per 
minute (0.0167 to 166.67 Hz) respectively. 
A characteristic of the method of testing disclosed in U.S. Pat. No. 
4,552,025 is that a sample of viscoelastic material is held at a 
predetermined temperature while the force induced in reaction to the 
deflection of the material at two or more oscillatory frequencies is 
measured. The sample is then held at another, higher, predetermined 
temperature while the said force is measured at one or more oscillatory 
frequencies. The method is intended primarily to give information, 
derivable from the measurements at the first predetermined temperature, 
about the rheological behaviour of rubber compounds at typical 
prevulcanization temperatures, and information about the curing 
characteristics of the same compound during vulcanisation at the second, 
higher temperature. 
We have now found that data derivable by testing samples of viscoelastic 
materials which do not thermoset during the period of the test are much 
more discriminating in distinguishing different materials or in 
identifying deviations from a standard if the sample is subjected to a 
rotatory, oscillatory shearing force having a greater amplitude of 
oscillation than any disclosed or suggested by the prior art. Oscillation 
frequencies towards the lower end of the ranges mentioned in the above 
prior art documents or below are employed. 
The method of the invention is a method of testing a sample of viscoelastic 
material held under pressure between two opposing, temperature-controlled 
dies, which comprises subjecting the sample to an oscillatory, rotary 
shearing force having a predetermined amplitude and frequency, and 
measuring a torque which is indicative of the response of the sample to 
the shearing force, characterised in that at least one measurement of said 
torque is made when the said predetermined amplitude is at least 
.+-.10.degree., but not greater than .+-.360.degree., and said frequency 
is within the range 0.001 to 2 Hz. 
The apparatus of the invention comprises two opposing dies movable between 
an open position and a closed position, and adapted, when in the closed 
position, to contain between them a sample of viscoelastic material under 
pressure, means for controlling the temperature of the dies, means for 
applying an oscillatory, rotary shearing force to a sample of viscoelastic 
material contained between the closed dies, and means for measuring a 
torque which is indicative of the response of the sample to the shearing 
force, characterised in that the means for applying the shearing force 
comprise means for applying the shearing force at at least one amplitude 
of oscillation within the range .+-.10.degree. to .+-.360.degree. and a 
frequency of oscillation within the range 0.001 to 2 Hz. 
In preferred embodiments of the method and apparatus, the shearing force is 
applied to the sample by oscillatory rotation of one of the dies with 
respect to the other, and the torque indicative of the response of the 
sample to the shearing force is the reaction torque measured on the other 
die. Other arrangements are possible, however. For example, the force 
could be applied to the sample by means of a rotor embedded in the sample 
as in the Mooney viscometer or the rheometer described in 1,036,904; and 
the torque which is measured to indicate the response of the sample to the 
oscillatory shearing force could be the torque applied to the said one of 
the dies or to the rotor. 
Preferably, the said at least one amplitude of oscillation is an amplitude 
within the range .+-.10 to .+-.200.degree., and more preferably within the 
range .+-.20.degree. to .+-.120.degree.. Depending on the viscoelastic 
material to be tested and the data which it is desired to derive from the 
test, torque measurements may be made at a single amplitude of oscillation 
or at a series of two or more different amplitudes. In the case of 
measurements at single amplitude, this is preferably an amplitude within 
the range .+-.20.degree. to .+-.120.degree., for example within the range 
.+-.40.degree. to .+-.120.degree. . In the case of measurements at a 
series of different amplitudes, the selected amplitudes preferably include 
two or more within the range .+-.10.degree. to .+-.120.degree., but the 
series can also include measurements at smaller amplitudes, for example 
.+-.5.degree., or larger amplitudes. Moreover, measurements at a given 
amplitude can be made at a single frequency or at a number of different 
frequencies of oscillation; and measurements at a series of amplitudes can 
be made at a fixed temperature throughout, or one or more measurements can 
be made at one temperature and one or more at a different temperature. 
The oscillatory rotation in the method and apparatus of the invention is 
preferably sinusoidal. Useful parameters for characterising viscoelastic 
materials derivable from torque measurements under such conditions are the 
elastic or storage modulus S', the viscous or loss modulus S" and the 
tangent of the loss angle (delta) which is the ratio S"/S'. S' can be 
calculated from the torque measured at the point of maximum displacement, 
while S" can be calculated from the torque at zero displacement. However, 
measurement of the torque at a series of sampling points throughout the 
oscillation can provide useful data about the sample. For example, the 
method of the present invention can incorporate the features of the method 
of U.S. Pat. No. 4,794,788 which comprises (A) separately subjecting both 
a sample of the material and a standard to a sinusoidal shearing force, 
(B) separately measuring a material response and a standard response at at 
least three displacement data points equally spaced throughout a cycle of 
oscillation (C) separately applying a calculation operation to the data 
points to (i) convert the material data points into values representing 
either a storage modulus or a loss modulus of the material; and to (ii) 
convert the standard data points into values representing a standard 
torque and a standard phase angle, and (D) correcting the values 
representing the storage modulus or loss modulus for the material. As 
explained in U.S. Pat. No. 4,794,788, the optimum number of data points is 
16 per cycle. 
In certain instances an improved characterisation of the viscoelastic 
material can be achieved by subjecting the torque response to harmonic 
analysis. The response of the viscoelastic material at large angle 
deformation produces a non-sinusoidal torque envelope. The shape of the 
torque curve can be fully described mathematically by using Fourier 
transformations by means of which all the dominant sine wave frequencies 
and amplitudes can be determined. 
Any or all of the parameters to be used for characterising the viscoelastic 
elastic material can be electronically derived from the torque 
measurements during the course of the test and continuously displayed. 
In the preferred form of die, the opposing faces are shallow, coaxial cones 
disposed so that the separation of the faces increases with the radial 
distance from the axis. A preferred arrangement is for the lower die face 
to have the form of a cone and for the upper die face to be an inverted 
cone, the use of flat-topped cones being particularly preferred. The die 
faces will normally be provided with radial grooves or similar means to 
prevent slippage of a sample of viscoelastic material held in the die. 
In preferred embodiments of the apparatus, the lower die is driven from a 
computer-controlled electric motor located beneath the die and having its 
output shaft coaxial with and rigidly coupled to the die. The computer is 
programmed so that the output shaft of the motor moves at the desired 
angular displacement and frequency or through a sequence of desired 
angular displacements and frequencies. Although a sinusoidal oscillation 
is often preferred, the arrangement described above allows the rotary 
oscillation of the lower die in other modes. For example, by suitable 
electronic processing of torque measurements in a particular embodiment of 
the invention using constant oscillating speed, it is possible to derive 
information concerning the rheological properties of viscoelastic 
materials which corresponds essentially to that provided by the Mooney 
viscometer. 
Such a method and apparatus in fact represent an improvement over the 
current Mooney method because the latter suffers from drift in torque 
measurements which is the result of the continuous rotation of the rotor. 
The form of oscillatory motion is not limited, and can be, for example, 
sinusoidal, constant angular velocity, ramp, triangular or any combination 
of different motions.

Referring to FIG. 1 of the drawings, the members (1), (2) and (3) are 
respectively left and right vertical, and horizontal components of an 
outer frame which is supported on a base (not shown). A lower die assembly 
comprising a die housing (4) and a housing (5) for a drive shaft (6) 
connected at its upper end to a lower die (not shown), is mounted in the 
horizontal member (3). An inner frame, which is located beneath the 
horizontal member (3), has vertical portions (7) and (8) and a lower 
horizontal portion (9). Tie rods (10) and (11) which pass through the 
horizontal member (3) are attached at their upper ends to an upper 
crosshead (12) and at their lower ends to a lower crosshead (13). An upper 
die assembly comprising an upper die housing (14) is mounted in the upper 
crosshead. 
A pneumatic cylinder (15) mounted beneath the horizontal portion (9) of the 
inner frame has a cylinder rod (16) which is connected to the lower 
crosshead (13). Actuation of the pneumatic cylinder causes the assembly 
consisting of the cylinder rod (16), lower crosshead (13) tie rods (10) 
and (11) and upper crosshead (12) to travel downwards, thus bringing the 
upper die housing (14), the lower die housing (4) and the dies into the 
closed position shown in FIG. 2. 
The drive system to the lower die comprises a computer-controlled electric 
motor (17), for example a Compumotor stepper motor with 25,000 steps per 
revolution, mounted with its output shaft (18) coaxial with the drive 
shaft (6) to the lower die, the two shafts being coupled by means of a 
sleeve (19). 
In FIG. 2 of the drawings, there are illustrated parts of upper and lower 
die assemblies. The lower edge of the upper die housing and the upper edge 
of the lower die housing are indicated at (21) and (22) respectively. 
Other parts shown are sealing plates (23) and (24), which are attached to 
the edges of the die housings, upper and lower dies plates, (25) and (26) 
respectively, and sealing rings (27) and (28). Each die plate has a 
cylindrical cavity (29) adapted to accommodate a temperature probe (30). 
The opposing faces (31) and (32) of the die plates which define the die 
cavity are in the form of shallow flat-topped cones having radial grooves 
(33). Thus a sample in the die cavity has a thin, flat circular portion in 
the middle and an outer portion which increases in thickness radially 
outwards. The function of &he channel (34) in the lower sealing plate (24) 
is to accommodate any overflow of the sample material which is expressed 
during closure of the dies. 
Parts of the upper and lower die assemblies which are not illustrated, 
being generally similar to those shown in FIG. 2 of U.S. Pat. No. 
4,552,025 are (in the upper assembly) a torque transducer, means 
connecting the upper die to the force transducer, and heating elements; 
and in the lower die assembly, a shaft coaxial with the lower die, means 
connecting the die to the shaft, a bearing housing for the shaft, and 
heating elements for the die. 
FIGS. 3, 4, 5 and 6 present graphically results obtained in tests on 
styrene-butadiene rubber SBR 1502 after exposing the rubber for various 
periods to U.V. radiation, thereby inducing gel formation in the rubber. 
The results illustrated in FIG. 3 were obtained by employing the procedure 
of the first step of the method of U.S. Pat. No. 4,552,025, namely by 
holding a sample of the rubber at a fixed temperature (100.degree. C.) 
while measuring the reaction torque at a number of different oscillatory 
frequencies. It will be seen that the plots of frequency against S' are 
not sufficiently separated to distinguish a non-irradiated sample 
(control) nor the samples of rubber which has been exposed to various 
periods of U.V. radiation from each other. In contrast, the results 
obtained by the method of the invention, as shown in FIGS. 4, 5 and 6, 
distinguish clearly between the different samples. 
The graph of FIG. 4 is a plot of S' against time at a fixed temperature, 
(100.degree. C.) amplitude and frequency of oscillation (90.degree. and 
0.0625 Hz respectively). The results are directly comparable with those of 
FIG. 3, part of each sample of rubber having been used for the prior art 
test method and part for the method according to the invention. It will be 
seen from FIG. 4 that the value of S' increases with the duration of UV 
exposure. The indicated value of S' is seen to decrease slowly over the 
period of the test. 
FIGS. 5 and 6 show the values 100.degree. C. and 0.0625 Hz of S' and Tan 
Delta measured at a series of amplitudes on samples obtained by 
irradiating a different SBR 1502 from that used in the previous tests. The 
exposure times ranged from 0 to 3 hours. It can be seen that S' increases 
and Tan delta decreases with exposure. On the graph of S', discrimination 
between the various samples is adequate at an angle of 30.degree., but 
better at larger angles. When Tan delta measurements are used for 
distinguishing the samples, a preferred minimum angle of oscillation would 
be about 40.degree.. 
FIG. 7(a) and (b) and FIG. 8(a) and (b) show how the shape of the curve of 
relative torque calculated from harmonic analysis plotted against phase 
angle varies with the amplitude of oscillation. The sinusoidal motion of 
the lower die which applies shearing force is indicated by the continuous 
lines. In FIGS. 7(a) and 8(a), the amplitude of oscillation is 20.degree.; 
in FIGS. 7(b) and 8(b) the amplitude of oscillation is 50.degree.. The 
data of FIG. 7(a) and (b) were derived from measurements at 100.degree. C. 
and 0.0625 Hz on ex-factory SBR-1502. Those of FIG. 8(a) and (b) were 
derived from measurements at 100.degree. C. and 0.0625 Hz on SBR-1502 
which has been subjected to U.V. radiation for 4.5 hours.