Stress relaxation measurement of rubber in tension—A new technique

Polymer Testing U (1992) 47-59

Stress Relaxation Measurement of Rubber in T e n s i o n - - A N e w Technique A. B. Othman* & C. Hepburn Institute of Polymer Technology and Materials Engineering; University of Technology, Loughborough, LEll 3TU, UK (Received 9 July 1991; accepted 30 July 1991)

ABSTRACT Stress relaxation measurements in tension are potentially an elegant way of assessing the accelerated ageing characteristics of rubber. Extensive work has been carried out to develop a method suitable for an international standard. Generally, the equipment developed has been relatively expensive and this has, perhaps, contributed to the lack of widespread adoption of stress relaxation as a routine measurement. Recently, a new technique for monitoring continuous stress decay in a stretched piece of rubber was developed. The technique uses simple trigonometry to calculate stresses from a three-point bending configuration. The development of the new technique and a comparison of stresses obtained between the conventional ways of monitoring stress decay are reported.

1 INTRODUCTION Stress relaxation is a m e t h o d which is often employed for the investigation of the time-dependent properties of rubbers. The same technique is frequently employed in ageing studies on rubber as a monitor of the effect of ageing on mechanical properties. Extensive work has been carried out to develop suitable equipment for stress relaxation. 1-2 The earlier development work on the technique * On leave from Rubber Research Institute of Malaysia, 50908, Kuala Lumpur, Malaysia. 47

Polymer Testing 0142-9418/92/$05.00 (~ 1992 Elsevier Science Publishers Ltd, England. Printed in Northern Ireland

48

A. B. Othman, C. Hepburn

of monitoring continuous stress decay in rubber involved continuous loading of the sample to the load measuring device, thereby limiting the number of tests which could be carried out at one particular time. This, and perhaps the relatively expensive equipment which is required, contributed to the lack of widespread adoption of the stress relaxation as a routine measurement. More recently, there has been significant progress in the development of the stress relaxation test? -5 They are the techniques and equipments developed by the Rubber and Plastics Research Association (RAPRA) and Loughborough University of Technology (LUT). These newer techniques measure the stress relaxation of rubber under compression and have since been adopted by the International Standard Organisation as their standard test methods. 6'7 The technique involves compressing a rubber disc in a specially designed jig, which could be easily dismantled from the load measuring device, but maintaining the forces onto the rubber. The stresses in the rubber under compression were manifested by the jig set-up and it could be periodically monitored using the set-up developed. The RAPRA technique uses an arbitrary sample compression rate while the LUT technique has a fixed compression rate, which could be changed if necessary. Those techniques have an advantage in cases where large numbers of samples are to be tested. The stresses in all the rubber under compression could be periodically and simultaneously monitored since the jigs holding the samples are detachable and the samples are not continuously attached to the load-measuring devices. The limitation to the amount of samples to be tested will be the availability of the sample jigs, not the load-measuring device; the former is cheaper and simpler to fabricate than the latter. The techniques and equipment developed so far, such as those developed by RAPRA and LUT, are applicable only to rubber samples subjected to compression deformation. Understandably, those developments were carried out due to the practical need of such testing equipments, particularly for monitoring performance of sealing rings and similar products, which are used in compression. A similar technique for rubber under tensile load has recently been successfully developed, and this paper discusses the new developments in the technique for monitoring stress-decay for sample under tensile deformation. The stress-relaxation under tension was considered because of the following: (1)

any effects of the environment could be expedited and accelerated by using thin strips;

Stress relaxation measurement of rubber in tension

(2) (3)

49

errors in the measurements of strain could be minimised since the sample will be relatively long; and small changes in the stress in the sample could be detected, thus making it useful for researchers and quality-control personnel.

2 PRINCIPLES OF TEST The new technique utilises a simple principle of trigonometry. Consider a schematic diagram of a horizontally extended rubber strip which is being pushed, at mid-point vertically (Fig. 1). When a vertical force, F, is applied to an extended strip of rubber of length 21, to give a deflection 0, the new length of the rubber strip will be 211. If f is the tensile force in the rubber held between A and B, then resolving the forces along the vertical direction will give F=2fsin 0

(1)

At small angle, sin 0 ~ 0 Therefore ll ~ 1 F

C

2fSine

21 - extended length y

-

of

sample

vertical displacement

F - applied force 0 - angle of deflection f - force in the extended sample 21,- extended length of sample under force F

l ~ . 1. Resolution of forces along a stretched piece of rubber.

50

A. B. Othman, C. Hepburn

Thus, eqn (1) can be written as

F=

Ely 1

(2)

where y is the vertical displacement or F/ f=~y

(3)

Thus, provided the angle 0 is small, the tensile force in a piece of stretched rubber strip could be determined using eqn (3), with known force F, length l and vertical deflection y. 2.1 Effect of angle of deflection

The above technique of measuring a tensile force in a stretched piece of rubber assumes the angle of deflection 0 to be small. Only at small 0, does sin 0 - 0

(4)

since the other components of the expansion series will be negligible. A simple calculation showed that when the angle of deflection is 10° or less, the differences between sin 0 and 0 are negligible (Table 1). Thus, if the angle of deflection is kept below 10°, the deviation is very small and it is fairly accurate to assume that sin 0 - 0. Graphically, the deviation in load for rubber extended to different elongations is shown in Fig. 2. The points refer to the experimental data while the lines are the linearity of the load-deflection plots. The deviations observed from the lines are small indicating that eqn (4) is valid for the range of deflection investigated (<10°).

TABLE 1 Effect of Angle of Deflection

0

sin 0 0

5 20 15 20 30

0.998 7 0.994 9 0.988 6 0.979 7 0.954 9

Stress relaxation measurement of rubber in tension

51

1.0 0.8,

,,.'" .A.-'~j:r.tt 'z/

0.6

A

z "O m O -.I

j2. J~

0.4

/ . - .o',~t'°" 2-" ,d~ .d~ A, Ja" 0.2 ./l~.,,(-,~,'lf -,U /~.-./:t . , o.o-t 2 4 o

.

....... . . ~. .......

30 % strain

. . . . A---

42% strain

-,- - o - :

4:% str:in

6

Deflection

8

(degrees)

Fig. 2. Deviation of load from linearity due to the increase in deflection for sample extended to different strains.

2.2 Effect o f an off-centre

application

o f force

The schematic representation and resolution of forces in an extended rubber strip subjected to a vertical force at mid-point to form a three-point bending configuration is shown in Fig. 1. Point C should be midway between A and B. Practically, locating the mid-point of the rubber strip may be difficult, but possible. In the event that the loading is at off-centre position, how much variation in the pushing force will occur? Consider a schematic representation of an off-centre loading (Fig. 3). F

l

S I~

v I-

Fig. 3.

A n off-centre loading.

Wl

A. B. Othman, C. Hepburn

52

If the force F is applied at a point C, where C is a distance away from the mid-point A B , then F = f sin 01 + f sin 02

(5)

y = (l + a) cos 01 = (1 - a) cos 02

(6)

At small angle, (7)

y = (l + a ) 0 1 ~ (1 - a ) 0 2

Then from eqn (5) F = f ( O ~ + 02)

Y

Y

2t/y l z -- a 2

or rearranging

f

F ( I 2 - a 2)

(8)

Ely

Thus, the force f changes with the difference between the squares of the extended length l, and the off-centre distance a. Theoretically, for any length l, an off-centre distance of 10% gives a 1% change in force f while a 20% off-centre loading gives about 4% change in force (Table 2). At small (<20%) off-centre positions, the predicted increase in force due to an off-centre loading was observed to be comparable to the TABLE

2

Effect of an Off-Centre Loading

Off-centre position, a (% of length, 1) 2 4 6 10 14 20 30 50 70

Variation of force (%) 0.04 0.16 0.36 1"0 1-96 4-0 9.0 25.0 49.0

Stress relaxation measurement of rubber in tension

53

50 • 40

m tO nO M.

Experimental

/

[] Predicted

i ¢

[]

30

Z lu

< ILl nO

20

Z

10

0 ' ~

0

-~2~'11-

~

20

•

,

•

40

,

60

80

OFF-CENTRE POSITION (% OF LENGTH L) ]Fig. 4.

Increase in force as a function o f an off-centre position.

experimental values (Fig. 4). This shows that the changes in force due to an off-centre loading is small, and under normal testing, for which the sample length is long (>100 mm), the variation due to a possible off-centre loading will be negligible.

3 THE E Q U I P M E N T The new technique of measuring stresses in an extended piece of rubber strip involves pushing/pulling vertically at the mid-point of the sample to give a three-point bending geometry. The stresses at preset vertical displacements are determined using the principles of trigonometry. The measurements could be carried out using any standard load measuring device such as a Universal Testing Machine, with suitable attachments. However, to make the test versatile and cheap, a portable set-up was designed and constructed. The set-up consists of a jig to hold the sample, a load frame and the electronic control console (Fig. 5).

54

A. B. Othman, C. Hepburn

(a)

(b) Fig° 5o Three-point bending relaxometer. (a) Whole set-up, and (b) sample jig with rubber sample subjected to vertical load (enlarged).

Stress relaxation measurement of rubber in tension Housing bar

Sample grip

Rubber strip

55

Threaded rod

Fig. 6. Plan view of the sample holder.

3.1 The jig The jig is made-up of a rectangular housing frame onto which the samples are gripped. The sample grips move along the threaded rod, enabling the extension of the sample to be set accordingly. The sample grips are secured onto the threaded rod using locking nuts (Fig. 6).

3.2 The load frame The rectangular load frame comprises a base unit, seven vertical columns and an upper transverse beam. A base platen is set into the upper section of the base unit. A moving crosshead, guided by two vertical rods, is located between the base unit and the upper transverse beam. The crosshead, to which is attached the mini-beam load cell, is ballscrew driven. Specimens to be tested are secured Onto the sample jig which is held rigidly onto the upper transverse beam. The sample vertical deflections are controlled by a preset gauge, having a fixed vertical movement of about 0.5 mm/step. The actual vertical displacement is measured using the dial gauge.

3.3 Electronic control console The electronic control console consists of a load measurement system, crosshead control system and sample extension system. The load measurement system comprises the load-cell, load-cell amplifier and a digital panel meter. The load-cells are interchangeable and the current model uses a 0-22 N load capacity. A load range switch has been incorporated to cater for different ranges of loading sensitivity. This prototype model has two sensitivity ranges, namely 2N and 20N full-scale loading. The load weighing system is calibrated using standard weights, and the output is displayed on the digital panel meter.

56

A. B. Othman, C. Hepburn

The crosshead system controls the vertical movement via a single ballscrew. The movement of the crosshead is set at a fixed distance by an opto-electrical switch. The sample extension system enables the gripped samples to be extended at a fixed rate. The extension rate could be varied from about 100 mm to 500 mm/min. 4 SAMPLE ASSEMBLY A N D L O A D I N G P R O C E D U R E Rubber strips, about 2 m m thick and 10mm wide are used as test-pieces. The test-pieces are secured onto the sample grips, and the jig rigidly mounted onto the top platen of the loading frame. The test-piece is extended after the jig is fixed into position using the sample extension system. The extension ratio of the sample is measured using a cathetometer, based on the gauge length marked on the sample strip prior to loading. The vertical force is applied approximately mid-point to the extended rubber strip via a wedge-shaped plunger to form a three-point bending geometry. The vertical movement could be set at 0.5 ram/step. The loads to push vertically the extended rubber strip at three different displacements are recorded and the stresses at each displacement calculated. The average of the three stresses is taken as the stress in the rubber at a given time. For the stress relaxation experiment, the vertical force is applied to the rubber strip at known time intervals, so that a series of stresses at specified time intervals can be obtained. 5 C O M P A R I S O N B E T W E E N D I F F E R E N T M E T H O D S OF M E A S U R I N G STRESS-DECAY There are several established methods of monitoring stress-decay in rubber subjected to tensile deformation. An accurate and simple technique is to fix the sample continuously to a force measuring device, such as a load-cell, and monitor the decay in stress via a digital or chart display. This technique has been widely used and proven to be reliable. 8 A comparative study of stresses obtained using the established conventional technique and the new, three-point bending technique was carded out. Sample strips, 2 mm thick, die-stamped from the same moulded sheet were used. The samples were extended at the same strain rate (200 mm/min), to various extensions at room temperature (23 °C). The decay in stress was monitored for up to 100 min and results are given in Tables 3 and 4.

Stress relaxation measurement of rubber in tension

57

TABLE 3 Comparison of Stresses Obtained Using Two Different Equipment for Unfilled Synthetic Polyisoprene Rubber Vulcanisate

Strain

(~)

Stress after 100 min relaxation ( MPa) Instron 1122 °

30 42 48 70 100

0.401 0.477 0.540 0.688 0.865

New Technique b

3 5 1 4 6

0.384 7 0.460 0 0-529 5 0.674 6 0-878 6

"Stress in a rubber strip monitored using Instron Universal Testing Machine. b Stress calculated from the resolution of forces in a three-point bending configuration. TABLE 4 Comparison Between Stresses in Filled NR (65 I R H D ) at Different Time Intervals (100% extension) Obtained Using Different Equipment

Time (rain)

1 2 3 5 7 10 20 30 50 70 100 Rates (per cent per decade)

Instron 1122

New stress-relaxometer a

Average stress (MPa)

CV (%)

Average stress (MPa)

CV (%)

2-133 4 2.084 1 2.067 6 2.037 8 2.018 1 1.997 7 1.954 3 1.931 1 1.902 5 1-900 2 1.850 6

3.27 2.43 3.12 3-04 3.01 2.97 2.66 2.68 2.59 2.56 2.41

2.170 8 2.099 3 2.058 6 2.044 6 2.029 8 2.000 3 1.977 3 1.960 5 1.913 6 1.892 8 1.874 2

4-29 4.38 3-19 3.13 2-94 2.25 2.67 3-00 2-99 2-67 2-83

6.78

6.31

* Three-point bending stress relaxometer.

Table 3 gives the results for unfilled polyisoprene, a synthetic rubber having very small changes in stress with time. The value of stresses were calculated after 100rain extension, and for the strain range investigated, the stresses obtained using the two different methods were

58

A. B. Othman, C. Hepburn

within experimental variation (+5%). Comparisons were also carded out using filled natural rubber vulcanized using sulphur semi-EV system. Five repeat tests were carded out and the average stresses and their coefficient of variation (CV) values are given in Table 4. The CV for the stresses was within experimental variation ( + 5 % ) and the stresses obtained using the two different techniques of measurement were comparable. This shows that the new technique of measuring stresses in an extended rubber strip is accurate and reliable and the stress values were not significantly different from those obtained using the conventional method.

6 CONCLUSION A new technique to measure the stress in an extended rubber strip has been developed. The technique utilises the principle of trigonometry to resolve forces in the three-point bending configuration. The values of stresses obtained were observed to be comparable to those obtained using the established conventional technique. The technique is simple and it employs an inexpensive testing equipment and sample jigs. It has the advantage of being able to be used for stress-relaxation studies on a large number of samples simultaneously since the sample strip is attached to a frame which is easily detachable from the load-measuring device, and the sample is not continuously attached to the load-cell. The problem of electrical drift was also eliminated. The samples used for the study consist of thin strips of rubber and this makes the technique useful for studies on rubber subjected to difficult environmental conditions.

ACKNOWLEDGEMENTS The author (ABO) would like to acknowledge the assistance given by Mr M. N. Shafie of the Rubber Research Institute of Malaysia on the construction of the electronic controls for the equipment.

REFERENCES 1. Dunn, J. R. & Scanlan, J., A Modified Helical Spring Stress Relaxometer for Automatic and Manual Operation. J. Appl. Poly. Sci., 4 (1960) 34-7.

Stress relaxation measurement of rubber in tension

59

2. Wallace, H. W., Instruction for "The Wallace Shawbury Self-Recording Age Tester". H. W. Wallace and Company, Croydon, UK, 1971. 3. RAPRA, The Shawbury-Wallace Compression Stress Relaxometer MklI. H. W. Wallace and Company Limited, Croydon, UK, 1986. 4. Fernando, K. P., Stress Relaxation in Compression: Instruments, Measurement and Their Interpretation for Rubbers, PhD thesis, Institute of Polymer Technology Loughborough University of Technology, Loughborough, UK, 1984. 5. Armah, J. C., Birley, A. W., Fernando, K. P., Hepburn, C. & Tahir, M., Stress Relaxation Measurements of Rubber in Compression: Equipment and Methodology. Rubb. Chem. Tech., 59 (1986) 765-78. 6. ISO, Rubber Vulcanized--Determination of Stress Relaxation in Compression at Normal and Elevated Temperatures (ISO 3384). International Standard Organisation, Switzerland, 1979. 7. ISO, Rubber Vulcanized--Determination of Stress Relaxation in Compression at Normal and Elevated Temperatures (ISO 3384 revised edition). International Standard Organisation, Switzerland, 1989. 8. MacKenzie, C. I. & Scanlan, J., Stress Relaxation in Carbon Black Filled Rubber Vulcanizates at Moderate Strains. Polymer, 2,5 (1984) 559-67.