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Creep Rate of Rubber in Tension

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Background and Aim
Creep is defined as the ‘’ time-dependent and permanent deformation of materials when subjected to a constant load or stress’’ (Callister 2011, p.265). The aim of this experiment is to find the creep rate of a rubber in tension. Rubbers are classified as elastomers, elastomers are polymers which have a high degree of crosslinking and it is this crosslinking that allows elastomers to return to their original shape after deformation. Elastomers exhibit viscoelastic behaviour; viscoelastic materials have both viscous and elastic characteristics when undergoing deformation. When a load is applied to a viscoelastic material the deformation is time dependent under constant temperature, this means that the strain increases with time.
Figure 1: The creep strain behaviour of a viscoelastic material under constant stress. The strain increases with time while stress remains constant. As the load is applied the strain increases instantaneously, this is the elastic behaviour of the material. In the recovery stage the strain does not return to zero even after a considerable amount of time, this illustrates the viscous property of the material. [Diagram] At: http://dspace.jorum.ac.uk/xmlui/bitstream/handle/10949/1033/Items/T838_1_section23.html (Accessed on 25/10/2014)

A typical creep test involves subjecting a specimen to a constant load or stress while keeping the temperature constant.
Procedure
Figure 2: An illustration of the experimental set-up.
Figure 2: An illustration of the experimental set-up.
The experimental set up is detailed in figure 2 below. The linear variable differential transformer (LDVT) is an electrical transformer used for measuring linear displacement. The experiment was conducted using the following steps: * A punger was attached to the LDVT * A micrometre with an accuracy of ±0.001mm was used to measure the compression distance (0-25mm). This was then repeated 3 times. * A voltage reading was taken for the corresponding distance using a voltmeter accurate to ±0.001V. The measurements were recorded three times. * LDVT
LDVT
A mass of 0.5kg was then placed on the experimental set up shown below and the voltage was recorded after 5 second time intervals for the first 30 seconds and then after every 30seconds until 275 seconds. The time was measured using a stopwatch from an iPhone with an accuracy of ±0.01 seconds. The procedure was repeated three times. * The above procedure was then repeated with a mass of 1kg and the voltage was recorded using the same time intervals detailed above. The test was repeated twice.
Results and Analysis
In the experimental setup the strain of the rubber was measured using the LDVT, the readings given from this were voltage readings; however displacement readings are required in order to find out the strain. Therefore a calibration method must be deployed to transform the voltage into a displacement or length. To achieve this, voltage readings were taken as a gauge attached to the LDVT was compressed. The results are detailed in table 1. Compression Displacement of the Gauge/ (mm) | Voltage/ (V) | | Test 1 | Test 2 | Test 3 | Average | 0 | 1.029 | 1.030 | 1.030 | 1.030 | 5 | 0.930 | 0.931 | 0.931 | 0.931 | 10 | 0.851 | 0.851 | 0.851 | 0.851 | 15 | 3.425 | 3.431 | 3.431 | 3.429 | 20 | 7.410 | 7.410 | 7.420 | 7.413 | 25 | 11.870 | 11.890 | 11.890 | 11.883 |
Table 1: table showing the voltage associated with certain lengths as the gauge was compressed
Once this information was obtained a graph of displacement against voltage was plotted in order to determine the relationship between the two. The graph is shown in figure 3 below.
Figure 3: relationship between voltage and displacement. The important part of the graph is the linear region as it shows a proportional relationship between voltage and displacement.

The graph in figure 3 shows a linear relationship after about a distance of 15mm therefore it is this area where the information can be used to calibrate the LDVT data. The linear region is then plotted below in figure 4. Figure 4: Graph showing the linear relationship between voltage and displacement, the equation of the line and the coefficient of determination are also displayed on the graph. The line equation can be used to convert voltages to distance and the high value signifies the line is a good fit.

The line equation in figure 4 can be used to convert the voltage readings taken as a mass is loaded onto the experimental setup in figure 1 to length and hence strain values. Since there is a linear relationship between voltage and displacement/length and the equation is: 0.8454x-9.3334 (1)
This means that for any given value of voltage(y) the displacement(x) can be calculated by substituting the voltage value for y in equation 1 and finding out x.

The results obtained as the 0.5kg mass was added are detailed below in table 2. Time (s) | voltage (V) | Displacement/mm | | Test 1 | Test 2 | Test 3 | length 1 | length 2 | length 3 | Average length | 0 | 0.850 | 0.845 | 0.844 | 12.046 | 12.040 | 12.039 | 12.042 | 5 | 0.858 | 0.910 | 0.968 | 12.055 | 12.117 | 12.185 | 12.119 | 10 | 0.874 | 0.929 | 0.999 | 12.074 | 12.139 | 12.222 | 12.145 | 15 | 0.890 | 0.944 | 1.032 | 12.093 | 12.157 | 12.261 | 12.170 | 20 | 0.898 | 0.954 | 1.051 | 12.102 | 12.169 | 12.283 | 12.185 | 25 | 0.906 | 0.964 | 1.070 | 12.112 | 12.181 | 12.306 | 12.199 | 30 | 0.915 | 0.974 | 1.075 | 12.123 | 12.192 | 12.312 | 12.209 | 35 | 0.923 | 0.982 | 1.084 | 12.132 | 12.202 | 12.322 | 12.219 | 65 | 0.959 | 1.017 | 1.135 | 12.175 | 12.243 | 12.383 | 12.267 | 95 | 0.986 | 1.040 | 1.161 | 12.207 | 12.270 | 12.414 | 12.297 | 125 | 1.005 | 1.056 | 1.191 | 12.229 | 12.289 | 12.449 | 12.322 | 155 | 1.021 | 1.069 | 1.207 | 12.248 | 12.305 | 12.468 | 12.340 | 185 | 1.034 | 1.078 | 1.222 | 12.263 | 12.315 | 12.486 | 12.355 | 215 | 1.047 | 1.087 | 1.233 | 12.279 | 12.326 | 12.499 | 12.368 | 245 | 1.067 | 1.095 | 1.243 | 12.302 | 12.335 | 12.511 | 12.383 | 275 | 1.076 | 1.102 | 1.251 | 12.313 | 12.344 | 12.520 | 12.392 |
Table 2: data recorded after a mass of 0.5kg was added, the lengths have been calculated from the measured voltage using the linear relationship between displacement and voltage indicated by equation 1

A mass of 1kg was then added to the experimental setup and the data was recorded in a table as shown in table 3. Time (s) | Voltage (V) | Displacement/mm | | Test 1 | Test 2 | length 1 | length 2 | Av length | 0 | 1.115 | 1.251 | 12.359 | 12.520 | 12.440 | 5 | 3.023 | 3.314 | 14.616 | 14.960 | 14.788 | 10 | 3.119 | 3.377 | 14.730 | 15.035 | 14.882 | 15 | 3.275 | 3.424 | 14.914 | 15.090 | 15.002 | 20 | 3.287 | 3.446 | 14.928 | 15.116 | 15.022 | 25 | 3.319 | 3.479 | 14.966 | 15.155 | 15.061 | 30 | 3.346 | 3.503 | 14.998 | 15.184 | 15.091 | 35 | 3.378 | 3.527 | 15.036 | 15.212 | 15.124 | 65 | 3.487 | 3.611 | 15.165 | 15.312 | 15.238 | 95 | 3.559 | 3.659 | 15.250 | 15.368 | 15.309 | 125 | 3.612 | 3.698 | 15.313 | 15.414 | 15.364 | 155 | 3.651 | 3.726 | 15.359 | 15.448 | 15.403 | 185 | 3.684 | 3.751 | 15.398 | 15.477 | 15.438 | 215 | 3.714 | 3.771 | 15.433 | 15.501 | 15.467 | 245 | 3.740 | 3.787 | 15.464 | 15.520 | 15.492 | 275 | 3.761 | 3.804 | 15.489 | 15.540 | 15.514 |
Table 3: recorded data when a mass of 1kg was added to the set-up.

From the obtained data in table 2 when a mass of 0.5kg was added the strain against time graph can be plotted.

Figure 5: strain versus time graph when a mass of 0.5kg was added.

Similarly the strain time graph for a mass of 1kg can be plotted from the data in table 3 and is illustrated below.

Figure 6: increase of strain with time as 1kg constant load was applied
Creep results can be represented as a time dependent creep modulus defined as; ECt= σ0ϵt (2)
Therefore for this experiment the time dependent creep modulus could be calculated for both the 0.5kg load and 1 kg load. The dimensions of the rubber before elongation were taken and recorded as shown in table 4. Dimensions/mm | Test 1/mm | Test 2/mm | Test 3/mm | Average/mm | Length | 11.71 | 11.71 | 11.71 | 11.71 | Thickness | 0.24 | 0.38 | 0.31 | 0.31 | Width | 0.19 | 0.19 | 0.19 | 0.19 |
Table 4: Dimensions of unloaded rubber
The cross sectional area of the rubber can therefore be calculated to be 5.89 × 10 -8m2. Consequently the stress for the 0.5kg mass is σ= FA=0.5×9.8 0.002174609= 2253.278739Nm-2. The stress for a 1kg mass is 1×9.80.002174609= 4506.557478Nm-2.
The time dependent strain will be taken as the strain after 275seconds which is 12.392 and 15.514 respectively for the 0.5kg load and 1kg load.
The time dependent creep modulus for the 0.5kg and 1kg load is therefore;
Ect(0.5kg)= 2253.2787390.012392=182 MPa
Ect1kg= 4506.5574780.015514=290 Mpa

Discussion
The graphs in figure 5 and 6 show the creep behaviour that is expected for an elastomer as a constant load is applied under constant temperature (shown in figure 1 above). They both show an instantaneous increase in strain as soon as the load is added. After the initial rapid increase in strain the strain then increases slowly with time as would be expected for a rubber - an elastomer. The strain in Figure 6 varies less with time compared to the graph in figure 5; this could be due to the applied load. The applied load in the graph in figure 6 is higher than the one in figure 5. This can be explained by the structure of polymers, initially the polymer chains are entangled and as a load is applied the chains start to straighten and align. As the chains straighten there are less entangled chains left therefore the rubber doesn’t stretch as much and hence strains very slowly and by a small amount.
Conclusion
The test was successful in showing the creep rate of rubber under a constant stress as the graphs and results were consistent with expected behaviour for a rubber. The graphs were particularly useful as they showed the initial increase in strain and the general shape expected as time increased. The test could be improved by having an automated system for measuring the voltage after the time intervals as that reduces errors such as human reaction time.
References
1. Callister. M.D, Rethwisch. G (2011). Materials Science and Engineering. 8th ed. Asia: John Wiley and Sons. p265, 574-578. 2. http://dspace.jorum.ac.uk/xmlui/bitstream/handle/10949/1033/Items/T838_1_section23.html (Accessed on 25/10/2014) 3. http://www.jameswalker.biz/en/pdf_docs/148-elastomer-engineering-guide (Accessed on 25/10/2014)

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...SAT WRITING ESSENTIALS SAT WRITING ESSENTIALS ® NEW YORK Copyright © 2006 LearningExpress All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by LearningExpress, LLC, New York. Library of Congress Cataloging-in-Publication Data: Starkey, Lauren B., 1962– SAT writing essentials / Lauren Starkey. p. cm. ISBN 1-57685-532-5 1. English language—Composition and exercises—Examinations—Study guides. 2. SAT (Educational test)—Study guides. I. Title. LB1631.5.S785 2006 378.1'662—dc22 2005027520 Printed in the United States of America 987654321 ISBN 1-57685-532-5 For more information or to place an order, contact LearningExpress at: 55 Broadway 8th Floor New York, NY 10006 Or visit us at: www.learnatest.com About the Author Lauren Starkey is a writer and editor who specializes in educational and reference works. Her thirteen years of experience include eight years on the editorial staff of the Oxford English Dictionary. The author of more than ten volumes, Lauren lives in Essex, Vermont, with her husband and three children. v Contents CHAPTER 1 Getting to Know the Writing Section of the New SAT Old versus New Strategies for Test Taking Scoring SAT Study Timetable 1 1 2 4 5 11 12 32 45 55 56 58 59 59 65 68 69 CHAPTER 2 The Multiple-Choice Section Identifying Sentence Errors Improving Sentences Improving Paragraphs CHAPTER 3 The Essay Strategies for Timed Essays Understanding the Prompts...

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