The objectives are: (1) to demonstrate tensile testing of materials and the application of the concepts of stress and strain; and (2) to yield a mathematical relationship between stress and strain for many artificial rubbers and plastics. The experiment, supplies, and procedure are presented

Allen, David J.

English

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STRESS-STRAIN C CTERISTICS OF RUBBER-LIKE 
MATEIHALS: EXPERWENT AND ANALYSIS 
David J. Allen 
School of Engineering Technology 
Northeastern University 
120 Snell Engineering Center 
Boston, Massachusetts 02115 
Telephone 6 17-437-2500 
https://ntrs.nasa.gov/search.jsp?R=19920021042 2020-03-17T11:25:38+00:00Z
STRESS-STRAIN CHAJXACTERISTICS OF RUBBER-LIKE MATERIALS: 
EXPERIMENT AND ANALYSIS 
David J. Allen 
School of Engineering Technology 
Northeastern University, Boston, Massachusetts 
KEY WORDS: rubber, neoprene, stress, strain, elasticity, 
tensile test, power equation. 
PREREQUISITE KEJOWLEDGE: The student should understand 
the concepts of stress and strain either previously or 
concurrently presented with experiment. 
OBJECTIVES: To demonstrated tensile testing of materials 
and the application of the concepts of stress and strain. To 
introduce a method of analysis of curvilinear data which will 
yield a mathematical relationship between stress and strain 
for many artificial rubbers and plastics. 
EQUIPMENT AND SUPPLIES: (1) No. 32 or No. 64  rubber 
(neoprene) bands; (2) Two S hooks approximately 5  cm long; ( 3 )  
One screw eye; ( 4 )  Lumber as required; ( 5 )  mm scale; ( 6 )  
micrometer; (7) Calibrated weights; (8) Log-log paper; (9) 
calculator. 
PROCEDURE: The students may either design their own 
testing apparatus or make one similar to the one shown in 
figure 1. If they design their own, design factors such as 
the amount of space required should be discussed, 
Students make a pair of gage marks near the middles of 
each side of a rubber band and measure the length between each 
pair of marks. These measurements are the initial unstrainied 
length, Lo. The thickness and width at each gage section is 
also made which will yield the initial cross sectional are.a, 
Ao. TWO sets of data are made from each test. 
The test is conducted by placing the specimen in the 
testing apparatus and adding incrementally calibrated weights, 
The length between the gage marks are'measured for each load, 
Optionally, the thickness and the width of the rubber band may 
be measured at each loading. The test is conducted to failure, 
Once the data is collected the students begin their 
analysis. The engineering stress may be computed from 
where a is the engineering stress and P is the load on the 
section. It is important not to forget that P is one half of 
the applied load since there are two sides of the rubber band. 
If the actual thickness, tACTUAL, and width, wACTUAL, are measured 
for each loading, the true stress can be determined from 
301 
PRECEDING PAGE BLAFiK PJOT FILMED 
where the actual cross sectional area is 
Strain is computed from 
where AL is the change in length from the original undeformed 
lengtlh to the one being computed. 
SCRNII EYE 
RUBBER BAND 
GAGE LENGTH 
S HOOK 
WEIGHTS 
I 1 
Figure 1 
'The stress and strain values are plotted on an arithmetic 
graph and a smoothed best fit curve is drawn. Typical results 
are shown in figure 2. Note that the curve is nonlinear. 
It would be useful to obtain a mathematical relationship 
between stress and strain but one is not readily apparent from 
figure 2. However, if the data are plotted on a log-log plot 
as shown in figure 3, the best-fit curve is obviously a 
straight line. 

The equation of a straight line takes the form of 
but since the graph is log-log the equation needs to be 
modified to 
lny=m-lnx+ lnb (6) 
or in terms of the stress-strain relationship 
lna =m.lne+lnb (7) 
which only leaves the determination of parameters m and b once 
the best-fit line is drawn. 
The slope, m, of the curve can be determined by choosing 
two arbitrary coordinates on the best-fit curve, say (€,,a,) 
and (~,,a,). The slope can now be defined as 
Once the parameter m has been computed from equation 8 
the parameter b can be determined. Reorganizing equation 7 
results in 
lnb= lna -m.lne (9 1 
Subskituting the arbitrary coordinates, (~,,a,) and 
  into equation 9 allows b to be computed from 
lnb = Inax-malne, = ha,-m-lne, (10) 
The value of lnb can be evaluated two different ways in 
eqhlation 10. This gives a check of the computations. Utilizing 
the Laws of logarithms equation 7 can be written as 
lna =lnem+lnb (11) 
This is the form called the power equation. Data whose plots 
show a straight line best-fit relationship on log-log graphs 
can be represented mathematically by equation 13. Using the 
above method on the data shown in figure 3 yields 
Many materials and systems will follow a power equation and it 
is worthwhile to make a log-log plot of data points following 
a curvilinear trend on an arithmetic plot. Allen and Phalen2 
extend this approach to the artificial rubbers used in single- 
ply roof systems. 
For a more thorough treatment true stress utilizing 
equation 2 versus strain may be analyzed. Arithmetic and log- 
log plots and the corresponding best-fit curves and equations 
for true stress vs. strain are compared with the engineering 
stress analysis given above. 
SELE%PLE DATA SWEETS: Self-Evident. 
INSTRUCTOR NOTES: Having the students design and build 
their own testing apparatus is a good project. The student8s 
interest and creativity is harnessed which results in a better 
appreciation of experimentation. A thorough discussion of 
factors involved in experimental design should be made without 
dampening the student" creativity. One student used rolls of 
pennies as weights and obtained good results. Ideas should be 
encouraged even though they may lead to unsatisfactory 
results. This provides a fertile ground for discussion. 
Some computer graphing and statistical programs provide 
linear regression analysis. They may use the tern vfgeometricBg 
equation rather than "powerm equation. Even if computer 
programs are available it is recommended that the student do 
the graphing and analysis by hand computations to reinforce 
the concepts introduced. The computer can be used as a check. 
This experiment also gives the students a better 
understanding and a physical "feel" of the concepts of stress 
and strain than that obtained by using a steel specimen in a 
testing machine. The large strains and applied loads are 
readily apparent. 
REFERENCES: 
(1) Giesecke, F.E., et.al., Engineering Graphics, Third 
ed., 1981, New York 
(2) Allen, D.J., and T.E. Phalen Jr.,"Stress-Strain 
Characteristics for EPDM, CSPE, and PVC for the 
Development of Stresses in Membranes Utilized as 
Single-Ply Roof Systems"",rroeeding of the 1991 
International Symposium on Roofing Technology, 1991 
SOURCES OF SUPPLY: A well stocked hardware store or home 
center can supply the materials needed for the testing 
apparatus. 


Stress-strain characteristics of rubber-like materials: Experiment and analysis

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