Methods
Two series of tests were conducted
to determine if crosshead extension can be used to calculate strain.
All tests were based upon ASTM D638. The first series of tests compared
the results of four different testing variations all conducted at
the same strain rate of 1/min. The purpose of this test was to verify
that stress, strain, and extension data are independent of test
specimen type and method of extensometry, and that the test methods
accurately represent the material properties. Table 1 provides details.
ASTM D638 Type I specimens are most commonly used for conventional
tensile testing; the ASTM D1822 Type L specimens are preferred for
high strain work because their reduced cross sectional area allows
higher strain rates to be reached using the same speed that would
be applied to a type I specimen at a lower strain rate.
These tests were designed to show
that type L specimens behave in the same manner as type I specimens
and that video extensometers give the same results as clip on extensometers.
One variable was changed at a time so that any difference in the
results could be attributed to that variable. The video extensometer
was set to twenty-five acquisitions per second. The results of these
four tests are plotted on Figures 1 and 2. Figure 1 shows nominal
strain (crosshead displacement divided by gauge length) versus measured
strain. Figure 2 shows stress versus measured engineering strain.
Measured strain (ε) is calculated by dividing the change
of gauge length (ΔL) by the initial gauge length (L).
ε = ΔL / L (1)
If it is necessary to establish a
relationship between extension and strain for two different types
of test specimens then the different gauge lengths of the specimens
need to be taken into account. If both specimen types are stretched
an equal distance the strain calculated for the type I specimen
will be five times smaller than the strain calculated for the type
L specimen because the gauge region is five times larger. In order
to compare the strains of the two different specimens a scaling
factor of five is needed. The strains from the type I specimens
must be multiplied by five, thus changing the effective gauge region
of the
samples from 50mm to 10mm.
Once the effective gauge region has been normalized the type L and
type I specimens can be compared directly.
The second series of tests were conducted
to determine how strain correlates to crosshead displacement at
varying strain rates. These tests were conducted using only type
I specimens. Type I specimens were tested at 0.1/min, 1/min, and
10/min which covers the range of strain rates that were possible
on UTM1. Nominal strain versus measured strain was plotted to see
if the curves at different strain rates would overlap therefore
showing that the relationship between crosshead extension and strain
was independent of strain rate. Finally a test was run on UTM2 using
type L test specimens without and extensometer.
Results
Figures 1 and 2 show that for all
four testing methods the relationship between nominal strain and
engineering strain is the same. The relationship holds well up to
the yield point; after yield the graphs do not correlate as well.
Explanations for this occurrence include the video extensometer
losing sight of the gauge region, the clip extensometer slipping,
or variable post yield behavior.
The second series of tests takes the
relationship between extension and strain one step further to show
that strain can be calculated from crosshead displacement at any
strain rate. Since the different testing methods all produced the
same result at one strain rate only one of the testing methods was
needed for testing at multiple strain rates. The type I specimens
were tested at 0.1/min, 1/min, and 10/min and the results were plotted.
Figure 3 shows nominal strain
versus strain at different strain rates. For each of the strain
rates the curves line up showing that strain and extensometer extension
relate in the same way regardless of strain rate. Figure 4 shows
the Stress versus Strain curves at varying strain rates. These plots
show that for this material the maximum stress occurs at the same
strain value every time but that the yield stress increases as strain
rate increases. To obtain high strain rate properties specimens
were tested first on the UTM1 using clip-on extensometer to find
how strain relates to crosshead displacement. Using the data from
that test a polynomial was fit to relate strain to crosshead displacement.
Using the polynomial fit curve, strain measurements were obtained
using crosshead displacement data from the high speed experiment.
Results are shown in Figure 4, graph labeled polynomial.
Figure 5, an Eyring plot, shows that as strain
rate increases the maximum value of the stress also increases in
a linear fashion.
Conclusions
These tests show that an extensometer
can be used to establish the relationship between crosshead extension
and strain. An extensometer must be used to find the strain values
that correlate to a given crosshead extension. Once this correlation
is made an extensometer is no longer necessary provided that the
relationship between crosshead displacement and strain is independent
of strain rate. For the polycarbonate tested, the relationship between
strain and crosshead extension is independent of specimen type,
extensometry and strain rate. As a result tests of type I specimen
and type L specimen can be compared directly. Tests can be run using
both specimen types for instance, a type I specimen can be used
to find the relationship between crosshead extension and strain
and then further testing can be conducted using a type L specimen
without an extensometer.
After peak stress, (yield point) is
achieved the correlation between nominal strain and measured strain
is not as good. This is because after the yield point the measured
strain values for the different testing methods vary greatly. These
variations result from error in extensometry and may be caused by
extensometer slip or by deterioration of the markings used for the
video extensometer. Only fair correlation could be obtained in the
post yield region.
A variable that can affect the
relationship between crosshead extension and strain is temperature.
These tests were conducted at constant room temperature, 23°C;
therefore they do not demonstrate any correlation between crosshead
extension and strain at variable temperatures. Further, it needs
to be shown that this methodology applies to plastics other than
polycarbonate.
Equipment
UTM1: Instron 5566 servo-mechanical
Universal testing machine.
UTM2: Instron 8872 servo-hydraulic universal testing machine
Clip Extensometer: Instron 2630-100, 2in linear clip-on extensometer
Video Extensometer: Hitachi KP-M2U
Acknowledgements
We wish to thank Professor Alan Zehnder, Cornell
University for his advice and expertise. Thank you to Mr. Brian
Croop, DatapointLabs for consulting with us during the testing phase
of our project. Thank you to Mr. Brian Lussier, DatapointLabs for
running many of the tests necessary to complete this study.
References
.
1. Lobo, H., Lorenzo, J., “High Speed Stress-Strain
Material Properties As Inputs For The Simulation Of Impact Situations,”
IBEC, Stuttgart, Germany (1997).
2.Grimson, A., Sinopoli, M., Lobo,
H., Fedewa, B., “Evaluation of High Strain Rate Test Methods
of Thermoplastic Polyolefins Used for Automotive Interior Structural
Analyses,” SPE TPO Conference, Detroit, (2003).
3. Croop, B., “Developing
Material Model Parameters for Impact Simulation of Plastics and
Foams,” ABAQUS User’s Conference, Boston (2004).
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