DISCUSION, CONCLUSIONES Y RECOMENDACION
5.1.1 Visión Global de la Ciencia Contable
The quality of results obtained from an FEA simulation strongly depend on the experimental
test data provided; Such an experimental test requires a material specimen to be subjected
to a load such as tensile, compression and shear from which stress-strain characteristics of
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out in this work for the purpose of characterising the behaviour of the lip seal material, when
subjected to tensile and compressive loads. In the case of the compression test, two different
test routines are adopted. In the first, the elastomer is constrained within a cup to explore the
bulk behaviour of elastomer and in the second, it is allowed to deform freely without any
constraint to obtain its properties.
An NBR is used as the elastomeric test sample, because it is the most widely used in seal
industries, due to its moderate cost, excellent resistance to oils, fuels and greases over a wide
range of temperature. It also possesses a very good resistance to swelling by aliphatic
hydrocarbons and is easy to process (Horve, 1996). The test specimens are shown in Figure
4.1 and 4.2.
Figure 4.1 Tensile test specimen (A) Physical model (B) CAD model, all dimensions in mm
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Figure 4.2 Compression test specimen (A) Physical model (B) CAD model, (all dimensions in
mm) (C) Cup (D) Plunger
The uniaxial test performed in this study was conducted at room temperature on an “INSTRON 3369”, a type of laser scanning extensometer which enables a non-contact strain measurement within the specimen during loading. The test machine crosshead speed was set
on 10𝑚𝑚/𝑠 to properly capture the stress-strain data of the specimen as it deforms. The elongation was automatically recorded on a host computer via the machine, through a data
acquisition Analogue to Digital Converter (ADC) every 10 𝑚𝑠𝑒𝑐𝑠 as the test commenced for both the tensile and compression test.
Figure 4.3 Experimental setup for tensile test
B C D
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Figure 4.4 Experimental setup for compression test (A) constrained (B) unconstrained
4.2.1 Tensile Test Result
For the tensile test, three tests were carried out on three NBR samples of the same dimensions
(Figure 4.1). The samples were subjected to an extension of 155%, and the stress-strain plot
obtained from one of the samples is shown in Figure. 4.5. Appendix B presents a plot of the
test result from three samples. From the graph, it can be seen that all the three samples have
very close slope value.
The graph in Figure 4.5 can be seen to exhibit a nonlinear curve (typical of an elastomer),
similar to what is obtained in (Crawford, 2002). The test was terminated when the maximum
strain value 155% as suggested in (James, 2013).
The test data obtained from the experiment were supplied to Abaqus® and a material
evaluation was carried out to determine the stability of the models available in the material
library, using a curve fitting approach. The evaluated plots are shown in Figure 4.6- 4.11 while
the parameters for stability evaluation are shown in Figure 4.12- 4.17. The material constant
for various hyperelastic models are shown in Table 4.1.
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Figure 4.5 Stress-strain curve of NBR test specimen at 155% tensile strain.
Figure 4.6 Tensile test curve vs. evaluated Mooney-Rivlin model. Nominal stress in Pa 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0 20 40 60 80 100 120 140 160 180 200 En gi n ee ri n g Str ess (M P a) Engineering Strain (%)
stress-strain curve
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Figure 4.7 Tensile test curve vs. evaluated Polynomial N2 model. Nominal stress in Pa
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Figure 4.9 Tensile test curve vs. evaluated Neo-Hooke model. Nominal stress in Pa
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Figure 4.11 Tensile test curve vs. evaluated Arruda-Boyce model.Nominal stress in Pa
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Figure 4.13 Evaluated tensile test data for stability check; Polynomial-N2 model
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Figure 4.15 Evaluated tensile test data for stability check; Neo-Hooke model
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Table 4.1 Material parameters for stable hyperelastic model of NBR at 155% tensile strain
Model Stability
status
Constants for stable models
Mooney Rivlin Stable
D1 C10 C01
0.0000 282213.482 722702.292
Ogden, N = 1 Stable
𝐼 MU_I ALPHA_I D_I
1 2063524.38 0.243512165 0.0000 Neo-Hooke Stable D1 C10 C01 0.0000 683799.451 0.0000 Yeoh Stable D1 C10 C01 D2 C20 C11 C02 D3 C30 C21 C12 C03 0.0000 979872.428 0.0000 0.0000 -157646.765 0.0000 0.0000 0.0000 19222.4063 0.0000 0.000 0 0.000
Arruda Boyce Stable
MU MU_0 LAMDA_M D
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4.2.2 Compression Test Result
For the compression test, the constrained NBR sample was seen to exhibit an incompressible
characteristic, until the test sample filled up the gland and began to leak out hence the sudden
change in the straight line shown in Figure 4.18. The initial straight line can be attributed to
the incompressibility of the model, discussed in section 3.6. For an elastomer under such
hydrostatic pressure, the volume of the material cannot change under this load (Abaqus,
2012).
In the case of the unconstrained sample, two different samples were tested, both having the
same diameter but different height (10.5mm and 19.5mm). The sample was made longer than
each other because of the effect of buckling that may arise in the longer specimen. They were
allowed to deform freely, in order to obtain data about elastomeric subjected to compressive
load. Rotary seals are usually compressed to approximately 28% real in their working
condition (James, 2013). However, for a more conservative characterisation, the compression
test in this study was carried out up to 44%.
The stress strain data for the unconstrained NBR of height 10.5mm is provided in Figure 4.19.
The test result of the other sample is presented in Appendix C. The data obtained from the
unconstrained sample test (10.5mm) is employed in this study because of its small size,
therefore eliminating the possibility of buckling. The sample was evaluated in a similar manner
to the tensile test carried out earlier. However, a negative sign convention was used to specify
to the software that the data supplied are in compression. The curve fitting data and material
evaluation for stability are provided in Figure 4.20-4.26 and Figure 4.27-4.33. The material
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Figure 4.18 Stress-strain curve of constrained NBR test specimen in compression.
Figure 4.19 Stress-strain curve of unconstrained NBR test specimen (10.5mm) at 44%
compressive strain. -60.00 -50.00 -40.00 -30.00 -20.00 -10.00 0.00 10.00 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 N o m in al st re ss (M Pa) Nominal strain
stress-strain
-6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00 -0.5 -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 N o m in al C o m p re ssi ve Str e ss (M Pa) Nominal Strainstress-strain
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Figure 4.20 Compression test curve vs. evaluated Arruda-Boyce model.Nominal stress in
Pa
Figure 4.21 Compression test curve vs. evaluated Mooney-Rivlin model.Nominal stress in
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Figure 4.22 Compression test curve vs. evaluated Neo-Hooke model.Nominal stress in Pa
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Figure 4.24 Compression test curve vs. evaluated Polynomial-N2 model.Nominal stress in Pa
Figure 4.25 Compression test curve vs. evaluated Van-Der-Waals model.Nominal stress in Pa
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Figure 4.26 Compression test curve vs. evaluated Yeoh model.Nominal stress in Pa
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Figure 4.28 Evaluated compression test data for stability check; Polynomial-N2 Model
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Figure 4.30 Evaluated compression test data for stability check; Neo-Hooke Model
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Figure 4.32 Evaluated compression test data for stability check; Arruda-Boyce Model
`
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Table 4.2 Material parameters for stable hyperelastic model of NBR at 44% compression