mechanical laboratory 2 lab #9: torsion test
TRANSCRIPT
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Mechanical Laboratory 2
Lab #9: Torsion Test
Ante Kulas
MMAE-419-L01
Professor: Dr. Murat Vural
TA: George Kim
11/02/2018
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ABSTRACT:
In process of determining if structure or system is sustainable for service torsion testing plays major role. The purpose of torsion testing is to introduce students to mechanical properties of for metals while in shear. Load is applied to the steel, aluminum and brass specimens until they fractured. Students were able to determine offset torsional yield strength, proportional limit, modulus of rupture,
modulus of rigidity and ductility for materials from torque and angle that was recorded. Understanding
of mechanical properties of material is crucial for engineering because choosing right material for design
will decide if design will give optimal results and minimize failure of systems and machines.
INTRODUCTION:
Main goal of this lab is better understanding of mechanical properties of metals by determining offset
torsional yield strength, proportional limit, modulus of rupture, modulus of rigidity and ductility for
materials from torque and angle that was recorded. Four materials were tested, structural steel
1045HR,1018HR, aluminum 6061-T6 and naval brass. After testing was done data for time, torque and
angle was recorded and from there mechanical properties were calculated. First step of calculations
included translating data for angle that was recorded in degrees to radians and it was called angle of
twist and notation for it was Οβ. Same thing was done for done with torque since data was translated
from ft-lb to in-kip and notation for it is T. To calculate central difference slope for each point equation
(1) was used, where i represent position of each point and N represent how far is upper and lower
position of data.
π π»
π πβ²(
πͺπ«
) = π»(π+π΅)βπ»(πβπ΅)
πβ²(π+π΅)βπβ²(πβπ΅) (1)
After central difference is found that have notation π π» , average central difference slope was found for
each data point by using equation (2), where n is number of central difference slope data points to take
average of N and n should be carefully picked because too small or too large will not help in smoothing
curve and may have contra effect. For most parts it was found that optimal N was around 20, and
optimal n was around 15.
π π»
π πβ²(
πͺπ«πππ
) = β
π π»
π πβ²(πͺπ«
)(π)π+ππ=πβπ
ππ+π (2)
Than re-constructed torque was found using (3) and plotted in Figures 10, 14, 18 and 22 v. angle of
twist per unit length, where π π»π is average central difference slope.
π»(π) = π»(πβπ) + π π»π(πβπ) β βπβ²(π) (3)
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Both slopes, π π»π and π π» were plotted with respect to angle of twist per unit length in Figures 11, 15,
19 and 23 and later were compared. Shear strain was calculated using equation (4), where r is radius of
specimen.
πΈ = π β πβ² (4)
Shear stress for elastic part is calculated using equation (5) and for plastic part is calculated using (6),
and both shear stresses were plotted vs. shear strain in Figures 12, 13, 16, 17, 20, 21, 24 and 25.
D stands for outside diameter of specimen.
ππππ = ππ β π΄π»
π β π«π (5)
π = π
πβπ βππ β [π β π π»π + ππ΄π»] (6)
PROCEDURE:
Torsion test machine (Figure 1) had one head that is stationary and other that is applying twisting
moment (torque) to specimen. Dimensions of specimens are shown in (Figure 2-3). On each specimen
two marks were placed with distance between them being two inches and it was gage length. Specimen
was placed in torsion machine and torque sensor is placed on specimen. Machine was then calibrated,
and twisting moment was applied. Experiment was repeated for four materials (structural steel
1045HR,1018HR, aluminum 6061-T6 and naval brass) and data for time, torque and angle was recorded
and from there mechanical properties were calculated. Specimens fractured surface can be sin in
(Figures 6-9), and on Figure 4 (1018HR steel and naval brass).
Figure 1. Experiment setup
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Figure 2. Specimen dimensions Figure 3. Specimen after fracture
Figure 4. Fractured specimens Figure 5. Torque sensor
Figure 6. 1045HR steel Figure 7. 1045HR steel Figure 8. 6061 AL Figure 9. Naval brass
RESULTS:
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Figure 10. a) Torque vs. twist angle (1045 HR Steel) b) detailed
Figure 11. a) Slope vs. twist angle (1045 HR Steel) b) detailed
Table 1. Calculated and collected values for 1045HR Steel
Offset torsional yield strength [ksi] 28.19
Proportional limit [ksi] 61.56
Modulus of rupture [ksi] 82.12
Modulus of rigidity [ksi] 25622
Ductility (Ξ³) at fracture) [%] 26.27
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Figure 12. Shear Stress vs. Shear Strain (1045 HR Steel) plot
Figure 13. Shear Stress vs. Shear Strain (1045 HR Steel) detailed plot
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Figure 14. a) Torque vs. twist angle (1018 HR Steel) b) detailed
Figure 15. a) Slope vs. twist angle (1018β]\ HR Steel) b) detailed
Table 2. Calculated and collected values for 1018HR Steel
Offset torsional yield strength [ksi] 20.24
Proportional limit [ksi] 46.72
Modulus of rupture [ksi] 64.56
Modulus of rigidity [ksi] 26959
Ductility (Ξ³) at fracture) [%] 56.8
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Figure 16. Shear Stress vs. Shear Strain (1018 HR Steel) plot
Figure 17. Shear Stress vs. Shear Strain (1018 HR Steel) detailed plot
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Figure 18. a) Torque vs. twist angle (6061 Aluminum) b) detailed
Figure 19. a) Slope vs. twist angle (6061 Aluminum) b) detailed
Table 3. Calculated and collected values for 6061Aluminum
Offset torsional yield strength [ksi] 18.75
Proportional limit [ksi] 24.7
Modulus of rupture [ksi] 34.11
Modulus of rigidity [ksi] 8727
Ductility (Ξ³) at fracture) [%] 42.44
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Figure 20. Shear Stress vs. Shear Strain (6061 Aluminum) plot
Figure 21. Shear Stress vs. Shear Strain (6061 Aluminum) detailed plot
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Figure 22. a) Torque vs. twist angle (Naval Brass) b) detailed
Figure 23. a) Slope vs. twist angle (Naval Brass) b) detailed
Table 4. Calculated and collected values for Naval Brass
Offset torsional yield strength [ksi] 19.06
Proportional limit [ksi] 35.55
Modulus of rupture [ksi] 55.79
Modulus of rigidity [ksi] 13602
Ductility (Ξ³) at fracture) [%] 28.52
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Figure 24. Shear Stress vs. Shear Strain (Naval Brass) plot
Figure 25. Shear Stress vs. Shear Strain (Naval Brass) detailed plot
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DISCUSSION:
When torsion from rough data is compared to re-constructed it is clear that reconstructed is smoothed
out version of rough data and it is more usable for further usage. Same goes with plots of central
difference slope and average central difference slope vs, angle of twist per unit length it is clear that
averaged slope is more usable since smoothed out. How much it is to be smoothed depends on values N
and n. Finding optimal values of those values is crucial to get plot smooth enough without ruining data.
Elastic and plastic shear stress vs. shear strain was plotted on the same plot even it is clear that elastic
part is correct only during elastic deformation, and plastic after that. Linear curve fit was done in linear
part of elastic shear stress plot so 2% line can be fitted and from there offset torsional yield strength can
be found so as modulus of rigidity (from slope of fitted line). Transition between plastic and elastic part
of plot is where proportional limit can be found. Modulus of rupture can be found just by finding
maximum shear stress in plastic plot. Ductility (Ξ³ at fracture) is shear stress in the moment when fracture
starts to happen.
CONCLUSION:
This lab gives students some inside on how different materials (structural steel 1045HR,1018HR,
aluminum 6061-T6 and naval brass) react under torsional load, and how it is possible to find material
properties that include offset torsional yield strength, proportional limit, modulus of rupture, modulus of
rigidity, ductility (shear strain at fracture) from data collected.
REFERENCES:
Mechanical Behavior of Materials 4th Ed. by Norman E. Dowling (Pearson, 2013 ISBN 0-13-139506-8)
Dr. Murat Vural, MMAE 419 Torsion Testing Handout, IIT, Chicago