Howard University
Washington, D.C.
Department of Mechanical Engineering
Torsion Testing
(Lab #5)
by
Apayo Apayo
for
Professor H.A. Whitworth
April 5, 2021
Abstract:
In this study, various specimens are subjected to torque until failure in order to examine
properties. These specimens include 0.1 Carbon Steel (Drawn), 0.1 Carbon Steel (Normalized),
0.4 Carbon Steel (Drawn), 0.4 Carbon Steel (Normalized), Cast Iron Grey Steel, and Half-Hard
Brass rods. A torsion test was performed in order to determine the mechanical properties of these
materials. The results from these tests displayed lower results than the accepted values for shear
modulus all around, some significantly so. Steel and brass were found to be ductile, while iron
was brittle.
Introduction:
Cast Iron is an alloy refined from iron that has the carbon removed. It is stronger and is
less fragile than the original material. It can also endure and evenly distribute heat. Gray cast iron
will contain higher levels of sulfur and manganese, and will have a lower tensile strength and
very low ductility. It is a ferrous alloy, being made with carbon and silicon. Steel is another alloy
of iron that contains carbon. The amount of carbon present is directly proportional with the
tensile strength, whereas it is inversely proportional with ductility. Typically, steel will have a
low carbon percentage (“H.A. Whitworth, Solid Mechanics Lab: Torsion Testing, Spring
2021”). There are two relevant refinement processes for steel, cold working (drawn) and
normalizing. Cold working is when a metal is strengthened without utilizing heat, resulting in a
permanent change to the crystal structure and increase in strength. Normalizing is when a metal
is hated to under the melting point and cooled in air to increase ductility. Normalized materials
have greater ductility, whereas cold working reduces it. Brass is a metal formed with copper and
zinc. It is a non ferrous alloy, meaning it does not contain any iron. It has increased hardness and
strength compared to copper, but still lower than steel. However, it is more ductile than steel.
Half Hard brass is more rigid and stronger than the original material. Torsion tests allow one to
determine mechanical properties such as ductility, torque, shear modulus, shear stress, shear
strain, torque at yielding, and stress at yielding. Ductile materials typically fail in shear and break
along the perpendicular axis. Brittle materials tend to be weaker in tension than shear, so it
usually breaks in the direction of the most tension.
Experimental Procedure & Results:
The apparatus required for this experiment were the Tecquipment Torsion testing
machine, the 6 testing specimens ( 0.1 Carbon Steel (Drawn), 0.1 Carbon Steel (Normalized), 0.4
Carbon Steel (Drawn), 0.4 Carbon Steel (Normalized), Cast Iron Grey Steel, and Half-Hard
Brass rods), VDAS software, and calipers. The torsion tester was fitted with a safety shield and a
fixed end with a load cell. The free end was supported by a bearing to measure rotation/twist,
and the wheel turned along with the shaft. After measuring the dimensions of the rods (diameter,
overall length, gauge length), the different metal bars were tested until failure. The angle of twist
was applied manually, the wheel being gently turned at a constant rate in order to have even data
collection. The data at failure was observed and recorded. The process was repeated for every
rod.
[See Appendix]
0.1 Carbon Steel Normalized
0.4 Carbon Steel Drawn
0.4 Carbon Steel Normalized
Gray Cast Iron
Half Hard Brass
Discussion of Results:
--0.1 Carbon Steel (Drawn)--
Ultimate Torque
The ultimate torque can be seen at 0.83462 radians, and is equal to 21.62 N-m.
Shear Modulus
1.
θ=(TL)/(GJ)
1.1.
G=(T/θ)*(L/J)
1.1.1.
G=Modulus of Rigidity
1.1.2.
T=Torque
1.2.
1.1.3.
θ=Theta
1.1.4.
T/θ=slope of linear region
1.1.5.
L=Gauge Length
1.1.6.
J=Polar moment of inertia
G=(98.133)*(76.87/130.66)
1.2.1.
57.7337 GPa
1.2.2.
Percent error
1.2.2.1.
Accepted: 79 GPa
1.2.2.2.
26.9%
Yield Torque
Intercept at (0.24647, 20.26152051) which shows torque at yielding to be 20.26
N-m(Newton-meter).
1.
Shear Modulus
1.1.
61,834 MPa
1.2.
= 61.834 GPa
1.3.
Percent Error
1.3.1.
2.
Shear Stress at yielding
2.1.
3.
21.7%
501.57 MPa
Ultimate Shear Strength
3.1.
499.7 MPa (See Appendix for data)
--0.1 Carbon Steel (Normalized)--
1.
Shear Modulus
1.1.
G= Torque at yielding
1.2.
G= (49.363)*(79.42/129.8)
1.2.1.
30.2 GPa
1.2.2.
Percent Error
1.2.2.1.
Accepted: 79 GPa
1.2.2.2.
61.77%
2.
Torque at yielding equal to 14.21 N-m
3.
Maximum torque at failure
3.1.
Found at (52.34661,21.3) [also see appendix]
3.2.
Maximum torque equal to 21.3 N-m
1.
Shear Modulus
1.1.
30202 MPa
1.2.
30.202 GPa
1.2.1.
Percent Error
1.2.1.1.
2.
Shear Stress at yielding
2.1.
3.
61.8%
343.424 MPa
Ultimate Shear Strength
3.1.
493.8 MPa
--0.4 Carbon Steel (Drawn)--
1.
Shear Modulus
1.1.
2.
3.
G= (95.046)*(79.31/129.8)
1.1.1.
= 58.07 GPa
1.1.2.
Percent Error
1.1.2.1.
Accepted: 79 GPa
1.1.2.2.
26.5%
Torque at yielding
2.1.
Intersection at (0.22166, 18.84)
2.2.
Torque at yielding equal to 18.84 N-m
Maximum torque at failure
3.1.
Found at (20.90398, 29.12) [also see appendix]
3.2.
1.
Shear Modulus
1.1.
58068 MPa
1.2.
58.068 GPa
1.3.
Percent Error
1.3.1.
2.
26.5%
Shear Stress at yielding
2.1.
3.
Maximum torque equal to 29.12 N-m
481.5 MPa
Ultimate Shear Strength
3.1.
632 MPa
--0.4 Carbon Steel (Normalized)--
1.
2.
Shear Modulus
1.1.
G=(62.114)*(77.8/127.23)
1.2.
= 37.98 GPa
1.3.
Percent Error
Accepted Value: 79 GPa
1.3.2.
51.9%
Torque at yielding
2.1.
3.
1.3.1.
Torque at yielding equal to 15.36 N-m
Maximum torque at failure
3.1.
Maximum torque equal to 30.06 N-m
1.
Shear Modulus
1.1.
37982 MPa
1.1.1.
1.2.
Percent Error
1.2.1.
2.
51.9%
Shear Stress at yielding
2.1.
3.
37.982 GPa
383.68 MPa
Ultimate Shear Strength
3.1.
708.3 MPa
--Grey Cast Iron--
1.
2.
Shear Modulus
1.1.
G=(58.372)*(79.01/133.28)
1.2.
= 34.6 GPa
1.3.
Percent error
Accepted: 41 GPa
1.3.2.
15.6%
Torque at yielding
2.1.
3.
1.3.1.
Torque at yielding equal to 14.996 N-m
Maximum torque at failure
3.1.
Maximum torque equal to 17.99 N-m
1.
Shear Modulus
1.1.
34602 MPa
1.1.1.
34.602 GPa
1.1.2.
Percent Error
1.1.2.1.
2.
Shear Stress at yielding
2.1.
3.
15.6%
357.1 MPa
Ultimate Shear Strength
3.1.
409.7 MPa
--Half Hard Brass--
1.
2.
Shear Modulus
1.1.
G=(41.804)*(76.2/128.08)
1.2.
= 24.871 GPa
1.3.
Percent Error
Accepted: 41
1.3.2.
37.8%
Torque at yielding
2.1.
3.
1.3.1.
Torque at yielding equal to 15.05 N-m
Maximum torque at failure
3.1.
Maximum torque equal to 18.57 N-m
1.
Shear Modulus
1.1.
24873MPa
1.1.1.
24.873 GPa
1.1.2.
Percent error
1.1.2.1.
2.
Shear Stress at yielding
2.1.
3.
37.8%
351.7 MPa
Ultimate Shear Strength
3.1.
435.7 MPa
Conclusion:
Steel and Half Hard Brass turned out to be ductile materials since they broke along the
perpendicular axis. Iron appeared to be brittle, breaking off at an angle. The stress strain graph
displays this also at the end of the graph. For Iron, the decrease in stress is visible, whereas that
is not the case for the other materials. Due to the percent error for samples (especially those for
steel) those results would not be very acceptable from this experiment. Most likely, the error
stems from human error during the measurements, experimental, and analytical stages. There
could possibly also be defects in the specimens or apparatus. The value for strength and modulus
also seem to be much lower for normalized steel compared to cold work.
Appendix:
https://docs.google.com/spreadsheets/d/1wp9oz5GfNOuwZFqZq47sDdbNrjcDdnM4vCiayvstK
CQ/edit?usp=sharing
https://docs.google.com/spreadsheets/d/1c98al0TOo5ELVP9QBXySlAnEf1IDMSk6wb0SbxiaF2
g/edit?usp=sharing
https://docs.google.com/spreadsheets/d/1QZVg3d6Hmtt9h9TMEvLhp8G0WSbXmzj4raYVs_Ru
qLo/edit?usp=sharing
https://docs.google.com/spreadsheets/d/1NFfH3-Yr2uNjZTAa2lmST-XkBPnUzfUPBvsfoj_KnFI
/edit?usp=sharing
https://docs.google.com/spreadsheets/d/149gpO8en0I1u4-TTRxG6CUGeUXC7hgLVKQa3eOZf
5p8/edit?usp=sharing
https://docs.google.com/spreadsheets/d/1uADpFADoqfKnVNMT6v_nRSrAk04FTSKhcpey2kc2
fTg/edit?usp=sharing