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Torsion Lab
By
Charisse Lewis
0729543
ME 354 AC
Date of this Lab Exercise: February 11, 2010
Date of Lab Report Submission: February 25, 2010
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Executive Summary:
Torsion testing is one of the basic mechanical tests that are conducted to obtain material
properties, such as the elastic modulus, strength, shear modulus, and shear strength. During this
torsion lab the Technovate model 9041 Torsion Tester was used to conduct the testing. The
materials used in this lab were 6061-T6 Aluminum, and A36 Steel. The setup for the lab took a
lot of attention to detail, making sure that the specimen was tightened into the grip just right, and
time, if the specimen was not clamped properly or failed inside the grip the test would have to be
redone.
The main purposes of the lab were to observe how the specimens of two materials that were used
reacted under torsion, and to verify the accuracy of the Power-Hardening and Ramberg-Osgood
applied torque predicting models. While observing the specimens of Aluminum and Steel data
was collected as well, so as to compare the two samples numerically to each other and to the
torque predictor models.
When the data for aluminum and steel are compared, the aluminum sample is more ductile than
steel is, which is shown in Figure C.1 in the results. This is evident because the aluminum
sample underwent more angle of twist per unit length than the steel specimen did.
The results show that the Power-Hardening and Ramber-Osgood torque predicting models work
well for Aluminum, which was the only material that had data applied to the models. The
maximum percent error, shown in Table C.3 in the results section, % Error, for the Power-
Hardening model was 0.706 % and for the Ramberg-Osgood it was 1.40 %. These two models
had the % Error maximums at opposite ends of the data set. The Power-Hardening model had
the greatest % Error when /L was a maximum, and the Ramberg-Osgood had the greatest %
Erro r when /L was a minimum.
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B. Procedure
The first thing that was done in the lab was the measuring of the diameter of the specimen gage
section using calipers, and to record that value for later calculations. After that, it was necessaryto draw a straight longitudinal line on the specimen so that the angle of twist of the specimen can
be observed during the test.
When installing the specimen in the machine it must first be installed in the bottom grip, and the
specimen has to be very tightly camped in the grip to ensure that it will not slip. Next, the pin
behind the lower grip that engages the ratchet mechanism must be located and make sure the pin
is pulled forward (this ensures that the ratchet is engaged). Then, the horizontal drive rod must
be unthreaded until the end of the threaded region has reached the threaded nut, just before the
threaded rod is disconnected from the base. Then the lever arm must be rotated counter-
clockwise, moved to the right, as far as possible.
At the top of the apparatus identify the wire ropes that transfer the torque to the top grip and
specimen, and loosen the two nuts as far as possible. Rotate the top grip clockwise, so as to
remove the slack in the wire ropes, and while holding the top grip in this position as firmly as
possible, tighten the grip. Make sure that the specimen is very tightly fastened in the top grip.Remove any remaining slack in the wire ropes by retightening the two nuts that were loosened
before, but monitoring the force sensor while that is being done. If the nuts are completely
tightened and slack still remains, tighten the threaded horizontal drive rod until an increase in
load is sensed.
After the specimen is tightly clamped into the machine, measure and record the distance between
the grips, but make sure to account for how far the bottom face of the upper jaw is recessed into
the upper plate in the measurement. Adjust the pointer so that it indicates zero degrees, and
zero the output of the force sensor.
All of the prior steps were the setup for the lab, and with those complete the data collection for
the lab may begin. Start applying known angles of twist to the lower grip, beginning with 2 o
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using the threaded drive rod, and record the force displayed on the force gage. After that
increase the angle of twist by 2 o until the total angle of twist is 30 o, recording the force shown on
the force gage at the end of each increase. Next, increase the angle of twist by 5 o. Continue to
take measurements at thi s increment until the ratchet in the lower grip clicks. This usually
occurs around 45 o, but it can occur at a total angle of twist larger than that, up to about 60 o, just
keep on increasing the angle of twist until the click occurs. If the click doesn t occur until
well after 60 o, it may be that the specimen was not correctly installed, and therefore may not give
a good data set, so it might be advisable to start over.
After hearing the click, record four measurements at increased angles of twi st, in increments of
45o. Record four more measurements, this time at increments of 90 o, and four more
measurements at increments of 180 o. Finally, record measurements for increased angles of twistin increments of 360 o, until specimen failure occurs.
After failure remove the broken halves of the specimen. Carefully examine the specimen and the
fracture surface, record what is necessary to discuss later if it is required.
C. Results
The data that was collected during the torsion testing lab was force (kg), and angle of twist.
Comparison of the measured values for torque (Appendix B) versus the angle of twist divided by
the length, /L, is shown in Figure C.1 below:
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Figure C.1: Measured Torque vs. /L for the A36 Steel and 6061-T6 Aluminum specimens thatwere tested.
On the next page, in Figure C.2, is an example of what one of the A36 Steel specimens looked
like after fracture. This example was representative of most of the steel specimens, so it is used
for determining how brittle or ductile the material was just based on the appearance of thefracture.
0
2
4
6
8
10
12
0 100 200 300 400 500 600 700
M e a s u r e
d T o r q u e
( N - M
)
/L (rad/m)
Measured Torque vs. /L
A36 Steel
6061-T6 Aluminum
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Figure C.2: Steel specimen at the point of failure, after fracture.
The values for force converted to Newtons, and the /L for aluminum is shown in Tables C.1and C.2. The other data that is shown in Table C.1 is for predicting torque according to the
Power-Hardening model. The data that is shown in Table C.2 other than the /L is the calculated
values necessary for the Ramberg-Osgood model for predicting applied torque.
Table C.1: The Power-Hardening model (Appendix D) for predicting torque with values thatare necessary for calculation
Angle (deg) Force (N) Angle (rad)
(rad/m)
Measure Torque (N-m)
Predicted Torque(P-H) (N-m)
0 0 0 0 0 02 10.3 0.0349 0.137 1.35 0.1794 10.5 0.0698 0.275 1.38 0.3576 11.3 0.105 0.412 1.48 0.5368 12.0 0.140 0.550 1.57 0.714
10 13.0 0.175 0.687 1.70 0.89312 14.0 0.209 0.825 1.83 1.0714 14.5 0.244 0.962 1.90 1.25
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16 16.8 0.279 1.10 2.20 1.4318 16.9 0.314 1.24 2.22 1.6120 17.4 0.349 1.37 2.28 1.7922 18.1 0.384 1.51 2.38 1.9624 19.6 0.419 1.65 2.57 2.1426 20.4 0.454 1.79 2.67 2.3228 21.6 0.489 1.92 2.83 2.5030 22.4 0.524 2.06 2.93 2.6835 24.5 0.611 2.40 3.21 3.1240 26.5 0.698 2.75 3.47 3.5745 28.4 0.785 3.09 3.73 3.9390 35.6 1.57 6.18 4.66 4.81
135 37.5 2.36 9.28 4.92 5.01180 40.2 3.14 12.4 5.27 5.12225 40.7 3.93 15.5 5.34 5.19315 41.7 5.50 21.6 5.46 5.31405 41.7 7.07 27.8 5.46 5.40
495 41.7 8.64 34.0 5.46 5.47585 41.7 10.2 40.2 5.46 5.52765 42.7 13.4 52.6 5.59 5.62945 42.9 16.5 64.9 5.62 5.69
1125 44.4 19.6 77.3 5.82 5.761305 44.4 22.8 89.7 5.82 5.811665 45.2 29.1 114 5.93 5.902025 46.2 35.3 139 6.06 5.982385 46.6 41.6 164 6.11 6.042745 47.1 47.9 189 6.17 6.093105 47.1 54.2 213 6.17 6.143465 47.2 60.5 238 6.18 6.183825 47.6 66.8 263 6.24 6.224185 47.6 73.0 288 6.24 6.264545 47.9 79.3 312 6.27 6.294905 48.2 85.6 337 6.31 6.325265 48.3 91.9 362 6.33 6.355625 48.8 98.2 387 6.40 6.385985 49.1 104 411 6.43 6.406345 49.1 111 436 6.44 6.426705 49.1 117 461 6.44 6.457065 49.1 123 485 6.44 6.477425 49.1 130 510 6.44 6.49
7785 49.1 136 535 6.44 6.518145 49.5 142 560 6.49 6.538505 49.3 148 584 6.47 6.548865 50.0 155 609 6.56 6.569225 50.0 161 634 6.56 6.58
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Table C. 2: The Ramberg-Osgood model (Appendix E) for predicting torque with values thatare necessary for calculation
(MPa) (rad/m) Predicted Torque(R-O) (N-m)0 0 0 0 0 0
50 3.33E-14 0.00196 0.00196 0.820 1.07100 4.64E-08 0.00391 0.00391 1.64 2.13150 0.000182 0.00587 0.00605 2.54 3.27200 0.0646 0.00782 0.0724 30.3 5.57250 6.13 0.00978 6.14 2580 6.99270 29.5 0.0106 29.5 12400 7.55280 62.0 0.0110 62.0 26000 7.83290 127 0.0113 127 53200 8.11300 253 0.0117 253 106000 8.39305 355 0.0119 355 149000 8.53310 495 0.0121 495 207000 8.67
315 686 0.0123 686 287000 8.81320 945 0.0125 945 396000 8.95325 1280 0.0127 1300 544000 9.09330 1770 0.0129 1770 743000 9.23335 2410 0.0131 2410 1010000 9.37340 3260 0.0133 3260 1370000 9.51345 4390 0.0135 4390 1840000 9.65350 5890 0.0137 5890 2470000 9.78355 7860 0.0139 7860 3300000 9.92
The comparison of the two predictive models, Power-Hardening and Ramberg-Osgood, to the
measured values of applied torque is in Figure C.3. This was done so that the students could
visually see how the predicted models compared to the measured values, instead of just seeing
data values.
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Figure C.3: The comparison of measured torque to the predictive models for the 6061-T6Aluminum specimen.
Data values are still an excellent way of representing the differences between the measured
values and the predicted values. This is done in Table C.3 below, which shows the values for the
measured torque at four different values of /L, the correspond ing predicted torque for thePower-Hardening and Ramberg-Osgood, and the % Error corresponding to differences from the
measured values.
Table C.3: The percent error of the predictive models, Power-Hardening (P-H) and Ramberg-Osgood (R-O), to the measured values for torque
/L (rad/m) Measured
Torque (N-m)
PredictedTorque (P-H)
(N-m) % Error
PredictedTorque (R-O)
(N-m) % Error100 5.86 5.85 0.222 % 5.95 1.40 %250 6.21 6.20 0.111 % 6.23 0.307 %400 6.41 6.39 0.391 % 6.38 0.596 %550 6.47 6.52 0.706 % 6.45 0.403 %
0
1
2
3
4
5
6
7
0 200 400 600 800
( / L )
( r a
d / m )
Torque (N-m)
Comparison of Measured Torque to Predictive Models for 6061-T6Aluminum
Ramberg Osgood
Power Hardening
Measured Torque
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D. Discussion
In this experiment the main goals were to observe the metals specimens to see how they act
when under torsion, and to verify the accuracy of the Power-Hardening and Ramberg-Osgood
predictive models for determining torque.
Observing the data collected for each of the metals in a graph of measured torque vs. /L, Figure
C.1, it can be seen that the Aluminum specimen is much more ductile than the steel specimen.
This is shown by the fact that the aluminum withstood a greater amount of angle of twist
compared to its length, and the steel endured a greater amount of torque prior to fracture.
Although, the steel was more brittle than the aluminum, the steel did behave as mostly ductile.
This is shown in figure C.2 in the Results section, where the steel specimen exhibited mostly
ductile behavior at fracture, which is shown by the flat fracture surface, and the small amount of
tearing at the edge. The aluminum sample looked very similar to that of the steel, with the
biggest difference being around the area of fracture where on the steel specimen it was course
like sand paper along the sides that were originally smooth (Figure C.2 in the Results). Both
samples initially had the straight line that was drawn on them before starting the testing, and by
the end of the lab it formed a spiral around the outside of the sample. The more uniform the
spacing that the spiral had, the better the data for the specimen would be.
As stated above the other main goal was to verify the accuracy of the Power-Hardening and
Ramberg-Osgood models for predicting torque. This can be shown by Figure C.3 in the results
section, which is a graph with the measured torque and the predictive models all on the same
graph. The predictive models for torque appear to be very close to the measured values, and they
are as shown in Table C.3, the percent error, % Error, of the predictive models as compared to
the measured values for torque. The values for the Power-Hardening had an increasing error
percentage as the values for /L increased, which means that this model is better for predicting
the torque being applied for smaller values of /L. With the Ramberg-Osgood, the opposite
thing happened, where the % Error was greatest in the beginning and then it became smaller as
the value for /L increased. Even though the % Errors varied from beginning to end, the values
for the % Error is still very small, with a max error for the Power-Hardening model being .706 %
and for the Ramberg-Osgood it was 1.40 %. Since the max percent errors are so small, it is a
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good assumption that both models are a good at predicting the applied torque, at least for a
ductile material.
The best way to test how applicable the Power-Hardening and Ramberg-Osgood models are for
predicting torque would be to test them with a lager variety of materials, and run more than one
test for each material. The materials used in this lab were both mostly ductile, and this showed
in the lab results, but this only gives results for ductile materials for the behavior of the applied
torque predictive models. If there was a more brittle material used in the lab alongside the
ductile materials it could be seen whether or not the predictive models apply. The minimum that
could have been done was try to apply the predictive models to steel, which as discussed is more
brittle than the aluminum.
Another problem that many groups experienced was tightening the specimens in the grips. If the
grips were too tight, the material would get scratched, and would tend to fail in that region. On
the other hand if the specimen wasn t tightened into the grips tightly enough, then the specimen
would slip, and the data set would be poor. The best way to resolve this would be to find a way
to gage how tight the specimen is in the grip, and have a specified grip strength (how tight the
grip is on the specimen) so that students know how much tighter it has to be, or if they have gone
too far.
Also, the machines that were used were very old, and the force gage was in kilograms (kg). The
force gage being in kg, which is a unit of mass and not force, was not terrible because it is not
difficult to convert kg to N, but it was also very touchy, probably due to how old it was. If
anyone hit the table at all the gage usually changed values, whether it increased or decreased the
value was not consistent either. This could also be a source of error between the measured and
predicted values.
Other possible sources of error include; not tightening the specimen into the grip enough,
tightening the specimen into the grip too much (as discussed above), the specimen being bent at
all when installed, and adding angle of twist at too rapid a pace. The first two sources of error
were already discussed above, but if the specimen was bent at all, this would create other forces
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other than the shear stress and shear strain. The predictive models would not be as accurate
because the initial assumption that was made about there only being shear stresses and forces
would be incorrect; all of the equations would be off and would not account for the additional
forces that are present. Also, if the angle of twist was added to the specimen too rapidly, then the
planes in the crystalline structure of the material would not have as much time to slide past each
other. Therefore the material would fracture sooner than a specimen that had the angle of twist
applied at a slower rate.
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Appendix A: The Technovate Torsion Test Machine
During this torsion lab the Technovate model 9041 Torsion Tester was used to test specimens
made of A36 Steel, and 6061-T6 Aluminum. In order to know how the lab works, it is necessary
to know the setup that is being used. Therefore, below in Figure A.1 is a picture of the top view
of the torsion tester with the key components labeled.
Figure A.1: To view of the Technovate model 9041 Torsion Tester, with key componentslabeled.
There is also a schematic of the above picture in Appendix B, which is used for discussing how
to calculate torque from the force reading collected. Below are two photos that display the
bottom half of the testing apparatus with the key components labeled. These pictures are for
reference throughout the report so that it is clear what is being discussed.
Top Lever
Wire Rope
Wire Rope
Force Gage
Top Grip
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Appendix B: Converting the Force Reading to Torque
The setup of the torsion test needs to be known in order to be able to calculate the torque beingapplied to the specimen, and this is shown in Figure B.1 below:
Figure B.1: Schematic top view of the Technovate Torsion Test Machine.
As shown above the grip and specimen are held in place by the wire ropes, one that is attached to
one side of the machine and one that is attached to the lever arm. The lever arm is held in place
at the pivot point and the force gage, both of which cause a force at either end of the beam. The
wire rope is the only other force acting on the lever arm, which is acting on the lever arm slightly
off center. This is shown in the form of a Free Body Diagram (FBD) in Figure B.2, on the next
page.
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Figure B.2: FBD for the lever arm with the three forces acting on it.
During the torsion experiment the data that was collected was the force at the force gage, and theforce was in kilograms (kg). First the force in kg had to be converted to Newtons (N), which is
done by multiplying the force value, in kg, by and then to calculate the torque on the
specimen it was necessary to calculate the force pulling on the wire rope. This was done using
static equilibrium moment equations centered at the pivot point, pp, shown here:
(Equation B.2)With Equation B.2,
is able to be obtained since
is the measured data from
the lab that was converted to N. With the force in the wire rope the torque applied to the
specimen can be calculated by multiplying the force in the wire rope times the radius of the top
grip, (the distance to the application of the torque). This is shown in Equation B.3 below.
(Equation B.3)The FBD for the forces acting on and the torque being applied to the top grip are shown in
Figure B.3 below.
Applied Force( )
Reaction Force
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Figure B.3: FBD of the grip with the wire ropes as the forces causing torque.
This is just the torque caused by one of the wire ropes, therefore the has to be doubled
in order to obtain the actual value for the torque applied to the specimen. In other words;
(Equation B.4)This is the measured torque in the specimen that is compared to the predicted torque from thePower-Hardening model (Appendix D), and the Ramberg-Osgood model (Appendix E).
Torque
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Appendix C: True and Effective Stress and Strain
The equation for effective stress is listed below as Equation C.1
( ) (Equation C.1)Since this lab was interested in finding predicted values for torque beyond yielding, the use of
true stress was used in calculations. Thus the equation for effective stress becomes:
( ) ( ) ( ) (Equation C.2)The effective stress equation can be rewritten to get the effective strain equation, as shown inEquation C.3.
( ) ( ) ( ) (Equation C.3)During the torsion test there was only one stress, , and one strain, , applied. Knowing that
there is only uniaxial stress, and uniaxial shear strain, Equation C.2 and Equation C.3 become:
(Equation C.4) (Equation C.5)
Equation C.4 an Equation C.5 are important for the application of the power-hardening and
Ramberg-Osgood torque predicting models as discussed in Appendix D and Appendix E,
respectively.
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Appendix D: Power-Hardening Model
Using the data collected from the torsion test that was conducted, a power-hardening model,
(Equation D.1), was fit to the measured force, (assuming true axial stress and true axial strain),response for 6061-T6 Aluminum.
(Equation D.1)
The coefficients in Equation D.1 are H , the strength coefficient, which is 413 MPa, and n , the
hardening exponent, which is .0633. Also, assuming the use of true stress and strain, as
discussed in Appendix A, and using Equations C.4 and C.5, a new equation for can be
developed that relates it to using the coefficients H and n, as shown in Equation D.2.
(Equation D.2)With this model the goal is to predict torque versus ( /L) response, and for this it is necessary to
find equations relating the two. The total applied torque is equal to the sum of the torque acting
on the elastic inner-region and the torque acting on the plastically-deformed outer-region, shown
below:
(Equation D.3)The elastic inner-region extends over , and in this region , where .Therefore:
(Equation D.4)The plastic outer-region extends over , and in this region Equation D.2 becomes
(Equation D.5)
[ ] (Equation D.6)Using Equation D.4 and D.6 the torque vs. ( /L) response can now be predicted based on the
Power-Hardening model. During this lab the Power-Hardening model was only applied to the
Aluminum 061 T6 sample data.
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Appendix E: Ramberg Osgood Model
An alternate approach to the Power-Hardening model for fitting data is the Ramberg-Osgood
model, which uses Equation E.1 as a base equation for relating the predicted torque to the ( /L)
response.
(Equation E.1)Just like the Power-Hardening model (Appendix C) the coefficients H and n are the strength
coefficient and the strain hardening exponent, respectively. The values for H and n are: H= 407
MPa, and n=0.0490. As discussed in Appendix C, the use of effective stress and effective strain
changes Equation E.1 into:
(Equation E.2)Where:
(Equation E.3)
The modulus of elasticity, E, for Aluminum 6061- T6 is 68.5 MPa, and the Poisson s ration, , is0.34 . Also, the equation becomes less daunting when a shear strength coefficient is defined,
, as shown below:
(Equation E.4)This changes Equation E.2 into:
(Equation E.5)
With all of these equations an equation for torque is made as shown below in Equation E.6.
(Equation E.6)
Where , meaning that the max shear stress occurs where the radius is the largest.Also:
(Equation E.7)
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(Equation E.8)
(Equation E.9)
(Equation E.10)
Equations E.6 through Equation E.10 are used to predict the torque vs. ( /L) response based onthe Ramberg-Osgood model, with ( /L) being equal to:
(Equation E.11)
Just like the Power-Hardening model the Ramberg-Osgood model was only fit to the Aluminum6061-T6 data set.
Recommended