U of I Fatigue Test and Measurement of Elastic Modulus by Wave Propagation Lab see instruction. You can use the example and PARAPHRASE some information fro

U of I Fatigue Test and Measurement of Elastic Modulus by Wave Propagation Lab see instruction. You can use the example and PARAPHRASE some information from it. ME220 : Materials Laboratory
Fatigue Test
and
Wave Propagation Experiment
Prof. Jow Ding
Summer 2020
ME220 : Materials Laboratory
Fatigue Loading:
A repetitive loading occurring at a stress level below material’s
yield strength or ultimate strength
Examples:
•
•
Rotation of shaft leads to repetitive loading
Shafts and axles often have stepped geometry to
accommodate power transmission components
such as gears or pulleys. This sudden changes in
cross section create stress concentration and are
potential spots for fatigue failure.
(a) Ground loads on the wings.
(b) Distribution of the wing bending moment induced by the ground
load.
(c) Stress in the lower wing induced by the ground and flight loads.
ME220 : Materials Laboratory
Why is fatigue study important?
90% of structural failure is due to fatigue.
ME220 : Materials Laboratory
Terminology related to fatigue loading
????? = ???????????????? ? ????????????????
???????? =
???????? =
?????
2
???????????????? +????????????????
2
stress range
alternating stress
mean stress
Stress fluctuates around the mean stress with an amplitude
equal to alternating stress
ME220 : Materials Laboratory
Fatigue Test: rotating beam fatigue test machine
????????
???? =
????
S: maximum bending stress
M: bending moment
I: moment of inertia
r: radius of the sample
S=0
S = Mr/I
S=0
Specimen is like a
rotating cantilever beam
S = – Mr/I
Notice that the mean stress is zero in this test
ME220 : Materials Laboratory
S-N curve and endurance limit Se
Raw data to be collected:
For each imposed S, record the number of cycles (N) to failure
Analysis of the data:
• Plot log S vs log N to get the S-N curve.
• Identify the endurance limit Se
Se : maximum alternating stress that can be applied
under zero mean stress without causing fatigue failure.
ME220 : Materials Laboratory
Approximation of S-N curve
Su : ultimate tensile strength
N = 103 : 0.9 Su ; N = 106 : 0.5 Su
Implication: Se can be estimated as half of the ultimate strength
ME220 : Materials Laboratory
Effect of mean stress and fatigue design
Goodman line: Based on ultimate tensile strength Su:
Soderberg line: Based on yield strength Sy:
???????? , ???????? ?
???????? , ???????? , ???????? ?
applied stresses
material properties
???????? ????????
+
=1
???????? ????????
???????? ????????
+
=1
???????? ????????
ME220 : Materials Laboratory
Fatigue failure characteristics:
Fracture surface of a shaft due to
fatigue failure
ME220 : Materials Laboratory
Fatigue failure characteristics:
Fatigue loading with constant amplitude
Fatigue loading with varying amplitude
ME220 : Materials Laboratory
Shot-peening surface treatment to increase fatigue life
Shot-peening introduces compressive stress on the surface
to suppress surface crack from growing
ME220 : Materials Laboratory
Wave Propagation Experiment
Purpose: use sound speed measurement to determine
the stiffness (Young’s modulus) of a material
Experiment Setup:
ME220 : Materials Laboratory
ME220 : Materials Laboratory
oscilloscope record:
wave speed can be measured as:
???? = 2????/?????
where L is the length of the bar
ME220 : Materials Laboratory
Determination of the Young’s modulus (E):
???? =
or
????
????
???? = ????????
2
???? ?
density
ME220 – Mechanics of Materials Laboratory
TEST TITLE: Fatigue and Wave Propagation Tests
NAME:
(refer to lab manual pp. 29-47)
FATIGUE TEST:
1. Summary (1/10) (The summary should be succinct (limited to one page), but contain
the following four pieces of information, namely, the purpose of the experiment;
experimental methods; results; and conclusion.)
2. Results (3/10)
1. Tabulate the test data (in the descending order of load) collected in two weeks
using the following format.
Bending Moment (M)
Stress (S)
Cycles To Failure(N) Cycles To Failure(N)
(in-lb)
(ksi)
(x102) (polished)
(x102) (shot-peened)
Note: put an asterisk symbol beside the cycle numbers (N) for those tests in which
the specimens did not break.
1. Plot all the data on the same graph paper using log scale for both S and N (refer to
Figure 5.4). Use different symbols for polished and shot-peened samples. If the
specimen did not break, put an arrow beside the symbol (Refer to figure 5.4). From
the plot, determine the endurance limit of A36 steel (polished condition only).
2. On the graph obtained in step 2, mark the correct fraction of 0.9 Su at 103 and 0.5 Su
106 cycles. Connect these two points by a straight line and draw a horizontal line after
(106, 0.5Su). Compare the line with the experimental data (polished condition only).
The Sy and Su for A36 steel are 48 and 68 ksi respectively.
4. Plot Soderberg and Goodman lines for your results.
5. Make a sketch of the fracture surface of a broken test specimen, showing crack
propagation or “beach” lines.
2
3. Question (5/10)
1.
How is the plot obtained in step b.3 compared with experimental data ? Is one half of
the ultimate strength a good estimation of the endurance limit for A36 steel ?
2.
Beach mark is a characteristic of the fracture surface in fatigue failure. What is it and
what is the cause?
3. Explain the meaning of the Soderberg and Goodman lines.
4. Briefly explain why shot-peening can in general increase the fatigue strength of the
material ?
5. A steel bar, whose ultimate tensile strength is 150,000 psi, is subjected to a fluctuating
tension – compression axial fatigue load that varies from a maximum of 75,000-lb in
tension to a minimum of 25,000-lb in compression. Estimate the minimum bar diameter
to prevent fatigue failure.
4. Conclusion (1/10)
Wave Propagation Test:
1. Summary (0.5/2) (The summary should be succinct (limited to one page), but contain the following
four pieces of information, namely, the purpose of the experiment; experimental methods; results; and
conclusion.)
2. Results (1/2)
a.
Plot the trace of gage outputs and explain each pulse, showing approximate time
between pulses.
b.
Calculate the modulus of elasticity for aluminum by measuring the stress pulse
3
velocity. Note that the density of aluminum is 168.5 lbm/ft3. Also notice that 1 slug =
32.2 lbm and 1 lbf = 1 slug x ft/sec2.
3. Conclusion (05/2)
4
CH1
0.06
0.04
CH1 Voltage (V)
“s”
CH1 “Volts”
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First Positive Peak:
Second Positive Peak:
Delta Time
X
Time (s)
7.8E-06
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First Negative Peak:
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0
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0
0.0008
0
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0
0
0.0008
0
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0
0
0
0.0008
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0.0016
0
0
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0
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0.0008
0
0
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-1E-05
-9.8E-06
-9.6E-06
-9.4E-06
-9.2E-06
-9E-06
-8.8E-06
-8.6E-06
-8.4E-06
-8.2E-06
-8E-06
-7.8E-06
-7.6E-06
-7.4E-06
-7.2E-06
-7E-06
-6.8E-06
-6.6E-06
-6.4E-06
-6.2E-06
-6E-06
0.0016
0.0024
0.0024
0.0024
0.0032
0.0024
0.0032
0.0032
0.004
0.004
0.0048
0.0048
0.0048
0.0056
0.0064
0.0064
0.0064
0.0072
0.0064
0.0072
0.008
0.0104
0.0096
0.0096
0.0104
0.012
0.0112
0.0128
0.0136
0.0136
0.0144
0.0152
0.0152
0.0168
0.0168
0.0176
0.0184
0.0192
0.0208
0.0208
0.0216
0.0232
0.0224
0.0224
0.0248
0.0248
0.0256
0.0256
0.0264
0.0272
0.028
0.028
-5.8E-06
-5.6E-06
-5.4E-06
-5.2E-06
-5E-06
-4.8E-06
-4.6E-06
-4.4E-06
-4.2E-06
-4E-06
-3.8E-06
-3.6E-06
-3.4E-06
-3.2E-06
-3E-06
-2.8E-06
-2.6E-06
-2.4E-06
-2.2E-06
-2E-06
-1.8E-06
-1.6E-06
-1.4E-06
-1.2E-06
-1E-06
-8E-07
-6E-07
-4E-07
-2E-07
6.35275E-21
2E-07
4E-07
6E-07
8E-07
1E-06
1.2E-06
1.4E-06
1.6E-06
1.8E-06
2E-06
2.2E-06
2.4E-06
2.6E-06
2.8E-06
3E-06
3.2E-06
3.4E-06
3.6E-06
3.8E-06
4E-06
4.2E-06
4.4E-06
0.0288
0.0304
0.0296
0.0304
0.0312
0.032
0.0328
0.0328
0.0336
0.0344
0.0344
0.0352
0.0352
0.0368
0.0368
0.0376
0.0376
0.0376
0.0376
0.0384
0.0392
0.04
0.04
0.0408
0.0408
0.0416
0.0408
0.0416
0.0424
0.0424
0.0432
0.0432
0.044
0.044
0.0448
0.0456
0.0456
0.0464
0.048
0.0472
0.0464
0.0464
0.0456
0.048
0.048
0.0472
0.048
0.048
0.048
0.0488
0.048
0.0488
4.6E-06
4.8E-06
5E-06
5.2E-06
5.4E-06
5.6E-06
5.8E-06
6E-06
6.2E-06
6.4E-06
6.6E-06
6.8E-06
7E-06
7.2E-06
7.4E-06
7.6E-06
7.8E-06
8E-06
8.2E-06
8.4E-06
8.6E-06
8.8E-06
9E-06
9.2E-06
9.4…
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