Unformatted text preview: Massachusetts Institute of Technology
Department of Aeronautics and
Astronautics
Cambridge, MA 02139 16.01/16.02 Unified Engineering I, II
Fall 2003 Systems Problem 10
Time Spent
(min) Name:
SP10
Due Date: 11/19/03 Announcements: Study
Time MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Aeronautics and Astronautics
16.010 / 16.020 Unified Engineering
Issued: November 6, 2003 Systems Problems #10
Due: 5 pm November 19th, 2003 MEASURING STRAIN AND MATERIAL PROPERTIES
Note: This Systems Problem has a prelab that must be completed before arriving at the
laboratory.
Objectives
After this lab, you will be able to:
• Apply a strain gauge to a specimen, solder wires to the pads, and make electrical
connections to a strain gauge amplifier
• Use strain gauges to determine material properties such as Young’s modulus and
Poisson’s ratio
• Discuss the elastic behavior of various materials and the experimental observation thereof
Introduction
In this systems problem you will apply an axial load to three different materials and
measure the axial and lateral strains using strain gauges that you apply to the materials. You
will then be able to estimate two material properties (Young’s modulus and Poisson’s ratio)
for each material and compare them to published values.
Poisson’s Ratio
You are already somewhat familiar with stress and strain in an axial direction, for instance in
the bar of a truss. For example, consider the material below: Figure 1. Material Under an Axial Load
An axial force F is being applied in the x1 direction. This results in a stress in the material
F
s
and a strain in the x1 direction: e 1 1 = 1 1 where E is the
in the x1 direction: s1 1 =
A
E
Young’s modulus. Because the material’s volume remains essentially constant, an
elongation in the x1 direction means that the material also contracts slightly in the x2 and x3
1 of 5 directions. So, we would expect e2 2, for example, to have some negative value if e1 1 is
positive. The ratio of the (negative) lateral strain to the axial strain is defined as the
Poisson’s ratio, n:
n1 2 =  e2 2
e1 1 The subscripts on n1 2 indicate that the Poisson’s ratio is representing the ratio of lateral (or
transverse) strain in the x2 direction over the axial strain in the x1 direction.
Strain Gauges
In SP9, the truss lab, we introduced strain gauges. Now we will take a slightly more
detailed look at their operation. As we discussed in SP9, the resistance R of a wire
(measured in Ohms) is given by:
rL
R=
A
where r is the wire material resistivity, L is the wire length, and A is the crosssectional area
of the wire. Now, if the wire is lengthened by DL, its resistance will change by some
amount DR:
r(L + DL)
R + DR =
A
(assuming the change in A is negligibly small). Dividing both sides by R:
R DR rL r D L
+
=
+
RR
AR AR
Noting that rL
= 1 , this reduces to:
AR
D R r DL D L
=
=
=e
R
AR
L So, the proportional change in R is equal to the strain of the wire. Due to nonideal
behavior of the strain gauge, there is actually a proportional constant called the Gauge
Factor (GF) that results in a larger change in resistance for a given strain than the above
equation predicts:
1 DR
e=
GF R
where GF is typically about 2.0. The baseline values for R is 120 W. Your task then is to
measure the change in resistance, and from it determine the strain in the material.
Figure 2 shows the wiring diagram for each strain gauge. In the lab, you will connect one
lead from the strain gauge to the terminal on the strain gauge reader labeled S+ and the
other lead to the terminal labeled D120. The strain gauge reader then measures the voltage
between S+ and S and from this determines the change in strain gauge resistance, DR. 2 of 5 Figure 2. Strain Gauge Wiring Diagram (Wheatstone Bridge Circuit)
(labeled terminals shown as white circles)
Lab Exercise
The straing gauging portion of the lab will be conducted in the electronic shop in the
basement of building 33, and the mechanical testing component in the hangar, where you
conducted the truss lab. Each lab session will take approximately 2 hours. You will work
in a team of six students. In each lab session, the lab team will test four different specimens,
each made of a different, industrially important aerospace material. The materials you will
test are:
• Aluminum – Al 7075
• Titanium – 6Al 4V
• A steel alloy
• A carbon fiber reinforced epoxy laminate. This will already have strain gauges attached
to it.
These materials have been cut into specimens as depicted in Figure 3 below. The team will
apply two strain gauges to each specimen (one in the axial direction, one in the lateral
direction). With teams of six applying two gauges to each of three metal specimens, each of
you will have the opportunity to apply a strain gauge to a specimen.
0.25 in DIA TYP strain
gauges
20 mm
400 mm Figure 3. Approximate dimensions of the material specimens, each
specimen is approximately 2 mm thick. 3 of 5 PreLab Assignment
Read through the entire lab handout carefully so that you have a clear idea of what
needs to be accomplished. Be sure to read the section on strain gauge application;
it will make the lab period go much more smoothly. Also, complete the questions
below and bring your solutions with you to lab. You may need to refer to Ashby
and Jones chapter 3 and Crandall section 5.4.
1. If the specimen described in Figure 3 is hung from a hook and a 100 pound
load is applied what will be the resulting stress (in each direction) in the vicinity of
the strain gauges for each material (aluminum, Titanium, CF composite and steel)?
2. For each of the four materials (aluminum, titanium, carbonfiber composite and
steel), what will be the approximate strain (in each direction) in the vicinity of the
strain gauges?
3. For the aluminum specimen, what will be the change in resistance of the two
strain gauges if the gauge factor is 2.06 and the baseline resistance R of the strain
gauge is 120 W ?
4. Referring to Figure 2, let V0 be the voltage difference between P+ and P . If
the change in resistance of the strain gauge is what you computed in #3, what
would be the voltage between S+ and S in the Wheatstone bridge circuit, in terms
of V0 ?
Laboratory Assignment
The technical instructors will assist you in applying the strain gauges and
soldering the leads to the pads. TA’s will be available to help you with the loading
of your specimens. Be sure to listen carefully to their instructions and follow
sound safety procedures. Carry out the following steps:
I. Apply a strain gauge to a specimen. This is a fairly complex and delicate
operation. You need to prepare the specimen, apply the gauge, and solder the
leads onto the pads. Since this is your first time, it will take about an hour.
There will be technical instructors (John Kane and Dave Robertson), who are
skilled in the art of strain gauging available to help you Please take your time
and do not hesitate to ask questions. Please read the section of this handout
on strain gauge application
II. Connect your leads to the strain gauge amplifier. Connect the leads of
your strain gauge to the terminal board for the strain gauge amplifier.
100
III. Apply the load and record the change in strain. You will be using the
lbs
loading apparatus and load cells from the truss lab to apply the load to your
specimens. For each of the four specimens in turn complete the following
steps:
(a) Balance the bridge. Hang your specimen from the hook provided. Attach the loading cable to the hole in the lower end of your specimen (b) Apply the load and record the strain. Using the hydraulic jack provided, apply load to the specimen. Do not exceed a stress of 50 MPa or a load of 500 lbs (whichever is smaller) for any of the specimens. Take enough load readings to obtain an accurate estimate of the Young’s Modulus and Poisson’s ratio, and to confirm that the material response is linear. 4 of 5 PostLab Assignment
5. For each material, make plots of applied stress versus strain (in axial and transverse
directions). Discuss your results and be sure to make note of any significant hysteresis or
nonlinearity.
6. For each of the four materials (aluminum, composite laminate, titanium, and steel), what
are your measured values of Young’s modulus and Poisson’s ratio? How do your
measured values compare with published values?
7. Estimate the accuracy of this experimental technique for measuring elastic properties
(Young’s modulus and Poisson’s ratio).
8. Discuss the fidelity of the engineering model in light of your experimental results (i.e.,
the degree to which linear elastic behavior was confirmed experimentally).
9. Discuss your experience in this lab. Did you experience any significant difficulties in
applying the strain gauges? 5 of 5 ...
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 Fall '05
 MarkDrela
 Aeronautics, Astronautics, Ratio, Massachusetts Institute of Technology, SP9

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