Applying Hooke's Law to a Shape Memory Alloy (SMA) to determine varying Spring Constants (k)
Objective
Determine relationship between Force and Distance (x) for a nonlinear spring made of
Nitinol (shape memory alloy), and the different Force Constants (k) of the SMA spring.
Materials :
One trained Nitinol spring, four slotted masses, metric ruler, s-hook, 6 Volt battery or low-amperage 6 volt power supply, 2 leads with alligator clips, thermocouple, thermocouple reader, drafter’s tape
Procedures (see picture)
1.
Attach the spring to the frame with the screw/washer at the top of the frame.
2.
Record the “rest” position of the spring (let x o
= 0.0 cm).
3.
Add a 50g mass to extend the spring beyond its rest position (x o
)
4.
Attach one lead to the top loop of the spring and then to the positive node of the battery.
5.
Attach a second lead to the bottom loop of the spring; do not attach it to the negative node of the battery until the spring has attained equilibrium.
6.
Attach the ends of the thermocouple to the center loop of your elongated spring and record the displacement (
 x), and the initial temperature T
0
.
7.
When you have finished recording the initial data and your partner is ready to proceed attach the second lead to the negative node of the battery.
8.
As your spring heats up the mass will rise, you will record the position of the mass and the temperature when the following occurs. a.
The mass begins to rise at a smooth rate of acceleration b.
The mass begins to decelerate c.
The mass stops.
9.
As soon as the mass stops (do not let the temperature exceed 38 o
C) detach the lead at the battery’s negative node and record the following positions and temperatures. a.
The mass begins to fall at a smooth rate of acceleration b.
The mass begins to decelerate c.
The mass stops.
10.
Take the load off the spring and reheat it until it is fully compressed.
11.
Repeat #1-10 for 6 more masses; do not let the mass exceed 150g.
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Applying Hooke's Law to a Shape Memory Alloy (SMA) to determine varying Spring Constants (k)
Thermocouple
Thermocouple
Reader
Battery/Power Supply
DATA TABLE
2
3
Trial Mass
(kg)
1
4
5
6
7
AVE
Δx
(m)
T
( o C)

T
( o C)
Mg
(N)
PE s
(J)
PE g
(J)
Q
(J)
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Applying Hooke's Law to a Shape Memory Alloy (SMA) to determine varying Spring Constants (k)
Calculations and Analysis
1.
For each spring, plot a graph of Force (N) vs. distance (Δx). Let g = 10 m/s 2 when converting the masses to Newtons using F = mg.
2.
Determine the slope (k) of the curve at 6 positions using the graphing calculator function for derivatives and write them in your data table. What are the units and what does the slope represent?
3.
Calculate the elastic potential energy in Joules for your spring at the various Δx’s that you found the k’s for. Plot this energy on a graph by using PEs = 1/2kx 2
for the vertical and Δx for the horizontal.
4.
Calculate the gravitational potential energy of the spring mass system for the positions recorded in #2.
5.
Using the Law of Conservation of Energy and determine the energy lost to the
6.
environment by finding the heat energy added to the spring by the battery using the formula for heat energy (Q = mc

T) and subtracting the sum of the elastic and gravitational potential energy for two of your Δx’s.
Calculate the efficiency of the SMA Spring using eff =
Q

PE
T
Q x 100 %
7.
Compare your force constant for the SMA spring to the spring from the Hooke’s
Law lab and draw a conclusion about the magnitude of the force constant k and the "stretchability" of an SMA spring.
8.
Using what you have learned about SMA’s and their pseudoelastic behavior, how mush more work can they do compared to a linear spring? Compare the results from the efficiency of the linear spring to the SMA spring.
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Applying Hooke's Law to a Shape Memory Alloy (SMA) to determine varying Spring Constants (k)
Material Facts Sheet
Subcategory: Metal; Nickel Alloy; Nonferrous Metal; Titanium Alloy
Close Analogs: MatWeb has a separate entry for the high temperature phase of Nitinol.
Key Words: Titanium Nickel Alloys, SMAs
Component Wt. %
Ni
Ti
55
45
Material Notes:
Shape Memory Alloys (SMA's) are novel materials which have the ability to return to a predetermined shape when heated. When an SMA is cold, or below its transformation temperature, it has a very low yield strength and can be deformed quite easily into any new shape--which it will retain. However, when the material is heated above its transformation temperature it undergoes a change in crystal structure which causes it to return to its original shape. If the SMA encounters any resistance during this transformation, it can generate extremely large forces. The most common shape memory material is an alloy of nickel and titanium called Nitinol (50 atom% Ni, 50 atom% Ti). This particular alloy has very good electrical and mechanical properties, long fatigue life, and high corrosion resistance.
Information provided by TiNi Alloy Company.
Physical Properties
Density
Mechanical Properties
Tensile Strength, Ultimate
Tensile Strength, Yield
Elongation at Break
Modulus of Elasticity
Poisson's Ratio
Shear Modulus
Metric
6.45 g/cc
English Comments
0.233 lb/in³
754 - 960 MPa 109000 - 139000 psi
100 MPa 14500 psi
15.5 %
28 GPa
0.3
10.8 GPa
15.5 %
1570 ksi
4060 ksi Approximate
0.3 Approximate
Calculated
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Applying Hooke's Law to a Shape Memory Alloy (SMA) to determine varying Spring Constants (k)
Electrical Properties
Electrical Resistivity
Magnetic Susceptibility
Thermal Properties
7.6e-005 ohm-cm
2.5e-006
7.6e-005 ohm-cm
2.5e-006 emu/g
Specific Heat Capacity
Thermal Conductivity
Melting Point
Solidus
0.32 J/g°C 0.0765 BTU/lb°F
10 W/m-K 69.4 BTU-in/hrft²-°F
1240 - 1310 °C
1240 °C
1310 °C
2260 - 2390
2260
2390
°F
°F
°F Liquidus
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Libana Zamudio Milender
Del Rio High School
100 Memorial Drive
Del Rio, Texas 78840
Email: libbyz@yahoo.com
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