2001 Summer Project Investigating the Effects of Resistance Due to Change as a Result of Deformation

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2001 Summer ProjectInvestigating the Effects
of Resistance Due to Change as a Result of
Deformation of Samples

• Pete Candreva
• Mike Supak
• R. A. Wesolowski

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Content
Purpose Conclusion/Application Procedure
Student Activity Four Point Test Solution
Set Findings Theory
Click on point of interest
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2001 Summer ProjectInvestigating the Effects
of Resistance Due to Change as a Result of
Deformation of Samples

• Pete Candreva
• Mike Supak
• R. A. Wesolowski

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Conducting Information

• 6th edition , Elements of Materials Science and
  Engineering, Lawrence H. Van Vlack,
  Addison-Wesley Publishing Co., 1989

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Materials that enable electrons to flow easily
are called charge carriers and they vary widely
with respect to conductivity (transfer of thermal
or electrical energy along a potential gradient)
, s, and with respect to resistivity (reciprocal
of conductivity), r. r is inversely
proportional to s. Materials can be divided into
three categories, conductors, semiconductors, and
insulators. Materials that have delocalized
electrons that are free to move throughout the
structure are considered conductors, and
materials that have strongly held electrons, and
diffusing ions, inclusive are ceramics and
polymers, are considered insulators. Materials
that fall between the conductors and the
insulators are referred to as semiconductors. The
charge on an electron, e, is 1.6 x 10-19
coulombs. In metals, the electrons move through
it, and in ionic materials, the charge is carried
by the diffusing ions.

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• is inversely proportional to r
• s 1/r
• and dependent on the number of charge carriers,
  n, the charge, q, and the mobility, m, where m,
  is equal to the drift speed divided by the
  electrical field E (E F/qV/d)
• m vd / E vd q/F vd d/V
• Metallic Bonds are interatomic bonds in metals
  characterized by delocalized electrons in the
  energy bands. The valence electrons are able to
  move throughout metals as a standing wave. There
  is NO NET CHARGE without an electrical field.
  When an electrical field, E, is introduced,
  electrons move to the positive electrode,
  acquiring more energy, and gaining more speed in
  that direction. Electrons moving in the opposite
  direction, reduce energy and speed. As a result a
  drift speed is developed. Drift speed is defined
  as the net velocity of all the electrons in a net
  electrical field.

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Crystals found within conducting metals contain a
periodicity that produces long range order. By
this we refer to the local atomic arrangement
that is repeated at regular intervals millions of
times in a three dimensional space.
Electrons, whose motion can be represented as a
wave, move through a periodic structure without
interruption. A metallic crystal lattice provides
an excellent medium for electron movement.
However, any irregularity in the repetitive
structures through which a wave travels may
deflect the wave.
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Electron path
Metallic Wire
Metallic Wire
Nuclei
Electron cloud
A metallic wire is made up of nuclei surrounded
by electron clouds. The electrons move
continuously throughout
the conducting wire. Notice, the path is not
necessarily a straight line path. In addition,
the path is that of ONE electron and in reality
there are n number of electrons based on the
materials and the amount of material involved.
Without any obstructions, the path is defined as
the mean free path.
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If the conducting material is deformed, then the
crystal orientation is changed and the
configuration of nuclei and electron clouds
could be altered, resulting in the change in the
electron movement.
Deformed wire
Metallic wire
Nuclei stretched apart
Fracture may have occurred obstructing electron
flow
Electron flow
As a result of the deformation, the electron
movement may reverse its direction.
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If an electron had been traveling toward the
positive electrode, and was then deflected, it no
longer gains velocity in that direction. The net
effect reduces drift speed. Irregularities in the
lattice decreases mobility. As a result of the
decrease in mobility, the conductivity decreases
and the resistivity increases. The average
distance that the electron can travel in its
wavelength pattern without deflection is called
the mean free path.
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Altering Resistivity
One way to alter resistivity is by increasing
temperature.
The resistivity of metals is linear with
temperature in the range of 100 to 500 K (-200 to
200 C)
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Metals Resistivity at 0º C
Temperature Resistivity
Ohm m
Coefficient yT, 0 C-1
Aluminum 27 0.0039 Copper 16 0.0039 Gold
23 0.0034 Iron 90 0.0045 Lead
190 0.0039 Magnesium 42 0.004 Nickel
69 0.006 Silver 15 0.0038 Tungsten 50
0.0045 Zinc 53 0.0037 Brass (Cu Zn)
60 0.002 Nichrome (Ni Cr)
1000 0.0004
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Another reduction in the free path of electrons
is the presence of solute atoms. A solid-solution
alloy always has a higher resistivity than does
its pure component materials. Introducing a
strain is the final approach to altering the
resistivity. Strain, e, is the dimensional
response to stress. (it is not a synonym for
stress) It is a fraction, not a percentage and it
is dimensionless. e D L / L0 Strain is
positive under tensile stresses and negative when
compressing stresses are applied.
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Deformation
Two types of deformation to be considered are
Elastic and Plastic deformation. Elastic
deformation is when a stress or strain (defined
later) is applied to an object causing the object
to be deformed from the original configuration.
However, when the stress or strain is removed
from the object, the object returns to its
original orientation. Elastic deformation is a
reversible strain or stress. If for example, the
stress applied is a tension, the object is made
longer. Removal of the stress returns the
material to the original state. When under
compression the material is shortened. Consider
the crystal structure of the example below
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When only elastic deformation exists, the strain
is proportional to the applied stress. The ratio
of stress to strain E s / e
stress/strain Any lengthening in compression of
the crystal structure in one direction, due to a
uniaxial force, produces an adjustment at right
angles to the force. The negative ratio between
lateral strain , and the direct tensile strain ez
, is called Poissons ratio, v, v - ey /
ez Plastic deformation is when a stress or
strain is applied to an object causing the object
to be deformed from the original configuration.
However, when the stress or strain is removed
from the object, the object does not return to
its original orientation. Consequently, the
original descriptive parameters may be altered,
such as the resistivity and conductivity of the
object.
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Definitions
F
Necking reduction in cross-sectional area as a
result of a tensile force being applied
Annealing Application of heat to a cold worked
metal to produce recrystallization
F
Hardness is a
resistance to penetration Ductility is permanent
strain that is realized before the test bar
fractures
Elongation
is plastic strain accompanying fracture Cubic
metals and their non-ordered alloys deform
predominantly by plastic shear or slip, in which
one plane of atoms slides over adjacent plane.
Shear deformation occurs with tension or
compression forces applied.
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Findings - Before Wire Deformation
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Data After Rolling Mill Deformation
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Deviation of Resistivity
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Four Point Test - Purpose

• To compute the resistance of a sample by setting
  a given current and measuring the voltage drop
  across the defined length of the sample.

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Four Point Test - Theory

• The four point test is a method of measuring the
  resistance of a given length of wire. It is
  based on the equation V IR where V is voltage,
  I is current, and R is resistance. If a simple
  series circuit exists with a given current then
  the voltage drop over a defined distance can be
  measured using a voltmeter. Thus the resistance
  can be computed as
• Resistance Voltage Drop / Current
• The accuracy of your reading can be tested by
  simply increasing the defined distance to any
  multiple and the voltage drop should also be a
  multiple of that change.

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Four Point Test - Procedure

• The four point test is a method of determining
  an amount of resistance over a set length of
  wire. This is done by using a power supply that
  has variable voltage and current. By completing
  the following method the resistance (R) can be
  computed.

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• A simple series circuit must be created between
  the power source and the wire sample that is to
  be tested.
• The current (I) must be set at a given amount
  over a specific distance.
• A voltage coming directly form the power supply
  will be entering the wire sample at point 1 and
  leaving the sample at point 4.
• The voltage drop (V) will be measured over the
  distance from point 2 and point 3 by using a
  voltmeter.

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Four Point Test - Calculations

• Example
• Current (I) 0.5 amps
• Voltage Drop (V) 6.8 volts
• Calculations
• R V / I
• 6.8 volts
• 0.5 amps
• 13.6 ohms

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Four Point Test
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2
3
4
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CURRENT WAS KEPT CONSTANT
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Four Point Test

• The four point test was named so because of the
  four contact points
• Point 1 2 The contact from either lead to
  either end of the wire sample.
• Point 3 4 The contacts from the voltmeter
  sensors to the points on the wire sample.

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Purpose
The purpose is to investigate the changes in
electrical properties, voltage, current and
resistance, as a result of the deformation of
material. An initial condition is the recognition
of the original state of the material. The
samples to be used are made of a metal that was
deformed in the process of making it wire.
(a) (b)
(c)
Play movie
Notice the pure material (a) is forced into a
cylinder and deformed by being pushed through the
openings of the device (b), until a wire is made
as a result of the forced deformation (c).
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It must be noticed that the original material
used, the wire, is in a deformed state with
regards to its length, thickness and resistivity
and/or conductivity. When we reference the
deformation of material henceforth, it is any
change from the initial state of the wire, that
we make reference. Because the materials initial
state is deformed, the values for the length and
thickness and resistivity must be measured and
calculated. Therefore, the purpose of
investigating the changes in the electrical
properties (V, I, R) as a result of the
deformation of the material is measured from its
initial state of being a wire.
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Procedure
1. Acquire three (3) sample wires of identical
length 2. Determine the diameter of each sample
using a micrometer at various points on the
sample, compute the area at these points and
average the area 3.  Using the Four Point Test,
determine the voltage over a designated length
of wire for a predetermined amperage 4. Compute
the resistance of the designated length of wire
using Ohms Law 5. Solve for the resistivity (r)
of the wire using R r L/A 6. Using an
electrical or a hand roller, deform the three
samples 7. Measure the length of the samples 8.
Measure the cross-sectional area of the deformed
sample at various points measure the diameter,
compute the area, and then average the
cross-sectional area 9. Using the Four Point
Test, determine the voltage over a designated
length of wire for a predetermined amperage 10.
Compute the resistance of the designated length
of wire using Ohms Law 11. Solve for the
resistivity (r) of the wire using R r L/A 12.
Anneal the three deformed samples (optional) 13.
Repeat steps 3, 4, and 5
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Content
Purpose Conclusion/Application Procedure
Student Activity Four Point Test Solution
Set Findings Theory
Click on point of interest
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Conclusion

• The purpose of this experiment was to investigate
  any changes in the electrical properties due to
  deformations of wire samples. Consequently, it
  was found that when a rolling mill deforms a wire
  sample, the cross-sectional area of the wire is
  changed as well as the length keeping a constant
  volume. This physical change will increase the
  resistance due to the cross-sectional reduction.
  Applying a 4-point test and using Ohms Law
  (VIR), it was found that the potential
  difference increased with current being held
  constant. Since resistance is directly
  proportional to the potential difference, the
  resistance was found to have increased as
  postulated. Having computed the resistance,
  knowing the length of the wire and the
  cross-sectional area of the sample used in the
  4-point test, one can determine the resistivity
  of the material using the following equation

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R ? l/A Even though the physical state of the
metal was changed it was noticed that the
resistivity between deformed states did not
change beyond statistical error of the measuring
devices. However, it should be noted, that the
resistance did change significantly due to the
change in the cross-sectional area in the
deformed wire.
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Application
From what was studied it became clear that the
value for ? remained constant when further
deformation occurred from the initial deformity
of the sample. A metal goes through extreme
deformation in the process of creating a wire, as
was shown. Therefore, any other deformation of a
said wire would not change its resistivity or
conductivity. Then what factors does one
investigate when using metals in electrical
situations? The most obvious factor in choosing
the best metal for a specific function depends on
its conductivity or resistivity. The other major
factor is the metals gauge. The cross-sectional
area will determine how much resistance will
occur. One can look up the resistivity of a
metal on a chart, being mindful that those values
are for undeformed states unless otherwise noted.
Having determined the resisitivity of a metal,
lets one know a physical property of the metal,
how conductive it will be, and whether the said
metal is in a deformed or undeformed state. This
is fundamental to the understanding of the
metals lattice structure and hence, its
stability.
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Further Exploring Critical Thinking
To advance the study of the effects of
deformation on the resistivity of a metal sample,
start the experiment with a piece of raw metal.
First, test for the resistivity of the substance
in its raw state. Second, test for the
resistivity of the substance after deformation,
the creation of a wire sample. Was the change in
the resistivity due to the energy loss as a
result of the extrusion process? Was this energy
loss in the form of heat? Since the deformed
metal has a greater resistance, therefore
impeding the electron flow, is this loss of
energy in electron movement the gain in potential
energy of the bond structure of the metal or is
the energy loss in the form of heat? Third, test
for the resistivity after the annealing process.
Does the heat introduced have to equal the heat
lost due to extrusion (was there any other type
of energy loss)? What effect is there in
annealing an already deformed metal? This
experiment will show the true effects of
deformation on a metal sample.
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Solution Set
Set 1 Set 2 Set 3 Set 4 Set 5
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Solution Set 1
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Solution Set 2
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Solution Set 3
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Solution Set 4
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Solution Set 5
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Student Activity

• Students are to
• Complete Charts Transferring Data from the Chart
  to the Grid Provided
• Compute Percentage of Error
• Complete a Lab Write-Up incorporating objectives,
  procedure, data conclusion

• In the conclusion include
• Make observation regarding Dr
• Make observation regarding D R and DV
• Conclude the effects of electron flow as we
  compare samples

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Student Activity Sets

• Student Activity Set 1
• Student Activity Set 2
• Student Activity Set 3
• Student Activity Set 4
• Student Activity Set 5

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Content
Purpose Conclusion/Application Procedure
Student Activity Four Point Test Solution
Set Findings Theory
Click on point of interest
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Student Activity Set 1
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Student Activity Set 2
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Student Activity Set 3
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Student Activity Set 4
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Student Activity Set 5
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DATA GRID
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C\My Documents\Wire.avi