Citation
Faraday measurement of magnetic hysteresis and megnetostriction of mild steels

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Title:
Faraday measurement of magnetic hysteresis and megnetostriction of mild steels
Creator:
Joyce, Sean Marcus
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English

Thesis/Dissertation Information

Degree:
Master's ( Master of science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Electrical Engineering, CU Denver
Degree Disciplines:
Electrical engineering
Committee Chair:
Gedney, Stephen D.
Committee Members:
Golkowski, Mark
Harid, Vijay

Notes

Abstract:
The focus of this thesis is the development of a measurement process to accurately record the non-linear hysteretic susceptibility and magnetostriction of ferromagnetic materials. On voyage, naval vessels will endure tremendous changes in magnetic or mechanical stress due to maneuvering and wave motion in the earth’s magnetic fields as well as continual changes in hydro-dynamic stresses. Such changes in stress change the magnetic properties of the steel, impacting the ship signature. This research aims at providing the ability to predict the changes in the magnetic properties of steels undergoing dynamic changes in magnetic and mechanical stresses. Doing so will facilitate the prediction and removal of magnetic signatures from naval vessels – providing the cloaking from underwater sensors that is essential to the survival of the vessel. Novel experimental methods have been developed in the CU Denver magnetics laboratory using a Faraday coil measurement system. These methods have enabled the accurate prediction of the essential physical parameters needed to predict non-linear susceptibility of mild steels as a function of magnetic fields and axial mechanical stresses. The apparatus and experimental results will be presented demonstrating the capabilities of the measurement system.

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University of Colorado Denver
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Auraria Library
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Copyright Sean Marcus Joyce. Permission granted to University of Colorado Denver to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

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Full Text
FARADAY MEASUREMENT OF MAGNETIC HYSTERESIS AND MAGNETOSTRICTION OF MILD STEELS
by
SEAN MARCUS JOYCE B.A., Indiana University, Bloomington, 2008
A. S., Red Rocks Community College, 2015
B. S., University of Colorado Denver, 2017
A thesis submitted to the Faculty of the University of Colorado in partial fulfillment of the degree of Masters of Science Electrical Engineering Program
2019


This thesis for the Master of Science degree by Sean Marcus Joyce has been approved for the Electrical Engineering Program By
Stephen D. Gedney, chair Mark Golkowski,
Vijay Harid


Joyce, Sean Marcus (M.S., Electrical Engineering Program)
Faraday Measurement of Magnetic Hysteresis and Magnetostriction of Mild Steels Thesis directed by Professor Stephen D. Gedney
ABSTRACT
The focus of this thesis is the development of a measurement process to accurately record the non-linear hysteretic susceptibility and magnetostriction of ferromagnetic materials. On voyage, naval vessels will endure tremendous changes in magnetic or mechanical stress due to maneuvering and wave motion in the earth’s magnetic fields as well as continual changes in hydro-dynamic stresses. Such changes in stress change the magnetic properties of the steel, impacting the ship signature. This research aims at providing the ability to predict the changes in the magnetic properties of steels undergoing dynamic changes in magnetic and mechanical stresses. Doing so will facilitate the prediction and removal of magnetic signatures from naval vessels - providing the cloaking from underwater sensors that is essential to the survival of the vessel. Novel experimental methods have been developed in the CU Denver magnetics laboratory using a Faraday coil measurement system. These methods have enabled the accurate prediction of the essential physical parameters needed to predict non-linear susceptibility of mild steels as a function of magnetic fields and axial mechanical stresses. The apparatus and experimental results will be presented demonstrating the capabilities of the measurement system.
The form and content of this abstract are approved. I recommend its publication
Approved: Stephen D. Gedney
iii


Table of Contents
CHAPTER I. INTRODUCTION AND BACKGROUND.................................................1
Introduction.........................................................................1
Background...........................................................................3
CHAPTER II. THEROY OF THE FARADAY COIL AND MEASUREMENT SYSTEM..........................6
Faradays Law.........................................................................6
Theory for the Thin-Wall Pipe Experiments............................................7
Measurement of the H field.........................................................8
Measurement of Flux in Pipe Samples................................................9
Measurement of Stress Applied to Pipe Samples.....................................11
Theory for Thin-Wall Ring Experiments...............................................11
Measurement of the H field in Ring Samples........................................12
Measurement of Flux in Ring Samples...............................................13
CHAPTER III. DESCRIPTION OF EXPREMENTAL SETUP AND MEASUREMENT SYSTEM..................14
Sample Descriptions and Measuring Devices for Thin-Wall Pipe Experiments............14
Sample............................................................................14
Data Acquisition Device...........................................................15
Power Supply......................................................................15
Pipe Sample Faraday Coil..........................................................16
Pipe Sample Solenoid..............................................................17
Hall Probe........................................................................18
Pipe Sample Test Fixture..........................................................19
Load Frame........................................................................20
Sample Descriptions and Measuring devices for Thin-Wall Ring Experiments............21
Sample............................................................................21
Ring Sample Inner Faraday Coil....................................................22
Ring Sample Outer Faraday Coil....................................................23
Ring Sample Test Fixture..........................................................24
Temperature Controlled Environment................................................25
Electro-Magnetic Interference.......................................................27
Measurement Procedures..............................................................28
Demagnetization Process...........................................................30
The Quasi-Static Step Method (QSM)................................................31
CHAPTER IV. EXPREMENTS AND MEASURED DATA..............................................34
Major Loop Example..................................................................34
Setup.............................................................................34
IV


Results..................................................................................34
X Initial via Minor Loops...................................................................37
Setup....................................................................................37
Results..................................................................................39
FORC data...................................................................................42
Setup....................................................................................42
Results..................................................................................45
Faraday Measurement of Magnetostriction.....................................................48
Setup....................................................................................48
Results..................................................................................50
Faraday Magnetostriction Effect on Hysteresis...............................................50
Setup....................................................................................50
Results..................................................................................52
Ring Major Loop Example.....................................................................53
Setup....................................................................................53
Results..................................................................................54
Ring FORCs Experiment.......................................................................55
Setup....................................................................................55
Results..................................................................................56
CHAPERV. CONCLUSION...........................................................................59
References....................................................................................60
v


CHAPTER I. INTRODUCTION AND BACKGROUND
Introduction
The focus of this thesis is to report on the creation of a measurement system that can accurately measure the physical parameters needed to validate the behavior of the magnetic materials, and the measurements taken by the Faraday Coil Method side electromagnetics lab at University of Colorado, Denver. This experimentation was derived from first principles and has been developed into functional apparatus. The apparatus consists of: a computer controller overseeing an amplifier to provide a magnetic field and a load frame to provide a stress field, various transducers to measure magnetic and stress related parameters, and a data acquisitions device that is able to record data taken from the transducers. Several experiments are presented using this apparatus.
The measurement system described in this writing uses a two device setup to measure the magnetization induced in the test material. The two devices are a Faraday coil and a Hall Effect probe, and when used to measure the field and flux through and in a ferromagnetic sample they can yield precise measurements of the magnetic state of the sample. While the Faraday coil and Hall Effect probe were chosen in this apparatus, other measurements methods were reviewed.
A super-conducting quantum interface device (SQUID) is able to measure very small fields, and can operate from very cold to very hot environments. The SQUID relies on quantum mechanical effect in conjunction is a super conducting detection coil to accurately measure the magnetic properties of materials. A SQUID is not ideal in this situation however, as it takes measurements very slowly. The experiments contained herein are done in minutes at the slowest, and a squid would not be able to create measurements in the allotted time frame.
A second approach would be to use a vibrating sample magnetometer (VSM), which physically moves a small sample through an accurately generated field to accurately measure the sample's magnetic moment. The VSM can perform experiments within the desired time frame, and to the accuracy needed
1


in the applications herein. However, it is exceedingly difficult to induce large amounts of continual and varying physical stress on the sample while it moves through the applied field. This makes a VSM ill-suited to measuring stress induced changes in magnetization. The Faraday coil and Hall Effect probe are easily placed in a load frame, and are able to take measurements within the desired time constraints, thus making them very well suited to the tasks presented herein.
The motivation for this experimental set-up is to quantify and validate the physical parameters used in building a multi-physics based empirical model for the description of ferromagnetic materials. The physical properties of interest are the magneto-hysteretic, anisotropic, magnetostrictive, and thermal behavior of the ferromagnetic materials. The experimentation preformed in the lab will be used to strengthen and verify the non-linear models used in the Magstrom software.
Various models of ferromagnetic hysteresis have been created. The Preisach model was presented in 1935 by Ferenc (Franz) Preisach in the German academic journal “Zeitschrift fur Physik” [1], It was then expanded upon by Ann Reimers and Edward Della Torre in 1998 [2], The model is founded on a superposition of reversible and irreversible magnetization
M=Mi+Mr. (1)
This can then be written in terms of normalized magnetization by reducing the terms on the RHS by M s, the saturate magnetization of the material.
M = SMsm, + (1 - S)MsmR S is the squareness of the material given as

(2)
(3)
where Mrem is the remnant magnetization of the material, nr and mR are normalized irreversible and reversible magnetizations defined as
2


(4)
mI{H) =
mR(H) =
M^H)
Mrem Mr(H)
Ms ~Mren
If Ms(I - S) = Ms(1 -Mrem /Ms) = Ms -Mrem then the differential susceptibility can be expressed as [2]:
dM ^ dm, ,, ^ dm„ ^ ^
X — “777 - s ——— + (1 — S)Ms — SMs%j + (1 — S)Ms%R
drl nH HH
dH 'â–  dH (5)
This model predicts reasonably well for small fixed hysteresis loop with fixed parameters. However, this model is lacking in its ability to predict a combination of varying major and minor loops.
The Jiles-Atherton model is formulated as a first order differential equation.
Ma„ ~Mm.
dMm. _______________
dH kS - a (Man - Mjn.) Mrev=c{Man-Mm.)
'H + aM
(6)
Ma„(H)+Ms
coth
H + aM
Mjn. is the irreversible magnetization, Mrev is the reversible magnetization, Mm is the anhysteretic magnetization, and 5 = {dH / dt)/\dH / dl \ is the sign of the field change. This model has 5 tunable parameters: the irreversible loss k , the anhysteretic behavior a , the reversible to irreversible proportions c , the effective field a , and the saturate magnetization Ms. Each of these parameters can be measured by a single hysteresis loop if the loop is taken far enough into saturation [3]. One problem with the Jiles-Atherton model is that it does not fit to data well if the reversals are outside of a small range magnitudes for a fixed set of parameters or for an arbitrary M .
To overcome the narrow portions of the hysteresis curve at which these models work, the C. Schneider model is used.
Background
The multi-physics based approach used in this thesis is based on C. Schnieder's exponential model of differential susceptibility:
3


^exp =XiXr eXP
aXB.
2 X,Hanh
Xr{M-Mr) Zr(Ms-M,j_
The variables from the model are all based on measureable physical parameters. is the initial
(7)
susceptibility. H is the coercive field. Hmh is the anhysteretic field. Ms is the saturate magnetization. Mr is the magnetization of the system at the last reversal. M -Mr is the change in magnetization since the last reversal. M is the current magnetization in the sample. %r is the poly crystalline texture given
. Figure 1 has a plot of a common hysteresis curve, with some of the important
as xT =
'l (M^1
{Msjj
V
features highlighted. The terms given to define (7) will be explained via Figure 1.
A Hysteretic Example
Figure 1 - An example of a hysteresis curve, with important features highlighted. (1) virgin state, (2) coercive filed, (3) remanence, (4a) positive reversal, and (4b) negative reversal
A single data point at (1) in Figure 1 shows a measurement of a sample in a demagnetized state. This means that the collection of magnetic moments that makes up the magnetic signature of the sample is in a totally entropic state, every magnetic domain is relaxed, and there is no order between the domains. If an increasing magnetic field is applied, the magnetization of the sample will follow the curve from point (1)
4


to point (4a), as an increasing number of domains rotate to align with the applied field. This line is called the virgin curve, and the definition of is found on this curve. is the slope at the virgin curve as the first few domains begin to rotate. That is, the slope of the curve just as it leaves point (1).
The marker (2) shows where the hysteresis curve crosses the M = 0 line. This crossing denotes the coercive field, H . The coercive field has physical meaning, which is the applied field that will exactly cancel the magnetization in the sample.
The marker (3) shows the remanent state of magnetization, or “remanence”. This is the magnetization of the sample if no field is applied, and is a function of reversal at markers (4a,b) .
Markers (4a) and (4b) are the positive and negative reversal points. This is where the applied field changes direction. If the applied field were reversed at a positive reversal after having a strength of oc A/m, then the magnetization at this point would be Ms, or the saturate magnetization of the sample. Ms is the magnetic field generated if all of the domains in a sample have had their magnetic dipoles perfectly aligned to point in the same direction [4].
5


CHAPTER II. THEROY OF THE FARADAY COIL AND MEASUREMENT SYSTEM
The Faraday Coil Measurement System is a two sensor method of measuring the magnetization induced in a sample. This system measures the magnetization of two geometries of samples. The first sensor is a Faraday coil, wrapped tightly about the sample. The second sensor is a transducer that can measure the ambient magnetic field in the experiment.
Faradays Law
The underlying principles of the Faraday Coil Measurement (FCM) method can be derived from first principles. Faraday's law predicts the voltage induced across the windings of a tightly coiled wire in the presence of a magnetic field as
Here Vmf (t) is the voltage across the coil, N is the number of turns in the coil, B is the magnetic flux,
Where H is the magnetic field, and M is magnetization in a magnetic material present in the cross-section. Substituting (9) into (8) leads to
(8)
and S is the cross sectional area of the coil. B can be expressed in terms of the magnetization and
magnetic field as
B = ju0^H+M)
(9)
(10)
Equation (10) serves as the heart of the measurements taken in this writing.
6


Theory for the Thin-Wall Pipe Experiments
Copper Winding
â–¼
Steel Pipe
Figure 2 - Experimental setup for the thin-wall pipe experiments
For this experiment, the coiled copper wire is assumed to be tightly wrapped around a steel pipe with an inner radius of a and an outer radius of b as shown in Figure 2. If the pipe is axially parallel to an x-directed magnetic field, and no other ferrous material contributes significantly to the experiment, then (10) can then be estimated as
vemf (0 * ~nMo frt(H^b2 +Mxx[b2 - a2)).
dt
Solving for Mx reveals an expression for the magnetization of the steel pipe as
« -
Nfin7i{b'
t
\Vemf(t)dt-NMoHx7rb2
(11)
(12)
7


Equation (12) implicitly shows the measurements needed to calculate the magnetization for the steel pipe. The voltage Vemf(t) is measured across the faraday coil, and has to be cumulative with time. The
magnetic field around the pipe, Hx can be measured by an axial Hall Effect probe whose sensor bisects the center of the Faraday coil.
In the calculation for the magnetization, it is assumed that the magnetization is constant about the cross section of the pipe (radially and azimuthally) as well as along the axial length of the Faraday coil. The axial magnetic field is also assumed to be constant over the entire cross sectional area of the coil as well as along the length. These assumptions are considered to be sound, if the pipe is significantly longer than the coil (at least 5 times longer), and if (b-a) Measurement of the H field
A Hall Effect sensor, placed at the center of a hollow pipe, is used to measure the H field within the sample. The field at the center of the hollow pipe is assumed to be uniform through this cross-section. A chip produced by Allegro, model A1324 has been used to both prototype and take the data presented herein.
The Hall probe measures fields continuously, but the package used in this application is prone to noise. The Allegro hall chip intrinsically has noise floor of approximately 100 A/m. This is a combination of environmental noise (with a large contributor being 60 Hz noise due to EMI) as well as conducted emissions through the Kepco power supply. To have confidence in our measurement a large number of samples must be taken while the applied field is held constant. If the noise has a zero mean, then much of it can be eliminated by averaging over this 'hold' period. The average is taken as
s
1 N
—S's■ >
(13)
8


where N is the number of samples taken during the averaging period. The value s is the average and s is an individual sample indexed by z. The estimation of the standard error of the mean of a sample set is given as
(14)
Where N is the sample size, cris the standard deviation, and SE is the standard error of the data set. As N increases the error of the estimation of the measurement decreases. In addition to increasing the number of samples over which the Hall probe is averaged, a time step can be chosen that will help fdter noise. An ideal a number of points to average over and scale by is chosen such that, the entire sample duration will be an integer multiple of a period of the strongest noise signal in the system.
To convert the averaged Hall Probe data into a magnetic field the averaged voltage is multiplied by a conversion factor given by the manufacturer of the probe. As specified in the data sheets
1 G 1 Oe 79.577 Aim = 15915.4 ± 757.876 Aim
5 ±0.25 mV 0.005 ±0.00025 V 0.005 ±0.00025 V V
(15)
The conversion factor CF is multiplied by the voltage averaged over the hold period V to find
HHaii=s-CFâ–  (16)
Measurement of Flux in Pipe Samples
The Faraday coil voltage is more difficult to measure. The Faraday coil measures the time rate of change of the magnetic flux as described in (12), with the assumption that is the measured field provided by the Hall Probe.
9


The flux through the coil is varied by changing an applied magnetic field by a separate current carrying winding. The small window when the field is switched from one hold point to the next hold point must be measured with precision to capture an accurate assessment of the transient flux. If the change in field were applied as a mathematical step, the window of change would be very narrow, and the peak voltage would surely exceed the 10 V limit on the data acquisition device. Instead a ramp is used to transition between applied fields. The ramp function has the additional advantage of lengthening the time over which the change happens, allowing for much greater control and measurability in the Faraday coil’s signal. The ramp’s slope can be configured both in duration and in step height in a LabVIEW program controlling the measurement.
Changing the duration of the ramp allows the user to capture one or more multiples of a period of the signal’s strongest noise, generally 60 Hz or 16.67 ms in duration. During integration this period of noise is averaged over, and if sampled correctly, it will lower the noise floor. The time step between data points must be considered here as well. The L/R time constant of the Faraday coil will determine the size of the time step. After the step and hold there must be enough data points to define the L/R response as the Faraday coil discharges its energy. This will require hardware that can take data very quickly.
Changing the step height of the ramp has a direct impact on the amount of voltage induced across the Faraday coil, and given by Faraday’s law of induction
00
EMF =------- (17)
dt
The magnitude of the electromotive force (EMF) induced across the Faraday coil is linearly proportional to the slope of the ramp. The amplitude of this voltage is important to consider, because the peak needs to be well above that of the noise inherent in the system, yet lower than the voltage threshold for the data acquisition device. While it is assumed that the total sample time for a single ramp-and-hold will be an integer multiple of the period of the strongest noise, a cleaner signal will have a voltage induced peak that is easily distinguished from any signal noise.
10


Measurement of Stress Applied to Pipe Samples
The MTS Landmark load frame records and outputs axial force applied to a sample. The measurement is taken in terms of force as the load frame has no knowledge of physical parameters of the sample under test, such as cross-sectional area or the Young's modulus. This recorded force must be converted to stress for our calculations. The force applied on a surface is measured in SI units as Pascals.
- = A
Where F is the axial force (N), A is the cross-sectional area (m), and = A
(19)
The surface area of the pipe used in the experiments described herein is 8.5 x 10
m
Theory for Thin-Wall Ring Experiments
The theory for the measurements taken during the ring sample measurements mirror the measurements taken for the pipe experiments. Equation (10) is still the basis for measuring the magnetization induced in the sample, however the calculation is adjusted for the azimuthal cross-sectional area of the ring, and the measurement method for the magnetization and the H field has changed due to physical constraints. The cross-section of the wall of the ring is considered square for the purposes of calculation and thus the cross-sectional area is defined by the height of the wall and the thickness of the wall. Following (10) -(12), the explicit calculation of magnetization is,
11


Here N is
AT, « —
J V (20)
Nju0 (cib )
a and b are the thickness and height of the wall of the ring, //„ is the free-space permeability, and the number of turns in the Faraday coil as shown in Figure 3.
a
Faraday
Winding
<
Field
Figure 3 - Experimental setup form thin-wall ring
Another key difference between the pipe sample experiments and the ring sample experiments is how data is collected. Holding the field constant for discrete amounts to time to allow averaging cannot be done, due to the accumulation of heat in the experiment from the driving Faraday coil's copper heat loss. Instead the field is changed continuously, and measurement methods are adjusted accordingly.
Measurement of the H field in Ring Samples
Measurement of the H field in the ring cannot be done with a Hall Effect sensor, as the ring has no
hollow region to imbed the sensor. Instead the field outside of the metal can be inferred through close measurement of the applied field. Since the field is being applied and measured azimuthally, there is a continuous path of metal that can contain the flux applied to the sample. This means that no magnetic
12


poles will form in the sample, and in turn no demagnetizing field will be generated to oppose the applied field. The only field generated in the experiment will be the applied field. A sense resistor with a known impedance has been placed in series with the driving Faraday coil, and the voltage across the sense resistor is closely monitored by the data acquisition device. This voltage is used to calculate the current on that line via Ohm's law. Since the length and the number of turns of the driving Faraday coil are known, then the field produced by the driving coil can be calculated as
c s
However, since H^ is uniform,
H«pp=I~i
(22)
where n is the number of turns in the coil, / is the current on the line, and / is the length of the coil computed as 2k U ^ ^ . This data is not averaged over, as the waveform provided by the driving
amplifier has a noise characteristic that is under the required tolerances.
Measurement of Flux in Ring Samples
Measuring the voltage across a Faraday coil provides the flux measurement, in much the same way as described in the pipe sample. Since the step and hold method cannot be used with the ring samples there is no consideration for ramp size and shape. The only mathematical tool available to combat intrinsic noise in the signal measured from the Faraday coil is the rate at which the signal is recorded. A sampling rate must be chosen that is a mode of the fundamental frequency of the strongest noise contributor (in this application 60 Hz is generally the strongest), and the rate has to be fast enough to describe the produced waveform with ample fidelity.
13


CHAPTER III. DESCRIPTION OF EXPREMENTAL SETUP AND
MEASUREMENT SYSTEM
The FCM method is defined by (12) and determined in Chapter 2, discussed two measuring devices needed to accurately describe the magnetization of a steel sample. However, a few other devices are needed for the experimental setup. These apparatus are discussed in this chapter.
Sample Descriptions and Measuring Devices for Thin-Wall Pipe Experiments
Sample
Each steel sample has been milled into a pipe, 206 mm long. The pipe has an inner diameter of 18mm and an outer diameter of 20.8 mm at the center. The outer diameter has a flare at each end that is 23.9 mm in diameter and extends in 30 mm from each end. This flare is threaded to fit into a non-magnetic titanium sample holder. A sample is pictured in Figure 4.
â– 
Figure 4 - Photo of a steel pipe sample with no preparation
Four types of steel have had been the subject of experimentation, and they are identified by their unique batch number. Two of the batch numbers are the same type of mild steel, and comparing them can give insight into the magnetic behavior of the steel across various batches. Each material was milled from a
14


plate 96” wide, 480” long and with a varying thickness. Chemical compositions along with the plate gauges are given in Tables 1 and 2, with each material differentiated by their respective melt numbers.
Table 1 - Chemical Make-up of the Various Sample Materials as a Weight %
Element C Mn P S Cu Si Ni Cr Mo Gauge
C0878 0.16 0.29 0.005 0.002 0.13 0.22 2.40 1.25 0.24 1.25”
C7614 0.16 0.23 0.006 0.001 0.15 0.21 2.93 1.46 0.40 1.75”
U6346 0.15 0.22 0.007 0.002 0.14 0.30 2.59 1.55 0.37 1.25”
U3926 0.14 0.23 0.010 0.003 0.15 0.32 2.53 1.55 0.37 1.75”
U8520 0.17 1.41 0.014 0.010 0.30 0.23 0.12 0.11 0.02 1.5”
W4G801 0.15 1.32 0.013 0.001 0.19 0.22 0.10 0.09 0.06 1.5”
Data Acquisition Device
Either a National Instruments USB-6466 or a USB-6343 Data Acquisitions device (DAQ) is responsible for coordinating the experiment by controlling a Kepco Bipolar 12-36 power supply (Kepco) and an MTS Landmark LVDT Servo-Hydraulic Test System (load frame), while taking data from various sensors. Figure 5 (right) is a photo of the USB-6466 with the dust cover open to show the voltage terminals. The voltage across the Faraday coil, the voltage across the sense resistor, and the voltage output from the Hall Probe are recorded by the DAQ. The DAQ is in turn controlled by a Lab VIEW program that has been written specifically to handle all of the experiment setup permutations.
Power Supply
To provide a magnetic field, a solenoid is driven by a Kepco 36-12 Bipolar Power Supply, which is in turn controlled by the DAQ. Figure 5 (left) is a photo of the two Kepco power supplies used in the lab. The Kepco is an analog power supply, and is being used as a voltage controlled current source. The voltage waveform created by the DAQ is amplified into a current waveform by the Kepco. The mapping from voltage to current is a linear scaling with a factor of 1.2, or lout = 1. 2U„.
15


Figure 5 - (left) the 2 Kepco Bi-polar Power Supplies used in the lab, (right) The NI6343 DAO-mx USB with its cover off
showing the internal CAT-5 connections
Pipe Sample Faraday Coil
The sample is fitted with a Faraday coil wrapped around a custom made bobbin fitted about the waist of the pipe. The bobbin was designed in-house using Solidworks, and 3D printed with a Prusa i3 MK2 printer using 1.75 mm PLA filament. The Faraday coil is wound from 27 gauge heavy coated magnetic wire, and 190 turns are fit into 39 mm axially along the pipe in 2 layers, shown in Figure 6. An Acme coil winding machine was used to ensure each turn was layered consistently. The leads of the Faraday coil were soldered to shielded CAT5 cable for modularity and noise reduction. Each lead to the Faraday coil is also attached to a 100 kfi> pull-down resistor to avoid a virtual ground in the coil.
16


Figure 6 -A Sample ofHY 100, fitted with a bobbin and a Faraday coil
Pipe Sample Solenoid
A solenoid provides the magnetic field that is applied to the sample. A 42.15 mm outer diameter PVC pipe was wrapped with 604 turns of 18 gauge magnet wire in two layers, as shown in Figure 7. An Acme coil winding machine was used to ensure consistency in the windings. The turn density of the resulting solenoid is 1887.5 tums/meter with an effective length of 0.32 meters. The length of the solenoid is half again as long as the pipe sample to create a uniform field over the length of the sample centered in the solenoid.
17


Figure 7 - Solenoid responsible for building the magnetic field for each experiment
Hall Probe
An A1324 Allegro Hall Effect sensor is mounted inside of the pipe, centered in the middle of the faraday coil, with the face of the sensor normal to the axial direction of the pipe. The Hall Effect senor is an analog three pin device, and is mounted to a custom cut dowel that holds the face of the chip normal to the direction of flux that is centered within the sample as shown in Figure 9. Powered by a static 5V line, the output voltage of the middle line corresponds to the strength of a field oriented normal to the face of the sensor. This voltage is continuously read by the DAQ via a CAT5 cable. The A1324 is capable of measuring fields up to ± 80,000 A/m with a resolution of 100 A/m in normal working conditions. This resolution is limited by the noise that is intrinsic to the chip and in the entire measuring system generally.
The hall probe was calibrated by comparing the measured filed to a known applied field. This applied field was supplied by a MicroSense Vibrating Magnetometer that had been calibrated to a NIST traceable standard. A sample of this calibration is shown in Figure 8. Both a stepped field and a swept field are compared during the calibration. The stepped field gives a very accurate magnitude comparison between the VSM field and the Hall Effect sensor. The sweep comparison was done to ensure that there is no time delay in the sensor, so the comparison of the Hall Effect sensor and the Faraday coil can be done in real time.
18


Figure 8 - Allegro Flail Probe mounted to a custom fitted dowel rod
Figure 9 - Comparison of the VSMfield to the calibrated Hall Effect sensor used in the thin-wall pipe experiments calibration
Pipe Sample Test Fixture
Two milled titanium fittings hold the sample, the dowel mounted Hall Effect sensor, and the solenoid in place during the experiment. Each fitting is screwed to the sample using the threads on the ends of the
19


sample. The dowel seats to one of the fittings, insuring that the Hall Effect chips takes measurements in the same location for each experiment. Figure 10 shows the assembled sample and test fixtures. Titanium is used for two reasons; it has no magnetic moment and will contribute no magnetic signal in the experiment, and it is strong enough to not yield during stress cycles.
Figure 10 - Titanium sample holders screwed onto the ends of an FIY100 sample
Load Frame
For the testing of magnetostrictive properties the UCD Lab has employed the use of an MTS Landmark LVDT Servo-Hydraulic Test System (load frame). The load frame can apply tension and compression axially to our samples via a Series 515 SilentFlo Hydraulic Power Unit. Hydraulic wedge grips are used to clamp and hold the titanium sample holders, with the sample between them. The wedge grips are high-carbon steel fittings with a rounded and textured recess that matches the outer diameter of the ends of the samples holders. Hydraulic power is used to apply radial force to the grips, forcing mirrored pairs of grips to clamp on the ends of the sample holder. Figure 11 shows the assembled sample and sample holders being held between the two sets of wedge grips, ready for stress testing. Simulations have been run in Magstrom to show that while the grips are made of a magnetic material, their distance from the solenoid is such that their magnetic contribution to the experiment is negligible [6].
20


Figure 11 - AITS Landmark's wedge grips holding the assembled sample set-up
Sample Descriptions and Measuring devices for Thin-Wall Ring Experiments
Sample
A collection thin-walled rings, each with a rectangular wall cross-section, have been lathed from several batches of mild steel. Each ring has a height of 25 mm, a wall thickness of 1.3 mm and an outer diameter of 54 mm. Two Faraday coils have been wrapped about the wall of the ring, both with windings running in axial direction. The inner coil serves as a sense coil, while the outer coil serves as the driving coil in the experiments contained herein. A silicone conformal coating has been applied to the bare steel before winding and after each layer of winding. This is to help ward off corrosion and provide a shock absorption barrier. Figure 12 shows both a bare ring sample, and a fully wrapped ring sample.
21


Figure 12 - (top) a bare ring sample before preparation
Ring Sample Inner Faraday Coil
The faraday coil for the ring samples is wound from 24 gauge heavy coated magnet wire, wrapped tightly over the entire surface of the ring as shown in Figure 13. Under the winding the magnet wire, the ring has been coated by a silicone conformal coating. This coating serves a twofold purpose, to help keep the magnet wire electrically separate from the steel, and to keep the steel and wire from damaging one another during handling.
22


Figure 13 - Photo of the Faraday windings wrapped around a ring sample
The windings of the ring are counted from a photo taken after winding, as exemplified in Figure 13. Since the inner Faraday winding are covered by the outer Faraday windings this photo gives a record of the windings that can be referenced as proof to the condition, count, and turn density of the coil. A bobbin was 3D printed to assist in the winding of the inner and outer coils.
Ring Sample Outer Faraday Coil
The outer Faraday coil serves as the driving coil for the system. This has been made from 24 gauge heavy magnet wire, and is wrapped in much the same manner as the inner Faraday coil. Again a photo has been taken of each sample just after winding the wire to give a record of the number of turns, the condition of the coil, and an assessment of the turn density of the coil. Figure 14 is an example of a ring that has been wrapped in the 24 gauge magnet wire. It is clear to see that the number of turns can be counted and recorded easily.
23


Figure 14 - Photo of the outer Faraday coil, just after being wrapped Ring Sample Test Fixture
The leads of the magnet wire after being wrapped tightly around the sample have proven to shift slightly, and rub against one another. This movement causes the enamel on the wire to erode, and expose the bare copper underneath. This bare copper causes shorts that can easily corrode data. Care has been taken to secure the leads in a manner that will keep the shifting to a minimum, while still allowing the DAQ easy access to the leads. A fixture was designed and 3D printed to accomplish these tasks. Figure 15 shows the Test fixture. The CAT-5 socket connects the inner Faraday coil to the CAT-5 cable to allow the Faraday coil voltage to be read by the DAQ. The banana sockets are connected to the outer cable and can handle the high amperage generated by the Kepco power supply.
24


Figure 15 - The Ring Sample Test Fixture
This test fixture is used for desktop applications, however it covers the winding to a great extent, and does not allow for heat to escape with high amperages are being passed through the driving solenoid.
Temperature Controlled Environment
The ring sample uses 24 gauge wire for its driving solenoid. The amperage that the wire needs to carry to get an applied field to 14,000 A/m is 6.9 A, calculated from (22). The resistance per unit length of the 24 gauge magnet wire is 0.0842 Q/m. The heat loss of the system due to the current traveling through the copper wires in the driving solenoid is given by
Pheat=I2R- (23)
This gives a loss 4.009 W/m. The 24 gage heavy coated magnet wire has a measured diameter of 0.523 mm. The length of wire used in the solenoid can be estimated as
C„*2 (a + b)*N, (24)
25


where a is the thickness of the ring, b is the height of the ring, and N is the number of turns of the solenoid around the ring. With a wall thickness of 1.35 mm a height of 25.3 mm and a turn count of 278 the length of wire wrapped used in the driving solenoid is around 15m long. This means at maximum applied field the solenoid generates roughly 60 W of power as heat loss. This heats the steel quite quickly. A cooling method was designed and built to help keep the sample near to a stable temperature. The design uses a blower motor to drive air over a copper tubing heat exchanger, and a photo of the cooler is presented in Figure 16.
A custom interface between the blower motor and a 6” PVC 45° elbow was designed and 3D printed.
The design was drawn in SolidWorks and printed in three sections on a Prusa mk2 3D printer out of 1.75 mm PLA. The three sections printed on the 3D printer were joined with common automotive Bondo. A 2’ section of 6” diameter PVC pipe was fitted to the second side of the 45° elbow. The 2’ PVC pipe section houses a heat exchanger made from 5/8 copper tubing. The tubing was bent around a 4” aluminum pipe and has 10 turns. The heat exchanger is fed by PVC tubing and a household fish-tank pump. The pump is capable of delivering 10 gallons a minute of cooled liquid to the heat exchanger. The sample sits just inside the exhaust of the 2’ PVC pipe, and has air, cooler by the heat exchanger, blow over its surface for the duration of the experiment. A sample holder was 3D printed out of PLA, to control the rate of air flow around the sample and hold the leads to the various measurement devices attached to the sample.
26


Figure 16 - Temperature controlled environment, complete with blower motor on the left and exhaust on the right
Electro-Magnetic Interference
All sensors are connected to the DAQ via shielded CAT5 Ethernet cables. The sensor cables can be a source of noise due to electromagnetic interference (EMI), including significant energy at 60 Hz due to radiation by the local power grid. The Faraday coil and Hall Effect sensors are connected to shielded CAT5 connectors so they can be easily connected to a shielded CAT5cable. Shielded CAT5 connectors are also used to connect the cables to the DAQ. The outer shield is grounded at the DAQ to reduce undesirable EMI.
27


Measurement Procedures
TJMD_Output
A pair of LabVIEW programs have been written to control both the Kepco amplifier and the data collection done by the DAQ. The first program (TJMDOutput) is the controller for the Kepco power supply and the MTS load frame, while the second program (TJMDInput) is responsible for coordinating the collection of data via the DAQ during the experiments. These two programs run in tandem, each using their own clock defined in the software, but synchronizing the clock at the start of runtime. Figure 17 shows the flow diagram and a general over view of both programs. Figure 18 shows an image of the user interfaces designed to allow a user to control these two programs.
The TJMD Output executes first, it takes all of the variables input by the user interface and from them builds the waveforms that will drive any devices paired to the DAQ. The program them allocates enough memory on the DAQ to hold all of the needed waveforms, initializes the clock, and
Figure 17 - Flow diagram for the LabVIEW controller programs
waits for the global 'ready' flag to be set.
The TJMD Input program is executed second. The input variables provided by the user though the
user interface in Figure 18 define the runtime and frequency used in reading the voltage channels from the
28


DAQ. The needed voltage channels are allocated on the DAQ and then the global 'ready' flag is set by TJMD Input. Both the input and output channels are driven when the ready flag is set, but each use their own clocks to execute the remainder of their own programs. The TJMDOutput program has several types of waveforms built into it, including but not limited to: stepped triangle, swept triangle, and swept sinusoidal. Each of these modes can be customized by the user. As an example the sinusoidal can have an exponential decay applied, or the triangle can a different slope, start and end point for each rise and fall of the wave. This customization is necessary for the great variety of experiments performed with the
FCM.
Figure 18 - The frontfacing controllers for the LabVIEW programs that control all of the experiments contained herein (right) is
the output program, while (left) is the input program
29


Demagnetization Process
The voltage induced across the Faraday coil is proportional to the time-derivative of the dynamic flux cutting through the coil. Consequently, the measurement of the physical magnetization by the FCM requires knowledge of the initial magnetization at the onset of the experiment. An absolute magnetization measurement requires a known magnetic state. The most reliable states are saturation or a demagnetized state. A saturate state is difficult to obtain since it requires very large fields to fully get into saturation. The complexity is compounded if the material under test is unknown, as saturate magnetization is a property of material. This also limits the measurement to begin with a major loop. Alternatively, a demagnetized state allows one to measure the virgin curve, or minor loops near a virgin state, as well as major loops. It also does not require an applied field that will near saturation. Consequently, the default known state for our measurements is a demagnetized state.
Before conducting each experiment the sample is demagnetized. The process used is to initially apply a 1 Hz sinusoidal magnetic field with an amplitude that is decreasing exponentially. The applied field should induce a magnetization that is at least 80 % of saturation. For the CUD pipe samples, this is typically on the order of 9000 A/m for the mild steel samples studied in this thesis. The exponential decrease is typically on the order of 3% per cycle. This is applied until the applied field has a magnitude less than 100 mA/m. This process does not lead to an absolute demagnetized state. However, it does lead to a magnetization in the sample that is on the order of 100 A/m or less and residual fields on the order of 0.1 A/m or less. Figure 19 shows a visual representation of the waveform for the demagnetization process. The decay rate was set to 10% so the oscillation would be apparent.
30


Figure 19 - The demagnetization waveform
The Quasi-Static Step Method (QSM)
Quasi-static magnetization induced in a ferromagnetic sample assumes that the magnetic field exposed to the sample is varying at a sufficiently slow rate that dynamic effects such as eddy currents or viscosity are negligible. The difficulty with making a quasi-static Faraday measurement is that if the time-rate of change of the magnetic flux linking the Faraday coil is too small, then the induced Faraday voltage can be unrecoverable. An alternate approach developed by Dr. Carl Schneider is to step the voltage and then hold it long enough to allow transients to die down, reaching a steady-state. A breakdown of a single step is presented in Figure 20. The magnetization can be evaluated using (12) by integrating through the transient. The steady-state value of the internal field is measured, avoiding dynamic effects.
The slope of the ramp is carefully determined. The ramp allows the use of both a time sensitive instrument and a time-rate-of-change sensitive instrument to be used simultaneously. In this case the time
31


sensitive instrument is a Hall Effect probe, and the time-rate-of-change sensitive instrument is a Faraday coil.
During a thin-wall pipe experiment takes data at a rate near 11 kHz and a ramp is usually 30 data points, or 2.7 ms, wide. This width allows the DAQ to capture the rise in voltage across the Faraday coil, while keeping the peak of the voltage rise high enough above the noise floor to keep the integration of the signal fairly noise free. If the ramp is too wide (that is, the slope is too small), then the time-rate-of-change of the flux that cuts through the cross-sectional area of the coil will be small, and the voltage change measured by the DAQ can get lost in the white noise on the channel. Too steep of a ramp and the peak voltage (the main contributor to the integration of the voltage channel) can occur between data samples, resulting in a magnetization state that is recorded as too small.
Figure 20 - Graphic Description of the Ouasi-Static Method
32


Pulse Excitation (waveform shape)
A typical hysteresis loop is achieved by exciting the solenoid with a triangular waveform. A triangle wave is preferred since it gives a clear reversal of the field at the apex of the pulse. For the quasi-static method, the waveform is approximated as a series of step and holds. However, an abrupt step in the solenoid voltage results in an overshoot due to an intrinsic LRC resonance. It is important to eliminate this overshoot for several reasons. Foremost, an overshoot of the solenoid field produces a local reversal in the magnetization, which is undesirable. To mitigate this, Schneider has placed a tuning capacitor in parallel with the solenoid to dampen the resonance. This also effectively delays the step. The CUD lab has chosen to use a controlled rise time for the voltage. That is use a ramped step rather than an abrupt step, as illustrate in Figure 20. The justification for this is that a finite rise time of the pulse reduces the spectral bandwidth of the signal to be well below the resonance of the LRC circuit, eliminating the overshoot. One could argue that the ramped step adds a delay similar to a capacitance.
Quasi-Static Method for Load Measurements
The QSM can be used to vary the stress applied to a samples in much the same way it is used to apply a magnetic field to the sample. The MTS load frame setup is used to apply this stress and is driven by the DAQ in exactly the same way the DAQ drives the Kepco power supply. The QSM is used to reduce the amount of noise in both the load channel and the Hall Effect sensor channel. The Allegro Hall probe has around 100 A/m worth of noise, out of the package. The changes in magnetization in the sample during a load cycle are within this order of magnitude. To bring this noise level down and find a meaningful measurement a period of averaging must be employed. The same averaging technique that is described below in Measurement of Flux in Pipe Samples section was used.
After a field has been applied to the sample, the remnant magnetization is known. As there is no other field near the experiment, any field that the Hall Effect sensor reads can be attributed to the magnetization of the sample. The conversion of voltage to Amperes per meter is taken from the Allegro Hall Effect sheets and calibrated within factory given tolerances.
33


CHAPTER IV. EXPREMENTS AND MEASURED DATA
Major Loop Example
Setup
This data was taken to show the shape of atypical hysteresis curve, and to discuss some of the parameters looked at when analyzing the data. Figure 21 shows a major loop, taken from pipe sample U6346 starting from a demagnetized state. The virgin curve was taken out to 18,000 A/m applied, and then the applied field was cycled from 18,000 A/m to -18,000 A/m and back again.
H Field [A/m]
Figure 21 - Hysteresis Loop taken from U6346, including virgin curve and major loop, measured via the Faraday method.
Results
To correlate data taken from the pipe to the model given in (7), a data analysis routine is used. The process begins with the hysteresis curve taken from the data run. Differential susceptibility is taken from the hysteresis curve by
34


Xd =i
(25)
M0-M
H0-H
M ,-M
i end
H ,-H
-, i + w> end
end
M -M
H. w ~H w
l- H—
2 2
â– , otherwise
where the first, second and third expressions are the forward, reverse and central difference operators for taking a finite derivative. The variable i is the iterator over which the field and flux arrays are differentiated, w is the width of sliding window over which the derivative is taken. //„ and M0 are the
first data points in the field and flux data arrays, and Hend and Mend are the last data points in the field and flux data arrays. Figure 22 shows the differential susceptibility taken from the hysteresis loop in Figure 21.
Plot X v H
Magnetization [A/m]
Figure 22 - The differential susceptibility of a typical pipe experiment major loop
35


The first data to be extracted from Figure 22 is the initial susceptibility and the saturate magnetization Ms using the anisotropy curve Xrev. The result of this fit is shown in Figure 23. The as the magnetization of the samples approaches saturation, the slope of the magnetization of the sample is well defined by Xrev. As Xrer is a function of only Ms and , fitting this curve to the differential susceptibility near saturation will yield values for the saturation magnetization and the initial susceptibility that describe the sample well.
-0.5
Magnetization [A/m]
x 10°
Plot X v H
Q-102 d)
O
=3
CO
101
Figure 23 - fitting Xrev to the differential susceptibility curve
Differential susceptibility is always calculated between reversals. The first reversal, or the starting point for the calculations in (25), has a magnetization value and a field value. The magnetization is recorded and used in the calculation of (7) for a given Mr, the magnetization at the previous reversal. Next values for II( and // are found through iteration to give the calculation of (7) a tight fit to the differential susceptibility taken from the sample. Figure 24 shows the differential susceptibility curve fit by (7). The deviations of %d from the model are due in part to the demagnetizing field created in the pipe as it magnetizes. This phenomena is known and addressed in later portions of this thesis.
36


Plot X v H
-1.5 -1 -0.5 0 0.5 1 1.5
Magnetization [A/m] *1°6
Figure 24 - A differential susceptibility of a pipe major loop fit with bothXrev and C. Schneider's full model
X Initial via Minor Loops
Setup
A method for measuring the initial susceptibility of a magnetic material from a minor loop has been developed. The sample is first demagnetized. Then starting from a near virgin state, the field is cycled through a minor loop and the M(H) curve is determined using the quasi-static measurement method. The differential susceptibility is estimated by numerically computing the slope dM/dH from the measured M(H) curve. This is directly compared to Schneider's exponential model [7]
Xi =X,Xre
Xr______
(XHC Hm ^ \AM\ + Ms-Mam j
(26)
where, Xj is the initial susceptibility, = 1 - (M/M^) is the polycrystalline texture, AM =M-Mr is the change in magnetization since the last reversal (tip of the minor loops), Hc is the coercive field, and or = 1 on the virgin curve, and or = 2 after the first reversal. For a minor loop, the magnetization can assumed to be considerably smaller than the saturation magnetization of the material. In this case,
37


f
M
1
(27)
and
(28)
As a result, for the minor loop near the virgin state:
|AM|
(29)
From the measured, data, one can form a function of Xd versus AM following a reversal. An exponential fit of this curve can then be used to accurately estimate the initial susceptibility and the coercive field.
To demonstrate this, a minor loop beginning from a virgin state with a maximum applied field of 300 A/m field was applied. The triangular wave excitation was developed with 30 A/m steps. Each step had a linear rise time of 2.7 ms, and then held constant for 42.3ms. The Faraday coil voltage was integrated over the entire 45 ms step, while the voltage from the hall-effect sensor is averaged over the last 42.3 ms. This allows eddy currents to be neglected, and to average out zero-mean time-dependent noise effects from both the hall-effect senor and the Faraday coil.
This procedure was applied to the 6 different steel hollow rod samples listed in Table 1. The left graph in Figures 15-20 represent the measured M(H) curves for each of the 6 steels using the Faraday
method. The right graph in Figures 15-20 illustrate x,i = —— computed numerically immediately after a
dH
negative reversal. There is noticeable noise in the %d plots due to the fact that a finite-difference approximation of data amplifies noise error. The Matlab curve fitting library was used to perform the fit of the Xj data by fitting it to the exponential function aebx, where x = AM. Then applying (29) to the
38


Magnitization [A/m] Magnitization [A/m]
fitted data, X; = a and If = I / (2Xib). The values for X; and If computed from these measurements
are provided by Table 1.
Results
Figure 25 - M v H curve for C0878-5 (left), Curve fit for the X v Ml curve after the first negative reversal (right)
X vs A-Magnitization
H Field [A/m]
Figure 26-MvH curve for C714-89A (left). Curve fit for the X v AM curve after the first negative reversal (right)
39


Magnitization [A/m] Magnitization [A/m]
Figure 27 -MvH curve for U6349-7-B (left), Curve fit for the A' v AM curve after the first negative reversal (right)
Figure 28 - M v H curve for U3926-6 (left), Curve fit for the A' v AM curve after the first negative reversal (right)
40


Magnitization [A/m] Magnitization [A/m]
X vs A-Magnitization
D Magnitization [A/m]
x 10
Figure 29 - M v H curve for U8520 (left). Curve ftfor the A' v AM curve after the first negative reversal (right)
H Field [A/m]
X vs A-Magnitization
Figure 30 -Mv H curve for W4G801-E18 (left), Curve fit for the X v AM curve after the first negative reversal (right)
41


Table 1. Initial susceptibility and coercive fields of different steels approximated using Faraday coil
measurements of minor loops
Material Xi He
C0878-5 68.95 440.38
C714-89A 69.5 530.72
U6346 72.86 419.17
U3926 71.82 528.61
W4G801 186.44 203.55
U8520 146.6 261.96
FORC data
Setup
A First-Order Reversal Curve (FORC) of a hysteretic material can yield several parameterizations of the material, including initial susceptibility. The measurement of a FORC begins by saturating a sample in a positive applied field. The applied field is then decreased to a reversal field Hr. The FORC is the magnetization curve that results as the applied field is increased back to saturation.
The measurement of quasi-static FORCs was performed using the step method for the six steel hollow pipe samples listed in Table 1. The rise time of the ramp was 2.7 ms, and the hold time was 42.3 ms. The Faraday coil was integrated over the entire 45 ms step, while the voltage from the hall-effect sensor was averaged over the last 42.3 ms. This eliminates eddy current effects, and averages out zero-mean noise from both the hall-effect senor and the Faraday coil. The applied field approximating a saturating field was 18,000 A/m.
The procedure used to measure the quasi-static FORC was as follows. The sample is first demagnetized. From the virgin state, it is run through a full major loop increasing the applied in 100 A/m
42


steps to a maximum of 18,000 A/m. The applied field is then taken to -18,000 A/m and then back to
18,000 A/m in 100 A/m steps. After this saturate loop, the applied field has been taken down to a predetermined applied reversal field // , and then back to 18,000 A/m in 50 A/m steps. The procedure in then repeated from demagnetization for each desired // .
FORC data for the six steel hollow rod samples listed in Table 1 are provided in Figures 21 to 26. The hysteresis figures show a superposition of the major loop and the set of FORCs for the field reversals listed in Table 2. All of the curves show a similar path coming from the positive saturate reversal, but clearly show a different path after each of the separate negative reversals; thus demonstrating the hysteretic effect of an applied field to the steel pipe.
The second graph in each figure is the differential susceptibility, or the change in magnetization of the sample with respect to the change in the applied field defined as dM / dH, computed along each FORC. The FORC curves described above have had their differential susceptibility plotted on a semi-log plot starting from their negative reversal. The cooperative theory predicts that immediately following a reversal, the differential susceptibility should be equal to the reversible susceptibility
xrev=x,
f M2^ V 1V1*
m
where A is the initial susceptibility of the material, Ms is the saturation magnetization of the material, and M is the magnetization. To illustrate this, a plot of Xrev is superimposed in each plot.
What is apparent in each FORC, is that the susceptibility increases linearly on the log plot with a linear slope from the reversal. This is governed by the term
x,
X.r.
i/lr
Xr___
' W\)
(31)
in the cooperative model of the susceptibility in (26). As the magnetization approaches saturation, the slope of susceptibility is again linear. This corresponds to the term
43


Jr
Hn
(32)
Xd = XiZr?
in the exponential, which becomes dominant as (Ms - M,yW) / Han becomes small compared to \AM\/(2Hc).
44


Results
Table 3. Applied reversal fields for the series of FORC measurements
Reversal Applied Reversal Field [A/m]
1st -6400
2nd -6000
3 rd -5600
4th -5200
5th -4800
6th -4400
7th -4000
8th -3600
gth -3200
10th -2800
11th -2400
12th -2000
13th -1600
14th -1200
15th -800
16th -400
17th 0
18th 400
19th 800
20th 1200
2ist 1600
22nd 2000
23rd 2400
24th 2800
25th 3200
26th 3600
27th 4000
28th 4400
29th 4800
30th 5200
45


Magnitization [A/m] Magnitization [A/m]
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
H Field [A/m] *i°4
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
H Field [A/m]
Figure 31 - C0878 Hysteresis Curve (left) and Differential Susceptibility (right)
Plot of Susceptibility v M
-1.5 -1 -0.5 0
H Field [A/m]
x 10
Figure 32 - C7614 Hysteresis Curve (left) and Differential Susceptibility (right)
46


Magnitization [A/m]
H Field [A/m]
Plot of Susceptibility v M
106
105
jf
< 104
c
o
1°3 N
E
O) 102
CD
2
101 10°
-2 -1.5 -1 -0.5 0 0.5 1
H Field [A/m]
Figure 33 - U6346 Hysteresis Curve (left) and Differential Susceptibility (right)
.5 -1 -0.5 0 0.5 1 1.5
H Field [A/m] *â„¢6
10’
E
<
c 103
o
V-â– 
CO
N
c 102
U)
CO
10°
Plot of Susceptibility v M
Figure 34 - U3926 Hysteresis Curve (left) and Differential Susceptibility (right)
47


Magnitization [A/m] Magnitization [A/m]
Plot of M v H
Plot of Susceptibility v M
10s
10°
-1.5 -1 -0.5 0 0.5 1 1.5
H Field [A/m]
Figure 35 — W4G801 Hysteresis Curve (left) and Differential Susceptibility (right)
-1.5 -1 -0.5 0 0.5 1 1.5
H Field [A/m] *1°6
Figure 36 - U8520 Hysteresis Curve (left) and Differential Susceptibility (right)
Faraday Measurement of Magnetostriction
Setup
The thin-walled pipe measuring apparatus, loaded with sample C0878, was loaded into the MTS load frame as shown in Figure 11. The sample was demagnetized with a sinusoidal demagnetizing field that
48


started at 9,000 A/m and decayed 3% each cycle. After the sample had been demagnetized, a major loop was applied with ±17,000 A/m, and then the sample was left at remanence. Stress was then applied to the sample, going to -30 kN and the reversing to 30kN and then back to a 0 kN equilibrium. The field was varied. The load waveform shown in Figure 37 was applied to the magnetized steel sample.
Load v. Time
n>
o
-10
-20
-30
-40



o\ 0.2 0.4 /6.S 0 00 1, ,2 1.



Time [s]
Figure 37 - The load applied to the sample, after it is brought to remnants
ct v. M
E
<
205

a rl ’ A N 195
pi 190
/ N a/Vj A A . An a
V^VvV^^185 V/v v VVvW% \A A
180
\nrVJ\Ar'F W Vy v
175
170
-40 -30 -20
-10 0 10 20 30
Stress (Mpa)
Figure 38 -Magnetization decrease due to applied stress
49


Results
Figure 37 shows the variation of the load applied versus time, with tension being a positive load and compression, negative. Figure 29 illustrates the internal field of the pipe during the variation of the load. Since there is no applied field, the internal field represents the demagnetizing field produced by the permanent magnetization in the pipe. The sample starts with a higher magnetization which then decreases under tension as we move the domain walls of the sample via stress. As the sample relaxes and moves into compression magnetization stays relatively stable, then when tension is applied to bring the sample back to a neutral state magnetization decreases again. The behavior is consistent with what is predicted by the Cooperative model for magnetostriction [8],
Faraday Magnetostriction Effect on Hysteresis
A closer look was taken at the effects of magnetostriction on hysteresis. In this experiment sample C0878 had a measured stress applied, and then was run through the demagnetization process. After the sample was subject to a minor loop, with a ±2,000 A/m reversal.
Setup
The thin-walled pipe measuring apparatus, loaded with sample C0878, was loaded into the MTS load frame as shown in Figure 11. For a control experiment the MTS was brought to a no-load state. The sample was demagnetized with a sinusoidal demagnetizing field that started at 9,000 A/m and decayed 3% each cycle. A QSM minor loop was applied to the sample, with a ±2,000 A/m reversal, and 100 A/m steps. The field was then left at the positive reversal. Data was taken every 90 ps during the process, with 100 data points per step. The ramp width was 30 data points. The blue curve in both the right and left plot in Figure 39 is the control data.
After the control data was taken the experiment varied the procedure by varying the amount of stress the sample was under during the magnetic sampling. The sample had a recorded stress applied, both compressive and tensile, applied via the MTS load frame. After the stress was applied, the sample was
50


Magnitization [A/m] Magnitization [A/m]
not demagnetized, and the same applied field from the control experiment was again applied. Again the field was left at the positive reversal between each successive applied stress. The stress was applied increasingly, for both the tension and the compression experiments. The data taken from these experiments is plotted in Figure 39 and Figure 40.
10Plot of M v H Under Compression
H Field [A/m]
0.6 â– 
0.4 â– 
0.2
-0.2
-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500
-0.4
-0.6
-0.8
-------0 MPa
--------11.7 MPa
-23.4 MPa
--------35.2 MPa
--------46.9 MPa
Figure 39 - (left) Multiple hysteresis loops taken under various compressions, (right) The susceptibility of the sample at various
compressions
Plot of Susceptibility v M Under Compression
-0 MPa -11.7 MPa 23.4 MPa
-0.5
0 0.5
M [A/m]
x 10
-2000 -1500 -1000 -500 0 500 1000 1500 2000
H Field [A/m]
> 10Plot of M v H Under Compression
Figure 40 - (left) Multiple hysteresis loops taken under various tensions, (right) The susceptibility of the sample at various
compressions
51


Results
Figure 39 clearly shows how the magnetization of the material changes with compressive stress. As the compressive stress is increased in the sample three phenomena become apparent. Increasing compression has a suppressive effect on the maximum achievable magnetization in this minor loop. This suppression in magnetic susceptibility keeps the field outside of the sample thereby increasing the field in the center of the pipe. This suppression is the second phenomenon, a decrease in the slope of %, seen in Figure 39 (right). Thirdly, the change in the relationship between magnetization and H field causes a change in the coercive field; Figure 39 (left) has increasing values for the H field at the zero crossing for magnetization with increasing compression. Interestingly, there is a point as which all of the curves intersect, regardless of compression.
Figure 40 shows the effects of tension on the sample. Again the same three phenomena as in the compression experiment are seen, however in tension the signs are reversed. The maximum magnetization in increased with increasing tension, and the internal field of the sample is accordingly decreased. The slope of % is increased, and the coercive field has been decreased. The common crossover between all applied stresses is seen, however it is seen at a much higher magnetization then in the compressive case.
These three phenomena are due to two fields, the Brown field and the Bozorth field [8]. The Brown filed is given as [8]
where 2S = +\u. In this case the identifiers 100 and 111 indicate the easy and hard axis. This data
is showing that they have a direct and predicable contribution to the magnetization of the sample.
(33)
and the Bozorth field is given as [8]
HBo( \mvf„XrM
f-kMs
(34)
52


Looking at the (right) side of the Figure 39 and Figure 40 the susceptibility of each of the magnetic loops
is shown. These susceptibilities are modified by
dHBr dHBo
Br dM ’ 50 dM
as,
=
dM ____
~dH ~ r
- DBr + DBo
(35)
(36)
Ring Major Loop Example
During the course of the experiments taken with the pipe sample the demagnetization feild that accumulated in the pipe sample began to be problematic in measuring physical parameters. An elegant solution to this was proposed by C. Schneider. The use of a sample in the shape of a ring would have no magnetic poles build as the sample magnetized, because there was a path to contain all of the flux within the material. If the flux were to be contained entirely inside the sample, then there would be no field produced to interfere with measurements.
Setup
Data was taken to show the shape of a typical hysteresis curve with the ring sample, and to discuss some of the parameters looked at when analyzing the data. Figure 41 Figure 21 shows a major loop, taken from a ring sample starting from a demagnetized state. The virgin curve was taken out to 13,000 A/m applied, and then the applied field was cycled from 13,000 A/m to -13,000 A/m and back again.
53


M vH
Figure 41 - Example Major loop taken with a ring sample
Results
Fitting the model was applied this major loop in much the same way as was done to the pipe. Differential susceptibility was calculated using equation (25). The anisotropy function Xrev was fit to the calculated differential susceptibility to find both saturation magnetization Ms and initial susceptibility . The full model was fit by adjusting values for the coercive field Hc and the anhysteretic field // iteratively.
Figure 42 shows the differential susceptibility, the anisotropy function and the model fit together.
54


Xv M
Figure 42 - Fitting of the differential susceptibility to the model developed by C. Schneider
Ring FORCs Experiment
Setup
From a remnant state, the ring sample was run through a full major loop increasing the to a maximum of 13,000 A/m. The applied field is then taken to -13,000 A/m and then back to 18,000 A/m. This was done with a swept triangle wave at 2 Hz. After this saturate loop, the applied field has been taken down to a predetermined applied reversal field Hr, and then back to 13,000 A/m. The procedure in then repeated from demagnetization for each desired Hr. Table 4 shows the values used for each reversal Hr.
55


Table 4. Reversal Values Used in the Ring Sample Experiments
Reversal Applied Field [A/m]
1st -1500
2nd -1250
3rd -1100
4th -1000
5th -950
6th -900
7th -850
8th -800
9th -750
10th -700
Fewer reversals were taken from the ring as compared to the pipe. The field span at which the ring goes through its highest susceptibility phase is considerably shorter than the high susceptibility field span in the pipe sample. This shortened window means that fewer FORCs can describe the behavior of the ring reasonably well.
Results
Each of the FORCs taken in the experiment are shown overlaid in Figure 43. Fitting each of the FORCs in the experiment yielded Figure 44. For each of the fits, all of the physical parameters were held constant except for the coercive field II( . Table 5 lists those parameters.
Table 5. Experimental Parameters for Ring FORC Experiment
Physical Parameter Value
Saturation Magnetization [A/m] 1640000
Initial Susceptibility 75
Anhysteretic Field [A/m] 1200
56


HP/IAIP
x 10
E
3
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-1


/

700 (Aym) -750 [Aym]
-800 [Aym] -8 50 (A/m)
-900 [AAn] -950 [Aym] 1000 lAyml
-1 1 100 |Aim| 250 (A/m) 500 [Aym]
-1

.5
-0.5 0 0.5
H [A/m]
1.5
x 104
Figure 43 - Ring sample FORCs shown as a hysteresis plot
Figure 44 - Susceptibility of each fork, shown with a fit to C. Schneider's model
57


Plotting the coercive field as a function of reversal point in Figure 45 shows an interesting trend.
Coercive Field H v Reversal Point
Vs
Figure 45 - Coercive field as a function of reversal
The data curves in Figure 44 show a 'bulge' on the right hand side of the curve when compared to the model. This is sheering is due to eddy currents delaying the magnetization of the sample. The rate at which this experiment was run is considerably faster than the rate at which the pipe sample experiments are run. This is to keep heat effects low in the sample.
58


CHAPERV. CONCLUSION
The primary aim of this thesis has been to create a measurement system that uses the FCM to measure the response of a ferromagnetic material to the effects of an applied field and applied stress. An apparatus was created to take these measurements; an input computer controller has been interfaced to a data acquisition device that can read data from separate transducers measuring different effects. A Hall Effect probe measures the field produced by a Faraday coil being driven by a bi-polar amplifier. A separate Faraday coil inductively measures the flux produced by the driven Faraday coil. The amplifier is controlled by an output computer controller which communicates with the input computer controller. The output computer controller for the amplifier is also capable of controlling the MTS, providing a stress environment capable of changing the magnetic properties of a ferromagnetic sample through magnetostriction. These changes are recorded by the Hall Effect probe. These all combine into one working apparatus, which is capable of taking magnetic and stress measurements quickly and accurately.
This apparatus was used to take measurements from two different geometries of samples, a pipe and a ring. An example of a major loop taken from the pipe was presented, along with a description of how data is interpreted. A series of minor loops measuring the initial susceptibility of several material was presented. Several sets of First Order Reversal Curves was then presented for various types of mild steel. The pipe was then subjected to two different types of stress tests; one showing the effects of varying stress on the magnetization of a sample, and the other showing the effects of stress on magnetic hysteresis. Experiments from the ring sample were then discussed. A major loop and a discussion of how data is interpreted was shown. And finally a set of FORCs from the ring sample were shown, complete with a model fitting.
59


References
[1] F. Preisach, "Uber die magnetische Nachwirkung," Zeitschriftfiir Physik, vol. 94, pp. 277-302, 1935.
[2] E. D. T. Ann Reimers, "Fast Preisach-Based Magnetization Model," IEEE Transactions on Magnetics , vol. 34, no. 6, pp. 3857-3866, 1998.
[3] D. A. D.C Jiles, "Ferromagnetic hysteresis," IEEE Transactions on Magnetics, Vols. MAG-19, no. 5, pp. 2183-2185, 1983.
[4] R. C. O'Flandley, Modern Magnetic Materials Principles and Applications, New York: John Wiley & Sons, Inc., 2000.
[5] S. G. R. A. John C. Young, "A Nystrom Solution of the Quasi-Magnetostatic Volume Intebral Equation for Eddy Current Analysis," IEEE Antennas and Propagation Society International Symposium, 2012.
[6] K. Townsend, "COMPUTATIONAL AND MEASUREMENT METHODS FOR FERROMAGNETIC HYSTERESIS IN DIFFERING STEEL ALLOYS (Masters Thesis)," May 2018.
[7] S. D. G. S. M. J. T. W. F. M. A. T. Carl S. Schneider, "Measreument and Exponential Model of Ferromagnetic Hysteresis," Physica B, UNDER REVIEW.
[8] C. S. Schneider, "Effects of stress on the shape of ferromagnetic hystresis loops," Journal of Applied Physics, vol. 97, no. 10, p. 10E503, 2005.
[9] C. S. Schneider, "Cooperative Anisotropic Theory of Ferromagnetic Hysteresis," in Trends in Material Science Research, New York, Nove Science Publishers, 2005, pp. 1 - 49.
[10] R. Bozorth, Ferromagnetisim, New Jersey: D. Van Nostrand Company, Inc., 1951.
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Full Text

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F ARADAY MEASUREMENT OF MAGNETIC HYSTERESIS AND MAGNETOSTRICTION OF MILD STEELS b y SEAN MARCUS JOYCE B.A ., Indiana University, Bloomington, 2008 A.S., Red Rocks Community College, 2015 B.S., University of Colorado Denver, 2017 A thesis submitted to the Faculty of the University of Colorado in partial fulfillment of the degree of Masters of Science Electrical Engineering Program 2019

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ii This thesis for the Master of Science degree by Sean Marcus Joyce has been approved for the Electrical Engineering Program B y Stephen D. Gedney, chair Mark Golkowski, Vijay Harid

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iii Joyce, Sean Marcus (M.S., Electrical Engineering Program) Faraday Measurement of Magnetic Hysteresis and Magnetostriction of Mild Steels Thesis directed by Professor Stephen D. Gedney ABSTRACT The focus of this thesis is the development of a measurement process to accurately record the non linear hysteretic susceptibility and magnetostriction of ferromagnetic materials. On voyage, naval vessels will endure tremendous changes in magnetic or mechanical stress due to maneuvering and wave motion in the dynamic stresses. Such changes in stress change the magnetic properties of the steel, impacting the ship signature. This research aims at providing the ability to predi ct the changes in the magnetic properties of steels undergoing dynamic changes in magnetic and mechanical stresses. Doing so will facilitate the prediction and removal of magnetic signatures from naval vessels providing the cloaking from underwater sens ors that is essential to the survival of the vessel. Novel experimental methods have been developed in the CU Denver magnetics laboratory using a Faraday coil measurement system. These methods have enabled the accurate prediction of the essential physica l parameters needed to predict non linear susceptibility of mild steels as a function of magnetic fields and axial mechanical stresses. The apparatus and experimental results will be presented demonstrating the capabilities of the measurement system. The form and content of this abstract are approved. I recommend its publication Approved: Stephen D. Gedney

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iv T able of Contents CHAPTER I. INTRODUCTION AND BACKGROUND ................................ ................................ .......... 1 Introduction ................................ ................................ ................................ ................................ ............... 1 Background ................................ ................................ ................................ ................................ ............... 3 CHAPTER II. THEROY OF THE F ARADAY COIL AND MEASUREMENT SYSTEM ...................... 6 Faradays Law ................................ ................................ ................................ ................................ ............ 6 Theory for the Thin Wall Pipe Experiments ................................ ................................ ............................. 7 Measurement of the H field ................................ ................................ ................................ .................. 8 Measurement of Flux in Pipe Samples ................................ ................................ ................................ . 9 Measurement of Stress Applied to Pipe Samples ................................ ................................ ............... 11 Theory for Thin Wall Ring Experiments ................................ ................................ ................................ 11 Measurement of the H field in Ring Samples ................................ ................................ ..................... 12 Measurement of Flux in Ring Samples ................................ ................................ ............................... 13 CHAPTER III. DESCRIPTION OF EXPREMENTAL SETUP AND MEASUREMENT SYSTEM ..... 14 Sample Descriptions and Measuring Devices for Thin Wall Pipe Experiments ................................ .... 14 Sample ................................ ................................ ................................ ................................ ................. 14 Data Acquisition Device ................................ ................................ ................................ ..................... 15 Power Supply ................................ ................................ ................................ ................................ ...... 15 Pipe Sample Faraday Coil ................................ ................................ ................................ ................... 16 Pipe Sample Solenoid ................................ ................................ ................................ ......................... 17 Hall Probe ................................ ................................ ................................ ................................ ........... 18 Pipe Sample Test Fixture ................................ ................................ ................................ .................... 19 Load Frame ................................ ................................ ................................ ................................ ......... 20 Sample Descriptions and Measuring devices for Thin Wall Ring Experiments ................................ .... 21 Sample ................................ ................................ ................................ ................................ ................. 21 Ring Sample Inner Faraday Coil ................................ ................................ ................................ ......... 22 Ring Sample Outer Faraday Coil ................................ ................................ ................................ ........ 23 Ring Sample Test Fixture ................................ ................................ ................................ ................... 24 Temperature Controlled Environment ................................ ................................ ................................ 25 Electro Magnetic Interference ................................ ................................ ................................ ................ 27 Measurem ent Procedures ................................ ................................ ................................ ........................ 28 Demagnetization Process ................................ ................................ ................................ .................... 30 The Quasi Static Step Method (QSM) ................................ ................................ ................................ 31 CHAPTER IV. EXPREMENTS AND MEASURED DATA ................................ ................................ ... 34 Major Loop Example ................................ ................................ ................................ .............................. 34 Setup ................................ ................................ ................................ ................................ ................... 34

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v Results ................................ ................................ ................................ ................................ ................. 34 X Initial via Minor Loops ................................ ................................ ................................ ....................... 37 Setup ................................ ................................ ................................ ................................ ................... 37 Results ................................ ................................ ................................ ................................ ................. 39 FORC data ................................ ................................ ................................ ................................ .............. 42 Setup ................................ ................................ ................................ ................................ ................... 42 Results ................................ ................................ ................................ ................................ ................. 45 Faraday Measurement of Magnetostriction ................................ ................................ ............................ 48 Setup ................................ ................................ ................................ ................................ ................... 48 Results ................................ ................................ ................................ ................................ ................. 50 Faraday Magnetostriction Effect on Hysteresis ................................ ................................ ...................... 50 Setup ................................ ................................ ................................ ................................ ................... 50 Results ................................ ................................ ................................ ................................ ................. 52 Ring Major Loop Example ................................ ................................ ................................ ..................... 53 Setup ................................ ................................ ................................ ................................ ................... 53 Results ................................ ................................ ................................ ................................ ................. 54 Ring FOR Cs Experiment ................................ ................................ ................................ ........................ 55 Setup ................................ ................................ ................................ ................................ ................... 55 Results ................................ ................................ ................................ ................................ ................. 56 CHAPER V. CONCLUSION ................................ ................................ ................................ .................... 59 References ................................ ................................ ................................ ................................ ................... 60

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1 C HAPTER I . INTRODUCTION AND BACKGROUND Introduction The focus of this thesis is to report on the creation of a measurement system that can accurately measure the physical parameters needed to validate the behavior of the magnetic materials, and the measurements taken by the Faraday Coil Method side electrom agnetics lab at University of Colorado, Denver. This experimentation was derived from first principles and has been developed into functional apparatus. The apparatus consists of : a computer controller overseeing an amplifier to provide a magnetic field and a load frame to provide a stress field, various transducers to measure magnetic and stress related parameters, and a data acquisitions device that is able to record data taken from the transducers. Several experiments are presented using this apparatu s. The measurement system described in this writing uses a two device setup to measure the magnetization induced in the test material. The two devices are a Faraday coil and a Hall Effect probe, and when used to measure the field and flux through and in a ferromagnetic sample they can yield precise measurements of the magnetic state of the sample. While the Faraday coil and Hall Effect probe were chosen in this apparatus, other measurements methods were reviewed. A super conducting quantum interface d evice (SQUID) is able to measure very small fields, and can operate from very cold to very hot environments. The SQUID relies on quantum mechanical effect in conjunction is a super conducting detection coil to accurately measure the magnetic properties of materials. A SQUID is not ideal in this situation however, as it takes measurements very slowly. The experiments contained herein are done in minutes at the slowest, and a squid would not be able to create measurements in the allotted time frame. A se cond approach would be to use a vibrating sample magnetometer (VSM), which physically moves moment. The VSM can perform experiments within the desired time fr ame, and to the accuracy needed

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2 in the applications herein. However, it is exceedingly difficult to induce large amounts of continual and varying physical stress on the sample while it moves through the applied field. This makes a VSM ill suited to measu ring stress induced changes in magnetization. The Faraday coil and Hall Effect probe are easily placed in a load frame, and are able to take measurements within the desired time constraints, thus making them very well suited to the tasks presented herein. The motivation for this experimental set up is to quantify and validate the physical parameters used in building a multi physics based empirical model for the description of ferromagnetic materials. The physical properties of interest are the magneto h ysteretic , anisotropic, mag netostrictive, and thermal behavior of the ferromagnetic materials. The experimentation preformed in the lab will be used to strengthen and verify the non linear models used in the Magström software. Various m odels of ferromagnetic hysteresis have been created. The Preisach model was presented in Zeitschrift für Physik [1] . It was then expanded upon by Ann Reimers an d Edward Della Torre in 1998 [2] . The model is founded on a superposition of reversible and irreversible magnetization . ( 1 ) This can then be written in terms of normalized magnetization by reducing the terms on the RHS by , the saturate magnetization of the material. ( 2 ) is the squareness of the material given as , ( 3 ) where is the remnant magnetization of the material. and are normalized irreversible and reversi ble magnetizations defined as

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3 ( 4 ) If then the differential susceptibility can be expressed as [2] : ( 5 ) This model predict s reasonably well for small fixed hysteresis loop with fixed parameters. However , t his model is lacking in its ability to predict a combination of varying major and minor loops. The Jiles Atherton model is formulated as a first order differential equati on. ( 6 ) is the irreversible magnetization, is the reversible magnetization, is the anhysteretic magnetization, and is the sign of the field change . This model has 5 tunable parameters: the irreversible loss , the anhy steretic behavior , the reversible to irreversible proportions , the effective field , and the saturate magnetization . E ach of these parameters can be measured by a single hysteresis loop if the loop is taken far enough into saturation [3] . One problem with t he Jiles Atherton model is that it does not fit to data well if the reversals are outside of a small range magni tudes for a fixed set of parameters or for an arbitrary . To overcome the narrow portions of the hysteresis curve at which these models work, the C. Schneider model is used . Background The multi physics based approach used in this thesis is exponential model o f differential susceptibility :

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4 . ( 7 ) T he variables from the model are a ll based on measureable physical parameter s . is the initial susceptibility. is the coercive field. is the anhysteretic field. is the saturate magnetization. is the magnetization of the system at the last reversal. is the change in magnetization since the last reversal. is the current magnetization in the sample. is the poly crystalline texture given as . Figure 1 has a plot of a commo n hysteresis curve, with some of the important features highlighted. The terms given to define ( 7 ) will be explained via Figure 1 . Figure 1 An example of a hysteresis curve, with important features highlighted. (1) virgin state, (2) coercive filed, (3) remanence , (4a) positive reversal, and (4b) negative reversal A single data point at (1 ) in Figure 1 shows a measurement of a sample in a demagnetized state. This means that the collection of magnetic moments that makes up the magnetic signature of the sample is in a totally entropic state, every magnetic domain is relaxed, and there is no order between the domains. If an increasing magnetic field is applied, the magnetization of the sample will follow the curve f rom point (1)

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5 to point (4a), as an increasing number of domains rotate to align with the applied field. This line is called the virgin curve, and the definition of is found on this curve. is the slop e at the virgin curve as the first few domains begin to rotate. That is, the slope of the curve just as it leaves point (1). The marker (2) shows where the hysteresis curve crosses the line. This crossing denotes the coercive field, . The coercive field has physical meaning, which is the applied field that will exactly cancel the magnetization in the sample. The marker (3) shows the rem ane nt state o f magnetization, remanence . This is the magnetization of the sample if no field is applied, and is a function of reversal at markers (4a,b) . Markers (4a) and (4b) are the positive and negative reversal points. This is where the applied field changes direction. If the applied field were reversed at a positive reversal after having a strength of A/m, then t he magnetization at this point would be , or the saturate magnetization of the sample. is the magnetic field generated if all of the domains in a sample have had their magnetic dipoles perfectly aligned to point in the same direction [4] .

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6 CHAPTER II . THEROY OF THE FARADAY COIL AND MEASUREMENT SYSTEM The Faraday Coil Measurement System is a two sensor method of measuring the magnetization indu ced in a sample. This system measures the magnetization of two geometries of samples. The first sensor is a Faraday coil, wrapped tightly about the sample. The second sens or is a transducer that can measure the ambient magnetic field in the experiment. Faradays Law The underlying principles of the Faraday Coil Measurement (FCM) method can be derived from first the windings of a tightly coiled wire in the presence of a magnetic field as . ( 8 ) Here is the voltage across the coil, is the number of turns in the coil, is the magnetic flux, and S is the cross sectional ar ea of the coil. can be expressed in terms of the magnetization and magnetic field as . ( 9 ) Where is the magnetic field, and is magnetization in a magnetic material present in the cross section . Substituting ( 9 ) into ( 8 ) leads to . ( 10 ) Equation ( 10 ) serves as the heart of the measurements taken in this writing.

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7 Theory for the Thin Wall Pipe Experiments For this experiment, the coiled copper wire is assumed to be tightly wrapped around a steel pipe with an inner radius of and an outer radius of as shown in Figure 2 . If the pipe is axially parallel to an x directed magnetic field, and no other ferrous material contributes significantly to the experiment, then ( 10 ) can then be es timated as . ( 11 ) Solving for reveals an expression for the magnetization of the steel pipe as . ( 12 ) Figure 2 Experimental setup for the thin wall pipe experiments

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8 Equation ( 12 ) implicitly shows the measurements needed to calculate the magnetization for the steel pipe. The voltage is measured across th e faraday coil, and has to be cumulative with time. The magnetic field around the pipe, ca n be measured by an axial Hall Effect probe whose sensor bisects the center of the Faraday coil. In the calculation for the magnetizatio n, it is assumed that the magnetization is constant about the cross section of the pipe (radially and azimuthally) as well as along the axial length of the Faraday coil. The axial magnetic field is also assumed to be constant over the entire cross section al area of the co il as well as along the length. These assumptions are considered to be sound, if the pipe is significantly longer than the coil (at least 5 times longer), and if (again at least 5 times longer). This has been theoretically modeled in Magström [5] . Measurement of the H field A Hall Effect sensor , placed at the center of a hollow pipe, is used to measure the H field within the sample. The field at the center of the hollow pipe i s assumed to be uniform through this cross section. A chip produced by Allegro, model A132 4 has been used to both prototy pe and take the data presented herein . The Hall probe measures fields continuously, but the package used in this application is pr one to noise . The Allegro hall chip intrinsically has noise floor of approximately 100 A/m. This is a combination of environmental noise (with a large contributor being 60 Hz noise due to EMI ) as well as conducted emissions through the Kepco power supply . To have confidence in our measurement a large number of samples must be taken while the applied field is held constant. If the noise has a zero mean, then much of , ( 13 )

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9 w here is the number of samples taken during the averaging period. The value is the average and is an individual sample indexed by . The estimation of the standard error of the mean of a sample set is given as . ( 14 ) Where is the sample size , is the standard deviation, and is the standard error of the data set. As increases the error of the estimation of the measurement decreases. In addition to increasing the number of samples over which the Hall probe is averaged , a time step can be chosen that will help filter noise . An ideal a number of point s to average over and scale by is chosen such that , the entire sample duration will be an integer multiple of a period of the strongest noise signal in the system. To convert the averaged Hall Probe data into a magnetic field the averaged voltage is multiplied by a conversion factor given by the manufacturer of the probe. As specified in the data sheets . ( 15 ) The conversion factor is multiplied by the voltage averaged over the hold period to find . ( 16 ) Measurement of Flux in Pipe Samples The Faraday coil voltage is more difficult to measure. The Faraday coil measures the time rate of change of the magnetic flux as described in ( 12 ) , with the assumption that is the measured field provided by the Hall Probe.

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10 The flux through the coil is varied by changing an applied magnetic field by a separate current carrying winding. The small window when the field is switched from one hold point to the n ext hold point must be measured with precision to capture an accurate assessment of the transient flux. If the change in field were applied as a mathematical step, the window of change would be very narrow, and the peak voltage would surely exceed the 10 V limit on the data acquisition device. Instead a ramp is used to transition between applied fields. The ramp function has the additional advantage of lengthening the time over which the change happens , allowing for much greater control and measurability signal duration and in step height in a LabVIEW progra m controlling the measurement. Changing the duration of the ramp allows the user to capture one or more multiples of a period of the , generally 60 Hz or 16.67 ms in duration . During integration this period of noise is averaged over, and if sampled correctly, it will lower the noise floor. The time step between data points must be considered here as well. The L/R time constant of the Faraday coil will determine the size of the time step. After the step and hold there must be enough data points to define the L/R response as the Faraday coil discharges its energy. This will require hardware that can take data very quickly. Changing the step height of the ramp has a direct impact on the amount of voltage induced across the ( 17 ) The magnitude of the electromotive force ( EMF ) induced across the Faraday coil is linearly proportional to the slope of the ramp. The amplitude of this voltage is important to consider, because the peak needs to be well above that of the noise inherent in the system , yet lower than the voltage threshold for the data acquisition device. While it is assumed that the total sample time for a single ramp and hold will be an integer multiple o f the period of the strongest noise, a cleaner signal will have a voltage induced peak that is easily distinguished from any signal noise.

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11 Measurement of Stress Applied to Pipe Samples The MTS Landmark load frame records and outputs axial force applied to a sample. The measurement is taken in terms of force as the load frame has no knowledge of physical parameters of the sample under test , such as cross . This recorded force must be converted to stres s for our calculations. The force applied on a surface is measured in SI units as Pascals. ( 18 ) Where is the axial force (N) , is the cross sectional area (m) , and is the applied stress (Pa) . The shape of the pipe varies along its length, however we have only measured the magnetic properties of the pipe at its axial center. To keep our calculation consistent, we must consider the surface area of the same region as our magnetic calculations. T he inner diameter of any of the pipe samples is measured to be 18 mm and the outer diameter of the pipe at its waist is measured to be 20.8 mm. The cross sectional area of the pipe is calculated as ( 19 ) The surface area of the pipe used in the experiments described herein is . Theory for Thin Wall Ring Experiments The theory for the measurements taken during the ring sample measurements mirror the measurements taken for the pipe experiments. Equation ( 10 ) is still the basis for measuring the magnetization induced in the sample, however the calculation is adjusted for the azimuthal cross sectional area of the ring, and the measurement method for the magnetization and the H field has changed due to physical constraints. The cross section of the wall of the ring is considered square fo r the purposes of calculation and thus the cross sectional area is defined by the height of the wall and the thickness of the wall. Following ( 10 ) ( 12 ) , t he explicit cal c u l ation of magnetization is,

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12 ( 20 ) Here and are the thickness and height of the wall of the ring , is the free space permeability, and is the numbe r of turns in the Faraday coil as shown in Figure 3 . Figure 3 Experimental setup form thin wall ring Another key difference between the pipe sample experiments and the ring sample experiments is how data is collect ed. Holding the field constant for discrete amounts to time to allow averaging cannot be done, due to the accumulation of heat in the experiment from the driving Faraday coil . Instead the field is changed continuously, and measurement methods are adjusted accordingly. Measurement of the H field in Ring Sample s Measurement of the H field in the ring cannot be done with a Hall Effect sensor, as the ring has no hollow region to imbed the sensor. Instead the field outside of the metal ca n be inferred through close mea surement of the applied field. Since the field is being applied and measured azimuthally, there is a continuous path of metal that can contain the flux applied to the sample. This means that no magnetic

PAGE 18

13 poles will form in t he sample, and in turn no demagnetizing field will be generated to oppose the applied field. The only field generated in the experiment will be the applied field. A sense resistor with a known impedance has been placed in series with the driving Faraday coil, and the voltage across the sense resistor is closely monitored by the data acquisition device. This voltage is used to calculate the current are known, then the fiel d produced by the driving coil can be calculated as ( 21 ) However, since is uniform, , ( 22 ) where is t he number of turns in the coil, is the current on the line , and is the length of the coil computed as . This data is not averaged over, as the waveform provided by the driving amplifier has a noise characteristic that is under the required tolerances. Measurement of Flux in Ring Samples Measuring the voltage across a Faraday coil provides the flux measurement, in much the same way as described in the pipe sample. Since the step and hold method cannot be used with the ring samples there is no consideration for ramp size and shape. The only mathematical tool available to combat intrinsic noise in the signal measured from the Faraday coil is the rate at which the signal is recorded. A sampling rate must be chosen that is a mode of th e fundamental frequency of the strongest noise contributor ( in this application 60 Hz is generally the strongest ), and the rate has to be fast enough to describe the produced waveform with ample fidelity.

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14 CHAPTER III . DESCRIPTION OF EXPREMENTAL SETUP A ND MEASUREMENT SYSTEM The FCM method is defined by ( 12 ) and determined in Chapter 2 , discussed two measuring devices needed to accurately describe the magnetization of a steel sample . However, a few other devices are needed for the experimental setup. These apparatus are discussed in this chapter. Sample Description s and Measuring Devices for Thin Wall Pipe Experiments Sample E ach steel sample has been milled into a pipe, 206 mm long. The pipe has an inner diameter of 18mm and an outer diameter of 20.8 mm at the center. The outer diameter has a flare at each end that is 23.9 mm in diameter and extends in 30 mm from each end. This flare is threaded to fit into a non magnetic titanium sample holder. A sample is pictured in Figure 4 . Figure 4 Photo of a steel pipe sample with no preparation Four types of steel have had been the subject of experimentation , and they are identified by their unique batch number. Two of the batch numbers are the same type of mild steel, and comparing them can give insight i nto the magnetic behavior of the steel across various batches. Each material was milled from a

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15 varying thickness. Chemical composition s along with the plate gauges are given in Tables 1 and 2, with each material differentiated by their respective melt numbers. Table 1 Chemical Make up of the Various Sample Materials as a Weight % Element C Mn P S Cu Si Ni Cr Mo Gauge C0878 0.16 0.29 0.005 0.002 0.13 0.22 2.40 1.25 0.24 C7614 0.16 0.23 0.006 0.001 0.15 0.21 2.93 1.46 0.40 U6346 0.15 0.22 0.007 0.002 0.14 0.30 2.59 1.55 0.37 U3926 0.14 0.23 0.010 0.003 0.15 0.32 2.53 1.55 0.37 U8520 0.17 1.41 0.014 0.010 0.30 0.23 0.12 0.11 0.02 W4G801 0.15 1.32 0.013 0.001 0.19 0.22 0.10 0.09 0.06 Data Acquisition Device Either a National Instruments USB 6466 or a USB 6343 Data Acquisitions device (DAQ) is responsible fo r coordinating the experiment by controlling a Kepco Bipolar 12 36 power supply (Kepco) and an MTS Landmark LVDT Servo Hydraulic Test System (load frame) , while taking data from various sensors. Figure 5 (right) is a phot o of the USB 6466 with the dust cover open to show the voltage terminals. The voltage across the Faraday coil , the voltage across the sense resistor, and the voltage output from the Hall Probe are recorded by the DAQ. The DAQ is in turn controlled by a LabVIEW program that has been written specifically to handle all of the experiment setup permutations . Power Supply To provide a magnetic field , a solenoid is driven by a Kepco 36 12 Bipolar Power Supply, which is in turn controlled by th e DAQ. Figure 5 (left) is a photo of the two Kepco power supplies used in the lab. The Kepco is an analog power supply, and is being used as a voltage c ontrolled current source. The voltage waveform created by the DAQ is amplified into a current waveform by the Kepco. The mapping from voltage to current is a linear scaling with a factor of 1.2, or .

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16 Figure 5 (left) the 2 Kepco Bi polar Power Supplies used in the lab, (right) The NI 6343 DAQ mx USB with its cover off showing the internal CAT 5 connections Pipe Sample Faraday Coil The sample is fitted with a Faraday coil wrapped around a custom made bobbin fitted about the waist of the pipe. The bobbin was designed in house using Solidworks, and 3D printed with a Prusa i3 MK2 printer using 1.75 mm PLA filament. The Faraday coil is wound from 27 gauge heavy coated magnetic wire, and 190 turns are fit into 39 mm axially along the pipe in 2 layers , shown in Figure 6 . An Acme coil winding machine was used to ensure each turn was layered consistently. The leads of the Faraday coil were soldered to shielded CAT 5 cable for modularity and noise reduction . Each lead to the Faraday down resistor to avoid a virtual ground in the coil.

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17 Figure 6 A Sample of HY100, fitted with a bobbin and a Faraday coil Pipe Sample Solenoid A solenoid provides the magnetic field that is applied to the sample. A 42.15 mm outer diameter PVC pipe was wrapped with 604 turns of 18 gauge magnet wire in two layer s , as shown in Figure 7 . An Acme coil winding machine was used to ensure consistency in the windings. The turn density of the resulting solenoid is 1887. 5 turns/meter with an effective length of 0.32 meters. The length of the solenoid is half again as long as the pipe sample to create a uniform field over the length of the sample centered in the solenoid.

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18 Figure 7 Solenoid responsible for building the magnetic field for each experiment Hall Probe An A1324 Allegro Hall Effect sensor is mounted inside of the pipe, centered in the middle of the faraday coil, with the face of the sensor normal to the axial direction of the pipe . The Hall Effect s enor is an analog three pin device, and is mounted to a custom cut dowel that holds the face of the chip normal to the direction of flux that is centered within the sample as shown in Figure 9 . Powered by a static 5V line, the output voltage of the middle line corresponds to the strength of a field oriented normal to the face of the sensor. This voltage is continuously read by the D AQ via a CAT5 cable . The A1324 is capable of measuring fields up to ± 80,000 A/m with a resolution of 100 A/m in normal working conditions. This resolution is limited by the noise that is intrinsic to the chip and in the entire measuring system generally . The hall probe was calibrated by comparing the measured filed to a known applied field. This applied field was supplied by a MicroSense Vibrating Magnetometer that had been calibrated to a NIST traceable standard. A sample of this calibration is shown in Figure 8 . Both a stepped field an d a swept field are compared during the calibration. The stepped field gives a very accurate magnitude comparison between the VSM field and the Hall Effect sensor. The sweep comparison was done to ensure that there is no time delay in the sensor, so the comparison of the Hall Effect sensor and the Faraday coil can be done in real time.

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19 Figure 8 Allegro Hall Probe mounted to a custom fitted dowel rod Figure 9 Comparison of the VSM field to the calibrated Hall Effect sensor used in the thin wall pipe experiments calibration Pipe Sample Test Fixture Two milled titanium fittings hold the sample, the dowel mounted Hall Effect sensor, and the solenoid in place during the experiment. Each fitting i s screwed to the sample using the threads on the ends of the

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20 sample. The dowel seats to one of the fittings, insuring that the Hall Effect chips takes measurements in the same location for each experiment. Figure 10 shows the assembled sample and test fixtures. Titanium is used for two reasons; it has no magnetic moment and will contribute no magnetic signal in the experiment, and it is strong enough to n ot yield during stress cycles. Figure 10 Titanium sample holders screwed onto the ends of an HY100 sample Load Frame For the testing of magnetostrictive properties the UCD Lab has employed the use of an MTS Lan d mark LVDT Ser vo Hydraulic Test System (load frame). The load frame can apply tension and compression axially to our samples via a Series 515 SilentFlo Hydraulic Power Unit. Hydraulic wedge grips are used to clamp and hold the titanium sample holders, with the sample b etween them . The wedge grips are high carbon steel fittings with a rounded and textured recess that matches the outer diameter of the ends of the samples holders. Hydraulic power is used to apply radial force to the grips, forcing mirrored pairs of grips to clamp on the ends of the sample holder. Figure 11 shows the assembled sample and sample holders being held between the two sets of wedge grips, ready f or stress testing. Simulations have been run in Magstr ö m to show that while the grips are made of a magnetic material, their distance from the solenoid is such that their magnetic contribution to the experiment is negligible [6] .

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21 Figure 11 MTS Landmark's wedge grips holding the assembled sample set up Sample Descriptions and Measuring devices for Thin Wall Ring Experiments Sample A collection thin walled rings, each with a rectangular wall cross section, have been lathed from several batches of mild steel. Each ring has a height of 25 mm, a wall thickness of 1.3 mm and an outer diameter of 54 mm. Two Faraday coils have been wrap ped about the wall of the ring, both with windings running in axial direction. The inner coil serves as a sense coil, while the outer coil serves as the driving coil in the experiments contained herein. A silicone conformal coating has been applied to th e bare steel before winding and after each layer of winding. This is to help ward off corrosion and provide a shock absorption barrier. Figure 12 shows both a bare ring sample, and a fully wrapped ring sample.

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22 Figure 12 (top) a bare ring sample before preparation Ring Sample Inner Faraday Coil The faraday coil for the ring samples is wound from 24 gauge heavy coated magnet wire, wrapped tightly over the entire surface of the ring as shown in Figure 13 . Under the winding the magnet wire, the ring has been coated by a silicone conformal coating . This coating serves a twofold purpose, to help keep the magnet wire electrically separate from the steel, and to keep the steel and wire from damaging one another during handling.

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23 Figure 13 Photo of the Faraday windings wrapped around a ring sample The windings of the ring are counted from a photo taken after winding, as exemplified in Figure 13 . Since the inner Faraday winding are covered by the outer Faraday windings this photo gives a record of the windings that can be referenced as proof to the condition, count, and turn density of the coil. A bobbin was 3D printed to assist i n the winding of the inner and outer coils. Ring Sample Outer Faraday Coil The outer Faraday coil serves as the driving coil for the system. This has been made from 24 gauge heavy magnet wire, and is wrapped in much the same manner as the inner Faraday co il. Again a photo has been taken of each sample just after winding the wire to give a record of the number of turns, the condition of the coil, and an assessment of the turn density of the coil. Figure 14 is an example of a ring that has been wrapped in the 24 gauge magnet wire. It is clear to see that the number of turns can be counted and recorded easily.

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24 Figure 14 Photo of the outer Faraday coil, just after being wrapped Ring Sample Test Fixture The leads of the magnet wire after being wrapped tightly around the sample have proven to shift slightly, and rub against one another. This movement causes the enamel on the wire to erode, and expose the bare copper underneath. This bare copper causes shorts that can easily corrode data. Care has been taken to secure the leads in a manner that will keep the shifting to a minimum, while still allowing the DAQ easy access to the leads . A fixture was designed and 3D printed to accomplish these tasks. Figure 15 shows the Test fixture. The CAT 5 socket connects the inner Faraday coil t o the CAT 5 cable to allow the Faraday coil voltage to be read by the DAQ. The banana sockets are connected to the outer cable and can handle the high amperage generated by the Kepco power supply.

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25 Figure 15 The Ring Sample Test Fixture This test fixture is used for desktop applications, however it covers the winding to a great extent, and does not allow for heat to escape with high amperages are being passed through the driving solenoid. Temperature Cont rolled Environment The ring sample uses 24 gauge wire for its driving solenoid. The amperage that the wire needs to carry to get an applied field to 14,000 A/m is 6.9 A , calculated from ( 22 ) . The resistance per unit length of the 24 gauge magnet wire is 0. 0842 due to the current traveling through the copper wires in the driving solenoid is given by . ( 23 ) This gives a loss 4.009 W/m. The 24 gage heavy coated magnet wire has a measured diameter of 0.523 mm. The length of wire used in the solenoid can be estimated as , ( 24 )

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26 where is the thickn ess of the ring, is the height of the ring, and is the number of turns of the solenoid around the ring. With a wall thickness of 1.35 mm a height of 25.3 mm and a turn count of 278 the length of wire w rapped used in the driving solenoid is around 15m long. This means at maximum applied field the solenoid generates roughly 60 W of power as heat loss. This heats the steel quite quickly. A cooling method was designed and built to help keep the sample ne ar to a stable temperature. The design uses a blower motor to drive air over a copper tubing heat exchanger, and a photo of the cooler is presented in Figure 16 . ° elbow was designed and 3D printed. The design was drawn in SolidWorks and printed in three sections on a Prusa mk2 3D printer out of 1.75 mm PLA. The three sections printed on the 3D printer were joined with common automotive Bondo. A ° section houses a heat exchang aluminum pipe and has 10 turns. The heat exchanger is fed by PVC tubing an d a household fish tank pump. The pump is capable of delivering 10 gallons a minute of cooled liquid to the heat ex changer. The sample sits just inside the exhaust and has air , cooler by the heat exchanger, blow over its surface for the duration of the experiment. A sample holder was 3D printed out of PLA, to control the rate of air flow around th e sample and hold the leads to the various measurement devices attached to the sample.

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27 Figure 16 Temperature controlled environment, complete with blower motor on the left and exhaust on the right Electro Magnetic Interferenc e All sensors are connected to the DAQ via shielde d CAT5 Ethernet cables. The sensor cables can be a source of noise due to electromagnetic interference (EMI), including significant energy at 60 Hz due to radiation by the local power grid. The Faraday co il and Hall Effect sensor s are connected to shielded CAT 5 connectors so they can be easily connected to a shielded CAT 5 cable. Shielded CAT 5 connectors are also used to connect the cables to the DAQ. The outer shield is grounded at the DAQ to reduce undes irable EMI.

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28 Measurement Procedures A pair of LabVIEW programs have been written to control both the Kepco amplifier and the data collection done by the DAQ. The first program (TJMD_Output) is the controller for the Kepco power supply and the MTS load fr ame , while the second program (TJMD_Input) is responsible for coordinating the collection of data via the DAQ during the experiments. These two program s run in tandem, each using their own clock defined in the software, but synchronizing the clock at the start of runtime. Fi gure 17 shows the flow diagram and a general over view of both programs. Figure 18 shows an image of the user interfaces designed to allow a user to control these two programs. The TJMD_Output executes first, it takes all of the variables input by the user interface and from them builds the waveforms that will drive any devices paired to the DAQ. The program them allocates enough memory on the DAQ to hold all of the needed waveforms, initializes the clock, and The TJMD_Input program is executed second. The input variables provided by the user though the user interface in Figure 18 define the runtime and frequency used in reading t he voltage channels from the Fi gure 17 Flow diagram for the LabVIEW controller programs

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29 DAQ. The needed voltage channels are alloca TJMD_Input. Both the input and output channels are driven when the ready flag is set, but each use their own clocks to execute the remainder of their own programs. The TJMD_Output program has seve ral types of waveforms built into it, including but not limited to: stepped triangle, swept triangle, and swept sinusoidal. Each of these modes can be customized by the user. As an example the sinusoidal can have an exponential decay applied, or the tria ngle can a different slope, start and end point for each rise and fall of the wave. This customization is necessary for the great variety of experiments performed with the FCM . Figure 18 The front facing controllers for the LabVIEW programs that control all of the experiments contained herein (right) is the output program, while (left) is the input program

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30 Demagnetization Process The voltage induced across the Faraday coil is proportio nal to the time derivative of the dynamic flux cutting through the coil. Consequently, the measurement of the physical magnetization by the FCM requires knowledge of the initial magnetization at the onset of the experiment. A n absolute magnetization meas urement requires a known magnetic state. The most reliable states are saturation or a demagnetized state. A saturate state is difficult to obtain since it requires very large fields to fully get into saturation. The complexity is compounded if the mater ial under test is unknown, as saturate magnetization is a property of material. This also limits the measurement to begin with a major loop. Alternative ly , a demagnetized state allows one to measure the virgin curve, or minor loops near a virgin state, a s well as major loops. It also does not require an applied field that will near saturation. Consequently, the default known state for our measurements is a demagnetized state. Before conducting each experiment the sample is demagnetized. The process u sed is to initially apply a 1 Hz sinusoidal magnetic field with an amplitude that is decreasing exponentially. The applied field should induce a magnetization that is at least 80 % of saturation. For the CUD pipe samples, th is is typically on the order o f 9000 A/m for the mild steel samples studied in this thesis . The exponential decrease is typically on the order of 3% per cy cle. This is applied until the applied field has a magnitude less than 100 mA/m. This process does not lead to an absolute demag netized state. However, it does lead to a magnetization in the sample that is on the order of 100 A/m or less and residual fields on the order of 0.1 A/m or less. Figure 19 shows a visual representation of the waveform for the de magnetization process. T he decay rate was set to 10% so the oscillation would be apparent.

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31 Figure 19 The demagnetization waveform The Quasi Static Step Method (QSM) Q uasi static magnetization induced in a ferromagnetic sample assumes that the magnetic field exposed to the sample is varying at a sufficiently slow rate that dynamic effects such as eddy currents or viscosity are negligible. The diffic ulty with making a quasi static Faraday measurement is that if the time rate of change of the magnetic flux linking the Faraday coil is too small, then the induced Faraday voltage can be unrecoverable. An alternate approach developed by Dr. Carl Schneider is to step the voltage and then hold it long enough to allow transients to die down, reaching a steady state. A breakdown of a single step is presented in Figure 20 . The magnetization can be evaluated using ( 12 ) by integrating through the transient. The steady state value of the internal field is measured, avoiding dynamic effects. The slope of the ramp is carefully determined. The ramp allows the use of both a time sensitive instrument and a time rate of change sensitive instrument to be used simultaneously. In this case the time

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32 sensitive instrument is a Hall Effect probe, and the time rate of change sensitive instrument is a Faraday coil. During a th in wall pipe experiment takes data at a rate near 11 kHz and a ramp is usually 30 data points, or 2.7 ms, wide. This width allows the DAQ to capture the rise in voltage across the Faraday coil, while keeping the peak of the voltage rise high enough above the noise floor to keep the integration of the signal fai rly noise free. If the ramp is too wide (that is, the slope is too small) , then the time rate of change of the flux that cuts through the cross sectional area of the coil will be small, and the voltage change measured by the DAQ can get lost in the white noise on the channel. Too steep of a ramp and the peak voltage ( the main contributor to the integration of the voltage channel) can occur between data samples, resulting in a magnetization state that is recorded as too small. Figure 20 Graphic Description of the Quasi Static Method

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33 Pulse Excitation (waveform shape) A typical hysteresis loop is achieved by exciting the solenoid with a triangular waveform. A triangle wave is preferred since it gives a clear reversal of the field at the apex of the pulse. For the quasi static method, the waveform is approximated as a series of step and holds. However, an abrupt step in the solenoid voltage results in an overshoot due to an intrinsic LRC resonance. It is important to elimi nate this overshoot for several reasons. Foremost, an overshoot of the solenoid field produces a local reversal in the magnetization, which is undesirable. To mitigate this, Schneider has placed a tuning capacitor in parallel with the solenoid to dampen the resonance. This also effectively delays the step. The CUD lab has chosen to use a controlled rise time for the voltage. That is use a ramped step rather than an ab rupt step, as illustrate in Figure 20 . The justification for this is that a finite rise time of the pulse reduces the spectral bandwidth of the signal to be well below the resonance of the LRC circuit, eliminating the overshoot. One could argue that the ramped step adds a delay similar to a capacitance. Quasi Static Method for Load Measurements The QSM can be used to vary the stress applied to a samples in much the same way it is used to apply a magnetic field to the sample. The MTS load f rame setup is used to apply this stress and is driven by the DAQ in exactly the same way the DAQ drives the Kepco power supply. The QSM is used to reduce the amount of noise in both the load channel and the Hall Effect sensor channel. The Allegro Hall pr obe has around 100 A/m worth of noise, out of the package. The changes in magnetization in the sample during a load cycle are within this order of magnitude. To bring this noise level down and find a meaningful measurement a period of averaging must be e mployed. The same averaging technique that i s described below in Measurement of Flux in Pipe Samples section was used. After a field has been applied to the sample, the remnant magnetization is known. As there is no other field near the experiment, any field that the Hall Effect sensor reads can be attributed to the magnetization of the sample. The conversion of voltage to Amperes per meter is taken from the Allegro Hall Effect sheets and calibrated within factory given tolerances.

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34 CHAPTER IV. EXPREMENTS AND MEASURED DATA Major Loop Example Setup This data was taken to show the shape of a typical hysteresis curve, an d to discuss some of the parameters looked at when analyzing the data. Figure 21 shows a major loop, taken from pipe sample U6346 starting from a demagnetized state . The virgin curve was taken out to 18,000 A/m appli ed, and then the applied field was cycled from 18,000 A/m to 18,000 A/m and back again. Figure 21 Hysteresis Loop taken from U6346 , including virgin curve and major loop, measured via the Faraday method. Results To correlate data taken from the pipe to the model given in ( 7 ) , a data analysis routine is used. The process begins with the hysteresis curve taken from the data run. Differential susceptibility is taken from the hysteresis curve by

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35 , ( 25 ) where the first, second and third expressions are the forward, reverse and central difference operators for taking a finite derivative. The variable is the iterator over which the field and flux arrays are differentiated, is the width of sliding window over which the derivative is taken. and are the first data points in the field and flux data arrays, and and are the last data points in the field and flux data arrays. Figure 22 shows the differential susceptibility taken from the hysteresis loop in Figure 21 . Figure 22 The differential susceptibility of a typical pipe experiment major loop

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36 The first data to be extracted from Figure 22 is the initial suscepti bility and the saturate magnetization using the anisotropy curve . The result of this fit is shown in Figure 23 . The as the magnetization of the samples approaches saturation, the slope of the magnetization of the sample is well defined by . As is a f unction of only and , fitting this curve to the differential susceptibility near saturation will yield values for the saturation magnetization and the initial susceptibility that describe the sample well . Figure 23 fitting Xrev to the differential susceptibility curve Differential susceptibility is always calculated between reversals. The first reversal, or the starting point for the calculations in ( 25 ) , has a magnetization value and a field value. The magnetization is recorded and used in the calculation of ( 7 ) for a given , the magnetization at the previous reversal. Next values for and are found through iteration to give the calculation of ( 7 ) a tight fit to the differential susceptibility taken from the sample. Figure 24 shows the differential susceptibility curve fit by ( 7 ) . The deviations of from the model are due in p art to the demagnetizing field created in the pipe as it magnetizes. This phenomena is known and addressed in later portions of this thesis .

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37 Figure 24 A differential susceptibility of a pipe major loop fit with both Xrev and C. Schneider's full model X Initial via Minor Loops Setup A method for measuring the initial susceptibility of a magnetic material from a minor loop has been developed. The sample is first demagnetized. Then starting from a near virgin state, the fi eld is cycled through a minor loop and the M(H) curve is determined using the quasi static measurement method. T he differential susceptibility is estimated by numerically computing the slope dM/dH from the measured M(H) curve. This is directly compared t [7] ( 26 ) where, is the initial susceptibility, is the polycrystalline texture, is the change in magnetization since the last reversal (tip of the minor loops), is t he coercive field, and on the virgin curve, and after the first reversal. For a minor loop, the magnetization can assumed to be considerably smaller than the saturation magnetization of the material. In this case,

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38 ( 27 ) and ( 28 ) As a result, for the minor loop near the virgin state: ( 29 ) F rom the measured, data, one can form a function of versus following a reversal. An exponential fit of this curve can then be used to accurately estimate the initial susceptibility and the coercive field. To demonstrate this, a minor loop beginning from a virgin state with a maximum applied field of 300 A/m fiel d was applied. The triangular wave excitation was developed with 30 A/m steps. Each step had a linear rise time of 2.7 ms, and then held constant for 42.3ms. The Faraday coil voltage was integrated over the entire 45 ms step, while the voltage from the hall effect sensor is averaged over the last 42.3 ms. This allows eddy currents to be neglected, and to average out zero mean time dependent noise effects from both the hall effect senor and the Faraday coil. This procedure wa s applied to the 6 differe nt steel hollow rod samples listed in Table 1. The left graph in Figures 15 20 represent the measured M(H) curves for each of the 6 steels using the Faraday method. The right graph in Figures 15 20 illustrate computed numerical ly immediately after a negative reversal. There is noticeable noise in the plots due to the fact that a finite difference approximation of data amplifies noise error. The Matlab curve fitting library was used to perform the fit of the data by fitting it to the exponential function , where . Then applying ( 29 ) to the

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39 fitted data, and . The values for and computed from these measurements are provided by Table 1. Results Figure 25 M v H curve for CO878 5 curve after the first negative rev ersal (right) Figure 26 M v H curve for C714 89A curve after the first negative reversal (right)

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40 Figure 27 M v H curve for U6349 7 B (left), Curve fit for the X v curve after the first negative reversal (right) Figure 28 M v H curve for U3926 6 (left), Curve fit for the X v M curve after the first negative reversal (right)

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41 Figure 29 M v H curve for U85 20 ( left), Curve fit for the X v M c urve after the first negative reversal (right) Figure 30 M v H curve for W4G801 E18 (left), Curve fit for the X v M curve after the first negative reversal (right)

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42 Table 1. Initial susceptibility and coercive fields of different steels approximated using Faraday coil measurements of minor loops Material Xi Hc C0878 5 68.95 440.38 C714 89A 69.5 530.72 U6346 72.86 419.17 U3926 71.82 528.61 W4G801 186.44 203.55 U8520 146.6 261.96 FORC data Setup A First Order Reversal Curve (FORC) of a hysteretic material can yield several parameterizations of the material, including initial susceptibility. The measurement of a FORC beg ins by saturating a sample in a positive applied field. The applied field is then decreased to a reversal field . T he FORC is the magnetization curve that results as the applied field is increased back to saturation . The measurement of quasi static FORCs was performed using the step me thod for the six steel hollow pipe samples listed i n Table 1. The rise time of the ramp was 2.7 m s, and the hold time was 42.3 ms. The Faraday coil was integrated over the entire 45 ms step, while the voltage from the hall effect sensor was averaged over the last 42.3 ms. This eliminates eddy current effects, and averages out zero mean noise from both the hall effect senor and the Faraday coil. The applied field approximating a saturating field was 18,000 A/m. The procedure used to measure the quasi s tatic FORC was as follows. The sample is first demagnetized. From the virgin state, it is run through a full major loop increasing the applied in 100 A/m

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43 steps to a maximum of 18,000 A/m. The applied field is then taken to 18,000 A/m and then back to 1 8,000 A/m in 100 A/m steps. After this saturate loop, the applied field has been taken down to a predetermined applied reversal field , and then back to 18,000 A/m in 50 A/m steps. The procedure in then repeated from demagnetiza tion for each desired . FORC data for the six steel hollow rod samples listed in Table 1 are provided in Figures 21 to 26. The hysteresis figures show a superposition of the major loop and the set of FORCs for the field reversals listed in Table 2. All of the curves show a similar path coming from the positive saturate reversal, but clearly show a different path after each of the separate negative reversals; thus demonstrating the hysteretic effect of an applied field to the stee l pipe. The second graph in each figure is the differential susceptibility, or the change in magnetization of the sample with respect to the change in the applied field defined as , computed along each FORC. The FORC curves described above have had their differential susceptibility plotted on a semi log plot starting from their negative reversal. The cooperative theory predicts that immediately following a reversal, the different ial susceptibility should be equal to the reversible susceptibility . ( 30 ) where is the initial susceptibility of the material, is the saturation magnetization of the material, and is the magnetization. To illustrate this, a plot of is superimposed in each plot. What is apparent in each FORC, is that the susceptibility increases linearly on the log plot with a linear slope from the reversal. This is governed by the term ( 31 ) in the cooperative model of the susceptibility in ( 26 ) . As the magnetization approaches saturation, t he slope of susceptibility is again linear. This corresponds to the term

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44 ( 32 ) in the exponential, which become s dominant as becomes small compared to .

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45 Results Table 3 . Applied reversal fields for the series of FORC measurements Reversal Applied Reversal Field [A/m] 1 st 6400 2 nd 6000 3 rd 5600 4 th 5200 5 th 4800 6 th 4400 7 th 4000 8 th 3600 9 th 3200 10 th 2800 11 th 2400 12 th 2000 13 th 1600 14 th 1200 15 th 800 16 th 400 17 th 0 18 th 400 19 th 800 20 th 1200 21 st 1600 22 nd 2000 23 rd 2400 24 th 2800 25 th 3200 26 th 3600 27 th 4000 28 th 4400 29 th 4800 30 th 5200

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46 Figure 31 C0878 Hysteresis Curve (left) and Differential Susceptibility (right) Figure 32 C7614 Hysteresis Curve (left) and Differential Susceptibility (right)

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47 Figure 33 U6346 Hysteresis Curve (left) and Differential Susceptibility (right) Figure 34 U3926 Hysteresis Curve (left) and Differential Susceptibility (right)

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48 Figure 35 W4G801 Hysteresis Curve (left) and Differential Susceptibility (right) Figure 36 U8520 Hysteresis Curve (left) and Differential Susceptibility (right) Faraday Measurement of Magnetostriction Setup The thin walled pipe measu ring apparatus , loaded with sample C0878, was loaded into the MTS load frame as shown in Figure 11 . The sample was demagnetized with a sinusoidal demagnetizing field that

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49 started at 9,000 A/m and decayed 3% each cycle. After the sample had been demagnetized, a major loop was applied with ± 17,000 A/m, and then the sample was left at remanence. Stress was then applied to the sampl e, going to 30 kN and the reversing to 30kN and then back to a 0 kN equilibrium. The fiel d was varied . The load waveform shown in Figure 37 was applied to the magnetized steel sample. Figure 37 The load applied to the sample, after it is brought to remnants Figure 38 Ma gnetization decrease due to applied stress

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50 Results Figure 37 shows the variation of the load applied versus time, with tension being a positive load and compression, negative. Figure 29 illustrates the internal field of the pipe during the variation of the load. Since there is no applied field, the internal field represents the demagnetizing field produced by the permanent magnetization in the pipe. The sample starts with a higher magnetization which then decreases u nder tension as we move the domain walls of the sample via stress. As the sample relaxes and moves into compression magnetization stays relatively stable, then when tension is applied to bring the sample back to a neutral state magnetization decreases aga in. The behavior is consistent with what is predicted by the Cooperative model for magnetostriction [8] . Faraday Magnetostriction Effect on Hysteresis A closer look was taken at the effects of magnetostriction on hysteresis. In this experiment sample C0878 had a measured stress applied, and then was run through the demagnetization process. After the sample was subject to a minor loop, with a ± 2,000 A/m reversal. Setup The thin walled pipe measuring apparatus, loaded with sample C0878, was loaded into the MTS load frame as shown in Figure 11 . For a control experiment th e MTS was bro u ght to a no load state. The sample was demagnetized with a sinusoidal demagnetizing field that started at 9,000 A/m and decayed 3% each cycle. A QSM minor loop was applied to the sample, with a ± 2,000 A/m reversal, and 100 A/m steps. The f ield was then left at the positive reversal. Data was taken every 90 µs during the process, with 100 data points per step. The ramp width was 30 data points. The blue curve in both the right and left plot in Figure 39 is the control data. After the control data was taken the experiment varied the procedure by varying the amount of stress the sample was under during the magnetic sampling. The sample ha d a recorded stress applied, both compressive and tensile, applied via the MTS load frame. After the stress was applied, the sample was

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51 not demagnetized, and the same applied field from the control experiment was again applied. Again the field was left a t the positive reversal between each successive applied stress. The stress was applied increasingly, for both the tension and the compression experiments. The data taken from these experiments is plotted in Figure 39 and Figure 40 . Figure 39 (left) Multiple hysteresis loops taken under various compressions, (right) The susceptibility of the sample at various compressions Figure 40 (left) Multiple hysteresis loops taken under various tensions, (right) The susceptibility of the sa mple at various compressions

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52 Results Figure 39 clearly shows how the magnetization of the material changes with compressive stress. As the compressive st ress is increased in the sample three phenomena become apparent. Increasing compression has a suppressive effect on the maximum achievable magnetization in this minor loop. This suppression in magnetic susceptibility keeps the field outside of the sample thereby increasing the field in the center of the pipe. This suppression is the second phenomenon, a decrease in the slope of , seen in Figure 39 (right). Thirdly, the change in the relationship between magnetization and H field causes a change in the coercive field; Figure 39 (left) has increasing values for the H field at the zero crossing for magnetization with increasing compression. Interestingly, there is a point as which all of the curves intersect, regardles s of compression. Figure 40 shows the effects of tension on the sample. Again the same three phenomena as in the compression experiment are seen, however in tension the s igns are reversed. The maximum magnetization in increased with increasing tension, and the internal field of the sample is accordingly decreased. The slope of is increased, and the coercive field has been decreased. The common crossover between all applied stresses is seen, however it is seen at a much higher magnetization then in the compressive case. T hese three phenomena are due to two fields, the Brown field and the Bozorth field [8] . The Brow n filed is given as [8] , ( 33 ) and the Bozorth field is given as [8] , ( 34 ) where . In this case the identifiers 100 and 11 1 indicate the easy and hard axis. This data is showing that they have a direct and predicable contribution to the magnetization of the sample.

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53 Looking at the (right) side of the Figure 39 and Figure 40 the susceptibility of each of the magnetic loops is shown. These susceptibilities are modified by , ( 35 ) as, . ( 36 ) Ring Major Loop Example During the course of the experiments taken with the pipe sample the demagnetization feil d that accumulated in the pipe sample began to be problematic in measuring physical parameters. An elegant solution to this was proposed by C. Schneider. The use of a sample in the shape of a ring would have no magnetic poles build as the sample magnetized, because there was a path to contain all of the flux within the material. If the flux were to be contained entirely inside the sample, then there would be no field produced to interfere with measurements. Setup Data was taken to show the shape of a typical hysteresis curve with the ring sample, and to discuss some of the parameters looked at when analyzing the data. Figure 41 Figure 21 shows a major loop, taken from a ring sample starting from a demagnetized state. The virgin curve was taken out to 13,000 A/m applied, and then the applied field was cycled from 13,000 A/m to 13,000 A/m and back again.

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54 Figure 41 Example Major loop taken with a ring sample Results Fitting the model was applied this major loop in much the same way as was done to the pipe. Differential susceptibility was calculated using equation ( 25 ) . The anisotropy function was fit to the calculated differential susceptibility to find both saturation magnetization and initial susceptibility . The full model was fit by adjusting values for the coercive field and the anhysteretic field iteratively. Figure 42 shows the differential susceptibility, the anisotropy function and the model fit together.

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55 Figure 42 Fitting of the differential susceptibility to the model develo ped by C. Schneider Ring FORCs Experiment Setup From a remnant state, the ring sample was run through a full major loop increasing the to a maximum of 13,000 A/m. The applied field is then taken to 13,000 A/m and then back to 18,000 A/m. This was done with a swept triangle wave at 2 Hz. After this saturate loop, the applied field has been taken down to a predetermined applied reversal fi eld , and then back to 13,000 A/m. The procedure in then repeated from demagnetization for each desired . Table 4 shows the values used for each reversal .

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56 Table 4. Reversal Values Used in the Ring Sample Experiments Reversal Applied Field [A/m] 1st 1500 2nd 1250 3rd 1100 4th 1000 5th 950 6th 900 7th 850 8th 800 9th 750 10th 700 Few er reversals were taken from the ring as compared to the pipe. The field span at which the ring goes through its highest susceptibility phase is considerably shorter than the high susceptibility field span in the pipe sample. This shortened window means that fewer FORCs can describe the behavior of the ri ng reasonably well. Results Each of the FORCs taken in the experiment are shown overlaid in Figure 43 . Fitting each of the FORCs in the experiment yielded Figure 44 . For each of the fits, all of the physical parameters were held constant except for the coercive field . Table 5 l ists those parameters. Table 5. Experimental Parameters for Ring FORC Experiment Physical Parameter Value Saturation Magnetization [A/m] 1640000 Initial Susceptibility 75 Anhysteretic Field [A/m] 1200

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57 Figure 43 Ring sample FORCs shown as a hysteresis plot Figure 44 Susceptibility of each fork, shown with a fit to C. Schneider's model

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58 Plotting the coercive field as a function of reversal point in Figure 45 shows an interesting trend. Figure 45 Coercive field as a function of reversal The data curves in Figure 44 model. This is sheering is due to eddy currents delaying the magnetization of the sample. The rate at which this experiment was run is considerably faster than the rate at which the pipe sample experiments are run. This is to keep heat effects low in the sample.

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59 CHAP ER V . CONCLUSION The primary aim of this thesis has been to create a measurement system that uses the FCM to measure the response of a ferromagnetic material to the effects of an applied field and applied stress. An apparatus was created to take these measurements; a n input computer controlle r has been interfaced to a data acquisition device that can read data from separate transducers measuring different effects. A Hall Effect probe measures the field produced by a Faraday coil being driven by a bi polar amplifier. A separ ate Faraday coil inductively measures the flux produced by the driven Faraday coil. Th e amplifier is controlled by a n output computer controller whic h communicates with the input computer controller . The output computer controller for the amplifier is al so capable of controlling the MTS, providing a stress environment capable of changing the magnetic properties of a ferromagnetic sample through magnetostriction. These changes are recorded by the Hall Effect probe. These all combine into on e working appa ratus, which is capable of taking magnetic and stress measurements quickly and accurately. This apparatus was used to take measurements from two different geometries of samples, a pipe and a ring. An example of a major loop taken from the pipe was presente d, along with a description of how data is interpreted. A series of minor loops measuring the initial susceptibility of several material was presented. Severa l sets of First Order Reversal C urves was then presented for various types of mild steel. The p ipe was then subjected to two different types of stress tests; one showing the effects of varying stress on the magnetization of a sample, and the other showing the effects of stress on magnetic hysteresis. Experiments from the ring sample were then discu ssed. A major loop and a discussion of how data is interpreted was shown. And finally a set of FORCs from the ring sample were shown, complete with a model fitting.

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60 References [1] F. Preisach, "Über die magnetische Nachwirkung," Zeitschrift für Physik, vol. 94, pp. 277 302, 1935. [2] E. D. T. Ann Reimers, "Fast Preisach Based Magnetization Model," IEEE Transactions on Magnetics , vol. 34, no. 6, pp. 3857 3866, 1998. [3] D. A. D.C Jiles, "Ferromagnetic hysteresis," IEEE Transactions on Magnetics , Vols. MAG 19, no. 5, pp. 2183 2185, 1983. [4] R. C. O'Handley, Modern Magnetic Materials Principles and Applications, New York: John Wiley & Sons, Inc., 2000. [5] S. G. R. A. John C. Young, "A Nystrom Solution of the Quasi Magnetostatic Volume Intebral Equation for Eddy Current Analysis," IEEE Antennas and Propogation Society International Symposium, 2012. [6] K. Townsend, "COMPUTATIONAL AND MEASUREMENT METHODS FOR FERROMAGNETIC HYSTERESIS IN DIFFERING STEEL ALLOYS (Masters Thesis)," May 2018. [7] S. D. G. S. M. J. T. W. F. M. A. T. Carl S. Schneider, "Measreument and Exponential Model of Ferromagnetic Hysteresis," Physica B, UNDER REVIEW. [8] C. S. Schneider, "Effects of stress on the shape of ferromagnetic hystresis loops," Journal of Applied Physics, vol. 97, no. 10, p. 10E503, 2005. [9] C. S. Schneider, "Cooperative Anisotropic Theory of Ferromagnetic Hysteresis," in Trends in Material Sc ience Research , New York, Nove Science Publishers, 2005, pp. 1 49. [10] R. Bozorth, Ferromagnetisim, New Jersey: D. Van Nostrand Company, Inc., 1951.