A Magnetic Flux Leakage NDE System for CANDU R Feeder Pipes
by
Thomas Don Mak
A thesis submitted to the Department of Physics, Engineering Physics & Astronomy in conformity with the requirements for
the degree of Master of Applied Science
Queen’s University Kingston, Ontario, Canada March 2010
Copyright c Thomas Don Mak, 2010
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Abstract
This work examines the application of different magnetic flux leakage (MFL) inspec- tion concepts to the non destructive evaluation (NDE) of residual (elastic) stresses in
R CANDU reactor feeder pipes. The stress sensitivity of three MFL inspection tech- niques was examined with flat plate samples, with stress-induced magnetic anisotropy
(SMA) demonstrating the greatest stress sensitivity. A prototype SMA testing sys- tem was developed to apply magnetic NDE to feeders. The system consists of a flux controller that incorporates feedback from a wire coil and a Hall sensor (FCV2), and a magnetic anisotropy prototype (MAP) probe. The combination of FCV2 and the MAP probe was shown to provide SMA measurements on feeder pipe samples and predict stresses from SMA measurements with a mean accuracy of ±38 MPa.
i Acknowledgments
First and foremost I would like to thank my supervisor, Dr. Lynann Clapham, for presenting me with this wonderful opportunity. Her guidance and expertise were
greatly appreciated. This work would have been far less interesting and enjoyable without the assistance
of Dr. Steven White. He acted as a teacher from the moment I began working under him as a summer student in 2006, and he provided invaluable assistance in all aspects of this project from its conception, from theory to design, data acquisition and signal
processing. I would also like to thank all members of the AECL Inspection Monitoring and
Dynamics Branch, in particular H´el`eneH´ebert. She helped organize meetings with AECL and provided helpful advice and encouragement. Thanks are due to Dirk Bouma, who was consulted frequently during the design
of the first flux control system (FCV1), as well as Gary Contant and Chuck Hearns for their help and supervision in the machine shop. I also thank Pat Wayman for all
her help during all phases of this project.
Several students provided valuable assistance: Ben Lucht helped with LATEX and
R MATLAB , and Davin Young spent many hours in the machine shop building probe components. ii Table of Contents
Abstract i
Acknowledgments ii
Table of Contents iii
List of Tables v
List of Figures vi
Chapter 1:
Introduction ...... 1
R 1.1 CANDU Feeder Pipes ...... 2 1.2 A Brief Introduction to Magnetic Circuits and Magnetic Flux Leakage Inspection ...... 5 1.3 Thesis Scope and Objectives ...... 7
1.4 Organization of Thesis ...... 8
Chapter 2: Theory and Background ...... 10
2.1 Stress and Strain ...... 10
iii 2.2 Maxwell’s Equations and The Quasi-Static Case ...... 15 2.3 Magnetic Materials ...... 16
2.4 Magnetic Methods of Stress Measurement ...... 29
Chapter 3: Flux Control Systems ...... 39 3.1 Negative Feedback Control and Operational Amplifiers ...... 40
3.2 Magnetic Flux Transducers ...... 42 3.3 Component Selection ...... 47
3.4 White’s Flux Control System (FCS) ...... 49 3.5 Flux Control Version 1 (FCV1): Hall Sensor Feedback ...... 51
3.6 Flux Control Version 2 (FCV2): Hall Sensor and Coil Feedback in Combination ...... 60
Chapter 4:
Magnetic Stress Detectors ...... 67 4.1 Test Sample and the Single Axis Stress Rig (SASR) ...... 69 4.2 Detectors, Data Acquisition and Data Analysis ...... 72
4.3 Experimental Procedures for Testing and Comparison of the Probe Systems ...... 75
4.4 Detector Results and Analysis ...... 76 4.5 Selected Detector ...... 90
Chapter 5:
Proposed Design: MAP Probe ...... 91 5.1 Magnetic Anisotropy Prototype (MAP) Probe ...... 92
iv 5.2 MAP Probe Testing with SA-106 Grade B Pipe ...... 96
Chapter 6: Summary and Conclusions ...... 107
6.1 Flux Control Systems ...... 107 6.2 Magnetic Stress Detectors ...... 108 6.3 Proposed MAP Probe Design ...... 109
6.4 Recommendations for Future Work ...... 110
Bibliography ...... 113
Appendix A:
FCV1 Details ...... 118
Appendix B: Skin Depth ...... 120
v List of Tables
3.1 Excitation and monitor coil properties. Inductance values were recorded
on-sample at 100 Hz. The monitor coil was wound around one of the core’s poles, making its area the same as the pole area...... 53 3.2 PCI-6229 I/O assignment and terminal configuration for FCV1. Ter-
minal configurations use the following abbreviations: referenced single- ended (RSE), non-referenced single-ended (NRSE), differential (DIFF).
For additional information on terminal configurations see [29]. . . . . 53 3.3 PCI-6229 I/O assignment and terminal configuration for FCV2. . . . 64
5.1 MAP probe properties. Feedback and excitation coils were wound on an external forming rig, which is why their area differs from the Supermendur core footprint...... 95
vi List of Figures
R 1.1 A simplified sketch of a CANDU 6 reactor face...... 3 1.2 A comparison of magnetic and electric circuits...... 6
2.1 The stress tensor for an element of a continuous structure in Cartesian coordinates...... 11
2.2 Residual stress formation in a bent beam...... 13 2.3 Ferromagnetic domain structure...... 18
2.4 A typical magnetization hysteresis loop for a ferromagnetic sample starting with zero magnetization...... 19
2.5 A schematic of four magnetic domains aligned along the ¡100¿ direc- tions of Fe...... 20 2.6 Demagnetizing field lines for: a) a single domain, b) two opposing
domains separated by a 180◦ wall, and c) four domains separated by
90◦ and 180◦ walls...... 24
2.7 Magnetostriction of a material with positive λs...... 25 2.8 The two types of magnetoelasticity: magnetostriction and the Villari
effect for a material with positive λs...... 26 2.9 The magnetization processes for samples with aligned and misaligned auxiliary fields and preferred crystalline axes...... 27
vii 2.10 A simplified Barkhausen noise apparatus...... 31 2.11 A bandpass filtered Barkhausen noise spectrum taken from 3 kHz to
600 kHz...... 32 2.12 A polar plot of angular MBN energy measurements...... 32 2.13 The application of magnetic flux leakage inspection in crack and cor-
rosion detection...... 34 2.14 The MFL signal from a segment of SA106-B schedule 80 pipe (a) ref-
erence measurement and (b) after the introduction of residual stresses through a localized impact. Maxima correspond to red and minima
correspond to blue, but no further colour scale information is available. 34
2.15 The rotation of the magnetic field just outside the sample (B~ out) rela-
tive to the magnetic field within the sample (B~ in) when µ2 > µ1. . . . 36
2.16 The orientation of B~ in and B~ out relative to the excitation core. . . . . 37
3.1 The components of a closed-loop control system shown in a block dia-
gram...... 41 3.2 The feedback system components contained within an op-amp. . . . . 43 3.3 The Hall effect for a Cartesian coordinate system...... 45
3.4 A sketch of White’s FCS...... 50 3.5 A simplified version of FCV1...... 52
3.6 Hall voltage (VH ) and excitation current (Iex) for a sinusoidal reference voltage...... 55
3.7 FCV1 response to a DC reference voltage of Vref = 0...... 56
3.8 Monitor coil voltage Vmc boosts the noise amplitude relative to the excitation field...... 58
viii 3.9 A simplified version of FCV2...... 61 3.10 An electrical schematic of FCV2 showing the feedback system and the
Hall sensor current source...... 63 3.11 The magnetic fields measured by the Hall sensor and feedback coil in FCV2...... 66
4.1 The three detector configurations used with the prototype excitation core...... 68
4.2 The mild steel plate used to test different detector configurations. . . 70 4.3 A schematic of the single axis stress rig used to introduce tensile stress in the flat plate sample...... 71
4.4 An assembled probe showing a detector mount assembly attached to the connector brace of the excitation core...... 72
4.5 DC MFL, AC MFL, and SMA detectors mounted to the excitation core. 74 4.6 The footprint of the excitation core on the sample for AC MFL, DC
MFL and SMA measurements...... 75
4.7 DC MFL measurements for Bex k σt and Bex ⊥ σt...... 78 4.8 The excitation field (dashed line) and signal voltage (solid line) for an
AC MFL measurement at zero applied stress...... 80
4.9 AC MFL measurements for Bex k σt and Bex k σc...... 82 4.10 A modified figure 1.15 redrawn for reference. The excitation core foot- print is indicated by dotted lines...... 83
4.11 G for four µr2/µr1 ratios. The 0◦ , 180◦ , and 360◦ probe orientations
place the probe parallel to the µ2 direction...... 85
4.12 Vsig(σ, φ) fit amplitudes for SMA measurements...... 87
ix 4.13 SMA measurements for tensile up to 130 MPa...... 89
5.1 A schematic of the Supermendur core of the MAP probe...... 93
5.2 A diagram of the MAP system...... 93 5.3 The pin diagram for the MAP system...... 95 5.4 A schematic of the three-point bending rig in the tensile configuration. 97
5.5 SMA dependence on excitation field amplitude...... 100
5.6 MAP stress response for an excitation field Bex = 75 mT sin(2πt55 Hz). 102 5.7 SMA dependence on tensile and compressive applied stress...... 104
5.8 Signal voltage Vsig(σa, φ) fit amplitude for approximately equivalent
compressive (σa = −44 MPa) and tensile (σa = 47 MPa) stresses. . . . 105
6.1 The recommended system for future work. (a) Two perpendicular U- cores can rotate the magnetic field at their center by adjusting the
excitation field generated by each core. Adapted from [39]. (b) The recommended anisotropy coil configuration for a tetrapole excitation
system. Coils 1 and 3 are connected in series, as are coils 2 and 4. . . 112
A.1 An electrical schematic of FCV1...... 119
7 1 1 B.1 Skin depth for a typical steel with µr = 100 and σe = 10 Ω− m− . . 121
x Chapter 1
Introduction
Engineered components have a finite service life governed by their design, manufac- turing processes, material properties and application. Components will eventually fail, terminating their service life. The causes of failure are commonly chemical or mechanical processes that alter component characteristics and material properties. When the cost of failure is sufficient, regular inspection of components becomes cost efficient: components near failure can be identified then repaired (extending their service life) or replaced (ending their service life before failure). There are many methods available for examining component degradation, but inspection techniques that do not require component disassembly or destruction are valued for their non- invasive nature; they are classified as non-destructive evaluation (NDE)1 techniques. The risk of component failure is derived from NDE data. Components are replaced when the risk of failure reaches a threshold value, determined by: the accuracy of the NDE method, the cost of replacement and the cost of failure. Accurate NDE
1The term non-destructive testing (NDT) is used synonymously with non-destructive evaluation (NDE).
1 CHAPTER 1. INTRODUCTION 2
inspection techniques reduce the cost of ownership of a system by reducing repair, replacement and failure costs.
This thesis focuses on the development of a magnetic NDE method to detect
R regions of residual stress in CANDU feeder pipes. Details of the magnetic flux leak-
R age (MFL) NDE technique and CANDU feeder pipes are provided in the following sections.
1.1 CANDU R Feeder Pipes
R CANDU (CANada Deuterium Uranium) reactors are heavy water-cooled, heavy water-regulated nuclear reactors designed by Atomic Energy of Canada Ltd. (AECL) in partnership with General Electric Canada2 and Ontario Power Generation3 (OPG).
Reactors that use standard water (H2O) as the moderator/coolant require enriched uranium fuel, composed of U-238 with 2% to 4% wt U-235. Heavy water moder-
R 4 ated/cooled reactors, such as the CANDU , can achieve criticality with naturally- occurring uranium, composed of U-238 with 0.7% wt U-235, because heavy water
(D2O) is a weaker neutron moderator than standard water [11].
R The primary heat transport circuit of a CANDU reactor uses pumps to push heavy water coolant over fuel bundles in the calandria5. A simplified sketch of a
R CANDU reactor face, showing most components of the primary heat transport cir- cuit is shown in figure 1.1. SA-106 grade B carbon steel feeder pipes (termed ‘feeders’ and labelled 3 in figure 1.1) transport heavy water coolant from heat transport pump
2Known as Canadian General Electric during the design partnership. 3Known as Hydro-Electric Power Commission of Ontario during the design partnership. 4A self sustaining fission reaction. 5A calandria is the reactor core of a CANDU R system CHAPTER 1. INTRODUCTION 3
6 6
4 4
1 2
3 3
1. outlet header 2. inlet header feeders3. 5 4. steam generators
5. end ttings 7 6. heat transport pumps 7. insulation cabinet
R Figure 1.1: A simplified sketch of a CANDU 6 reactor face. Adapted from the CAN- TEACH library (http://canteach.candu.org/library/19990113.pdf). input headers (labeled 2 in figure 1.1) to pressure tube inlet end fittings (labeled 5 in
figure 1.1) on the reactor face. The coolant is heated as it passes through the calan- dria, then exits via the pressure tube outlet end fittings and is passed through feeders to outlet headers (labeled 1 in figure 1.1), where it is cooled by steam generators and returned to the heat transport pumps.
There are over 700 feeders per reactor. The feeders must access the end fitting matrix at the reactor face and maintain minimum clearances of approximately 20 mm, CHAPTER 1. INTRODUCTION 4
which requires a variety of feeder bending arrangements. The SA-106 grade B carbon steel feeders have schedule 80 wall thickness with nominal diameters of 2.0” or 2.5” and bend radii of 1.5× the diameter. Ovality caused during the bending process and Corrosion introduce variation in pipe wall thickness; the 2.5” diameter pipes can vary in wall thickness from 4 mm to 8 mm. The minimum tensile yield strength of SA-106 grade B carbon steel is 240 MPa [1]. An outlet feeder pipe was removed from service in 1997 following detection of a coolant leak. The leak was attributed to cracking within the pipe, which was analyzed by AECL with a variety of techniques, including neutron diffraction to determine if residual stresses contributed to the failure. The neutron diffraction data indicated that residual stresses in the vicinity of the crack were elevated. Ultimately, cracking was attributed to a combination of an elevated stress distribution and flow-accelerated
6 corrosion caused by 311◦ C heavy water [40]. The cracking that results from a combination of tensile stress and a corrosive environment is called stress-corrosion cracking (SCC). Following the original 1997 leak, SCC has been found in a number of outlet feeders [16]. It was further determined that the SCC found in feeders was initiated by yield strength tensile stresses on the inner pipe surface. Canadian Nuclear Safety Commission (CNSC) safety regulations require the pre- vention of leakage from feeder piping systems. If a feeder leak is detected in an active reactor, a shutdown leakage limit of 20 kg/h is enforced. The costs associated with forced reactor outages and the replacement of pressure boundary components are high: a minimum shutdown time of 40 h is required at a cost of approximately $20 000/h. Because of this cost, reactor operators attempt to avoid forced outages
6Flow-accelerated corrosion is a process whereby the normally protective oxide layer on carbon steel dissolves into a stream of flowing water or wet steam. CHAPTER 1. INTRODUCTION 5
by performing regular NDE inspections of components at the reactor face. Ideally, operators would replace feeders that are at risk for developing SCC during scheduled
maintenance shut-downs; however, there is currently no commercial NDE system that can evaluate the stress distribution in feeders at the reactor face, which is thought to be primary cause of feeder SCC.
AECL approached the Queen’s University Applied Magnetics Group (AMG) through the University Network for Excellence in Nuclear Engineering (UNENE) and proposed
that the group develop a ferromagnetic NDE stress evaluation technique for the pur-
R pose of measuring residual stresses in CANDU feeders. Two projects were proposed: a doctoral thesis focused on the use of magnetic Barkhausen noise, and a master’s thesis concentrating on the adaptation of a magnetic flux leakage technique to feed- ers. The doctoral project was completed by Steven White in 2009 [39]. The present thesis focuses on the development of a magnetic flux leakage technique that address the unique problems associated with NDE stress evaluation of feeders.
1.2 A Brief Introduction to Magnetic Circuits and
Magnetic Flux Leakage Inspection
Magnetic systems make use of ‘magnetic circuits,’ a concept that exploits similarities between electric and magnetic field equations and allows magnetic systems to be rep- resented schematically. Figure 1.2 shows some analogs between electric and magnetic circuits. Just as electric circuits rely on an electric scalar potential difference (V ) to generate an electromotive force (EMF) that drives electric current (I) through
a resistance (R), magnetic circuits rely on a magnetomotive force (MMF) to drive CHAPTER 1. INTRODUCTION 6
current source light bulb (a) (b) wire coil Is N turns current I flux
+
_ core battery
Physical System air gap
wire
(c) (d) wire resistance core reluctance current I Rwire flux load bulb resistance air gap reluctance
+ R N load s V _
NI S MMF source voltage source Circuit Schematic Circuit
Electric Magnetic
Figure 1.2: A comparison of magnetic and electric circuits. Figures (a,b) show sketches of physical systems, while the electrical and magnetic schematics of the systems are given in figures (c,d). magnetic flux (Φ) through a reluctance (R).
Referring to the electric circuit case shown in figures 1.2 (a,c), a battery provides voltage V required to drive I through the light bulb load. For an equivalent magnetic circuit, the MMF of figures 1.2 (b,d) is provided by a current-carrying coil of N turns supporting current current Is. This coil generates a magnetic flux Φ, which passes through the core (RC ) and air gap (RG). Magnetic flux leakage (MFL) inspection systems measure the magnetic flux out- side of a magnetized sample, called ‘leakage’ flux, and correlate it to sample proper- ties, commonly changes in cross-section area caused by dents, gouges and pits. These measurements are conceptually quite simple: a magnetic circuit is assembled using a permanent magnet to generate a flux Φ through the magnet-sample circuit. The magnetic reluctance of sample regions with low cross-sectional area (eg. corrosion CHAPTER 1. INTRODUCTION 7
pits) is increased, causing flux to leak into the surrounding environment. Once flux has left the sample it can be detected by a magnetic flux transducer, such as a Hall probe or giant magnetoresistance sensor. The transducer signal can be interpreted to determine the nature of the defect that caused the flux leakage. MFL is, as its name suggests, a measurement of leakage flux that emerges from a magnetized sample. To generate effective comparisons between different measure- ments, the flux Φ through different samples, or regions on a sample must be con- sistent. Traditionally, commercial MFL systems overcome this issue by generating flux with large permanent magnets that magnetically saturate the sample; however these magnets are large, bulky and difficult to manipulate. These commercial MFL systems are not suitable for the current application, the ferromagnetic feeder array at
R a CANDU reactor face makes safe handling of large permanent magnets impossible.
1.3 Thesis Scope and Objectives
As outlined earlier, this thesis project focuses on the adaptation of magnetic NDE
R technology, specifically flux leakage systems, to CANDU feeder pipes. The system developed in this thesis should function as an early prototype for an industrial system.
The scope was limited to the following specific project objectives:
1. design a magnetic flux leakage-based probe that can accommodate the space
and geometry (lift-off) constraints imposed by the feeder pipe environment
2. conduct laboratory testing on plate samples to determine the extent of stress sensitivity of the probe designs CHAPTER 1. INTRODUCTION 8
3. conduct testing on samples with feeder pipe geometry with a focus on general- ized stresses
4. conduct testing on feeder pipe samples
1.4 Organization of Thesis
This thesis is organized as follows:
• Chapter 2 presents a brief review of electrodynamic theories used to describe the stress-dependence of magnetic flux leakage and magnetic anisotropy within
ferromagnetic materials.
• Chapter 3 outlines the two flux control designs developed with the goal of
producing consistent and repeatable magnetic excitation fields in the feeder samples.
• Chapter 4 presents three different stress detectors (to be used with the flux control systems) and initial stress sensitivity results from those detectors.
• In chapter 5, a prototype system designed specifically for stress measurements
on feeder pipes is presented. This system was designed based on results pre- sented in chapters 3 and 4, and tested on a 2.5” SA-106 grade B pipe. Test
results are presented in this chapter.
• Chapter 6 summarizes the findings of this work and provides suggestions for future system improvements. CHAPTER 1. INTRODUCTION 9
All designs, figures, drawings, measurements and physics probes described in this work are the original work of the author unless otherwise noted. Exceptions include: the single axis stress rig described in section 4.1, and the three-point bending rig presented in section 5.2.1. Chapter 2
Theory and Background
This chapter presents a theoretical summary of stress, strain, and quasi-static mag- netic behavior to provide a basis for magnetic domain theory, design decisions, and signal analysis techniques presented in later chapters. A review of stress and strain principles is given in section 2.1. Section 2.2 begins with Maxwell’s equations and leads to discussion of the quasi-static case. The classi-
fication of magnetic materials is presented in section 2.3, along with an overview of magnetic domain theory and magnetization processes. In section 2.4 different mag- netic stress measurement techniques are presented. Notation in this chapter is consistent with that used in Griffiths (reference [12]).
2.1 Stress and Strain
Stress is a measure of the force acting per unit area within a body. The stress state of an element within a body1, shown in figure 2.1, can be determined by a nine
1A body is an structure composed of a continuous distribution of elements (also known as points).
10 CHAPTER 2. THEORY AND BACKGROUND 11
σzz z
σzx σzy
σzx σyz
σxx σxy σyx σyy
x y
Figure 2.1: The stress tensor for an element of a continuous structure in Cartesian coor- dinates. component stress tensor σ, given by
σxx σxy σxz σ = σyx σyy σyz . (2.1) σzx σzy σzz Diagonal tensor elements σxx, σyy, and σzz represent normal (tensile and compressive) stress components, while off-diagonal elements represent shear stress components.
Stress may vary within a body, causing different elements to have different stress tensors. A complete description of the stresses within a body is therefore given by a tensor field. Ideally, each body element would have zero volume; however, all physical measurements must be performed over a sample volume, with stress averaged over that volume. The characteristics of the sample volume greatly affect the details of the stress field in a crystalline material. Consider any steel sample: a typical body will consist CHAPTER 2. THEORY AND BACKGROUND 12
of numerous small crystals (called grains) in multiple orientations. A small sam- ple volume may be less than the average grain size2, leading to an inhomogeneous, anisotropic material at the microscopic scale. If the sample volume is large enough to enclose several million crystals, steel may be considered homogeneous, as the properties of any single crystal become insignifi- cant. If the body is not strongly textured3 it may also be considered isotropic. The maximum stress a material can support before undergoing plastic deformation is defined as the yield stress σyield. Application of an external force to an object results in deformation. Deformation is elastic up to σyield, that is, the deformation
vanishes if the force is removed. External stress beyond σyield causes irreversible plastic deformation that remains once the stress source is removed, shown in figure 2.2 for a bent beam. Removal of this external stress disrupts the stress distribution within
the body, causing it to reacquire some of its initial shape via elastic deformation. Because it has been permanently deformed, it cannot return completely to its original
form, thus the elastic stress distribution remains within the material. These elastic stresses are called residual stress and are often present in engineered components
manufactured by plastic deformation processes, such as extruded pipes and bent beams. In addition to non-uniform plastic deformation such as that shown in figure 2.2, other sources of residual stress are welding stresses, intergranular misfit stresses,
thermal expansion stresses, etc [27]. As stress is a type of force, it cannot be measured directly and must be inferred
from some other physical parameter, typically geometrical deformation, typically known as ‘engineering strain,’ or simply ‘strain.’ The engineering strain tensor ε
2A grain is a domain of mater that has the same structure as a single crystal. 3Texture is the distribution of crystal orientations within a polycrystalline sample. A material is said to be strongly textured if a there is a preferential crystal orientation. CHAPTER 2. THEORY AND BACKGROUND 13
(a)
tensile stress
(b) compressive stress Force Force
compressive stress (c)
tensile stress
Figure 2.2: Residual stress formation in a bent beam. (a) The beam in an unstressed state. (b) A downward force applied to the ends of the beam causes plastic deformation. There is tensile stress above a neutral surface (shown with a dashed line) and compressive stress below it. (c) Once the external force is removed, internal ‘residual’ stresses redistribute to elastically deform the body toward its original state. CHAPTER 2. THEORY AND BACKGROUND 14
expresses geometrical deformation as a ratio of the change in dimension ∆d to the initial dimension d0. Diagonal components of ε are normal strains in the x, y, and z directions, and are given by
∆d d − d0 εi=j = = , (2.2) d0 d0
where d is the dimension after deformation. Off diagonal components (εi=j) are equal 6 to one-half the engineering shear strain.4 Each entry in ε generates a corresponding stress entry in σ. The relationship between tensor entries is defined by a fourth order stiffness tensor Cijkl, such that
σjk = kl Cijklεkl. EngineeringP applications generally simplify the relationship between stress and strain by assuming isotropic materials, in which case a geometrical deformation can be characterized by two parameters: Young’s modulus (Y ), and Poisson’s ratio (ν).5 This simplification means the relationship between stress and strain can be expressed using a generalized Hooke’s law equation as: Y ν σ = ε + (ε + ε + ε ) . (2.3) ij 1 + ν ij 1 − 2ν xx yy zz Strain can be measured in many ways on macroscopic and microscopic scales. Resistive strain gages are commonly used to evaluate macro-stresses, while diffraction techniques using neutrons or x-rays are can be used for micro-stress analysis. There are parameters other than strain affected by stress. Most importantly for the purpose of this thesis, magnetic properties of ferromagnetic alloys are affected by the stress
field, and have the potential to be used for macroscopic stress analysis.
4Engineering shear strain is the complement of the angle between two initially perpendicular line segments. 5 Shear modulus (Gm) is not included in this list as it is defined by Gm = Y/ [2 (1 + ν)]. CHAPTER 2. THEORY AND BACKGROUND 15
2.2 Maxwell’s Equations and The Quasi-Static Case
Maxwell’s four equations ρ ∇ · E~ = (2.4) ǫ0 ∂B~ ∇ × E~ = − (2.5) ∂t
∇ · B~ = 0 (2.6)
∂E~ ∇ × B~ = µ J~ + µ ǫ , (2.7) 0 0 0 ∂t and the Lorentz force law
F~ = q E~ + ~v × B~ (2.8) describe the relationship between electric and magnetic fields, and the effect these fields have on charged particles. In the above equations, t is time, B~ is the magnetic field (also referred to as magnetic flux density), E~ is an electric field, J~ is the current density field, F~ is force, q is electric charge, ρ is electric charge density, ~v is velocity,
and ǫ0 and µ0 are the permittivity and permeability of free space. In most magnetic experiments, including the work presented in this thesis, fields vary at a sufficiently low rate that magnetostatics can be used to describe electric
∂E~ field behavior. In this ‘quasi-static’ case, the displacement current term (µ0ǫ0 ∂t ) of ∂E~ equation 2.7 can be neglected because J >> ǫ0 ∂t . Thus equation 2.7 becomes
∇ × B~ = µ0J.~ (2.9)
The current density J~ is the sum of two components:
J~ = J~b + J~f , (2.10) where J~b is the bound current due to electron spin and angular momentum, and CHAPTER 2. THEORY AND BACKGROUND 16
current generated by the movement free particles is represented by J~f . The magne- tization field (M~ ) is attributed to bound currents:
∇ × M~ = J~b, (2.11) and the auxiliary field (H~ ) to free currents:
∇ × H~ = J~f . (2.12)
Equations 2.9, 2.10, 2.11, and 2.12 can be rearranged to give
B~ = µ0 M~ + H~ . (2.13)
2.3 Magnetic Materials
Equation 2.13 can be expressed using magnetic susceptibility (χm) or relative perme-
ability (µr) tensors as
~ ~ ~ B = µ0µrH = µ0 (1 + χm) H. (2.14)
~ ~ Both µr and χm are used to express the response of Jb to Jf and relate that response to magnetic flux density. For simplicity, many materials are assumed to have linear
and isotropic magnetic properties, thus making the susceptibility tensor a constant
(χm). Materials are categorized by their χm value, the most common categories being: diamagnetic, paramagnetic, ferrimagnetic, and ferromagnetic.6 Diamagnetism occurs when atoms or molecules have no net magnetic moment, meaning electrons constitute a closed shell. As such, nearly all organic compounds and polyatomic gases are diamagnetic [7]. Typical diamagnetic materials have a small,
5 negative susceptibility, on the order of χm ≈ −10− . H~ interacts with electrons to
6Other varieties of magnetism are omitted for brevity. CHAPTER 2. THEORY AND BACKGROUND 17
decrease B~ through the application of Lenz’s law to the orbital rotation of electrons about nuclei. Superconductors are considered nearly perfectly diamagnetic with χm ≈ −1, completely expelling the magnetic field from within the material. Paramagnetism is caused by atoms or molecules with a net magnetic moment generated by unpaired electrons. In the absence of an applied field, these moments
are randomly oriented and cancel each other, leading to zero net magnetization of the body. When a field is applied, these moments rotate to the direction of the
field; however, thermal agitation prevents atomic moments from achieving complete alignment. The end result is partial alignment with H~ , leading to small positive
5 3 susceptibilities on the order of 10− to 10− . Ferro and ferrimagnetism result from a material’s chemical makeup and crystal structure. As with paramagnetism, the atoms or molecules that comprise the crystal
have a net magnetic moment generated by unpaired valence electrons. In a ferro- magnetic material, crystalline lattice spacings are such that valence electron spins of
adjacent atoms are aligned via the quantum mechanical exchange interaction. Aligned moments group together in magnetic domains, as shown in figure 2.3. Domain walls
separate domains of different orientations. External magnetic fields cause shifts in the domain structure, ultimately align- ing magnetic domains with the field. Because domains are composed of billions of
magnetic moments, ferromagnetic materials have large magnetic susceptibilities, up
6 to χm ≈ 10 . Ferromagnets retain some magnetization in the absence of an H~ field. Ferrimagnetism is a combination of ferromagnetism and anti-ferromagnetism, which is simply the opposite of ferromagnetism. Ferrite substances are composed of iron double-oxides and at least one other metal; magnetic ions occupy different lattice CHAPTER 2. THEORY AND BACKGROUND 18
Figure 2.3: Ferromagnetic domain structure. Magnetic domain orientation is shown with arrows. Domain walls appear in white. Taken from [12].
sites some of which are coupled ferromagnetically and others anti-ferromagnetically.
The overall effect results in susceptibilities ranging from 10 to 104.
The isotropic and linear χm approximation is usually valid for paramagnetic and diamagnetic substances; however, the domain structure of ferromagnetic and ferri- magnetic materials generates strong magnetic anisotropy and hysteresis effects. A typical M-H loop for a ferromagnetic material in an oscillating H field is shown in figure 2.4. The figure shows that a demagnetized sample exposed to an auxiliary
field will magnetize along the initial magnetization curve (dashed line) to Ms, the saturation magnetization. A subsequent decrease in H decreases the the sample’s magnetization to the remnant (or residual) magnetization (Mr), defined as the mag- netization of the sample at H = 0. Further decreases of H leads to the coercive field
(H = Hc), defined as the auxiliary field at which the magnetization returns zero. As
H continues to decrease, the sample goes into negative saturation −Ms. The area of CHAPTER 2. THEORY AND BACKGROUND 19
magnetic Barkhausen noise Ms
Mr
initial magnetization curve
Hc Hc Magnetization, M Magnetization,
-Ms
Auxiliary Field, H
Figure 2.4: A typical magnetization hysteresis loop for a ferromagnetic sample starting with zero magnetization. M increases with H along the initial magnetization curve to saturation at Ms. Further variation of H changes sample magnetization as shown around the loop. The inset shows magnetic Barkausen noise, which is discussed further in section 2.4.1. a B-H hysteresis loop corresponds to the energy lost to irreversible processes within the sample [33].
2.3.1 Magnetic Domain Theory
Since the focus of the thesis is ferromagnetic materials (specifically steel), additional discussion of their behavior is warranted, specifically with respect to their domain
configuration and behavior under magnetization. As mentioned earlier, magnetic domains are groups of aligned magnetic moments found in ferromagnetic and ferri- magnetic materials. Within each domain the material is magnetized to the saturation
magnetization Ms, because dipoles within each domain are aligned. Even though do- mains are magnetically saturated, a bulk sample is generally composed of domains CHAPTER 2. THEORY AND BACKGROUND 20
[100]
(a) [010]
90o wall
(b) 180o wall
Figure 2.5: A schematic of four magnetic domains aligned along the [100] and [010] directions of Fe. (a) Each domain is made up of many aligned magnetic moments, but the four domains together produce no net magnetization. (b) Domain walls act as transition regions between domains of different orientation. Two types of domain wall are shown: 90◦ and 180◦. with randomly oriented magnetization vectors, producing no net sample magnetiza- tion. An example of this is illustrated in figure 2.5(a). Figure 2.5(b) shows that domains are separated by domain walls; these are transition regions in which mag- netic moments gradually rotate between different orientations such that they align with domains on either side of the wall. Domain wall thickness is a function of ma- terial properties. In Fe, domain walls span approximately 120 atoms [7]. Domain walls between domains with opposite magnetization vectors are termed ‘180◦ walls.’ Adjacent domains with perpendicular magnetizations are separated by boundaries termed ‘90◦ walls.’ CHAPTER 2. THEORY AND BACKGROUND 21
The domains shown in figure 2.5 are in the [100] and [010] directions; two of the ‘easy’ crystallographic magnetization directions of the h100i set.7 Magnetic saturation of iron in this ‘easy’ direction is achieved at a lower field density than the h110i and h111i directions, because domains with body centered cubic structures naturally align to h100i. The perpendicular arrangement of the h100i set results in strong 90◦ and
180◦ domain formation; however, the domain structure can become more complex near surfaces and inclusions.
The magnetic domain structure of ferromagnetic materials results from the mini- mization of the sum of six energy terms: the exchange energy (εex), the magnetocrys- talline anisotropy energy (εmca) the magnetostatic energy (εms), the magnetoelastic energy (ελ), the domain wall energy (εwall), and the Zeeman energy (εp). Thus, the total energy (εtotal) for a single iron crystal is
εtotal = εex + εmca + εms + ελ + εwall + εp. (2.15)
Minimizing εtotal results in the domain structure of ferromagnetic material. Each energy contribution is explained below.
Exchange Energy
8 The exchange energy (εex) is due to the quantum mechanical exchange interaction between adjacent atoms first described by Heisenberg in 1926 [14] and applied to
7The this document follows standard crystallographic notation. The normal of a specific plane is indicated by (100), while the set of equivalent planes is denoted by {100}. Directions are indicated by square brackets as [100]; the complete set of equivalent directions is given by angular brackets as h100i. 8When two atoms are adjacent, there is a finite probability their electrons will exchange places, thus the term exchange energy. Consider electron A moving about proton A and electron B moving about proton B. As electrons are indistinguishable, there is a possibility that the electrons exchange places such that electron B moves about proton A, and electron A moves about proton B. This consideration introduces an additional exchange energy term into the expression for the total energy of the two atoms. CHAPTER 2. THEORY AND BACKGROUND 22
ferromagnetism in 1928 [15]. For a set of atoms located throughout a lattice at ~ri,
each with spin S~(~ri), the exchange energy can be written as the sum over each atom pair [10]:
εex = − J (|~ri − ~rj|) S~(~ri) · S~(~rj), (2.16) Xjk where J (r) is the exchange integral, which occurs in the calculation of the exchange
effect. The magnitude of J (r) drops off rapidly for large r, meaning only the nearest
neighbor spins contribute significantly to equation 2.16. If J (r) is positive, εex is a minimum when the spins are parallel and maximum when they are anti-parallel. If
J (r) < 0, the lowest energy state results from anti-parallel spins. The alignment of neighboring spins observed in ferromagnetism results from a positive exchange integral.
It should be noted that the minimization of εex specifies only the orientation of magnetic moments relative to each other, it does not specify the orientation of the moments relative to crystallographic axes.
Magnetocrystalline Anisotropy Energy
The magnetocrystalline anisotropy energy (εmca) is the energy stored in domains aligned to the non-easy directions of a crystal. Applied fields must do work to rotate the magnetization direction M~ s of a domain away from an easy direction, therefore energy must be stored in domains aligned to non-easy directions. In 1929, Akulov
[3] showed that εmca can be expressed in terms of a series expansion of the direction CHAPTER 2. THEORY AND BACKGROUND 23
9 cosines (αi, i = 1, 2, 3) of M~ s relative to the crystal axes:
ε 2 2 2 2 2 2 2 2 2 mca = VD K0 + K1 α1α2 + α2α3 + α3α1 + K2 α1α2α3 + ... , (2.17) where VD is domain volume, and K0, K1, K2 are anisotropy constants specific to
3 the material (in units of J/m ). It is typical to neglect K0 in equation 2.17 because it is independent of angle and only consider the K1 and K2 terms when evaluating the series [6]. In Fe, εmca tends to align magnetic moments to the h100i directions, making them directions of easy magnetization.
Magnetostatic Energy
The magnetostatic energy (εms) is the energy stored in a magnet’s demagnetizing field, given by [6]: 1 ε = µ H 2 d3r, (2.18) ms 2 0 d Z∞ where H~d is the demagnetizing field and the integral is evaluated over all space. In Fe, minimization of only the exchange and magnetocrystalline energies would lead to a single magnetic domain parallel to h100i; however, this configuration would produce a significant demagnetizing field, such as that shown shown in figure 2.6(a).
The creation of an opposing domain decreases H~d (figure 2.6(b)), while a set of four domains separated by 90◦ and 180◦ walls (figure 2.6(c)) further decreases H~d. Thus, minimizing εms results in the formation of 90◦ and 180◦ domain walls.
9 Consider a domain in a cubic crystal: let M~ s make angles a1, a2, a3 with the crystal axes, then α1, α2, α3 are the cosines of those angles. CHAPTER 2. THEORY AND BACKGROUND 24
(a) (b) (c)
Figure 2.6: Demagnetizing field lines for: a) a single domain, b) two opposing domains separated by a 180◦ wall, and c) four domains separated by 90◦ and 180◦ walls.
Domain Wall Energy
Domain wall energy (εwall) is the energy associated with the formation of a single domain wall. As shown in figure 2.5(b), a domain wall consists of a region in which magnetic moments in adjacent atoms gradually change direction. Both εmca and
εex increase due to this gradual rotation of magnetic moments, and these increases give εwall. The energy associated with the formation of a new wall requires that the decrease associated with εms be greater than the corresponding increase in εwall.
Zeeman Energy
The Zeeman energy (εp) is the energy of the interaction between H~ and M~ [17], given by
3 εp = −µ0 M~ · H~ d r. (2.19) Z∞ H~ is generated with free currents or permanent magnets. εp varies with H~ , leading to changes in the magnetic energy and domain reorganization. εp is minimized when M~ and H~ are aligned. CHAPTER 2. THEORY AND BACKGROUND 25
demagnetized state
Δ d0 d
magnetic saturation
H
Figure 2.7: Magnetostriction of a material with positive λs.
Magnetoelastic Energy
The magnetization of a ferromagnetic material is accompanied by a change in dimen- sion, a phenomenon termed ‘magnetostriction’ by Joule [18]. Conversely, external stresses applied to a ferromagnetic material result in a change in magnetic properties, a response termed the Villari effect [38]. Together, these effects are referred to as magnetoelasticity. Magnetostrictive strain (λ) is the strain tensor generated by magnetostriction.
The strain at magnetic saturation parallel to the direction of magnetization is termed the saturation magnetostriction λs, shown in figure 2.7. Measurement of magne- tostriction takes the same form as equation 2.2, giving λs = ∆d/d0. Typical λs values
5 are small, on the order of 10− and can be greater (positive magnetostriction) or less (negative magnetostriction) than zero. Magnetostriction is anisotropic, thus different crystalline axes have different saturation magnetostrictions, indicated by λ hkl . In h i 5 5 iron, λ 100 = 2.1 × 10− , while λ 111 = −2.1 × 10− . h i h i
Because of magnetostrictive anisotropy, magnetoelastic energy (ελ) is written in terms of the saturation magnetization along specific crystalline axes; for example in CHAPTER 2. THEORY AND BACKGROUND 26
(a) magnetostriction H H
(b) Villari E"ect
σ0 σ0
domain uniaxial auxiliary magnetization stress eld
Figure 2.8: The two types of magnetoelasticity: magnetostriction and the Villari effect for a material with positive λs. (a) A change in domain structure caused by H~ produces magnetostrictive strains and elongation parallel to the auxiliary field. (b) Uniaxial strain results in elongation and an increased number of 180◦ domains.
Fe, the h100i set is used as the reference direction, giving
3 2 2 3 ελ = − λ 100 σ0 cos γ − ν sin γ d r, (2.20) 2 h i Z where σ0 is a uniaxial stress, γ is the angle between the domain magnetization and
applied stress in the sample volume, and ν is Poisson’s ratio [17]. In Fe, ελ < εmca, meaning magnetoelastic considerations alone are insufficient to rotate the domain
orientation away from the h100i axes; however, external stress may cause preferential alignment to a particular h100i direction.
Figure 2.8 shows the difference between magnetostriction and the Villari effect. Increases in H~ cause expansion of domains parallel to the auxiliary field, leading to
increased sample magnetization and eventual saturation. The sample elongates as domains grow. Conversely, the Villari effect is an increase in the number of domains
(assuming positive λs) parallel to an applied stress σ0. CHAPTER 2. THEORY AND BACKGROUND 27
Ms
H aligned to MCA direction H misaligned with MCA directions Magnetization, M Magnetization,
Auxiliary Field Magnitude, H
H aligned to MCA direction
H
H misaligned with MCA directions
reversible irreversible domain and irreversible wall motion rotation wall motion and annihilation and annihilation
Figure 2.9: The magnetization processes for samples with aligned and misaligned auxiliary fields and preferred crystalline axes. H~ is taken from left to right. Domain configuration and corresponding H and M values are shown for demagnetized samples brought to saturation along their initial magnetization curves. Recall that MCA is magnetocrystalline anisotropy, and εmca causes magnetic moments to align to certain crystallographic directions.
2.3.2 Magnetization Processes
The domain configuration of a ferromagnet changes in response to shifts in the Zeeman
energy (εp ) produced by varying H~ . Increasing εp causes domains to reconfigure to minimize the total magnetic energy of the system by increasing the average alignment between H~ and M~ . There are three process by which domains can reconfigure: domain wall motion, domain creation and annihilation, and domain rotation. Each of these processes is shown in figure 2.9 and discussed further in this section. CHAPTER 2. THEORY AND BACKGROUND 28
Domain wall motion occurs in domains that are partially aligned to the auxiliary field (M~ ·H~ > 0). As shown in figure 2.9, these domains increase in volume via domain wall motion at the expense of misaligned domains. Low auxiliary fields (H~ ) produce elastic (reversible) domain wall motion. Domain wall motion becomes irreversible at high fields.
Misaligned domains become unfavorably small when εwall > εms. These domains are annihilated and their moments merge with existing domains. Domain creation and annihilation are irreversible processes. If H~ is along an axis favored by εmca, magnetic saturation (a single domain state) will be achieved with only domain wall motion and annihilation.
When H~ is not aligned to a favored crystalline axis, competition between εp and
εmca results in rotation of the remaining domains toward H~ , until the remaining domains align leaving a single domain. This is shown at the bottom right of figure 2.9 where rotation results in the final saturated state.
2.3.3 Bulk Magnetic Anisotropy
Figure 2.9 shows the domain reconfiguration processes in the order (from left to right) of the energy required to produce them. When H~ is aligned with a crystalline axis favored by εms, domain rotation - the most energy intensive reconfiguration process - is not required to achieve magnetic saturation; hence a single domain state can be achieve at the lowest εp. These directions are referred to as magnetic ‘easy’ directions, or easy axis. Bulk magnetic anisotropy occurs when an entire polycrystalline sample displays an easy direction resulting from crystallographic texture (εmca) or strain (ελ). Crystallographic texture (or simply ‘texture’) refers to a preferred distribution of CHAPTER 2. THEORY AND BACKGROUND 29
crystallographic orientations in a polycrystalline sample. A random distribution of grain orientations has no texture: no orientations are represented more than others. In the absence of any stress influences, such a sample would be magnetically isotropic. If a particular grain orientation is favored over others, the sample is said to have texture in the favored orientation. Textured ferromagnetic samples tend to exhibit bulk magnetic anisotropy, that is, they may have bulk magnetic properties that vary with orientation. For example, the easy directions in Fe are h100i, and an Fe sample with h100i texture will have a bulk easy axis in the texture direction. Strain can align domains to a crystallographic orientation through minimization of ελ. Consider a tensile stress producing a tensile strain along [100] in a single Fe crystal. ελ is minimized by increasing the population of domains aligned to [100] and [100],¯ forming a magnetic easy direction along [100]. In order to account for tensile strain effects in a polycrystalline sample, a magnetic easy direction forms along the h100i directions most closely parallel to the strain. Compressive strain in Fe generates unfavorable domain orientations, decreasing the domain population parallel to the applied strain. Thus, compression along [100] decreases the number of [100] and [100]¯ domains, but increases the quantity of [010], [010],¯ [001], and [001]¯ domains.
2.4 Magnetic Methods of Stress Measurement
There are a number different methods of magnetic non-destructive evaluation (NDE), all of which relate changes in a material’s magnetic properties to structural anomalies, such as cracks, dents and pits, and localized stresses. This section reviews the theory and use of three magnetic NDE concepts: magnetic flux leakage, magnetic Barkhausen CHAPTER 2. THEORY AND BACKGROUND 30
noise, and stress-induced magnetic anisotropy. Magnetic flux leakage and stress- induced magnetic anisotropy were used as the basis for sensors developed for this thesis. Magnetic Barhkausen noise measurements were used by White for his Ph.D. thesis, a parallel project to this thesis. The basics of magnetic Barkhausen noise NDE are presented to enable an appreciation for the work in this thesis when compared to
White’s results.
2.4.1 Magnetic Barkhausen Noise (MBN)
Domain wall motion is not a continuous process, but rather motion that occurs in discrete steps, as shown earlier in figure 2.4 (inset). These discontinuities are called Barkhausen events after the physicist who discovered the effect in 1919 [4]. They occur at frequencies up to several hundred kiloHertz, and as such can generate voltage pulses (called Barkhausen noise) in a search coil placed nearby. The nature of Barkhausen emissions is closely tied to the microstructure of the magnetic material and can give insight into microscopic characteristics and stress state.
A symplified Barkhausen noise apparatus is shown in figure 2.10. An excitation coil is driven by an AC voltage source, typically at frequencies below 1 kHz so that the excitation field can be distinguished from the Barkhausen signal (> 100 kHz)
through bandpass or highpass filtering. Barkhausen noise signals from the sample are detected using a pickup coil10 mounted with its axis parallel to the sample surface
normal, and can be analyzed in terms of frequency content, pulse hight distribution, Barkhausen power density, and Barkhausen energy.
Because of the relationship between domain wall distribution and stress state,
10Also referred to as a search coil, pickup coil, or signal coil. CHAPTER 2. THEORY AND BACKGROUND 31
excitation coil
core
pickup coil sample V
Figure 2.10: A simplified Barkhausen noise apparatus. the Barkhausen spectrum can be used to evaluate stress in ferromagnetic materials. Studies within the Applied Magnetics Group of Queen’s University frequently examine a parameter termed ‘Barkhausen noise Energy,’ defined as τ 2 EBN = VBN dt, (2.21) Z0 where τ is the period of the excitation signal, and VBN is the voltage of the Barkhausen noise pulses. Figure 2.11 shows a bandpass filtered Barkhausen noise spectrum for a sinusoidal excitation field. Barkhausen noise decreases as the sample moves toward saturation, with peak noise occurring in the vicinity of the coercive point. Barkhausen noise-based stress measurement methods rely on the magnetic anisotropy introduced by stress. Barkhausen spectra such as that shown in figure 2.11 are col- lected at regular angular intervals (typically between 5◦ and 15◦ ) about a point on the sample, and EBN is evalutated for each spectrum. Plots of EBN as a function of the angle of the excitation field relative to a reference direction, shown in figure 2.12, give insight into the magnetic easy direction and thus the surface stresses in the sample.
Peak Barkhausen energy occurs along the easy direction and with proper calibration
EBN can be related to stress. Depth sensitivity is limited for Barkhausen signals due to their high frequency. CHAPTER 2. THEORY AND BACKGROUND 32
400 300 Magnetic Flux Density, B (mT) 200 150
0 0
Pickup Coil Voltage (mV) -200 -150 B Field Barkhausen noise -400 -300 0 7.75 15.5 23.25 31 Time (ms)
Figure 2.11: A bandpass filtered Barkhausen noise spectrum taken from 3 kHz to 600 kHz. The excitation field amplitude is 250 mT at a frequency of 31 Hz. Taken from [39].
2 EBN (mV s) rolling direction
mV2s
Figure 2.12: A polar plot of angular MBN energy measurements. Peak EBN values along the 0◦ -180◦ axis indicate the easy axis, which is in the rolling direction. Minimum EBN values give the hard axis along 90◦ -270◦ . Taken from [25]. CHAPTER 2. THEORY AND BACKGROUND 33
Signal attenuation within the sample caused by eddy currents limits the maximum depth from which Barkhausen signals can be detected to between 0.01-1.5 mm [39]
(this attenuation is discussed further in appendix B).
2.4.2 Magnetic Flux Leakage (MFL)
The magnetic flux leakage inspection method relies on the perturbation of magnetic
flux caused by defects in the sample. Localized stress may also result in MFL signals. When examining cracks and defects, the sample is magnetized to saturation using a strong DC field typically generated by a permanent magnet, shown in figure 2.13. Any shifts in cross-sectional area cause magnetic flux to ‘leak’ into the surrounding region. This ‘leakage’ flux can then be measured with an appropriate transducer, typically a Hall probe or giant magnetoresistance sensor. Although the technique is relatively simple in application, signal analysis is problematic, and numerous studies within the Queen’s Applied Magnetics Group have focused on signal interpretation for defects such as corrosion pits and generalized corrosion, dents and gouges. MFL corrosion detection systems are widely used because of their ability to characterize the size and depth of a flaw, and a matrix of scanners can be used to scan the complete surface of a specimen in one pass [26].
In addition to detecting defects, the MFL technique can be utilized to probe for regions of anomalous stress or microstructure. These regions represent localized variations in permeability. In general these regions of permeability variation will produce MFL signals of smaller magnitude than defect signals. Figure 2.14 shows the
MFL signal recorded by a Hall sensor scanned over the surface of SA106-B schedule 80 pipe before and after the introduction of a region of locally high stress. CHAPTER 2. THEORY AND BACKGROUND 34
N S Magnet
Flux lines
Sample
Figure 2.13: The application of magnetic flux leakage inspection in crack and corrosion detection.
(a) (b) 7.5 7.5 0o 0o
5 5 (cm) (cm) 2.5 2.5
0 2.5 5 7.5 10 0 2.5 5 7.5 10 (cm) (cm)
Figure 2.14: The MFL signal from a segment of SA106-B schedule 80 pipe (a) reference measurement and (b) after the introduction of residual stresses through a localized impact. Maxima correspond to red and minima correspond to blue, but no further colour scale information is available. CHAPTER 2. THEORY AND BACKGROUND 35
2.4.3 Stress-Induced Magnetic Anisotropy (SMA)
In the absence of stress and texture, a polycrystalline ferromagnetic material will have isotropic magnetic properties. The presence of stress introduces magnetic anisotropy through minimization of ελ, an effect known as stress-induced magnetic anisotropy (SMA). SMA measurements were pioneered by Langman in 1981 ([21], [20], [23], [22]) in a series of experiments on mild steel samples. Langman examined the relationship between the stress state of a sample and the angle (δ) between the magnetic field within the sample (B~ in) and the field just
outside the sample’s surface (B~ out). B~ in was determined using two perpendicular
sensing coils wound through holes drilled in the sample. B~ out was measured by a Hall sensor positioned directly above the sensing coils. The Hall sensor was rotated
to determine the direction of B~ out, while the vector sum of the sensing coil signals
provided the orientation of B~ in. Magnetic fields were generated by an excitation
core which was rotated to provide different orientation of B~ out and B~ in. This section follows the derivation of an expression for δ presented in reference [21] that will be required for SMA signal analysis in chapter 4. Within a uniaxially stressed sample there are typically two perpendicular principal
magnetic directions (1 and 2) of permeability µ1 and µ2, and relative permeability µr1
and µr2. In materials with positive magnetostriction (λs > 0), such as Fe, the greater of the two permeabilities is parallel to tensile stress, while the smaller permeability is
perpendicular to it. Supposing that µ2 > µ1, then the magnetic field B~ in within the
sample will be enhanced in the µ2 direction relative to µ1, as shown in figure 2.15.
When B~ in is applied at an angle θ relative to µ2, the magnetic field B~ out just outside
the sample will be rotated away from B~ in by an angle δ. CHAPTER 2. THEORY AND BACKGROUND 36
μ1
Bin1
Bout δ Bin
θ
Bin2 μ2
Figure 2.15: The rotation of the magnetic field just outside the sample (B~ out) relative to the magnetic field within the sample (B~ in) when µ2 > µ1.
δ can be determined from trigonometry using the ratio of relative permeabilities and angle θ. Figure 2.15 shows how B~ in can be resolved into the principle directions as
Bin1 = B sin θ (2.22)
and Bin2 = B cos θ. (2.23)
Using B~ = µoµrH~ and assuming the sample is surrounded by air, the components of
B~ out can be resolved into the principle directions as:
Bin Bout1 = sin θ (2.24) µr1 Bin and Bout2 = cos θ. (2.25) µr2 Dividing equation 2.24 by equation 2.25 gives the ratio of external magnetic field components as B µ out1 = r2 tan θ = tan(δ + θ); (2.26) Bout2 µr1 which can be rearranged to ( µr2 − 1) tan θ δ = arctan µr1 . (2.27) 1 + µr2 tan2 θ µr1 ! Langman found that equation 2.27 was a reasonable prediction of the behavior of CHAPTER 2. THEORY AND BACKGROUND 37
40
30 Direction of Bout relative to φ
20
10
0 10 20 30 40 50 60 70 80 Degrees Probe angle, φ (degrees) -10
-20
Direction of Bin -30 relative to φ
-40 Bout φ B in Tension
μ2
Figure 2.16: The orientation of B~ in and B~ out relative to the excitation core. The excitation core footprint is shown by dotted lines in the inset diagram. Tensile stress was used to produce µ2 > µ1. Taken from [21]. magnetic fields; however, it does not describe the orientation of the excitation core relative to δ and θ. The angle between the excitation core poles and µ2, taken as φ, is not θ or δ, but between the two. This relationship is shown in figure 2.16, which
shows that θ and δ deviate about from the probe angle (φ) by as much as 30◦. Langman’s original SMA experiments were suitable for specially prepared samples that could have perpendicular sensing coils wound through them. Later SMA mea-
surement techniques developed different sensor configurations for use on unprepared samples, such as Kishimoto’s magnetic anisotropy sensor [34], which employs a sens-
ing coil wound around a detecting core mounted perpendicular to the excitation core CHAPTER 2. THEORY AND BACKGROUND 38
and the sample’s surface. Modern SMA apparatus use a magnetic transducer, typi- cally a sensing coil, oriented to measure the magnetic field perpendicular to both the excitation field and sample surface. These coils produce no signal in isotropic sam- ples, but SMA causes shifts B~ out away from the excitation core so that it is detected by the coil. Chapter 3
Flux Control Systems
A dominant problem in magnetic NDE is ensuring that a consistent and repeatable magnetic flux is coupled into the sample. This is a problem for all sample geometries, including flat plates, where flux can be affected by surface preparation and varying sample permeability. Studies on flat plates can address the issue by inserting lift-off spacers between the magnetic field source and sample, ensuring a relatively consistent air gap: however, the curved surfaces of pipes present a more challenging geometry. Magnetic stress evaluation methods developed within the Queen’s Applied Mag- netics Group rely on measuring the magnetic anisotropy in the sample [19], [37], [5]. This normally implies that sensors must be physically rotated about a location to perform a measurement. The curvature of a pipe wall does not lend itself to sensor rotation: air gaps change with probe orientation, thereby altering the reluctance of the magnetic circuit for each angular measurement.
For this thesis, a new magnetic flux control system was developed to compensate for the difficulties of magnetic flux leakage-based stress measurements on pipe ge- ometries. This flux control system was developed in two stages: first using only Hall
39 CHAPTER 3. FLUX CONTROL SYSTEMS 40
sensor feedback (called flux control version 1 or FCV1), then expanded to both Hall sensor and coil feedback (called flux control version 2 or FCV2).
In the following chapter, the basic principles of feedback control are presented in section 3.1. Section 3.2 describes the magnetic transducers used for feedback control (Hall sensors and wire coils). The components used in FCV1 and FCV2 are discussed in section 3.3. The design, performance, and shortcomings of FCV1 are presented in section 3.5. Section 3.6 discussed the design of FCV2 and presents a brief analysis of its performance.
3.1 Negative Feedback Control and Operational
Amplifiers
Control systems can be separated into two groups: those without feedback (termed open-loop), and those with feedback (termed closed-loop). Open-loop systems do not adjust their output to changing conditions. Applied to a magnetic circuit, any distur- bance, such as changing temperature or variable magnet liftoff, causes the output to drift from the desired value. In a closed-loop system, shown in figure 3.1, the output is ‘fed back’ and compared with a reference input value. The difference between the two (called an error signal) is amplified by the forward path gain (a) to minimize deviation between reference and output values. This type of system is said to have negative feedback.1 There are three primary properties of negative feedback systems [35]:
1. “They tend to maintain their output despite variations in the forward path or 1There are also positive feedback systems, which sum the output and reference, but they will not be discussed in this thesis since they were not used. CHAPTER 3. FLUX CONTROL SYSTEMS 41
adder error signal input or + forward path output reference gain a -
feedback path
Figure 3.1: The components of a closed-loop control system shown in a block diagram. The reference value is compared with the output, generating an error signal used to adjust the output. The forward path converts inputs to outputs with the forward path gain a. The feedback path is the mechanism through which the output is fed back for comparison with the reference. The error signal is the difference between the reference and output values.
in the environment.” When negative feedback is properly applied and operat-
ing stably, the output remains constant if the system is given enough time to compensate for any changes that occur.
2. “They require a forward path gain which is greater than that which would be necessary to achieve the required output in the absence of feedback.” Feedback decreases overall system gain, defined as the ratio of output to input. Consider
two systems with the same forward path gain (a), one with feedback and the other without. The system without feedback can achieve a greater overall gain
than a system with feedback.
3. “The overall behavior of the system is determined by the nature of the feedback
path.” Since feedback systems compensate for variations in the forward path, the overall behavior of the system is determined by the feedback path.
Both FCV1 and FCV2 use operation amplifiers (op-amps), shown in figure 3.2, as the adder and forward path mechanism, with some type of external negative feedback mechanism to provide flux control. The feedback mechanism, which is not shown in CHAPTER 3. FLUX CONTROL SYSTEMS 42
figure 3.2, connects from the output terminal of the op-amp to the inverting input terminal. Op-amps with negative external feedback follow two ‘Golden Rules’ [32]:
1. “The output attempts to do whatever is necessary to make the voltage difference between the inputs zero.” This rule results from the incredibly high forward
path gain (a) of op-amps, typically greater than 10 000. A minute voltage dif- ference between the inverting and non-inverting terminals causes the output to
saturate. The op-amp adjusts the output voltage such that the external feed- back network brings the voltage difference between the two input terminals to
zero. This statement is equivalent to “Negative feedback is functioning properly and the output is set to its desired value.”
2. “The inputs draw no current.” This rule results from the very high input impedance of op-amps. Typical input currents are in the sub microamp range, and this provides a convenient simplification.
3.2 Magnetic Flux Transducers
Two types of magnetic flux transducers were used in this project: wire coils and Hall sensors. Both of these devices are common and well understood, and each has their own advantages. This section provides a brief overview of the function of each device, following derivations in [39] and [8].
3.2.1 Wire Coils
The force acting on a charged particle is given by equation 2.8 in chapter 2. For most substances, the free current density J~f is proportional to the force per unit charge CHAPTER 3. FLUX CONTROL SYSTEMS 43
non-inverting input (+) V+
adder + output forward path gain a Vo error - signal
inverting input (-)
V-
Figure 3.2: The feedback system components contained within an op-amp. The op-amp is represented by a triangle with three terminals: the non-inverting input at voltage V+, the inverting input at voltage V , and the output termnial at voltage Vo. The output voltage − is given by the forward path gain a multiplied by the difference between the inverting and non-inverting terminals, such that Vo = a (V+ − V ). − through conductivity σe, such that
J~f = σe E~ + ~vd × B~ , (3.1) where ~vd is the the average velocity of particles within the material (called the drift velocity, because it is typically very small). Equation 3.1 is called Ohm’s law. It is common for ~vd × B~ << E~ , thus Ohm’s law can be approximated as
J~f = σeE.~ (3.2)
Equation 3.2 is equivalent to the standard equation for resistance R in direct current (DC) circuits: V R = , (3.3) I where V is the voltage across the device, and I is the current passing through it. The resistance is a function of conductor geometry and conductivity σe. CHAPTER 3. FLUX CONTROL SYSTEMS 44
The electromotive force (EMF) around a closed path ∂S (E∂S)is defined as
E∂S = E~ · d~l, (3.4) I∂S and the magnetic flux through the surface S (ΦS) is defined as
ΦS = B~ · dA.~ (3.5) ZS Taking ∂S to be the closed path that bounds the surface S, equation 2.5 can be converted to integral form using Stokes’ theorem, giving ∂B~ E~ · d~l = − · dA.~ (3.6) ∂t I∂S ZS Equations 3.4 and 3.5 can be applied to equation 3.6 to give dΦ E = − S , (3.7) ∂S dt
where E∂S is more commonly known as the ‘back EMF.’ In the presence of a time- varying magnetic field, electrons in a conductive material will form free currents that oppose the existing field. These currents are generated by E∂S and are called ‘eddy currents.’ Consider a coiled wire of resistance R carrying current I. If the coil contains N turns of area S and is subject to a time-varying magnetic flux, the voltage across the
coil (Vcoil) is given by dΦ dB V = RI + N S = RI + NS S , (3.8) coil dt dt
where BS is the average magnetic flux density through area S. When considering sensing coils, the RI term in equation 3.8 is neglected, leaving only the magnetic field
term. Equation 3.8 indicates that a voltage will be induced in a coil of wire if that coil
surrounds a region where the magnetic flux is changing. Coil wires can be used as CHAPTER 3. FLUX CONTROL SYSTEMS 45
z y B
x
Ex Jf side view VH
y
x B z + + + + + + + + + + + + + + + +
E E J x y f VH top view
------
Figure 3.3: The Hall effect for a Cartesian coordinate system. B~ is inz ˆ. Electric current density J~f is inx ˆ, caused by thex ˆ component of E~ , Ex. Build up of electrons along the −yˆ facing wall produces an electric field component in the y direction, Ey. The Hall voltage (VH ) is measured across the two sides facing ±yˆ. magnetic field sensors in air, however in many applications coils are wound around specific components to measure the overall flux through the component. Sensing coils are cheap and easy to manufacture. The main drawback to sensing coils is their time dependence requirement: coils are only capable of measuring time-varying magnetic
fields. Thus they are appropriate for time-varying (AC) magnetic fields, however coils cannot be used to measure flux in a permanent (DC) magnetic circuit. Hall sensors, discusses in the following section, do not suffer from this limitation.
3.2.2 Hall Sensors
The Hall effect was discovered in 1879 by Edwin Hall when he attempted to determine if the force exerted on a current carrier in a magnetic field was experienced by the bulk of the material or only by the charge carriers (electrons) [13]. Hall discovered a transverse voltage across the bulk of a silver test sample, perpendicular to current
flow and the magnetic field, as shown in figure 3.3. This voltage is called the Hall voltage (VH ). CHAPTER 3. FLUX CONTROL SYSTEMS 46
Consider figure 3.3 in the absence of B~ for a metal sample: electrons flow from
right to left at drift velocity vd, generating current density Jf . With the introduction of B~ = Bzˆ, moving electrons are deflected in the −yˆ direction and accumulate on that side of the sample. Electrons continue to accumulate, increasing Ey until
Ey = vdB. (3.9)
Unfortunately, equation 3.9 is not particularly useful in this form. Drift velocities are rarely known and it is more convenient to measure a voltage than Ey. Thus a Hall coefficient H is used to convert equation 3.9 to
VH = HB, (3.10) where H is a function of the probe’s charge carrier concentration, dimension, and source current.
Sensors based on the Hall effect require a supply current. Thus Hall sensors typi- cally have four terminals: two supply current (Ic) terminals for incoming and outgoing supply current, and two Hall voltage terminals for the positive (VH+) and negative
(VH ) voltage values. The Hall voltage that appears in equation 3.10 measured across − the positive and negative voltage terminals as
VH = VH+ − VH . (3.11) − Modern Hall effect sensors are semi-conducting devices that vary in cost from a few dollars up to several hundred dollars depending on calibration qualities, response linearity and several other parameters.
Hall sensors and wire coils measure magnetic fields by exploiting different elec- tromagnetic effects, which lead to slightly different applications for the two sensors.
Hall sensors measure AC and DC magnetic fields, whereas coils are insensitive to CHAPTER 3. FLUX CONTROL SYSTEMS 47
DC fields, but can be used to measure flux through specific components by winding sensing coils around the region of interest. Hall sensors are enclosed devices and must be placed external to any components of interest.2 The Hall voltage signal is there- fore only proportional to the flux passing through the sensors itself. Because of this shortcoming, the placement of Hall sensors within magnetic circuits must be made carefully, in order that the Hall voltage signal accurately reflects the flux through the circuit.
3.3 Component Selection
Both FCV1 and FCV2 contained similar components. The primary difference between the systems was the feedback signal. This section outlines components common to both FCV1 and FCV2.
3.3.1 Data Acquisition
R A National Instruments PCI-6229 Multifunction DAQ (PCI-6229) was used to gen- erate reference voltage signals (Vref ) and record all of the feedback system’s output signals. This DAQ featured 4 analog output channels (AO(0...3)) with a ±10V range about ground and 16 bit resolution. 32 single-ended multiplexed analog input chan- nels (AI(0...31)) with a maximum sampling rate of 250 kHz aggregate over all channels can be used for data acquisition in the PCI-6229s. Analog inputs have 16 bit resolu- tion over each voltage range (±10V, ±5V, ±1V, ±0.2V)[28]. PCI-6229 DAQs were not purchased specifically for this project, but were used because they were available and their specifications were adequate for both FCV1
2They cannot be placed inside a sample, and therefore cannot measure the flux inside a sample. CHAPTER 3. FLUX CONTROL SYSTEMS 48
and FCV2.
3.3.2 Amplifier
Due to the abundance of speakers found in consumer goods, there is a large selection of low-cost solid state power amplifiers. The excitation coils of a flux-controlled circuit present similar load impedances to speakers found in audio equipment [39].
R 3 The National Semiconductor LM4701 audio amplifier was selected to act as the adder/forward path in both FCV1 and FCV2 feedback systems [31]. The LM4701 is a low noise amplifier, designed to supply 30 W into 8 Ω from 20 Hz to 20 kHz with total harmonic distortion + noise of 0.08% given proper heat dissipation. Supply voltage can be up to ±32 V. Typical open-loop gain is a = 110 dB.
R TM These amplifiers feature National Semiconductor ’s SPiKe protection circuitry, which protects the op-amp from voltage, current, and thermal overload.
3.3.3 Power Supply
R A Power-One HCC24-2.4-AG regulated DC power supply with ±24 V outputs at 2.4 A was selected to provide power to amplifiers, Hall sensors, and all other compo-
nents.
3.3.4 Hall Sensors
F.W. Bell 4 BH-700 Hall effect sensors were used as magnetic flux density transducers for both FCV1 and FCV2. These sensors were used for their linear response and
3The LM4701 is now obsolete. It has been replaced by LM4765 and LM4781 multi-channel amplifiers. 4A division of Sypris Test & Measurement. CHAPTER 3. FLUX CONTROL SYSTEMS 49
small size [9]. These Hall sensors were used in two different applications. The first, described in this chapter, was as part of the flux control system, where the BH-700 was used to monitor the flux density in the magnetic excitation circuit. These Hall probes were also used as MFL stress detectors, described in chapter 4, to detect the magnetic flux signal emanating from the sample itself. Note that in the latter case the Hall probes are termed ‘detectors,’ in the former they are termed ‘sensors.’
3.4 White’s Flux Control System (FCS)
For his doctoral thesis dealing with magnetic Barkhausen noise, Steve White designed a magnetic flux control system that relied on the feedback from a coil wound near the base of an excitation core pole, termed a ‘feedback coil,’ to regulate the magnetic flux generated by an excitation coil. This feedback system was termed the ‘Flux Control System,’ or ‘FCS.’ Figure 3.4 is a simplified sketch illustrating the basic premise of this control method. Vref is an arbitrary reference voltage waveform, and Vex and VF + are voltage measurements referenced to ground. The ideal op-amp is configured as an adder such that the sum of the currents into the inverting input through resistors
Rref , RG, and RF 1 is zero V V V ref + F + + ex = 0. (3.12) Rref RF 1 RG
Resistors RF 1 and RF 2 were chosen to be much greater than the resistance of the feedback coil. The two resistors were placed across the coil to improve system
stability. As the same current flows in RF 1 and RF 2, the voltage across the feedback CHAPTER 3. FLUX CONTROL SYSTEMS 50
V ex
Vref Rref RG
RF1 V F+ RF2
Figure 3.4: A sketch of White’s FCS. The resistor RG was used to limit gain to provide a stable output. A feedback coil wound around one of the poles acted as the flux feedback transducer.
coil (VF ) is given by R V = 1 + F 2 V . (3.13) F R F + F 1 Solving equations 3.12 and 3.13 for Vref gives R R V = − ref V − ref V . (3.14) ref R + R F R ex F 1 F 2 G This system was designed to control flux independent of probe liftoff; therefore the
contribution of Vex to Vref was problematic, as Vex was unknown. Ideally, the gain-
limiting resistor RG could be removed (effectively setting RG → ∞), which would
nullify the contribution of Vex to equation 3.14. However, in this maximum-gain configuration, any offset between the amplifier terminals would be multiplied by the
full amplifier gain (a). Without any feedback to compensate for these offsets, Vex will gradually shift to the voltage supply rails. To avoid this issue, White maximized the
system’s performance by decreasing RG from ∞ until the circuit stabilized.
The reference voltage (Vref ) and the voltage across the feedback coil (VF ) differed by the Vex term as R + R V = V − F 1 F 2 . (3.15) ref F R G CHAPTER 3. FLUX CONTROL SYSTEMS 51
The error introduced by a non-infinite RG was reduced by a digital error correc- tion (DEC) algorithm implemented in the FCS software control and data acquisition
5 system. The DEC algorithm iteratively adjusted the reference voltage (Vref ) until the target feedback voltage (VF ) was achieved.
3.5 Flux Control Version 1 (FCV1): Hall Sensor
Feedback
The thesis project by White paired a flux control system (FCS) with MBN mea- surements to perform stress analysis on SA106-Grade B steel pipes. As described in the preceding section, White used feedback coils wound around the base of each of the excitation cores. In the present project, a Hall sensor was selector to act as the feedback path for the flux control system, as they are capable of recording both time-varying and constant magnetic fields, and MFL measurements frequently use permanent magnets to generate the excitation field.
3.5.1 FCV1 Hardware
The primary advantage of a Hall sensor feedback system over a coil-based system is the ability to be used with DC excitation fields. The original concept for this project
(FCV1) was to pair a Hall sensor feedback flux control system with a Hall detector for stress measurement. The control system would guarantee that a consistent flux was coupled into the sample, while the Hall detector would measure the leakage flux, which would be sensitive to variations in the stresses within the sample.
5This DEC system designed by White is only valid for periodical reference waveforms. CHAPTER 3. FLUX CONTROL SYSTEMS 52
V , I R F ex ex V s Vref + s LM4701 - GND excitation coil
monitoring coil ferrite excitation core VH-
Vmc lift-o spacer Ic
VH+ sample
Hall sensor
Figure 3.5: A simplified version of FCV1. A Hall sensor with supply current Ic is located in a plastic lift-off spacer attached to the bottom of the ferrite excitation core. This sensor measures the B component normal to the sample surface, and feeds back a Hall voltage to be compared to Vref .
FCV1 was designed as the Hall sensor feedback system, shown as a simplified sketch in figure 3.5. A detailed electrical schematic of FCV1 is included in appendix
A. Referring to figure 3.5, FCV1 was designed to control the flux entering the sample by measuring the flux density (B) with a Hall sensor located in an air gap between
the sample and excitation core (the excitation core shown in the figure is ferrite). Vref is the user-defined reference voltage corresponding to the desired B in the air gap.
Note that in figure 3.5, VH is grounded, therefore VH = VH+. The voltage Vs across − a 0.2 Ω series resistor (Rs = 0.2 Ω) was monitored to measure excitation current Iex. The output of the LM4701 was fused at 0.5 A with a slow blow fuse (F = 0.5 A) to prevent damage to the excitation coil. A monitoring coil was wound around a pole of CHAPTER 3. FLUX CONTROL SYSTEMS 53
turns 1052 excitation coil inductance 0 .26H resistance 27 Ω turns 37 monitoring coil inductance 8 .7 mH resistance 1Ω.1 ferrite excitation core pole area 264 mm2
Table 3.1: Excitation and monitor coil properties. Inductance values were recorded on- sample at 100 Hz. The monitor coil was wound around one of the core’s poles, making its area the same as the pole area.
Variable PCI-6229 Terminal Connection Configuration Vref AO0 RSE VH AI0 NRSE Vs AI1 NRSE Vmc AI2 DIFF GND AIsense
Table 3.2: PCI-6229 I/O assignment and terminal configuration for FCV1. Terminal con- figurations use the following abbreviations: referenced single-ended (RSE), non-referenced single-ended (NRSE), differential (DIFF). For additional information on terminal configu- rations see [29]. the ferrite core to monitor the FCV1 performance when operated in AC mode. The output voltage from this coil was designated Vmc. The properties of the excitation and monitoring coils are given in table 3.1. Voltage input and output (I/O) was handled through the PCI-6229 board. I/O connections and terminal configurations are given in table 3.2. CHAPTER 3. FLUX CONTROL SYSTEMS 54
3.5.2 FCV1 LabVIEW R Interface
R FCV1 was controlled through a basic LabVIEW 8.5 user interface (UI), which
was developed as part of the thesis work. Vref was controlled by an included Lab-
R VIEW waveform generator (file: ‘NI Basic Function Generator.VI’). There were four user-specified controls: signal type, amplitude, DC offset, and frequency. The
signal type selected the output waveform as either sine, triangle, sawtooth, or square. Amplitude, DC offset, and frequency are self explanatory. DC signals were generated
by setting the waveform amplitude to null and the DC offset to the desired value.
3.5.3 FCV1 Performance
The performance of FCV1 was examined by determining how effectively it was able
to produce an excitation field, and corresponding Hall voltage VH , that was equal to
the reference voltage waveform Vref . The Hall sensor and monitoring coil were used
to measure the excitation field. Figure 3.6 shows VH , Vref and Iex for a sinusoidal
reference voltage with an amplitude of 50 mV and a frequency of 10 Hz (Vref =
50mV sin(2πt10Hz)). Hall voltage (VH ) exactly matches the reference voltage (Vref ),
making the two signals difficult to distinguish in the figure. However, VH contains a
significant noise component that is not present in Vref . This noise is also apparent in
the excitation current (Iex) waveform.
The amount of noise observed in VH and Iex was unexpected, as White’s coil-based FCS system did not display this noise characteristic. It was found that the noise was
independent of the Vref waveform and would occur in both AC (figure 3.6)and DC
Vref (figure 3.7) system modes. Figure 3.7 indicates that noise noise in Iex peaks at approximately 2 mA. Since the ferrite core saturates at an excitation current of CHAPTER 3. FLUX CONTROL SYSTEMS 55
FCV1 Performance for Vref = 50 mV sin(2πt10 Hz) 0.06 0.06
Vref
VH 0.04 0.04
I ex Excitation
0.02 0.02 urn,(A) Current, (V) 0 0 I Voltage ex −0.02 −0.02
−0.04 −0.04
−0.06 −0.06 0 0.02 0.04 0.06 0.08 0.1 Time, t (s)
Figure 3.6: Hall voltage (VH ) and excitation current (Iex) for a sinusoidal reference voltage. VH lies on Vref , making the two lines indistinguishable.
95 mA (shown in figure 3.8), this 2 mA noise signal is non-trivial. In order to further investigate the noise behavior of FCV1, the 37 turn monitoring coil shown in figure 3.5 was mounted on one of the excitation core poles. The coil voltage (Vmc) was proportional to the time-derivative of B in the excitation circuit, boosting the high-frequency noise signal relative to the low frequency (sub 50 Hz) excitation field, thereby allowing a detailed analysis of the noise component.
Figure 3.8 shows Vmc, Iex and VH for each of three Vref waveforms (each plot
represents a different reference waveform). The noise component of VH and Iex is not
obvious at this scale, but is clearly visible in Vmc. A fast Fourier transform (FFT) of
R 6 Vmc performed in LabVIEW using the spectral analysis tool indicated a dominant noise frequency of 700 Hz. When the excitation core was removed from the sample, it
6The ‘Spectral Measurements’ express VI. CHAPTER 3. FLUX CONTROL SYSTEMS 56
FCV1 Performance for Vref = 0 mV 3
2
(mA) 1 ex I
0
-1 Excitation Current,
-2
-3 0 20 40 60 80 100 Time, t (ms)
Figure 3.7: FCV1 response to a DC reference voltage of Vref = 0. Only the excitation current waveform is shown. VH was omitted for clarity. CHAPTER 3. FLUX CONTROL SYSTEMS 57
was noted that the frequency and amplitude of the noise in the monitor coil decreased, suggesting that the noise was a function of excitation coil inductance.
The noise was ultimately traced to oscillations in the excitation voltage (Vex). The output from the LM4701 amplifier fluctuated between ±24 V (its voltage supply rails) at 700 Hz. The inductance of the excitation core decreased this 24 V amplitude voltage fluctuation to a 2 mA current oscillation.
3.5.4 FCV1 Shortcomings
The instability observed in FCV1 was due to the Hall sensor feedback mechanism. The explanation for this is as follows: referring back to equation 3.10, the Hall voltage
(VH ) is directly proportional to the magnetic field density (B) through the transducer.
These two values are linked by a Hall constant (H) such that VH = HB.
The magnetic field (Bex) generated by an excitation coil is proportional to the current (Iex) through the coil, giving
Bex ∝ Iex. (3.16)
Equation 3.16 can be derived from equation 2.9 (the quasi-static case of Ampere’s law) or from the Biot-Savart law. Using equations 3.10 and 3.16, we arrive at
VH ∝ Iex ∝ Bex. (3.17)
Therefore, a system using Hall voltage as the feedback mechanism must control the excitation current to reliably regulate Bex. The LM4701 is a voltage amplifier, yet in FCV1 it was configured as a current controller. FCV1 would be better served with a current amplifier in place of the LM4701: however, excitation coils are generally very inductive, therefore the time derivative of the excitation current is proportional CHAPTER 3. FLUX CONTROL SYSTEMS 58
(a) Vref = 95 mV sin(2πt10 Hz)
0.3 0.3 Excitation
V 0.2 H 0.2 I ex 0.1 (A) 0.1 Current, Vmc
0 0 Voltage (V) I ex - 0. 1 - 0.1
- 0. 2 - 0.2 0 0.02 0.04 0.06 0.08 0.1 Time, t (s)
(b) Vref = 95 mV sin(2πt20 Hz)
0.4 0.2 Excitation
0.2 0.1 urn,(A) Current,
0 0 Voltage (V) I
- 0. 2 - 0.1 ex
- 0. 4 - 0.2 0 0.02 0.04 0.06 0.08 0.1 Time, t (s)
(c) Vref = 50 mV sin(2πt30 Hz) 0.4 0.1 Excitation
0.2 0.05 urn,(A) Current, 0 0 Voltage (V)
- 0. 2 - 0.05 I ex
- 0. 4 - 0.1 0 0.02 0.04 0.06 0.08 0.1 Time, t (s)
Figure 3.8: Monitor coil voltage Vmc boosts the noise amplitude relative to the excitation field. Waveforms for three different sinusoidal reference voltages are shown: two 95 mV signals at 10 and 20 Hz (figures (a) and (b)), and a 50 mV signal at 30 Hz (figure (c)). A 95 mV reference voltage amplitude was enough to drive the ferrite core to saturation, indicated by the lumps at peak Iex values. CHAPTER 3. FLUX CONTROL SYSTEMS 59
to the excitation voltage (Vex) such that dI ex ∝ V . (3.18) dt ex Equation 3.18 indicates that to effectively control current through an excitation coil, the current amplifier requires infinite voltage rails. These systems simply do not exist.
White’s FCS system relied on LM4701 amplifiers paired with coils as the feedback
mechanism. The voltage across a feedback coil (Vfc) wound around the pole of the excitation core is then proportional to time-derivative of the flux through the core,
giving dB V ∝ ex . (3.19) fc dt The proportionality arguments of equations 3.16, 3.18 and 3.19 lead to dB V ∝ ex ∝ V . (3.20) fc dt ex
This direct proportionality between the feedback coil signal Vfc and excitation coil
voltage Vex indicates that a coil-based feedback mechanism is better suited for voltage control of a standard operational amplifier. This was the premise of the second flux control system, FCV2.
It should be noted that further investigation and analysis of the dynamic proper- ties of FCV1 may have resolved the instability observed in the system. However, due to time constraints and the fact that the FCS system functioned properly, FCV1 was abandoned in favor of a new design with coil feedback. CHAPTER 3. FLUX CONTROL SYSTEMS 60
3.6 Flux Control Version 2 (FCV2): Hall Sensor
and Coil Feedback in Combination
While Hall sensors are well suited to current controlled flux control systems systems, voltage controlled systems are best coupled with feedback coils. In Steven White’s thesis work, the flux control system used feedback coils paired with LM4701 ampli-
fiers to regulate the flux passing through samples. This is why the FCS excitation signals contained significantly less noise than those produced by the FCV1 system in the current study. However, relying on coil feedback only requires error correction software to compensate for DC offsets in the system.7 The second design employed in the current project, FCV2, was designed with both coil and Hall sensor feedback to eliminate the need for error correction software and to provide a fully hardware-based magnetic flux controller.
3.6.1 FCV2 Hardware
A new amplifier configuration was required to combine Hall sensor and feedback coil control. As with the FCV1 system, an LM4701 op-amp was used to power the FCV2 circuit, which is shown in figure 3.9. B was measured through the ferrite excitation core by integrating the monitor coil into the feedback loop, producing Vfc, and also (as with FCV1) in the air gap between the core and sample by a Hall sensor, producing
VH+ and VH . Note that both of the Hall voltage terminals were allowed to float in − FCV2.
FCV2 can be analyzed according to the Golden Rules given in section 3.1. When
7See [39] p. 73. CHAPTER 3. FLUX CONTROL SYSTEMS 61
RG Rref
Vref R H V R + F Vex, Iex s VH+ + Vs LM4701 R - fc V GND V - excitation fc coil
RH VH- ferrite RG excitation core feedback coil lift-o Vfc spacer I V c V H+ H- sample
Hall sensor
Figure 3.9: A simplified version of FCV2. There are only a few changes from figure 3.5. Vfc has been integrated into the feedback circuit, and one end of the feedback coil was grounded. Neither VH+ or VH was grounded. − CHAPTER 3. FLUX CONTROL SYSTEMS 62
the inverting (-) and non-inverting (+) terminals to draw no current, the voltages at each terminal, V and V+ respectively, are given by − RG(Vref RH + VH Rref ) V+ = − (3.21) RH RG + Rref RG + Rref RH and R (V R + V R ) V = G fc H H+ fc . (3.22) − RH RG + RfcRG + RfcRH Negative feedback was used, therefore the voltage at both input terminals must be
the same, giving
V+ = V . (3.23) −
When RG = RH = Rfc = Rref , equations 3.21, 3.22, and 3.23 can be solved for Vref to give
Vref = Vfc + VH+ − VH = Vfc + VH . (3.24) −
Equation 3.24 can be written in terms of the excitation field Bex(t), feedback coil
turns (Nfc), feedback coil area (Afc) and Hall constant H, such that dB (t) V (t) = N A ex + HB (t). (3.25) ref fc fc dt ex Figure 3.9 is a simplified version of FCV2, useful for a general discussion of the feedback system and reference voltage waveform. Figure 3.10 presents a more detailed
electrical schematic of the feedback system including the current source used for BH-
700 Hall sensors in FCV2. The Hall sensor control current (Ic) was supplied by a National Semiconductor LM337 negative voltage regulator run in current-control
mode [30]. The 0.2 and 180 Ω resistors in series with the BH-700 sensor put VH+ and
8 VH within the PCI-6229’s ±10 V input range. Resistors in the feedback system − 8 VH was always less than 1 V, but VH+ and VH− had to be within ±10 V of ground for the PCI-6229 to make the differential measurement VH = VH+ − VH−. CHAPTER 3. FLUX CONTROL SYSTEMS 63
feedback Hall sensor current supply
3 Out LM337 2 In
Adj Ic 1μF +24 V 10 Ω 1 1 V 11 ex
10 kΩ 1 kΩ 1 kΩ 1 μF
0.2 Ω 1 kΩ
Vref +Ic excitation coil 1 kΩ Red 1 VH- 8
Blue + V V F = 0.5A Rex L s H+ 2 ex BH-700 LM4701 Yellow V H- V - Black H+ 7 4 1 kΩ 3,5 0.2 Ω -Ic 1 μF Lfc
-24 V Rfc V 180 Ω fc 1 kΩ feedback coil 1 kΩ -24V
10 MΩ
Figure 3.10: An electrical schematic of FCV2 showing the feedback system and the Hall sensor current source. The LM4701 acts as an amplifier and adder for the feedback system. The Hall sensor current source is the LM337 voltage regulator, configured in current-control mode. Pin numbers are shown for the LM4701 and LM337, as well as BH-700 lead colors. White circles indicate external connections to voltage supplies (±24 V) or to the PCI-6229 DAQ (Vref , VH , VH+, Vfc, Vs, Vex). − were set to 1kΩ, while the fuse and series resistance (Rs) were unchanged from FCV1
(F = 0.5 A and Rs = 0.2 Ω). A voltage divider of 10 kΩ and 1 kΩ resistors, giving a voltage divider ratio of 1/11, was used to directly measure the excitation voltage; a parameter that had not been examined in FCV1. The divider was required to bring the maximum excitation voltage |Vex| = 24 V into the measurement range of the PCI-6229 DAQ. The PCI-6229 terminals were reconfigured to accommodate the new feedback system. I/O connections and terminals configurations for FCV2 are given in table CHAPTER 3. FLUX CONTROL SYSTEMS 64
Variable PCI-6229 Terminal Connection Configuration Vref AO0 RSE VH AI0 DIFF Vs AI1 NRSE Vfc AI2 DIFF Vex AI3 NRSE Vsig AI4 DIFF GND AIsense
Table 3.3: PCI-6229 I/O assignment and terminal configuration for FCV2.
3.3. A sensor input line that recorded the magnetic detector output signal (Vsig) was added as a differential input.
3.6.2 FCV2 Software
R The software and user interface was rebuilt for FCV2. LabVIEW Express VIs used for data acquisition and signal generation in FCV1 were replaced with purpose-built timing and triggering code. This improved synchronization between input and output channels, and improved the voltage and time resolution of the data acquisition system.
Excitation and feedback coil parameters, such as those in table 3.1, were used to calculate Vfc, VH , and subsequently Vref for a user-specified excitation magnetic field density (Bex). The transition from the user-specified reference voltage used in FCV1 to Bex for FCV2 was done to highlight the relationship between Vfc, VH , and Bex shown in equation 3.25.
Degaussing code was added so that any residual magnetization resulting from previous measurements or magnetic exposure could be removed from the sample prior to measurements. This ensured that measurements with FCV2 could be performed on demagnetized samples. This code was absent in FCV1 because the system never CHAPTER 3. FLUX CONTROL SYSTEMS 65
matured to the point of performing a measurement.
3.6.3 FCV2 Performance
The performance of FCV2 was examined using the same ferrite excitation core as
FCV1. Figure 3.11(a) shows the magnetic flux density measured by the feedback coil (Bfc) and Hall sensor (BH ), and how they compare to the reference excitation
magnetic field density (Bref ). The matching is excellent, with the slight offset between
BH and Bref due to miscalibration of the Hall constant, which was an adjustable parameter in FCV2’s software.
Offsets between Bfc, BH and Bref peak at the maximum and minimum of the reference waveform, shown in figure 3.11(b). Bfc is closely matched to Bref , with a maximum offset of |Bfc − Bref | = 0.15 mT. BH deviates further from the refer- ence field, with a peak deviation of 2.5 mT at Bref = 100 mT. Additionally there is a -0.75 mT shift in BH with respect to Bref . DC offsets of less than 1 mT and peak deviation of approximately 2% were considered acceptable errors in Hall sensor
calibration. The 700 Hz noise observed in FCV1 was eliminated in FCV2. The FCV2 system was subsequently combined with a detector system, discussed in the following chapter,
to perform several magnetic stress measurements on flat plate samples. CHAPTER 3. FLUX CONTROL SYSTEMS 66
(a) FCV2 Performance for Bref = 100 mT sin(2πt55 Hz) 100
80 Bref BH 60 Bfc 40
20
0
−20
−40
Magnetic Field Density (mT) −60
−80
−100 0 5 10 15 20 Time, t (ms)
(b) Hall Sensor and Feedback Coil Magnetic Field Offsets 1.5
1
0.5
0
-0.5
-1
-1.5 Magnetic Field Density (mT) -2 BH - Bref -2.5 Bfc - Bref
-3 0 5 10 15 20 Time, t (ms)
Figure 3.11: The magnetic fields measured by the Hall sensor and feedback coil in FCV2. (a) The reference field was 100 mT in amplitude at a frequency of 55 Hz. Bref and Bfc curves lie on top of each other, making them nearly indistinguishable. Offsets, shown in the bottom figure (b), were calculated by subtracting measured field density (Bfc, BH ) from Bref . Chapter 4
Magnetic Stress Detectors
The magnetic excitation system based on FCV2 provided an effective, consistent and repeatable method of coupling magnetic flux into samples. The next stage in the process involved adding a detector to measure the magnetic signal emanating from the sample when an excitation field was generated by FCV2. A this point it is convenient to define some important terms. The ‘detector’ refers to the magnetic flux transducer used to measure stress-induced leakage flux emanating from the sample. This detector is located between the poles of the excitation magnet and can be either a wire coil or a Hall probe. Detectors are not to be confused with feedback ‘sensors’ (referring to the feedback Hall sensor and feedback coil sensor) used in the excitation flux control system. Finally, the term ‘probe’ refers to the entire physical device, consisting of the detector, excitation coil, core, feedback Hall sensor and feedback coil.
Three detector configurations were tested with the FCV2 probe. These configu- rations are shown in figure 4.1. The first, figure 4.1 (a), was a Hall detector aligned parallel to the sample surface normal, termed the ‘DC MFL’ detector. The second,
67 CHAPTER 4. MAGNETIC STRESS DETECTORS 68
(a) (b)
(c) measured B component
wire coil
Hall detector
Figure 4.1: The three detector configurations used with the prototype excitation core. (a) DC MFL: a Hall detector oriented parallel to the surface normal. (b) AC MFL: a wire coil with its axis parallel to the surface normal. (c) SMA: a wire coil with the coil axis perpendicular to a line between the excitation core poles and the surface normal. shown in figure 4.1 (b), was a wire coil with its axis aligned to the sample surface normal, termed the ‘AC MFL’ detector. Finally, figure 4.1 (c) shows a wire coil with its axis perpendicular to both the sample surface and a line joining the poles of the excitation core. This was termed the ‘SMA’ detector and was used for stress-induced anisotropy measurements. A flat plate sample subjected to a variable uniaxial applied load was used to evalu- ate the stress sensitivity of the probe for each of the the three detector configurations. The remainder of this chapter is organized in the following sections:
• Section 4.1 provides an overview of the steel sample and the Single Axis Stress
Rig - the apparatus used to apply stress to the sample.
• Section 4.2 describes in detail the three detector configurations shown in figure 4.1, as well as the data acquisition system.
• Section 4.3 outlines the experimental procedures used to test the three detector CHAPTER 4. MAGNETIC STRESS DETECTORS 69
configurations
• Section 4.4 presents the results for each of the detector tests.
4.1 Test Sample and the Single Axis Stress Rig
(SASR)
To determine the effectiveness of different detector configurations, a flat plate sample was subjected to a uniaxial tensile stress via a single axis stress rig (SASR). Details of the test sample and SASR are described here.
4.1.1 Test Sample
Measurements were performed on a 2.8 mm thick hot-rolled mild steel plate, 500 mm long and 216 mm wide, shown in figure 4.2. Tensile strength tests on these samples indicated a yield strength of 291 MPa, a Young’s modulus of Y = 219 GPa [2], and
Poisson’s ratio to be ν = 0.278 [24]. The sample was used in previous Ph.D. thesis work by Catalin Mandache [24]. For this work, two electrochemically milled 18 mm diameter holes were located in the
R center of the plate. A total of three Vishay Measurements Group EA-06-250BF300 strain gages were mounted at different locations on the plate, as indicated in figure 4.2.
Strain gage 1 measured the strain along the length of the plate, which corresponded to the applied stress direction. Gages 2 and 3, located on the opposite side of gage
1, were used to determine the uniformity of the applied strain. Measurements using the prototype probes were performed at the location indi- cated in figure 4.2. This location was selected to avoid any stress concentrations or CHAPTER 4. MAGNETIC STRESS DETECTORS 70
500 t
measurement 94.5 = -ν σ
strain c location 125 gage 2 18 27 216 strain strain gage 1 gage 3 108 compressive stress σ stress compressive in the ‘perpendicular’ direction
applied tensile stress σt in the ‘parallel’ direction
Figure 4.2: The mild steel plate used to test different detector configurations. Strain gage locations are shown by rectangles. Gage 1, indicated by a dashed line, was located on the underside of the plate. Gages 2 and 3 were located on the upper plate surface. Two 18 mm hole defects were at the center of the plate. All dimensions are in mm. other localized stress effects resulting from the sample edges or hole defects.
4.1.2 The Single Axis Stress Rig (SASR)
The single axis stress rig (SASR) was designed and built within the Applied Magnetics Group to serve as a general purpose stressing device for the application of tensile stresses. It was configured to apply to ‘single axis’ tensile loads along the length of
flat plate samples, such as that indicated in figure 4.2. A schematic diagram of the SASR is shown in figure 4.3. Two sets of steel jaws clamp down on either end of the sample. One set of jaws is connected to a fixed bridge, while the other is connected to a gliding bridge that moves along guidance rods. Two hydraulic jacks extend when pressurized by a manual pump. Extension of the pistons within the hydraulic jacks pushes the gliding bridge along the guide rods, applying tensile stress (σt) to the sample clamped in the jaws. As a result of CHAPTER 4. MAGNETIC STRESS DETECTORS 71
sample jaws gliding bridge
sample xed bridge guidance rods
spacer cylinder
hydraulic jack
support beam
Figure 4.3: A schematic of the single axis stress rig used to introduce tensile stress in the flat plate sample.
Poisson’s ratio effects, compressive stress is also generated across the width of the sample (σc) given by
σc = −νσt. (4.1)
The pressure in hydraulic lines was monitored by an Omega Engineering Inc. PX302-10KGV pressure transducer connected to an Omega Engineering Inc. DP25-S digital meter. A more detailed description of the SASR and its operation is provided in reference [24].
4.1.3 Strain Measurement
The three EA-06-250BF300 strain gages mounted on the sample were connected to
R a Vishay Measurements Group SB-10 Balance and Switch used to calibrate the strain gages and sequentially switch between the output of each gage. The SB-10 was
R connected to a Vishay Measurements Group P3500 Strain Indicator, which provided a direct indication of the strain measured by the gages. CHAPTER 4. MAGNETIC STRESS DETECTORS 72
detector mount assembly detector mount assembly detector brace outer brace R 9.2 mm
lifto! spacer feedback Hall sensor housed within a lifto! spacer
feedback coil
connector brace 64 mm ferrite excitation core excitation coil
(a) (b)
Figure 4.4: An assembled probe showing a detector mount assembly attached to the connector brace of the excitation core. (a) Important components are indicated in the figure. The spring of the detector mount is not visible in this figure; it is hidden between the detector brace and outer brace. (b) A photo of the assembled system, built by the author.
4.2 Detectors, Data Acquisition and Data Analy-
sis
The three different detectors - DC MFL, AC MFL, and SMA - were attached to the
excitation core with a detector mount assembly, shown in figure 4.4(a). The detector mount assembly consisted of three primary parts: a detector brace that housed the
detector, a spring (not shown) to push the detector brace against the sample, and an outer brace that housed the detector and spring system and attached it to the excitation core. Each of the detectors was fixed to its own mounting assembly, which
could be quickly connected to the excitation core. The assembled core and detector system is called a probe. A photograph of the assembled probe is shown in figure
4.4(b) CHAPTER 4. MAGNETIC STRESS DETECTORS 73
Figure 4.5 shows a plan, underside view of each detector mounted to the excitation core. The details of each detector are outlined below.
DC MFL
The Hall sensor used for DC MFL measurements was a F.W. Bell BH-700 sensor; this was the same Hall sensor used in both FCV1 and FCV2 flux control systems.
1 The processed output signal from this detector was denoted VDCM .
AC MFL
An air-core 200 turn coil wound from 44 AWG wire with an average loop area of 3.1 mm2 was used for the AC MFL detector. This coil was circular with an inner
diameter of 0.98 mm and an outer diameter of 2.99 mm. The processed output voltage
of this detector was denoted VACM .
SMA
The SMA detector was a rectangular air-core 69 turn coil wound from 44 AWG wire with an area of 2.86mm2. The coil was 2.15 mm long and 1.35 mm high. The 2.15 mm length dimension lay along the sample’s surface, while the height dimension projected away from it. The coil was constructed as a rectangle, and oriented as described, in order to maximize the ‘measurement region’ in close proximity to the sample’s surface.
VSMA denoted voltage of this detector after signal processing.
1 R The output voltage signals of the detectors were acquired as Vsig by the LabVIEW software: however, each detector required different signal processing methods, such as averaging and fitting, to produce a useful signal. The signal processing for each detector is outlined in section 4.4. CHAPTER 4. MAGNETIC STRESS DETECTORS 74
DC MFL AC MFL SMA
Figure 4.5: DC MFL, AC MFL, and SMA detectors mounted to the excitation core. The detectors were locked into their mounts with epoxy. The detectors are not shown to scale.
4.2.1 Data Acquisition
Signals from the three different detectors were acquired by the PCI-6229 DAQ as Vsig, configured as indicated in table 3.3 (located in chapter 3).
The DC MFL, AC MFL, and SMA detector signals were conditioned differently depending on the output voltage magnitude of each transducer. DC MFL measure- ments were input directly to the PCI-6229 as a differential measurement across the
VH+ and VH terminals of the Hall detector. AC MFL and SMA signals were ampli- − R fied by an Ithaco Model 565 preamplifier in transformer mode, producing a gain of 60 dB prior to being input into the PCI-6229. CHAPTER 4. MAGNETIC STRESS DETECTORS 75
applied tensile
stress σt σt σt c
90o
180o 0o
o
c c 270 σ Bex σ B Bex ex
compressive stress σ stress compressive AC MFL and DC MFL AC MFL and DC MFL SMA measurement tensile measurement compressive measurement
Figure 4.6: The footprint of the excitation core on the sample for AC MFL, DC MFL and SMA measurements. The direction of B~ ex is indicated by white lines between the excitation core poles.
4.3 Experimental Procedures for Testing and Com-
parison of the Probe Systems
Tensile stress was applied to the sample by pressurizing the hydraulic jacks of the
SASR. Measurements were performed with each of the three detector/probe combina- tions: DC MFL, AC MFL, and SMA. These measurements were recorded at different stress levels to determine which detector was most sensitive to stress effects. Figure 4.6 shows the orientation of the probe excitation core relative to the stress direction for DC MFL, AC MFL and SMA detectors. As shown in the first two dia- grams of figure 4.6, AC MFL and DC MFL measurements were performed with the probe parallel (called the ‘parallel’ configuration) and perpendicular (called the ‘per- pendicular’ configuration) to the applied stress. The parallel configuration enabled a measurement of tensile strain sensitivity, while the perpendicular configuration was a measurement of compressive strain2.
SMA measurements were performed by rotating the probe over 360◦ about the
2The SASR could only produce tensile strain. The Poisson effect was exploited to examine AC MFL and DC MFL compressive sensitivity. CHAPTER 4. MAGNETIC STRESS DETECTORS 76
measurement location, stopping to make measurements at 15◦ intervals. Thus, each ‘stress measurement’ consisted of 25 data sets3. Taking φ as the angle between the
probe and the direction of tensile stress, φ = 0◦, 180◦, 360◦ probe orientations aligned
the probe along σt, the applied stress direction, while φ = 90◦, 270◦ aligned the
probe with the largest compressive stress (σc) direction. φ was taken to increase anti-clockwise from zero. All measurements were performed within the elastic deformation range of the
sample. A degaussing cycle4 was completed before each measurement to remove any residual magnetization from the sample.
4.4 Detector Results and Analysis
Voltage signals from the DC MFL, AC MFL, and SMA detectors were recorded in
the FCV2 software as signal voltage (Vsig) waveforms. This section describes the
method by which raw Vsig waveforms were processed to produce VDCM , VACM and
VSMA values. Each detector/probe system is considered in this section.
4.4.1 DC MFL
DC MFL measurements were performed using the probe with an excitation field mag- nitude of 100 mT on flat plate samples in the SASR. A DC MFL Hall detector voltage
(VDCM ) measurement was recorded for increasing stress values up to a maximum ten- sile stress of 107 MPa. 3There were a total of 25 waveforms recorded for each SMA measurement because data was acquired at both φ = 0◦ and φ = 360◦. 4A degauss cycle removes residual magnetization from the sample by cycling through hysteresis loops of decreasing magnitude. CHAPTER 4. MAGNETIC STRESS DETECTORS 77
The configuration of the FCV2 software interface required that the DC excita- tion fields used in DC MFL measurements were input as sine functions with null amplitude, a 15 Hz frequency, and a 100 mT offset term. This resulted in ‘DC MFL
Vsig distributions’ consisting of 3333 Vsig data points recorded over a 67 ms window. 3333 data points for a 15 Hz signal corresponds to the system’s sampling frequency of 50 KHz, while 67 ms is simply the period of a 15 Hz wave.
VDCM was taken as the average signal voltage of a DC MFL Vsig distribution.
Uncertainty in VDCM was calculated using the standard method for uncertainty in a mean5.
Figure 4.7 shows VDCM for both parallel (Bex k σt) and perpendicular (Bex ⊥ σt) orientations of the excitation field. Linear trend lines and their associated equations
for σt in MPa and VDCM in mV are also shown.
Both data sets demonstrate that VDCM is proportional to applied stress. As seen
in figure 4.7, when Bex is parallel to the applied stress direction, increasing stress causes the signal to decrease. When Bex lies along the direction of compressing stress, higher values of compressive stress cause the signal to increase. This relationship can be explained by the positive magnetostriction of Fe: tensile stress increases sample permeability in the direction of applied stress, which causes less flux to be forced out of the sample. The compressive stress resulting from Poisson’s effect produced the opposite outcome in VDCM ; the decrease in permeability caused more flux to be forced out of the sample, increasing signal magnitude.
The large difference between parallel and perpendicular signals in the absence
5Consider N measurements of x with the same uncertainty in each measurement. The mean −1 −1/2 measurement (¯x) is given byx ¯ = N x. The error in the mean (σx¯) is then σx¯ = σN , where σ is the standard deviation of the N measurements of x. See reference [36] for additional information. P CHAPTER 4. MAGNETIC STRESS DETECTORS 78
DC MFL Stress Sensitivity 20.85
20.8 fit t 20.75 t fit
20.7 (mV)
20.65 DCM V 20.6
20.55
20.5 DC MFL Signal, 20.45
20.4
20.35 −40 −20 0 20 40 60 80 100 120 Applies Stress, σ (MPa)
Figure 4.7: DC MFL measurements for Bex k σt and Bex ⊥ σt. For Bex k σt measure- ments, stress σt ranged from 0 to 107 MPa. In Bex ⊥ σt measurements, compressive stress σc varied between 0 and −34 Mpa. Linear fits and their associated equations are shown for each data set. Error bars for the perpendicular data points appear as vertical lines through the circles. CHAPTER 4. MAGNETIC STRESS DETECTORS 79
of stress (at σ = 0) is likely due to significant anisotropy within the sample in its unstressed state, likely a result of manufacturing and previous experiments.
Although the data clearly indicate a trend, the scatter in data would make quan- titative measurement of stress somewhat problematic using this method.
4.4.2 AC MFL
As with DC MFL measurements, AC MFL data was recorded in both parallel and perpendicular probe orientations. The excitation field used was a 55 Hz sine wave with an amplitude of 100 mT described by
Bex = 100 mT sin(2πt55 Hz). (4.2)
VACM readings were recorded with this excitation field up to a maximum SASR tensile stress of 128 MPa and a maximum compressive stress of 35 MPa.
Vsig was sampled at a frequency of 50 KHz over one complete 18 ms period, shown in figure 4.8. Also shown in this diagram is the corresponding Bex waveform. Vsig
waveforms were cosine waves, which was expected from a sinusoidal Bex excitation field.
Vsig waveforms were expected to be functions of applied stress (Vsig(σ)). They were
R fit in MATLAB to a sinusoidal function with three degrees of freedom according to
Vsig(σ) = Af (σ) sin(2πt55 Hz + Bf ) + Cf , (4.3)
where Af (σ) is the amplitude, Bf is phase and Cf is offset. Phase and offset were
expected to be constant at Bf = π/2 radians and Cf = 0. Amplitude was the only
parameter expected to be affected by the applied stress on the sample, as Af (σ) was directly proportional to the flux density passing through the AC MFL signal coil, CHAPTER 4. MAGNETIC STRESS DETECTORS 80
Vsig for the Parallel AC MFL Measurement at Null Stress 225 250
100 200
75 150 inlVoltage, Signal 50 100 (mT)
ex 25 50
0 0 V sig −25 −50 (mV)
−50 −100 Excitation Field, B
−75 −150
−100 Bex −200 Vsig −125 −250 0 5 10 15 20 Time, t (ms)
Figure 4.8: The excitation field (dashed line) and signal voltage (solid line) for an AC MFL measurement at zero applied stress. The probe was in the parallel orientation for this measurement. CHAPTER 4. MAGNETIC STRESS DETECTORS 81
therefore fit amplitude was taken as the AC MFL signal voltage, giving
VACM = Af (σ). (4.4)
Figure 4.9 shows VACM for both parallel and perpendicular probe configurations
(Bex k σt and Bex k σc respectively). Uncertainty in VACM was determined by the 95% confidence interval of the fit to equation 4.3. Most of the measurements in figure
4.9 agree within error, indicating no significant relationship between VACM and σ beyond uncertainty. While there may be a trend in the data, it is not one which is understandable. As such, this method was deemed to be of little use for any practical application.
4.4.3 SMA
SMA measurements were the most demanding of the three measurement types, in terms of both the time required to perform each measurement and the amount of data analysis needed to convert Vsig waveforms to VSMA values. Before unprocessed
Vsig waveforms can be presented, it is necessary to expand on some of Langman’s work presented in section 2.4.3.
SMA: A Theoretical Development of Angular Dependence
The SMA probe was rotated about a point, thus capturing information regarding the direction and magnitude of stress6. Langman described the angle between magnetic
fields inside (B~ in) and outside (B~ out) the sample (designated δ) as a function of the relative permeabilities along two perpendicular principle magnetic directions (µr1 and
6While AC and DC MFL measurements were recorded with the probe in two different configu- rations (parallel and perpendicular to applied stress), this was done to examine the measurements’ sensitivity to compressive stress. CHAPTER 4. MAGNETIC STRESS DETECTORS 82
AC MFL Stress Sensitivity 199
198 t
197 (mV) 196 ACM V 195
194
AC MFL Signal, 193
192
191 −40 −20 0 20 40 60 80 100 120 140 Applies Stress, σ (MPa)
Figure 4.9: AC MFL measurements for Bex k σt and Bex k σc. For Bex k σ measurements, stress ranged from 0 to 128 MPa. In Bex ⊥ σ measurements, stress varied between 0 and 123 Mpa. CHAPTER 4. MAGNETIC STRESS DETECTORS 83
μ1
Bin1
Bout δ B θ in
φ
μ2 Bin2
Figure 4.10: A modified figure 2.15 redrawn for reference. The excitation core footprint is indicated by dotted lines.
µr2, with µr2 > µr1), and the angle of the excitation field density relative to the µ2 direction (θ). A modified figure 2.15 is presented here as figure 4.10 for convenient
reference. In the present application, the direction parallel to applied stress corresponds to
µr2, and µr1 corresponds to the perpendicular direction. Equation 2.27 was given as ( µr2 − 1) tan θ δ = arctan µr1 . 1 + µr2 tan2 θ µr1 ! This equation provided accurate δ values in Langman’s earlier study; however, to use this equation in its current form requires knowledge of the magnetic field orientation within the sample, something that is not possible in the present application. However,
it is possible to develop an alternate relationship by expressing θ in terms of φ (recall
that φ is probe angle relative to µr2, indicated in figure 4.10). A reasonable description for this relationship was found to be µr1 1 ( − 1) tan φ θ = φ + arctan µr2 , (4.5) 3 1 + µr1 tan2 φ µr2 ! based on data presented in figure 2.16 and reference [21]. The relationship between equation 2.27 and equation 4.5 can be explained by considering the two terms in equation 4.5 independently. CHAPTER 4. MAGNETIC STRESS DETECTORS 84
Both B~ in orientation (θ) and probe orientation (φ) were measured relative to the
µ2 direction, which accounts for the separate φ term in equation 4.5. The arctan(...)
component shifts θ from φ toward µ2. The factor of 1/3 was selected based on the angles between φ, B~ in and B~ out shown in figure 2.16.
The two principle magnetic directions (µr1 and µr2) cause the magnitude of Bout to depend on the orientation of the internal magnetic field. This relationship can be expressed as B 2 B 2 B = in1 + in2 . (4.6) out µ µ s r1 r2 Using equations 2.22 and 2.23, equation 4.6 can be rearranged to B sin θ 2 cos θ 2 out = + , (4.7) B µ µ in s r1 r2 which gives the magnitude of Bout per unit Bin. An SMA sensing coil voltage signal will be a function both the magnitude, orien- tation, and rate of change of B~ out, as well as probe properties (number of turns and coil area). Thus the SMA signal voltage in terms of Bin is ∂ V = NAG (B ) , (4.8) ∂t in where the G term is called the ‘geometry factor.’ G compensates for the different
magnitudes and orientations of B~ in and B~ out, as well probe orientation. For the SMA detector described in this thesis, which is a coil rotated 90◦ from the probe angle φ, the geometry factor takes the form 1/2 sin θ 2 cos θ 2 G = + sin (θ + δ − φ) , (4.9) µ µ " r1 r2 # where θ is given by equation 4.5 and δ is determined by equation 2.27, both of which are functions of probe angle φ. The square-root term, shown in square brackets, gives CHAPTER 4. MAGNETIC STRESS DETECTORS 85
0.3
μr2/μr1 = 4
μr2/μr1 = 3 0.2
0.1
μr2/μr1 = 2 0
μr2/μr1 = 1
Geometry Factor , G -0.1
-0.2
-0.3 0 50 100 150 200 250 300 350 Probe Angle, φ (deg)
Figure 4.11: G for four µr2/µr1 ratios. The 0◦ , 180◦ , and 360◦ probe orientations place the probe parallel to the µ2 direction.
the magnitude of Bout from Bin, it was taken directly from equation 4.7. The sin(...)
term extracts the component of B~ out parallel to the coil’s axis.
Figure 4.11 shows the geometry factor G over a complete probe rotation (φ = 0◦ to
360◦) for several theoretical µr2/µr1 ratios. For the case of µr2/µr1 = 1 the geometry factor is zero, indicating that isotropic samples would produce no signal in the SMA
coil. Other relative permeability ratios produce sinusoidal, 180◦ periodic geometry factors, with amplitude increasing with µr2/µr1. Peak G values occur when the probe is shifted 45◦ anti-clockwise from the direction of greatest permeability. CHAPTER 4. MAGNETIC STRESS DETECTORS 86
SMA Results and Analysis
The excitation field used in SMA measurements was a 55 Hz sine wave with a 100 mT amplitude, identical to the field used for AC MFL measurements (refer to equation
4.2). Measurements were performed up to a maximum sample tensile stress of 130 MPa.
For each SMA measurement the probe was rotated 360◦ in 15◦ increments, with
Vsig waveforms collected for each increment. Vsig waveforms, functions of both stress
R (σ) and probe orientation (φ), were fit in MATLAB to the equation
Vsig(σ, φ) = Af (σ, φ) sin(2πt55 Hz + Bf ) + Cf , (4.10) where Cf is fit offset, Bf is fit phase, and Af (σ, φ) is fit amplitude, which was expected to be a function of both applied stress and probe angle. Both offset and phase were expected to be constant.
Figure 4.12 shows Af (σ, φ) for four stress levels (σ = 0 MPa, 61.6 MPa, 97.7 MPa, 129 MPa). Uncertainty values were taken as the 95% confidence intervals of the fit.
The effects of stress on Af (σ, φ) can be seen in the first 90◦of rotation, where the signal follows an inverted sinusoidal line for σ = 0 MPa, decreases in amplitude as stress
increases to σ = 61.6 MPa, then inverts to a standard sine waveform at σ = 97.7 MPa, and finally increases in amplitude for σ = 129 MPa.
Based on the amplitude of Af (σ, φ) and anisotropy analysis presented earlier in this section, it can be seen that the initial bulk magnetic easy axis of the sample is in the perpendicular direction7, which agrees with previous studies performed in these
plates [24]. Increasing tensile stress along the parallel direction causes a corresponding
7Recall that peaks in the anisotropy signal occur 45◦ anti-clockwise from the direction of greatest permeability. CHAPTER 4. MAGNETIC STRESS DETECTORS 87
SMA Vsig(σ, φ) Amplitude for Bex = 100 mT sin(2πt55 Hz)
σ = 0 MPa 115
110
105
100
95
σ = 61.6 MPa 115
110
105
100 ) (mV) φ
, 95 σ ( f A
σ = 97.7 MPa 115
Fit Amplitude, 110
105
100
95
σ = 129 MPa 115
110
105
100
95
−50 0 50 100 150 200 250 300 350 400 Probe Angle, φ (deg)
Figure 4.12: Vsig(σ, φ) fit amplitudes for SMA measurements. Each data set consists of 25 points recorded at 15◦ intervals between 0◦ and 360◦. 0◦ , 180◦ , and 360◦ probe orientations placed the probe (and excitation field) parallel to the applied stress. CHAPTER 4. MAGNETIC STRESS DETECTORS 88
increase in magnetic permeability, bringing the sample close to an isotropic state for σ = 66.1 MPa. At σ = 91.7 MPa, the easy axis has shifted to the parallel orientation.
To arrive at VSMA, the Vsig amplitude waveforms shown in figure 4.12 were fit to a 180◦-periodic sine function according to 2π A (σ, φ) = A (σ) sin φ + B + C . (4.11) f f2 180 f2 f2 As with the initial fit (see equation 4.10), the phase (Bf2) and offset (Cf2) parameters were expected to be constant: though they were fit in MATLAB, they were confirmed to remain relatively constant. The amplitude was expected to be proportional to the stress applied to the sample, thus
VSMA = Af2(σ). (4.12)
Figure 4.13 shows the SMA signal voltage (VSMA) obtained from fits to equation 4.11. The data shows a linear increase in SMA signal amplitude with applied stress and sufficiently low uncertainties for data points to be clearly distinguished. The
‘initial measurement’ data set corresponds to the data presented earlier in figure 4.12. The ‘repeated measurement’ data set was acquired after the initial measurement at
approximately equivalent applied stress levels. Between measurements the probe was removed from the sample and replaced at the same location. The purpose of the repeated measurement was to evaluate the repeatability of SMA measurements.
The two data sets agree within uncertainty, although the repeated measurement has consistently higher uncertainty than the initial measurement. CHAPTER 4. MAGNETIC STRESS DETECTORS 89
Anisotropy Signal from a Mild Steel Plate 15
initial measurement 10 repeated measurement (mV) 5 SMA V
0
−5 SMA Signal Voltage, −10
−15 −20 0 20 40 60 80 100 120 140 Applied Stress, σ (MPa)
Figure 4.13: SMA measurements for tensile up to 130 MPa. CHAPTER 4. MAGNETIC STRESS DETECTORS 90
4.5 Selected Detector
Of the three detectors tested, only the AC MFL coil demonstrated no stress sensitiv- ity. This could have been due to the apparatus or data processing methods, as the measurement was of the same nature as DC MFL tests.
DC MFL measurements behaved generally as expected: VDCM decreased with the probe parallel to tensile stress, and increased with the probe oriented along com- pressive stress. However, significant scatter in the data suggested that quantitative measurements may be difficult with a DC MFL-based probe.
The SMA detector indicated a strong relationship between applied stress and both the initial measurement (as Af (σ, φ)), as well as the VSMA value. SMA measurements are also capable of providing additional information about the orientation of stresses within the sample, and were demonstrated to be repeatable. For these reasons, an SMA sensing coil was selected as the magnetic flux transducer for the second probe design. Chapter 5
Proposed Design: The Magnetic Anisotropy Prototype Probe
Previous chapters described the testing of different feedback systems and sensor con- figurations with a general-use excitation core. The general-use core was relatively
large (the pole area was 264 mm2 with a back spine length of 64 mm) and was tested on flat plate samples. This chapter describes the features of a prototype probe devel-
R oped specifically for use on CANDU feeders, termed the Magnetic Anisotropy Pro- totype (MAP) probe, that combined a smaller, Supermendur-cored excitation core with the FCV2 flux control system and an SMA detector coil. Section 5.1 outlines the design characteristics of the MAP probe, while section 5.2 describes experiments
R conducted on a section of pipe similar to the feeders found in CANDU reactors.
91 CHAPTER 5. PROPOSED DESIGN: MAP PROBE 92
5.1 Magnetic Anisotropy Prototype (MAP) Probe
The optimized probe for stress measurement in feeders, termed the Magnetic Anisotropy Prototype probe (MAP probe), consisted of a Supermendur1 U-core excitation elec- tromagnet coupled with a 200 turn SMA coil. A BH-700 feedback Hall sensor and a feedback coil were integrated into the MAP probe so that it could be used with
FCV2. It should be noted that the MAP probe will not fit within the clearances of a CANDU reactor face: it is too tall. However, the components selected for the probe were chosen so that modification to certain parts, such as the connector assembly,
R would allow the system to be used in a CANDU feeder pipe environment. The Supermendur core, shown in figure 5.1, consists of thin layers of a 49% Co,
49% Fe, 2% V alloy. The layers are held together with a non-conductive epoxy that limits the formation of eddy currents, which decreases power loss within the core, making it ideal for AC magnetic applications. The core is small, with a height of 15.76 mm and a footprint of 38.18 mm2, and was integrated into a housing assembly appropriate for SMA measurements.
The MAP assembly, shown in figure 5.2(a), was built around the Supermendur core. For the probe to function with FCV2, a feedback Hall sensor, feedback coils and excitation coils were mounted to the core. These coils, and other important MAP components are shown in figure 5.2. The connector brace, shown in white, fits tightly into a stainless steel disk (shown in figure 5.2 (b)) which is free to rotate in a larger aluminum mount that can be clamped to samples.
1‘Supermendur’ is the product name of a discontinued layered magnetic alloy from Carpenter Technologies. CHAPTER 5. PROPOSED DESIGN: MAP PROBE 93
9.52
16.99 R 4.19
4.01
11.75
4.01
Figure 5.1: A schematic of the Supermendur core of the MAP probe. The core is shown to scale. All dimensions are in millimeters.
SMA detector coil detector coil piston stainless lifto! spacer steel disk
feedback feedback coil Hall sensor
excitation coil
Supermendur excitation core
spring
aluminum mount connector brace
(a) (b)
Figure 5.2: (a) A diagram of the MAP probe. Only the corner of the Supermendur core of figure 5.1 is visible; it is shown in black. Connector pin 1 corresponds to the bottom right pin, connector pin 12 corresponds to the top left pin. (b) A photograph of probe set in mounting hardware. CHAPTER 5. PROPOSED DESIGN: MAP PROBE 94
Excitation and feedback coils were wound using MWS Wire Industries PN Bond2 magnet wire and placed on each pole of the excitation core. A thin layer of Teflon tape
was placed between the core and coils to protect the coils; it appears as a white band between the feedback coils and liftoff spacers in figure 5.2. Both the excitation and feedback coils were wound in pairs: the excitation system was made of two 36 AWG
250 turn coils, the feedback system consisted of two 36 AWG 25 turn coils. Excitation and feedback coils were placed on each pole of the excitation and connected in series
effectively creating one 500 turn excitation coil and one 50 turn feedback coil (from this point onward these coils will be referred to in the singular). The SMA detector
coil was mounted in a spring-loaded piston to ensure repeatable SMA coil coupling with the sample. The SMA coil used in the MAP probe was 200 turns, wound out of 44 AWG PN bond wire around a ferrite core. Table 5.1 summarizes the properties of
the excitation, feedback and SMA coil properties used in the MAP probe. The SMA coil was encased in epoxy within a plastic piston assembly. As mentioned
previously, a small spring (Gardner Spring part 36000G) pushes against the back of the piston to ensure repeatable detector coil coupling to the sample. The piston is
housed in a brass mounting bracket that connects it to the Supermendur core and connector brace. The connector brace was machined out of plastic and contained 12 pin Tyco Elec-
tronics AMP male connector. The connection diagram for this terminal is given in figure 5.3.
2PN Bond wire is an insulated copper wire with a superimposed film of thermoplastic bonding material. Heat or solvent will cause the bonding layer to soften and fuse layers of wire together. This allows coils to be wound in unusual shapes or on jigs since the coils are bonded turn to turn. CHAPTER 5. PROPOSED DESIGN: MAP PROBE 95
two 250 turn coils in series turns 2 × 250 = 500 excitation coil resistance 23Ω .5 wire gage 36 AWG PN Bond core material Supermendur 6 2 coil area 4 .5 mm × 10 mm = 45 × 10− m two 25 turn coils in series turns 2 × 25 = 50 feedback coil resistance 2 .15Ω wire gage 36 AWG PN Bond core material Supermendur 6 2 coil area 4 .5 mm × 10 mm = 45 × 10− m turns one 200 turn coil resistance 16Ω .9 anisotropy coil wire gage 44 AWG PN Bond core material Ferrite 6 2 coil area 2 mm × 2 mm = 4 × 10− m
Table 5.1: MAP probe properties. Feedback and excitation coils were wound on an external forming rig, which is why their area differs from the Supermendur core footprint.
7 VH+ VH- 1
+ - 8 Ic Ic 2
9 Vex- Vex- 3
10 Vfc- Vfc+ 4
12 1 11 NC NC 5
12 Vsig- Vsig+ 6
Figure 5.3: The pin diagram for the MAP system. NC indicates no connection at that terminal. CHAPTER 5. PROPOSED DESIGN: MAP PROBE 96
5.2 MAP Probe Testing with SA-106 Grade B Pipe
To evaluate the stress sensitivity of the MAP probe, it was clamped to a length of 2.5 inch nominal diameter SA-106 grade B pipe mounted in a three-point bending rig (3PBR). The bending rig and sample are described in section 5.2.1, while results are given in sections 5.2.2 and 5.2.3.
5.2.1 The Three-Point Bending Rig (3PBR) and SA-106 Grade
B Sample
The Three-Point Bending Rig (3PBR), shown in figure 5.4, was designed by Steven
White to apply compressive and tensile axial loads to a 3.18 m long, 2.5 inch nominal diameter Schedule 80 SA-106 grade B pipe, hereafter referred to as the SA-106 sample, using three 6 ton bottle jacks mounted on a steel I-beam. The top of the pipe directly above the middle jack was taken as the surface origin (0 cm, 0◦) in (axial, hoop) coordinates, according to the coordinate system indicated in figure 5.4.
The application of tensile and compressive axial (σa) loads required different tow- ing strap configurations. In the tensile configuration, shown in figure 5.4, the SA-106
sample was strapped at its ends and a tensile axial stress state (σa > 0) at the measurement location (top surface) was achieved by raising the middle jack. In the compressive configuration (not shown) the pipe was strapped at the center with two
towing straps. Compressive axial stress (σa < 0) was applied by raising the two outer
jacks. Hoop stress (σh) was generated for both configurations by Poisson effects.
R Four Vishay EA-06-250BF350 general purpose 350Ω strain gages with gage fac- tors of 2.100 ± 0.5% and a transverse sensitivy of 0.0 ± 0.5% were mounted to the CHAPTER 5. PROPOSED DESIGN: MAP PROBE 97
measurement location (20.0±0.5 cm, 0±5o)
surface origin (0 cm, 0o)
strain gauges
SA-106 Grade B pipe
I-beam
radial 6-ton bottle jacks
towing straps hoop
axial
Figure 5.4: A schematic of the three-point bending rig in the tensile configuration. Com- ponents and key locations are indicated. The pipe surface origin is labeled (0 cm, 0◦) in (axial, hoop) coordinates. This figure has been adapted from reference [39]. CHAPTER 5. PROPOSED DESIGN: MAP PROBE 98
sample to measure hoop and axial strain. The two axial strain (εa) gages are centered at (9.1 cm, 0◦) and (30.2 cm, 0◦). The two remaining gages are oriented to meausre hoop strain (εh) and are centered at (11.5 cm, 0◦) and (28.5 cm, 0◦). The surface of the pipe surrounding and between the strain gages was sanded to a smooth finish to
R allow proper gage mounting. The strain gages were connected to a Vishay Measure- ments Group SB-10 Balance and Switch for calibration and switching. The SB-10
R was connected to a Vishay Measurements Group P3500 Strain Indicator. SA-106 grade B piping has a minimum specified yield strength of 240 MPa, a
Young’s modulus of Y = 202.7 GPa at 21◦ C and a Poisson’s ratio of ν = 0.3 [1], [39]. The generalized form of Hooke’s law for an isotropic material (refer to equation 2.3) in cylindrical coordinates gives the axial stress (σa) as Y ν σ = ε + (ε + ε + ε ) , (5.1) a 1 + ν a 1 − 2ν a h r and hoop stress (σa) as Y ν σ = ε + (ε + ε + ε ) , (5.2) h 1 + ν h 1 − 2ν a h r where εr is radial strain. No strain gage was mounted to record εr; however, previous neutron diffraction studies have shown it to be small compared to εa and εh [39], therefore εr = 0 provided a reasonable simplification. εa and εh were recorded by the axial and hoop strain gages described above. The MAP probe was placed in the middle of the strain gages at (20.0 ± 0.5 cm, 0 ± 5◦), indicated in figure 5.4. Linear interpolation was used to approximate strain at the measurement location. CHAPTER 5. PROPOSED DESIGN: MAP PROBE 99
5.2.2 SMA Excitation Field Response
The 3PBR was used to characterize MAP anisotropy signal excitation field response. The MAP probe was mechanically clamped to the SA-106 sample at (20.0 ± 0.5 cm,
0 ± 5◦) in (radial, hoop) coordinates and the pressure valves of each jack in the 3PBR was released, bringing the system to a zero applied stress state. Excitation
waveforms used with the MAP probe were sinusoidal with amplitude A and frequency f, described by:
Bex = A sin (2πf) . (5.3)
The excitation frequency f affects two parameters of the SMA signal: amplitude and
skin depth. As with any wire coil, SMA signal amplitude increases with the time-
rate of change of the detected field (∂Bex/∂t). Skin depth (δ) refers to the depth to which an electromagnetic field propagates within a conductor, and is defined as the
distance at which wave amplitude decreases to 1/e ≈ 0.368 of the value at the sample surface. This attenuation is caused by ohmic losses within the conductive medium
and is discussed in detail in appendix B. Skin depth for a typical ferromagnetic steel is given by:3
2 0.5 δ = 1.59 × 10− m.s f. (5.4) p An excitation frequency of f = 55 Hz gives a skin depth of δ = 2.15 mm. The
magnetic field is 95% attenuated at 3δ = 6.45 mm, which covers the majority of the 7.01 mm pipe wall thickness of the SA-106 sample. Lower frequencies would penetrate
deeper into the sample, but produce lower amplitude voltage response in the SMA detector coil. An excitation frequency of f = 55 Hz was found to provide a good
3 7 −1 −1 Assuming a conductivity (σe) of σe = 10 Ω m , and a relative permeability of µr = 100. CHAPTER 5. PROPOSED DESIGN: MAP PROBE 100
(a) SA-106 Sample Anisotropy (b) SA-106 Sample Signal Error to Signal Ratio 180 8
160 7
140 6 (mV) 120 5 SMA V 100 4 80
3 60 Percent Uncertainty (%) 2
SMA Signal Voltage, 40
20 1
0 0 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 Excitation Field Amplitude, A (mT) Excitation Field Amplitude, A (mT)
Figure 5.5: SMA dependence on excitation field amplitude for σa = 0. VSMA was calcu- lated using the same method described in section 4.4. (a) The anisotropy signal VSMA. (b) The percent error associated with each measurement. balance of penetration and signal amplitude.
The relationship between SMA signal voltage (VSMA) and excitation field ampli- tude (A) was characterized by performing SMA measurements with the MAP probe on the SA-106 sample at excitation field amplitudes varying from A = 25 mT to
125 mT in in 25 mT increments. The maximum excitation field amplitude of 125 mT was determined by the current capacity of the 36 AWG excitation coils used in the
MAP probe. The results are presented in figure 5.5 (a), were it can be seen that VSMA increases relatively linearly with A. The explanation for this relationship is simple: the magnetic flux detected by the SMA coil is a relatively constant fraction of the
total magnetic flux in the system.
The percent uncertainty associated with each VSMA measurement, determined CHAPTER 5. PROPOSED DESIGN: MAP PROBE 101
by the 95% confidence interval of the fit (as described in section 4.4), is shown in figure 5.5 (b). The percent uncertainty decreases from low excitation field values to
a minimum of 3.5% at A = 100 mT, then increases for A = 125 mT. Because of the slight difference in uncertainties between 75 mT and 100 mT excitation fields, an excitation field amplitude of A = 75 mT was used for measurements on the 3PBR.
5.2.3 SA-106 Grade B SMA Stress Response
The stress response of the MAP sensor configured as described in section 5.2.2, with a
55 Hz, 75 mT excitation field, are shown in figure 5.6 (a) for tensile stress. The back-
ground measurement at σa = 0 MPa agrees within error to that presented in figure 5.5. As shown in figure 5.6, increases in axial tension were accompanied by increases
in VSMA, but the observed VSMA changes were small and the four different Vsig(σa, φ) waveforms shown in figure 5.6 (b) are difficult to distinguish, unlike previous SMA
results presented in figure 4.12. The probe was aligned with angles φ = 0◦, 180◦, 360◦ along the pipe axis (parallel to σa), and φ = 90◦, 270◦ along the pipe hoop (parallel to
σh). The results in figure 5.6 (b) indicate an initial easy axis along the axial direction which increases in permeability with σa.
Additional MAP Probe Modifications
Initial MAP results were less stress-sensitive than desired. Minor modifications were made to the SMA coil mount and liftoff pads in an attempt to increase sensitivity and decrease measurement uncertainty. Movement of the sensor during measurements was believed to contribute to inconsistent coil coupling, which increased measurement uncertainty. To counteract this effect, a piece of electrical tape (0.36 mm thick) was CHAPTER 5. PROPOSED DESIGN: MAP PROBE 102
(a) 2.5” SA-106 Grade B Anisotropy Signal (b) SMA Vsig(σa ,φ) Amplitude 110 150
100 105 (mV) 50 ) (mV)
SMA 100 V σ, φ ( f
A 0
95
−50 Fit Amplitude, SMA Signal Voltage, 90 σa= 0 MPa −100 σa= 16.3 MPa σa σa= 45.8 MPa σa= 67.3 MPa 85 −150 −20 0 20 40 60 80 −100 0 100 200 300 400 Axial Stress, σa(MPa) Probe Angle, φ (deg)
Figure 5.6: MAP stress response for an excitation field Bex = 75 mT sin(2πt55 Hz). (a) VSMA values. (b) The Vsig(σa, φ) values for each probe orientation. Error bars are omitted for clarity. CHAPTER 5. PROPOSED DESIGN: MAP PROBE 103
placed between the SMA detector coil and sample to provide more consistent coupling between the detector coil and sample. Liftoff spacer thickness was slightly reduced
to ease the current burden of the excitation coils.
Modified MAP Results and Analysis
The modified MAP was tested with the same excitation field as the original design. With the 3PBR in the tensile configuration, axial tensile stresses were varied from 0 to
270 MPa. The 3PBR was then configured to apply compressive stress to the SA-106 sample, and compressive stresses were varied from 0 to -68 MPa. Measurements were
performed by recording Vsig(σa, φ) waveforms for φ = 0◦ to φ = 360◦ in 15◦increments. Stress test results from the modified MAP are presented in figure 5.7. The initial increasing tensile stress measurement results in an increasing VSMA, while compressive stress produce a decrease in VSMA. The background readings (σa = 0) for both measurements agree within error.
Tensile and compressive MAP data was evaluated with a linear least-squares fit, producing
VSMA(mV) = 0.183σa(MPa) + 69.9 (5.5)
as the line of best fit. This linearization is also shown in figure 5.7. All data points
agree with the linear fit within uncertainty; however there does appear to be slight oscillatory trend about the line of best fit.
The mean uncertainty in MAP probe SMA measurements was found to be ±7 mV, with a minimum uncertainty of ±5 mV and a maximum uncertainty of ±10 mV. Solv- ing equation 5.5 for σa indicates that a ±7 mV uncertainty in VSMA corresponds to a ±38 MPa uncertainty in stress. Therefore the current MAP probe can evaluate elastic CHAPTER 5. PROPOSED DESIGN: MAP PROBE 104
2.5” SA-106 Grade B Anisotropy Signal 130
tensile 120 compressive linear fit
110 (mV)
100 SMA V
90
80
70 SMA Signal Voltage,
60
50 −100 −50 0 50 100 150 200 250 300
Axial Stress, σa(MPa)
Figure 5.7: SMA dependence on tensile and compressive applied stress. Vertical dashed lines indicate σa = 0 and σa = 240 MPa. CHAPTER 5. PROPOSED DESIGN: MAP PROBE 105
SMA Vsig(σa, φ) Amplitude 80
60
40
20 ) (mV) , φ a σ
( 0 f A
−20
−40
Fit Amplitude, −60 σa = 47 MPa σa = -44 MPa
−80
−100 −50 0 50 100 150 200 250 300 350 400 Probe Angle, φ (deg)
Figure 5.8: Signal voltage Vsig(σa, φ) fit amplitude for approximately equivalent compres- sive (σa = −44 MPa) and tensile (σa = 47 MPa) stresses. The uncertainty associated with each data point is smaller than the data marker.
stress in feeders from VSMA values with an accuracy of approximately ±38 MPa. It was observed that the uncertainty associated with compressive measurements was, in general, much larger than the uncertainty of equivalent tensile measurements.
Figure 5.8 shows the signal voltage amplitude (Af (σa, φ)) for σa = 47 MPa and σa = −44 MPa. There is only a small difference in amplitude between the two stress levels at φ = 45◦ and φ = 315◦ , approximately 3 mV; however Af (−44MPa, φ = 135◦, 225◦) is approximately 20 mV less than Af (47 MPa, φ = 135◦, 225◦). The discrepancy be- tween peak Af (σa, φ) values was the primary cause of the increased uncertainty as- sociated with compressive measurements. The SMA detector coil of the MAP probe was irreparably damaged while inves- tigating the cause of the compressive measurement peak distribution, ending data CHAPTER 5. PROPOSED DESIGN: MAP PROBE 106
collection with this probe. Chapter 6
Summary and Conclusions
Residual stress measurement is a priority for industries where the cost of failure is significantly greater than the cost of regular inspection. A technique based on stress-induced magnetic anisotropy (SMA) may present a viable method for in situ residual stress measurement on components where tight clearances and varying sur- face conditions hinder other stress measurement methods. This thesis focused on the development of hardware, software and signal analysis methods necessary to apply
R SMA measurement to SA-106 Grade B feeder pipes used in CANDU nuclear reac- tors. In this chapter the success of this project will be evaluated based on the project objectives specified in section 1.3.
6.1 Flux Control Systems
Two magnetic flux control systems, FCV1 and FCV2, were designed to compensate for geometry effects resulting from the curved surface of a pipe wall. FCV1 relied exclusively on feedback from a Hall sensor located between the sample and excitation
107 CHAPTER 6. SUMMARY AND CONCLUSIONS 108
core. This control system was found to be unstable due to the nature of the feedback path.
The second flux control system (FCV2) was designed with two feedback mecha- nisms: a wire coil (called the feedback coil) wound around the base of the excitation core, and a Hall sensor (called the feedback Hall sensor) fixed between the excitation core and sample. The hardware control system of FCV2 compared the magnetic flux density at these two points with a user-defined reference value, and adjusted the exci- tation voltage (the voltage across the excitation coil) to produce the desired magnetic field.
R The software requirements of FCV2 were implemented in LabVIEW . A program was designed to calculate reference waveform parameters (Vref ) from a user-specified excitation magnetic field (Bex). This software was also used for data acquisition and output via a PCI-6229 DAQ. FCV2 fulfills a portion of the first project objective, which was to “design a magnetic flux leakage-based probe that can accommodate the space and geometry (lift-off) constraints imposed by the feeder pipe environment.”
6.2 Magnetic Stress Detectors
Three magnetic stress detectors were tested on mild steel plate samples with a pro- totype excitation core controlled by FCV2. Each detector was designed to function somewhat differently: a Hall sensor was used with DC excitation fields (DC MFL), a wire coil was used with AC excitation fields (AC MFL), and a specially oriented coil was used in anisotropy measurements (SMA). The AC MFL measurement showed no significant stress sensitivity. DC MFL measurements indicated a stress dependent CHAPTER 6. SUMMARY AND CONCLUSIONS 109
trend, but significant scatter would have made it problematic for quantitative stress measurement.
SMA measurements were the most time-intensive to perform, requiring a full probe rotation per measurement, and the most computationally intensive to analyze. How- ever, flat plate tests indicated that this measurement was significantly more sensitive to stress than the others. Because of the high stress sensitivity SMA measurements were selected as the most likely candidate to produce reasonable stress measurements from SA-106 grade B feeder pipes, and a prototype SMA-based probe (the Magnetic Anisotropy Prototype probe) was designed accordingly.
The flat plate magnetic stress detector tests were carried out to complete the second project objective: to “conduct laboratory testing on plate samples to determine the extent of stress sensitivity of the probe designs.”
6.3 Proposed MAP Probe Design
The Magnetic Anisotropy Prototype (MAP) probe - a small Supermendur excitation coil coupled with a ferrite core SMA coil and FCV2 compatible feedback components
R - was designed specifically for use on CANDU feeder pipes. The probe was designed to rest in a brace clamped to the sample, where it could be rotated about a point to perform an anisotropy measurement.
MAP stress sensitivity was examined in tensile and compressive stress tests using the three-point bending rig and a 2.5” nominal diameter SA-106 grade B pipe sam- ple. While the stress-induced magnetic anisotropy signal voltage (VSMA) recorded in MAP measurements indicated clear stress dependence, the uncertainty associated with MAP VSMA indicate that the probe is not yet suited for industrial use. MAP CHAPTER 6. SUMMARY AND CONCLUSIONS 110
testing completed objective three, which was to “conduct testing on samples with feeder pipe geometry with a focus on generalized stresses.”
6.4 Recommendations for Future Work
There are several aspects of this project that could be developed further. Section 6.4.1 details how certain project objectives could be brought to completion and section 6.4.2 examines additional work that could improve both FCV1 and FCV2. Section 6.4.3 suggests a new probe design that may yield improved results.
6.4.1 Project Objectives
Not all of the project objectives outlined in section 1.3 were fully met. Many of the shortcomings of this project result from the MAP, either by virtue of design or due to the sudden failure of its SMA coil. Project objective one was to “design a magnetic flux leakage-based probe that can accommodate the space and geometry (lift-off) constraints imposed by the feeder pipe environment.” FCV2 fulfilled a portion of that requirement by providing a method of coupling a consistent and repeatable flux into the sample, as discussed in section 6.1. However, the rest of the objective was not met: the MAP probe will not fit within the
R confines of a CANDU reactor face due to the connector brace and manual rotation of the probe. Some modifications to the MAP design would meet this objective, such as a redesigned connection system and a servo-based mechanical rotation system, but this was not explored further in this project. CHAPTER 6. SUMMARY AND CONCLUSIONS 111
Project objective three was to “conduct testing on samples with feeder pipe geom- etry with a focus on generalized stresses.” While this objective was already described as completed, it would have been beneficial to perform further measurements at dif- ferent excitation frequencies to extract additional depth information. The fourth objective was to “conduct testing on feeder pipe samples.” This ob- jective was not met due to failure of the SMA stress detection coil in the MAP. The detection coil was 200 turns, wound out of 44 AWG wire around a ferrite core. Fail- ure occurred when the wires connecting the coil to the connector brace snapped. The break occurred at the edge of the epoxy encasing the SMA coil and could not be repaired, ending data collection. This objective could be completed by rebuilding the MAP probe SMA coil.
6.4.2 Control Systems
While some justifications of the shortcomings of FCV1 and the success of FCV2 are presented in section 3.5.4, a detailed control-theory analysis of both FCV1 and
FCV2 would yield further information about the noise observed in FCV1 and the performance limits of FCV2. It is also possible that additional analysis of FCV1 may yield information relating to possible modifications that would produce a functioning
Hall sensor feedback system.
6.4.3 Suggested Design Modifications
The objective of this work was to develop a magnetic stress inspection system that
R could be used as an early prototype for an industrial CANDU feeder pipe inspection
R technology. One of the difficulties of designing a system for use at a CANDU reactor CHAPTER 6. SUMMARY AND CONCLUSIONS 112
x core
y core detector coil 1
coil mount excitation coil 4 42 feedback coil
sample 3
(a) (b)
Figure 6.1: The recommended system for future work. (a) Two perpendicular U-cores can rotate the magnetic field at their center by adjusting the excitation field generated by each core. Adapted from [39]. (b) The recommended anisotropy coil configuration for a tetrapole excitation system. Coils 1 and 3 are connected in series, as are coils 2 and 4.
face is accessibility: an elaborate network of coolant feeders with a minimum inter-
pipe clearance of 20 mm make it difficult for operators and tools to reach inspection locations. The design presented in chapter 5 does not fit within the clearances of
R CANDU feeder pipes and requires manual rotation. To overcome both of these issues, a four pole excitation system (termed a tetrapole system) such as the the spring-loaded tetrapole prototype (SL4P) designed by Steven White for magnetic
Barkhausen noise measurements [39], could be used to generate the excitation field. The SL4P consists of two Supermendur U-cores oriented perpendicular to one another, as shown in figure 6.1 (a), and can rotate the magnetic field at the center of the cores by superimposing different excitation field amplitudes in the x and y cores. An anisotropy coil, shown in figure 6.1 (b), consisting of four wire coils could be used to detect the anisotropy signal. The coils would be connected in pairs (1 to 3 and 2 to 4), and the anisotropy signal would be taken as the quadrature sum of the coil voltages. This tetrapole probe design would potentially enable measurements to be made on feeder pipes without the need for manual probe rotation. Bibliography
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[38] E. Villari. Ueber die aenderungen des magnetischen moments, welche der zug und das hindurchleiten eines galvanischen stroms in einem stabe von stahl oder eisen hervorbringen. Annalen der Physik, 202(9):87–122, 1865.
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FCV1 Details
Flux control version 1 (FCV1) was modified several times in attempts to stabilize the excitation waveform. The basic principle of the control system remained consistent with that presented in section 3.5; the modifications where capacitors and low-pass filters that were used to damp out high frequency signals. Figure A.1 shows the electrical schematic of one of the final iterations of FCV1. Section 3.5 presents data collected exclusively from this system. Further modification of this design did not yield significantly improved performance.
118 APPENDIX A. FCV1 DETAILS 119
Hall sensor current supply
+24 V 27 kΩ
generate ground referenced Hall voltage +24 V +24 V 1.2 kΩ 1 kΩ 1 μF 1 1 μF 8 13 + 2 2 + 1 kΩ LM4701 12 LM747-A - 7 4 - 3,5 1 1 kΩ 4 1 μF 1 μF -24 V -24 V
+24 V 1 μF +Ic
Red 1 μF V Blue H+ 13 BH-700 2 Yellow V + V H- 6 12 H Black + 1 kΩ 1 kΩ LM747-A 10 LM747-B - -Ic 1 - 4 7 1 kΩ 9 1 μF 52 Ω 1 μF -24 V 5 W +24 V
20 Ω 1 kΩ 5 W 1 kΩ
Hall voltage comparison to reference +24 V
1 μF V 1 excitation coil ref 8 V + Rex Lex s 2 F = 0.5A LM4701 - 7 4 VH 3,5 0.2 Ω 1 μF -24 V
Figure A.1: An electrical schematic of FCV1. All resistors are 0.25 W unless otherwise indicated. LM747 op-amps are dual amplifier packages. Different amplifiers within an LM747 are designed A and B. Appendix B
Skin Depth
Consider a plane electromagnetic wave of magnetic field amplitude B0 incident on a
1 semi-infinite conducting medium of conductivity σe. The amplitude of the magnetic field within the conductor decreases due to ohmic losses as the wave penetrates fur- ther in the medium. The term ‘skin depth’ refers to this attenuation, which occurs according to the exponential law [12]:
z√πµσef B(z) = B0e− , (B.1) where B(z) is the amplitude of the wave within the conductor, B0 is the amplitude of the wave outside the conductor, z represents the direction of propagation, µ is the permeability of the medium, and f is the frequency of the electromagnetic wave. The
terms in the square root of equation B.1 are rearranged to define the skin depth (δ) as 1 δ = , (B.2) πσf µ r e 1Extending from −∞ < x < ∞, −∞ < y < ∞, −∞ < z ≤ 0 in Cartesian coordinates.
120 APPENDIX B. SKIN DEPTH 121
Skin Depth in Generic Steel 16
14
12 (mm)
δ 10
8
Skin Depth, 6
4
2
0 0 20 40 60 80 100 Frequency, f (Hz)
7 1 1 Figure B.1: Skin depth for a typical steel with µr = 100 and σe = 10 Ω− m−
giving
z/δ B(z) = B0e− . (B.3)
After one δ the amplitude of the magnetic field is reduced by a factor of 1/e. For most engineering applications, waves are considered to be attenuated at z = 3δ Figure B.1 shows the variation of skin depth with frequency for a typical steel
7 1 1 with relative permeability of µr ≈ 100 and conductivity σe = 10 Ω− m− .