Rapid Non-Destructive Residual Stress Analysis of...

DEFENCE DÉFENSE&

Defence R&D Canada – Atlantic

Copy No. _____

Defence Research andDevelopment Canada

Recherche et développementpour la défense Canada

Rapid Non-Destructive Residual Stress

Analysis of Steel Structures

Phase 2, Assessment and Testing of the PrototypeMagnetic Barkhausen Noise Analysis System

Thomas W. Krause, P. McNairnay, V. Babbar, A. Samimi, P. WeetmanRoyal Military College of Canada

Lynan ClaphamQueen's University

Prepared By:Royal Military College of CanadaPO Box 17000, Station ForcesKingston, Ontario, Canada Contract Project Manager: Dr. Thomas Krause, 613-541-6000, ext 6415PWGSC Contract Number: FE S1431CIA01CSA: Dr. Shannon P. Farrell, Defence Scientist, 902-427-3437

Contract Report

DRDC Atlantic CR 2013-202

March 2014

The scientific or technical validity of this Contract Report is entirely the responsibility of the contractor and the contents do not necessarily have the approval or endorsement of Defence R&D Canada.

This page intentionally left blank.

Rapid Non-Destructive Residual Stress Analysis of Steel Structures Phase 2, Assessment and Testing of the Prototype Magnetic Barkhausen Noise Analysis System

Thomas W. Krause, P. McNairnay, V. Babbar, A. Samimi, P. Weetman Royal Military College of Canada Lynan Clapham Queen's University Prepared By: Royal Military College of Canada PO Box 17000, Station Forces Kingston, Ontario, Canada Contract Project Manager: Dr. Thomas Krause, 613-541-6000, ext 6415 PWGSC Contract Number: FE S1431CIA01 CSA: Dr. Shannon P. Farrell, Defence Scientist, 902-427-3437

The scientific or technical validity of this Contract Report is entirely the responsibility of the Contractor and the contents do not necessarily have the approval or endorsement of Defence R&D Canada.

Defence R&D Canada – Atlantic

Contract Report


March 2014

Approved by

Original signed by Dr. Leon M. Cheng

Dr. Leon M. Cheng

Head / Dockyard Laboratory Atlantic

Approved for release by

Original signed by Dr. Leon M. Cheng

Dr. Leon M. Cheng

Chair / Document Review Panel

© Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence, 2014

© Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale,

2014

DRDC Atlantic CR 2013-202 i

Abstract ……..

The Royal Military College of Canada (RMCC) was contracted by DRDC to develop a prototype

portable Magnetic Barkhausen Noise Analysis (MBNA) system for qualitative rapid residual

stress analysis of structural ferromagnetic steels. The unique design offers rapid interrogation of

ferromagnetic materials and a tunable depth of analysis. During phase I, a prototype laboratory

MBNA measurement system was designed and constructed. This report describes progress

achieved during phase II of the three phase project.

During phase II (current work) a deeper understanding of the MBNA functionality and inner

workings was achieved through experimental testing and modelling. The laboratory system was

improved. Experimental testing and modeling were used to achieve greater accuracy of stress

values at varying depth within ferromagnetic steel. This analysis provides the basis for design of

the portable MBNA system that is to be delivered at the end of phase III. The laboratory MBNA

has been demonstrated to be effective for rapid identification of regions of high tensile stress and

stress gradients – a precursor to crack initiation. A field-ready portable system will be supplied to

DRDC Atlantic by March 2014.

Résumé ….....

RDDC a donné comme contrat au Collège militaire royal du Canada (CMRC) d'élaborer un

prototype de système portatif d’analyse du bruit magnétique Barkhausen (ABMB) qui permet une

étude qualitative rapide de contraintes résiduelles au sein d’aciers ferromagnétiques structuraux.

Grâce à sa conception unique, ce système permet d’analyser des matériaux ferromagnétiques

rapidement et à diverses profondeurs. Au cours de la première phase d’élaboration, un prototype

de laboratoire a été conçu et fabriqué. Le présent rapport porte sur les progrès réalisés pendant la

seconde phase d’un projet de conception tripartite.

La seconde phase (travaux en cours) du projet a permis de mieux connaître la capacité et le

fonctionnement du système de laboratoire au moyen de modèles et d’essais expérimentaux, ainsi

que de perfectionner le système. Les modèles et les essais expérimentaux ont servi à accroître

l’exactitude des mesures de contraintes à diverses profondeurs au sein d’aciers ferromagnétiques,

de même qu’à établir le concept de base du système portatif d’ABMB devant être livré au terme

de la troisième phase. On a démontré que le système de laboratoire permet d’identifier

efficacement et rapidement des zones présentant de fortes contraintes de traction et de fortes

variations de contraintes, lesquelles constituent des signes précurseurs de fissuration. Un système

portatif utilisable sur le terrain sera fourni à RDDC Atlantique d’ici mars 2014.

ii DRDC Atlantic CR 2013-202


DRDC Atlantic CR 2013-202 iii

Executive summary

Rapid Non-Destructive Residual Stress Analysis of Steel Structures: Phase 2, Assessment and Testing of the Prototype Magnetic Barkhausen Noise Analysis System

T.W. Krause; P. McNairnay; V. Babbar; A. Samimi; P. Weetman; L. Clapham; DRDC Atlantic CR 2013-202; Defence R&D Canada – Atlantic; March 2014.

Introduction: Residual stress analysis surveys represent a means to gain insight into the extent of

pre-existing fabrication-induced stress and the stress-redistribution in response to repair processes

(such as weld cladding). While similar approaches (ex., X-ray diffraction, hole drilling) offer

more accurate results, these approaches are labor intensive. The extensive surface preparation

also restricts the scope of analysis, density of data points and modifies the stress within the

material.

There is a need for development of a portable, non-destructive (no surface preparation) and rapid

interrogation technique that offers tunable depth of analysis in ferromagnetic submarine steels.

The Royal Military College of Canada (RMCC) was contracted to develop a prototype portable

Magnetic Barkhausen Noise Analysis (MBNA) system. During phase I, a prototype laboratory

MBNA measurement system was designed, constructed and tested. The goal for Phase II was to

improve the functionality of the laboratory system, conduct stress dependent measurements under

elastic strain conditions, and design and assemble components for a portable MBNA system. This

document describes activities undertaken by RMCC during the second year of a three year

project.

Results: During phase II (current work) a deeper understanding of the MBNAs functionality and

inner workings was achieved through experimental testing and modelling. The laboratory system

was improved. Experimental testing and modeling were used to achieve greater accuracy of stress



has been demonstrated to be effective for rapid identification of regions of high tensile stress and

stress gradients – a precursor to crack initiation.

Significance: This MBNA system will enable an increase to the periodicity and scope of

inspections of critical components and structures. The non-destructive nature of the MBNA

system will allow the timely return to service of inspected structures/components in an

unmodified (by surface preparation) condition. Explicit understanding of the residual stress fields

on naval structures and components will provide the requisite data to enhance the validity of

numerical models and experimentation supporting operations and design life.

Future plans: Further experimental and theoretical work is required to define physical system

parameters for quantitative stress calculations. A field-ready portable system will be supplied to

DRDC Atlantic by March 2014.

iv DRDC Atlantic CR 2013-202

Sommaire .....


T.W. Krause; P. McNairnay; V. Babbar; A. Samimi; P. Weetman; L. Clapham; DRDC Atlantic CR 2013-202; R & D pour la défense Canada – Atlantique; mars 2014.

Introduction : L’analyse des contraintes résiduelles constitue un moyen de connaître

l’importance de contraintes préexistantes provoquées en cours de fabrication, ainsi que la

nouvelle répartition des contraintes après des réparations (p. ex. placage par soudure). Bien que

des résultats plus exacts puissent être obtenus grâce à des approches similaires (p. ex. diffraction

des rayons et perforation), ces dernières exigent davantage de main-d’œuvre, de même qu’une

préparation poussée des surfaces analysées, ce qui restreint la portée des analyses, limite la

densité des points de données et transforme les contraintes dans les matériaux étudiés.

Il serait utile de disposer d’un système portatif d’analyse rapide et non destructive (aucune

préparation des surfaces) qui permet d’étudier à diverses profondeurs des aciers ferromagnétiques

de sous-marins. RDDC a donné comme contrat au Collège militaire royal du Canada (CMRC)

d'élaborer un prototype de système portatif d’analyse du bruit magnétique Barkhausen (ABMB).

Au cours de la première phase d’élaboration, un prototype de laboratoire a été conçu, fabriqué et

éprouvé. La seconde phase visait à améliorer la capacité du système, à prendre des mesures en

fonction des contraintes dans diverses conditions de déformation élastique, ainsi qu’à concevoir et

à assembler les composants d’un système d’ABMB portatif. Le présent document porte sur les

activités entreprises par le CMRC au cours de la seconde année d’un projet triennal.

Résultats : La seconde phase (travaux en cours) du projet a permis de mieux connaître la capacité

et le fonctionnement du système d’ABMB au moyen de modèles et d’essais expérimentaux, ainsi

que de perfectionner le système. Les modèles et les essais expérimentaux ont servi à accroître

l’exactitude des mesures de contraintes à diverses profondeurs au sein d’aciers ferromagnétiques,

de même qu’à établir le concept de base du système portatif d’ABMB devant être livré au terme

de la troisième phase. On a démontré que le système de laboratoire permet d’identifier

efficacement et rapidement des zones présentant de fortes contraintes de traction et de fortes

variations de contraintes, lesquelles constituent des signes précurseurs de fissuration.

Portée : Le système d’ABMB permettra d’accroître la fréquence et la portée des inspections

visant des composants et des structures essentiels. Les analyses non destructives que l’on peut

effectuer avec celui-ci favorisent une remise en service opportune des composants et des

structures inspectés dans leur état d’origine (aucune préparation des surfaces). En connaissant de

manière approfondie la nature des zones de contraintes résiduelles formées au sein de structures

et de composants navals, il est possible de recueillir des données qui permettent d’améliorer la

validité d’expériences et de modèles numériques sous-tendant des opérations et l’établissement de

la durée de vie utile.

DRDC Atlantic CR 2013-202 v

Recherches futures : D’autres expériences et travaux théoriques doivent être exécutés pour

établir des paramètres de systèmes physiques relatifs aux calculs quantitatifs des contraintes. Un

système portatif utilisable sur le terrain sera fourni à RDDC Atlantique d’ici mars 2014.

vi DRDC Atlantic CR 2013-202


DRDC Atlantic CR 2013-202 vii

Table of contents

Abstract …….. ................................................................................................................................. i

Résumé …..... ................................................................................................................................... i

Executive summary ......................................................................................................................... ii

Sommaire ..... .................................................................................................................................. iv

Table of contents ........................................................................................................................... vii

1 Introduction ............................................................................................................................... 1

1.1 References ..................................................................................................................... 1

2 Magnetic Barkhausen Noise Analysis System ......................................................................... 2

2.1 Design and Components ................................................................................................ 2

2.2 Components and Assembly ........................................................................................... 3

Probe Assembly ................................................................................................... 3 2.2.1

2.2.1.1 Probe .......................................................................................................... 3

2.2.1.2 Coils ........................................................................................................... 3

2.2.1.3 Connections................................................................................................ 5

2.2.1.4 Cables ......................................................................................................... 6

2.2.1.5 Preamplifier................................................................................................ 7

2.2.1.6 BNC-2110 .................................................................................................. 7

Flux Control System (FCS) and Power Supply ................................................... 7 2.2.2

2.2.2.1 FCS ............................................................................................................ 7

2.2.2.2 Power Supply ........................................................................................... 10

PC and Software ................................................................................................ 10 2.2.3

2.2.3.1 National Instruments Cards ...................................................................... 10

2.2.3.2 Software ................................................................................................... 11

2.3 Operation ..................................................................................................................... 11

Powering Up the System ................................................................................... 11 2.3.1

Setting up the Probe on a Sample ...................................................................... 12 2.3.2

Defining Universal Software Settings ............................................................... 13 2.3.3

Defining the Measurement Settings ................................................................... 14 2.3.4

Defining the Analysis Settings .......................................................................... 15 2.3.5

Running the Measurement ................................................................................. 17 2.3.6

2.4 Results ......................................................................................................................... 17

2.5 Analysis and Troubleshooting ..................................................................................... 19

No Convergence ................................................................................................ 19 2.5.1

2.6 References ................................................................................................................... 20

3 Evaluation of Stress Dependence of Magnetic Barkhausen Noise in an HY-80 Steel

Sample .................................................................................................................................... 21

3.1 Introduction ................................................................................................................. 21

3.2 Experimental Set-up and procedure ............................................................................ 21

viii DRDC Atlantic CR 2013-202

Uni-Axial Testing .............................................................................................. 21 3.2.1

3.2.1.1 Gripping Mechanism ............................................................................... 22

3.2.1.2 Strain Gages ............................................................................................. 23

Flux-Controlled Magnetic Measurement System .............................................. 23 3.2.2

Measurement Analysis ....................................................................................... 24 3.2.3

3.3 Results ......................................................................................................................... 25

Stress-strain plot ................................................................................................ 25 3.3.1

MBN Envelopes................................................................................................. 26 3.3.2

MBN Energy ...................................................................................................... 28 3.3.3

Angular MBN Measurements and Magnetic Anisotropy .................................. 28 3.3.4

3.4 Summary and Future Work ......................................................................................... 29

3.5 References ................................................................................................................... 30

4 Biaxial Stress Models ............................................................................................................. 32

4.1 Background.................................................................................................................. 32

4.2 Obtaining Magnetization Curves as a Function of Applied Magnetic Field ............... 34

4.3 Model I: The Phenomenological Model ...................................................................... 36

Theory ................................................................................................................ 36 4.3.1

Results: Application to uniaxial stress. .............................................................. 38 4.3.2

4.4 Model II: The Magnetic Object Model ....................................................................... 39

Theory ................................................................................................................ 39 4.4.1

4.4.1.1 Boltzmann Distribution ............................................................................ 41

4.4.1.2 Expectation Values .................................................................................. 42

4.4.1.3 Extension to Multiply Oriented Grains .................................................... 42

Results: Application of Model II to uniaxial stress. .......................................... 42 4.4.2

4.5 Conclusions ................................................................................................................. 45

4.6 References ................................................................................................................... 46

5 Conclusions and Future Work ................................................................................................ 47

Annex A Additional Information for Operation ......................................................................... 49

A.1 FCS potentiometer/gain calibration ............................................................................. 49

A.2 Data Set Descriptions .................................................................................................. 49

Distribution list .............................................................................................................................. 50

DRDC Atlantic CR 2013-202 ix

List of figures

Figure 1: Block diagram of system components. ............................................................................ 3

Figure 2: CAD models (a and b) and photo (c) of assembled probe. .............................................. 4

Figure 3: Pin Layout for excitation/feedback coils. ........................................................................ 5

Figure 4: Pin Layout for excitation/feedback coils on probe. ......................................................... 5

Figure 5: Picture of pickup coil pins. .............................................................................................. 6

Figure 6: Cable pictures and pin layouts. ........................................................................................ 6

Figure 7: Preamplifier with probe coaxial input. ............................................................................. 7

Figure 8: BNC-2110 with preamp coax input. ................................................................................ 8

Figure 9: Circuit diagram for a single channel of the FCS[7]. ........................................................ 9

Figure 10: FCS board and box. ...................................................................................................... 10

Figure 11: Picture of preamp at described settings. ....................................................................... 12

Figure 12: Probe mounted on sample. ........................................................................................... 13

Figure 13: Initial screen of MBN Acquire program. ..................................................................... 14

Figure 14: Picture of Universal Probe Settings (R and L of coils, etc.). ....................................... 14

Figure 15: Measurement tab with step numbers overlaid. ............................................................. 15

Figure 16: Analysis tab with step numbers overlaid. .................................................................... 16

Figure 17: This is the caption for the figure shown above. ........................................................... 17

Figure 18: Typical MBN measurement results shown on the analysis tab. ................................... 18

Figure 19: Typical MBN measurement results shown on the data display tab. ............................ 18

Figure 20: Monsanto Tensometer T20 tensile test machine. ......................................................... 22

Figure 21: Wedge clamp. .............................................................................................................. 22

Figure 22: HY-80 Sample with the bonded aluminum tabs and strain gage. ................................ 23

Figure 23: Strain gage with grid length and width of 1.57 mm. .................................................... 23

Figure 24: Schematic diagram of the flux-controlled MBN system. ............................................. 24

Figure 25: MBN signal. ................................................................................................................. 25

Figure 26: Stress-Strain curve. ...................................................................................................... 25

Figure 27: MBN envelope variations with stress parallel (upper) and transverse (lower) to the

direction of uni-axial stress. ........................................................................................ 27

Figure 28: MBN energy variations with stress parallel and transverse to the direction of uni-

axial stress. .................................................................................................................. 28

Figure 29: Angular MBN variations with stress. ........................................................................... 29

x DRDC Atlantic CR 2013-202

Figure 30: Dog-bone shape for high-stress deformations (upper) and octagonal-shape sample

for bi-axial stress study (lower). .................................................................................. 30

Figure 31: Schematic of MBN apparatus with feedback flux control [1]. .................................... 33

Figure 32: The instantaneous MBN voltage signal and the resulting RMS voltage from a

sinusoidal applied magnetic field [2]. ......................................................................... 33

Figure 33: The RMS Barkhausen voltage over one period for a quasi-static, sinusoidal applied

magnetic field of 12Hz, 1018 carbon steel [2] (upper). The corresponding

hysteresis (dashed line) and anhysteretic (solid line) curves (lower). M-, and M+

are the top and bottom of the M vs. H hysteresis curves. ............................................ 36

Figure 34: Plot of the normalized γ versus σx for the experimental data. ..................................... 39

Figure 35: A representation of the magnetic object. ..................................................................... 40

Figure 36: Change in the magnetic object when an external magnetic field is applied. The red

and green lines represent possible domain wall motions due to this field. ................. 40

Figure 37: The average number of 180 degree domain walls as a function of tensile stress

with zero applied magnetic field. ................................................................................ 43

Figure 38: Average number of 180 degree domain walls versus applied magnetic field at three

tensile stresses. ............................................................................................................ 44

Figure 39: The anhysteretic curve of magnetization versus magnetic field for the same

stresses as Figure 38. ................................................................................................... 45

DRDC Atlantic CR 2013-202 1

1 Introduction

Identification of significant residual stress variations and characterization of the resident stress

state within naval structures can contribute valuable information to risk assessments. This

provides some assurance that in-service induced stresses will not compromise structural integrity

under normal operating conditions. At present, X-ray diffraction (XRD) methods are used for

in-situ sampling of the residual stress state of structural steel surfaces. Although XRD techniques

are believed to offer the most accurate in-situ stress surveys, the need for surface preparation

restricts the scope of their application. A complementary technology for stress measurement is

based on Magnetic Barkhausen Noise Analysis (MBNA).

MBNA can provide a more rapid interrogation of a steel surface with the intention of identifying

local maxima in residual stress, which can then be confirmed with XRD. Barkhausen noise from

ferromagnetic steel materials is the result of abrupt domain wall motions that arise during the

magnetization process. The level of Barkhausen noise is affected by domain wall configurations

within the steel material and their interaction with pinning sites. These domain wall

configurations are strongly affected by the material’s stress state [1]. The measurement of

residual stresses in conventional steels has demonstrated good agreement with X-ray determined

residual stress [2].

The scope of the overall project will be to optimize the magnetization capability and

configuration of the MBNA measurement system for rapid measurement of stress in

ferromagnetic steels. This shall require three phases that are anticipated to take place over three

years [2]. During the first phase of this project, a prototype laboratory MBNA measurement

system was designed and constructed [3]. The phase II goal was to improve the functionality of

the laboratory system, conduct stress dependent measurements under elastic strain conditions and,

design and assemble components for a portable MBNA system.

This report describes progress achieved in Phase II of a project to develop a MBNA capability for

qualitative rapid residual stress analysis of structural ferromagnetic steels, particularly naval

steels such as HY-80. This includes modification of probes to provide greater proportional

sampling at varying depth within ferromagnetic steel (>0.25 mm), experimental testing and a

theoretical analysis of preliminary measurements.

1.1 References

[1] T.W. Krause, A. Pattantyus and D.L. Atherton, ‘Investigation of Strain Dependent Magnetic

Barkhausen Noise in Steel’, IEEE Trans. Magn. 31, (1995) 3376-3378.

[2] ‘Development of Magnetic Barkhausen Noise Analysis Residual Stress Measurement

System: for qualitative rapid residual stress analysis of structural ferromagnetic steels.’

SLA #: RMCC Serial #2009-0302-SLA ANNEX #: PA11029.

[3] T.W. Krause, P. McNairnay, V. Babbar, A. Samimi, P. Weetman and L. Clapham, “Rapid

Non-Destructive Residual Stress Analysis of Steel Structures: Phase 1, The Prototype Magnetic

Barkhausen Noise Analysis System“, DRDC Atlantic CR 2012-168, September 2012.

2 DRDC Atlantic CR 2013-202

2 Magnetic Barkhausen Noise Analysis System

Magnetic Barkhausen Noise (MBN) is the discrete jumps in magnetization that can be observed

during the magnetization process of ferromagnetic materials [1,2]. MBN results from the abrupt

motion of domain walls between pinning sites and therefore, depends on the intrinsic domain

structure within the sample [3-5]. The domain structure itself is affected by grain size [5],

texture[3,4], microstructure [6] and the presence of residual and applied stresses [5,6]. Therefore,

characteristics of the measured signal can be correlated with various physical properties of a

target ferromagnetic sample [3-6]. For the system described here, the stress induced changes to

the domain structure that affect the MBN signals are the target application.

2.1 Design and Components

The tetrapole MBN system described in this manual measures MBN signals under flux controlled

conditions, where a specified flux density at each of the poles of the U-core excitation magnet is

maintained [7]. The four pole configuration of the probe allows for rapid angular measurements

by means of flux superposition, while the flux control circuitry and software allows for

reproducible results under varying test conditions.

The system consists of three main components; the probe, the flux control system (FCS) and the

LabVIEW software. The probe generates a magnetic field using excitation coils wound around

magnetic U-cores. The combined probe and core is placed on the material under inspection

creating a magnetic circuit. The alternating magnetic field in the sample generates the desired

MBN signal, which is sensed by a small pickup coil at the centre of the probe. The generated

MBN signal is sent to a low noise preamplifier and subsequently to a National Instruments DAQ

card in a PC where it is recorded.

The probe consists of two Supermendur [7,10] U-core magnets, oriented with respect to each

other so that they complete two orthogonal magnetic flux paths when applied to a target steel

sample. The magnetic field generating system consists of an excitation coil, on each of the poles

that generates the time dependent variation of flux in the magnetic circuit, along with feedback

coils at the pole ends, which respond to changes in flux closest to the sample surface and which

are input to the FCS. The FCS controls the voltages driving the four excitation coils and reads the

voltage induced in the feedback coils. The feedback coil voltage is fed into an inverting summing

amplifier, which acts as an analog error correction that stabilizes the excitation waveform [7-9].

The FCS in combination with the four poles of the two U-cores facilitate the generation of

angular varying flux generation via flux superposition within the sample. Once the FCS has

achieved the specified waveform accuracy, the software applies a digital error correction (DEC)

algorithm to increase accuracy even further. The DEC samples the feedback coil voltage and

iteratively changes the excitation signal until the feedback signals match the target feedback

signal. After the DEC has achieved its accuracy threshold, the pickup voltage (MBN signal) is

sampled over a number of cycles. The software also allows the user to process the raw waveform

with several analysis tools.


2.2 Components and Assembly

This section lists the major components that make up the system and describes how it is

assembled. Each component is briefly described and its relation to other components outlined.

This section should allow the user to assemble all components of the MBN lab system in the

proper configuration. A block diagram of the major system components is shown in Figure 1

below. Each of these components will be described in detail below.

Figure 1: Block diagram of system components.

Probe Assembly 2.2.1

2.2.1.1 Probe

The probe consists of a 3D printed ABS housing, which holds two orthogonal U-cores each with

an excitation and feedback coil. In the centre of the probe is a pickup coil wound around a ferrite

core. Both the cores and pickup coil are spring loaded to ensure minimal liftoff from the sample

surface.

Figure 2a is a CAD model of all probe components. Figure 2b is a CAD model of the assembled

probe, while 2c shows a photo of the assembled probe. The tall core is held in the main housing

over the short core, which screws into the main housing with four springs. The pickup coil sits in

a copper shield holder, which slides into the pickup housing using a spring to hold it in place.

2.2.1.2 Coils

The excitation coils are wound from 36 AWG bond wire, have 500 turns and are 5.5 mm long.

The feedback coils are also wound from 36 AWG bond wire, have 50 turns and are 1 mm long.

The pickup coil is wound with 44 AWG bond wire, has 100 turns and is 1 mm long.


Figure 2: CAD models (a and b) and photo (c) of assembled probe.

A

B C


2.2.1.3 Connections

The probe has two sets of connections. The excitation and feedback coils are connected to a two

by eight header grid as shown in Figure 3. The pickup coil is connected separately (to avoid

interference) and has a two header receptacle with sockets as shown in Figures 4 and 5.

1 Vex 1 9 VS 1

2 VF 1 10 GND 1

3 Vex 2 11 VS 2

4 VF 2 12 GND 1

5 VF 3 13 GND 1

6 Vex 3 14 VS 3

7 VF 4 15 GND 1

8 Vex 4 16 VS 4

Figure 3: Pin Layout for excitation/feedback coils.

Figure 4: Pin Layout for excitation/feedback coils on probe.


Figure 5: Picture of pickup coil pins.

2.2.1.4 Cables

The probe uses two cables. The main cable carries the excitation feedback signals between the

probe and FCS. It is a shielded cable with sixteen 28 AWG colour coded cables, with banana plug

connectors on one end for the FCS and a two by eight header receptacle with sockets. The pickup

coil cable is a shielded coaxial cable with one end converted to a two pin header that connects to

the probe.

Figure 6: Cable pictures and pin layouts.

Pins


2.2.1.5 Preamplifier

The signal from the pickup coil is very weak and thus requires a low noise preamplifier. The

SR560 from Stanford Instruments, shown in Figure 7, is a configurable low noise preamplifier,

with multiple gain and filter settings. The coaxial connection from the probe plugs into the single

input of the preamplifier and the output connects to the position A1 on the BNC-2110.

Figure 7: Preamplifier with probe coaxial input.

2.2.1.6 BNC-2110

The BNC-2110 is a National Instruments adapter that converts coaxial input from the

preamplifier to the 68 pin standard National Instruments connection. The signals are then

transmitted to the National Instruments PCI 6133 DAQ [11] in the computer.

Flux Control System (FCS) and Power Supply 2.2.2

2.2.2.1 FCS

The FCS contains the flux feedback circuitry which, as mentioned, is an inverting summing

amplifier feedback loop. There are a total of four channels, one for each excitation/feedback coil

pair. The circuit diagram for a single channel is shown in Figure 9.


Figure 8: BNC-2110 with preamp coax input.


Figure 9: Circuit diagram for a single channel of the FCS[7].


The FCS is a custom printed circuit board powered by a ±24 V source. Regulators on the board

provide ±15 V and +5 V rails for various circuit components and cooling fans. Each channel has

two potentiometers that control the gain of the circuit and are calibrated prior to running the

system. The calibration procedure is described in Appendix A1. The FCS has two main sets of

connections; two NI 68 pin connectors that run to the PCI 6259 DAQ in the PC and 16 banana

plug connectors that are connected to the probe.

Figure 10: FCS board and box.

2.2.2.2 Power Supply

The power supply is a Power One HCC24-2.4-AG with low noise, low ripple and multiple

voltage outputs. The power supply provides ±24 V at a maximum current of 2.4 A each. To run

the system at ±29 V, the HCC5-6-AG, which provides ±5 V, can be connected in series.

PC and Software 2.2.3

2.2.3.1 National Instruments Cards

The PC contains two NI DAQs, which control the FCS and record the MBN signal. The PCI 6259

DAQ has two cables that connect to the FCS. The 6259 outputs the analog reference excitation

voltages and samples the actual excitation voltages, the feedback voltages and the shunt resistor

voltages. It also uses digital output to control mute functions as well as select voltage following or

flux feedback mode. The PCI 6133 DAQ is used solely to sample the MBN signal.


2.2.3.2 Software

The system is controlled and operated using a LabView code on the PC. Depending on the

application, settings can be changed in the program, which is highly customizable. The program

is split into three main sections; measurement, analysis and data display. The user sets the

measurement parameters in the measurement tab and chooses the automated analysis settings in

the analysis tab. Processed data is displayed in the data display tab. There are also universal

parameters that must be set during calibration of the system.

2.3 Operation

This section provides a step-by-step guide for making a basic MBN measurement. This section

should allow the user to power up all the equipment, setup the probe on a sample and run the

software to take a MBN measurement.

Powering Up the System 2.3.1

1. Turn on the PC and open the LabVIEW program named MBN Acquire v11.

2. Turn on the power supply to the FCS.

3. Turn on the FCS.

4. Turn on the Preamplifier.

Allow the components to heat up for a few minutes as temperature changes can affect the system

operation. Also ensure the FCS case fan is running to prevent overheating. The preamplifier

should be set to a gain of 60 dB (1000x) and the low pass filter should have a cut off frequency

set at 100 kHz (Figure 11).


Figure 11: Picture of preamp at described settings.

Setting up the Probe on a Sample 2.3.2

1. Orientate the probe axes relative to a reference direction on the sample.

2. Gently apply pressure to the probe using a clamp or other pressure application device until all

four poles are in contact with the sample surface.

3. Ensure that any sources of interference (AC power lines, magnets etc.) are far from the probe

and the cables connected to the probe.

The probe can also be mounted on the sample after the software settings have been chosen by the

user. The probe can also be applied to the sample manually, but will require a constant

application of pressure.


Figure 12: Probe mounted on sample.

Defining Universal Software Settings 2.3.3

The LabVIEW program front panel opens up on the measurement tab, Figure 13. Above this tab

are several universal settings that do not change from measurement to measurement. The standard

settings and values are shown in Figure 14 below. The table on the right contains values specific

to the probe being used. If the probe is replaced these values should be changed to reflect the new

probe’s coil inductances and impedances. All other universal settings do not need to be changed

for basic measurements.


Figure 13: Initial screen of MBN Acquire program.

Figure 14: Picture of Universal Probe Settings (R and L of coils, etc.).

Defining the Measurement Settings 2.3.4

1. Ensure the measurement tab is selected.

2. On the left side of the measurement tab select the “Waveform” tab.

3. Select signal type as “sine wave”.


4. Choose a signal frequency. Note: the convergence of the control algorithm is very sensitive to

the signal frequency. In general the frequency should be between 10 Hz and 50 Hz.

5. Choose the tetrapole angle (the angle at which the flux is generated in the sample). See

Figure 15.

6. On the “Waveform” tab select either the “Voltage” or “Flux” tab to choose voltage control or

flux control.

7. Voltage Control: Select the excitation voltage (Maximum voltage of excitation waveform).

8. Flux Control: Select the flux density (Maximum flux through feedback coils) and ensure that

the Digital Error Correction (DEC) is enabled.

9. Select the number of periods over which the software will take the measurement.

10. On the bottom right side of the “measurements” tab set the RMS threshold error. Note: it is

initially set to 1% and setting it above 3% often leads to inconsistent data. Inconsistent data is

defined as an MBN signal that is either not reproducible or indistinguishable from MBN

signals taken obtained from different samples or/and at different flux/voltage settings. As a

result, data taken above 3% RMS threshold error is of little value in characterizing a sample.

Figure 15: Measurement tab with step numbers overlaid.

Defining the Analysis Settings 2.3.5

1. On the “measurements” tab select “auto analyze” (located at the top left).


2. Select the “Analysis Setup” tab.

3. At the bottom of the screen enter directory in which the data will be saved and enter a sample

name.

4. Click the yellow button next to the data sets you wish to save (located at the bottom of the

tab). Note: a list with brief descriptions of each data set is in Appendix A2.

5. Select the “Data Display” tab.

6. Click the yellow button next to the data set you wish to save (located at the bottom of the

tab).

Figure 16: Analysis tab with step numbers overlaid.


Figure 17: This is the caption for the figure shown above.

Running the Measurement 2.3.6

1. Select the “Measurements” tab.

2. Click “Run Measurement” (located in the top left corner on the “Waveform” tab).

On the measurements tab, the operation of the system can be observed as it attempts to converge

toward the target voltage or flux waveform. The RMS error of the measured signal to the target is

displayed in the graph on the bottom right of the “measurements” tab. Once this drops below the

threshold the pickup coil’s signal will be sampled over the number of selected cycles. Once the

signal has been sampled, the software will analyze the data and display the results in the “Data

Display” tab. The data will also be saved to the previously specified directory.

2.4 Results

After the system has sampled the pickup coil signal, the software will save the data as well as

perform some initial analysis, which can be viewed in the “Analysis” and “Data Display” tabs.

Figures 18 and 19 show a sample of the raw and processed data in the two tabs, respectively.

The central graph in Figure 18 shows the power spectra of the pickup signal with and without

background noise and both time and frequency averaged. The window below this shows the time

waveforms of the pickup signal. The three graphs on the right show the dynamic power spectra

for the background pickup signal, the raw signal and the signal with background removed.


Figure 18: Typical MBN measurement results shown on the analysis tab.

Figure 19: Typical MBN measurement results shown on the data display tab.


The central graph in Figure 19 can be changed to show several different datasets but its main

function is to display the Barkhausen signal energy as a function of angle for sweep

measurement. The left side of the figure displays the reference voltages, excitation voltages,

excitation currents, time rate change of flux, flux density and the calculated Barkhausen noise

envelope. The right side of the figure shows some calculated values for a single measurement.

2.5 Analysis and Troubleshooting

This section covers the most common problems encountered while operating the system and how

to resolve them.

No Convergence 2.5.1

When the system is taking a measurement, the user should monitor the “RMS Error” graph on the

“Measurement” tab. This graph tracks the error in the voltage or flux waveform as a percentage of

the target. Once all four waveforms are beneath the specified threshold the pickup coil is sampled.

Occasionally the error will remain above the threshold for a long time indicating that the

waveforms are not converging on the specified target waveform. In such an event the

measurement should be stopped in order to prevent over heating of the probe coils. The FCS is

limited in its ability to control waveforms at all flux densities and frequencies and thus

non-convergence does not necessarily indicate a hardware problem, the following is a list of

possible hardware sources for no convergence.

1. Loose connections: A poor electrical connection can prevent the FCS from properly

controlling the waveform. The following connections should be checked:

- NI 68-PIN Cables to FCS should not be loose.

- Excitation/Feedback banana plugs at FCS.

- Excitation/Feedback connection at probe. Dust, dirt or other residue can prevent a

good connection.

2. Broken or damaged coil:

- Check the resistances of each excitation and feedback coil. All values should be

similar and should not change when the probe is moved (indicating a partial

connection).

3. Short circuit:

- Check for short circuits between excitation/feedback coils and the magnetic cores.


2.6 References

[1] Chikazumi, S. and Charap, S. H. Physics of Magnetism, Krieger, Florida, 1964, p. 260.

[2] B. D. Cullity and C. D. Graham, Introduction to Magnetic Materials, A John Wiley & Sons,

Inc., Publication, Second Edition (2009), p. 456.

[3] T.W. Krause, L. Clapham, and D.L. Atherton, J. Appl. Phys. 75, pp. 7983-7988 (1994).

[4] T. W. Krause, K. Mandal and D. L. Atherton, Modelling of Magnetic Barkhausen Noise in

Single and Dual Easy Axis Systems in Steel, J. Magn. Magn. Mater. 195, (1999) 193-205.

[5] T. W. Krause, L. Clapham, A. Pattantyus and D. L. Atherton, Investigation of the Stress-

Dependent Magnetic Easy Axis in Steel Using Magnetic Barkhausen Noise, J. Appl. Phys. 79, (7), 15

April (1996) 4242-4252.

[6] D.C. Jiles, Dynamics of Domain Magnetization, Czecholsovak J. of Physics, 50, pp. 893-988

(2000).

[7] White, S. A. A Barkhausen Noise Testing System for CANDU® Feeder Pipes. Queen’s

University, Kingston, Ontario, Canada. 2009, p 60.

[8] S. White, T. W. Krause and L. Clapham, Measurement Science and Technology, 18,

pp. 3501-3510 (2007).

[9] S. White, L. Clapham and T.W. Krause, “A multi-channel magnetic flux controller for

periodic magnetizing conditions.” IEEE Trans. Instr. and Meas. 61, no. 7, (2012) pp. 1896-1907.

[10] H.L.B Gould and D.H. Wenny, “Supermendur a new rectangular loop magnetic material,”

Elect. Eng., vol. 76, no. 3, pp. 208–211 1957).

[11] National Instruments Corporation, www.ni.com. DAQ M Series, M Series User Manual,

2008.


3 Evaluation of Stress Dependence of Magnetic Barkhausen Noise in an HY-80 Steel Sample

The dependence of magnetic Barkhausen noise (MBN) on uniaxial tensile stress in a HY-80 steel

sample was investigated. The HY-80 plate sample had dimensions of 200×34×0.75 mm. HY-80 is

a high strength steel with a typical grain size of about 7 micron and yield strength of 550 MPa.

The goal of this study was to evaluate the stress dependence of Barkhausen noise for

measurement of in situ residual stress of submarine hull. The experimental apparatus consists of a

tensometer and strain gages for uni-axial tensile test, and a flux-controlled MBN probe for

magnetic measurements. The results indicate an increase of the MBN signal with increasing

applied uniaxial tensile stress, which is consistent with previously measured behavior of steels

under applied tensile stress conditions.

3.1 Introduction

Magnetic Barkhausen Noise (MBN) results from abrupt local changes in magnetization that may

be sensed by a pickup coil during the magnetization of a ferromagnetic material [1, 2]. MBN is

most often associated with motion of domain walls between pinning sites, and is therefore a

function of the domain structure within ferromagnetic materials [3-5]. The domain structure itself

is affected by grain size [5], texture [3, 4], microstructure [6] and the presence of residual and

applied stresses [5, 6]. Therefore, characteristics of the measured signal can potentially be an

indication of various physical properties of a particular ferromagnetic material [3-6], with the

potential to be sensitive to the residual stress state of the material.

This report documents the effects of a uniaxial tensile stress, applied to an HY-80 steel sample,

on MBN measurements, for development of MBN as a stress measurement tool [7]. The MBN

measurements are performed under flux controlled conditions, where a specified flux density at

each of the poles of the U-core excitation magnet is maintained [8-10].

3.2 Experimental Set-up and procedure

Uni-Axial Testing 3.2.1

Uni-axial tensile stress is applied using a Monsanto Tensometer T20 tensile test machine, which

features digital display of force and crosshead speed. As shown in Figure 20, the tensometer is a

horizontal screw-driven device with a constant crosshead speed of 1 mm/min and accuracy of 1%

for both crosshead speed and applied load. This speed provides a quasi-static tensile test with a

low strain rate, which is required to achieve uniform strain in steel samples and to minimize the

errors in the load cell output [11, 12].


Figure 20: Monsanto Tensometer T20 tensile test machine.

3.2.1.1 Gripping Mechanism

The tensile machine is equipped with wedge grips as shown in Figure 21. According to ASTM

standards [13], for proper gripping and alignment of samples, the entire length of each wedge face

must be in contact with sample ends. Therefore, roughed-surface square aluminum tabs were

bonded to sample ends using epoxy as shown in Figure 22. These tabs provide proper gripping,

which prevents slippage, minimizes stress concentration induced by the grips, and accommodates

a nonmagnetic component in the grips, important for decoupling potential magnetization in the

primarily steel tensometer.

Figure 21: Wedge clamp.


Figure 22: HY-80 Sample with the bonded aluminum tabs and strain gage.

3.2.1.2 Strain Gages

For accurate strain measurements, one uni-axial strain gage (EA-06-062AQ-350,

Micro-Measurements Group) with a gage factor of 2.115±0.15% was mounted on each of the

samples. These gages had a grid length and width of 1.57 mm and are mounted in the middle of

the samples.

Figure 23: Strain gage with grid length and width of 1.57 mm.

Flux-Controlled Magnetic Measurement System 3.2.2

Control of flux in the magnetic circuit is found to be an effective method to obtain consistency in

MBN measurements by reducing the distortions in the periodic magnetic flux waveforms [9, 14,

15,]. This study uses a novel hybrid flux controller, which was designed in our research group

[10]. The controller combines the real time control of analog feedback with the accuracy of an

iterative digital feedback algorithm to allow rapid measurement and effectively minimize errors

in the control loop. This is in contrast to conventional flux controllers, which use either digital or

analog feedback, leading to slow or inaccurate measurements.


The deviations from a sinusoidal flux waveform, i.e., the form factor error, is <0.1% for

excitation frequencies higher than 2 Hz, and the root-mean-square (rms) flux rate error is <1% for

excitation frequencies higher than 10 Hz [10]. Figure 23 shows a simplified schematic diagram of

the flux-controlled MBN system. A digital-to-analog converter (DAC) generates a reference

voltage, 𝑉𝑟𝑒𝑓 , which is then fed into an analog feedback amplifier. Excitation coil voltage, 𝑉𝑒𝑥,

and measured feedback coil voltage, 𝑉𝐹, are sampled by an analog-to-digital converter (ADC) and

processed through a personal computer (PC). 𝑉𝑟𝑒𝑓 is modified in each iteration and the control

loop repeats until 𝑉𝐹 meets the target feedback coil voltage.

The probe is a Supermendur tetrapole [10], which has two U-shaped cores with 500 turn

excitation coil and a 50 turn feedback coil on each of its poles. The feedback coils monitor the

flux at the excitation magnet poles, which are at the closest distance to the sample surface. The

cylindrically symmetric pick-up coil is spring loaded with its solenoid winding axis normal to the

sample surface. The pick-up assembly has 100 turns of 44 AWG copper coils with a ferrite core

and a conductive brass shield to minimize the sensing radius for the probe configuration. The

90% sensing radius of the pick-up coil is about 2.4 mm at 30 Hz. The pick-up coil couples to

magnetization changes projected out of the sample surface. The voltage induced into the pick-up

coil is fed to an Ithaco 1201 preamplifier and the low frequency excitation signal is filtered out.

Therefore, it is the high frequency Barkhausen emissions (>1 kHz), which contribute to the

voltage induced in the pick-up coil. The probe is mounted about 1 cm away from the strain gage.

Figure 24: Schematic diagram of the flux-controlled MBN system.

Measurement Analysis 3.2.3

A typical MBN signal has two bursts of energy in each full cycle of the sinusoidal applied

magnetic flux rate with both positive and negative components as shown in Figure 25. The

envelope signal labeled “MBN” is calculated to simplify data analyses. MBN energy (𝐵𝑁𝐸) is

then defined as the time integral of the voltage squared signal. The system uses a statistical

approach, which is implemented in LabVIEW 8.2, to produce a root-mean-square MBN envelope

(𝐵𝑁𝑒𝑛𝑣 = 𝑉𝐵𝑁(𝑟𝑚𝑠)) of the induced voltage. The total energy is then calculated as [16]:

𝐵𝑁𝐸 = ∫(𝐵𝑁𝑒𝑛𝑣)2𝑑𝜑, (1)

in which 𝜑 is the feedback signal phase corresponding to time within the cycle.


Figure 25: MBN signal.

3.3 Results

Stress-strain plot 3.3.1

The sample was progressively stressed up to 50% of its yield strength (about 227 MPa) and

surface MBN measurements were taken. Figure 26 plots the engineering stress (force divided by

the initial cross sectional area of the sample) versus strain. Linearity of stress-strain plot was

monitored throughout the measurements in order to ensure a uniform stress along the sample, and

to avoid any misalignment due to improper gripping.

Figure 26: Stress-Strain curve.


MBN Envelopes 3.3.2

The variations in MBN emissions with stress were investigated at a 30 Hz excitation frequency

and 100 mT flux density measured at the excitation magnet poles. This frequency and flux level is

low enough to maintain a constant static value for the domain wall width, and to minimize the

disturbance of domain wall geometry, while providing rapid MBN measurements. The sample

was demagnetized prior to each measurement to remove any residual magnetization. The results

were reproducible with less than 1% variation. Figure 27 plots the envelope variations with stress

for directions parallel and perpendicular to applied stress. The main feature of the envelopes is the

increase in the peak height and sharpness under conditions of increasing tensile stress. Due to

Poisson’s effect, a transverse compressive strain is induced, which decreases the peak height and

widens the envelope shape.


Figure 27: MBN envelope variations with stress parallel (upper)

and transverse (lower) to the direction of uni-axial stress.


MBN Energy 3.3.3

The variations in peak height and shape of the envelopes were quantified by introducing the total

energy (𝐵𝑁𝐸), as described by Eq. 1 and plotted in Figure 28. The observed MBN energy

variations are similar to energy variations of high-strength SAE 9310 steel, as observed earlier by

Mierczak et al [17]. As shown in Figure 28, the energy level transverse to the applied stress

direction is higher than the energy parallel to the applied tensile stress with sharper variations.

This suggests a magnetic anisotropy in the sample, attributed to roll magnetic anisotropy [18].

Figure 28: MBN energy variations with stress parallel and

transverse to the direction of uni-axial stress.

Angular MBN Measurements and Magnetic Anisotropy 3.3.4

Angular surface MBN measurements were taken with the excitation field progressively oriented

at eighteen equally spaced angles over 180◦ (i.e., 10◦ apart) using the tetrapole. Figure 29 shows

the polar plot of surface MBN energies. Under zero stress condition, there is a strong magnetic

easy axis along the width of the sample. This easy axis is likely due to residual compressive

stresses within the as-received sample. By further increasing the uni-axial stress, another easy

axis emerged along the stress direction, and the initial easy axis due to residual stress becomes

smaller.


Figure 29: Angular MBN variations with stress.

3.4 Summary and Future Work

Preliminary flux-controlled Barkhausen measurements were performed on a HY-80 steel sample

under applied uni-axial tensile stress conditions. Variations of MBN signal were examined as a

function of stress up to 50% of the sample’s yield strength. For the next step of our studies, we

have prepared a standard dog-bone shape sample to study the influence of higher stress levels and

plastic deformation on Barkhausen signals as shown in Figure 30(a) below. A more complex case

of bi-axial stress will also be investigated, in which an octagonal shaped sample of HY-80 as

shown in Figure 30(b) will be used.


(a)

(b)

Figure 30: Dog-bone shape for high-stress deformations (upper)

and octagonal-shape sample for bi-axial stress study (lower).

3.5 References

[1] Chikazumi, S. and Charap, S. H. Physics of Magnetism, Krieger, Florida, 1964, p. 260.

[2] B. D. Cullity and C. D. Graham, Introduction to Magnetic Materials, A John Wiley & Sons,

Inc., Publication, Second Edition (2009), p. 456.

[3] T.W. Krause, L. Clapham, and D.L. Atherton, Characterization of the magnetic easy axis in

pipeline steel using magnetic Barkhausen noise, J. Appl. Phys. 75, pp. 7983-7988 (1994).

[4] T. W. Krause, K. Mandal and D. L. Atherton, Modelling of Magnetic Barkhausen Noise in

Single and Dual Easy Axis Systems in Steel, J. Magn. Magn. Mater. 195, (1999) 193-205.

[5] T. W. Krause, L. Clapham, A. Pattantyus and D. L. Atherton, Investigation of the

Stress-Dependent Magnetic Easy Axis in Steel Using Magnetic Barkhausen Noise, J. Appl. Phys.

79, (7), 15 April (1996) 4242-4252.

[6] D.C. Jiles, Dynamics of Domain Magnetization, Czecholsovak J. of Physics, 50,

pp. 893-988 (2000).


[7] ‘Development of Magnetic Barkhausen Noise Analysis Residual Stress Measurement

System: Phase II, Development of Portable MBNA System’, SLA#: RMCC Serial#2009-0302-

SLA, ANNEX #: PA11029, Oct. 2012.

[8] White, S. A. A Barkhausen Noise Testing System for CANDU® Feeder Pipes. Queen’s

University, Kingston, Ontario, Canada. 2009, p 60.

[9] S. White, T. W. Krause and L. Clapham, Measurement Science and Technology, 18,

pp. 3501-3510 (2007).

[10] S. White, L. Clapham and T.W. Krause, “A multi-channel magnetic flux controller for

periodic magnetizing conditions.” IEEE Trans. Instr. and Meas. 61, no. 7, (2012) pp. 1896-1907.

[11] ASTM E112-12, Standard Test Methods for Determining Average Grain Size, (2013).

[12] Joseph R. Davis, Tensile Testing, ASM International, 2nd edition (2004).

[13] ASTM E8/E8M-11, Standard Test Methods for Tension Testing of Metallic Materials,

(2012).

[14] O. Stupakov, J. Pala, T. Takagi, and T. Uchimoto, Governing conditions of repeatable

Barkhausen noise response, J. Mag. Mag. Mater., 321 (2009) 2956-2962.

[15] H. Patel, S. Zurek T. Meydan, D. Jiles and L. Li, A new adaptive automated feedback

system for Barkhausen signal measurement, Sensors and Actuators A, Vol. 129 (2006) 112-117.

[16] H. Kwun, Investigation of the dependence of Barkhausen noise on stress and the angle

between the stress and magnetization directions, J. Magn. Magn. Mater. 49 (1985) 235-240.

[17] L. Mierczak, D. C. Jiles, G. Fantoni, A New Method for Evaluation of Mechanical Stress

Using the Reciprocal Amplitude of Magnetic Barkhausen Noise, IEEE. Trans. Mag. 47 (2) (2011)

459-465.

[18] L. Clapham, C. Heald, T. Krause and D.L. Atherton, The Origin of a Magnetic Easy Axis

in Pipeline Steel, J. Appl. Phys. 86, (1999) 1574-1580.


4 Biaxial Stress Models

Magnetic measurement of residual stress, or at a minimum, comparison of residual stresses over

an area such as a submarine hull, will require a means of determining relevant magnetic

parameters and how they are modified by stress. This report summarizes the current progress of

two models that will be used to estimate the stress in high strength steels using surface Magnetic

Barkhausen Noise (MBN) measurements. In both models, the MBN is first used to construct a

local magnetization (M) versus applied magnetic field (H) curve. The first model (I) is

phenomenological and based on the magnetization model of Jiles and Atherton [D. Jiles and D.

Atherton, Theory of Ferromagnetic Hysteresis, J. of Mag. and Mag. Mat., 61, 48-60, (1986).]. All

physical details are described by various fitting coefficients. Data from the companion report

[A. Samimi, T. W. Krause and L. Clapham, Evaluation of Stress Dependence of Magnetic

Barkhausen Noise in a HY-80 Steel Sample, DRDC Report, March 2013] is used in the results

section of this model. The second model (II) is the more physical magnetic object model

[T. Krause, L.Clapham, A. Pattantyus and D. Atherton, Investigation of the stress-dependent

magnetic easy axis in steel using magnetic Barkhausen noise, J. Appl. Phys., 79, 4242, (1996)]

which creates idealized magnetic domain configurations for each grain. Using statistical

mechanical arguments, we can then model the anhysteretic M versus H curve.

4.1 Background

Magnetic Barkhausen Noise (MBN) arises from discontinuous changes in the magnetization of a

material when subjected to an applied magnetic field. An excitation coil produces a magnetic

field in the sample. The resulting discontinuous magnetization changes generate a voltage in the

pickup coil (𝑉𝐵𝑁). A schematic of a surface Barkhausen apparatus which uses a feedback coil for

flux control is shown in Figure 31 [1,2].

It is well known that stress is a significant factor in the magnetization response, primarily through

the magnetostrictive effect [3]. Conceptually therefore, the magnetization response of a system

can give information on its stress state. Extracting this information from surface MBN would

provide a valuable non-destructive evaluation tool. In order to use this, one must first model the

relation between stress and magnetization response. Models I and II to be discussed in this report

are two such possibilities. Model I is a phenomenological model that is simpler to implement than

Model II. However, it requires a number of fitting parameters to be determined. Although it can

provide useful information of the system, it lacks the predictive power to answer more

fundamental physical questions such as the effect of grain size on magnetization response.

Model II requires more theoretical and computational resources than Model I, it is based on the

magnetic object model and directly accounts for magnetic domain structures in the material. As

such, one can examine more physical effects than Model I.


Figure 31: Schematic of MBN apparatus with feedback flux control [1].

After some signal processing, 𝑉𝐵𝑁 and the resulting RMS (VRMS) values will look like that of

Figure 32. [ 2].

Figure 32: The instantaneous MBN voltage signal and the resulting

RMS voltage from a sinusoidal applied magnetic field [2].


4.2 Obtaining Magnetization Curves as a Function of Applied Magnetic Field

In the cases considered, the applied magnetic field is sinusoidal. The magnetic field generated

from the field coil will be denoted by �̃�(𝑡), which is related to the current in the coil by Ampere’s

law. The field within the sample depends on the relative permeability of the sample and the

magnetic circuit as well as the existence of flux leakage. It is assumed that the field in the sample,

𝐻(𝑡) is linearly related to the field produced in the coil:

𝐻(𝑡) = 𝑓𝐻�̃�(𝑡) (1)

where 𝑓𝐻 is a factor that needs to be experimentally or theoretically determined. For the types of

materials being discussed, it will generally be on the order of 10−4.

As observed in Figure 32, the Barkhausen voltage is a rapidly oscillating function. The smoother

RMS voltage will be used as a method to determine the magnetization response in the sample. It

has been postulated that the RMS voltage can be related to the change of magnetization using a

“RMS jump sum” [4]:

𝑉𝑅𝑀𝑆(𝑡) ∝ ∆|𝑀(𝑡)| (2)

where ∆|𝑀(𝑡)| is the change in magnitude of the magnetization in the sample. Note that this is

the local magnetization over the region being examined, not the system magnetization. The local

magnetization is appropriate for this work as we are investigating the local stress properties as

well.

The proportionality constant in equation (2) is difficult to quantify because of the properties of the

pick-up coil and the relation between magnetization change, out-of-plane moment rotation and

generated eddy currents. At this point, it will be left as the unknown parameter 𝑓𝑚. Therefore,

𝑉𝑅𝑀𝑆(𝑡) will be written as:

𝑉𝑅𝑀𝑆(𝑡) ≡ ∆|�̃�(𝑡)| = 𝑓𝑚∆|𝑀(𝑡)| (3)

Since 𝑉𝑅𝑀𝑆 cannot distinguish the direction of change of magnetization, the change in direction

must be determined from the physics of the system. In Figure 33 we examine in more detail a

particular experiment from the companion report [2]. Figure 33a shows the RMS voltage

response and 33b shows the resulting magnetization versus applied magnetic field curves. The

ranges 0 T/2 and T/2 T in 3a each represent half of the period. One of the half periods will

correspond to positive change in magnetization and the other negative. Since �̃�(𝑡) = ∫ 𝑑�̃�, we

can tell by the area under the curve of each half-period, which corresponds to the top curve

(decreasing magnetization with decreasing field: �̃�+, d�̃�<0 ) and which to the bottom

(increasing magnetization with increasing field �̃�-, d�̃�>0).

When constructing the hysteresis curve, we must also find the values of the maximum and

minimum magnetizations obtained. Referring to Figure 33a, times 0 and T will correspond to the

maximum magnetization and time T/2 will correspond to the minimum magnetization. We will

assume that the curve is symmetric so that �̃�𝑚𝑎𝑥 = −�̃�𝑚𝑖𝑛, which is found from:

�̃�𝑚𝑎𝑥 =1

4∑ |∆�̃�𝑖|𝑖 =

1

4∑ 𝑉𝐵𝑘,𝑖𝑖


The hysteresis curve can now be created using:

�̃�(𝑡) = ∫ 𝑑�̃�𝑡

𝑜≈ �̃�𝑚𝑖𝑛 + ∑ ∆�̃�𝑖

𝑖𝑡𝑖=1 (4)

Plotting �̃�(𝑡) versus �̃�(𝑡) gives the hysteresis curve shown by the dashed lines in Figure 33b.

While the hysteresis curve is useful for estimating losses and pinning effects in the system, the

present work is concerned with stress effects. For this, one needs only the anhysteretic curve. The

anhysteretic curve is the magnetization response that would occur if there were no hysteresis in

the sample and is approximated as the average between the top and bottom halves of the

hysteresis curve �̃�𝑎𝑛(�̃�) = (�̃�+(�̃�) + �̃�−(�̃�))/2.

In the quasi-static case considered here, the primary contribution to hysteresis is pinning defects.

These defects are also the reason one detects a Barkhausen signal. Thus a true anhysteretic

response would be impossible to observe with Barkhausen methods. Essentially, the Barkhausen

response is a technique used to track the local hysteretic magnetization response in the system.

This hysteretic magnetization response in then used to estimate an ideal anhysteretic response in

order to use the existing physical theoretical framework [5,6]. From this point on, we will drop

the subscript “an” from �̃�𝑎𝑛 as we will only be dealing with the anhysteretic magnetizations.

The smaller the hysteresis, the more accurate this approximation will be. Therefore, it is

important to perform the experiments as close to the quasi-static approximation as possible. The

solid black line in Figure 33b shows the anhysteretic curve calculated for this experiment.


Figure 33: The RMS Barkhausen voltage over one period for a quasi-static, sinusoidal

applied magnetic field of 12Hz, 1018 carbon steel [2] (upper). The corresponding

hysteresis (dashed line) and anhysteretic (solid line) curves (lower). �̃�-,

and �̃�+ are the top and bottom of the �̃� vs. �̃� hysteresis curves.

4.3 Model I: The Phenomenological Model

Theory 4.3.1

A phenomenological relationship between the magnetization, applied magnetic field and stress,

based on the Jiles-Atherton model [5,6] and extended to two dimensions is given by [7,8]:

�̃�-, d�̃�>0 �̃�+, d�̃�<0

�̃�+, d�̃�<0

�̃�-, d�̃�>0 �̃�

�̃�


𝑀𝑥

𝑀𝑆𝑥= ℒ (

|𝑯𝑒|

𝑎𝑥)

𝐻𝑒,𝑥

|𝑯𝑒|

(5a)

𝑀𝑦

𝑀𝑆𝑦= ℒ (

|𝑯𝑒|

𝑎𝑦)

𝐻𝑒,𝑦

|𝑯𝑒|

(5b)

Where the Langevin function ℒ(𝑥) ≡ coth(𝑥) −1

𝑥 is used and comes from integrating over all

possible magnetization orientations in the Boltzmann distribution function.

It is assumed that 𝑎𝑥 = 𝑎𝑦 = 𝑎 =𝑘𝐵𝑇

𝜇𝑜𝑚 , 𝑘𝐵 is Boltzmann’s constant, 𝑇is temperature, 𝜇𝑜 is the

permeability of free space and m is the magnitude of a single magnetic moment. A value of

𝑎 = 3000 is common for these types of materials [9]. The terms 𝑀𝑆𝑥 = 𝑚𝑁𝑥 and 𝑀𝑆𝑦 = 𝑚𝑁𝑦

are the saturation magnetizations in the x and y directions, respectively. If we assume that the

180o domain density (N) is constant, then the 180

o domain densities for each direction (Nx and Ny)

will sum to N. We will therefore write 𝑀𝑆𝑥 = 𝑥𝑀𝑆 and 𝑀𝑆𝑦 = (1 − 𝑥)𝑀𝑆, with x=Nx /N. If

x ≠ 1/2 , there is an asymmetry in initial conditions such as a residual stress in the system.

Applying more stress or a magnetic field to the system will change the domain fractions, but

those will be accounted for through the other terms in equations (5a) and (5b).

The effective magnetic field 𝐻𝑒 can be written as:

𝑯𝑒 = (𝐻𝑥 + 𝛾𝑀𝑥 + 𝛾′𝑀𝑦 , 𝐻𝑦 + 𝛾′𝑀𝑥 + �̅�𝑀𝑦 ) (6)

Where 𝛾 = 𝛼 + 𝛽𝜎𝑥 + 휀𝜎𝑦 , 𝛾′ = 𝛼′ and �̅� = �̅� + �̅�𝜎𝑥 + 휀�̅�𝑦, with the coefficients being

related to the magnetostriction and interband coupling effects [9,10].

Again, what is actually be measured is |�̃�| and �̃�, not M and H (which are internal to the

sample). In addition, surface Barkhausen analysis doesn’t give the individual x or y components

of the magnetization, only magnitude.

Assuming the components of magnetization can be written as �̃�𝑥 = cos(𝜑)�̃� and

�̃�𝑦 = sin (𝜑)�̃�, equations (5) and (6) can be written as;


cot(𝜑) =𝑀𝑆𝑥

𝑀𝑆𝑦[

𝑓𝐻�̃�𝑥+�̃�(γ cos(𝜑)+𝛾′ sin(𝜑))

𝑓𝐻�̃�𝑦+�̃�(γ′ cos(𝜑)+�̅� sin(𝜑))], (7)

[�̃�𝑥

𝑀𝑆𝑥]

2

+ [�̃�𝑦

𝑀𝑆𝑦]

2

= [ℒ(|𝑯𝑒|)]2, (8)

𝑯𝑒 = (𝑓𝐻�̃�𝑥 + �̃�(γ cos(𝜑) + 𝛾′ sin(𝜑)), 𝑓𝐻�̃�𝑦 +

�̃�(γ′ cos(𝜑) + �̅� sin(𝜑)) ) (9)

Equations (7) to (9) are the basis of the model. Equation (7) can be written as a fourth order

polynomial equation and solved analytically [11] for 𝜑 in terms of the other unknowns. Using

equations (7) to (9) for differing values of applied magnetic field, one can conceptually solve for

the four parameters x, 𝛾, 𝛾′and �̅� simultaneously. Using a set of known stresses, these parameters

can be used to characterize the coefficients 𝛼, 𝛽, 휀, 𝛼′, �̅�, �̅� and 휀 ̅and can then be used to find any

unknown stress acting on the system by:

[𝜎𝑥

𝜎𝑦] = 𝐷 [

휀̅ −휀−�̅� 𝛽

] [𝛾 − 𝛼

𝛾′ − �̅�], 𝐷 = (𝛽휀̅ − �̅�휀)−1

Results: Application to uniaxial stress. 4.3.2

In the absence of 2D stress data, we have tested the model with 1D results (𝜎𝑦 = 0) from the

companion report [2]. The method correctly predicts that 𝛾 = 𝛼 + 𝛽𝜎𝑥. As we see the results in

Figure 34 are very close to linear. The coefficients 𝛼, 𝛽 can then be found from the slope and

intercept of this curve and used to determine stress from magnetic Barkhausen measurements.


Figure 34: Plot of the normalized 𝛾 versus 𝜎𝑥 for the experimental data.

4.4 Model II: The Magnetic Object Model

A magnetic object is an idealized closed magnetic domain structure. For this work, the chosen

object is schematically represented in Figure 35 [12]. For the small grain-sized high-strength

steels under consideration, it is approximated that each grain is a magnetic object. External

magnetic fields (H) and stresses () can then be applied to this object.

Theory 4.4.1

By energy minimization, the applied stress and magnetic field will influence the number of 180

degree domain walls in the system. The applied magnetic field will also shift over the domain

walls as shown in Figure 36. The red lines represent how the first 180 degree domain wall could

move, resulting in all the moments aligning in the H direction to the left of the red lines. It is also

possible that the second domain wall could move (represented by the green lines) and so on. The

distance the ith wall has moved (ti) is also shown on the figure, which at a minimum is the size of

the unit cell of the material.


Figure 35: A representation of the magnetic object.

Figure 36: Change in the magnetic object when an external magnetic field is applied.

The red and green lines represent possible domain wall motions due to this field.


The energy of a magnetic object with n 180 degree domain walls accounting for magneto-elastic,

domain wall, Zeeman and demagnetization energies is [12]:

𝐸𝑛 = −3

2𝜆100{𝑉𝑛,180[𝜎1 cos2(𝜃) + 𝜎2 sin2(𝜃)] + 𝑉𝑛,90[𝜎1 sin2(𝜃) +

𝜎2 cos2(𝜃)]} + 3𝛿𝜆100𝐴𝑛,180(𝜎1 cos2(𝜃) + 𝜎2 sin2(𝜃)) + 𝛾180𝐴𝑛,180 −

𝜇𝑜𝑯 ∙ 𝑴𝑛 + 𝜇𝑜𝑁𝑀𝑛2 (10)

with 180 degree domain volume 𝑉𝑛,180 = 𝑎𝑏𝑇 −𝑇

2∑ (

𝑏

𝑛− 2𝑡𝑖)

2𝑛𝑖=1 and 180 degree cross-

sectional area 𝐴𝑛,180 = 𝑇(𝑎𝑛 − 𝑏) + 2𝑇 ∑ 𝑡𝑖𝑛𝑖=1 . The total magnetization is proportional to the

amount of domain wall shift: 𝑴𝑛 = 2𝜇𝑇𝑎 ∑ 𝑡𝑖𝑛𝑖=1 𝑥180 and N is the demagnetization factor.

Equation (10) can be written in a form convenient for calculation of probability distributions by

factoring out the wall displacements:

𝐸𝑛,{𝑡𝑖}(𝜎1, 𝜎2, 𝐻) = 𝑎𝑛(𝜎1, 𝜎2) + 𝑏𝑛(𝜎1, 𝜎2, 𝐻) ∑ 𝑡𝑖𝑛𝑖=1 +

𝑐𝑛(𝜎1, 𝜎2, 𝐻) ∑ 𝑡𝑖2𝑛

𝑖=1 (11)

where the subscript {𝑡𝑖} symbolizes the set of all wall displacements. That is, for an object with n

walls, wall 1 could move over a distance t1, wall 2 a distance t2 and so on, up to wall n. a distance

of tn. Thus {𝑡𝑖} represents all possible combinations of these displacements. The coefficients in

equation (11) will be shown in more detail later.

4.4.1.1 Boltzmann Distribution

It is assumed that the system is large enough that Boltzmann statistics are applicable at

equilibrium. I.e., the magnetic objects can be considered as distinguishable “particles” from a

statistical mechanics point of view. Boltzmann statistics requires the use of Stirling’s

approximation in its derivation. A 5cm x 5cm sample with magnetic object sizes of 25m x m

has 424 magnetic objects. For 100 objects, the error in Stirling’s approximation is about 1%. For

1000 objects, the error is about 0.07%. The Boltzmann distribution for this system is given

by [13]:

𝑃𝑛,{𝑡𝑖}(𝜎1, 𝜎2, 𝐻) =𝑒

−𝐸𝑛,{𝑡𝑖}

/Ω

𝑍(𝜎1,𝜎2,𝐻), (12)

where Ω is the Boltzmann factor and Z is the partition function:

𝑍(𝜎1, 𝜎2, 𝐻) = ∑ ∑ 𝑒−𝐸𝑛,{𝑡𝑖}/Ω𝑏/2𝑛

{𝑡𝑖}=−𝑏/2𝑛𝑛 → ∑ 𝑒− [𝑎𝑛 ]/Ω𝑛 (𝐼𝑛)𝑛,

𝐼𝑛 = ∑ 𝑒−[ 𝑏𝑛𝑡 +𝑐𝑛𝑡2 ]/Ω𝑡


The Boltzmann factor will not be equal to kBT because it also accounts for the size of and number

of states in the magnetic objects.

4.4.1.2 Expectation Values

The average number of 180 degree domain walls is given by:

< 𝑁(𝜎1, 𝜎2, 𝐻) >= ∑ ∑ 𝑛𝑃𝑛,{𝑡𝑖}(𝜎1, 𝜎2, 𝐻)𝑏/2𝑛{𝑡𝑖}=0𝑛 =

1

𝑍∑ 𝑛𝑒− [𝑎𝑛 ]/Ω(𝐼𝑛)𝑛

𝑛 (13)

and the average magnetization:

< 𝑀(𝜎1, 𝜎2, 𝐻) >=2𝜇𝑇

𝑍∑ 𝑒− [𝑎𝑛 ]/Ω𝑛(𝐼𝑛)𝑛−1𝐽𝑛𝑛 ,

𝐽𝑛 = ∑ 𝑡𝑒−[ 𝑏𝑛𝑡 +𝑐𝑛𝑡2 ]/Ω𝑏/2𝑛𝑡=−𝑏/2𝑛 (14)

4.4.1.3 Extension to Multiply Oriented Grains

In this case it is assumed that the magnetic objects are oriented at j possible angles 𝜙𝑗. One makes

replacements 𝜃 → 𝜃 − 𝜙𝑗 and 𝛽 → 𝛽 − 𝜙𝑗 and accounts for a probability, 𝑊𝑗, that the magnetic

object is oriented at angle 𝜙𝑗. Equation (12) is generalized to:

𝑃𝑗,𝑛,{𝑡𝑖}(𝜎1, 𝜎2, 𝐻) =𝑊𝑗𝑒

−𝐸𝑗,𝑛,{𝑡𝑖}

/Ω

𝑍(𝜎1,𝜎2,𝐻) (15)

This will be examined in more detail in a future work.

Results: Application of Model II to uniaxial stress. 4.4.2

We examine the ideal case when all the grains are oriented parallel to the applied stress and

magnetic field: 𝜎1 = 𝜎, 𝜎2 = 0 and 𝜃 = 𝛽 = 0. Parameters nm, 100=2.07x10-5

,

180=1.6x10-3

J/m2 and a=b=T=5 m are chosen [12]. Under these assumptions, the coefficients in

equation (11) reduce to:

𝑎𝑛(𝜎) = −3

2𝜆100𝑎𝑏𝑇𝜎 + (3𝛿𝜆100𝜎 + 𝛾180)𝑇(𝑎𝑛 − 𝑏), (16)

𝑏𝑛(𝜎, 𝐻) = 3𝑇𝜆100𝜎 (2𝛿 −𝑏

𝑛) + 𝛾1802𝑇 + 2𝑇𝑎𝜇(𝛼𝑒(𝜇+< 𝑀 >) −

𝐻 ), (17)

𝑐𝑛(𝜎, 𝐻) = 3𝑇𝜆100𝜎 (18)


In equation (17), 2𝑇𝑎𝜇𝛼𝑒(𝜇+< 𝑀 >) is the demagnetization energy, which is approximated as a

local term related to each 180 degree domain wall plus an average term due to the influence of the

domain wall with all the other domains.

Figure 37 shows that the average number of 180 degree domain walls increases as tensile stress is

applied under zero external magnetic field. This is expected by energy minimization: setting

an = 0 in equation (16). As well, experimental studies confirm this tendency [14].

Figure 37: The average number of 180 degree domain walls as a function of

tensile stress with zero applied magnetic field.

In Figure 38, the variation of average number of 180 degree domain walls is shown for three

stresses as a function of applied magnetic field. Note that the graphs are symmetric as it takes the

same energy to move the domain wall to the right or to the left (rotate the moments 180 degrees

up or down). The average number is maximal at zero magnetic field and corresponds to the values

shown in Figure 37. As a magnetic field is applied, the number of walls decreases more rapidly

for the higher stresses. This occurs because as the field is applied, the walls start to move, as

shown in Figure 36. Eventually they will move all the way to the next domain oriented in the

same direction and will thus bring about domain annihilation. A larger initial domain number

means thinner domains and thus wall annihilation will happen earlier.


Figure 38: Average number of 180 degree domain walls versus

applied magnetic field at three tensile stresses.

Figure 39 shows the variation of magnetization versus magnetic field for the situation described

in Figure 38. The shape of the anhysteretic curve depends on the parameters used. Figure 39

follows the pattern of one that needs an applied magnetic field of 0.05 T to overcome

demagnetization. Note that as tensile stress increases, it reduces this energy barrier, which is

expected from equation (10) and from Figure 38 where we start with more initial domains, which

rapidly annihilate. It is also observed from this figure that the slope of the curves (the magnetic

permeability) at zero magnetic field increases with increasing tension. Further work is being

conducted to determine the appropriate parameters to model the anhysteretic curve shown in

Figure 33b.

It is observed in Figure 39 that all three curves reach saturation at the same magnetic field. This is

approximately true for highly oriented textures. However, for less or randomly oriented textures

and different grain sizes, the differences in field strength at saturation will be significant as

domain rotation effects must also be added. This is a subject for further study, but the framework

has been presented in equation (15) of the section Extension to Multiply Oriented Grains.


Figure 39: The anhysteretic curve of magnetization versus magnetic field

for the same stresses as Figure 38.

4.5 Conclusions

We have presented two models to determine stress from surface Barkhausen measurements. Both

models require as a first step that the Barkhausen voltage response be converted to an anhysteretic

magnetization versus applied magnetic field. The first model is more phenomenological and has

been directly applied to experimental results from the companion DRDC report [2]. The results

show that for a 1D system, the model can characterize the material and then be used to calculate

stress. The model is applicable for up to 2D stresses and will be applied to that case when

experimental results are available. The second model is more physical than the first, but is more

computationally intensive. Further development of the model is required for it to be directly used

with experimental results. However, preliminary results suggest qualitative agreement with

characteristic magnetization versus magnetic field relations.


4.6 References

[1] S. White, A Barkhausen Noise Testing System for CANDU Feeders, Ph.D. Thesis, Queen’s

University, 2009.

[2] A. Samimi, T. W. Krause and L. Clapham, Evaluation of Stress Dependence of Magnetic

Barkhausen Noise in a HY-80 Steel Sample, DRDC Report, SLA#: RMCC Serial#2009-0302-

SLA, ANNEX #: PA11029, March 31 2013.

[3] S. Chikazumi, Physics of Magnetism, Wiley, 1964.

[4] L. Mierczak, D. Jiles, and G. Fantoni, A New Method for Evaluation of Mechanical Stress

Using the Reciprocal Amplitude of Magnetic Barkhausen Noise, IEEE Transactions on Magnetics

47, 459 (2011).

[5] D. Jiles and D. Atherton, Theory of Ferromagnetic Hysteresis, J. of Mag. and Mag. Mat., 61,

48, (1986).

[6] D. Jiles, Dynamics of Domain Magnetization and the Barkhausen Effect, Czech. J. Phys. 50,

893 (2000).

[7] A. Bergqvist, A Simple Vector Generalization of the Jiles-Atherton Model of Hysteresis,

IEEE Trans. Mag., 32, 4213 (1996).

[8] J. Leite, N. Sadowski, N. Batistela, J. Bastos and A De Espíndola, Inverse Jiles – Atherton

Vector Hysteresis Model, IEEE Transactions on Magnetics 40, 1769 (2004).

[9] M. Sablik and D. Jiles, Coupled Magnetoelastic Theory of Magnetic and Magnetostrictive

Hysteresis, IEEE Transactions on Magnetics 29, 2113 (1993).

[10] M. Sablik and D. Jiles, A model for hysteresis in magnetostriction, J. Appl. Phys. 64, 5402

(1988).

[11] W. M. A . Faucette, Geometric Interpretation of the Solution of the General Quartic

Polynomial, Amer. Math. Monthly 103, 51 (1996).

[12] T.W. Krause, L. Clapham, A. Pattantyus and D. L. Atherton, Investigation of the

stress-dependent magnetic easy axis in steel using magnetic Barkhausen noise, J. Appl. Phys., 79,

4242 (1996).

[13] L.D. Landau and E.M. Lifshitz, Statistical Physics, Pergamon Press, 1970.

[14] J.W. Shilling, G.L. Houze, Jr., , Magnetic Properties and Domain Structure in

Grain-Oriented 3 % Si-Fe, IEEE Trans. Magn., 10, 195 (1974).


5 Conclusions and Future Work

The goal for phase II was to improve the functionality of the laboratory system, conduct stress

dependent measurements under elastic strain conditions and, design and assemble components for

a portable MBNA system. Preliminary flux-controlled Barkhausen measurements were performed

on a HY-80 steel sample under applied uni-axial tensile stress conditions. Variations of MBN

signal were examined as a function of stress up to 50% of the sample’s yield strength. For the

next step of our studies, we have prepared a standard dog-bone shape sample to study the

influence of higher stress levels and plastic deformation on Barkhausen signals. A more complex

case of bi-axial stress will also be investigated, in which an octagonal shaped sample of HY-80

will be used.

We have presented two models to determine stress from surface Barkhausen measurements. Both

models require as a first step that the Barkhausen voltage response be converted to an anhysteretic

magnetization versus applied magnetic field. The first model is more phenomenological and has

been directly applied to experimental results from the companion DRDC report. The results show

that for a 1D system, the model can characterize the material and then be used to calculate stress.

The model is applicable for up to 2D stresses and will be applied to that case when experimental

results are available. The second model is more physical than the first, but is more

computationally intensive. Further development of the model is required for it to be directly used

with experimental results. However, preliminary results suggest qualitative agreement with

characteristic magnetization versus magnetic field relations.

The next phase will focus on further experimental testing and modelling to improve design and

validate the portable MBNA System. Results will be compared/contrasted with similar

measurements made using XRD (at the near surface) and Neutron diffraction (at varying depths).

This will likely start with measurements on 350wt ship steel plates that were previously

characterized with X-ray and neutron diffraction. If time permits laboratory mock-ups of

submarine pressure hull plates will be evaluated as well. It is anticipated that a working portable

field-ready MBNA field system will be supplied by March 2014.


Annex A Additional Information for Operation

A.1 FCS potentiometer/gain calibration

The FCS is unstable at certain analog gain values which are determined by the

potentiometers located on the FCS circuit board. Each channel contains two

potentiometers, one which acts as a balancing resistor for the positive input of the

LM3886T op-amp and another, which controls the flux feedback gain.

High gains reduce convergence times but also result in instabilities. As a result the

potentiometers should be set to zero initially. The system should then be run and checked

for convergence. If the system converges the potentiometers may be turned up slowly,

with a system test each time in order to check for convergence.

A.2 Data Set Descriptions

Selected BN (BN) – Raw sampled pickup coil waveform data. The saved data contains

the background signal, which is sampled before the measurement and the MBN signal

during the measurement, allowing for background subtraction. Also included is a time

averaged signal of the pickup waveforms.

Power Spectra (PS) – Measure of the energy distribution across the frequencies of the

pickup waveform. It is calculated by multiplying the Fourier transform of the signal by its

complex conjugate. The average power spectrum is also calculated.

Dynamic PS (DPS) – Power spectrum of pickup signal as a function of the phase of the

signal. It represents the power spectrum during the course of one pickup waveform.

Averaged Raw Data (ARD) – All system parameters for the measurement (i.e., excitation

voltages, excitation currents, feedback flux, etc.).

BNenv – The BN envelope, which the RMS of the normalized power spectrum of the

pickup signal. It represents the power of the BN signal over time or phase.

NPSBN – The normalized pickup power spectrum over the full period of the signal.

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audience may be selected.))

Unlimited

13. ABSTRACT (A brief and factual summary of the document. It may also appear elsewhere in the body of the document itself. It is highly desirable

that the abstract of classified documents be unclassified. Each paragraph of the abstract shall begin with an indication of the security classification

of the information in the paragraph (unless the document itself is unclassified) represented as (S), (C), (R), or (U). It is not necessary to include

here abstracts in both official languages unless the text is bilingual.)

Magnetic Barkhausen Noise Analysis (MBNA) provides non-destructive rapid interrogation of

ferromagnetic materials and offers tunable depth of analysis and portability. The Royal Military

College of Canada (RMCC) was contracted by DRDC to develop a prototype portable MBNA

system for qualitative rapid residual stress analysis of structural ferromagnetic steels. During

phase I, a prototype laboratory MBNA measurement system was designed and constructed. This

report describes progress achieved during phase II of the three phase project.

During phase II (current work) a deeper understanding of the MBNAs functionality and inner

workings was achieved through experimental testing and modelling. The laboratory system was

improved. Experimental testing and modeling were used to achieve greater accuracy of stress



has been demonstrated to be effective for rapid identification of regions of high tensile stress

and stress gradients – a precursor to crack initiation. A field-ready portable system will be

supplied to DRDC Atlantic by March 2014.

14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Technically meaningful terms or short phrases that characterize a document and could be

helpful in cataloguing the document. They should be selected so that no security classification is required. Identifiers, such as equipment model

designation, trade name, military project code name, geographic location may also be included. If possible keywords should be selected from a

published thesaurus, e.g., Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus identified. If it is not possible to select

indexing terms which are Unclassified, the classification of each should be indicated as with the title.)

Non-destructive testing, Residual stress analysis, Magnetic Barkhausen noise analysis,

Ferromagnetic steel, Transient pulse

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