Study of magnetic anisotropy in api 5l steels from crystallographic texture and barkhausen noise measurements le manh tu 2016 dc en m y m locked

ESCUELA SUPERIOR DE INGENIERÍA QUÍMICA E INDUSTRIAS EXTRACTIVAS Programa de Doctorado en Ciencias en Ingeniería Metalúrgica y Materiales STUDY OF MAGNETIC ANISOTROPY IN API 5L STEELS F

ESCUELA SUPERIOR DE INGENIERÍA QUÍMICA E INDUSTRIAS EXTRACTIVAS

Programa de Doctorado en Ciencias en Ingeniería Metalúrgica y Materiales

STUDY OF MAGNETIC ANISOTROPY IN API 5L

STEELS FROM CRYSTALLOGRAPHIC TEXTURE AND BARKHAUSEN NOISE MEASUREMENTS

A thesis submitted the Instituto Politécnico Nacional for the

degree of Doctor of Phylosophy

Presented by:

MSc Tu Le Manh

Thesis advisors:

Dr Francisco Caleyo Cereijo

Dr José Manuel Hallen López

Mexico City, 2016

ABSTRACT

The magnetocrystalline energy (MCE) is an intrinsic magnetic anisotropy that defines the magnetic easy and hard axes in a crystal and, through the crystallographic texture, the magnetic anisotropy in a polycrystal MCE has a great practical interest in technological applications of ferromagnetic materials

In this work, the magnetic anisotropy was studied in API 5L steels from crystallographic texture and Barkhausen noise (BHN) measurements for different sample geometries (steel plates and circular discs) and microstructural and crystallographic texture characteristics

Experimental measurements were carried out to determine the angular dependence of Barkhausen noise

in the band from remanence to saturation of the hysteresis loop of these steels The crystallographic texture of the samples was analyzed by two methods: X-ray diffraction and Electron Back-scatter Diffraction (EBSD)

From the texture data measured by X-ray diffraction, the orientation distribution function of the polycrystal was determined to estimate the average magnetocrystalline energy in the investigated steels using the series expansion method In the case of the EBSD microtexture measurements, the average magnetocrystalline energy was determined by averaging the contribution over the individual grain orientations of the measured EBSD data

The estimation of the magnetocrystalline energy from the orientation maps measured by EBSD microtexture measurements was found to be in good agreement with the predictions made from X-ray global texture for all the investigated steels The statistically sufficient number of grains for the accurate estimation of MCE using EBSD microtexture measurements in the studied steels was determined to be

in the order of several hundreds to a thousand

The ability of BHN measurements to determine the magnetocrystalline energy was validated for different sample geometries, microstructures and crystallographic textures This was achieved by comparing the BHN-derived MCE estimations with the predictions from X-ray global texture and microtexture measurements In the studied materials, the average MCE estimated from the BHN measurements were found in close agreement with the predictions made from X-ray texture and EBSD microtexture measurements

A stochastic physical model and a simulation mathematical framework were developed in order to explain the observed correlation between the MCE and BHN signals in the band from saturation to remanence In this band of the hysteresis loop, the BHN activity is mainly associated with the nucleation

and growth of domains of reverse magnetization The proposed stochastic model helps evaluate the angular dependence of the MCE for API 5L steel samples from their crystallographic texture, grain size distribution, and carbon content These microstructural characteristics were used to model the distribution of magnetic free poles at grain and interface boundaries in the steel and, consequently, the number and strength of reverse-domain nucleation and growth events as the materials goes from saturation to remanence The statistical distributions of the reversed-domain nucleation and irreversible growth fields were obtained for a large number of grain boundaries and used to estimate the BHN signal

at each angular position of interest

The modeled angular dependence of the average MCE was in good agreement, both in shape and relative magnitude (from one material to the next) with the average MCEs previously derived from BHN measurements and also predicted from crystallographic texture measurements This points out to the fact that the strong correlation between the BHN signal and the MCE in the band from saturation to remanence is due to role that the MCE plays in the formation of magnetic free poles at grain boundaries The results obtained in this thesis prove that the proposed model is capable of reproducing previous experimental results and explaining the relationship between the MCE and BHN signals, based on the knowledge of microstructural (grain size, volume fraction of the pearlite phase) and texture characteristics (crystal orientation, grain boundary misorientation) of the investigated steels

RESUMEN

La energía magnetocristalina define la anisotropía intrínseca de los materiales ferromagnéticos y es un parámetro muy importante para sus aplicaciones tecnológicas Esta energía define los ejes fáciles y difíciles de magnetización en el cristal, y a través de la textura cristalográfica, la anisotropía magnética

en el policristal En este trabajo se estudia la anisotropía de las propiedades magnéticas de aceros API 5L a partir de mediciones de texturas cristalográficas y ruido Barkhausen (BHN, por sus siglas en inglés) para diferentes geometrías de muestras, microestructuras y texturas cristalográficas de estos aceros

Las muestras estudiadas se elaboraron en forma de placas cuadradas y discos circulares Las mediciones experimentales se realizaron para determinar la dependencia angular de la actividad BHN en la banda de tiempo de saturación a remanencia Esta actividad ha sido reportada recientemente como significativamente dependiente de la energía magnetocristalina La textura cristalográfica de las muestras se analizó por dos métodos experimentales diferentes, difracción de Rayos X y de electrones retrodispersados (EBSD, por sus siglas en inglés)

A partir de las mediciones de la textura cristalográfica, se determinó la función de distribución de orientaciones cristalinas del policristal para estimar la energía magnetocristalina promedio en el mismo

Se estableció la correlación entre la dependencia angular de las señales de BHN y la energía magnetocristalina promedio calculada por las mediciones experimentales de textura cristalográfica

Se realizaron la modelación y simulación del ruido Barkhausen en estos materiales a partir de parámetros microestructurales como el tamaño de grano, la textura cristalográfica y la distribución de fronteras de granos La modelación se realizó utilizando la aproximación estocástica a partir de distribuciones estadísticas de parámetros como tamaño de grano, orientación cristalográfica y diferencia

de orientación en la frontera de granos

La comparación de las estimaciones de la energía magnetocristalina a partir de la textura cristalográfica medida por difracción de rayos-X y a través de mediciones de difracción de electrones (EBSD) permite determinar las condiciones óptimas para la estimación de propiedades magnéticas a partir de mediciones locales de textura En esta comparación fue utilizada como referencia las predicciones de dicha energía por medio de mediciones de textura cristalográfica por difracción de rayos-X

Se confirmó que la técnica EBSD puede ser utilizada para estimar con una exactitud relativamente buena la energía magnetocritsalina siempre y cuando el número de granos sea suficientemente grande,

teniendo en cuenta que el rango recomendable es entre unos cientos hasta mil granos para materiales con diferente tamaño promedio de grano

Se obtuvo una fuerte correlación entre las energías magnetocristalinas predichas mediante ambas técnicas de textura global por rayos-X y de electrones retrodispersados EBSD y las obtenidas a partir de las mediciones de ruido de Barkhausen

Para explicar el origen de la correlación experimental de la dependencia angular entre la energía magnetocristalina y la actividad Barkhausen en la banda de saturación a remanencia, se desarrolló un modelo físico basado en el conocimiento de los parámetros microestructurales como la textura cristalográfica, tamaño de grano, contenido de carbono, las orientaciones cristalinas y distribución de diferencia de orientación en el material En este modelo, los parámetros microestructurales fueron utilizados para simular la distribución de las cargas libres en las fronteras e interfases de grano y el número y la magnitud de eventos de la nucleación y crecimiento de dominios reversos en el proceso de magnetización de saturación a remanencia Las distribuciones estadísticas de campos de nucleación y crecimiento irreversible de dominios reversos se obtuvieron para un número suficientemente grande de fronteras de granos y fueron utilizadas para estimar la señal de BHN en cada posición angular de interés

La dependencia angular de la energía magnetocristalina modelada coincidió en forma y magnitud relativa (de un material a otro) con la energía promedio estimada por medio de ruido de Barkhausen y las predicciones hechas a partir de la textura global medida por rayos-X Este resultado explica que la fuerte correlación entre la energía magnetocristalina y la actividad de ruido de Barkhausen en la banda

de saturación a remanencia se debe al papel que juega la energía magnetocristalina en la formación de las cargas libres en las fronteras de granos del material en la banda de saturación a remanencia

El modelo estocástico propuesto y validado en este trabajo es capaz de explicar la fuerte correlación observada entre la energía magnetocristalina y el ruido de Barkhausen en la banda de saturación a remanencia, así como de reproducir las evidencias experimentales de dicha correlación sobre la base del conocimiento de los parámetros microestructurales (el tamaño de grano y la fracción volumétrica de perlita) y las características de texturas cristalográficas (orientación cristalina y diferencia orientación en las fronteras de granos)

DEDICATIONS

To my parents, Lê Thành Lập and Lý Thị Mùi!

To my brothers and sisters (Tuyến, Chiến, Thanh, Hùng, Huế, and Tâm)!

To Mai!

ACKNOWLEDGEMENT

My sincerest thanks to: Instituto Politécnico Nacional

Escuela Superior de Ingeniería Química e Industrias Extractivas Departamento de Metalurgia y Materiales

I would like to express my sincerest gratitude to my professor advisor, Dr Francisco Caleyo Cereijo This thesis would not be possible without his help, advice, guidance, expertise, time dedication, education, and encouragement

I would like to thank to my advisor Dr José Manuel Hallen López for his education, advice, encouragement, and supports

My special thanks to Dr J H Espina Hernández and Dr J A Benitez Pérez for their unconditional helps and guidance in the measurement systems and other theoretical aspects as well

I would like to thank to Dr Jorge Roberto Vargas Garcia, Dr Elsa Miriam Arce Estrada, Dr Federico Chávez Alcala, and Dr Hector Javier Dorantes Rosales for their valuable argument and suggestions Many thanks to all Mexican and Cuban friends for all their unconditional helps And especially, to Alejandra Islas Encalada, Master student and personal in charge of the laboratory for her contribution and help during the experimental development and Ayrton Luis Sierra Marquez for his corroboration in the EBSD measurements

I would like to send my major gratitude to:

- The Embassy of the Socialist Republic of Vietnam in Mexico and all friends working in the Embassy, especially, to Sr Dao Van Dung, First Secretary of the Embassy of the Socialist Republic of Vietnam in Mexico, who always bring me the necessary help and encouragement during my doctoral study

- The Embassy of Mexico in Vietnam and the Vietnam International Education Development (VIED), Ministry of Education and Training of Vietnam, for their support and unconditional helps in the scholarship grant process

- Secretaría de Relaciones Exteriores (SRE), Mexico for the financial support and unconditional helps during my doctoral study in Mexico

This thesis was supported by Excellent Scholarship of the Mexican Government through the Secretaría

de Relaciones Exteriores, Mexico

The support of CIDIM-IPN is also acknowledged

Hg Growth field A/m

angular dependence of MCE agrees with BHN measurements

domains of reverse magnetization

m/s

μ0 Magnetic permeability in vacuum H/m (Henri per meter)

orientations “{}” and “< >” mean family

of planes and/or crystal directions

TABLE OF CONTENTS

ACTA DE REVISIÓN

CARTA CESIÓN DE DERECHOS

ABSTRACT iv

RESUMEN vi

DEDICATIONS viii

ACKNOWLEDGEMENT ix

NOMENCLATURE x

TABLE OF CONTENTS xiii

LIST OF FIGURES xiv

CHAPTER 1: INTRODUCTION 1

1.1 Correlation between crystallographic texture and magnetic properties of ferromagnetic materials 3

1.1.1 X-ray global texture approach 3

1.1.2 EBSD microtexture approach 4

1.2 Magnetic easy axis and stress anisotropy in steels and their correlation with BHN 5

1.3 Correlation between MCE and Barkhausen noise 6

1.4 Available models for Barkhausen noise 6

1.5 The nucleation of reverse domains 7

CHAPTER 2: MAGNETIC ANISOTROPY 11

2.1 Fundamentals of magnetism and magnetic anisotropy 11

2.1.1 Hysteresis loop 12

2.1.2 Domain structure 13

2.1.3 Magnetocrystalline anisotropy energy 14

2.1.4 Determination of MCE in polycrystalline materials 17

2.1.4.1 MCE from X-ray global texture 17

2.1.4.2 MCE determination from EBSD 20

2.1.5 Magnetostatic energy 23

2.1.6 External field energy 24

2.1.7 Domain wall energy 24

2.2 Magnetic anisotropy from Barkhausen noise analysis 25

2.2.1 Barkhausen noise 25

2.2.2 Magnetic anisotropy from BHN measurements 26

2.2.3 Review of current models of Barkhausen noise 29

2.2.4 Nucleation and growth of reverse domains 32

2.2.4.1 Goodenough´s model 32

2.2.4.2 Experimental evidence of nucleation of reverse domains in low-carbon steels 35

CHAPTER 3: MATERIALS AND METHODS 38

3.1 MATERIALS 38

3.2 EXPERIMENTAL I 44

3.2.1 Barkhausen noise setup 44

3.2.2 Determination of MCE from Barkhausen noise 46

3.2.3 Barkhausen noise in the API 5L steels 47

3.2.3.1 BHN measurements in the square samples 48

3.2.3.2 BHN measurements in the circular samples 49

3.2.4 X-ray Global Texture 51

3.2.4.1 Texture components in pipeline steels 52

3.2.4.2 Analysis of X-ray texture measurements in pipeline steels 53

3.3 Experimental II 59

3.3.1 MCE from Electron Back-scatter Diffraction measurements 59

3.3.2 Electron Back-scatter Diffraction measurements 61

3.4 Modelling and simulation of magnetic free poles at grain boundaries 67

CHAPTER 4: MAGNETOCRYSTALLINE ENERGY FROM CRYSTALLOGRAPHIC TEXTURE MEASUREMENTS 71

4.1 Magnetocrystalline Energy from X-ray Texture Measurements 71

4.1.1 MCE predictions from X-ray texture in Group 1 71

4.1.2 MCE predictions from X-ray texture in Group 2 76

4.2 Magnetocrystalline energy from EBSD microtexture measurements 81

4.2.1 EBSD-derived MCE in steels of Group 1 81

4.2.2 EBSD-derived MCE in the steels of Group 2 83

4.2.3 Comparison between the MCEs derived from EBSD and X-ray texture 86

4.2.4 EBSD measurements strategy for MCE estimation 88

4.2.4.1 Equivalent orientations 88

4.2.4.2 Number of grains 91

4.2.4.3 MCE analysis in different sample planes 95

Chapter IV Conclusions 98

CHAPTER 5: STUDY OF THE CORRELATION BETWEEN MAGNETOCRYSTALLINE ENERGY AND BARKHAUSEN NOISE 100

5.1 Estimation of MCE from BHN measurements in APL 5L steels 100

5.1.1 Correlation between MCE and BHN in square samples 100

5.1.2 Correlation between MCE and BHN in circular samples 102

5.1.3 Comparison between BHN-derived MCEs in circular and square samples 110

5.2 Correlation between EBSD microtexture-derived MCE and Barkhausen noise measurements 113

Chapter V Conclusions 117

CHAPTER 6: MODEL FOR THE CORRELATION BETWEEN MAGNETOCRYSTALLINE ENERGY AND BARKHAUSEN NOISE 118

6.1 Model formulation 118

6.2 Modelling the average MCE from Barkhausen noise 120

6.3 General model for correlating MCE and BHN 123

6.3.1 Nucleation of domains at grain boundaries 123

6.3.2 Model for the correlation between MCE and BHN in API 5L steels 125

6.4 Model validation 127

6.5 Explanation of the correlation between MCE and BHN 130

Chapter VI Conclusions 134

CHAPTER 7: CONCLUSIONS AND FUTURE WORKS 135

7.1 CONCLUSIONS 135

7.2 FUTURE WORKS 138

7.2.1 Velocity of nucleation and growth of reverse domains 138

7.2.2 Estimation of MCE from BHN measurements in materials under stress 140

7.2.3 MCE determination from the magnetization curves 141

REFERENCES 142

LIST OF FIGURES

Fig 2.1: Typical hysteresis loop in ferromagnetic materials The dashed curve is the so-called virgin magnetization curve [58] 12 Fig 2.2: a) Closure domain in ferromagnetic materials b) Domain wall motion during the magnetization process [52] 13

Fig 2.3: a) Definition of direction cosines (1,2,3) of the magnetization vector, M, (or any direction) in

spherical coordinates in a cubic system, b) Example of the MCE anisotropy surface for pure iron with positive K 1

anisotropy constant This material exhibits easy axes along the <100> crystallographic directions and hard axes along

<111> and <110> 15 Fig 2.4: Magnetization change along easy and hard axes versus applied field in Fe and Ni crystals [58] 16 Fig 2.5: E(,)determination from the ODF, f(g), of a low-carbon steel obtained by X-ray texture measurements

From left to right, representations are the pole figure and ODF of the material, the MCE surface, and a polar plot of the MCE in the rolling plane of the material 20

Fig 2.6: MCE obtained for a cubic crystal with different orientations g, a) MCE surface in 3D representation and in

the rolling plane determined for the orientation (001)[100] b) MCE determined for the orientation (110)[001] 21 Fig 2.7: Determination of the MCE on the plane RD-TD from individual grain orientations in a polycrystalline sample The average MCE of the bulk sample results from the contribution of all individual grains in the sample volume 22 Fig 2.8: E(,) from EBSD measurements as determined by using the Direct Method; E(,)is estimated as the average MCE for all individual orientations obtained from the EBSD measurements 23 Fig 2.9: Barkhausen noise (a) Region of large Barkhausen jumps around coercivity in the hysteresis curve and (b) typical Barkhausen noise signals in a ferromagnetic material 25 Fig 2.10: Experimental evidence of the correlation between MCE and BHN measurements after [44] The angular dependence of the RMS value of BHN measurements (blue curves) in the SR band shows a good agreement with the average MCE predictions from X-ray texture (red curves) on the rolling plane The upper part of the figure shows the average MCE anisotropy surface and the lower part indicates the comparison between MCE and BHN

measurements 28 Fig 2.11: Model of nucleation of reverse domains at a grain boundary after Goodenough [56] 33

Fig 2.12: Nucleation of domains reversed magnetization evidenced by Fresnel images when the applied is reduced

from saturation to remanence [98]: a) 18.14 kA/m, b) 4.7 kA/m, c) 3.2 kA/m, d) 0 kA/m 36 Fig 3.1: a) Geometry of the studied samples and their location relative to the pipeline section; RD, TD, and ND refer

to the rolling, transverse, and normal directions of pipe and constitute the sample coordinate system, respectively; b) Circular samples obtained in the RD-TD, ND-RD, and TD-ND planes with 1 cm of diameter and thickness δ = 2.5 mm; c) Square samples obtained in the rolling (RD-TD) plane with an area of 7.5 × 7.5 cm 2 and thickness δ = 2.5

mm 39 Fig 3.2: Microstructures of the investigated steels, a) X56, grain size: 14 µm, b) X52; grain size: 18 µm), and X60; grain size: 24 µm Micrographs show a microstructure consisting of ferrite (white etching constituent) and pearlite (black etching constituent) grains 41 Fig 3.3: Microstructures of the investigated steels, a) X56, b) X52, c) X60, d) Sample A, e) Sample B, and f) Sample

C The dark and bright colors represent the ferrite and pearlite phases, respectively 42 Fig 3.4: SEM micrographs showing morphology of pearlite grains obtained by SEM in the investigated steels, a) X56-ND, b) X52-ND, and c) X60-ND The dark and bright phases represent the cementite and ferrite, respectively 43 Fig 3.5 : Experimetal setup for square samples: (a) Band of interest (AB; MCE-BHN) to determine the average MCE from saturation to remanence (b) BHN measurement setup 1) Goniometer; 2) Sample; 3) BHN measurement head; 4) Measurement/control unit 44 Fig 3.6: Experimental setup for the Barkhausen measurements of the circular steel samples: A) Acquisition system

of the BHN signals; B) New goniometer for circular samples: (1) sample, (2) pole pieces, (3) Angular scale, and (4)

sample rotation knob; C) excitation head The circular sample is magnetized with the help of the dedicated pole pieces, while the one-plane goniometer allows the sample to be manually rotated (right-bottom) 45 Fig 3.7: Schematic diagram of the experimental setup for the determination of MCE from BHN signals in the square samples of API 5L steels in Group 1 (a) Goniometer (S), (b) BHN acquisition system, (c) BHN signal and its

envelope, (d) MCE determined from AB band of the BHN signals 47 Fig 3.8: Examples of the BHN envelopes in the square samples of Group 1 48 Fig 3.9: Barkhausen noise patterns in circular samples The red curve is the BHN envelop calculated from the raw signal Typical BHN signal in a) sample A, b) sample B, c) sample C, d) X56 ND; the yellow curve represents the BHN envelop in samples e) X52ND and f) X60ND There is only one yellow curve in d 50 Fig 3.10: BHN envelopes calculated for three angular positions: 0°, 45°, and 90° in the circular API 5L steel

samples: a) Group 1, b) Group 2 51 Fig 3.11: Ideal orientations in BCC steels represented in {200} and {222} pole figures and the  2 = 45° section of the ODF 52 Fig 3.12: Representation of some fiber textures in BCC steels in the {111} pole figure 53 Fig 3.13: Recalculated {110}, {200}, and {222} pole figures and  2 = 45° section of the ODF for the X56ND steel 54 Fig 3.14: Recalculated {110}, {200}, and {222} pole figures and  2 = 45° section of the ODF for the X52 54 Fig 3.15: Recalculated {110}, {200}, and {222} pole figures and  2 = 45° section of the ODF for the X60 steel 55 Fig 3.16: Recalculated {110}, {200}, and {222} pole figures and  2 = 45° section of the ODF for sample A 56 Fig 3.17: The Recalculated {110}, {200}, and {222} pole figures and  2 = 45° section of the ODF for sample B 57 Fig 3.18: Recalculated {110}, {200}, and {222} pole figures and  2 = 45° section of the ODF for sample C 58 Fig 3.19: Comparison of textures in the studied steels The intensity density of components along  fiber was plotted

in two-dimensional section of the ODF by fixing  1 = 0° and  2 = 45° 59 Fig 3.20: (a) Reference system used to define the average MCE in a polycrystal (b) MCE surface of a cubic crystal with K 1 > 0, K 2 > 0, and orientation g 2 = (0, 45, 0) deg (in Euler angles) (c) Contribution of the crystal to the MCE in the direction () = (90,45) deg (d) Contribution of each grain of the polycrystal to the average MCE in a given sample direction 60 Fig 3.21: Area selection in circular samples used for EBSD measurements The arrows indicate the direction of area reduction in the original orientation map 62 Fig 3.22: EBSD measurements in the X56 steel obtained on the rolling plane: a) Orientation map given by the inverse pole figure of ND, b) Calculated {200} and {222} pole figures, and c)  2 = 45° section of the ODF 63 Fig 3.23: EBSD measurements in the X52 steel obtained in rolling plane: a) Orientation map, b) {200} and {222} pole figures, and c)  2 = 45° section of the ODF 63 Fig 3.24: EBSD measurements in the sample X60: a) Orientation map, b) {200} and {222} pole figures, and c)  2 = 45° section of the ODF 64 Fig 3.25: EBSD measurements in the sample A: a) Orientation map, b) Estimated {200} and {222} pole figures, and c)  2 = 45° section of the estimated ODF 65 Fig 3.26: EBSD measurements in the sample B: a) Orientation map, b) Estimated {200} and {222} pole figures, and c)  2 = 45° section of the estimated ODF 65 Fig 3.27: EBSD measurements in the sample C: a) Orientation map, b) Estimated {200} and {222} pole figures, and c)  2 = 45° section of the estimated ODF 66 Fig 3.28: Comparison between EBSD microtexture and X-ray texture measurements in the studied steels through the: a)  2 = 45° section of the ODF from EBSD microtexture and b) from X-ray global texture 67 Fig 3.29: Model of free charges density at a grain boundary The black and pink arrows represent the applied field and magnetization vectors, respectively The red, blue, and green lines are the crystal edges The shaded plane is the grain boundary plane S 1 , S 2 , and S 3 axes refer to the sample coordinate system 68 Fig 3.30: Single orientation produced from the ODF for simulating magnetic free poles at grain boundaries from crystallographic texture data measured by X-ray diffraction in X56, X52, and X60 steels, a) Recalculated pole figures, b) Distribution of individual orientations 69

Fig 3.31: Grain size distributions in the steel samples used in the modelling and simulation of magnetic free poles at grain boundaries (see also Chapter 6) a) X56ND, b) X52ND, c) X60ND, d) sample A, e) sample B, and f) sample C 70 Figure 4.1: 3D MCE anisotropy surface and the    = 45° section of the orthorhombic ODF for materials in Group 1: a) X56, b) X52, c) X60, d) Ideal orientations in the    45° section of the orthorhombic ODF 72 Fig 4.2: MCE in each measured planes of the X56 steel: a) MCE on the rolling plane, b) MCE on the RD-TD plane, c) MCE on the RD-ND plane, d) Comparison of MCEs on the three planes The measured plane is red-shaded in the reference cube 73 Fig 4.3: MCE on each measured planes for the X52 steel: a) MCE on the rolling plane, b) MCE on the RD-TD plane, c) MCE on the RD-ND plane d) Comparison of MCEs on the three planes The measured plane is red-shaded

in the reference cube 74 Fig 4.4: MCE on each measured planes for the X60 steel: a) MCE on the rolling plane, b) MCE on the RD-TD plane, c) MCE on the RD-ND plane d) Comparison of MCEs on the three planes The measured plane is red-shaded

in the reference cube 75 Fig 4.5: 3D MCE anisotropy surface and the    = 45° section of the orthorhombic ODF for materials in Group 2: a) Sample A b) Sample B, c) Sample C d) Ideal orientations in the   = 45° section of the orthorhombic ODF 76 Fig 4.6: MCE on each measured plane of sample A: a) MCE on the rolling plane, b) MCE on the RD-TD plane, c) MCE on RD-ND plane, and d) Comparison of the MCEs on the three planes The measured plane is red-shaded in the reference cube 78 Fig 4.7: MCE on each measured plane of the sample B: a) MCE on the rolling plane, b) MCE on the RD-TD plane, c) MCE on RD-ND plane, and d) Comparison of the MCEs on the three planes The measured plane is red-shaded in the reference cube 79 Fig 4.8: MCE on each measured plane of sample C: a) MCE on the rolling plane, b) MCE on the RD-TD plane, c) MCE on RD-ND plane, and d) Comparison of the MCEs on the three planes The measured plane is red-shaded in the reference cube 80 Fig 4.9: MCE estimation from EBSD measurements for the X56 steel a) Orientation map, b) Average MCE of this steel derived from the orientation map 82 Fig 4.10: MCE estimation from EBSD measurements for the X52 steel a) Orientation map, b) Average MCE of this steel derived from the orientation map 83 Fig 4.11: MCE estimation from EBSD measurements for the X60 steel a) Orientation map, b) Average MCE of this steel derived from the orientation map 83 Fig 4.12: MCE estimation from EBSD measurements for the sample A a) Orientation map, b) Average MCE of this steel derived from the orientation map 84 Fig 4.13: MCE estimation from EBSD measurements for the sample B, a) Orientation map, b) Average MCE of this steel derived from the orientation map 85 Fig 4.14: MCE estimation from EBSD measurements for the sample C a) Orientation map, b) Average MCE derived of this steel from orientation map 86 Fig 4.15: Normalized MCEs obtained from X-ray and EBSD texture measurement: a) X56, b) X52, c) X60, d) Sample A, e) Sample B, g) Sample C The red and olive curves show the MCEs determined from X-ray texture and EBSD microtexture measurements, respectively 87 Fig 4.16: SSE in function of Ng for the three X56, X52, and X60 steels The continuous curve indicates the direct method estimation of the MCE from the orientation maps without EQs, while the dashed curve corresponds to the estimations made using the EOs 90 Fig 4.17: MCE calculated for sample C from the X-ray texture measurements (olive curve) compared with the estimations made from the raw EBSD orientation maps (green curve), and from the EBSD orientation map and the corresponding grain EOs (magenta curve) 90 Fig 4.18: Qualitative comparison of the MCEs determined with the Direct Method from the EBSD/OIM orientation maps in the X56ND steel for different numbers of grains a) Raw data with 1200 grains b) Raw data with 860 grains c) Raw data with 600 grains d) Raw data with 300 grains e) Raw data with 180 grains f) Raw data with 1200 grains and their EOs g) Raw data with 860 grains and their EOs h) Raw data with 600 grains and their EOs i) Raw data with 300 grains k) Raw data with 180 grains and their EOs 92

Fig 4.19: Qualitative comparison of the MCEs determined with the Direct Method from the EBSD/OIM orientation maps in the X52ND steel for different numbers of grains a) Raw data with 1155 grains b) Raw data with 784 grains c) Raw data with 469 grains d) Raw data with 250 grains e) Raw data with 150 grains f) Raw data with 1155 grains and their EOs g) Raw data with 784 grains and their EOs h) Raw data with 469 grains and their EOs, c) Raw data with 250 grains and their EOs h) Raw data with 150 grains and their EOs 93 Fig 4.20: Qualitative comparison of the MCEs determined with the Direct Method from the EBSD/OIM orientation maps in the X60ND steel for different numbers of grains a) Raw data with 910 grains b) Raw data with 645 grains c) Raw data with 564 grains d) Raw data with 312 grains e) Raw data with 172 grains f) Raw data with 910 grains and their EOs g) Raw data with 645 grains and their EOs h) Raw data with 564 grains and their EOs i) Raw data with 312 grains k) Raw data with 172 grains and their EOs 94 Fig 4.21: EBSD orientations maps for the three sample`s planes in the studied API 5L steels: a) X56, b) X52, and c) X60 steels 95 Fig 5.1: Normalized MCEs from BHN (olive curve) and X-ray texture (red curve) measurements in the square samples: a) X56 steel, b) X52 steel, and c) X60 steel 101 Fig 5.2: Average MCEs determined from a) BHN and b) from X-ray texture measurements for the three steel

samples (X56, X52, and X60) 101 Fig 5.3: Average MCE estimated in the X56 circular steel samples from X-ray global texture and BHN

measurements a) MCE anisotropy surface obtained from X-ray texture, b) MCE anisotropy curve on the rolling plane, X56ND, c) MCE anisotropy curve on the TD-ND plane, X56RD, and d) MCE anisotropy curve on the RD-

ND plane, X56TD The normalized MCE curves obtained from crystallographic texture and BHN measurements are shown in red and blue, respectively 103 Fig 5.4: Average MCE estimated in the X52 circular steel samples from X-ray global texture and BHN

measurements a) MCE anisotropy surface obtained from X-ray texture, b) MCE anisotropy curve on the rolling plane, X52ND, c) MCE anisotropy curve on the TD-ND plane, X52RD, and d) MCE anisotropy curve on the RD-

ND plane, X52TD The normalized MCE curves obtained from crystallographic texture and BHN measurements are shown in red and blue, respectively 104 Fig 5.5: Average MCE estimated in the X60 circular steel samples from X-ray global texture and BHN

measurements a) MCE anisotropy surface obtained from X-ray texture, b) MCE anisotropy curve on the rolling plane, X60ND, c) MCE anisotropy curve on the TD-ND plane, X60RD, and d) MCE anisotropy curve on the RD-

ND plane, X60TD The normalized MCE curves obtained from crystallographic texture and BHN measurements are shown in red and blue, respectively 105

Fig 5.6: a) Anisotropy surface of the MCE surface for sample A obtained from X-ray texture measurements b)

Normalized MCEs estimated the on rolling plane from BHN (blue curve) and X-ray texture (red curve)

measurements For this particular sample, the isotropic part of the MCE is kept due the low anisotropy shown by the material on the rolling plane 107

Fig 5.7: a) Anisotropy surface of the MCE surface for sample B obtained from X-ray texture measurements b)

Normalized MCEs estimated the on rolling plane from BHN (blue curve) and X-ray texture (red curve)

measurements 108

Fig 5.8: a) Anisotropy surface of the MCE surface for sample B obtained from X-ray texture measurements, b)

Normalized MCEs estimated the on rolling plane from BHN (blue curve) and X-ray texture (red curve)

measurements 109 Fig 5.9: MCEs determined from BHN measurements in the: a) square samples and b) circular samples 111 Fig 5.10: EBSD-derived orientation maps and pole figures of the steel samples in Group 1 together with the

comparison of the angular dependence of the measured RMS voltage in the MCE-BHN band with the average MCE energy estimated from EBSD microtexture data using the direct method 114 Fig 5.11: EBSD-derived orientation maps and pole figures of the steel samples in Group 2 together with the

comparison of the angular dependence of the measured RMS voltage in the MCE-BHN band with the average MCE energy estimated from EBSD microtexture data using the direct method 116 Fig 6.1: (a) MCE obtained from the simulation of magnetic free pole at grain boundaries, (b) MCE predicted from crystallographic texture measurements, and (c) MCE estimated from Barkhausen noise measurements in the SR band for the three pipeline steels (X56, X52, and X60) 122

Fig 6.2: Model of nucleation of reverse domains at a grain boundary g GB (red line) On the left side of the figure, the negative (-) and positive (+) symbols represent the free charges formed at the both sides of the grain boundary and

the top of reverse domains g 1 and g 2 show the grain orientations, nˆ is the vector normal to the grain boundary plane, which forms with the reverse magnetizations angles  and  is the angle between the field H the rolling

direction (RD) of the sample On the right-hand side of the figure, the nucleated domain is assumed to have a

prolated-ellipsoid form with the semi-minor axis r and semi-major axis l, which are related by r =l. 124 Fig 6.3: a) Modeled MCE using the proposed stochastic approach b) Modeled average free poles density at grain boundaries c) MCEs derived from BHN measurements on the rolling plane for the steel samples in Groups 1 and 2 d) MCE prediction from X-ray texture 128

Fig 6.4: Mechanism to explain the correlation between the MCE and BHN 132

CHAPTER 1: INTRODUCTION

Low carbon steels such as API 5L steels are widely used in pipelines for the transportation of oil and gas products in the petroleum industry, not only due to their excellent mechanical properties, but also because they have very good magnetic properties It is well known that the magnetic properties of pipeline steels can be affected by several metallurgical parameters such as physical-chemical composition and phase, grain size, microstructure [1, 2], crystallographic textures [3], stress, temperature, and magnetic field [4] Through the application of this principle, the vast majority of nondestructive methods have been developed based on the magnetic properties of functional materials

There are several magnetic measurement techniques for the in-line inspection (ILI) of operating pipelines such as magnetic flux leakage (MFL) ILI, Barkhausen noise (BHN), magnetoacoustic emission, and the method of metal magnetic memory [5] These techniques, which are known as Non-destructive Testing (NDT) methods as ILI classifies, are used to detect macro and micro-defects associated with metal loss and cracks in steel structures and residual stress (by means of BHN) through the application of an intense magnetic field to the component under inspection Although MFL is an effective method for pipeline inspection [6-9], it still has some limitations with respect to MFL signals such as the strong variation of MFL signal amplitude and subsequent difficulty in sizing defects when the pipe suffers high stress levels (up to 70 % of the yield stress

of the pipeline material) generated during operating conditions associated with oil and gas transportation In order to improve the MFL detection efficiency and its ability to assess the stress-dependent magnetic properties, the determination of the magnetic easy axis and magnetic anisotropy in pipeline steels was proposed through the study of the angular-dependent method of BHN measurements [6] It was concluded in reference [7-9] that pipeline steels may exhibit bulk magnetic easy direction along the pipe axis and the effect of cold working during manufacturing process is responsible for this magnetic anisotropy rather than the influence of crystallographic texture

Many other papers also deal with the correlation of magnetic anisotropy and magnetic easy axis with BHN measurements in plastically deformed low-carbon steels [10] and materials under stress [11-16] It can be observed that in the reviewed works, the analyzed anisotropies are associated with the magnetomechanical effects by considering the main peak of BHN signals around the

coercivity point in the hysteresis loop This effect includes all the contribution of other anisotropic components, which cannot be separated in the analysis

According to reference [17], magnetic anisotropy includes several forms such as magnetocrystalline energy (MCE) and other induced anisotropies such as shape, surface, and stress anisotropies The use of an anisotropy component during any analysis depends on the practical consideration and specific situation found in the material (for example: the material state can be stressed or unstressed; the magnetization within the material is not along an easy direction, etc.) in which the competence of energy forms is determined by minimizing the total energy of the magnetic system, which in fact is not necessarily to be a minimum energy condition [18] It has been known that in an unstressed sample under the Curie temperature the magnetic anisotropy is mainly contributed by MCE, which is an intrinsic magnitude associated with the crystal lattice [19] The domain structure of the material is determined by the MCE, which is often larger in magnitude (by several orders) than the contribution of any induced anisotropy [20] By consequence, MCE has a strong influence on the way that ferromagnetic materials can be used and manufactured so that the study on the MCE has attracted a great deal of practical interest in the last decades and has been the focus of recent researches as well

It is important to note that, in the case of ILI of operating pipelines, the pipe wall remains magnetized after the inspection This so-called remanent magnetization can play a significant role

in the degradation mechanisms of the pipeline [21] This fact was reported in reference [22] in which the residual magnetic fields were measured close to 0.3 - 0.4 T in API 5L steels inspected

by a MFL tool, while along the axial direction of the pipeline can reach 0.85 T after a saturation magnetization of 2.07 T is applied The strength of both the applied and remanent magnetic field along different directions of the pipe wall depends of the magnetic properties of the steel used to make the pipeline [23] In addition, the combination of microscopic parameters such as microstructure, grain orientation, crystallographic texture, and other induced magnitude like stress may change the behavior and character of the anisotropy within the material

During a MFL inspection the pipe wall is magnetized near to saturation This fact may cause changes in the position of the net magnetization vector of the pipe with respect to its original direction before the inspection In such a case, it results very difficult the determination of the bulk magnetic easy axes in the pipeline, as magnetic properties also depend on the history of the material magnetization due to hysteresis In this regard, the best way to accurately determine the magnetic easy axes in ferromagnetic materials is by means of the average MCE Although several

methods such as torque curves, magnetization curves, and crystallographic textures [24] (commonly from X-ray global texture) exist for the MCE measurement and estimation, they are not easy to handle and impossible to carry out in field conditions either nondestructively or destructively The latter requirements can be satisfied perfectly if one considers the ability of BHN measurements to investigate magnetic anisotropy in steels as has been reported by most of the reviewed works [3-16, 23] However, a relationship between the MCE and BHN measurements, which may open up a promising branch for the non-destructive application of BHN signals, is actually a new research field with a very little number of publications until this moment The influence of crystallographic texture on the determination of the magnetic easy axis in pipeline steels is still not well understood Without doubts, an appropriate way to evaluate this relationship can be achieved through the determination of the average MCE The following review of related works, which have been done about the MCE and BHN up to the present, can help clarify in depth this observation

1.1 Correlation between crystallographic texture and magnetic properties of ferromagnetic materials

1.1.1 X-ray global texture approach

The calculation of the average MCE for a polycrystal is of great practical importance even though the method for the determination of the MCE for a single crystal has been known and explained in the literature [17, 24, 25] The MCE of a crystal can be extrapolated to a polycrystal by averaging the contribution of the MCE of each individual grain (crystallite) in a given sample Therefore, it

is possible to use the crystallographic texture to estimate the average polycrystal MCE since its behavior mainly depends on the angular position and magnitude of the magnetization vector considering spherical coordinates The strong correlation between crystallographic texture and MCE, and its principle of calculation, can be found in a large number of published papers [26-34]

In fact, the common way to estimate the anisotropy in a polycrystalline material by means of crystallographic texture studies is to average certain property over the orientation distribution function calculated from experimental pole figure measurements using X-ray diffraction This latter, known as the X-ray global textures, offers the highest measurement statistics among the available experimental methods The series expansion method proposed by Bunge [26] is extensively applied for the determination of the MCE This is a reliable method that can be used as

a reference for comparison with other techniques

It has also been confirmed that in the band from saturation to remanence of the hysteresis loop of a ferromagnetic material like iron, magnetic properties depend uniquely on crystallographic texture [26] This is an important fact to be used in the study of magnetic anisotropy in this thesis in which this anisotropy will be explored in the band from saturation to remanence using the BHN measurements that will be discussed latter in Chapter 3

The most important works about the determination of magnetic anisotropy from crystallographic texture measurements have been mainly conducted for FeSi steels for electrical transformers and generators as well as for other soft and hard magnetic [26, 27] and hexagonal materials [28] In these works, crystallographic texture was correlated with several magnetic properties such as magnetocrystalline energy, magnetostriction, and magnetoresistance The most interested magnitude is always MCE, whereas the others, such as the induced anisotropy, have attracted little attention [27 - 34] Also, in FeSi steels other properties including hysteresis loss and permeability are correlated with texture for analyzing the anisotropic behavior [30] of magnetic components such as AC transformer cores, while in another approach the average MCE determined from X-ray texture was correlated with saturation magnetization [35]

In the reviewed researches, the X-ray global texture was fundamental for the determination of the MCE due to the large statistical significance of these measurements The number of grains encountered in X-ray measurements in general is in order of hundreds of thousands, even millions This entails a statistical support that is practically unachievable in microtexture measurements using Electron Back-Scatter Diffraction (EBSD) [37]

1.1.2 EBSD microtexture approach

It has been known that one of the best ways to study magnetic properties in ferromagnetic materials is by means of the determination of MCE from crystallographic textures, which can be measured not only from X-ray global texture, but also from individual grain orientation obtained through EBSD microtexture measurements [35, 36, 38]

By averaging the contribution of individual grains using a direct method (not harmonic related algorithms, see section 2.1.3), MCE can be also calculated from EBSD microtextures as mentioned in [36] in which it was found a good correlation between the material’s texture with the high induction in FeSi steels, and later in [38] where the magnetic induction was estimated using several parameters such as the magnetic free pole density together with MCE and grain size However, the method of MCE determination from EBSD measurements was not well documented

expansion-in these reports

EBSD is a surface characterization technique that reveals detailed information about the microstructure, phases, grain size distribution, grain orientation and misorientation, and misorientation angle distribution of the material EBSD has been used for the evaluation of the effect of grain boundaries and grain boundary distribution in the BHN signals [39] However, it has not yet been reported how large the number of measured individual grain orientations must be

in order to accurately estimate the MCE from EBSD data Also, the angular dependence of derived MCE is of interest It is important to bear in mind that it is very difficult to obtain a statistically significant number of orientations from EBSD data as compared to what can be achieved from X-ray measurements

EBSD-Despite the important role that EBSD has in the study of microtextures, there is a lack of information related to the estimation of the angular dependence of the MCE from single orientations obtained through EBSD data using direct methods (not harmonic) In this thesis, it will be thoroughly discussed the physical and mathematical principles, the measurement strategy, and the number of grains required for the accurate determination of the MCE from EBSD-derived microtexture data All these will be explored in order to establish the conditions required for the application of EBSD technique in the study of magnetic anisotropy in API 5L steels

1.2 Magnetic easy axis and stress anisotropy in steels and their correlation with BHN

Among the non-destructive methods based on the exploitation of magnetic properties of materials, BHN is one of the most effective for the determination of easy magnetic axes, stress induced-anisotropy evaluation [7- 14, 36], and the characterization of other microstructural features such as grain size, and carbon content [39-42] These features are of paramount importance for pipeline inspections aimed at the detection and sizing of macro-defects like metal losses due to generalized and pitting corrosion Hence, BHN measurements have been extensively used to determine the magnetic easy and hard axes in soft ferromagnetic materials such as ASTM steels [44-46] and pipeline steels [43, 47] To do such determinations, the angular dependent method is commonly used, in which an outstanding feature of the BHN signal (RMS value, for example) is measured as

a function of the angle of the applied magnetic field with respect to a reference direction (the sample's rolling direction being a good example)

The common idea of these works is based on the assumption that BHN jumps are mainly generated by the magnetization discontinuity caused by the domain wall motion in the region around the coercivity point of the hysteresis curve [44, 45] Thus the main BHN peak, the one with the higher magnitude and duration, has been used to carry out the correlation between

material's properties and BHN measurements [46] However, BHN has been known as the contribution of both events: irreversible domain wall motion and irreversible domain rotation [47, 49] While the large intensity of BHN jumps corresponds to the irreversible domain wall motion process, the smaller jumps are responsible by the irreversible domain rotation process, associated with the nucleation and growth of reverse domains in the band from saturation to remanence These events remain unexploited in most of the previous research attempts related to the correlation with magnetic properties using BHN measurements Indeed, the experimental separation of these two processes in the analysis of BHN signals for the correlation with a particular magnetic property is still difficult This seems to be the reason why the correlation between MCE and BHN had not been observed and reported, previously

1.3 Correlation between MCE and Barkhausen noise

A connection between MCE and BHN activity was unknown until experimental observation of the correlation between the MCE and BHN signals was discovered in the earlier work by our research group [47]

The reported experimental evidence of the angular dependence of BHN on MCE on in three API steels revealed that the BHN can help estimate the MCE in the band from saturation to remanence (SR) of the hysteresis curve However, the used samples (square plates with the area of 7.5 x 7.5

material in other planes different from the rolling plane The information that can be obtained from transverse planes can provides important insights about magnetic properties of the material and their relations to microstructural features such as grain shape anisotropy and pearlite banding

In fact, it is difficult to obtain samples on transverse planes from the steel pipe as large as the aforementioned squared API steel samples Otherwise, the observation obtained only from the three types of steels previously studied is not sufficient to generalize the dependence of the BHN signals on the MCE in other ferromagnetic materials The use of samples with different types of geometry, microstructure and crystallographic texture is necessary to prove the ability of BHN measurements in the SR band for determining the MCE in ferromagnetic materials

1.4 Available models for Barkhausen noise

A large number of models have been developed from the theory of domain wall motion in order to interpret the BHN signals, while others have explained the correlation between the stress

anisotropy and Barkhausen noise Among the existing models for the Barkhausen effect, the most important ones are those of Alessandro, Beatrice, Bertotti, and Montosori (ABBM) [48], and Jiles [49] Both models use stochastic approaches to simulate the Barkhausen phenomenon

Most of the available models focus on describing the Barkhausen phenomenon and its generation due to the domain wall motion around coercivity in the hysteresis loop Therefore, the observed correlation between the MCE and BHN in the band from saturation to remanence in pipeline steels cannot be explained using these models

1.5 The nucleation of reverse domains

The nucleation of reverse domains in ferromagnetic materials has been explained by a large number of authors The most important works can be mentioned such as Néel-Brown´s model [50- 52] and Aharoni´s model [53] The Stoner-Wohlfarth´s model [54] developed for magnetic particles also was used extensively to describe the magnetization reversal process The common achievement of these models is that they can be applied successfully when the magnetic system deals with separated grains or particles, including nano-systems in which a nanoparticle can be considered as a single domain This can simplify the calculation involved because the magnetization curves now can be obtained by the Stoner- Wohlfarth ´s model However, this assumption would not be possible for a material in a macro scale in which the single domain is normally split in multiple domains to reduce magnetostatic energy and where, in addition, the interaction from grain to grain across the grain boundary is significant The evidence for the latter argument can be found in [55, 64] where it is stated that the magnetostatic energy of a uniaxial polycrystal is about one-half of that of the isolated grains and that, accordingly, the domain with in

For a polycrystal, Goodenough [56] developed a model which considers the formation and growth

of reverse domains at grain boundaries (nucleation sites) This model seems to be the best one to describe the Barkhausen activity generated in the SR band

As result of this review, it becomes clear that it is necessary to carry out a deep, thorough study about the magnetic properties of API 5L steels used in pipeline systems and their magnetic behavior during and after their inspection with magnetic NDT methods Especially, it is of great interest to study the magnetic anisotropy of these materials in order to contribute to the current, rather incomplete knowledge about this anisotropy and its impact on the magnetic inspection of operating pipelines

In summary, the aspects that motivate this study can be narrow down to the following ones

 The fact that remanent magnetization develops in pipelines after MFL inspection

 The need to accurately determine destructively and nondestructively the magnetic easy axes in pipeline steels through BHN measurements

 The need for BHN measurement systems for a wider range of sample geometries, microstructures and crystallographic textures

 To need to prove whether EBSD can be used to determine the MCE or not, and

 The lack of a physical model capable to explain the observed correlation between the MCE and BHN measurements in the SR band

Despite the practical importance of the MCE, its relationship to BHN activity has not been thoroughly studied in ferromagnetic materials in general and in pipeline steels in particular The fast and nondestructive estimation of the MCE has been impossible in ferromagnetic materials using conventional techniques The best way to make this goal possible is through the use of BHN measurements, but it is difficult to separate the MCE from the contribution of other induced components by means of currently available analysis methods

In this thesis, for the first time, the anisotropy of magnetic properties is studied using both X-ray global texture and EBSD microtexture measurements in API steels to explain the correlation between the MCE and BHN measurements It is also for the first time that a physical model capable to explain the observed correlation is proposed and developed from the microstructural features and crystallographic texture of the material

The hypotheses of the present study are:

1 It is possible to accurately determine the magnetocrystalline energy of API 5L steels from BHN measurements in samples with different geometries, microstructures, and crystallographic textures The BHN-estimated magnetocrystalline energy will agree with the predictions made from the crystallographic texture of these steels

2 It is possible to model the BHN response of these steels from the knowledge of their microstructural characteristics, crystallographic texture (from X-ray diffraction measurements) and grain boundary distribution (from EBSD measurements)

3 The magnetocrystalline energy in the investigated of API 5L steels can be predicted not only from X-ray diffraction measurements, but also from microtexture data obtained

through EBSD measurements Both predictions will agree if the number of measured grains (to be determined) is large enough

EBSD-Based on these hypotheses, the main objective of this thesis is:

To study the magnetic anisotropy of API 5L steels through Barkhausen Noise

measurements, macrotexture and microtexture measurements, and the modelling and simulation of the Barkhausen Noise phenomenon from the obtained experimental data

In order to fulfill this objective, the specific objectives of this thesis are:

1 Crystallographic texture and BHN measurements of samples of API 5L steels (grade X52, X56, and X60) on different planes (rolling, transverse, and normal) for different crystallographic textures in samples with square and circular geometry using a new method for the case of circular samples

2 Optimization of the BHN measurements for this new method with respect to the time band influenced by magnetocrystalline energy of the material Separation in the BHN signal bands due to the magnetocrystalline energy (saturation to remanence) and to induced anisotropy (movement of 180° domain walls)

3 Development of a new model relating the BHN response of the material to its crystallographic texture (from X-ray measurements), microstructural features (grain size, grain shape, and phases distribution), and grain boundary misorientation angle distribution (from EBSD measurements) The model will include stochastic features (modeling from probabilistic distributions of the above-mentioned parameters of interest)

4 Determination of the conditions (number of grains, dependence on the texture acuity) required to obtain accurate estimation of the magnetocrystalline anisotropy of the investigated steels from microtexture EBSD data This methodological aspect of the present study will help clarify when it is possible to extrapolate the results of the microtexture (local) study on crystalline anisotropy to the bulk sample

The expected results of the present study can be summarized in:

1 It is expected to obtain further evidence of the capability of the Barkhausen noise measurements to determine magnetocrystalline energy of the investigated materials

2 This expectation includes the development of a new method of BHN measurement capable

of characterizing the magnetic anisotropy of pipeline steels in several planes

3 Also, it is expected to find a good correlation between the magnetic anisotropy measurements through BHN measurements and the predictions of this anisotropy made from global (X-ray) crystallographic texture measurements

4 It is to anticipate the development of a new model for the response of the BHN signal in the hysteresis loop region where is determined by the MCE (saturation to remanence) This model is based on aspects such as the microstructure, texture and grain boundary misorientation angle distribution of the material in order to simulate the dependence of the BHN with the magnetocrystalline anisotropy energy

5 From the methodological point of view, it is expected to find the conditions (number of grains, dependence on the texture acuity) required to obtain accurate estimates of the magnetocrystalline anisotropy of the investigated steels from microtexture (EBSD) data This will help clarify when it is possible to extrapolate the results of the microtexture (local) study on crystalline anisotropy to the bulk

CHAPTER 2: MAGNETIC ANISOTROPY

Magnetic anisotropy refers to the fact that the magnetic properties of a certain material depend on the direction of the applied magnetic field A material property is anisotropic when it depends on the orientation of the sample with respect to some external frame [57] All ferromagnetic materials possess anisotropy due to their crystalline structure, which is characterized by the periodic arrangement of their unit cell As consequence of the directional dependence, the magnetic materials are classified in two categories, hard and soft [58] In fact, there is no clear distinction between the theories of magnetic anisotropy in hard and soft magnetic materials

The understanding of the magnetic anisotropy should start from the basic knowledge of magnetism This chapter reviews some basic concepts of magnetism, types of magnetic energy, Barkhausen noise It also reviews related works that have been done about magnetic anisotropy using crystallographic texture techniques and Barkhausen noise measurements

2.1 Fundamentals of magnetism and magnetic anisotropy

In a ferromagnetic material, the magnetic induction B is strongly increased when applying an

external field H [17, 25, 58]

)(

B  (2.1) where H is the applied field (A/m) and M is the magnetization per unit volume (A/m) The

the material

Equation (2.1) is the fundamental base to describe not only the magnetic behavior of materials but also the relationship between the magnetic properties and Barkhausen phenomenon (that will be discussed in detail latter in Section 2.2)

The magnetization, M, is proportional to the applied field, H

H

M  (2.2)

The principal feature of ferromagnetic materials is their ability to retain a remanent magnetization after leaving saturation This means that even in the absence of a magnetic field they present a non-zero magnetization, where their magnetic moments are, in average, aligned in the same

direction and sense Consequently, a characteristic feature of these materials is to show hysteresis

in their curves of the magnetization as a function of the magnetic field [59]

2.1.1 Hysteresis loop

It has been known that the magnetic behavior of ferromagnetic materials depends on the

magnetization history of the material [59] For the sake of demonstration, the hysteresis curve or

B-H loop is the good evidence of the aforementioned dependence The traditional method to

evaluate the magnetic properties of ferromagnetic materials is by means of the magnetization

curves or hysteresis loop (Fig 2.1) Furthermore, the existence of magnetic domains can be

explained by the magnetization curve [60, 61] Figure 2.1 shows a typical example of the

hysteresis loop of a ferromagnetic material

From the demagnetization state, point O, the sample is magnetized by increasing the applied field

H until reaching saturation at point S The dashed curve OS formed by this magnetization process

is known as the virgin curve From saturation at point S in Fig 2.1, the H field is reduced by

removing the field until R, remanence or retentability, where H is zero while the resulting B

lower rate Then, the H field has to be reversed up to point C, where B has zero value with H

necessary to achieve a null magnetic flux B [58]

Fig 2.1: Typical hysteresis loop in ferromagnetic materials The dashed curve is the so-called

virgin magnetization curve [58]

oriented When applying an external field, H, the motion of domain walls is promoted, and the

resulting domains are oriented irreversibly in a direction favorable to the applied field (see Fig 2.2b)

of domains is in the order of ten per grain with a width of some micrometers

It is well known that the domain structure is defined by the competence between different types of energies such as magnetocrystalline energy, magnetostatic energy, exchange energy, and domain wall energy [63] In the present thesis, the MCE is the main focus of study due to the practical interest of the determination of magnetic easy axes in ferromagnetic materials

2.1.3 Magnetocrystalline anisotropy energy

MCE is defined as the work that must be done to rotate the magnetization vector way from the one

of the easy axes of the crystal [64] The physical origin of the MCE is due mainly to spin-orbit coupling This refers to a coupling between the spin and the orbital motion of each electron When

an external field tries to reorient the spin of an electron, the orbit of that electron also tends to be re-oriented But the orbit is strongly coupled with the lattice and therefore resists the attempt to rotate the spin axis In effect, the energy required to rotate the spin system of a domain away from the easy direction, which is known as the MCE, is just the energy required to overcome the spin-orbit coupling [64]

It has been known that the MCE has a great practical interest because it influences the way of use and manufacturing of ferromagnetic materials This can be visualized through the examples about the role that MCE plays in the manufacturing of hard and soft magnetic materials in reference [65] where it is stressed that, for hard magnetic materials, the MCE is required to be uniaxial and as large as possible to create the strong preference of magnetization along the easy axis direction due

to the fact that this strong preference helps permanent magnets resist demagnetization in reverse field In contrast, in soft magnetic materials (for example: FeSi and NiFe alloys), the MCE requires to be as small as possible to allow magnetization saturation to rapidly occur in the lowest possible field

In a stress-free crystal MCE is responsible for the dependence of anisotropy energy on the crystallographic directions Owing to this property, in ferromagnetic materials the easy and hard axes preferentially exist along particular directions The direction where the anisotropy energy is minimum is called "the easy axis", while the direction for which the anisotropy energy is maximum, is christened "the hard axis" The determination of the MCE in a crystal and in a polycrystalline material is outlined in the following section and later in Section 2.1.4

For a cubic crystal, let the direction cosines of magnetization vector, M, be (1,2,3) with

respect to the three crystallographic axes, as shown in Fig 2.3 Because of the symmetry

characteristics that the MCE must fulfill, it is appropriate to express the magnetization direction in

spherical coordinates The direction cosines of M can be written as

where  and are the polar and azimuthal angles, respectively (Fig 2.3)

b)

Fig 2.3: a) Definition of direction cosines (1,2,3) of the magnetization vector, M, (or any direction)

in spherical coordinates in a cubic system, b) Example of the MCE anisotropy surface for pure iron with positive K 1 anisotropy constant This material exhibits easy axes along the <100> crystallographic

directions and hard axes along <111> and <110>

The basic equation for the MCE calculation in a cubic crystal is [25-27, 64]

2 3 2 2 2 1 2 2 3 2 1 2 3 2 2 2 2 2 1

),

where K 0 , K 1 , and K 2 are the anisotropy constants for a particular material and are expressed in J/cm3

)(

),(  K1 1222 2232 1232

According to the results of magnetization measurements of single ferromagnetic crystals carried out on the direction of the applied field for Fe, Ni, and Co, it is well established that for BCC Fe (Feα) the easy axes are <100>, while <110> and <111> are the hard axes In the case of Ni crystals, <111> is the easy axes, while <110> and <100> are the hard axes

If K1 is positive, for a crystal of Feα, according to Eq (2.7) the MCE anisotropy surface has a minimum along the <100> directions or easy directions, while other directions, as indicated by a

red vector in Fig 2.3, have higher values of MCE, and the maximum energy is along the directions <111> accordinglyE(,)  100 E(,)  110 E(,)  111 (Fig 2.4)

  111 ( , )  110 ( , )  100

)

,

for the sake of illustration of magnetic anisotropy and is not, however, the object of study in this thesis

Figure 2.4 shows evidences of the previous confirmation by the comparison of magnetization curves in easy and hard axes for Fe and Ni Both cases demonstrate that along the easy axes the applied field required to saturate soft ferromagnetic materials is much lower than in their hard directions

Fig 2.4: Magnetization change along easy and hard axes versus applied field in Fe and Ni crystals [58]

This behavior is similar to the anisotropy of mechanical properties, as can be seen in the following example With respect to the mechanical anisotropy, it is stated that crystallographic texture in steels has a direct effect upon their mechanical properties because the strength of any crystalline material such as steel is different along different crystallographic directions [66] For example, the strength of the body centered cubic structure of iron is strongest along the cube diagonal or <111> direction It is less strong along the face diagonal, <110>, and weakest along the cubic edge,

<100> This means that the <111> direction is preferred for good mechanical properties Whereas,

for magnetic properties, the <100> direction is preferred as easy direction of magnetization with a lower energy required for the saturation of magnetic system

The origin of the anisotropy of soft and hard magnetic polycrystalline materials is the same, that being the averaged contribution of the magnetic anisotropy of all grains (crystallites) in the material A microscopic anisotropy of a grain and a particle is either dictated by the constants of the magnetocrystalline energy or by the shape of the particle The average MCE of polycrystalline specimen must, therefore, be obtained by averaging the grain anisotropy over the grain orientation distribution function that describes the crystallographic texture of a polycrystal, as explained in details below and in [26, 27] In other words, the so-called structure-related magnetic anisotropy is the dependence of magnetic properties on its crystallographic direction in the crystal, and this orientation dependence is due to the MCE Other sources of magnetic anisotropy such as induced (rolling, magnetic annealing) and due to magnetoelastic effects have to be considered, if it is necessary and practicable, in a polycrystalline material [27-33]

2.1.4 Determination of MCE in polycrystalline materials

2.1.4.1 MCE from X-ray global texture

The anisotropic behavior of a crystal is not sufficient to understand and to draw conclusions about the properties for the polycrystal, which has more than one crystal (grain) In order to study the anisotropy of magnetic properties in a polycrystal, it is important to know the crystallographic texture or the distribution of crystal orientations in it

distribution function (ODF) f(g) (g being the crystal orientation)can be determined for any

dg g f g E

E

ES

)(),,()

,

The isotropic part of E(g) is important to compare the degree or strength of the anisotropy

BCC iron, K0 = 2/3K1 [25] However, this study is focused on the anisotropic behavior of the MCE and BHN activity and the angular dependence of their average value in the samples under

If the ODF f(g) of the material has been determined from other method than its series expansion,

the value of the texture coefficients C l  can still be determined as

are the complex conjugated of the symmetric generalized spherical harmonics [67]

If f(g) is known for each orientation gi = (1, , 2)i in Euler space (ES), a discrete form of the

   : discretization step for Euler space; commonly set to 5 deg

If the sample and crystal (cubic) symmetries are taken into account, the symmetric generalized spherical harmonics can be determined from

*

.

)(2

)(

In the expression for the harmonics:. *

T  , the index n in n and S l4mn(g)must be replaced by2() or () when the symmetry of the sample is assumed to be orthorhombic or triclinic, respectively

From Eq (2.10), the angular dependence of the average magnetocrystalline anisotropy of a rolled

determined ODF The crystallographic texture described by its orientation distribution function

(ODF) or f(g) acts as a weight function This can be carried out by two powerful techniques for

texture analysis: X-rays global texture and EBSD microtexture measurements

ODF of the sample whose texture was obtained by means of X-ray measurements

Fig 2.5: E(,)determination from the ODF, f(g), of a low-carbon steel obtained by X-ray texture

measurements From left to right, representations are the pole figure and ODF of the material, the MCE surface, and a polar plot of the MCE in the rolling plane of the material

In this material, the average MCE at E(/2,)represents a nearly-isotropic behavior due to the contribution of the {111}ND fiber texture on the rolling plane

2.1.4.2 MCE determination from EBSD

in the sample coordinate system, MCE can be easily calculated from an individual grain orientation along a given direction Fig 2.6 shows the calculation of the MCE for a given crystal

g2 = (110)[001] The results obtained from these two orientations (Fig 2.6) clearly show the dependence of the MCE on both the crystallographic direction and crystal orientation Both the magnitude and shape of the calculated MCEs for these two orientations are significantly different

nearly zero

This analysis is very useful in the case when one needs to know which texture component is dominating the MCE shape in comparison with the prediction from X-ray texture measurements Once the MCE associated with each individual grain orientation is known, the magnitude of the anisotropy energy for the polycrystalline aggregate can be easily determined by the average of the MCEs of the aggregate of grains which is the contribution of all the individual crystallites according to their orientation (Fig 2.7)

b)

Fig 2.6: MCE obtained for a cubic crystal with different orientations g, a) MCE surface in 3D

representation and in the rolling plane determined for the orientation (001)[100] b) MCE determined for the orientation (110)[001]

g E

N

E

1

),,(

1),

Equation (2.15) outlines the idea of the so-called Direct Method for the calculation of the MCE

from individual grain orientations measured by microtexture techniques such as EBSD

Fig 2.7 illustrates how the MCE can be calculated for a polycrystalline sample; this method includes averaging MCE over the individual orientations using Eq (2.15) and the MCE shapes for each grain orientation