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

INSTITUTO POLITÉCNICO NACIONAL 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 Study of magnetic anisotropy in API 5L steels Abstract 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 Study of magnetic anisotropy in API 5L steels Abstract 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 Study of magnetic anisotropy in API 5L steels Resumen 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 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 tamo 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 tamo 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 una exactitud relativamente buena la energía magnetocritsalina siempre y cuando el número de granos sea suficientemente grande, Study of magnetic anisotropy in API 5L steels Resumen teniendo en cuenta que el rango recomendable es entre unos cientos hasta mil granos para materiales diferente tamo 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) 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) Study of magnetic anisotropy in API 5L steels 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! Dedications Study of magnetic anisotropy in API 5L steels Acknowledgement 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 Study of magnetic anisotropy in API 5L steels Nomenclature NOMENCLATURE Symbol and Abbreviations Name Unit E ( ,  ) Average magnetocrystalline energy J/m3  Electrical conductivity Ω⋅m  Magnetic flux rate Wb/m2 Average size of BHN events M Cl  Texture coefficient Pl m () Normalized associated Legendre generalized spherical functions : *  l T Symmetric (g) harmonics B lm Symmetry coefficients  Magnetic free poles density  Magnetic susceptibility * Reduced magnetic free poles density APF Additional pole figure B Magnetic induction T BHN Barkhausen noise V DW Domain wall EBSD Electron back-scatter microscopy Eexchange Exchange energy J/m3 Emag Magnetostatic energy J/m3 EPF Experimental pole figure Ewall Domain wall energy J/m3 H Magnetic field strength A/m Hc Coercive field A/m Hd Demagnetization field A/m T (Tesla) Study of magnetic anisotropy in API 5L steels Conclusions time it has been proven that the use of sample-related equivalent orientations increases drastically the accuracy of the MCE estimations even for a number of grains as reduced as two hundreds As a consequence, EBSD proven to be a powerful microstructural characterization technique that helped further validate the novel result of the strong correlation between the MCE and BHN This is very promising for the in-field estimation of magnetic anisotropy of operating pipelines to be inspected by magnetic flux leakage inspection technologies The use of EBSD also validates the Direct Method as suitable for the determination of the average MCE in a polycrystal from individual grain orientations The observed strong correlation between the average MCE of the material and the energy of the BHN activity in the band from saturation to remanence has been explained as part of this work This correlation is related to the strong influence that crystallographic texture has on the number and size of Barkhausen jumps (events) associated with the nucleation of reverse domains at grain boundaries and their subsequent growth as the materials goes from saturation to remanence On the other hand, this influence can be attributed to the role that the crystallographic texture plays in the distribution of grain-to-grain misorientation within the material and, consequently, to the formation of free poles at grain boundaries due to the divergence of magnetization across them Therefore, BHN energy is proportional to the magnetic free poles density at grain boundaries, and this is proportional to the MCE; therefore, the BHN energy in the SR band is proportional to the MCE The stochastically modeled angular dependence of the average MCE in the studied API 5L steels is in good agreement, both in shape and relative magnitude (from material to material and from sample to sample) with the BHN-derived MCE and the predictions made from crystallographic texture measurements This points out to the fact that the strong correlation between the BHN signal and the MCE in the SR band is due to the role that the MCE plays in the formation of magnetic free poles at grain boundaries as explained above The results obtained in this work show that the proposed model is capable of reproducing the experimental measurements and explaining the relationship between the MCE and BHN signal from the microstructural and texture characteristics of these steels The model proposed in this thesis for the correlating between the MCE and the BHN activity in the band from saturation to remanence is presented for the first time according to the experience of the author in this field 136 Study of magnetic anisotropy in API 5L steels Conclusions The main results obtained in this thesis have been published in ISI International Journals and presented in international conferences as follows:  “On the correlation between magnetocrystalline energy and Barkhausen noise in API 5L steels: a stochastic model” Tu Le Manh, Caleyo, F and Hallen, J M., EspinaHernández, J H., J H., Pérez-Benítez, J A Journal of Electrical Engineering Vol 66, No 7/s (2015) 45-49  “Estimation of magnetocrystalline energy from Barkhausen noise measurements in API 5L steels” Tu Le Manh, Caleyo, F., Espina-Hernández, J H., J H., PérezBenítez, J A., Hallen, J M International Journal of Applied Electromagnetics and Mechanics, vol 48, no 2,3, pp 171-179, 2015  “Identification of different processes in magnetization dynamics of API steels using magnetic Barkhausen noise” Pérez-Benítez, J A, Espina-Hernández, J H., Tu Le Man, Caleyo, F and Hallen, J M J Appl Phys., Vol 48, No 29 (2015), 295002, 12pp doi: 10.1088/0022-3727/48/29/295002  "Estimation of magnetocrystalline anisotropy energy from Barkhausen noise measurements in API 5L steels", Tu Le Manh, F Caleyo, J.M Hallen, J.A PerezBenitez, J.H Espina Proceedings of the 13th International Workshop on I & II Dimensional Magnetic Measurement and Testing, Torino, Italy, 10 - 12 September (2014) Paper C3, pp 39-40 ISBN 978-88-8202-054-5  "On the correlation between magnetocrystalline energy and barkhausen noise in API 5L steels: A stochastic model", Tu-Le Manh, F Caleyo, J.M Hallen, J.A PerezBenitez, J.H Espina-Hernandez Proceedings of the International Scientific Conference - Magnetic Measurements 2015, Košice, Slovakia, 25th – 28th August (2015) Paper O2-01, pp 36 ISBN 978-80-553-2177-6 137 Study of magnetic anisotropy in API 5L steels Conclusions 7.2 FUTURE WORKS The results obtained in this thesis show evidence of the ability of BHN measurements for the determination of the MCE in pipelines steels The developed model explains that the origin of the strong correlation between the MCE and the BHN activity in in SR band is due to the formation and growth of the reverse domains at grain boundaries These are the source of the BHN events in this band and are associated to the nucleation field Hn Therefore, the accurate determination of Hn is a very important goal to pursue in future developments of this theme 7.2.1 Velocity of nucleation and growth of reverse domains By similarity with Eq (2.27), which describes the domain wall motion for the massive changes of domain walls in the regions around coercivity, the domain wall velocity of domains of reverse magnetization in the band from saturation to remanence can be derived as [55] m d 2x  v    vdt  J s H n cos( i   ) dt (7.1) The velocity of an irreversibly-growing domain of reverse magnetization is v dR  2 dt cos  i (7.2) where R is the component of the semi-minor axis on the cross sectional plane through the magnetic sample and  i is the angle formed by the direction the magnetization within the domain with the normal to the grain boundary The velocity of the nucleation and subsequent growth of reverse domains can be written as vng  dR J s  ( H n  H )[cos  cos(2 i  )] dt  where: H0  R Js   2   100 s l2  is the restoring force of the domain wall A is the domain wall thickness K1 138 (7.3) Study of magnetic anisotropy in API 5L steels  J s2 (  J s2 m ) Conclusions is the magnetic viscous damping coefficient  m : gyromagnetic ratio  : relaxation frequency According to Hauser [90, 91] dB J s  dt  (7.4) l 2vng (7.5)  Taking into account the reverse magnetization process, the reverse magnetization ratio is mrev  M rev M s  nkVk  nkVk   Ms M sVt Vt (7.6) where nk is the number of reverse domains and Vk is the volume associated with the reverse domain k-th, and Vt is the total volume of domains In this approach, it is assumed that the number of reverse domains is proportional to the number of magnetic free poles at grain boundaries, the mrev can be substituted simply by m pole  n pole (7.7) NG where: npole is the number of magnetic free poles at grain boundaries and NG is total number of grain boundaries Using the relationship between Eqs (7.4), (7.5), and (7.7), it follows that Acoil J s2 dB J s  vng  m pole ( H n  H )[cos  cos(2 i   )] dt l Asample l (7.8) Considering the function below F ( , )  cos  cos(2 i  ) Equation (7.8) can be re-written as M Nulcation  Cm pole( H n  H ) F ( , ) (7.9) where C is a proportionality constant Finally, M Nulcation   p m pole ( H n  H ) F ( , ) (7.10) where p is a proportionality constant In order to apply Eq (7.10), the domain structure of the investigated steels is very important for a 139 Study of magnetic anisotropy in API 5L steels Conclusions good estimation of an associated magnetic property According to the reference [97], the magnetic domains can be measured in situ using Fresnel images or any other conventional technique The purpose of the magnetic domain observation in API 5L steels is to determine the size and number of domains formed at a grain boundary during the nucleation process and how they grow from their nucleuses Therefore, once Hn can be exactly determined, the region of BHN signals that depends on MCE can be accurately determined both theoretically and experimentally This is also a critical aspect to study in the future in order to improve the model developed in this work for the BHN activity in the SR band 7.2.2 Estimation of MCE from BHN measurements in materials under stress In order to evaluate the behavior of the MCE from BHN measurements in conditions as close as possible to actual condition of the material when using as part of a structural component, it is important to extend the present study to samples under stress An important magnitude associated with the induced anisotropy in stressed material is characterized by the magnetostrictive energy The effect of the magnetostrictive energy into the total magnetic anisotropy of the sample is of great interest for future studies as well The magnetic energy due to stress can be quantified for a cubic crystal as [106] E  K1 ( 12 22   22 32   12 32 )  100 s ( 12 12   12 22   32 32 )  3111 s ( 1 2 1   2 3 2   1 3 1 ) (7.11) where:  ,  ,  are the direction cosines of the stress σs 100 and 111 are the saturation magnetostriction constants in the directions and , respectively Setting the stress vector in the same direction as the magnetization vector Ms, equation (7.11) can be written as E  ( K1  3111 s )(12 22   22 32  12 32 )  100 s (14   24   34 ) (7.12) In a polycrystalline material, the angular dependence of E can be assessed by taking into account the crystal orientation g E Anis ( ,  , g )  ( K1  3111 s )( g21 g22   g22 g23   g21 g23 )  100 s ( g41   g42   g43 ) (7.13) As in the prediction of the MCE from crystallographic texture, E Anis ( ,  , g ) can be determined from the X-ray measured ODF The prediction of the magnetic energy using Eq (7.13) could be compared with the angular dependence of the RMS values of BHN measurements in the band 140 Study of magnetic anisotropy in API 5L steels Conclusions from saturation to remanence to evaluate the effect of stress in the estimation of the MCE in real conditions Since the magneto-mechanical effects are associated with the induced anisotropy, they have been neglected in the determination of the MCE in the investigated steels However, this aspect will be very useful in the real estimation of the MCE from BHN measurements Thus, knowing the MCE shape and magnitude in the real condition is very important to accurately determine the magnetic easy axis in the pipelines due to the fact that they normally suffer significant stress during operation 7.2.3 MCE determination from the magnetization curves It is well known that another way to estimate the MCE is based on the magnetization curves using the area method described in reference [64] The principles of this area method are based on the following expression M E    HdM (7.14) In an attempt to include the angular dependence in the MCE estimation from the area method, Eq (7.14) can be written as M E ( , M ( ))    HdM ( ) (7.15) For each angular position from to 180° in ten-degree steps, the hysteresis loop can be measured The angular dependence of the area formed by the magnetization curve is then be determined and compared with the BHN-derived MCE in the band from saturation to remanence If these energies calculated by both methods are in good agreement, the ability of the BHN in estimating the MCE can be further validated and the value of the applied field responsible for the observed correlation can be determined through the comparison of these results Once this field is obtained, it would be possible to determine the MCE from BHN measurements in an automatic way 141 Study of magnetic anisotropy in API 5L steels Reference REFERENCES [1] Chem, C W Magnetism and metallurgy of soft magnetic materials (1977) North-Holland, pp 98 [2] Nkwachukwu, C (2011) Investigation of Magnetic Properties and Barkhausen Noise of Electrical 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