Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

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Session Overview
Session
PC-2a: Poster Session (Room B) / Nondestructive Evaluation and Advanced Signal Processing 2
Time:
Wednesday, 15/Nov/2023:
1:30pm - 3:00pm

Session Chair: Prof. Kota Watanabe
Session Chair: Dr. Weiying Cheng
Session Chair: Dr. Yoshitsugu Otomo

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Presentations
ID: 283 / PC-2a: 1
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: Pipeline, Equivalent magnetic circuit, leakage flux, edge effect

EQUIVALENT MAGNETIC CIRCUIT MODELING OF AXIALLY ORIENTED PIPELINE CONSIDERING LEAKAGE FLUX EFFECT

Chong LI, Lijian YANG

Shenyang University of Technology, China, People's Republic of

Currently, analytical methods used to analyze the internal magnetic fields of pipelines seldom consider the leakage flux generated during magnetization. This paper uses the magnetic field segmentation method to establish pipeline axial equivalent magnetic circuit model that considers edge effect magnetic resistance of the detection area.



ID: 190 / PC-2a: 2
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: non-destructive testing, electromagnetic pulse-induced acoustic testing, acoustic emission, reinforced concrete, debonding

LENGTH SIZING OF CONCRETE REBAR DEBONDING BY ELECTROMAGNETIC PULSE-INDUCED ACOUSTIC TESTING

Sho TAKEDA1, Tetsuya UCHIMOTO1, Xinwu ZHOU1,2, Mitsuo HASHIMOTO3, Toshiyuki TAKAGI4

1Institute of Fluid Science, Tohoku University, Japan; 2Graduate School of Engineering, Tohoku University, Japan; 3Polytechnic University, Japan; 4Tohoku Forum for Creativity, Organization for Research Promotion, Tohoku University, Japan

An electromagnetic pulse-induced acoustic testing (EPAT) method was investigated for length sizing of a debonding between rebar and concrete of reinforced concrete. In EAPT, a pulsed electromagnetic field is applied to vibrate a rebar inside a reinforced concrete and excite elastic waves on a rebar. The elastic wave signal is detected by an acoustic emission sensor to evaluate the properties and condition of the material. By comparing the signal reach time of the elastic waves between specimens with and without a debonding, it was clarified that EPAT can be used as a length sizing method of rebar debonding.



ID: 112 / PC-2a: 3
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: electrical impedance tomography, machine learning, nondestructive evaluation, construction material, inverse problem

ADVANTAGES OF THE CONVOLUTIONAL NEURAL NETWORK IN VISUALIZING PRECISE POSITION AND SIZE BY ELECTRICAL IMPEDANCE TOMOGRAPHY

Keiya MINAKAWA1, Keigo OHTA1, Hiroaki KOMATSU1, Yunmi KIM3, Tomoko FUKUYAMA2, Takashi IKUNO1

1Tokyo University of Science; 2Ritsumeikan University; 3Hanbat National University

In visualizing inner structures in constructional materials to maintain buildings, it is important to know the size and position of the foreign objects precisely. Spatial resolutions of conductivity distributions obtained using two algorithms for electrical impedance tomography (EIT), one of the simplest and lowest cost methods for non-destructive visualization, were evaluated in terms of the position and size of foreign objects in the specimens. From theoretical and experimental aspects, we obtained that the machine learning-assisted method is more suitable for the EIT algorithm.



ID: 313 / PC-2a: 4
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: nondestructive testing, Demagnetization, Magnetic Testing

NOVEL DEMAGNETIZATION METHOD AFTER MAGNETIC TESTING

Michitaka HORI, Kazuki AKIYAMA, Daisuke NAGATA

Nihon Denji Sokki Co., LTD., Japan

In recent years, remanent magnetization after non-destructive inspection using magnetization and after transfer by electromagnet type magnets has become a problem. The influence of external magnetic fields and the demand for demagnetization accuracy in industry will be presented. Therefore, we propose a new demagnetization method and report basic demagnetization experiments and application examples of demagnetization of steel plates.



ID: 117 / PC-2a: 5
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: Silicon steel sheets, Residual stress, Magnetic permeability, Leakage magnetic flux, Three-dimensional nonlinear magnetic field FEM analysis

PROPOSAL OF MAGNETIC MEASUREMENT METHOD TO DETECT MAGNETIC PROPERTY DEGRADATION IN SHEAR PART OF SILICON STEEL SHEETS

Keisuke YOSHIMURA1, Hitoshi AOKI1, Hiroyuki NOSE2, Yuji GOTO1

1Oita University, Japan; 2IHI Corporation

Silicon steel sheets are widely used as electromagnetic yoke materials in electric motors and generators. These yoke materials have various shapes and are sheared by die presses, etc., but residual stress is generated on the sheared surface. It is known that the magnetic permeability of ferromagnetic materials generally decreases in the residual stress area, and electrical equipment using sheared silicon steel sheets may not produce the designed output. Generally, X-ray test equipment is used to measure the residual stress in the processed part, but a simpler test method is required. In this research, a DC magnetic field is applied to a silicon steel plate, and leakage magnetic flux is generated from the sheared surface. In this paper, a magnetic measurement method is proposed to evaluate the magnetic properties of the sheared surface machined part from the distribution of the leakage magnetic flux. The usefulness of this proposed method is examined by three-dimensional nonlinear magnetic field FEM analysis and verification experiments.



ID: 221 / PC-2a: 6
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: nondestructive evaluation, eddy current testing, remote field eddy current testing, 3D FEM, ferromagnetic material

SENSITIVETY IMPROVEMENT OF REMOTE FIELD EDDY CURRENT TESTING METHOD FOR FERROMAGENTIC PIPES

Kai KOMATSUBARA1, Dionishio TAKAKURA1, Yanhui GAO1, Yuji GOTOH1, Weimin GUAN2, Kazuhiro MURAMATSU3

1Oita University, Japan; 2Wuhan University, China; 3Saga University, Japan

The remote field eddy current testing (ECT) method is known to be effective in detecting external surface defects in ferromagnetic pipes used in petrochemical and steel industries. In previous research, it is clarified that the detection signal is decreased because of the phase angle difference between flux density due to the excitation current and eddy current approaches 180 degrees and cancels each other out. In this paper, an improved remote field ECT probe with ferromagnetic cores inserted inside the excitation and search coils is proposed to deviate phase angle to 180 degrees. The measured sensitivity of the proposed probe is increased by 15% compared with the conventional one. The mechanism is analysed in detail by using 3D nonlinear eddy current analysis using finite element method.



ID: 166 / PC-2a: 7
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: carburizing steel, Hysteresis magnetization curve, Conductivity, Play model method, finite element method.

NUMERICAL ANALYSIS EVALUATION OF CARBURIZING DEPTH MEASUREMENT METHOD FOR SURFACE CARBURIZING STEEL USING AC MAGNETIC FIELD

Syunsuke MIO1, Kohei KAWADA1, Naoki KANEMARU1, Yuji GOTOH2

1Graduate School of Engineering,Oita University, Japan; 2Department of Innovative Engineering, Faculty of Science and Technology, Oita University

Carburizing and quenching is a type of surface hardening method used to improve durability, such as wear resistance. In carburizing and quenching, only the surface part of the steel material is carburized, making it possible to create a steel material with a hard surface and high toughness inside the steel material. It is important for quality control to measure the hardening layer depth of this carburized material. There is a difference in the hysteresis magnetization curve and electrical conductivity between the carburized layer and the non-carburized layer. Therefore, an electromagnetic inspection method is proposed to measure the depth of the carburized layer by detecting these electromagnetic property differences. In this paper, the usefulness of the proposed method is demonstrated through 3D nonlinear FEM analysis using the play model method, which considers the hysteresis magnetization curves and conductivity of carburized and non-carburized layers. In addition, the Verification experiment is also be conducted.



ID: 397 / PC-2a: 8
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: NDE, FRP, composites, eddy current testing, capacitive imaging, dual-mode sensor

DUAL-MODE SENSOR FOR EDDY CURRENT AND CAPACITIVE NONDESTRUCTIVE EVALUATION OF FIBER REINFORCED POLYMER COMPOSITES

Oleksii KARPENKO, Mahmoodul HAQ, Lalita UDPA, Satish UDPA

Michigan State University, United States of America

Nondestructive evaluation (NDE) of Fiber reinforced plastics (FRP) is essential, but challenging owing to the presence of interlaminar interfaces and anisotropy of material properties. The present paper provides for a dual-mode concentrical sensor which may be used for flaw detection in FRP composites using eddy current testing (ECT) and capacitive imaging (CI). Combining ECT and CI techniques provides necessary synergy to detect different types of flaws in electrically conductive and insulating FRP. The proposed sensor consists of a central pancake coil and an outer ring coil. Both coils are printed on a multi-layered flexible PCB such that the windings in each layer provide the same direction of current flow. ECT and CI inspection modalities are realized by establishing proper electrical connections between the coils. Validation of the sensing technique is provided on carbon FRP and glass FRP samples with simulated flaws such as fiber breakage and interlaminar delaminations.



ID: 296 / PC-2a: 9
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: Magnetic Barkhausen noise, Numerical model, Magnetic domains, Barrier field

A NUMERICAL SCHEME FOR 3D SIMULATION OF MAGNETIC BARKHAUSEN NOISE IN MAGNETIC NDE

Zhijun WANG, Pengpeng SHI, Ke DENG, Hong-En CHEN, Zhenmao CHEN

Xi'an Jiaotong University, China

The magnetic Barkhausen noise (MBN) effect, caused by the jumps of the magnetic domains, is demonstrated sensitive to the microstructure of ferromagnetic materials, which makes it a valuable tool for evaluating the micro damage and monitoring the magnetic domain motion. This paper presents a novel 3D numerical model for MBN problem by simulating the motion of magnetic domains during magnetization evolution procedure in the applied magnetic field. The model incorporates the pinning effect of micro damage by spatially randomly distributed barriers, and characterizes the discontinuous domain jumping by comparing the barrier potential and 3D magnetic field simulated with equivalent magnetic polarization method. The proposed model exhibits potential to investigate the MBN phenomenon under complex load and damage conditions and can aid in the optimization of MBN testing devices.



ID: 298 / PC-2a: 10
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: Thermal Barrier Coating, Laser Acoustic Wave, Thickness Measurement, Delamination Defect

THERMAL BARRIER COATING INSPECTION WITH GRATING LASER ACOUSTIC WAVE SPECTRUM METHOD

Cuixiang PEI, Chen QIAN, Yuhang CHEN, Zhenmao CHEN

Xi'an Jiaotong University, China, People's Republic of

Thermal barrier coating (TBC) is widely used for the purposes of heat insulation and protection in high-temperature structural component such as aero-engine and heavy-duty gas turbine. Aiming at the difficulty of TBC measurement with conventional nondestructive testing method, a new method of surface acoustic wave spectrum analysis based on grating laser generation is proposed for both thickness measurement and delamination defect inspection of TBC. Firstly, the dispersion curve of surface acoustic waves in thermal barrier coating is obtained. Numerical simulation of grating laser acoustic signal and spectrum is then performed. Finally, both thickness measurement and debonding defect inspection of TBC with the proposed method is validated experimentally.



ID: 413 / PC-2a: 11
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: EMAT, ultrasonic surface wave, finite element simulation, pulse compression, meander coil

A NEW DESIGN OF ULTRASONIC SURFACE WAVE EMAT

Zenghua LIU1, Yanhong GUO2

1Faculty of Information Technology, Beijing University of Technology, 100124 Beijing, China; 2Faculty of Materials and Manufacturing, Beijing University of Technology, 100124 Beijing, China

The surface state of metal material is closely related to its service life. Electromagnetic acoustic transducers (EMATs) can realize the nondestructive evaluation of the surface of metal materials because of its non-contact detection characteristics. However, EMAT relies on the principle of electromagnetic induction when exciting ultrasonic waves, so it has the disadvantage of low energy conversion efficiency. In this study, a new design is proposed, and the amplitude of signal is improved by combining linear frequency modulation (LFM) signal with variable-pitch meander coil. The finite element method is used to compare the conventional EMAT with the new designed ultrasonic surface wave EMAT. The numerical analysis results show that the combination of LFM signal and variable-pitch meander coil can greatly improve the amplitude of ultrasonic surface wave.



ID: 208 / PC-2a: 12
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: sensor, eddy current

DESIGN AND ANALYSIS OF EDDY CURRENT TESTING PROBE BASED ON "EIGHT" SHAPE TRANSMITTER COILS FOR CRACK DETECTIO

Yi REN1, Kai ZHENG1, Qing ZHANG2, Jin WANG1, Hong ZHANG3, Ximing CHEN3, Chunxiong DING1

1Special Equipment Safety Supervision Inspection Institute of Jiangsu Province, China, People's Republic of; 2College of electrical engineering and control science, Nanjing Tech University, Nanjing, China; 3College of automation engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China

The detection of cracks with any orientations is a main challenge for the eddy current testing (ECT). In this paper, we propose a flexible printed circuit board (FPCB) probe based on "EIGHT" shape transmitter coils (Tx coils) to solve this problem. Firstly, the detection principle of the probe is given. Secondly, the angle of the Tx coils is designed through experiments, results shows that Tx coils with an angle of 60 is better. Finally, the probe is used for cracks with different orientations. Results show that the probe can detect both 0 - and 90-degree cracks.



ID: 176 / PC-2a: 13
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: carbon fiber reinforced plastic (CFRP), electromagnetic force vibration, Lorentz force, Nondestructive Evaluation

INSPECTION OF CARBON FIBER REINFORCED PLASTIC (CFRP) PLATE USING ELECTROMAGNETIC FORCE VIBRATION

Yuichiro HOSONO1, Shoutarou NIWA2, Takeru OHASHI3, Yuuji GOTOH1

1Faculty of Science and Technology, Oita University; 2Graduate School of Engineering, Oita University; 3IHI Corporation

The carbon fiber reinforced plastic (CFRP) material is a lightweight, high-strength material that combines carbon fiber and resin and takes advantage of the characteristics of each. This material is widely used in parts that require high strength, such as aircraft, automobiles, and hydrogen tanks. Although this material has high strength, if it is subjected to a large impact, it may cause internal delamination or internal defects. The detecting of these delamination and defects is important for strength and quality assurance of CFRP materials. In this research, the inspection method for detecting backside defects in CFRP plate is proposed from the measurement of the vibration intensity of electromagnetic force vibration. When the proposed measurement method was applied to a CFRP plate with a backside defect, the signal output was large at the defect site, indicating that this measurement method is effective.



ID: 334 / PC-2a: 14
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: Hysteresis cycles, magnetic incremental permeability, magnetic barkhausen noise, domain wall motion

INVESTIGATION OF ELASTIC STRESS DEPENDENCY OF MAGNETIC BEHAVIORS OF NON-ORIENTED ELECTRICAL STEEL

Shurui ZHANG1,2,3, Benjamin DUCHARNE2,4, Sho TAKEDA1, Gael SEBALD4, Tetsuya UCHIMOTO1,4

1Institute of Fluid Science (IFS), Tohoku University, Sendai, Japan; 2Univ. Lyon, INSA Lyon, LGEF EA682, Villeurbanne, France; 3Graduate School of Engineering, Tohoku University, Sendai, Japan; 4ELyTMaX IRL3757, CNRS, Univ Lyon, INSA Lyon, Centrale Lyon, Université Claude Bernard Lyon 1, Tohoku University, Sendai, Japan

This study monitored the Barkhausen noise, the incremental permeability, and the flux density in the same experimental conditions to evaluate the tensile elastic stress influence on magnetic behaviors. Hysteresis loops were reconstructed for all these measurements and used to define common indicators to establish correlations with elastic stress. Simulation tests based on the Jiles-Atherton-Sablik theory were run in parallel to confirm the relations between the elastic stress and assist in investigating the magnetization mechanisms.



ID: 116 / PC-2a: 15
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: electromagnetic nondestructive evaluation, pulsed eddy current, layered conductor, buried defect, quantitative screening

NEAR- AND REMOTE-FIELD PULSED EDDY CURRENT INTEGRATED EVALUATION OF FLAWS BURIED IN CONDUCTIVE STRUCTURES

Bingjie SU, Yong LI, Zhengshuai LIU, Yanzhao REN, Jin WANG, Zhenmao CHEN

Xi’an Jiaotong University, China, People's Republic of

In a bid to simultaneously exploit the advantages of pulsed eddy current and pulsed remote-field eddy current for evaluation of buried defects in layered conductors, in this paper, the near- and remote-field pulsed eddy current integrated testing (NRPEC) alongside an axi-symmetric probe has been proposed. Simulations are conducted to reveal the field characteristics underlying the proposed method and analyse the signal response to hidden flaws. In parallel, an NRPEC system has been built up. Based on the images of near-field and remote-field signal features, a fusion algorithm is proposed to fuse the signal features of near-field and remote-field signals for defect testing with the enhanced signal-to-noise ratio. Results from simulations and experiments indicate that based on the fused signal feature, high-accuracy imaging of hidden defects in a double-layer conductor can be achieved via NRPEC with the improved signal-to-noise ratio.



ID: 106 / PC-2a: 16
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: Fusion reactor, Divertor, Plasma-facing unit, Cracking.

APPLICATION OF EDDY CURRENT TESTING TO THE SURFACE INSPECTION OF DIVERTOR TUNGSTEN MONOBLOCKS.

Fanwei YU1, Takuma TOMIZAWA1, Noritaka YUSA1, Masayuki TOKITANI2

1Tohoku university, Japan; 2National Institute for Fusion Science, Japan

This study evaluates the applicability of using eddy current testing to detect the cracks that appear on the surface of full-tungsten divertor monoblocks. Tungsten blocks with artificial slits were inspected by a differential plus point probe. The results reveal that deep cracks away from the edge can be confirmed well and confirming the amplitude of signals due to an edge would be effective to detect a crack near the edge.



ID: 232 / PC-2a: 17
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: nondestructive evaluation, ultrasound, roughness, attenuation

DECREASE AT SPECIFIC FREQUENCIES IN FREQUENCY SPECTRUM OF ULTRASONIC WAVES REFLECTED ON ROUGH SURFACE

Hiroyuki NAKAMOTO1, Kazuma TERADA1, Philippe GUY2, Tetsuya UCHIMOTO3,4

1Kobe University, Japan; 2INSA Lyon, France; 3Tohoku University, Japan; 4ELyTMaX IRL3757, Japan

Flow-accelerated corrosion thins the pipe wall and makes a periodic rough surface on the inner pipe wall. The objective of this study is to develop a non-destructive evaluation method of the inner rough surface. To evaluate the roughness of the inner rough surface, a reflected wave from the surface with periodic flaws is acquired, and a frequency spectrum is calculated from the reflected wave. When the flaws are periodic, the spectrum decreases at a specific frequency. This effect on the spectrum is verified by experimental and simulation data, and a method for evaluating roughness is discussed.



ID: 168 / PC-2a: 18
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: Detection,weld defect,PECT,Tx-Rx sensor,simulation model

DETECTION OF DEFECTS IN DISSIMILAR METAL WELDS BASED ON THE TX-RX PECT PROBES

Jin WANG1, Kai ZHENG1, Yi REN1, Chunxiong DING1, Haitao WANG2

1Special Equipment Safety Supervision Inspection Institute of Jiangsu Province, China, People's Republic of; 2Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

The nuclear power equipment contains a large number of dissimilar metal welded structures, which are easy to be damaged, therefore need to be inspected. Detection of defects in dissimilar metal welds can be carried out using non-coaxial Transmitter-Receiver (Tx-Rx) PECT (pulsed eddy current testing) probes. However, considering the diverse materials and complex structure, the detection method needs to be further studied. In this paper, firstly, a simulation model is established to discuss the effects of the material distribution and the position of the excitation coil on the eddy current distribution in the dissimilar metal welded specimens. It is used for probe design. Secondly, the experimental platform is established to verify the simulation results, and the peak value of differential signal is used to analyze weld defects quantitatively.



ID: 191 / PC-2a: 19
Regular_Abstract (short paper) Submission
Topics: Nondestructive Evaluation (Electromagnetic and Mechanical methods) and Advanced Signal Processing (NEASP)
Keywords: incremental permeability, stresses, electrical sheet

INCREMENTAL PERMEABILITY FOR STRESSES ASSESSMENT

Eric WASNIEWSKI1,2,3,5, Laurent DANIEL2,3, Benjamin DUCHARNE4,5, Fan ZHANG1

1CETIM, 52 avenue Félix Louat 60300 Senlis, France; 2Université Paris-Saclay, CentraleSupélec, CNRS, Laboratoire de Génie Électrique et Électronique de Paris, 91192, Gif-sur-Yvette, France; 3Sorbonne Université, CNRS, Laboratoire de Génie Électrique et Électronique de Paris, 75252, Paris, France; 4Univ Lyon, INSA Lyon, LGEF EA682, 69621 Villeurbanne, France; 5ELyTMaX IRL3757, Univ Lyon, INSA Lyon, Centrale Lyon, Université Claude Bernard Lyon 1, Tohoku University, Sendai 980-8577, Japan

Incremental permeability measurement is one of the electromagnetic non-destructive tests (NDT) used to characterise industrial parts and evaluate cementation depth, hardness, or residual stresses. Residual stresses are a determining factor for the performance, integrity, and service life of structural steels. A precise assessment of internal stresses makes it possible to anticipate possible breakdown and degradation with disastrous consequences. The first part of the study explores the dependence of the magnetic incremental permeability of a Grain-Oriented Iron-Silicon steel on the amplitude and orientation of applied uniaxial stresses. The second part proposes a model to predict this magnetic signature.



 
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