JP4660751B2 - Method and apparatus for inspecting material containing magnetic material - Google Patents

Method and apparatus for inspecting material containing magnetic material Download PDF

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JP4660751B2
JP4660751B2 JP2005057442A JP2005057442A JP4660751B2 JP 4660751 B2 JP4660751 B2 JP 4660751B2 JP 2005057442 A JP2005057442 A JP 2005057442A JP 2005057442 A JP2005057442 A JP 2005057442A JP 4660751 B2 JP4660751 B2 JP 4660751B2
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茂夫 小竹
博士 川上
浩一 長谷
充洋 太田
泰之 鈴木
智胤 青山
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Mie University NUC
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Description

本発明は、磁性体を含む材料の破面における破断時の破面進展方向や亀裂起点、延性・脆性破壊、破壊進行時の応力等の分布を測定する検査方法及び検査装置に関するものである。 The present invention relates to an inspection method and an inspection apparatus for measuring a fracture surface propagation direction at the time of fracture, a crack starting point, ductility / brittle fracture, stress distribution at the time of fracture progress, and the like.

従来、鉄鋼材料等の強磁性体を含む材料は、磁歪効果の逆に相当する「逆磁歪効果」が存在し、弾性変形等、外部応力の負荷に比例して透磁率や磁化などの磁性の性質が変化するため、それを使った非破壊検査や塑性変形状態の解析が、広く試みられてきた。例えば、非特許文献1では、磁気センサーとしてホール素子(磁束密度センサー)を用いた走査ホール素子顕微鏡によって、材料の内部応力と磁場強度を測定し、それを非破壊検査に使うことが示された。 Conventionally, materials including ferromagnetic materials such as steel materials have an “inverse magnetostrictive effect” corresponding to the inverse of the magnetostrictive effect, and magnetic properties such as permeability and magnetization are proportional to external stress such as elastic deformation. Since properties change, non-destructive inspection and plastic deformation analysis using them have been widely attempted. For example, Non-Patent Document 1 shows that a scanning Hall element microscope using a Hall element (magnetic flux density sensor) as a magnetic sensor measures the internal stress and magnetic field strength of a material and uses them for nondestructive inspection. .

一方、事故調査や製品の品質管理、製造プロセスなどにおいて、破壊形態を解析する必要性がある場合、その多くは、破面形態の単なる観察(光学又は電子顕微鏡を使用)から得られる情報を元にしたフラクトグラフィーにより、脆性破壊、延性破壊、疲労破壊、亀裂開始点などの判定を行ってきた。例えば、特許文献1が公知である。 On the other hand, when there is a need to analyze fracture forms in accident investigations, product quality control, manufacturing processes, etc., many of them are based on information obtained from simple observation of the fracture surface form (using an optical or electron microscope). The determination of brittle fracture, ductile fracture, fatigue fracture, crack initiation point, etc. has been made by the fractography. For example, Patent Document 1 is known.

太田昭男他、電気学会論文誌A, 123巻7号(2003)p.611-617.Akio Ota et al., IEEJ Transactions, Vol. 123, No. 7 (2003) p.611-617.

特開2000−266613号公報JP 2000-266613 A

しかしながら、破壊時の破面にかかる応力や亀裂の進展方向等の情報については、通常の破壊が高速に推移すること、破面が付着物に覆われて詳細が観察しにくいこと、破壊が事故の発生後に生ずること、などの理由から容易に評価することが難しかった。また従来の評価方法では、試料を電子顕微鏡などの真空装置に入れる必要があるなど、測定条件に制約があり、大気中で大きさによらず簡便に評価することは難しかった。さらに、3次元の磁束密度ベクトルの変化を積極的に破壊現象の解明に応用する技術は存在しなかった。 However, with regard to information such as the stress applied to the fracture surface at the time of fracture and the direction of crack propagation, the normal fracture is moving at high speed, the fracture surface is covered with deposits, and it is difficult to observe details, It was difficult to evaluate easily because it occurred after the occurrence. Further, in the conventional evaluation method, there are restrictions on measurement conditions such as the need to put the sample in a vacuum apparatus such as an electron microscope, and it has been difficult to easily evaluate in the atmosphere regardless of the size. Furthermore, there is no technology that positively applies the change in the three-dimensional magnetic flux density vector to the elucidation of the breakdown phenomenon.

そこで、本発明の強磁性体を含む材料の検査方法は、そのような従来の方法が有する問題点を解決するために考えられたものである。 Therefore, the method for inspecting a material containing a ferromagnetic material according to the present invention has been considered in order to solve the problems of such a conventional method.

本発明は、磁性体を含む材料の検査方法において、磁束密度センサーとしてホール素子を用い、該材料の破断表面を、3次元的に移動走査させて磁場強度と磁場ベクトルを検出することを特徴とする。又、その検査方法において、ホール素子と、該材料の破断表面との距離を概一定に保持して移動走査させることを特徴とする。さらに、ホール素子と、該材料の破断表面との距離を概一定に保持して移動走査させることを特徴とする。
測定対象の磁性体とは、例えば鉄のα相を含む鉄合金や鉄鋼材料がある。又、ホール素子とは、半導体中を流れる電流に対して垂直に掛かる磁界強度に比例して、電流と磁界方向に垂直にローレンツ力が働き電圧が発生するという原理に基づき、三つの異なる方向の磁場強度を測るセンサーを用いることにより、磁場強度と磁場ベクトルを検出することができる。
なお、本発明による破断面検査方法では、磁性体破断表面を走査させて得られる各点の磁場ベクトル方向の磁場強度を求め、この磁場強度が最大になる点を内部亀裂開始点と判断することを特徴としている。
The present invention is characterized in that, in a method for inspecting a material containing a magnetic material, a Hall element is used as a magnetic flux density sensor, and a fracture surface of the material is moved and scanned three-dimensionally to detect a magnetic field strength and a magnetic field vector. To do. Further, the inspection method is characterized in that the scanning is performed while the distance between the Hall element and the fracture surface of the material is kept substantially constant. Furthermore, it characterized and the Hall element, that to move scanned by holding a distance between the material of the fracture surface in the approximate constant.
Examples of the magnetic material to be measured include iron alloys and steel materials containing an iron α phase. The Hall element is based on the principle that a Lorentz force works in the direction perpendicular to the current and the magnetic field direction in proportion to the magnetic field strength applied perpendicularly to the current flowing in the semiconductor. By using a sensor that measures the magnetic field strength, the magnetic field strength and the magnetic field vector can be detected.
In the fracture surface inspection method according to the present invention, the magnetic field strength in the magnetic field vector direction at each point obtained by scanning the magnetic material fracture surface is obtained, and the point at which this magnetic field strength is maximum is determined as the internal crack start point. It is characterized by.

この発明の磁性体を含む材料の検査方法によれば、破壊時に破面近傍に負荷された応力により逆磁歪現象として発生した漏れ磁束ベクトルの分布の変化から、破壊された試料の破壊亀裂進展方向、亀裂開始点、破壊時の応力分布を明らかにすることができる。 According to the method for inspecting a material containing a magnetic material according to the present invention, the direction of fracture crack propagation of a fractured sample from the change in the distribution of leakage magnetic flux vector generated as an inverse magnetostriction phenomenon due to stress loaded near the fracture surface at the time of fracture. It is possible to clarify the crack initiation point and the stress distribution at the time of fracture.

図1に示すように、試料をXYZステージに乗せ、3次元またはそれ以下の磁束密度測定が可能な磁気センサーを計りたい破面近傍に配置する。破面からの距離が一定になるようにステージのz方向の高さを調整後、破面近傍の3次元方向の磁束密度を測定する。測定した残留磁束ベクトルを磁気測定装置により定量化し、コンピューターに記録する。コンピューターによりセンサーの分解能以下で破面上をXY方向にステージを走査させ、破面上の3次元磁束密度ベクトルの分布を得る。 As shown in FIG. 1, a sample is placed on an XYZ stage, and a magnetic sensor capable of measuring a three-dimensional or lower magnetic flux density is arranged in the vicinity of a fracture surface to be measured. After adjusting the height of the stage in the z direction so that the distance from the fracture surface is constant, the magnetic flux density in the three-dimensional direction near the fracture surface is measured. The measured residual magnetic flux vector is quantified by a magnetometer and recorded in a computer. The computer scans the stage in the XY directions on the fracture surface below the resolution of the sensor, and obtains the distribution of the three-dimensional magnetic flux density vector on the fracture surface.

本発明の磁性体を含む材料の検査方法を以下に記す。試料として、20×10×20mmの耐熱合金鋼に、シャルピー衝撃試験によって破断せしめた。破断後の試料破面の磁性を、図1に示す装置を用いて、3次元磁束密度センサーを走査(走査線間隔0.2mm、速度1秒/ステップ)した。その際、破面からの距離が一定になるようにステージのz方向の高さを調整することにより破断面にセンサーをほぼ接した状態に置き、x、y、z各方向の磁束密度を磁束密度測定装置により電気信号に変換後、AD変換器によりデジタル化し、PCにより各位置での3次元磁束密度ベクトルデータを記録した。その後、次の位置へXYステージにより移動させ、これをXY平面上に繰り返すことにより、3次元磁束密度ベクトルの破面上の分布図を得た。すなわち、逆磁歪現象として現れる磁化の漏れ磁束密度の分布の変化から、試料の破壊亀裂進展方向、亀裂開始点、破壊時の応力分布を明らかにすることができる。 The inspection method of the material containing the magnetic body of the present invention will be described below. As a sample, 20 × 10 × 20 mm heat-resistant alloy steel was broken by a Charpy impact test. The magnetism of the fracture surface of the sample after fracture was scanned with a three-dimensional magnetic flux density sensor (scanning line interval 0.2 mm, speed 1 second / step) using the apparatus shown in FIG. At that time, by adjusting the height of the stage in the z direction so that the distance from the fracture surface is constant, the sensor is placed in contact with the fracture surface, and the magnetic flux density in each of the x, y, and z directions is determined as the magnetic flux. After being converted into an electrical signal by a density measuring device, it was digitized by an AD converter, and three-dimensional magnetic flux density vector data at each position was recorded by a PC. After that, by moving to the next position by the XY stage and repeating this on the XY plane, a distribution map of the three-dimensional magnetic flux density vector on the fracture surface was obtained. That is, from the change in the distribution of the leakage magnetic flux density of magnetization that appears as an inverse magnetostriction phenomenon, the fracture crack propagation direction, crack start point, and stress distribution at the time of fracture can be clarified.

破壊後の強磁性体を含む材料の破面には、破壊時に破面近傍に負荷された応力により、逆磁歪現象として磁化が発生し、残留磁化が破面表面に観測される。そのため亀裂開始点など破壊時に高い応力状態が存在していた場合、高い残留磁化の変化が破壊時の応力状態の軌跡として残る。 Magnetization occurs as an inverse magnetostriction phenomenon on the fracture surface of the material containing the ferromagnetic material after the fracture due to the stress applied near the fracture surface at the time of the fracture, and residual magnetization is observed on the fracture surface. Therefore, when a high stress state such as a crack starting point exists at the time of fracture, a high change in residual magnetization remains as a locus of the stress state at the time of fracture.

また破面亀裂境界線に垂直に残留磁化の変化が残ることから、破面の進展方向を推定することが出来る。さらに破面全体の破壊時に掛かった応力の分布が評価できる。 In addition, since the change in the remanent magnetization remains perpendicular to the fracture surface crack boundary line, the progress direction of the fracture surface can be estimated. Furthermore, it is possible to evaluate the distribution of stress applied during the fracture of the entire fracture surface.

鉄鋼などの材料では、破壊時に破面に掛かった応力と垂直方向に、破面境界線に垂
直に磁化が向くため、破面全体として亀裂開始点をN極(またはS極)とし、破面終点領域を反対の極となるように、漏れ磁束密度が変化する。得られた漏れ磁束分布図を図2に示す。
In materials such as steel, the magnetization is oriented perpendicular to the fracture boundary line in the direction perpendicular to the stress applied to the fracture surface at the time of fracture, so the fracture start point of the fracture surface as a whole is the N pole (or S pole). The leakage magnetic flux density is changed so that the end point region has an opposite pole. The obtained leakage magnetic flux distribution diagram is shown in FIG.

内部亀裂開始点が存在した場合、図2に示すように破面中に磁化の極のピークとして表れ、別に電子顕微鏡のミクロな凹凸画像から破壊形態に特徴的な形態を観察する破面形態解析(フラクトグラフィー)を行い、この位置に内部亀裂開始点に典型的に見られる魚の目のような形をした破面形態であるフィッシュ・アイ状の破面電子顕微鏡写真が観察された。 When there is an internal crack initiation point, as shown in Fig. 2, it appears as a peak of magnetization pole in the fracture surface, and the fracture surface morphology analysis that observes the morphology characteristic of the fracture morphology from the micro uneven image of the electron microscope separately (Fractography) was performed, and a fish-eye-shaped fracture surface electron micrograph was observed at this position, which is a fracture surface shape shaped like a fish eye typically seen at the internal crack initiation point.

得られた漏れ磁束ベクトルの変化方向から破面亀裂進展の様子が得られる。亀裂進展の様子を図3に示す。 From the change direction of the obtained leakage magnetic flux vector, it is possible to obtain a state of fracture surface crack propagation. The state of crack growth is shown in FIG.

また漏れ磁束ベクトルの変化量から、各破面位置での破壊時の応力が得られる。図4に破壊時のシャルピー衝撃エネルギーと最大磁束密度との関係を示す。破壊時の衝撃エネルギーの大きさに対応して、応力が増加することから、破壊時の応力が大きいほど、磁束密度が高くなる傾向にあることが分かる。 Moreover, the stress at the time of a fracture | rupture in each fracture surface position is obtained from the variation | change_quantity of a leakage magnetic flux vector. FIG. 4 shows the relationship between the Charpy impact energy at break and the maximum magnetic flux density. Since the stress increases corresponding to the magnitude of the impact energy at the time of breakdown, it can be seen that the magnetic flux density tends to increase as the stress at the time of breakdown increases.

さらに、延性破面では破壊に要するエネルギーが増大する傾向から、破断面に掛かる応力は増大するため磁束密度は大きく増加し、逆に脆性破面では破断面に掛かる応力は小さく、磁束密度は減少する。このことから検査材破断面の脆性破面・延性破面の区別が簡便に付く。 Furthermore, since the stress required for fracture increases at the ductile fracture surface, the stress applied to the fracture surface increases, so the magnetic flux density increases greatly. Conversely, at the brittle fracture surface, the stress applied to the fracture surface decreases, and the magnetic flux density decreases. To do. This makes it easy to distinguish between a brittle fracture surface and a ductile fracture surface on the specimen fracture surface.

磁歪係数の符号により、応力と発生する磁化ベクトルの向きは異なるため、素材により漏れ磁束の分布と応力との関係を考慮する必要がある。 Since the direction of the stress and the generated magnetization vector differs depending on the sign of the magnetostriction coefficient, it is necessary to consider the relationship between the leakage flux distribution and the stress depending on the material.

図1に示す、本発明の磁性体を含む材料の検査装置では、少なくとも該材料の破断面を、3次元またはそれ以下の磁束密度測定が可能なホール素子等の磁性センサーを非磁性探針(0.5mm長さ以下)を用いて、破面から一定距離で走査させることにより、破面表面近傍の漏れ磁束ベクトルの分布を測定できる。この際、試料と針との間の電気抵抗を測定することにより、破面からの距離が一定になるようにステージのz方向の高さを調整する。また試料破面の高さが大きく違わない場合には、磁気プローブを支える支柱やセンサー部にバネ等で弾性をもたせることにより、接触を保つこともできる。この場合、探針の長さ(磁性センサーと試料との距離)が2mm以上となると、測定感度が著しく低下した。最適値は、0.5mm長さ以下であった。 In the inspection apparatus for a material containing a magnetic material according to the present invention shown in FIG. 1, a magnetic sensor such as a Hall element capable of measuring a three-dimensional or lower magnetic flux density is provided at least on the fracture surface of the material. 0.5 mm or less) can be used to measure the distribution of the leakage magnetic flux vector in the vicinity of the fracture surface. At this time, the height of the stage in the z direction is adjusted so that the distance from the fracture surface is constant by measuring the electrical resistance between the sample and the needle. Further, when the height of the sample fracture surface is not greatly different, contact can be maintained by providing elasticity to the support and sensor unit supporting the magnetic probe with a spring or the like. In this case, when the length of the probe (distance between the magnetic sensor and the sample) was 2 mm or more, the measurement sensitivity was significantly lowered. The optimum value was 0.5 mm or less.

図5に示す、本発明の磁性体を含む材料の検査装置のセンサー部では、一次元のホール素子等の磁気センサーの先端に透磁率の高い材料からなる針である鉄針等(1mm長さ)を介して、磁気センサーを計りたい破面に接触させることにより、計りたい破面位置から一定距離で、より精度の高い空間分解能をもつ漏れ磁束分布図を得ることが出来る。この際、試料と針との間の電気抵抗を測定することにより、破面からの距離が一定になるようにステージのz方向の高さを調整する。また試料破面の高さが大きく違わない場合には、磁気プローブを支える支柱やセンサー部にバネ等で弾性をもたせることにより、接触を保つこともできる。この場合、鉄針等の長さ(磁性センサーと試料との距離)が2mm以上となると、測定感度が著しく低下した。最適値は、1mm以下であった。 In the sensor unit of the inspection apparatus for a material containing a magnetic material according to the present invention shown in FIG. 5, an iron needle or the like (1 mm length) which is a needle made of a material having high magnetic permeability at the tip of a magnetic sensor such as a one-dimensional Hall element. ), A magnetic flux distribution map with higher accuracy in spatial resolution can be obtained at a fixed distance from the position of the fracture surface to be measured by bringing the magnetic sensor into contact with the fracture surface to be measured. At this time, the height of the stage in the z direction is adjusted so that the distance from the fracture surface is constant by measuring the electrical resistance between the sample and the needle. Further, when the height of the sample fracture surface is not greatly different, contact can be maintained by providing elasticity to the support and sensor unit supporting the magnetic probe with a spring or the like. In this case, when the length of the iron needle or the like (distance between the magnetic sensor and the sample) was 2 mm or more, the measurement sensitivity was significantly lowered. The optimum value was 1 mm or less.

本実施例では、接触型の針を用いて、磁束密度センサーと破断表面との距離を概一定に保ったが、ここに非接触型のセンサーを用いても良い。例えば、渦電流方式や電気容量方式の距離センサーを用いることもできる。針を使うと、破断表面や針が僅かに削られてしまうという欠点があるが、非接触型のセンサーではそのようなことがない。また他の接触式距離センサー(差動トランス等)を磁気ブロー部の走査前方に配置することにより、計測する位置の高さを予め測定して、磁束密度センサーの位置を制御することができる。 In this embodiment, the distance between the magnetic flux density sensor and the fracture surface is kept almost constant using a contact type needle, but a non-contact type sensor may be used here. For example, an eddy current type or capacitance type distance sensor may be used. When a needle is used, there is a drawback that the fracture surface and the needle are slightly shaved, but this is not the case with a non-contact type sensor. Further, by arranging another contact type distance sensor (differential transformer or the like) in front of the magnetic blower scanning, the position of the magnetic flux density sensor can be controlled by measuring the height of the position to be measured in advance.

さらに、破断表面で反射した赤外線の入射角度から距離を測定する、レンズによる破断表面の像の位相差検知、及びCCDカメラの像を電気信号に変換した後その波形解析によって距離を測定する等光学的なセンサーを用いても、磁束密度センサーと破断表面との距離を概一定に保つことができる。 In addition, the optical distance is measured by measuring the distance from the incident angle of infrared light reflected from the fracture surface, detecting the phase difference of the image of the fracture surface by the lens, and converting the image of the CCD camera into an electrical signal, and then measuring the distance by analyzing the waveform. Even if a typical sensor is used, the distance between the magnetic flux density sensor and the fracture surface can be kept substantially constant.

センサーをSQUID等の超伝導量子干渉計による磁束密度センサーにすることによ
り、より微弱な漏れ磁束密度の評価が可能となり、わずかな応力の変化が評価できる。
By making the sensor a magnetic flux density sensor using a superconducting quantum interferometer such as SQUID, it becomes possible to evaluate a weaker magnetic flux density and evaluate a slight change in stress.

さらにセンサーを巨大磁気抵抗素子や磁気原子間力顕微鏡にすることにより、より
空間分解能の高い漏れ磁束密度の評価が可能となり、より精密な測定が出来る。
Furthermore, by using a giant magnetoresistive element or magnetic atomic force microscope as the sensor, it is possible to evaluate the leakage magnetic flux density with higher spatial resolution, and more precise measurement is possible.

本発明の残留漏れ磁束ベクトルによる破面の評価法を用いると、事故や災害等で破壊された機械や建築物の材料の破面を大気中で測定することで、破壊形態の推定や亀裂開始点の位置、亀裂進展方向等の評価が、試料の大きさによらず可能となる。又破壊形態の制御された材料を開発する目的で、材料試験をすることに利用可能である。さらに破壊を利用した加工プロセスにおける加工パラメーターの条件を調整する目的で使用することもできる。したがって、材料の破壊挙動の制御・応用に資すること大である。 Using the fracture surface evaluation method based on the residual leakage magnetic flux vector of the present invention, the fracture surface of a machine or building material destroyed in an accident or disaster is measured in the atmosphere to estimate the fracture mode and start cracks. Evaluation of the position of a point, the crack propagation direction, etc. becomes possible regardless of the size of the sample. It can also be used for material testing for the purpose of developing controlled materials in fracture mode. Furthermore, it can also be used for the purpose of adjusting the conditions of the machining parameters in the machining process using fracture. Therefore, it is important to contribute to the control and application of the fracture behavior of materials.

本発明の実施の一形態を示した図である。It is the figure which showed one Embodiment of this invention. 本発明により測定された磁性体を含む材料の破面の磁束密度ベクトル分布を示した図である。It is the figure which showed the magnetic flux density vector distribution of the fracture surface of the material containing the magnetic body measured by this invention. 磁性体を含む材料の破面の磁束密度ベクトル分布とそこから推定された亀裂進展の様子を示した図である。It is the figure which showed the mode of the crack progress estimated from the magnetic flux density vector distribution of the fracture surface of the material containing a magnetic body. 磁性体を含む材料の破面に現れた最大磁束密度と破壊の際のシャルピー衝撃吸収エネルギーの関係を示した図である。It is the figure which showed the relationship between the maximum magnetic flux density which appeared on the fracture surface of the material containing a magnetic body, and the Charpy impact absorption energy in the case of destruction. 本発明の実施の一形態におけるセンサー部を示した図である。It is the figure which showed the sensor part in one Embodiment of this invention.

符号の説明Explanation of symbols

1 3次元磁束密度センサー
2 センサー素子部
3 磁気測定装置
4 制御用コンピューター
5 試料破面
6 自動XYZステージ
7 破壊進展方向
8 磁束密度のバー
9 3次元磁束密度センサー
10 探針
11 試料
12 試料破面


1 3D magnetic flux density sensor
2 Sensor element section 3 Magnetic measurement device 4 Control computer 5 Sample fracture surface 6 Automatic XYZ stage 7 Fracture progress direction 8 Magnetic flux density bar 9 Three-dimensional magnetic flux density sensor 10 Probe 11 Sample 12 Sample fracture surface


Claims (2)

磁性体を含む材料の破断原因を調べる検査方法において、
前記材料の破断表面上に磁束密度センサーを配置し、前記破断表面と前記磁束密度センサーとの距離を略一定に保持して3次元的に移動走査させて磁場強度と磁場ベクトルを測定し、
前記磁場ベクトルの強度が最大になる点を内部亀裂開始点と判断することを特徴とする磁性材料の破断面検査方法。
In the inspection method of examining fracture cause material containing magnetic substance,
A magnetic flux density sensor is disposed on the fracture surface of the material, and the distance between the fracture surface and the magnetic flux density sensor is held substantially constant to move and scan three-dimensionally to measure the magnetic field strength and the magnetic field vector ,
A method for inspecting a fracture surface of a magnetic material, wherein a point at which the intensity of the magnetic field vector is maximized is determined as an internal crack start point.
磁性体を含む材料の破断原因を調べる検査装置であって、An inspection device for examining the cause of breakage of a material including a magnetic material,
前記材料の破断表面上に磁束密度センサーを配置し、前記破断表面と前記磁束密度センサーとの距離を略一定に保持して3次元的に移動走査させて磁場強度と磁場ベクトルを測定し、A magnetic flux density sensor is disposed on the fracture surface of the material, and the distance between the fracture surface and the magnetic flux density sensor is held substantially constant to move and scan three-dimensionally to measure the magnetic field strength and the magnetic field vector,
前記磁場ベクトルの強度が最大になる点を内部亀裂開始点と判断することを特徴とする磁性材料の破断面検査装置。An apparatus for inspecting a fracture surface of a magnetic material, wherein a point at which the intensity of the magnetic field vector is maximized is determined as an internal crack start point.
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