JP2023134245A - Fatigue breakdown starting point and fatigue limit estimation method - Google Patents

Fatigue breakdown starting point and fatigue limit estimation method Download PDF

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JP2023134245A
JP2023134245A JP2022039658A JP2022039658A JP2023134245A JP 2023134245 A JP2023134245 A JP 2023134245A JP 2022039658 A JP2022039658 A JP 2022039658A JP 2022039658 A JP2022039658 A JP 2022039658A JP 2023134245 A JP2023134245 A JP 2023134245A
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秀樹 上田
Hideki Ueda
泰三 牧野
Taizo Makino
浩 白水
Hiroshi Shiromizu
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Nippon Steel Corp
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Abstract

To provide a method for accurately estimating a fatigue breakdown starting point and a fatigue limit of a measurement object on the basis of the dissipation energy distribution of the measurement object measured by using an infrared imaging device.SOLUTION: A method according to the present invention calculates a relation between stress width σa and dissipation energy q for a plurality of portions of a measurement object by imaging the measurement object by using an infrared imaging device while sequentially adding repeated loads with the different stress width σa to the measurement object, calculates for each of the plurality of portions a second-order differential value d2 obtained by performing second-order differentiation of the relation with the stress width σa, calculates for each of the plurality of portions a second-order differentiation correction value d2' obtained by multiplying the second-order differential value d2 by a fatigue limit dispersion degree R considering Vickers hardness HV of the measurement object, estimates the portion where the maximum value d2'max of the second-order differentiation correction value d2' is obtained in the plurality of portions as a fatigue breakdown starting point of the measurement object, and estimates the stress width σa in which the maximum value d2'max is obtained as a fatigue limit of the measurement object.SELECTED DRAWING: Figure 2

Description

本発明は、赤外線撮像装置を用いて測定した被測定物の散逸エネルギー分布に基づき、被測定物の疲労破壊起点及び疲労限度を精度良く推定する方法に関する。 The present invention relates to a method for accurately estimating the fatigue fracture origin and fatigue limit of a measured object based on the dissipated energy distribution of the measured object measured using an infrared imaging device.

被測定物に発生する応力分布を非接触で測定する方法として、赤外線撮像装置（サーモグラフィ）を用いた熱弾性応力測定法が提案されている（例えば、非特許文献１参照）。
熱弾性応力測定法は、被測定物が断熱的に弾性変形する際に温度変化が生じるという熱弾性効果を利用し、繰り返し負荷が付加される被測定物を赤外線撮像装置を用いて撮像することで被測定物の温度分布の時間的変化（所定時間内における温度分布の変化）を測定し、この測定した温度分布の時間的変化を被測定物の応力分布の時間的変化（所定時間内における応力分布の変化）に換算する方法である。応力分布の初期値を把握していれば（実際に応力分布を測定して把握している場合のみならず、想定可能な場合も含む）、この初期値に応力分布の時間的変化を加算することで、所定時間経過後の応力分布を測定可能である。 A thermoelastic stress measurement method using an infrared imaging device (thermography) has been proposed as a method for non-contactly measuring the stress distribution generated in a measured object (see, for example, Non-Patent Document 1).
The thermoelastic stress measurement method utilizes the thermoelastic effect in which a temperature change occurs when the measured object undergoes adiabatic elastic deformation, and uses an infrared imaging device to image the measured object under repeated loads. The temporal change in the temperature distribution of the measured object (change in temperature distribution within a predetermined time) is measured, and the temporal change in the measured temperature distribution is calculated as the temporal change in the stress distribution of the measured object (change in temperature distribution within a specified time). This is a method of converting into changes in stress distribution (changes in stress distribution). If the initial value of the stress distribution is known (not only when the stress distribution is actually measured and understood, but also when it can be predicted), the temporal change in the stress distribution is added to this initial value. This makes it possible to measure the stress distribution after a predetermined period of time has elapsed.

この熱弾性応力測定法を用いて被測定物の温度分布の時間的変化を測定する際、例えば、被測定物の周囲の熱（赤外線）が被測定物の表面で反射し、赤外線撮像装置で受光される場合がある。換言すれば、赤外線撮像装置を用いて測定した被測定物の温度分布の時間的変化に、上記のような外乱要因の他、被測定物内での熱伝導や、後述のエネルギー散逸に起因した発熱のように、熱弾性効果によって生じる温度変化（被測定物から放射される赤外線の強度変化）以外の要因で生じた温度変化が含まれる場合がある。 When measuring temporal changes in the temperature distribution of a measured object using this thermoelastic stress measurement method, for example, the heat (infrared rays) surrounding the measured object is reflected by the surface of the measured object, and the infrared imaging device Light may be received. In other words, in addition to the above-mentioned disturbance factors, changes in the temperature distribution of the measured object measured using an infrared imaging device are affected by heat conduction within the measured object and energy dissipation as described below. In some cases, such as heat generation, temperature changes caused by factors other than temperature changes caused by thermoelastic effects (changes in the intensity of infrared rays emitted from the object to be measured) are included.

このため、非特許文献１に記載の技術では、赤外線撮像装置から出力された画像信号から、測定対象とする熱弾性効果によって生じる温度変化に応じた信号波形をロックイン処理している。すなわち、赤外線撮像装置から出力された画像信号から、所定の周波数成分のみを抽出している。
具体的には、例えば、被測定物に繰り返し負荷を付加する疲労試験機から出力され、付加する繰り返し負荷と同じ周波数の参照信号を利用する。この参照信号で画像信号を同期検波し、参照信号に応じた周波数帯域の画像信号成分のみ（参照信号と同じ周波数を有する画像信号成分のみ又は参照信号と同じ周波数を含む狭周波数帯域の画像信号のみ）を抽出することで、測定すべき熱弾性効果によって生じる温度変化のＳ／Ｎ比を向上させている。そして、抽出した画像信号成分の大きさと、予め記憶されている画像信号成分の大きさ及び温度の対応関係とに応じて、被測定物の温度分布の時間的変化（赤外線撮像装置で撮像した撮像画像を構成する画素毎の温度の時間的変化）を算出する。次に、被測定物の温度分布の時間的変化と、温度の時間的変化及び応力の時間的変化の間の所定の関係式とに基づき、被測定物の応力分布の時間的変化を算出する。具体的には、被測定物の温度分布の時間的変化と、以下の式（１）で表される関係式とに基づき、被測定物の応力分布の時間的変化を算出する。
Δσ＝－１／Ｋ・ΔＴ／Ｔ ・・・（１）
上記の式（１）において、ΔＴは温度の時間的変化を、Δσは応力の時間的変化を、Ｔは被測定物の温度を、Ｋは熱弾性係数を意味する。熱弾性係数Ｋは被測定物の材質によって決まる物性値であり、例えば被測定物が鉄鋼材料から形成されている場合、Ｋ＝３．５×１０－１２［Ｐａ－１］となる。
このように、ロックイン処理を用いれば、被測定物の応力分布の時間的変化、ひいては被測定物の応力分布を精度良く算出することが可能である。 Therefore, in the technique described in Non-Patent Document 1, lock-in processing is performed on a signal waveform corresponding to a temperature change caused by a thermoelastic effect to be measured, from an image signal output from an infrared imaging device. That is, only predetermined frequency components are extracted from the image signal output from the infrared imaging device.
Specifically, for example, a reference signal output from a fatigue testing machine that repeatedly applies a load to the object to be measured and that has the same frequency as the applied repetitive load is used. The image signal is synchronously detected using this reference signal, and only the image signal component in the frequency band corresponding to the reference signal (only the image signal component having the same frequency as the reference signal or only the image signal in a narrow frequency band including the same frequency as the reference signal) ), the S/N ratio of the temperature change caused by the thermoelastic effect to be measured is improved. Then, according to the magnitude of the extracted image signal component and the correspondence relationship between the magnitude of the image signal component and the temperature stored in advance, the temporal change in the temperature distribution of the object to be measured (the image captured by the infrared imaging device) is determined. Temporal change in temperature for each pixel that makes up the image is calculated. Next, the temporal change in the stress distribution of the measured object is calculated based on the temporal change in the temperature distribution of the measured object and a predetermined relational expression between the temporal change in temperature and the temporal change in stress. . Specifically, the temporal change in the stress distribution of the measured object is calculated based on the temporal change in the temperature distribution of the measured object and the relational expression expressed by the following equation (1).
Δσ=-1/K・ΔT/T...(1)
In the above equation (1), ΔT means the temporal change in temperature, Δσ means the temporal change in stress, T means the temperature of the object to be measured, and K means the thermoelastic coefficient. The thermoelastic coefficient K is a physical property value determined by the material of the object to be measured. For example, when the object to be measured is made of a steel material, K=3.5×10 −12 [Pa −1 ].
In this way, by using the lock-in process, it is possible to accurately calculate the temporal change in the stress distribution of the object to be measured, and by extension, the stress distribution of the object to be measured.

被測定物に繰り返し負荷を付加することによって、上記の熱弾性効果に起因した温度分布の時間的変化とは別に、エネルギー散逸に起因した温度分布の時間的変化も発生する。
非特許文献２に記載のように、エネルギー散逸に起因した温度分布の時間的変化は、被測定物に最大応力と最小応力とが作用した際に、それぞれ発熱成分として発生すると考えられており、散逸エネルギーは、温度の時間的変化における、被測定物に付加する繰り返し負荷の周波数の２倍の周波数成分として定義される。この散逸エネルギーをΔＴＤとし、赤外線撮像装置を用いて測定した温度の時間的変化（ロックイン処理前の温度の時間的変化）をΔＴＭとし、熱弾性効果に起因した温度の時間的変化（ロックイン処理後の温度の時間的変化）をΔＴＥとすると、外乱要因や熱伝導を考慮しない場合、以下の式（２）が成立する。
ΔＴＤ＝ΔＴＭ－ΔＴＥ ・・・（２）
したがって、散逸エネルギー分布は、赤外線撮像装置を用いて測定可能である。具体的には、例えば、赤外線撮像装置を用いて測定した温度分布の時間的変化から、前述のようにロックイン処理によって算出した熱弾性効果に起因した温度分布の時間的変化を減算することによって算出可能である。 By repeatedly applying a load to the object to be measured, apart from the temporal change in temperature distribution due to the thermoelastic effect described above, a temporal change in temperature distribution due to energy dissipation also occurs.
As described in Non-Patent Document 2, it is believed that temporal changes in temperature distribution due to energy dissipation occur as exothermic components when maximum stress and minimum stress act on the measured object, respectively. Dissipated energy is defined as a frequency component that is twice the frequency of a repetitive load applied to an object under test in a temporal change in temperature. This dissipated energy is ΔT D , the temporal change in temperature measured using an infrared imaging device (temporal change in temperature before lock-in processing) is ΔT M , and the temporal change in temperature due to the thermoelastic effect ( When the temporal change in temperature after the lock-in process is ΔT E , the following equation (2) holds true when disturbance factors and heat conduction are not considered.
ΔT D = ΔT M - ΔT E ...(2)
Therefore, the dissipated energy distribution can be measured using an infrared imager. Specifically, for example, by subtracting the temporal change in temperature distribution due to the thermoelastic effect calculated by the lock-in process as described above from the temporal change in temperature distribution measured using an infrared imaging device. It is possible to calculate.

また、非特許文献２には、赤外線撮像装置を用いて測定した被測定物の散逸エネルギーに基づき、被測定物の疲労限度を推定することが提案されている。
具体的には、被測定物に応力幅（＝最大応力－最小応力）の異なる繰り返し負荷を順次付加（例えば、付加する繰り返し負荷の応力幅を段階的に増加させ、各応力幅の繰り返し負荷を数千サイクル程度付加）しながら、赤外線撮像装置を用いて被測定物を撮像することで、繰り返し負荷毎に被測定物の温度分布の時間的変化を測定する。そして、繰り返し負荷毎に測定した被測定物の温度分布の時間的変化に基づき、繰り返し負荷毎に被測定物の散逸エネルギー分布を算出し、この繰り返し負荷毎に算出した被測定物の散逸エネルギー分布に基づき、応力幅と散逸エネルギーとの関係を算出する。 Furthermore, Non-Patent Document 2 proposes estimating the fatigue limit of an object to be measured based on the dissipated energy of the object measured using an infrared imaging device.
Specifically, repeated loads with different stress widths (=maximum stress - minimum stress) are sequentially applied to the object to be measured (for example, the stress width of the applied repeated loads is increased stepwise, and the repeated loads of each stress width are By using an infrared imaging device to image the object under test (approximately several thousand cycles), temporal changes in the temperature distribution of the object are measured for each repeated load. Then, the dissipated energy distribution of the measured object is calculated for each repeated load based on the temporal change in the temperature distribution of the measured object measured for each repeated load, and the dissipated energy distribution of the measured object calculated for each repeated load is calculated. Based on this, calculate the relationship between stress width and dissipated energy.

図１は、応力幅と散逸エネルギーとの関係を模式的に示す図である。図１において「◆」でプロットした点が、応力幅の異なる繰り返し負荷毎に算出した散逸エネルギーである。図１に示すように、両者の関係には、ある応力幅を境にして散逸エネルギーが急増する急増点が本来的に生じる。そして、この急増点における繰り返し負荷の応力幅が、いわゆるＳ－Ｎ線図によって求められる疲労限度に対応すると考えられている。
したがって、応力幅と散逸エネルギーとの関係を算出し、散逸エネルギーが急増する急増点を検出すれば、この急増点における繰り返し負荷の応力幅を疲労限度として推定可能である。 FIG. 1 is a diagram schematically showing the relationship between stress width and dissipated energy. In FIG. 1, the points plotted with "◆" are the dissipated energy calculated for each repeated load with a different stress width. As shown in FIG. 1, in the relationship between the two, there inherently occurs a sharp increase point where the dissipated energy sharply increases after a certain stress width. It is believed that the stress width of repeated loading at this rapid increase point corresponds to the fatigue limit determined by a so-called SN diagram.
Therefore, by calculating the relationship between the stress width and the dissipated energy and detecting a sharp increase point where the dissipated energy rapidly increases, it is possible to estimate the stress width of repeated loads at this rapid rise point as the fatigue limit.

しかしながら、赤外線撮像装置を用いて測定される散逸エネルギー分布から得られる、応力幅と散逸エネルギーとの関係は、実際には、図１に示した通りのものになるとは限らず、被測定物が残留応力を含む熱処理材や溶接材である場合や、測定時に外乱要因の影響が大きい場合には、散逸エネルギーのばらつきが大きくなったり、全体的に散逸エネルギーが一定の勾配で単調増加してしまい、疲労限度を精度良く推定できる急増点が明確に生じない場合がある。 However, in reality, the relationship between the stress width and the dissipated energy obtained from the dissipated energy distribution measured using an infrared imaging device is not necessarily as shown in Figure 1; When heat-treated or welded materials contain residual stress, or when the influence of disturbance factors is large during measurement, the dissipated energy may vary widely, or the overall dissipated energy monotonically increases at a constant slope. , there are cases where a sharp increase point at which the fatigue limit can be accurately estimated does not occur clearly.

また、図１に示すような応力幅と散逸エネルギーとの関係は、被測定物の疲労破壊起点における散逸エネルギーをプロットすることを前提にしているが、被測定物が熱処理をした鉄鋼材料から形成されていたり、被測定物が溶接材である場合の溶接部近傍では、組織の違いや残留応力によって、疲労破壊起点の特定が困難な場合があり、応力集中する部位が必ずしも疲労破壊起点になるとは限らない。 Furthermore, the relationship between stress width and dissipated energy as shown in Figure 1 is based on the assumption that the dissipated energy at the fatigue fracture origin of the measured object is plotted, but if the measured object is made of heat-treated steel material, It may be difficult to identify the origin of fatigue fracture due to differences in structure and residual stress in the vicinity of the weld where the object to be measured is a welded material. is not limited.

特許文献１、２には、赤外線カメラから得られた温度画像から、測定対象物に関する、加振の基本周波数の成分の温度振幅に対する第二高調波成分の温度振幅の関係を求め、前記関係を、二次曲線である第一の近似線と二次曲線である第二の近似線によりフィッティングし、前記第一の近似線と前記第二の近似線の交点に基づき前記測定対象物の疲労限度応力を求める方法が提案されている。
また、特許文献３には、赤外線カメラが撮影した温度画像から、測定対象物に対する加振の基本周波数成分及び第２高調波成分の温度振幅画像を取得し、第２高調波成分の温度振幅画像の最大を示す領域内において、基本周波数成分の温度振幅画像に対する荷重特性の傾きが最大であるピクセル領域の散逸エネルギーから疲労限度を推定する方法が提案されている。
しかしながら、特許文献１～３に記載の方法は、図１に示すような応力幅と散逸エネルギーとの関係において、疲労限度に対応すると考えられる散逸エネルギーの急増点を検出するものではない。また、特許文献１～３に記載の方法は、疲労破壊起点を推定するものではない。 Patent Documents 1 and 2 disclose that the relationship between the temperature amplitude of the fundamental frequency component of excitation and the temperature amplitude of the second harmonic component of the object to be measured is determined from a temperature image obtained from an infrared camera, and the relationship is calculated. , fitting is performed using a first approximation line that is a quadratic curve and a second approximation line that is a quadratic curve, and the fatigue limit of the measurement object is determined based on the intersection of the first approximation line and the second approximation line. A method for determining stress has been proposed.
Furthermore, Patent Document 3 discloses that a temperature amplitude image of the fundamental frequency component and a second harmonic component of excitation of the object to be measured is acquired from a temperature image taken by an infrared camera, and a temperature amplitude image of the second harmonic component is obtained. A method has been proposed for estimating the fatigue limit from the dissipated energy of the pixel region where the slope of the load characteristic with respect to the temperature amplitude image of the fundamental frequency component is the maximum within the region showing the maximum of .
However, the methods described in Patent Documents 1 to 3 do not detect a point where the dissipated energy increases rapidly, which is considered to correspond to the fatigue limit, in the relationship between the stress width and the dissipated energy as shown in FIG. Further, the methods described in Patent Documents 1 to 3 do not estimate the starting point of fatigue fracture.

なお、非特許文献３には、疲労限度がビッカース硬さに比例することが記載されている。 Note that Non-Patent Document 3 states that the fatigue limit is proportional to Vickers hardness.

矢尾板達也、他２名、「赤外線カメラによる応力測定と疲労限界点の予測測定」、自動車技術会秋季学術講演会、Ｎｏ．９８－０３、（２００３）Tatsuya Yaoita and 2 others, “Stress measurement using an infrared camera and predictive measurement of fatigue limit point,” Society of Automotive Engineers of Japan Autumn Academic Conference, No. 98-03, (2003) 塩澤大輝、他６名、「散逸エネルギ計測に基づいたＴｉ－６Ａｌ－４Ｖ合金の疲労限度推定」、日本材料学会第６９期学術講演会講演論文集、Ｎｏ．１３２、（２０２０）Daiki Shiozawa and 6 others, “Estimation of fatigue limit of Ti-6Al-4V alloy based on dissipated energy measurement,” Proceedings of the 69th Academic Conference of the Society of Materials Science, No. 132, (2020) 「初心者のための疲労用語の解説」、日本材料学会疲労部門委員会、（２０１５）“Explanation of fatigue terminology for beginners”, Fatigue Division Committee, Japan Society of Materials Science, (2015)

特開２０１８－１０５７０９号公報Japanese Patent Application Publication No. 2018-105709 特開２０１９－１４８５０７号公報JP 2019-148507 Publication 特開２０１６－０２４０５６号公報JP2016-024056A

本発明は、上記のような従来技術の問題点を解決するためになされたものであり、赤外線撮像装置を用いて測定した被測定物の散逸エネルギー分布に基づき、被測定物の疲労破壊起点及び疲労限度を精度良く推定する方法を提供することを課題とする。 The present invention has been made to solve the problems of the prior art as described above, and is based on the dissipated energy distribution of the measured object measured using an infrared imaging device. The objective is to provide a method for estimating fatigue limits with high accuracy.

前記課題を解決するため、本発明者らは鋭意検討した結果、被測定物の複数の部位（疲労破壊起点になる可能性のある部位）に対して、被測定物に付加する繰り返し負荷の応力幅と散逸エネルギーとの関係を算出した後、この関係を応力幅で２階微分して得られる２階微分値に着目すれば、２階微分値の最大値（複数の部位に対して算出した全ての２階微分値の最大値）が得られた部位が被測定物の疲労破壊起点に対応し、２階微分値の最大値が得られた応力幅が被測定物の疲労限度に対応する可能性があることを知見した。換言すれば、被測定物の残留応力や外乱要因の影響により、応力幅と散逸エネルギーとの関係を図示するだけでは明確な急増点が生じていない場合であっても、２階微分値の最大値が得られた部位が疲労破壊起点に対応し、２階微分値の最大値が得られた応力幅が本来の急増点に相当するものになる可能性があることを知見した。
ただし、本発明者らは、２階微分値の最大値を算出するだけでは、被測定物の疲労破壊起点及び疲労限度を十分な精度で推定できない場合があることを知見した。そこで、本発明者らは、非特許文献３に記載のように、疲労限度がビッカース硬さに比例することを利用して２階微分値を補正することに着眼して、更に鋭意検討を行った。その結果、ビッカース硬さから推定される疲労限度（ビッカース硬さに所定の定数を乗算して算出される疲労限度）を基準とし、応力幅がこの基準から離れるに従って、その値が小さくなるパラメータ（本発明では、このパラメータを「疲労限度分散度」と称する）を２階微分値に乗算する補正を行えば、補正後の２階微分値（本発明では、これを「２階微分補正値」と称する）の最大値（複数の部位に対して算出した全ての２階微分補正値の最大値）が得られた部位が被測定物の疲労破壊起点に精度良く対応し、２階微分補正値の最大値が得られた応力幅が被測定物の疲労限度に精度良く対応することを知見した。 In order to solve the above-mentioned problem, the present inventors conducted extensive studies and found that the stress of repeated loads applied to multiple parts of the measured object (parts that may become the starting point of fatigue failure) After calculating the relationship between the width and the dissipated energy, if we focus on the second-order differential value obtained by second-order differentiating this relationship with the stress width, we can calculate the maximum value of the second-order differential value (calculated for multiple parts). The part where the maximum value of all second-order differential values was obtained corresponds to the fatigue fracture origin of the object to be measured, and the stress width where the maximum value of the second-order differential values was obtained corresponds to the fatigue limit of the object to be measured. I found out that there is a possibility. In other words, due to the residual stress of the object to be measured and the influence of disturbance factors, even if there is no clear sharp increase in the relationship between stress width and dissipated energy, the maximum second derivative It was found that the location where the value was obtained corresponds to the starting point of fatigue fracture, and that the stress width where the maximum value of the second order differential value was obtained may correspond to the original rapid increase point.
However, the present inventors have found that simply calculating the maximum value of the second-order differential value may not allow the fatigue fracture origin and fatigue limit of the object to be estimated with sufficient accuracy. Therefore, as described in Non-Patent Document 3, the present inventors focused on correcting the second-order differential value by utilizing the fact that the fatigue limit is proportional to the Vickers hardness, and conducted further intensive studies. Ta. As a result, the fatigue limit estimated from the Vickers hardness (the fatigue limit calculated by multiplying the Vickers hardness by a predetermined constant) is used as the standard, and as the stress width moves away from this standard, the parameter ( In the present invention, this parameter is referred to as the "fatigue limit dispersion degree"). The part where the maximum value (the maximum value of all second-order differential correction values calculated for multiple parts) of It was found that the stress width at which the maximum value of was obtained accurately corresponds to the fatigue limit of the object to be measured.

本発明は、本発明者らの上記の知見に基づき完成したものである。
すなわち、前記課題を解決するため、本発明は、被測定物に応力幅σａの異なる繰り返し負荷を順次付加しながら、赤外線撮像装置を用いて前記被測定物を撮像することで、前記繰り返し負荷毎に前記被測定物の温度分布の時間的変化を測定し、前記繰り返し負荷毎に測定した前記被測定物の温度分布の時間的変化に基づき、前記繰り返し負荷毎に前記被測定物の散逸エネルギー分布を算出し、前記繰り返し負荷毎に算出した前記被測定物の散逸エネルギー分布に基づき、前記被測定物の複数の部位に対して、それぞれ応力幅σａと散逸エネルギーｑとの関係を算出する関係算出ステップと、算出した前記関係を前記応力幅σａで２階微分して得られる前記応力幅σａ毎の２階微分値ｄ２を、前記複数の部位毎に算出する２階微分値算出ステップと、算出した前記応力幅σａ毎の２階微分値ｄ２に前記応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる前記応力幅σａ毎の２階微分補正値ｄ２’を、前記複数の部位毎に算出する２階微分補正値算出ステップと、前記複数の部位のうち、前記複数の部位に対して算出した全ての前記２階微分補正値ｄ２’の最大値ｄ２’ｍａｘが得られた部位を、前記被測定物の疲労破壊起点として推定する疲労破壊起点推定ステップと、前記最大値ｄ２’ｍａｘが得られた前記応力幅σａを前記被測定物の疲労限度として推定する疲労限度推定ステップと、を有し、前記疲労限度分散度Ｒは、以下の式（Ａ）で表される、疲労破壊起点及び疲労限度推定方法を提供する。
Ｒ＝１－ａｂｓ（１－σａ／（α・ＨＶ）） ・・・（Ａ）
上記の式（Ａ）において、σａは応力幅［ＭＰａ］であり、ＨＶは前記被測定物のビッカース硬さ［ＨＶ］であり、αは定数である。また、ａｂｓ（・）は括弧内の絶対値を意味する。 The present invention was completed based on the above findings of the present inventors.
That is, in order to solve the above problem, the present invention sequentially applies repeated loads with different stress widths σa to the measured object, and images the measured object using an infrared imaging device. measure the temporal change in the temperature distribution of the measured object, and calculate the dissipated energy distribution of the measured object for each repeated load based on the temporal change in the temperature distribution of the measured object measured for each repeated load. and calculating the relationship between the stress width σa and the dissipated energy q for each of the plurality of parts of the measured object based on the dissipated energy distribution of the measured object calculated for each repeated load. a second-order differential value calculation step of calculating, for each of the plurality of parts, a second-order differential value d2 for each of the stress widths σa obtained by second-order differentiating the calculated relationship with the stress width σa; The second-order differential correction value d2' for each stress width σa obtained by multiplying the second-order differential value d2 for each stress width σa by the fatigue limit dispersion R for each stress width σa is calculated for each of the plurality of parts. a step of calculating a second-order differential correction value to calculate a second-order differential correction value, and a step of calculating a second-order differential correction value d2' max of all the second-order differential correction values d2' calculated for the plurality of parts among the plurality of parts. , a fatigue fracture origin estimation step of estimating the fatigue fracture origin of the object to be measured; a fatigue limit estimation step of estimating the stress width σa from which the maximum value d2' max is obtained as a fatigue limit of the object to be measured; , and the fatigue limit dispersion R is expressed by the following equation (A), which provides a fatigue fracture origin and a fatigue limit estimation method.
R=1-abs(1-σa/(α・HV))...(A)
In the above formula (A), σa is the stress width [MPa], HV is the Vickers hardness [HV] of the object to be measured, and α is a constant. Moreover, abs(.) means the absolute value in parentheses.

本発明によれば、関係算出ステップにおいて、被測定物の複数の部位に対して、それぞれ応力幅σａと散逸エネルギーｑとの関係を算出し、２階微分値算出ステップにおいて、この関係を応力幅σａで２階微分して得られる応力幅σａ毎の２階微分値ｄ２を、複数の部位毎に算出する。そして、２階微分補正値算出ステップにおいて、応力幅σａ毎の２階微分値ｄ２に応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる応力幅σａ毎の２階微分補正値ｄ２’を、複数の部位毎に算出する。２階微分値ｄ２に乗算する疲労限度分散度Ｒは、式（Ａ）で表されるため、被測定物のビッカース硬さＨＶに比例する値α・ＨＶ（ビッカース硬さＨＶから推定される疲労限度に相当）を基準とし、応力幅σａがこの基準α・ＨＶに等しい場合に、Ｒは最大値である１となり、応力幅σａが基準α・ＨＶから離れるに従って、Ｒは小さな値となる。このため、本発明者らが知見した通り、疲労破壊起点推定ステップにおいて、複数の部位のうち、複数の部位に対して算出した全ての２階微分補正値ｄ２’の最大値ｄ２’ｍａｘが得られた部位を、被測定物の疲労破壊起点として精度良く推定可能である。また、疲労限度推定ステップにおいて、最大値ｄ２’ｍａｘが得られた応力幅σａを被測定物の疲労限度として精度良く推定可能である。 According to the present invention, in the relationship calculation step, the relationship between the stress width σa and the dissipated energy q is calculated for each of the plurality of parts of the object to be measured, and in the second-order differential value calculation step, this relationship is calculated as the stress width A second-order differential value d2 for each stress width σa obtained by second-order differentiation with respect to σa is calculated for each of a plurality of parts. Then, in the second-order differential correction value calculation step, the second-order differential correction value d2' for each stress width σa is obtained by multiplying the second-order differential value d2 for each stress width σa by the degree of fatigue limit dispersion R for each stress width σa. is calculated for each of multiple parts. Since the fatigue limit dispersion R, which is multiplied by the second-order differential value d2, is expressed by the formula (A), the fatigue limit dispersion R is proportional to the Vickers hardness HV of the object to be measured. When the stress width σa is equal to this reference α·HV, R has a maximum value of 1, and as the stress width σa moves away from the reference α·HV, R becomes a smaller value. Therefore, as found by the present inventors, in the fatigue fracture origin estimation step, the maximum value d2' max of all second-order differential correction values d2' calculated for a plurality of parts among the plurality of parts is obtained. It is possible to accurately estimate the location where the fatigue failure occurred as the fatigue fracture origin of the object to be measured. Furthermore, in the fatigue limit estimation step, the stress width σa from which the maximum value d2' max is obtained can be accurately estimated as the fatigue limit of the object to be measured.

なお、本発明において、応力幅σａと散逸エネルギーｑとの関係を算出する被測定物の複数の部位は、疲労破壊起点になる可能性のある部位の中から選択すればよい。具体的には、例えば、算出した散逸エネルギー分布の中で散逸エネルギーが大きく、なお且つ、同じ赤外線撮像装置を用いて算出した応力分布の中で応力が大きな部位を選択することが考えられる。
また、本発明において、ビッカース硬さＨＶは、繰り返し負荷を付加する前の被測定物に対して、公知のビッカース硬さ試験機を用いて測定すればよい。この際、ビッカース硬さの測定箇所は、応力幅σａと散逸エネルギーｑとの関係を算出する被測定物の複数の部位近傍に設定することが好ましい。また、被測定物そのものではなく、被測定物と同じ材質・形状を有する試験片を用いてビッカース硬さＨＶを測定することも可能である。
さらに、本発明において、式（Ａ）中のαは、非特許文献３に記載のように、例えば、α＝１．６に設定される。 In the present invention, the plurality of parts of the object to be measured for calculating the relationship between the stress width σa and the dissipated energy q may be selected from among parts that are likely to become fatigue fracture starting points. Specifically, for example, it is conceivable to select a portion where the dissipated energy is large in the calculated dissipated energy distribution and the stress is large in the stress distribution calculated using the same infrared imaging device.
Furthermore, in the present invention, the Vickers hardness HV may be measured using a known Vickers hardness tester on the object before being subjected to repeated loads. At this time, it is preferable that the points where the Vickers hardness is measured are set in the vicinity of a plurality of portions of the object to be measured where the relationship between the stress width σa and the dissipated energy q is calculated. Furthermore, it is also possible to measure the Vickers hardness HV using a test piece having the same material and shape as the object to be measured, rather than the object to be measured itself.
Furthermore, in the present invention, α in formula (A) is set to α=1.6, for example, as described in Non-Patent Document 3.

本発明者らの知見によれば、２階微分値ｄ２に代えて、１階微分値ｄを用いても、被測定物の疲労破壊起点及び疲労限度を精度良く推定可能である。
すなわち、前記課題を解決するため、本発明は、被測定物に応力幅σａの異なる繰り返し負荷を順次付加しながら、赤外線撮像装置を用いて前記被測定物を撮像することで、前記繰り返し負荷毎に前記被測定物の温度分布の時間的変化を測定し、前記繰り返し負荷毎に測定した前記被測定物の温度分布の時間的変化に基づき、前記繰り返し負荷毎に前記被測定物の散逸エネルギー分布を算出し、前記繰り返し負荷毎に算出した前記被測定物の散逸エネルギー分布に基づき、前記被測定物の複数の部位に対して、それぞれ応力幅σａと散逸エネルギーｑとの関係を算出する関係算出ステップと、算出した前記関係を前記応力幅σａで１階微分して得られる前記応力幅σａ毎の１階微分値ｄを、前記複数の部位毎に算出する１階微分値算出ステップと、算出した前記応力幅σａ毎の１階微分値ｄに前記応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる前記応力幅σａ毎の１階微分補正値ｄ’を、前記複数の部位毎に算出する１階微分補正値算出ステップと、前記複数の部位のうち、前記複数の部位に対して算出した全ての前記１階微分補正値ｄ’の最大値ｄ’ｍａｘが得られた部位を、前記被測定物の疲労破壊起点として推定する疲労破壊起点推定ステップと、前記最大値ｄ’ｍａｘが得られた前記応力幅σａを前記被測定物の疲労限度として推定する疲労限度推定ステップと、を有し、前記疲労限度分散度Ｒは、以下の式（Ａ）で表される、
疲労破壊起点及び疲労限度推定方法としても提供される。
Ｒ＝１－ａｂｓ（１－σａ／（α・ＨＶ）） ・・・（Ａ）
上記の式（Ａ）において、σａは応力幅［ＭＰａ］であり、ＨＶは前記被測定物のビッカース硬さ［ＨＶ］であり、αは定数である。また、ａｂｓ（・）は括弧内の絶対値を意味する。 According to the findings of the present inventors, even if the first-order differential value d is used instead of the second-order differential value d2, the fatigue fracture origin and fatigue limit of the object to be measured can be estimated with high accuracy.
That is, in order to solve the above problem, the present invention sequentially applies repeated loads with different stress widths σa to the measured object, and images the measured object using an infrared imaging device. measure the temporal change in the temperature distribution of the measured object, and calculate the dissipated energy distribution of the measured object for each repeated load based on the temporal change in the temperature distribution of the measured object measured for each repeated load. and calculating the relationship between the stress width σa and the dissipated energy q for each of the plurality of parts of the measured object based on the dissipated energy distribution of the measured object calculated for each repeated load. a first-order differential value calculating step of calculating a first-order differential value d for each of the stress widths σa obtained by first-order differentiating the calculated relationship with the stress width σa for each of the plurality of parts; The first-order differential correction value d' for each stress width σa obtained by multiplying the first-order differential value d for each stress width σa by the fatigue limit dispersion R for each stress width σa is calculated for each of the plurality of parts. a step of calculating a first-order differential correction value, and a step of calculating a first-order differential correction value for the plurality of parts, and a part from which the maximum value d' max of all the first-order differential correction values d' calculated for the plurality of parts is obtained. , a fatigue fracture origin estimation step of estimating the fatigue fracture origin of the object to be measured; a fatigue limit estimation step of estimating the stress width σa from which the maximum value d' max is obtained as a fatigue limit of the object to be measured; , and the fatigue limit dispersion R is expressed by the following formula (A):
It is also provided as a fatigue fracture origin and fatigue limit estimation method.
R=1-abs(1-σa/(α・HV))...(A)
In the above formula (A), σa is the stress width [MPa], HV is the Vickers hardness [HV] of the object to be measured, and α is a constant. Moreover, abs(.) means the absolute value in parentheses.

本発明によれば、赤外線撮像装置を用いて測定した被測定物の散逸エネルギー分布に基づき、被測定物の疲労破壊起点及び疲労限度を精度良く推定可能である。 According to the present invention, it is possible to accurately estimate the fatigue fracture origin and fatigue limit of a measured object based on the dissipated energy distribution of the measured object measured using an infrared imaging device.

応力幅と散逸エネルギーとの関係を模式的に示す図である。FIG. 3 is a diagram schematically showing the relationship between stress width and dissipated energy. 第１実施形態に係る疲労破壊起点及び疲労限度推定方法のステップを概略的に示すフロー図である。FIG. 2 is a flow diagram schematically showing steps of a fatigue fracture origin and fatigue limit estimation method according to the first embodiment. 図２に示す関係算出ステップＳＴ１で算出される、被測定物の散逸エネルギー分布の一例を示す図である。3 is a diagram showing an example of the dissipated energy distribution of the object to be measured, which is calculated in the relationship calculation step ST1 shown in FIG. 2. FIG. 応力幅σａと散逸エネルギーｑとの関係の一例を示す図である。FIG. 3 is a diagram showing an example of the relationship between stress width σa and dissipated energy q. 図４に示す応力幅σａと散逸エネルギーｑとの関係と、この関係から算出した２階微分値ｄ２と、を示す図である。5 is a diagram showing the relationship between the stress width σa and the dissipated energy q shown in FIG. 4, and the second-order differential value d2 calculated from this relationship. FIG. 図５に示す応力幅σａ毎に算出した疲労限度分散度Ｒの一例を示す。An example of fatigue limit dispersion R calculated for each stress width σa shown in FIG. 5 is shown. 図４に示す応力幅σａと散逸エネルギーｑとの関係と、図５に示す応力幅σａ毎の２階微分値ｄ２に図６に示す応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる２階微分補正値ｄ２’と、を示す図である。The relationship between the stress width σa and the dissipated energy q shown in FIG. 4 is obtained by multiplying the second-order differential value d2 for each stress width σa shown in FIG. FIG. 3 is a diagram showing a second-order differential correction value d2'. 第２実施形態に係る疲労破壊起点及び疲労限度推定方法のステップを概略的に示すフロー図である。FIG. 7 is a flow diagram schematically showing steps of a fatigue fracture origin and fatigue limit estimation method according to a second embodiment. 実施例の概要を説明する説明図である。It is an explanatory diagram explaining an outline of an example. 実施例の関係算出ステップＳＴ１で算出した応力幅σａと散逸エネルギーｑとの関係と、この関係から２階微分値算出ステップＳＴ２で算出した２階微分値ｄ２と、を示す図である。It is a figure showing the relationship between the stress width σa and the dissipated energy q calculated in the relationship calculation step ST1 of the example, and the second-order differential value d2 calculated from this relationship in the second-order differential value calculation step ST2. 実施例の関係算出ステップＳＴ１で算出した応力幅σａと散逸エネルギーｑとの関係と、この関係から１階微分値算出ステップＳＴ２’で算出した１階微分値ｄと、を示す図である。FIG. 3 is a diagram showing the relationship between the stress width σa and the dissipated energy q calculated in the relationship calculation step ST1 of the embodiment, and the first-order differential value d calculated from this relationship in the first-order differential value calculation step ST2'. 図１０及び図１１に示す応力幅σａ毎に算出した疲労限度分散度Ｒを示す。The fatigue limit dispersion degree R calculated for each stress width σa shown in FIGS. 10 and 11 is shown. 実施例の関係算出ステップＳＴ１で算出した応力幅σａと散逸エネルギーｑとの関係と、図１０に示す応力幅σａ毎の２階微分値ｄ２に図１２に示す応力幅σａ毎の疲労限度分散度Ｒを乗算して得られた２階微分補正値ｄ２’と、を示す図である。The relationship between the stress width σa and the dissipated energy q calculated in the relationship calculation step ST1 of the example, the second-order differential value d2 for each stress width σa shown in FIG. 10, and the fatigue limit dispersion degree for each stress width σa shown in FIG. 12 It is a figure which shows the second-order differential correction value d2' obtained by multiplying R. 実施例の関係算出ステップＳＴ１で算出した応力幅σａと散逸エネルギーｑとの関係と、図１１に示す応力幅σａ毎の１階微分値ｄに図１２に示す応力幅σａ毎の疲労限度分散度Ｒを乗算して得られた１階微分補正値ｄ’と、を示す図である。The relationship between the stress width σa and the dissipated energy q calculated in the relationship calculation step ST1 of the example, the first-order differential value d for each stress width σa shown in FIG. 11, and the fatigue limit dispersion degree for each stress width σa shown in FIG. 12 It is a figure which shows the first-order differential correction value d' obtained by multiplying R.

以下、添付図面を適宜参照しつつ、本発明の実施形態（第１実施形態及び第２実施形態）に係る疲労破壊起点及び疲労限度推定方法（以下、適宜、単に「推定方法」という）について説明する。 Hereinafter, with appropriate reference to the attached drawings, a fatigue fracture origin and fatigue limit estimation method (hereinafter referred to simply as "estimation method") according to embodiments (first embodiment and second embodiment) of the present invention will be explained. do.

＜第１実施形態＞
図２は、第１実施形態に係る疲労破壊起点及び疲労限度推定方法のステップを概略的に示すフロー図である。
図２に示すように、第１実施形態に係る推定方法は、関係算出ステップＳＴ１と、２階微分値算出ステップＳＴ２と、２階微分補正値算出ステップＳＴ３と、疲労破壊起点推定ステップＳＴ４と、疲労限度推定ステップＳＴ５と、を有する。以下、各ステップＳＴ１～ＳＴ５について順に説明する。 <First embodiment>
FIG. 2 is a flow diagram schematically showing the steps of the fatigue fracture origin and fatigue limit estimation method according to the first embodiment.
As shown in FIG. 2, the estimation method according to the first embodiment includes a relationship calculation step ST1, a second-order differential value calculation step ST2, a second-order differential correction value calculation step ST3, a fatigue fracture origin estimation step ST4, and a fatigue limit estimation step ST5. Below, each step ST1 to ST5 will be explained in order.

［関係算出ステップＳＴ１］
関係算出ステップＳＴ１では、疲労試験機等によって、被測定物に応力幅（＝最大応力－最小応力）σａの異なる繰り返し負荷を順次付加しながら、赤外線撮像装置を用いて被測定物を撮像することで、繰り返し負荷毎に被測定物の温度分布の時間的変化を測定する。具体的には、被測定物に付加する繰り返し負荷の応力幅σａを、応力比（＝最小応力／最大応力）を一定にした条件で段階的に増加させ、各応力幅σａの繰り返し負荷を数千サイクル程度付加しながら、赤外線撮像装置を用いて被測定物を撮像することで、繰り返し負荷毎に被測定物の温度分布の時間的変化を測定する。そして、繰り返し負荷毎に測定した被測定物の温度分布の時間的変化に基づき、繰り返し負荷毎に被測定物の散逸エネルギー分布を算出する。
具体的には、赤外線撮像装置から出力された画像信号から、熱弾性効果によって生じる温度変化に応じた信号波形をロックイン処理する（付加する繰り返し負荷と同じ周波数の参照信号で画像信号を同期検波し、参照信号に応じた周波数帯域の画像信号成分のみを抽出する）。そして、赤外線撮像装置から出力された画像信号（ロックイン処理前の画像信号）によって得られた被測定物の温度分布の時間的変化から、ロックイン処理によって抽出した画像信号成分によって得られた熱弾性効果に起因した被測定物の温度分布の時間的変化を減算することで、被測定物の散逸エネルギー分布を算出する。
なお、関係算出ステップＳＴ１の上記の手順を実行するための赤外線撮像装置としては、例えば、ＦＬＩＲ社製のＸ６５８０シリーズ（冷却式、温度分解能０．０２℃、画素数最大６４０×５１２ピクセル、フレームレート最大３５０Ｈｚ）を、散逸エネルギー分布の算出用ソフトウェアとしては、同社製のＡｌｔａｉｒＬＩを用いることができる。 [Relationship calculation step ST1]
In the relationship calculation step ST1, images of the object to be measured are taken using an infrared imaging device while sequentially applying repeated loads with different stress widths (=maximum stress - minimum stress) σa to the object to be measured using a fatigue testing machine or the like. Then, the temporal changes in the temperature distribution of the object to be measured are measured for each repeated load. Specifically, the stress width σa of the repeated load applied to the object to be measured is increased stepwise under the condition that the stress ratio (= minimum stress / maximum stress) is kept constant, and the repeated load of each stress width σa is increased several times. By imaging the object to be measured using an infrared imaging device while applying approximately 1,000 cycles, temporal changes in the temperature distribution of the object to be measured are measured for each repeated load. Then, the dissipated energy distribution of the measured object is calculated for each repeated load based on the temporal change in the temperature distribution of the measured object measured for each repeated load.
Specifically, from the image signal output from the infrared imaging device, the signal waveform corresponding to the temperature change caused by the thermoelastic effect is subjected to lock-in processing (synchronous detection of the image signal with a reference signal of the same frequency as the repeated load to be applied). Then, only the image signal components in the frequency band corresponding to the reference signal are extracted). Then, from the temporal change in the temperature distribution of the measured object obtained from the image signal output from the infrared imaging device (image signal before lock-in processing), the heat obtained by the image signal component extracted by lock-in processing is calculated. The dissipated energy distribution of the measured object is calculated by subtracting the temporal change in the temperature distribution of the measured object due to the elastic effect.
In addition, as an infrared imaging device for executing the above-mentioned procedure of the relationship calculation step ST1, for example, the As the software for calculating the dissipated energy distribution, AltairLI manufactured by the same company can be used.

次に、関係算出ステップＳＴ１では、上記のようにして、繰り返し負荷毎に算出した被測定物の散逸エネルギー分布に基づき、被測定物の複数の部位に対して、それぞれ応力幅σａと散逸エネルギーｑとの関係を算出する。
図３は、関係算出ステップＳＴ１で算出される、被測定物の散逸エネルギー分布（散逸エネルギー分布を示す画像）の一例を示す図である。図４は、応力幅σａと散逸エネルギーｑとの関係の一例を示す図である。図３に示す散逸エネルギー分布は、濃度の濃い（黒い）画素ほど、散逸エネルギーが大きいことを示している。図３及び図４に示す例では、疲労破壊起点になる可能性のある図３に示すＡｒｅａ－１、Ａｒｅａ－２、Ａｒｅａ－３（それぞれ縦横数～十数ピクセルずつの画素領域）の３箇所の部位に対して、それぞれ応力幅σａと散逸エネルギーｑとの関係を算出している。ただし、本発明はこれに限るものではなく、４箇所以上の部位に対して関係を算出してもよいし、２箇所の部位に対して関係を算出してもよい。図４（ａ）はＡｒｅａ－１に対して算出した関係を、図４（ｂ）はＡｒｅａ－２に対して算出した関係を、図４（ｃ）はＡｒｅａ－３に対して算出した関係を示す。図４に示す関係は、図３に示すような散逸エネルギー分布を繰り返し負荷毎に（段階的に増加させた異なる応力幅σａ毎に）算出し、Ａｒｅａ－１～Ａｒｅａ－３における散逸エネルギーの代表値（具体的には、平均値）を繰り返し負荷毎にプロットしたものである。なお、代表値としては、平均値に限るものではなく、例えば、最大値を用いることも可能である。 Next, in relation calculation step ST1, stress width σa and dissipated energy q are calculated for multiple parts of the object to be measured based on the dissipated energy distribution of the object to be measured calculated for each repeated load as described above. Calculate the relationship between
FIG. 3 is a diagram showing an example of the dissipated energy distribution (image showing the dissipated energy distribution) of the object to be measured, which is calculated in the relationship calculation step ST1. FIG. 4 is a diagram showing an example of the relationship between the stress width σa and the dissipated energy q. The dissipated energy distribution shown in FIG. 3 shows that the higher the density (black) of a pixel, the greater the dissipated energy. In the examples shown in FIGS. 3 and 4, three locations, Area-1, Area-2, and Area-3 (each pixel area of several to ten-odd pixels in length and width) shown in FIG. The relationship between the stress width σa and the dissipated energy q is calculated for each part. However, the present invention is not limited to this, and the relationship may be calculated for four or more sites, or the relationship may be calculated for two sites. Figure 4(a) shows the relationship calculated for Area-1, Figure 4(b) shows the relationship calculated for Area-2, and Figure 4(c) shows the relationship calculated for Area-3. show. The relationship shown in Fig. 4 is calculated by calculating the dissipated energy distribution shown in Fig. 3 for each repeated load (for each different stress width σa that is increased stepwise), and the representative dissipated energy in Area-1 to Area-3 is calculated. The values (specifically, the average values) are plotted for each repeated load. Note that the representative value is not limited to the average value, and for example, the maximum value may also be used.

[２階微分値算出ステップＳＴ２]
図４に示す応力幅σａと散逸エネルギーｑとの関係は、ノイズによってプロットした点が上下に振動しており、急増点が明確ではない。
そこで、２階微分値算出ステップＳＴ２では、関係算出ステップＳＴ１で算出した関係を応力幅σａで２階微分して得られる応力幅σａ毎の２階微分値ｄ２を、複数の部位（Ａｒｅａ－１、Ａｒｅａ－２、Ａｒｅａ－３）毎に算出する。 [Second-order differential value calculation step ST2]
In the relationship between the stress width σa and the dissipated energy q shown in FIG. 4, the plotted points oscillate up and down due to noise, and the sharp increase point is not clear.
Therefore, in the second-order differential value calculation step ST2, the second-order differential value d2 for each stress width σa obtained by second-order differentiating the relationship calculated in the relationship calculation step ST1 with respect to the stress width σa is calculated for a plurality of parts (Area-1 , Area-2, Area-3).

２階微分値ｄ２を算出する際には、まず１階微分値ｄを算出する。１階微分値ｄは、応力幅σａと散逸エネルギーｑとの関係を応力幅σａで１階微分して得られる値である。図４（ａ）に示すように、１階微分値ｄは、隣り合うプロット点の応力幅σａの変化量をΔσａとし、隣り合うプロット点の散逸エネルギーの変化量をΔｑとすると、以下の式（３）で算出される。
ｄ＝Δｑ／Δσａ ・・・（３）
すなわち、小さい方からｎ番目のプロット点の１階微分値ｄをｄｎとし、小さい方からｎ番目のプロット点の応力幅σａをσｎ、散逸エネルギーｑをｑｎとし、小さい方からｎ－１番目のプロット点の応力幅σａをσｎ－１、散逸エネルギーｑをｑｎ－１とすれば、１階微分値ｄｎは、例えば、以下の式（３）’で算出される。
ｄｎ＝（ｑｎ－ｑｎ－１）／（σｎ－σｎ－１） ・・・（３）’ When calculating the second-order differential value d2, first the first-order differential value d is calculated. The first-order differential value d is a value obtained by first-order differentiating the relationship between the stress width σa and the dissipated energy q with the stress width σa. As shown in FIG. 4(a), the first-order differential value d is calculated by the following formula, where Δσa is the amount of change in stress width σa of adjacent plot points, and Δq is the amount of change in dissipated energy of adjacent plot points. Calculated in (3).
d=Δq/Δσa...(3)
That is, let d n be the first-order differential value d of the nth plot point from the smallest one, let σ n be the stress width σa of the nth plot point from the smallest one, let q n be the dissipated energy q, and let n− If the stress width σa at the first plot point is σ n-1 and the dissipated energy q is q n-1 , the first-order differential value d n is calculated, for example, by the following equation (3)'.
d n =(q n -q n-1 )/(σ n -σ n-1 ) ...(3)'

２階微分値ｄ２は、隣り合うプロット点の１階微分値ｄの変化量をΔｄとすれば、図４（ａ）に示すように、以下の式（４）で算出される。
ｄ２＝Δｄ／Δσａ ・・・（４）
すなわち、小さい方からｎ番目のプロット点の２階微分値ｄ２をｄ２ｎとし、小さい方からｎ－１番目のプロット点の１階微分値ｄをｄｎ－１とすれば、２階微分値ｄ２ｎは、例えば、以下の式（４）’で算出される。
ｄ２ｎ＝（ｄｎ－ｄｎ－１）／（σｎ－σｎ－１）＝｛（ｑｎ－ｑｎ－１）／（σｎ－σｎ－１）－（ｑｎ－１－ｑｎ－２）／（σｎ－１－σｎ－２）｝／（σｎ－σｎ－１）・・・（４）’
上記の式（４）’において、ｑｎ－２は小さい方からｎ－２番目のプロット点の散逸エネルギーｑであり、σｎ－２は小さい方からｎ－２番目のプロット点の応力幅σａである。 The second-order differential value d2 is calculated by the following equation (4), as shown in FIG. 4(a), assuming that the amount of change in the first-order differential value d of adjacent plot points is Δd.
d2=Δd/Δσa...(4)
That is, if the second-order differential value d2 of the n-th plot point from the smallest one is d2 n , and the first-order differential value d of the n-1st plot point from the smallest one is d n-1 , then the second-order differential value d2n is calculated, for example, using the following equation (4)'.
d2 n = (d n - d n-1 )/(σ n - σ n-1 ) = {(q n - q n-1 )/(σ n - σ n-1 ) - (q n-1 - q n-2 )/(σ n-1 -σ n-2 )}/(σ n -σ n-1 )...(4)'
In the above equation (4)', q n-2 is the dissipated energy q of the n-2nd plot point from the smallest one, and σ n-2 is the stress width σa of the n-2nd plot point from the smallest one. It is.

図５は、図４に示す応力幅σａと散逸エネルギーｑとの関係と、この関係から算出した２階微分値ｄ２と、を示す図である。図５において、２階微分値ｄ２は「＋」でプロットしている。図５（ａ）はＡｒｅａ－１に対して算出したものを、図５（ｂ）はＡｒｅａ－２に対して算出したものを、図５（ｃ）はＡｒｅａ－３に対して算出したものを示す。
図５（ａ）に示すように、Ａｒｅａ－１では、応力幅σａがσ７のときに２階微分値ｄ２が最大値になっている。図５（ｂ）に示すように、Ａｒｅａ－２でも、応力幅σａがσ７のときに２階微分値ｄ２が最大値になっているが、応力幅σａがσ９のときにも２階微分値ｄ２が最大値に近い値になっている。図５（ｃ）に示すように、Ａｒｅａ－３では、応力幅σａがσ１０のときに２階微分値ｄ２が最大値になっている。そして、Ａｒｅａ－１～Ａｒｅａ－３の各部位における２階微分値ｄ２の最大値を比較すると、Ａｒｅａ－１における応力幅σａがσ７のときの２階微分値ｄ２が、全ての部位Ａｒｅａ－１～Ａｒｅａ－３における２階微分値ｄ２の最大値になっている。このため、仮に、全ての部位Ａｒｅａ－１～Ａｒｅａ３における２階微分値ｄ２の最大値が得られた部位を、被測定物の疲労破壊起点と推定し、全ての部位Ａｒｅａ－１～Ａｒｅａ３における２階微分値ｄ２の最大値が得られた応力幅σａを、被測定物の疲労限度と推定するのであれば、図５に示す例では、疲労破壊起点がＡｒｅａ－１であり、疲労限度が応力幅σ７になる。しかしながら、本発明者らの知見によれば、この結果は、疲労試験を行って確認される疲労破壊起点や、疲労試験から得られるＳ－Ｎ線図から求められる疲労限度と合致しない。このため、第１実施形態に係る推定方法では、以下に述べるように、疲労限度がビッカース硬さに比例することを利用して２階微分値ｄ２を補正した２階微分補正値ｄ２’を用いて推定する。 FIG. 5 is a diagram showing the relationship between the stress width σa and the dissipated energy q shown in FIG. 4, and the second-order differential value d2 calculated from this relationship. In FIG. 5, the second-order differential value d2 is plotted as "+". Figure 5(a) shows what is calculated for Area-1, Figure 5(b) shows what is calculated for Area-2, and Figure 5(c) shows what is calculated for Area-3. show.
As shown in FIG. 5(a), in Area-1, when the stress width σa is σ7 , the second-order differential value d2 is the maximum value. As shown in Figure 5(b), in Area-2 as well, the second-order differential value d2 reaches its maximum value when the stress width σa is σ 7 , but it also reaches the second-order differential value when the stress width σa is σ 9 . The differential value d2 is close to the maximum value. As shown in FIG. 5(c), in Area-3, when the stress width σa is σ10 , the second-order differential value d2 is the maximum value. Then, when comparing the maximum value of the second-order differential value d2 in each part of Area-1 to Area-3, it is found that the second-order differential value d2 when the stress width σa in Area-1 is σ 7 is the same in all parts Area-1. This is the maximum value of the second-order differential value d2 in Areas 1 to 3. For this reason, it is assumed that the part where the maximum value of the second-order differential value d2 in all parts Area-1 to Area-3 is obtained is the fatigue fracture origin of the measured object, and If the stress width σa at which the maximum value of the floor differential value d2 is obtained is estimated as the fatigue limit of the measured object, in the example shown in FIG. 5, the fatigue fracture origin is Area-1, and the fatigue limit is The width becomes σ 7 . However, according to the findings of the present inventors, this result does not match the fatigue fracture origin confirmed by conducting a fatigue test or the fatigue limit determined from the SN diagram obtained from the fatigue test. For this reason, the estimation method according to the first embodiment uses a second-order differential correction value d2' that corrects the second-order differential value d2 by utilizing the fact that the fatigue limit is proportional to Vickers hardness, as described below. Estimate.

[２階微分補正値算出ステップＳＴ３]
２階微分補正値算出ステップＳＴ３では、２階微分値算出ステップＳＴ２で算出した２階微分値ｄ２を補正する際に、疲労限度分散度Ｒを用いる。
非特許文献３には、疲労限度がビッカース硬さに比例することが記載されている。したがって、被測定物のビッカース硬さをＨＶとし、所定の定数をαとすれば、疲労限度は、α・ＨＶで推定される。すなわち、疲労限度推定値をσａ＿ｓｔｄとすれば、疲労限度推定値σａ＿ｓｔｄは、以下の式（５）で表される。
σａ＿ｓｔｄ＝α・ＨＶ ・・・（５）
そして、２階微分補正値算出ステップＳＴ３では、疲労限度分散度Ｒとして、疲労限度推定値σａ＿ｓｔｄを基準とし、応力幅σａがこの基準から離れるに従って、その値が小さくなるパラメータを用いる。具体的には、以下の式（６）で表される疲労限度分散度Ｒを用いる。
Ｒ＝１－ａｂｓ（１－σａ／σａ＿ｓｔｄ） ・・・（６）
上記の式（５）を式（６）に代入することにより、以下の式（Ａ）が得られる。
Ｒ＝１－ａｂｓ（１－σａ／（α・ＨＶ）） ・・・（Ａ）
上記の式（Ａ）において、σａは応力幅［ＭＰａ］であり、ＨＶは前記被測定物のビッカース硬さ［ＨＶ］であり、αは定数である。また、ａｂｓ（・）は括弧内の絶対値を意味する。ビッカース硬さＨＶは、例えば、繰り返し負荷を付加する前の被測定物に対して、公知のビッカース硬さ試験機を用いて測定すればよい。
図６は、図５に示す応力幅σａ毎に算出した疲労限度分散度Ｒの一例を示す。図６から分かるように、疲労限度推定値σａ＿ｓｔｄを基準とし、応力幅σａがこの基準から離れるに従って、疲労限度分散度Ｒの値が小さくなっている。 [Second-order differential correction value calculation step ST3]
In the second-order differential correction value calculation step ST3, the fatigue limit dispersion degree R is used when correcting the second-order differential value d2 calculated in the second-order differential value calculation step ST2.
Non-Patent Document 3 describes that the fatigue limit is proportional to Vickers hardness. Therefore, if the Vickers hardness of the object to be measured is HV and the predetermined constant is α, the fatigue limit is estimated as α·HV. That is, if the fatigue limit estimated value is σa _std , the fatigue limit estimated value σa _std is expressed by the following equation (5).
σa_std = α・HV...(5)
Then, in the second-order differential correction value calculation step ST3, a parameter is used as the degree of fatigue limit dispersion R, which uses the estimated fatigue limit value σa_std as a reference, and whose value decreases as the stress width σa departs from this reference. Specifically, the fatigue limit dispersion R expressed by the following equation (6) is used.
R=1-abs(1-σa/ σa_std )...(6)
By substituting the above equation (5) into equation (6), the following equation (A) is obtained.
R=1-abs(1-σa/(α・HV))...(A)
In the above formula (A), σa is the stress width [MPa], HV is the Vickers hardness [HV] of the object to be measured, and α is a constant. Moreover, abs(.) means the absolute value in parentheses. The Vickers hardness HV may be measured, for example, using a known Vickers hardness tester on the object before being subjected to repeated loads.
FIG. 6 shows an example of fatigue limit dispersion R calculated for each stress width σa shown in FIG. As can be seen from FIG. 6, with the fatigue limit estimated value σa_std as a reference, the value of the fatigue limit dispersion R becomes smaller as the stress width σa moves away from this reference.

そして、２階微分補正値算出ステップＳＴ３では、２階微分値算出ステップＳＴ２で算出した応力幅σａ毎の２階微分値ｄ２に応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる応力幅σａ毎の２階微分補正値ｄ２’を、複数の部位（Ａｒｅａ－１、Ａｒｅａ－２、Ａｒｅａ－３）毎に算出する。
図７は、図４に示す応力幅σａと散逸エネルギーｑとの関係と、図５に示す応力幅σａ毎の２階微分値ｄ２に図６に示す応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる２階微分補正値ｄ２’と、を示す図である。図７において、２階微分補正値ｄ２’は「×」でプロットしている。図７（ａ）はＡｒｅａ－１に対して算出したものを、図７（ｂ）はＡｒｅａ－２に対して算出したものを、図７（ｃ）はＡｒｅａ－３に対して算出したものを示す。 Then, in the second-order differential correction value calculation step ST3, the stress obtained by multiplying the second-order differential value d2 for each stress width σa calculated in the second-order differential value calculation step ST2 by the fatigue limit dispersion R for each stress width σa A second-order differential correction value d2' for each width σa is calculated for each of a plurality of parts (Area-1, Area-2, Area-3).
FIG. 7 shows the relationship between the stress width σa and the dissipated energy q shown in FIG. 4, and the fatigue limit dispersion degree R for each stress width σa shown in FIG. It is a figure which shows the second-order differential correction value d2' obtained by multiplication. In FIG. 7, the second-order differential correction value d2' is plotted as "x". Figure 7(a) shows what is calculated for Area-1, Figure 7(b) shows what is calculated for Area-2, and Figure 7(c) shows what is calculated for Area-3. show.

[疲労破壊起点推定ステップＳＴ４]
疲労破壊起点推定ステップＳＴ４では、複数の部位（Ａｒｅａ－１、Ａｒｅａ－２、Ａｒｅａ－３）のうち、複数の部位に対して算出した全ての２階微分補正値ｄ２’の最大値ｄ２’ｍａｘが得られた部位を、被測定物の疲労破壊起点として推定する。
図７に示す例では、Ａｒｅａ－３において、全ての２階微分補正値ｄ２’の最大値ｄ２’ｍａｘが得られているため、Ａｒｅａ－３が被測定物の疲労破壊起点として推定されることになる。 [Fatigue fracture origin estimation step ST4]
In the fatigue fracture origin estimation step ST4, the maximum value d2' max of all second-order differential correction values d2' calculated for a plurality of parts (Area-1, Area-2, Area-3) is calculated. The location where is obtained is estimated as the starting point of fatigue failure of the object to be measured.
In the example shown in FIG. 7, since the maximum value d2' max of all second-order differential correction values d2' is obtained in Area-3, Area-3 is estimated to be the fatigue fracture origin of the measured object. become.

[疲労限度推定ステップＳＴ５]
疲労限度推定ステップＳＴ５では、最大値ｄ２’ｍａｘが得られた応力幅σａを被測定物の疲労限度として推定する。
図７に示す例では、Ａｒｅａ－３におけるσ１０において最大値ｄ２’ｍａｘが得られているため、σ１０が被測定物の疲労限度として推定されることになる。 [Fatigue limit estimation step ST5]
In the fatigue limit estimation step ST5, the stress width σa from which the maximum value d2' max is obtained is estimated as the fatigue limit of the object to be measured.
In the example shown in FIG. 7, the maximum value d2' max is obtained at σ 10 in Area-3, so σ 10 is estimated as the fatigue limit of the object to be measured.

以上に説明した第１実施形態に係る疲労限度推定方法によれば、関係算出ステップＳＴ１において、被測定物の複数の部位（図３に示す例では、Ａｒｅａ－１～Ａｒｅａ－３の３箇所の部位）に対して、それぞれ応力幅σａと散逸エネルギーｑとの関係を算出し、２階微分値算出ステップＳＴ２において、この関係を応力幅σａで２階微分して得られる応力幅σａ毎の２階微分値ｄ２を、複数の部位毎に算出する。そして、２階微分補正値算出ステップＳＴ３において、応力幅σａ毎の２階微分値ｄ２に応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる応力幅σａ毎の２階微分補正値ｄ２’を、複数の部位毎に算出する。被測定物のビッカース硬さＨＶに比例する疲労限度推定値σａ＿ｓｔｄ（σａ＿ｓｔｄ＝α・ＨＶ）を基準とし、応力幅σａがこの基準である疲労限度推定値σａ＿ｓｔｄに等しい場合に、疲労限度分散度Ｒは最大値である１となり、応力幅σａが疲労限度推定値σａ＿ｓｔｄから離れるに従って、疲労限度分散度Ｒは小さな値となる。このため、本発明者らが知見した通り、疲労破壊起点推定ステップＳＴ４において、複数の部位のうち、複数の部位に対して算出した全ての２階微分補正値ｄ２’の最大値ｄ２’ｍａｘが得られた部位を、被測定物の疲労破壊起点として精度良く推定可能である。また、疲労限度推定ステップＳＴ５において、最大値ｄ２’ｍａｘが得られた応力幅σａを被測定物の疲労限度として精度良く推定可能である。 According to the fatigue limit estimation method according to the first embodiment described above, in the relationship calculation step ST1, a plurality of parts of the object to be measured (in the example shown in FIG. 3, three parts Area-1 to Area-3) For each stress width σa, the relationship between the stress width σa and the dissipated energy q is calculated for each part), and in the second-order differential value calculation step ST2, this relationship is second-order differentiated by the stress width σa. A floor differential value d2 is calculated for each of the plurality of parts. Then, in the second-order differential correction value calculation step ST3, the second-order differential correction value d2 for each stress width σa is obtained by multiplying the second-order differential value d2 for each stress width σa by the degree of fatigue limit dispersion R for each stress width σa. ' is calculated for each of multiple parts. Based on the estimated fatigue limit value σa _std (σa _std = α・HV) which is proportional to the Vickers hardness HV of the measured object, when the stress width σa is equal to the estimated fatigue limit value σa _std which is this standard, the fatigue limit is determined. The degree of dispersion R has a maximum value of 1, and as the stress width σa moves away from the estimated fatigue limit value σa_std , the degree of fatigue limit dispersion R becomes a smaller value. Therefore, as found by the present inventors, in the fatigue fracture origin estimation step ST4, the maximum value d2' max of all second-order differential correction values d2' calculated for a plurality of parts among the plurality of parts is The obtained location can be accurately estimated as the starting point of fatigue fracture of the object to be measured. Furthermore, in the fatigue limit estimation step ST5, the stress width σa from which the maximum value d2' max is obtained can be accurately estimated as the fatigue limit of the object to be measured.

＜第２実施形態＞
図８は、第２実施形態に係る疲労破壊起点及び疲労限度推定方法のステップを概略的に示すフロー図である。
本発明者らの知見によれば、２階微分値ｄ２に代えて、１階微分値ｄを用いても、被測定物の疲労破壊起点及び疲労限度を精度良く推定可能である。第２実施形態に係る推定方法は、１階微分値ｄを用いる点のみが第１実施形態に係る推定方法と異なり、その他の部分は第１実施形態に係る推定方法と同様であるため、以下、第１実施形態と異なる点についてのみ簡単に説明し、同様の部分については説明を省略する。 <Second embodiment>
FIG. 8 is a flow diagram schematically showing the steps of the fatigue fracture origin and fatigue limit estimation method according to the second embodiment.
According to the findings of the present inventors, even if the first-order differential value d is used instead of the second-order differential value d2, the fatigue fracture origin and fatigue limit of the object to be measured can be estimated with high accuracy. The estimation method according to the second embodiment differs from the estimation method according to the first embodiment only in that the first differential value d is used, and the other parts are the same as the estimation method according to the first embodiment. , only the points that are different from the first embodiment will be briefly described, and the description of the similar parts will be omitted.

図８に示すように、第２実施形態に係る推定方法は、関係算出ステップＳＴ１と、１階微分値算出ステップＳＴ２’と、１階微分補正値算出ステップＳＴ３’と、疲労破壊起点推定ステップＳＴ４’と、疲労限度推定ステップＳＴ５’と、を有する。以下、各ステップＳＴ１～ＳＴ５’について順に説明する。 As shown in FIG. 8, the estimation method according to the second embodiment includes a relationship calculation step ST1, a first-order differential value calculation step ST2', a first-order differential correction value calculation step ST3', and a fatigue fracture origin estimation step ST4. ', and a fatigue limit estimation step ST5'. Below, each step ST1 to ST5' will be explained in order.

［関係算出ステップＳＴ１］
関係算出ステップＳＴ１で実行する内容は、図２に示す第１実施形態に係る推定方法の関係算出ステップＳＴ１と同様である。 [Relationship calculation step ST1]
The content executed in the relationship calculation step ST1 is the same as the relationship calculation step ST1 of the estimation method according to the first embodiment shown in FIG.

［１階微分値算出ステップＳＴ２’］
１階微分値算出ステップＳＴ２’では、関係算出ステップＳＴ１で算出した関係を応力幅σａで１階微分して得られる応力幅σａ毎の１階微分値ｄを、複数の部位（例えば、Ａｒｅａ－１、Ａｒｅａ－２、Ａｒｅａ－３）毎に算出する。
第１実施形態に係る推定方法の２階微分値算出ステップＳＴ２では、前述の式（４）（より具体的には、式（４）’）を用いて２階微分値ｄ２を算出したが、１階微分値算出ステップＳＴ２’では、前述の式（３）（より具体的には、式（３）’）を用いて１階微分値ｄを算出する。 [First-order differential value calculation step ST2']
In the first-order differential value calculation step ST2', the first-order differential value d for each stress width σa obtained by first-order differentiation of the relationship calculated in the relationship calculation step ST1 with respect to the stress width σa is applied to multiple parts (for example, Area- 1, Area-2, Area-3).
In the second-order differential value calculation step ST2 of the estimation method according to the first embodiment, the second-order differential value d2 was calculated using the above-mentioned formula (4) (more specifically, formula (4)'). In the first-order differential value calculation step ST2', the first-order differential value d is calculated using the above-mentioned equation (3) (more specifically, equation (3)').

［１階微分補正値算出ステップＳＴ３’］
１階微分補正値算出ステップＳＴ３’でも、１階微分値算出ステップＳＴ２’で算出した１階微分値ｄを補正する際に、疲労限度分散度Ｒを用いる。この疲労限度分散度Ｒは、第１実施形態に係る推定方法の２階微分補正値算出ステップＳＴ３で用いるものと同様（図６参照）である。
そして、１階微分補正値算出ステップＳＴ３’では、１階微分値算出ステップＳＴ２’で算出した応力幅σａ毎の１階微分値ｄに応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる応力幅σａ毎の１階微分補正値ｄ’を、複数の部位毎に算出する。 [First-order differential correction value calculation step ST3']
In the first-order differential correction value calculation step ST3', the fatigue limit dispersion degree R is also used when correcting the first-order differential value d calculated in the first-order differential value calculation step ST2'. This fatigue limit dispersion degree R is the same as that used in the second-order differential correction value calculation step ST3 of the estimation method according to the first embodiment (see FIG. 6).
In the first-order differential correction value calculation step ST3', the first-order differential value d for each stress width σa calculated in the first-order differential value calculation step ST2' is multiplied by the fatigue limit dispersion R for each stress width σa. A first-order differential correction value d' for each stress width σa is calculated for each of the plurality of parts.

［疲労破壊起点推定ステップＳＴ４’］
疲労破壊起点推定ステップＳＴ４’では、複数の部位のうち、複数の部位に対して算出した全ての１階微分補正値ｄ’の最大値ｄ’ｍａｘが得られた部位を、被測定物の疲労破壊起点として推定する。 [Fatigue fracture origin estimation step ST4']
In the fatigue fracture origin estimation step ST4', the part for which the maximum value d' max of all the first-order differential correction values d' calculated for the plurality of parts is obtained is determined as the fatigue of the measured object. Estimated as the starting point of failure.

[疲労限度推定ステップＳＴ５’]
疲労限度推定ステップＳＴ５’では、最大値ｄ’ｍａｘが得られた応力幅σａを被測定物の疲労限度として推定する。 [Fatigue limit estimation step ST5']
In the fatigue limit estimation step ST5', the stress width σa from which the maximum value d' max is obtained is estimated as the fatigue limit of the object to be measured.

以上に説明した第２実施形態に係る疲労限度推定方法によっても、疲労破壊起点推定ステップＳＴ４’において、複数の部位のうち、複数の部位に対して算出した全ての１階微分補正値ｄ’の最大値ｄ’ｍａｘが得られた部位を、被測定物の疲労破壊起点として精度良く推定可能である。また、疲労限度推定ステップＳＴ５’において、最大値ｄ’ｍａｘが得られた応力幅σａを被測定物の疲労限度として精度良く推定可能である。 Also in the fatigue limit estimation method according to the second embodiment described above, in the fatigue fracture origin estimation step ST4', all the first-order differential correction values d' calculated for a plurality of parts among the plurality of parts are The location where the maximum value d' max is obtained can be accurately estimated as the fatigue fracture origin of the object to be measured. Furthermore, in the fatigue limit estimation step ST5', the stress width σa from which the maximum value d' max is obtained can be accurately estimated as the fatigue limit of the object to be measured.

＜実施例＞
以下、本発明の実施形態（第１実施形態及び第２実施形態）に係る推定方法を実行した実施例について説明する。
図９は、本実施例の概要を説明する説明図である。図９（ａ）は、本実施例で用いた被測定物としての試験片１を模式的に示す図である。試験片１としては、ＳＣＭ鋼の焼入れ材を用いた。図９（ｂ）は、図９（ａ）に示す試験片１の破線２で囲った領域について、関係算出ステップＳＴ１で算出された散逸エネルギー分布の一例を示す図である。 <Example>
Hereinafter, an example in which the estimation method according to the embodiments (first embodiment and second embodiment) of the present invention is executed will be described.
FIG. 9 is an explanatory diagram illustrating the outline of this embodiment. FIG. 9(a) is a diagram schematically showing the test piece 1 as the object to be measured used in this example. As test piece 1, a hardened SCM steel material was used. FIG. 9(b) is a diagram showing an example of the dissipated energy distribution calculated in the relationship calculation step ST1 for the area surrounded by the broken line 2 of the test piece 1 shown in FIG. 9(a).

本実施例では、試験片１の複数の部位（後述のＡｒｅａ－１～Ａｒｅａ－３）近傍の部位について、公知のビッカース硬さ試験機を用いて、ビッカース硬さＨＶを予め測定した。測定したビッカース硬さＨＶは、３００［ＨＶ］であった。
そして、本実施例の関係算出ステップＳＴ１では、試験片１を、繰り返し負荷を付加する疲労試験機に取り付け、応力幅σａ＝２５０～６００ＭＰａ（応力比：－１、繰り返し周波数：７Ｈｚ）の範囲で段階的に応力幅σａを増加させ、各応力幅σａの繰り返し負荷を２０００サイクルずつ付加した。この状態で、赤外線撮像装置を用いて試験片１を撮像することで、繰り返し負荷毎に試験片１の温度分布の時間的変化を測定した。赤外線撮像装置としては、ＦＬＩＲ社製のＸ６５８０シリーズを用い、フレームレートを１４９Ｈｚに設定して、繰り返し負荷毎に１０ｓｅｃ間の測定を行なった（１０ｓｅｃ間における温度分布の変化を測定した）。そして、ＦＬＩＲ社製のＡｌｔａｉｒＬＩを用いて、散逸エネルギー分布を算出した。図９（ｂ）は、上記の手順で算出した散逸エネルギー分布の一例である。
次に、本実施例の関係算出ステップＳＴ１では、図９（ｂ）に示すような散逸エネルギー分布に基づき、試験片１の３箇所の部位（図９（ｂ）に示すＡｒｅａ－１、Ａｒｅａ－２、Ａｒｅａ－３）に対して、それぞれ応力幅σａと散逸エネルギーｑとの関係を算出した。Ａｒｅａ－１～Ａｒｅａ－３は、いずれも１５×１５ピクセル（２ｍｍ×２ｍｍに相当）の画素領域である。上記の関係における散逸エネルギーｑとしては、Ａｒｅａ－１～Ａｒｅａ－３における散逸エネルギーの平均値を用いた。 In this example, the Vickers hardness HV was measured in advance at multiple sites (Area-1 to Area-3 described later) of the test piece 1 using a known Vickers hardness tester. The measured Vickers hardness HV was 300 [HV].
Then, in the relationship calculation step ST1 of this example, the test piece 1 is attached to a fatigue testing machine that applies repeated loads, and the test piece 1 is tested in the range of stress width σa = 250 to 600 MPa (stress ratio: -1, repetition frequency: 7 Hz). The stress width σa was increased stepwise, and a repeated load of each stress width σa was applied for 2000 cycles. In this state, the test piece 1 was imaged using an infrared imaging device to measure temporal changes in the temperature distribution of the test piece 1 for each repeated load. As an infrared imaging device, an X6580 series manufactured by FLIR was used, the frame rate was set to 149 Hz, and measurements were performed for 10 seconds for each repeated load (changes in temperature distribution were measured for 10 seconds). Then, the dissipated energy distribution was calculated using AltairLI manufactured by FLIR. FIG. 9(b) is an example of the dissipated energy distribution calculated by the above procedure.
Next, in the relationship calculation step ST1 of this example, based on the dissipated energy distribution as shown in FIG. 9(b), three parts of the test piece 1 (Area-1, Area- 2, Area-3), the relationship between the stress width σa and the dissipated energy q was calculated. Area-1 to Area-3 are all pixel areas of 15×15 pixels (equivalent to 2 mm×2 mm). As the dissipated energy q in the above relationship, the average value of the dissipated energy in Area-1 to Area-3 was used.

本実施例の２階微分値算出ステップＳＴ２では、関係算出ステップＳＴ１で算出した関係を応力幅σａで２階微分して得られる応力幅σａ毎の２階微分値ｄ２を、Ａｒｅａ－１～Ａｒｅａ－３毎に算出した。
図１０は、本実施例の関係算出ステップＳＴ１で算出した応力幅σａと散逸エネルギーｑとの関係と、この関係から２階微分値算出ステップＳＴ２で算出した２階微分値ｄ２と、を示す図である。図１０において、２階微分値ｄ２は「＋」でプロットしている。図１０（ａ）はＡｒｅａ－１に対して算出したものを、図１０（ｂ）はＡｒｅａ－２に対して算出したものを、図１０（ｃ）はＡｒｅａ－３に対して算出したものを示す。
同様に、本実施例の１階微分値算出ステップＳＴ２’では、関係算出ステップＳＴ１で算出した関係を応力幅σａで１階微分して得られる応力幅σａ毎の１階微分値ｄを、Ａｒｅａ－１～Ａｒｅａ－３毎に算出した。
図１１は、本実施例の関係算出ステップＳＴ１で算出した応力幅σａと散逸エネルギーｑとの関係と、この関係から１階微分値算出ステップＳＴ２’で算出した１階微分値ｄと、を示す図である。図１１において、１階微分値ｄは「＋」でプロットしている。図１１（ａ）はＡｒｅａ－１に対して算出したものを、図１１（ｂ）はＡｒｅａ－２に対して算出したものを、図１１（ｃ）はＡｒｅａ－３に対して算出したものを示す。 In the second-order differential value calculation step ST2 of this embodiment, the second-order differential value d2 for each stress width σa obtained by second-order differentiation of the relationship calculated in the relationship calculation step ST1 with respect to the stress width σa is calculated from Area-1 to Area-1. Calculated every -3.
FIG. 10 is a diagram showing the relationship between the stress width σa and the dissipated energy q calculated in the relationship calculation step ST1 of this embodiment, and the second-order differential value d2 calculated from this relationship in the second-order differential value calculation step ST2. It is. In FIG. 10, the second-order differential value d2 is plotted as "+". Figure 10(a) shows what is calculated for Area-1, Figure 10(b) shows what is calculated for Area-2, and Figure 10(c) shows what is calculated for Area-3. show.
Similarly, in the first-order differential value calculation step ST2' of this embodiment, the first-order differential value d for each stress width σa obtained by first-order differentiating the relationship calculated in the relationship calculation step ST1 with respect to the stress width σa is Calculated for each area from -1 to Area-3.
FIG. 11 shows the relationship between the stress width σa and the dissipated energy q calculated in the relationship calculation step ST1 of this embodiment, and the first-order differential value d calculated from this relationship in the first-order differential value calculation step ST2'. It is a diagram. In FIG. 11, the first-order differential value d is plotted as "+". Figure 11(a) shows what is calculated for Area-1, Figure 11(b) shows what is calculated for Area-2, and Figure 11(c) shows what is calculated for Area-3. show.

本実施例の２階微分補正値算出ステップＳＴ３及び１階微分補正値算出ステップＳＴ３’では、前述のように予め測定した試験片１のビッカース硬さＨＶを用いて、疲労限度推定値σａ＿ｓｔｄを算出した。具体的には、前述の式（５）の右辺に、α＝１．６、ＨＶ＝３００［ＨＶ］を代入することで、疲労限度推定値σａ＿ｓｔｄ＝４８０［ＭＰａ］を算出した。そして、このσａ＿ｓｔｄ＝４８０［ＭＰａ］を前述の式（６）の右辺に代入することにより、疲労限度分散度Ｒを算出した。
図１２は、図１０及び図１１に示す応力幅σａ毎に算出した疲労限度分散度Ｒを示す。 In the second-order differential correction value calculation step ST3 and the first-order differential correction value calculation step ST3' of this embodiment, the estimated fatigue limit value σa_std is calculated using the Vickers hardness HV of the test piece 1 measured in advance as described above. Calculated. Specifically, the estimated fatigue limit value σa _std =480 [MPa] was calculated by substituting α=1.6 and HV=300 [HV] into the right side of the above equation (5). Then, the fatigue limit dispersion degree R was calculated by substituting this σa _std =480 [MPa] into the right side of the above-mentioned equation (6).
FIG. 12 shows the fatigue limit dispersion R calculated for each stress width σa shown in FIGS. 10 and 11.

そして、本実施例の２階微分補正値算出ステップＳＴ３では、図１０に示す応力幅σａ毎の２階微分値ｄ２に、図１２に示す応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる応力幅σａ毎の２階微分補正値ｄ２’を、Ａｒｅａ－１、Ａｒｅａ－２、Ａｒｅａ－３毎に算出した。
図１３は、本実施例の関係算出ステップＳＴ１で算出した応力幅σａと散逸エネルギーｑとの関係と、図１０に示す応力幅σａ毎の２階微分値ｄ２に図１２に示す応力幅σａ毎の疲労限度分散度Ｒを乗算して得られた２階微分補正値ｄ２’と、を示す図である。図１３において、２階微分補正値ｄ２’は「×」でプロットしている。図１３（ａ）はＡｒｅａ－１に対して算出したものを、図１３（ｂ）はＡｒｅａ－２に対して算出したものを、図１３（ｃ）はＡｒｅａ－３に対して算出したものを示す。
同様に、本実施例の１階微分補正値算出ステップＳＴ３’では、図１１に示す応力幅σａ毎の１階微分値ｄに、図１２に示す応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる応力幅σａ毎の１階微分補正値ｄ’を、Ａｒｅａ－１、Ａｒｅａ－２、Ａｒｅａ－３毎に算出した。
図１４は、本実施例の関係算出ステップＳＴ１で算出した応力幅σａと散逸エネルギーｑとの関係と、図１１に示す応力幅σａ毎の１階微分値ｄに図１２に示す応力幅σａ毎の疲労限度分散度Ｒを乗算して得られた１階微分補正値ｄ’と、を示す図である。図１４において、１階微分補正値ｄ’は「×」でプロットしている。図１４（ａ）はＡｒｅａ－１に対して算出したものを、図１４（ｂ）はＡｒｅａ－２に対して算出したものを、図１４（ｃ）はＡｒｅａ－３に対して算出したものを示す。 In the second-order differential correction value calculation step ST3 of this embodiment, the second-order differential value d2 for each stress width σa shown in FIG. 10 is multiplied by the fatigue limit dispersion R for each stress width σa shown in FIG. The second-order differential correction value d2' for each obtained stress width σa was calculated for each Area-1, Area-2, and Area-3.
FIG. 13 shows the relationship between the stress width σa and the dissipated energy q calculated in the relationship calculation step ST1 of this embodiment, the second-order differential value d2 for each stress width σa shown in FIG. 10, and the relationship for each stress width σa shown in FIG. 12. It is a figure which shows the second-order differential correction value d2' obtained by multiplying the fatigue limit dispersion degree R of. In FIG. 13, the second-order differential correction value d2' is plotted as "x". Figure 13(a) shows what is calculated for Area-1, Figure 13(b) shows what is calculated for Area-2, and Figure 13(c) shows what is calculated for Area-3. show.
Similarly, in the first-order differential correction value calculation step ST3' of this embodiment, the first-order differential value d for each stress width σa shown in FIG. 11 is multiplied by the fatigue limit dispersion R for each stress width σa shown in FIG. The first-order differential correction value d' for each stress width σa was calculated for each Area-1, Area-2, and Area-3.
FIG. 14 shows the relationship between the stress width σa and the dissipated energy q calculated in the relationship calculation step ST1 of this embodiment, the first-order differential value d for each stress width σa shown in FIG. 11, and the relationship for each stress width σa shown in FIG. 12. It is a figure which shows the first-order differential correction value d' obtained by multiplying the fatigue limit dispersion degree R of. In FIG. 14, the first-order differential correction value d' is plotted as "x". Figure 14(a) shows what is calculated for Area-1, Figure 14(b) shows what is calculated for Area-2, and Figure 14(c) shows what is calculated for Area-3. show.

図１３から分かるように、本実施例では、Ａｒｅａ－３において、全ての２階微分補正値ｄ２’の最大値ｄ２’ｍａｘが得られ、この最大値ｄ２’ｍａｘが得られた応力幅σａは５２５ＭＰａであった。このため、本実施例では、２階微分補正値ｄ２’を用いる場合（第１実施形態に係る推定方法を用いる場合）、Ａｒｅａ－３が被測定物の疲労破壊起点として推定され、５２５ＭＰａが被測定物の疲労限度として推定されることになる。
また、図１４から分かるように、本実施例では、Ａｒｅａ－３において、全ての１階微分補正値ｄ’の最大値ｄ’ｍａｘが得られ、この最大値ｄ’ｍａｘが得られた応力幅σａは５２５ＭＰａであった。このため、本実施例では、１階微分補正値ｄ’を用いる場合（第２実施形態に係る推定方法を用いる場合）も同様に、Ａｒｅａ－３が被測定物の疲労破壊起点として推定され、５２５ＭＰａが被測定物の疲労限度として推定されることになる。
本発明者らは、上記の推定結果が、試験片１に実際に疲労試験を行い、疲労試験を行って確認された疲労破壊起点や、疲労試験から得られるＳ－Ｎ線図から求められた疲労限度と良く一致することを確認できた。したがって、本発明に係る推定方法によれば、赤外線撮像装置を用いて測定した被測定物の散逸エネルギー分布に基づき、被測定物の疲労破壊起点及び疲労限度を精度良く推定可能であるといえる。 As can be seen from FIG. 13, in this example, the maximum value d2' max of all second-order differential correction values d2' is obtained in Area-3, and the stress width σa at which this maximum value d2' max is obtained is It was 525 MPa. Therefore, in this example, when using the second-order differential correction value d2' (when using the estimation method according to the first embodiment), Area-3 is estimated as the starting point of fatigue failure of the measured object, and 525 MPa is the fatigue fracture origin of the measured object. This is estimated as the fatigue limit of the object to be measured.
Furthermore, as can be seen from FIG. 14, in this example, the maximum value d' max of all first-order differential correction values d' is obtained in Area-3, and the stress width at which this maximum value d' max is obtained is σa was 525 MPa. Therefore, in this example, when using the first-order differential correction value d' (when using the estimation method according to the second embodiment), Area-3 is similarly estimated as the fatigue fracture origin of the object to be measured, 525 MPa is estimated as the fatigue limit of the object to be measured.
The present inventors found that the above estimation results were obtained from the fatigue fracture origin confirmed by actually performing a fatigue test on test piece 1 and the S-N diagram obtained from the fatigue test. It was confirmed that the results were in good agreement with the fatigue limit. Therefore, according to the estimation method according to the present invention, it is possible to accurately estimate the fatigue fracture origin and fatigue limit of the measured object based on the dissipated energy distribution of the measured object measured using an infrared imaging device.

ｄ・・・１階微分値
ｄ’・・・１階微分補正値
ｄ１’ｍａｘ・・・最大値
ｄ２・・・２階微分値
ｄ２’・・・２階微分補正値
ｄ２’ｍａｘ・・・最大値
ｑ・・・散逸エネルギー
ＳＴ１・・・関係算出ステップ
ＳＴ２・・・２階微分値算出ステップ
ＳＴ２’・・・１階微分値算出ステップ
ＳＴ３・・・２階微分補正値算出ステップＳＴ３
ＳＴ４、ＳＴ４’・・・疲労破壊起点推定ステップ
ＳＴ５、ＳＴ５’・・・疲労限度推定ステップ
σａ・・・応力幅 d...1st order differential value d'...1st order differential correction value d1' max ...Maximum value d2...2nd order differential value d2'...2nd order differential correction value d2' max ... Maximum value q...Dissipated energy ST1...Relationship calculation step ST2...Second-order differential value calculation step ST2'...First-order differential value calculation step ST3...Second-order differential correction value calculation step ST3
ST4, ST4'...Fatigue fracture origin estimation step ST5, ST5'...Fatigue limit estimation step σa...Stress width

Claims (2)

被測定物に応力幅σａの異なる繰り返し負荷を順次付加しながら、赤外線撮像装置を用いて前記被測定物を撮像することで、前記繰り返し負荷毎に前記被測定物の温度分布の時間的変化を測定し、前記繰り返し負荷毎に測定した前記被測定物の温度分布の時間的変化に基づき、前記繰り返し負荷毎に前記被測定物の散逸エネルギー分布を算出し、前記繰り返し負荷毎に算出した前記被測定物の散逸エネルギー分布に基づき、前記被測定物の複数の部位に対して、それぞれ応力幅σａと散逸エネルギーｑとの関係を算出する関係算出ステップと、
算出した前記関係を前記応力幅σａで２階微分して得られる前記応力幅σａ毎の２階微分値ｄ２を、前記複数の部位毎に算出する２階微分値算出ステップと、
算出した前記応力幅σａ毎の２階微分値ｄ２に前記応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる前記応力幅σａ毎の２階微分補正値ｄ２’を、前記複数の部位毎に算出する２階微分補正値算出ステップと、
前記複数の部位のうち、前記複数の部位に対して算出した全ての前記２階微分補正値ｄ２’の最大値ｄ２’ｍａｘが得られた部位を、前記被測定物の疲労破壊起点として推定する疲労破壊起点推定ステップと、
前記最大値ｄ２’ｍａｘが得られた前記応力幅σａを前記被測定物の疲労限度として推定する疲労限度推定ステップと、を有し、
前記疲労限度分散度Ｒは、以下の式（Ａ）で表される、
疲労破壊起点及び疲労限度推定方法。
Ｒ＝１－ａｂｓ（１－σａ／（α・ＨＶ）） ・・・（Ａ）
上記の式（Ａ）において、σａは応力幅［ＭＰａ］であり、ＨＶは前記被測定物のビッカース硬さ［ＨＶ］であり、αは定数である。また、ａｂｓ（・）は括弧内の絶対値を意味する。 By sequentially applying repeated loads with different stress widths σa to the measured object and imaging the measured object using an infrared imaging device, temporal changes in the temperature distribution of the measured object can be observed for each repeated load. and calculate the dissipated energy distribution of the measured object for each repeated load based on the temporal change in the temperature distribution of the measured object measured for each repeated load, and calculate the dissipated energy distribution of the measured object for each repeated load. a relationship calculation step of calculating the relationship between the stress width σa and the dissipated energy q for each of the plurality of parts of the measured object based on the dissipated energy distribution of the measured object;
a second-order differential value calculation step of calculating, for each of the plurality of parts, a second-order differential value d2 for each of the stress widths σa obtained by second-order differentiating the calculated relationship with the stress width σa;
The second-order differential correction value d2' for each stress width σa obtained by multiplying the calculated second-order differential value d2 for each stress width σa by the degree of fatigue limit dispersion R for each stress width σa is calculated for each of the plurality of parts. a step of calculating a second-order differential correction value for each time;
Among the plurality of parts, a part where a maximum value d2' max of all the second-order differential correction values d2' calculated for the plurality of parts is obtained is estimated as a fatigue fracture origin of the object to be measured. a fatigue fracture origin estimation step;
a fatigue limit estimating step of estimating the stress width σa from which the maximum value d2' max is obtained as the fatigue limit of the object to be measured;
The fatigue limit dispersion R is expressed by the following formula (A):
Fatigue fracture origin and fatigue limit estimation method.
R=1-abs(1-σa/(α・HV))...(A)
In the above formula (A), σa is the stress width [MPa], HV is the Vickers hardness [HV] of the object to be measured, and α is a constant. Moreover, abs(.) means the absolute value in parentheses. 被測定物に応力幅σａの異なる繰り返し負荷を順次付加しながら、赤外線撮像装置を用いて前記被測定物を撮像することで、前記繰り返し負荷毎に前記被測定物の温度分布の時間的変化を測定し、前記繰り返し負荷毎に測定した前記被測定物の温度分布の時間的変化に基づき、前記繰り返し負荷毎に前記被測定物の散逸エネルギー分布を算出し、前記繰り返し負荷毎に算出した前記被測定物の散逸エネルギー分布に基づき、前記被測定物の複数の部位に対して、それぞれ応力幅σａと散逸エネルギーｑとの関係を算出する関係算出ステップと、
算出した前記関係を前記応力幅σａで１階微分して得られる前記応力幅σａ毎の１階微分値ｄを、前記複数の部位毎に算出する１階微分値算出ステップと、
算出した前記応力幅σａ毎の１階微分値ｄに前記応力幅σａ毎の疲労限度分散度Ｒを乗算して得られる前記応力幅σａ毎の１階微分補正値ｄ’を、前記複数の部位毎に算出する１階微分補正値算出ステップと、
前記複数の部位のうち、前記複数の部位に対して算出した全ての前記１階微分補正値ｄ’の最大値ｄ’ｍａｘが得られた部位を、前記被測定物の疲労破壊起点として推定する疲労破壊起点推定ステップと、
前記最大値ｄ’ｍａｘが得られた前記応力幅σａを前記被測定物の疲労限度として推定する疲労限度推定ステップと、を有し、
前記疲労限度分散度Ｒは、以下の式（Ａ）で表される、
疲労破壊起点及び疲労限度推定方法。
Ｒ＝１－ａｂｓ（１－σａ／（α・ＨＶ）） ・・・（Ａ）
上記の式（Ａ）において、σａは応力幅［ＭＰａ］であり、ＨＶは前記被測定物のビッカース硬さ［ＨＶ］であり、αは定数である。また、ａｂｓ（・）は括弧内の絶対値を意味する。 By sequentially applying repeated loads with different stress widths σa to the measured object and imaging the measured object using an infrared imaging device, temporal changes in the temperature distribution of the measured object can be observed for each repeated load. and calculate the dissipated energy distribution of the measured object for each repeated load based on the temporal change in the temperature distribution of the measured object measured for each repeated load, and calculate the dissipated energy distribution of the measured object for each repeated load. a relationship calculation step of calculating the relationship between the stress width σa and the dissipated energy q for each of the plurality of parts of the measured object based on the dissipated energy distribution of the measured object;
a first-order differential value calculating step of calculating, for each of the plurality of parts, a first-order differential value d for each of the stress widths σa obtained by first-order differentiating the calculated relationship with the stress width σa;
The first-order differential correction value d' for each stress width σa obtained by multiplying the calculated first-order differential value d for each stress width σa by the fatigue limit dispersion R for each stress width σa is calculated for each of the plurality of parts. a step of calculating a first-order differential correction value for each time;
Among the plurality of parts, a part where a maximum value d' max of all the first-order differential correction values d' calculated for the plurality of parts is obtained is estimated as a fatigue fracture origin of the object to be measured. a fatigue fracture origin estimation step;
a fatigue limit estimating step of estimating the stress width σa from which the maximum value d' max is obtained as a fatigue limit of the object to be measured;
The fatigue limit dispersion R is expressed by the following formula (A):
Fatigue fracture origin and fatigue limit estimation method.
R=1-abs(1-σa/(α・HV))...(A)
In the above formula (A), σa is the stress width [MPa], HV is the Vickers hardness [HV] of the object to be measured, and α is a constant. Moreover, abs(.) means the absolute value in parentheses.
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