Method for estimating fatigue fracture origin and fatigue limit

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

[Technical Field]

[0001] The present invention relates to a method for accurately estimating the fatigue fracture initiation point and fatigue limit of a test object based on the dissipated energy distribution of the test object measured using an infrared imaging device. [Background technology]

[0002] As a method for non-contact measurement of stress distribution occurring in an object to be measured, a thermoelastic stress measurement method using an infrared imaging device (thermography) has been proposed (see, for example, Non-Patent Document 1). The thermoelastic stress measurement method utilizes the thermoelastic effect, which occurs when a temperature change occurs when a test object undergoes adiabatic elastic deformation, and measures the time change in the temperature distribution of the test object (the change in temperature distribution within a specified time) by using an infrared imaging device to capture images of the test object to which a repeated load is applied, and converts this measured time change in temperature distribution into the time change in stress distribution of the test object (the change in stress distribution within a specified time).If the initial value of the stress distribution is known (including not only cases where the stress distribution is actually measured and known, but also cases where it is possible to estimate it), it is possible to measure the stress distribution after a specified time has passed by adding the time change in stress distribution to this initial value.

[0003] When measuring the change over time in the temperature distribution of an object using this thermoelastic stress measurement method, for example, heat (infrared rays) surrounding the object may be reflected from the surface of the object and received by the infrared imaging device. In other words, the change over time in the temperature distribution of an object measured using an infrared imaging device may include temperature changes caused by factors other than the thermoelastic effect (changes in the intensity of infrared rays emitted from the object), such as heat conduction within the object and heat generation due to energy dissipation (described later), in addition to the above-mentioned disturbance factors.

[0004] For this reason, the technology described in Non-Patent Document 1 performs lock-in processing on the signal waveform corresponding to the temperature change caused by the thermoelastic effect to be measured from the image signal output from the infrared imaging device. In other words, 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 applies a cyclic load to a test object and having the same frequency as the applied cyclic load is used. The image signal is synchronously detected using this reference signal, and only image signal components in a frequency band corresponding to the reference signal (only image signal components having the same frequency as the reference signal or only image signal components in a narrow frequency band including the same frequency as the reference signal) are extracted, thereby improving the S / N ratio of the temperature change caused by the thermoelastic effect to be measured. Then, the time change in the temperature distribution of the test object (the time change in temperature for each pixel constituting the image captured by the infrared imaging device) is calculated based on the magnitude of the extracted image signal components and a pre-stored correspondence between the magnitude of the image signal components and temperature. Next, the time change in the stress distribution of the test object is calculated based on the time change in the temperature distribution of the test object and a predetermined relational expression between the time change in temperature and the time change in stress. Specifically, the time change in the stress distribution of the test object is calculated based on the time change in the temperature distribution of the test object and the relational expression expressed by the following equation (1). Δσ=-1 / K ΔT / T (1) In the above formula (1), ΔT is the change in temperature over time, Δσ is the change in stress over time, T is the temperature of the object being measured, and K is the thermoelastic coefficient. The thermoelastic coefficient K is a physical property determined by the material of the object being measured. For example, if the object being measured is made of steel, K = 3.5 × 10 -12 [Pa -1 ]. In this way, by using the lock-in process, it is possible to accurately calculate the change over time in the stress distribution of the object to be measured, and ultimately the stress distribution of the object to be measured.

[0005] When a load is repeatedly applied to the object to be measured, in addition to the temporal change in temperature distribution caused by the thermoelastic effect described above, a temporal change in temperature distribution caused by energy dissipation also occurs. As described in Non-Patent Document 2, the time-dependent change in temperature distribution due to energy dissipation is considered to occur as heat components when maximum and minimum stresses act on the object being measured, and the dissipated energy is defined as the frequency component in the time-dependent change in temperature that is twice the frequency of the repeated load applied to the object being measured. This dissipated energy is defined as ΔT D The change in temperature over time measured using the infrared imaging device (the change in temperature over time before the lock-in process) is defined as ΔT M The temperature change due to the thermoelastic effect (the temperature change after the lock-in process) is defined as ΔT E Then, if disturbance factors and heat conduction are not taken into consideration, the following equation (2) holds. ΔT D =ΔT M -ΔT E ···(2) Therefore, the dissipated energy distribution can be measured using an infrared imaging device, and specifically, can be calculated by subtracting the change in temperature distribution over time due to the thermoelastic effect calculated by the lock-in process as described above from the change in temperature distribution over time measured using the infrared imaging device.

[0006] 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, cyclic loads with different stress amplitudes (= maximum stress - minimum stress) are sequentially applied to the object to be measured (for example, the stress amplitude of the applied cyclic load is increased stepwise and cyclic loads of each stress amplitude are applied for several thousand cycles), while the object to be measured is imaged using an infrared imaging device, and the temporal change in the temperature distribution of the object to be measured for each cyclic load is measured.Then, based on the temporal change in the temperature distribution of the object to be measured for each cyclic load, the dissipated energy distribution of the object to be measured for each cyclic load is calculated, and the relationship between stress amplitude and dissipated energy is calculated based on this dissipated energy distribution of the object to be measured for each cyclic load.

[0007] Figure 1 is a diagram that shows a schematic diagram of the relationship between stress amplitude and dissipated energy. The points plotted with "♦" in Figure 1 represent the dissipated energy calculated for each repeated load with different stress amplitudes. As shown in Figure 1, the relationship between the two inherently has a point where the dissipated energy increases sharply beyond a certain stress amplitude. The stress amplitude of the repeated load at this point is thought to correspond to the fatigue limit determined by the so-called SN diagram. Therefore, by calculating the relationship between the stress amplitude and the dissipated energy and detecting the point at which the dissipated energy increases sharply, the stress amplitude of the repeated load at this point can be estimated as the fatigue limit.

[0008] However, the relationship between stress amplitude and dissipated energy obtained from the dissipated energy distribution measured using an infrared imaging device is not necessarily as shown in Figure 1. If the object being measured is a heat-treated or welded material that contains residual stress, or if the influence of external disturbance factors is significant during measurement, the dissipated energy may vary greatly, or the dissipated energy may increase monotonically at a constant gradient overall, and there may not be a clear point of sudden increase at which the fatigue limit can be accurately estimated.

[0009] Furthermore, the relationship between stress amplitude and dissipated energy shown in Figure 1 is based on the premise that the dissipated energy at the fatigue fracture initiation point of the object being measured is plotted. However, if the object being measured is made of heat-treated steel material, or if the object being measured is a welded material, it may be difficult to identify the fatigue fracture initiation point near the weld due to differences in structure and residual stress, and the area where stress is concentrated may not necessarily be the fatigue fracture initiation point.

[0010] Patent Documents 1 and 2 propose a method of determining the relationship between the temperature amplitude of the fundamental frequency component of vibration and the temperature amplitude of the second harmonic component of the object to be measured from a temperature image obtained from an infrared camera, fitting the relationship using a first approximation line which is a quadratic curve and a second approximation line which is also a quadratic curve, and determining the fatigue limit stress of the object to be measured based on the intersection of the first approximation line and the second approximation line. Furthermore, Patent Document 3 proposes a method of obtaining temperature amplitude images of the fundamental frequency component and second harmonic component of vibration applied to the object being measured from a temperature image captured by an infrared camera, and estimating the fatigue limit from the dissipated energy of the pixel region where the slope of the load characteristic relative to the temperature amplitude image of the fundamental frequency component is greatest within the region showing the maximum of the temperature amplitude image of the second harmonic component. However, the methods described in Patent Documents 1 to 3 do not detect the point at which the dissipated energy increases sharply, which is thought to correspond to the fatigue limit, in the relationship between stress amplitude and dissipated energy as shown in Figure 1. Furthermore, the methods described in Patent Documents 1 to 3 do not estimate the fatigue fracture initiation point.

[0011] Incidentally, Non-Patent Document 3 describes that the fatigue limit is proportional to the Vickers hardness. [Prior art documents] [Non-patent literature]

[0012] [Non-Patent Document 1] Tatsuya Yaoita and two others, "Stress measurement using an infrared camera and prediction of fatigue limit points," Society of Automotive Engineers of Japan Autumn Academic Conference, No. 98-03, (2003) [Non-patent document 2] Daiki Shiozawa et al., "Fatigue limit estimation of Ti-6Al-4V alloy based on dissipated energy measurement," Proceedings of the 69th Annual Meeting of the Society of Materials Science, Japan, No. 132, (2020) [Non-patent document 3] "Explanation of Fatigue Terminology for Beginners", Fatigue Division Committee of the Society of Materials Science, Japan (2015) [Patent documents]

[0013] [Patent Document 1] Japanese Patent Application Laid-Open No. 2018-105709 [Patent Document 2] Japanese Patent Application Publication No. 2019-148507 [Patent Document 3] Japanese Patent Application Laid-Open No. 2016-024056 Summary of the Invention [Problem to be solved by the invention]

[0014] The present invention has been made to solve the problems of the conventional technology as described above, and its object is to provide a method for accurately estimating the fatigue fracture initiation point and fatigue limit of a test object based on the dissipated energy distribution of the test object measured using an infrared imaging device. [Means for solving the problem]

[0015] To solve the above problems, the inventors conducted extensive research and found that by calculating the relationship between the stress amplitude of a cyclic load applied to a test object and dissipated energy for multiple locations (locations that may be fatigue fracture initiation points) and then second-order differentiating this relationship with respect to the stress amplitude, the location at which the maximum second-order differential value (the maximum of all second-order differential values ​​calculated for multiple locations) is obtained may correspond to the fatigue fracture initiation point of the test object, and the stress amplitude at which the maximum second-order differential value is obtained may correspond to the fatigue limit of the test object. In other words, even if a clear point of sudden increase does not occur simply by plotting the relationship between stress amplitude and dissipated energy due to the influence of residual stress or external disturbances in the test object, the location at which the maximum second-order differential value is obtained may correspond to the fatigue fracture initiation point, and the stress amplitude at which the maximum second-order differential value is obtained may correspond to the actual point of sudden increase. However, the present inventors have found that simply calculating the maximum second-order derivative value may not be sufficient to estimate the fatigue fracture initiation point and fatigue limit of a test object with sufficient accuracy. Therefore, the present inventors have conducted further intensive research, focusing on correcting the second-order derivative value by utilizing the fact that the fatigue limit is proportional to the Vickers hardness, as described in Non-Patent Document 3. As a result, they have found that if the second-order derivative value is corrected by multiplying it by a parameter (referred to as the "fatigue limit dispersion" in the present invention) whose value decreases as the stress width deviates from the reference fatigue limit (the fatigue limit estimated from the Vickers hardness (the Vickers hardness multiplied by a predetermined constant)) , the site at which the maximum value of the corrected second-order derivative value (referred to as the "corrected second-order derivative value" in the present invention) (the maximum value of all the corrected second-order derivative values ​​calculated for multiple sites) is obtained accurately corresponds to the fatigue fracture initiation point of the test object, and the stress width at which the maximum corrected second-order derivative value is obtained accurately corresponds to the fatigue limit of the test object.

[0016] 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 cyclic loads with different stress amplitudes σa to an object to be measured, while imaging the object using an infrared imaging device, thereby measuring a change in temperature distribution of the object to be measured for each cyclic load, calculating a dissipated energy distribution of the object to be measured for each cyclic load based on the change in temperature distribution of the object to be measured for each cyclic load, and calculating a stress amplitude σa and a dissipated energy distribution for each of a plurality of portions of the object to be measured based on the dissipated energy distribution of the object to be measured calculated for each cyclic load. a second-order differential value calculation step of calculating, for each of the plurality of portions, a second-order differential value d2 for each stress width σa obtained by second-order differentiating the calculated relationship with the stress width σa; a second-order differential value calculation step of calculating, for each of the plurality of portions, a second-order differential correction value d2' for each of the stress width σa obtained by multiplying the calculated second-order differential value d2 for each of the stress widths σa by a fatigue limit dispersion R for each of the stress widths σa; and a second-order differential correction value calculation step of calculating, for each of the plurality of portions, a maximum value d2' of all the second-order differential correction values ​​d2' calculated for the plurality of portions.max a fatigue fracture initiation estimating step of estimating the portion where the maximum value d2' is obtained as the fatigue fracture initiation point of the object to be measured; max and a fatigue limit estimation step of estimating the stress width σa obtained as the fatigue limit of the object to be measured, wherein the fatigue limit dispersion R is expressed by the following formula (A): R=1-abs(1-σa / (α·HV)) ···(A) In the above formula (A), σa is the stress amplitude [MPa], HV is the Vickers hardness [HV] of the object to be measured, and α is a constant. Furthermore, abs(·) means the absolute value in parentheses.

[0017] According to the present invention, in the relationship calculation step, the relationship between stress amplitude σa and dissipated energy q is calculated for each of multiple locations on the object to be measured. In the second-order derivative calculation step, this relationship is second-order differentiated with respect to the stress amplitude σa to calculate a second-order derivative d2 for each stress amplitude σa for each of the multiple locations. In the second-order derivative correction value calculation step, the second-order derivative d2 for each stress amplitude σa is multiplied by the fatigue limit variance R for each stress amplitude σa to calculate a second-order derivative correction value d2' for each of the multiple locations. Since the fatigue limit variance R by which the second-order derivative d2 is multiplied is expressed by Equation (A), a value α·HV proportional to the Vickers hardness HV of the object to be measured (corresponding to the fatigue limit estimated from the Vickers hardness HV) is used as a reference. When the stress amplitude σa is equal to this reference α·HV, R has a maximum value of 1. As the stress amplitude σa deviates from the reference α·HV, R decreases. Therefore, as the inventors have found, in the fatigue fracture initiation point estimation step, the maximum value d2' of all the second-order differential correction values ​​d2' calculated for the plurality of parts among the plurality of parts is max The part where the maximum value d2' is obtained can be accurately estimated as the fatigue fracture initiation point of the object to be measured. max The obtained stress width σa can be accurately estimated as the fatigue limit of the object to be measured.

[0018] In the present invention, the multiple locations on the object to be measured for calculating the relationship between the stress amplitude σa and the dissipated energy q may be selected from locations that may be fatigue fracture initiation points. Specifically, for example, it may be possible to select locations where the dissipated energy is large in the calculated dissipated energy distribution and where the stress is large in the stress distribution calculated using the same infrared imaging device. In the present invention, the Vickers hardness HV may be measured using a known Vickers hardness tester on the test object before the application of a cyclic load. In this case, it is preferable to set the Vickers hardness measurement points near multiple locations on the test object where the relationship between the stress amplitude σa and the dissipated energy q is calculated. It is also possible to measure the Vickers hardness HV using a test piece having the same material and shape as the test object, rather than the test object itself. Furthermore, in the present invention, α in the formula (A) is set to, for example, α=1.6, as described in Non-Patent Document 3.

[0019] According to the findings of the present inventors, the fatigue fracture initiation point and fatigue limit of the object can be estimated with high accuracy even when the first-order differential value d is used instead of the second-order differential value d2. That is, in order to solve the above problem, the present invention provides a method for measuring a change in temperature distribution of an object to be measured with an infrared imaging device while sequentially applying cyclic loads with different stress amplitudes σa to the object, thereby measuring a change in temperature distribution of the object with time for each cyclic load, calculating a dissipated energy distribution of the object to be measured with each cyclic load based on the change in temperature distribution of the object to be measured with each cyclic load, and calculating a stress amplitude σa for each of a plurality of portions of the object to be measured based on the dissipated energy distribution of the object to be measured with each cyclic load. and dissipated energy q; a first-order differential value calculation step of calculating, for each of the plurality of portions, a first-order differential value d for each stress width σa obtained by first-order differentiating the calculated relationship with respect to the stress width σa; a first-order differential value calculation step of calculating, for each of the plurality of portions, a first-order differential correction value d' for each of the stress width σa obtained by multiplying the calculated first-order differential value d for each of the stress widths σa by a fatigue limit dispersion R for each of the stress widths σa; and a first-order differential correction value calculation step of calculating, for each of the plurality of portions, a maximum value d' of all the first-order differential correction values ​​d' calculated for the plurality of portions. max a fatigue fracture initiation estimation step of estimating a portion where the maximum value d' is obtained as a fatigue fracture initiation point of the object to be measured; max and a fatigue limit estimating step of estimating the obtained stress width σa as the fatigue limit of the object to be measured, wherein the fatigue limit dispersion R is expressed by the following formula (A): It is also provided as a method for estimating the fatigue fracture initiation point and fatigue limit. R=1-abs(1-σa / (α·HV)) ···(A) In the above formula (A), σa is the stress amplitude [MPa], HV is the Vickers hardness [HV] of the object to be measured, and α is a constant. Furthermore, abs(·) means the absolute value in parentheses. [Effects of the Invention]

[0020] According to the present invention, it is possible to accurately estimate the fatigue fracture initiation point and fatigue limit of a test object based on the dissipated energy distribution of the test object measured using an infrared imaging device. [Brief explanation of the drawings]

[0021] [Figure 1] FIG. 1 is a diagram schematically illustrating the relationship between stress amplitude and dissipated energy. [Figure 2] FIG. 1 is a flow chart showing the steps of a method for estimating a fatigue fracture initiation point and a fatigue limit according to a first embodiment. [Figure 3] 3 is a diagram showing an example of a dissipated energy distribution of an object to be measured, calculated in the relationship calculation step ST1 shown in FIG. 2. FIG. [Figure 4] FIG. 10 is a diagram showing an example of the relationship between stress amplitude σa and dissipated energy q. [Figure 5] 5 is a diagram showing the relationship between the stress amplitude σa and the dissipated energy q shown in FIG. 4, and the second derivative value d2 calculated from this relationship. FIG. [Figure 6] An example of the fatigue limit dispersion R calculated for each stress width σa shown in FIG. 5 is shown below. [Figure 7] 7 is a diagram showing the relationship between stress amplitude σa and dissipated energy q shown in FIG. 4, and a second-order derivative correction value d2′ obtained by multiplying the second-order derivative value d2 for each stress amplitude σa shown in FIG. 5 by the fatigue limit dispersion R for each stress amplitude σa shown in FIG. 6. [Figure 8] FIG. 10 is a flow chart showing the steps of a method for estimating a fatigue fracture initiation point and a fatigue limit according to a second embodiment. [Figure 9] FIG. 1 is an explanatory diagram illustrating an outline of an embodiment. [Figure 10] FIG. 10 is a diagram showing the relationship between stress amplitude σa and dissipated energy q calculated in the relationship calculation step ST1 of the embodiment, and the second-order differential value d2 calculated from this relationship in the second-order differential value calculation step ST2. [Figure 11] FIG. 10 is a diagram showing the relationship between stress amplitude σa and dissipated energy q calculated in relationship calculation step ST1 of the embodiment, and the first-order differential value d calculated from this relationship in first-order differential value calculation step ST2′. [Figure 12] The fatigue limit dispersion R calculated for each stress width σa shown in Figs. 10 and 11 is shown. [Figure 13]12 shows the relationship between the stress amplitude σa and the dissipated energy q calculated in the relationship calculation step ST1 of the embodiment, and the second-order derivative correction value d2′ obtained by multiplying the second-order derivative value d2 for each stress amplitude σa shown in FIG. 10 by the fatigue limit dispersion R for each stress amplitude σa shown in FIG. 12. [Figure 14] 12 shows the relationship between the stress amplitude σa and the dissipated energy q calculated in the relationship calculation step ST1 of the embodiment, and the first-order differential correction value d′ obtained by multiplying the first-order differential value d for each stress amplitude σa shown in FIG. 11 by the fatigue limit dispersion R for each stress amplitude σa shown in FIG. 12. DETAILED DESCRIPTION OF THE INVENTION

[0022] Hereinafter, a fatigue fracture initiation and fatigue limit estimation method (hereinafter simply referred to as "estimation method") according to embodiments (first and second embodiments) of the present invention will be described with reference to the accompanying drawings as appropriate.

[0023] First Embodiment FIG. 2 is a flow diagram schematically illustrating steps of a method for estimating a fatigue fracture initiation and a fatigue limit according to the first embodiment. 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 initiation estimation step ST4, and a fatigue limit estimation step ST5. Each of steps ST1 to ST5 will be described below in order.

[0024] [Relationship calculation step ST1] In the relationship calculation step ST1, cyclic loads with different stress amplitudes (= maximum stress - minimum stress) σa are sequentially applied to the object under test using a fatigue testing machine or the like, while an infrared imaging device is used to capture images of the object under test, thereby measuring the temporal change in the temperature distribution of the object under test for each cyclic load. Specifically, the stress amplitude σa of the cyclic load applied to the object under test is gradually increased under conditions where the stress ratio (= minimum stress / maximum stress) is kept constant, and the object under test is imaged using the infrared imaging device while applying cyclic loads of each stress amplitude σa for several thousand cycles, thereby measuring the temporal change in the temperature distribution of the object under test for each cyclic load. Then, the dissipated energy distribution of the object under test for each cyclic load is calculated based on the temporal change in the temperature distribution of the object under test measured for each cyclic load. Specifically, the signal waveform corresponding to the temperature change caused by the thermoelastic effect is subjected to lock-in processing from the image signal output from the infrared imaging device (the image signal is synchronously detected using a reference signal with the same frequency as the applied cyclic load, and only the image signal component in the frequency band corresponding to the reference signal is extracted).Then, the dissipated energy distribution of the object is calculated by subtracting the temporal change in the temperature distribution of the object caused by the thermoelastic effect, which is obtained from the image signal component extracted by lock-in processing, from the temporal change in the temperature distribution of the object obtained from the image signal output from the infrared imaging device (the image signal before lock-in processing). As an infrared imaging device for executing the above procedure of the relationship calculation step ST1, for example, the X6580 series manufactured by FLIR (cooled type, temperature resolution 0.02°C, maximum pixel count 640 x 512 pixels, maximum frame rate 350Hz) can be used, and as software for calculating the dissipated energy distribution, AltairLI manufactured by the same company can be used.

[0025] Next, in the relationship calculation step ST1, the relationship between the stress amplitude σa and the dissipated energy q is calculated for each of the 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. FIG. 3 shows an example of the dissipated energy distribution (image showing the dissipated energy distribution) of the object to be measured, calculated in the relationship calculation step ST1. FIG. 4 shows an example of the relationship between stress amplitude σa and dissipated energy q. In the dissipated energy distribution shown in FIG. 3, the darker the pixel, the greater the dissipated energy. In the example shown in FIGS. 3 and 4, the relationship between stress amplitude σa and dissipated energy q is calculated for each of three areas shown in FIG. 3: Area-1, Area-2, and Area-3 (each of which is a pixel area of ​​several to several dozen pixels vertically and horizontally) that may be fatigue fracture initiation points. However, the present invention is not limited to this, and relationships may be calculated for four or more areas, or for two areas. FIG. 4(a) shows the relationship calculated for Area-1, FIG. 4(b) shows the relationship calculated for Area-2, and FIG. 4(c) shows the relationship calculated for Area-3. The relationship shown in Fig. 4 is obtained by calculating the dissipated energy distribution as shown in Fig. 3 for each repeated load (for each different stress amplitude σa that is increased stepwise), and plotting the representative value (specifically, the average value) of the dissipated energy in Area-1 to Area-3 for each repeated load. Note that the representative value is not limited to the average value, and for example, the maximum value can also be used.

[0026] [Second-order differential calculation step ST2] In the relationship between stress amplitude σa and dissipated energy q shown in Figure 4, the plotted points fluctuate up and down due to noise, and the point of sudden increase is not clear. Therefore, in the second-order differential value calculation step ST2, the relationship calculated in the relationship calculation step ST1 is second-order differentiated with respect to the stress amplitude σa to calculate the second-order differential value d2 for each stress amplitude σa for each of the multiple regions (Area-1, Area-2, Area-3).

[0027] When calculating the second-order differential value d2, the first-order differential value d is first calculated. The first-order differential value d is the value obtained by first differentiating the relationship between the stress amplitude σa and the dissipated energy q with respect to the stress amplitude σa. As shown in Figure 4(a), the first-order differential value d is calculated using the following equation (3), where the change in the stress amplitude σa between adjacent plot points is Δσa and the change in the dissipated energy between adjacent plot points is Δq. d=Δq / Δσa (3) That is, the first derivative d of the nth smallest plot point is d n The stress amplitude σa of the nth plot point from the smallest is σ n , dissipated energy q to q n The stress amplitude σa at the smallest (n-1) plot point is σ n-1 , dissipated energy q to q n-1 Then, the first derivative d n is calculated, for example, by the following formula (3)'. d n =(q n -q n-1 ) / (σ n -σ n-1 ) ···(3)'

[0028] As shown in FIG. 4(a), the second-order differential value d2 is calculated by the following formula (4), where Δd is the amount of change in the first-order differential value d between adjacent plotted points. d2=Δd / Δσa (4) That is, the second derivative d2 of the nth smallest plot point is d2 n The first derivative d of the smallest (n-1) plot point is d n-1 Then, the second derivative d2 n is calculated, for example, by the following formula (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 formula (4)', q n-2 is the dissipated energy q of the smallest (n-2) plot point, and σ n-2 is the stress amplitude σa of the smallest (n-2) plotted point.

[0029] Figure 5 shows the relationship between the stress amplitude σa and dissipated energy q shown in Figure 4, and the second derivative d2 calculated from this relationship. In Figure 5, the second derivative d2 is plotted with a "+". Figure 5(a) shows the calculation for Area-1, Figure 5(b) shows the calculation for Area-2, and Figure 5(c) shows the calculation for Area-3. As shown in Figure 5(a), in Area-1, the second derivative d2 reaches its maximum value when the stress amplitude σa is σ7. As shown in Figure 5(b), in Area-2, the second derivative d2 reaches its maximum value when the stress amplitude σa is σ7, but also approaches its maximum value when the stress amplitude σa is σ9. As shown in Figure 5(c), in Area-3, the second derivative d2 reaches its maximum value when the stress amplitude σa is σ 10The second-order differential value d2 is maximum when the stress amplitude σa is σ7. Comparing the maximum values ​​of the second-order differential value d2 in each of Area-1 to Area-3 reveals that the second-order differential value d2 in Area-1 when the stress amplitude σa is σ7 is the maximum value of the second-order differential value d2 in all of Area-1 to Area-3. Therefore, if we assume that the location where the maximum value of the second-order differential value d2 is obtained in all of Area-1 to Area-3 is the fatigue fracture initiation point of the test object, and that the stress amplitude σa where the maximum value of the second-order differential value d2 is obtained in all of Area-1 to Area-3 is the fatigue limit of the test object, then in the example shown in FIG. 5 , the fatigue fracture initiation point is Area-1, and the fatigue limit is the stress amplitude σ7. However, according to the inventors' findings, this result does not match the fatigue fracture initiation point confirmed by performing a fatigue test or the fatigue limit determined from the SN diagram obtained from the fatigue test. Therefore, in the estimation method according to the first embodiment, as described below, the fatigue limit is estimated using a corrected second-order differential value d2' obtained by correcting the second-order differential value d2 by utilizing the fact that the fatigue limit is proportional to the Vickers hardness.

[0030] [Second-order derivative correction value calculation step ST3] In the second-order differential correction value calculation step ST3, the fatigue limit dispersion 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 the Vickers hardness. Therefore, if the Vickers hardness of the object to be measured is HV and a predetermined constant is α, the fatigue limit can be estimated as α·HV. In other words, the estimated fatigue limit is σa _std Then, the estimated fatigue limit σa _std is expressed by the following equation (5). σa _std =α HV (5) Then, in the second-order derivative correction value calculation step ST3, the fatigue limit dispersion R is calculated by the fatigue limit estimated value σa _std The parameter is used, and the value decreases as the stress width σa deviates from this standard. Specifically, the fatigue limit dispersion R expressed by the following formula (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 amplitude [MPa], HV is the Vickers hardness [HV] of the object being measured, and α is a constant. Furthermore, abs(·) indicates the absolute value in parentheses. Vickers hardness HV may be measured, for example, using a known Vickers hardness tester on the object being measured before applying a repeated load. FIG. 6 shows an example of the fatigue limit dispersion R calculated for each stress width σa shown in FIG. 5. As can be seen from FIG. 6, the fatigue limit estimated value σa _std As the stress width σa deviates from this standard, the value of the fatigue limit dispersion R becomes smaller.

[0031] Then, in the second-order derivative correction value calculation step ST3, the second-order derivative value d2 for each stress width σa calculated in the second-order derivative value calculation step ST2 is multiplied by the fatigue limit dispersion R for each stress width σa to calculate the second-order derivative correction value d2' for each stress width σa for each of the multiple regions (Area-1, Area-2, Area-3). Figure 7 shows the relationship between the stress amplitude σa and the dissipated energy q shown in Figure 4, and the corrected second-order derivative d2' obtained by multiplying the second-order derivative d2 for each stress amplitude σa shown in Figure 5 by the fatigue limit dispersion R for each stress amplitude σa shown in Figure 6. In Figure 7, the corrected second-order derivative d2' is plotted with an "x". Figure 7(a) shows the calculation for Area-1, Figure 7(b) shows the calculation for Area-2, and Figure 7(c) shows the calculation for Area-3.

[0032] [Fatigue fracture origin estimation step ST4] In the fatigue fracture initiation estimation step ST4, the maximum value d2' of all the second-order differential correction values ​​d2' calculated for the plurality of areas (Area-1, Area-2, Area-3) is calculated. max The location where this is obtained is estimated to be the fatigue fracture initiation point of the object being measured. In the example shown in FIG. 7, in Area-3, the maximum value d2′ of all the second-order differential correction values ​​d2′ is max Therefore, Area-3 is estimated to be the fatigue fracture initiation point of the test object.

[0033] [Fatigue limit estimation step ST5] In the fatigue limit estimation step ST5, the maximum value d2' max The stress amplitude σa obtained is estimated as the fatigue limit of the object being measured. In the example shown in Figure 7, σ in Area-3 10 The maximum value d2' max Since we have obtained σ 10 is estimated as the fatigue limit of the object being measured.

[0034] According to the fatigue limit estimation method of the first embodiment described above, in the relationship calculation step ST1, the relationship between the stress amplitude σa and the dissipated energy q is calculated for each of the multiple regions of the object (three regions, Area-1 to Area-3, in the example shown in FIG. 3), and in the second-order derivative calculation step ST2, this relationship is second-order differentiated with respect to the stress amplitude σa to calculate a second-order derivative d2 for each of the multiple regions. Then, in the second-order derivative correction value calculation step ST3, the second-order derivative d2 for each of the stress amplitude σa is multiplied by the fatigue limit dispersion R for each of the stress amplitude σa to calculate a second-order derivative correction value d2' for each of the multiple regions. The fatigue limit estimated value σa proportional to the Vickers hardness HV of the object is calculated. _std (σa _std =α·HV) as the standard, and the estimated fatigue limit σa _std When the fatigue limit dispersion R is equal to the maximum value of 1, the stress width σa is equal to the estimated fatigue limit σa _std Therefore, as the inventors have found, in the fatigue fracture initiation point estimation step ST4, the maximum value d2' of all the second-order differential correction values ​​d2' calculated for the plurality of portions among the plurality of portions is maxThe part where the maximum value d2' is obtained can be accurately estimated as the fatigue fracture initiation point of the object to be measured. max The obtained stress width σa can be accurately estimated as the fatigue limit of the object to be measured.

[0035] Second Embodiment FIG. 8 is a flow diagram schematically illustrating steps of a method for estimating a fatigue fracture initiation point and a fatigue limit according to the second embodiment. According to the findings of the present inventors, the fatigue fracture initiation point and fatigue limit of a test object can be estimated with high accuracy even when the first-order differential value d is used instead of the second-order differential value d2. The estimation method according to the second embodiment differs from the estimation method according to the first embodiment only in that the first-order differential value d is used, and the remaining points are the same as the estimation method according to the first embodiment. Therefore, only the points that differ from the first embodiment will be briefly described below, and a description of the similar points will be omitted.

[0036] 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', a fatigue fracture initiation estimation step ST4', and a fatigue limit estimation step ST5'. Each of steps ST1 to ST5' will be described below in order.

[0037] [Relationship calculation step ST1] The content executed in the relation calculation step ST1 is the same as that in the relation calculation step ST1 of the estimation method according to the first embodiment shown in FIG.

[0038] [First-order differential calculation step ST2'] In the first-order differential value calculation step ST2', the relationship calculated in the relationship calculation step ST1 is first differentiated with respect to the stress amplitude σa to calculate a first-order differential value d for each stress amplitude σa for each of a plurality of regions (e.g., 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 is calculated using the above-mentioned formula (4) (more specifically, formula (4)'), whereas in the first-order differential value calculation step ST2', the first-order differential value d is calculated using the above-mentioned formula (3) (more specifically, formula (3)').

[0039] [First-order differential correction value calculation step ST3'] In the first-order differential correction value calculation step ST3′, the fatigue limit dispersion R is also used to correct the first-order differential value d calculated in the first-order differential value calculation step ST2′. This fatigue limit dispersion 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). Then, in the first-order differential correction value calculation step ST3', the first-order differential value d' for each stress width σa is calculated for each of the multiple parts by multiplying the first-order differential value d for each stress width σa calculated in the first-order differential value calculation step ST2' by the fatigue limit dispersion R for each stress width σa.

[0040] [Fatigue fracture initiation estimation step ST4'] In the fatigue fracture initiation estimation step ST4', the maximum value d' of all first-order differential correction values ​​d' calculated for the plurality of parts is calculated. max The location where this is obtained is estimated to be the fatigue fracture initiation point of the object being measured.

[0041] [Fatigue limit estimation step ST5'] In the fatigue limit estimation step ST5', the maximum value d' max The stress amplitude σa obtained is estimated as the fatigue limit of the object being measured.

[0042] In the fatigue limit estimation method according to the second embodiment described above, in the fatigue fracture initiation estimation step ST4′, the maximum value d′ of all the first-order differential correction values ​​d′ calculated for the plurality of parts among the plurality of parts is calculated. max The location where the maximum value d' is obtained can be accurately estimated as the fatigue fracture initiation point of the object to be measured. maxThe obtained stress width σa can be accurately estimated as the fatigue limit of the object to be measured.

[0043] <Example> Hereinafter, examples in which the estimation methods according to the embodiments (first and second embodiments) of the present invention are implemented will be described. 9A and 9B are explanatory diagrams illustrating an outline of this example. FIG. 9A is a diagram schematically illustrating a test piece 1 used as a measurement object in this example. A quenched SCM steel material was used as the test piece 1. FIG. 9B is a diagram illustrating an example of the dissipated energy distribution calculated in the relation calculation step ST1 for the region surrounded by the dashed line 2 of the test piece 1 shown in FIG. 9A.

[0044] In this example, the Vickers hardness HV was measured in advance using a known Vickers hardness tester for areas near a plurality of areas (Area-1 to Area-3 described below) of the test piece 1. The measured Vickers hardness HV was 300 [HV]. In the relationship calculation step ST1 of this example, the test piece 1 was attached to a fatigue testing machine that applies cyclic loads. The stress amplitude σa was gradually increased within the range of 250 to 600 MPa (stress ratio: -1, repetition frequency: 7 Hz). Repeated loads of each stress amplitude σa were applied 2000 cycles. Images of the test piece 1 were taken using an infrared imaging device to measure the temporal change in the temperature distribution of the test piece 1 after each repeated load. The infrared imaging device used was a FLIR X6580 series, with a frame rate set to 149 Hz. Measurements were performed for 10 seconds after each repeated load (the change in temperature distribution over 10 seconds was measured). The dissipated energy distribution was then calculated using a FLIR Altair LI. Figure 9(b) shows an example of the dissipated energy distribution calculated using the above procedure. Next, in the relationship calculation step ST1 of this embodiment, the relationship between the stress amplitude σa and the dissipated energy q was calculated for each of three areas of the test piece 1 (Area-1, Area-2, and Area-3 shown in FIG. 9(b)) based on the dissipated energy distribution as shown in FIG. 9(b). Area-1 to Area-3 are all pixel areas of 15 x 15 pixels (equivalent to 2 mm x 2 mm). The average value of the dissipated energy in Area-1 to Area-3 was used as the dissipated energy q in the above relationship.

[0045] In the second-order differential value calculation step ST2 of this embodiment, the relationship calculated in the relationship calculation step ST1 was second-order differentiated with respect to the stress amplitude σa to calculate a second-order differential value d2 for each stress amplitude σa for each of Area-1 to Area-3. Figure 10 shows the relationship between the stress amplitude σa and the dissipated energy q calculated in the relationship calculation step ST1 of this embodiment, and the second-order derivative d2 calculated from this relationship in the second-order derivative calculation step ST2. In Figure 10, the second-order derivative d2 is plotted with a "+". Figure 10(a) shows the calculation for Area-1, Figure 10(b) shows the calculation for Area-2, and Figure 10(c) shows the calculation for Area-3. Similarly, in the first-order differential value calculation step ST2' of this embodiment, the first-order differential value d for each stress amplitude σa obtained by first-order differentiation of the relationship calculated in the relationship calculation step ST1 with respect to the stress amplitude σa was calculated for each of Area-1 to Area-3. Figure 11 shows the relationship between the stress amplitude σa and the dissipated energy q calculated in the relationship calculation step ST1 of this embodiment, and the first-order derivative d calculated from this relationship in the first-order derivative calculation step ST2'. In Figure 11, the first-order derivative d is plotted with a "+". Figure 11(a) shows the calculation for Area-1, Figure 11(b) shows the calculation for Area-2, and Figure 11(c) shows the calculation for Area-3.

[0046] In the second-order differential correction value calculation step ST3 and the first-order differential correction value calculation step ST3′ of this embodiment, the Vickers hardness HV of the test piece 1 measured in advance as described above is used to calculate the fatigue limit estimated value σa _std Specifically, by substituting α = 1.6 and HV = 300 [HV] into the right side of the above equation (5), the estimated fatigue limit value σa _std = 480 [MPa]. _std = 480 [MPa] was substituted into the right side of the above-mentioned formula (6) to calculate the fatigue limit dispersion R. FIG. 12 shows the fatigue limit dispersion R calculated for each stress amplitude σa shown in FIGS.

[0047] In the second-order derivative correction value calculation step ST3 of this embodiment, the second-order derivative value d2' for each stress range σa was calculated for each Area-1, Area-2, and Area-3 by multiplying the second-order derivative value d2 for each stress range σa shown in Figure 10 by the fatigue limit dispersion R for each stress range σa shown in Figure 12. Figure 13 shows the relationship between stress amplitude σa and dissipated energy q calculated in relationship calculation step ST1 of this embodiment, and the corrected second-order derivative d2' obtained by multiplying the second-order derivative d2 for each stress amplitude σa shown in Figure 10 by the fatigue limit dispersion R for each stress amplitude σa shown in Figure 12. In Figure 13, the corrected second-order derivative d2' is plotted with an "x". Figure 13(a) shows the calculation for Area-1, Figure 13(b) shows the calculation for Area-2, and Figure 13(c) shows the calculation for Area-3. Similarly, in the first-order differential correction value calculation step ST3′ of this embodiment, the first-order differential value d′ for each stress range σa was calculated for each Area-1, Area-2, and Area-3 by multiplying the first-order differential value d for each stress range σa shown in FIG. 11 by the fatigue limit dispersion R for each stress range σa shown in FIG. 12. Fig. 14 shows the relationship between stress amplitude σa and dissipated energy q calculated in relationship calculation step ST1 of this embodiment, and the first-order derivative correction value d' obtained by multiplying the first-order derivative value d for each stress amplitude σa shown in Fig. 11 by the fatigue limit dispersion R for each stress amplitude σa shown in Fig. 12. In Fig. 14, the first-order derivative correction value d' is plotted with "x". Fig. 14(a) shows the calculation for Area-1, Fig. 14(b) shows the calculation for Area-2, and Fig. 14(c) shows the calculation for Area-3.

[0048] As can be seen from FIG. 13, in this embodiment, the maximum value d2′ of all the second-order differential correction values ​​d2′ in Area-3 is max The maximum value d2' is obtained. max The stress amplitude σa obtained was 525 MPa. Therefore, in this example, when the second-order differential correction value d2' is used (when the estimation method according to the first embodiment is used), Area-3 is estimated as the fatigue fracture initiation point of the object under test, and 525 MPa is estimated as the fatigue limit of the object under test. As can be seen from FIG. 14, in this embodiment, the maximum value d′ of all first-order differential correction values ​​d′ in Area-3 is max The maximum value d' is obtained. max The stress amplitude σa obtained was 525 MPa. Therefore, in this example, when the first-order differential correction value d' is used (when the estimation method according to the second embodiment is used), Area-3 is also estimated as the fatigue fracture initiation point of the object, and 525 MPa is estimated as the fatigue limit of the object. The inventors have actually performed a fatigue test on the test piece 1 and confirmed that the above estimation results are in good agreement with the fatigue fracture initiation confirmed by the fatigue test and the fatigue limit determined from the SN diagram obtained from the fatigue test. Therefore, it can be said that the estimation method according to the present invention makes it possible to accurately estimate the fatigue fracture initiation and fatigue limit of a test object based on the dissipated energy distribution of the test object measured using an infrared imaging device. [Explanation of symbols]

[0049] d 1st derivative d' First derivative correction value d1' max Maximum value d2: second derivative d2': Second-order derivative correction value d2' max Maximum value q...dissipated energy ST1: Relation calculation step ST2: 2nd derivative calculation step ST2': First-order differential calculation step ST3: Second-order differential correction value calculation step ST3 ST4, ST4': Fatigue fracture initiation estimation step ST5, ST5': Fatigue limit estimation step σa stress width

Claims

1. a relationship calculation step of measuring a change in temperature distribution over time of the object to be measured for each of the repeated loads by sequentially applying cyclic loads with different stress amplitudes σa to the object to be measured using an infrared imaging device, calculating a dissipated energy distribution of the object to be measured for each of the repeated loads based on the change in temperature distribution over time of the object to be measured for each of the repeated loads, and calculating a relationship between the stress amplitude σa and the dissipated energy q for each of multiple portions of the object to be measured based on the dissipated energy distribution of the object to be measured calculated for each of the repeated loads; a second-order differential value calculation step of calculating a second-order differential value d2 for each stress width σa obtained by second-order differentiating the calculated relationship with respect to the stress width σa for each of the plurality of portions; a second-order differential correction value calculation step of multiplying the calculated second-order differential value d2 for each stress width σa by the fatigue limit dispersion R for each stress width σa to calculate a second-order differential correction value d2′ for each of the plurality of portions; The maximum value d2' of all the second-order differential correction values ​​d2' calculated for the plurality of parts among the plurality of parts ｍａｘ a fatigue fracture initiation estimation step of estimating the site where the above-mentioned value is obtained as the fatigue fracture initiation site of the object to be measured; The maximum value d2' ｍａｘ and a fatigue limit estimating step of estimating the stress width σa obtained as a fatigue limit of the object to be measured, The fatigue limit dispersity R is represented by the following formula (A): Methods for estimating fatigue fracture origin and fatigue limit. R=1-abs(1-σa / (α・HV))...(A) In the above formula (A), σa is the stress amplitude [MPa], HV is the Vickers hardness [HV] of the object to be measured, α is a constant, and abs(·) means the absolute value in parentheses.

2. a relationship calculation step of measuring a change in temperature distribution over time of the object to be measured for each of the repeated loads by sequentially applying cyclic loads with different stress amplitudes σa to the object to be measured using an infrared imaging device, calculating a dissipated energy distribution of the object to be measured for each of the repeated loads based on the change in temperature distribution over time of the object to be measured for each of the repeated loads, and calculating a relationship between the stress amplitude σa and the dissipated energy q for each of multiple portions of the object to be measured based on the dissipated energy distribution of the object to be measured calculated for each of the repeated loads; a first-order differential value calculation step of calculating a first-order differential value d for each of the plurality of portions by first-order differentiating the calculated relationship with respect to the stress width σa; a first-order differential correction value calculation step of multiplying the calculated first-order differential value d for each stress width σa by the fatigue limit dispersion R for each stress width σa to calculate a first-order differential correction value d' for each of the plurality of portions; The maximum value d' of all the first-order differential correction values ​​d' calculated for the plurality of parts among the plurality of parts ｍａｘ a fatigue fracture initiation estimation step of estimating the site where the above-mentioned value is obtained as the fatigue fracture initiation site of the object to be measured; The maximum value d' ｍａｘ and a fatigue limit estimating step of estimating the stress width σa obtained as a fatigue limit of the object to be measured, The fatigue limit dispersity R is represented by the following formula (A): Methods for estimating fatigue fracture origin and fatigue limit. R=1-abs(1-σa / (α・HV))...(A) In the above formula (A), σa is the stress amplitude [MPa], HV is the Vickers hardness [HV] of the object to be measured, α is a constant, and abs(·) means the absolute value in parentheses.

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