Stress measurement method and program

Abstract

Provided is a method or the like for efficiently and accurately measuring the stress within a predetermined region on the surface of a joint regardless of the plate width ratio. 【Solution means】The present invention executes a coupled FEM analysis to obtain σ cal = a·f b The stress calculation formula represented by is pre-constructed for each plate width ratio R t in step S1, a constant calculation formula for calculating constants a and b from the plate width ratio R t is pre-constructed in step S2, a repetitive load of frequency f tIR is applied to the joint to be measured with the plate width ratio R IR , and the stress σ IR within a predetermined region of the joint to be measured is measured using the thermoelastic stress measurement method in step S3. By substituting the plate width ratio R tIR into the constant calculation formula, constants a and b corresponding to the plate width ratio R tIR are calculated, and the stress calculation formula is derived in step S4. By substituting the frequency f IR and the frequency f a into the stress calculation formula, the correction coefficient c is calculated in step S5. The appropriate stress is calculated by multiplying the stress σ IR by the correction coefficient c in step S6.

Description

[Technical Field]

[0001] This invention relates to a method and program for measuring stress in a predetermined area (such as near the joint) on the surface of a joint (such as a welded joint) formed by overlapping and joining two plate materials in the thickness direction, when a shear load is repeatedly applied to the joint, using a thermoelastic stress measurement method. In particular, this invention relates to a method and program that can efficiently and accurately measure stress in a predetermined area on the surface of a joint using a thermoelastic stress measurement method, regardless of the plate width ratio of the plate materials constituting the joint. [Background technology]

[0002] Joints formed by overlapping and joining two plates in the thickness direction (e.g., arc-welded joints, spot-welded joints, etc.) are widely used in automobiles, social infrastructure equipment, buildings, and the like. For the maintenance and management of these joints, it is important to evaluate their fatigue strength, and for that purpose, it is important to evaluate the surface stress that becomes the starting point of fatigue failure when repeated loads are applied to the joint.

[0003] Finite element analysis (hereinafter referred to as "FEM" as appropriate) is sometimes used as a method to evaluate the stress generated when repeated loads are applied to objects under measurement, such as joints. However, since numerical analysis models for FEM analysis are created by quantifying geometric information on a computer, it is difficult to accurately model complex shapes such as the welds of welded joints, for example. Furthermore, because numerical analysis models for FEM analysis are divided into elements (meshes) such as hexahedrons, they may not be able to reflect the subtle irregularities of the welded joint. Therefore, it can be difficult to accurately evaluate the stress in the welded joint of a welded joint using only FEM analysis.

[0004] Therefore, a non-contact method for measuring stress on the surface of an object under test has been proposed, which involves measuring thermoelastic stress using an infrared imaging device (thermography) (see, for example, Non-Patent Document 1). The thermoelastic stress measurement method utilizes the thermoelastic effect, where a temperature change occurs when an object undergoes adiabatic elastic deformation (heat is generated when compressive stress occurs, and heat is absorbed when tensile stress occurs). By continuously imaging an object subjected to repeated loads using an infrared imaging device, the temporal change in the object's temperature (temperature change within a predetermined time) is measured, and this measured temporal change in temperature is converted into the temporal change in the object's stress (stress change within a predetermined time). If the initial stress value is known (including not only cases where the stress has been actually measured and known, but also cases where it can be anticipated), the stress after a predetermined time has elapsed can be measured by adding the temporal change in stress to this initial value.

[0005] When measuring the temporal change in temperature of an object using this thermoelastic stress measurement method, heat (infrared radiation) from the surrounding environment of the object may be reflected by the object's surface and received by the infrared imaging device. In other words, the temporal change in temperature of an object measured using an infrared imaging device may include temperature changes caused by factors other than the temperature change caused by the thermoelastic effect (change in the intensity of infrared radiation emitted from the object). Since the temperature change caused by the thermoelastic effect is extremely small, if the infrared reflectivity on the surface of the object is large, the temperature change caused by the thermoelastic effect may be masked by the change in the infrared reflection intensity on the surface of the object, and the temporal change in stress of the object may not be calculated accurately.

[0006] Therefore, in the technology described in Non-Patent Document 1, a signal waveform corresponding to the temperature change caused by the thermoelastic effect being measured is locked in 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 with the same frequency as the applied load is output from a fatigue testing machine that repeatedly applies a load to the object under test. The image signal is synchronously detected using this reference signal, and only the image signal components of the frequency band corresponding to the reference signal (only image signal components with the same frequency as the reference signal or only image signals in a narrow frequency band that includes the same frequency as the reference signal) are extracted. This improves the signal-to-noise ratio of the temperature change caused by the thermoelastic effect to be measured. Then, the temporal change in the temperature of the object under test (the temporal change in temperature for each pixel constituting the image captured by the infrared imaging device) is calculated according to the magnitude of the extracted image signal components and the pre-stored correspondence between the magnitude and temperature of the image signal components. Next, the temporal change in the stress of the object under test is calculated based on the temporal change in the temperature of the object under test and a predetermined relational expression between the temporal change in temperature and the temporal change in stress.

[0007] Thus, by using the lock-in process, it is theoretically possible to accurately calculate the temporal change in stress of the object being measured, and consequently, the stress of the object itself. Furthermore, since the stress of the object is calculated based on images captured using an infrared imaging device, it can be applied to complex shapes such as welded joints.

[0008] However, when a shear load is repeatedly applied to a joint formed by overlapping and joining two plates in the thickness direction, bending stress acts near the joint (for example, the weld in the case of a welded joint), resulting in opposing stresses on both sides of the plates. That is, tensile stress occurs on one side and compressive stress occurs on the other side. As a result, heat is absorbed on one side and heat is released on the other side, and the temperature change becomes small due to the mutual influence of heat diffusion. If the frequency of the repeated load is a low frequency of about 5 Hz, there is a problem that the measured stress will be smaller than the actual stress occurring at the joint.

[0009] Although Patent Documents 1 to 4 propose methods for improving the measurement accuracy of thermoelastic stress measurement methods, they do not solve the above-mentioned problems.

[0010] Patent documents 5 and 6 propose a method to solve the above problem by combining a thermoelastic stress measurement method with coupled finite element analysis as described in Patent Document 7, which will be discussed later. In the case of joints such as lap fillet arc welded joints, the plate width ratio, which is the ratio of the minimum width of the plate material in a predetermined area of ​​the joint to the maximum width of the plate material constituting the joint, may be set to various values. However, the methods described in Patent Documents 5 and 6 do not consider the effect of the plate width ratio on stress (only the case where the plate width ratio = 1.0 is considered).

[0011] Furthermore, Patent Document 7 describes a method for calculating the stress (external stress) at a joint (welded joint) formed by overlapping plate materials when a shear load is repeatedly applied to the joint (spot-welded joint) by performing a coupled finite element method (coupled FEM analysis) of the stress field and temperature field using the maximum load (assumed maximum load) and minimum load (assumed minimum load) of the repeated load, which simulates the thermoelastic stress measurement method. Specifically, in the coupled FEM analysis described in Patent Document 7, after performing the stress analysis step, the heat flux calculation step and the heat transfer analysis step are repeatedly performed for a predetermined time (the same time as the predetermined time for continuously imaging the joint (spot welded joint) using an infrared imaging device), and then the conversion step is performed. In the stress analysis step, stress analysis is performed using the maximum load (assumed maximum load) and minimum load (assumed minimum load) of the repeated load to calculate the stress in the numerical analysis model. In the heat flux calculation step, the heat flux is calculated using the stress of the numerical analysis model calculated in the stress analysis step, the material properties of the joint (spot welded joint) (e.g., the thermoelastic modulus, density, and specific heat of the plate material), and the frequency (period) of the repeated load. In the heat transfer analysis step, a heat transfer analysis is performed using the heat flux calculated in the heat flux calculation step, and the temperature of the numerical analysis model is calculated. In the conversion step, the temperature of the joint (welded area) (external surface temperature) is calculated based on the temperature of the numerical analysis model after a predetermined time has elapsed, and this temperature is converted into the stress (external surface stress) of the joint (welded area). According to the coupled FEM analysis described in Patent Document 7, it is possible to calculate stress (external stress) equivalent to the stress (external stress) of a joint (welded joint) measured using the thermoelastic stress measurement method. [Prior art documents] [Non-patent literature]

[0012] [Non-Patent Document 1] Tatsuya Yaoita, et al., "Stress Measurement and Predictive Measurement of Fatigue Limit Point Using an Infrared Camera," Society of Automotive Engineers of Japan Autumn Academic Conference, No. 98-03, (2003) [Patent Documents]

[0013] [Patent Document 1] Japanese Patent Publication No. 2018-179730 [Patent Document 2] Japanese Patent Publication No. 2015-001392 [Patent Document 3] Japanese Patent Publication No. 2016-024057 [Patent Document 4] Japanese Patent Publication No. 2018-128431 [Patent Document 5] Japanese Patent Publication No. 2025-058521 [Patent Document 6] Japanese Patent Publication No. 2025-058522 [Patent Document 7] Japanese Patent Publication No. 2022-032646 [Overview of the project] [Problems that the invention aims to solve]

[0014] The present invention was made to solve the problems of the prior art described above, and aims to provide a method and program for efficiently and accurately measuring the stress in a predetermined area of ​​the surface of a joint (for example, the joint and the area adjacent to the joint, or the vicinity of the joint) when a shear load is repeatedly applied to a joint (such as a welded joint) formed by overlapping and joining two plate materials in the thickness direction, using a thermoelastic stress measurement method, regardless of the plate width ratio. [Means for solving the problem]

[0015] To solve the aforementioned problems, the inventors focused on combining a thermoelastic stress measurement method with coupled FEM analysis described in Patent Document 7, similar to the methods described in Patent Documents 5 and 6, and diligently investigated the effect of the plate width ratio on stress. The inventors' investigations are described below.

[0016] By performing coupled FEM analysis on the numerical analysis model of the joint, the stress σ within a predetermined region of the joint can be determined. cal The following is calculated. In this process, by changing the frequency f of the repeated shear load applied to the joint and performing coupled FEM analysis, the stress σ corresponding to each frequency f is calculated. cal It is possible to calculate the stress σ calculated by performing this coupled FEM analysis. cal This refers to the stress σ measured using the thermoelastic stress measurement method. IR This will result in a value equivalent to [this]. On the other hand, by performing a static finite element method analysis (static FEM analysis) using the maximum load of the repeated shear load applied to the joint, the actual (ideal) stress σ within a predetermined region of the joint can be determined. a It is possible to calculate this. In this specification, actual stress means stress equivalent to the actual stress that can be measured using strain gauges, etc. Alternatively, actual stress σ a This can also be calculated by performing a coupled FEM analysis with frequency f set to a relatively high frequency of 20 Hz or higher. This is because the stress value calculated by performing a coupled FEM analysis with frequency f set to a relatively high frequency of 20 Hz or higher will be equivalent to the actual stress value that can be measured using strain gauges, etc. Therefore, by dividing the actual stress σ a by the stress σ cal corresponding to each frequency f, the correction coefficient c (= σ a / σ IR = σ a / σ cal = σ a / σ IR ), which is the reciprocal of the index representing the degree of attenuation of the stress σ IR measured using the thermoelastic stress measurement method with respect to the actual stress σ a , can be calculated. Then, by multiplying the stress σ a by the correction coefficient c, it is considered possible to calculate an appropriate stress (a stress that can be expected to be equivalent to the actual stress σ IR cal a Figure 1 shows an example of the result of measuring the distribution of the stress σ IR in a predetermined region (near the welded part) AS by applying a repeated load P in the shear direction with a frequency of 5 Hz to a fillet weld joint, using the thermoelastic stress measurement method. Figure 2 shows an example of the result calculated by performing a coupled FEM analysis of the distribution of the stress σ cal in a predetermined region (near the welded part) AS under the condition of applying a repeated load P in the shear direction with a frequency of 5 Hz to a numerical analysis model (1 / 2 symmetric model) corresponding to the same fillet weld joint as in Figure 1. Figure 3 shows an example of the result calculated by performing a coupled FEM analysis of the distribution of the stress σ a in a predetermined region (near the welded part) AS under the condition of applying a repeated load P in the shear direction with a frequency of 20 Hz to a numerical analysis model (1 / 2 symmetric model) corresponding to the same fillet weld joint as in Figure 1. The inventors have confirmed that the maximum stress in the distribution of this stress σ a is equal to the maximum stress in the predetermined region AS measured using a strain gauge.

[0018] As can be seen by comparing Figure 1 and Figure 2, the stress distribution measured using the thermoelastic stress measurement method (Figure 1) and the stress distribution calculated by performing a coupled FEM analysis under the same conditions as the thermoelastic stress measurement method, with a cyclic load P of 5 Hz, are stress distributions with equivalent maximum stress values. Furthermore, as can be seen by comparing Figure 2 and Figure 3, the stress distribution calculated by performing a coupled FEM analysis under the condition of applying a cyclic load P at a frequency of 5 Hz (Figure 2) has a smaller maximum stress than the stress distribution calculated by performing a coupled FEM analysis under the condition of applying a cyclic load P at a frequency of 20 Hz (Figure 3). Therefore, the stress σ measured using the thermoelastic stress measurement method IR By multiplying by the correction factor c as described above, when the plate width ratio of the plates constituting the joint is constant, the actual stress σ a It can be said that it is possible to accurately calculate the appropriate stress corresponding to the situation.

[0019] Next, the inventors investigated the effect of the plate width ratio on stress. Figure 4 is a perspective view showing the outer diameter of a numerical analysis model (finite element analysis model) of a lap fillet arc welded joint used to examine the effect of the plate width ratio on stress. In Figure 4, the X direction indicates the direction (shear direction) in which the repeated load P is applied to the joint (lap fillet arc welded joint) 10. The Y direction indicates the overlapping direction (plate thickness direction) of the plate materials 11 and 12 that constitute the joint 10. The Z direction indicates the direction perpendicular to the X and Y directions and corresponds to the plate width direction of the plate materials 11 and 12 that constitute the joint 10. The meanings of the X and Z directions shown in Figures 1 to 3 above, and the X, Y and Z directions shown in Figure 7 below, are the same as those shown in Figure 4. The joint 10 shown in Figure 4(a) has a plate thickness t of 1.4 mm for the plates 11 and 12, and a maximum width W for the plates 11 and 12. a The minimum width W of the plate materials 11 and 12 in the predetermined area (area near the weld) AS is 25 mm. b It is also 25mm. Therefore, the maximum width W of the boards 11 and 12 a The minimum width W of the plate materials 11 and 12 in a predetermined region AS. bThe ratio of board widths is R. t (=W b / W a ) becomes 1.0. The joint 10 shown in Figure 4(b) has a plate thickness t of 1.4 mm for the plates 11 and 12, and a maximum width W for the plates 11 and 12. a The minimum width W of the plate materials 11 and 12 in the predetermined area (area near the weld) AS is 25 mm. b The width is 10 mm. Therefore, the width ratio R of the boards 11 and 12 t This becomes 0.4.

[0020] The inventors applied a cyclic shear load P with a load difference (maximum load - minimum load) of 3.0 kN and a stress ratio of 0.05 to each numerical analysis model shown in Figure 4, and performed coupled FEM analysis under conditions where the frequency f of the cyclic load P was changed in the range of 1 to 20 Hz, thereby determining the stress σ within a predetermined region AS. cal The result was calculated. Figure 5 shows the frequency f calculated by coupled FEM analysis and the stress σ within the predetermined region AS for each numerical analysis model shown in Figure 4. cal The relationship is shown in Figure 5, where the stress σ within the predetermined region AS is shown. cal The maximum stress among them is plotted. As shown in Figure 5, the board width ratio R t Regardless of frequency f and stress σ cal It has a correlation with stress σ cal It was found that this can be accurately approximated by a power function of frequency f (the function shown by the dashed line in Figure 5). That is, the stress σ within a predetermined region from frequency f is expressed by the following equation (1). cal It was found that a stress calculation formula can be constructed to accurately calculate stress. σ cal =a·f b ...(1)

[0021] Using the stress calculation formula represented by equation (1) above, a predetermined frequency f of 20 Hz or higher can be calculated. a By substituting this, the actual stress σ a The stress σ is considered to be equivalent to cala The frequency f used in the thermoelastic stress measurement method is calculated and set to the frequency fIR By substituting this, the stress σ calIR Calculate the stress σ cala stress σ calIR By dividing by σ, the correction coefficient c(=σ) cala / σ calIR The stress σ is calculated using the thermoelastic stress measurement method. IR By multiplying by the correction factor c, the actual stress σ a It is considered possible to calculate the appropriate stress according to the conditions.

[0022] However, as can be seen from Figure 5, the constants a and b in the stress calculation formula represented by equation (1) above are the plate width ratio R t The value is different for each case. Therefore, in the method using the above stress calculation formula, the plate width ratio R of the joint being measured is used. t If it changes, the board width ratio R t It is necessary to perform a coupled FEM analysis accordingly to construct a stress calculation formula (constants a and b need to be calculated). Therefore, this approach is inefficient because it increases computation time costs and requires a huge amount of data storage capacity.

[0023] Therefore, the inventors conducted further intensive studies and found that the constants a and b in the stress calculation formula are both equal to the plate width ratio R. t It is correlated with the constant a and constant b, and the plate width ratio R t We found that it can be approximated accurately by a predetermined function of the plate width ratio R. t We found that we can construct constant calculation formulas to accurately calculate constants a and b from this data. Therefore, the above stress calculation formula is applied to the plate width ratio R t Each stress is pre-constructed, and the constants a and b in this stress calculation formula are set to the plate width ratio R. t If you organize them individually and construct the above constant calculation formula in advance, the plate width ratio of the joint to be measured will be R tIR The frequency is f IR By applying a repeated load, the stress σ within a predetermined area on the surface of the joint to be measured is determined using the thermoelastic stress measurement method. IR When measuring, the constant calculation formula includes the plate width ratio R.tIR By simply substituting, the board width ratio R tIR The constants a and b corresponding to the stress can be calculated efficiently. Therefore, by substituting the calculated constants a and b into the stress calculation formula, the plate width ratio R can be calculated. tIR A stress calculation formula is derived corresponding to the frequency f, and the derived stress calculation formula is applied to the frequency f. IR and a predetermined frequency f of 20 Hz or higher a By substituting this value, the correction coefficient c is calculated, and the stress σ is measured using the thermoelastic stress measurement method. IR By multiplying this by a correction factor c, it is possible to efficiently and accurately calculate the appropriate stress for the joint being measured, corresponding to the actual stress within a predetermined area.

[0024] This invention was completed based on the findings of the inventors described above. In other words, to solve the above problem, the present invention provides a method for measuring the stress in a predetermined region of a joint formed by overlapping and joining two plate materials in the thickness direction when a repeated shear load is applied to the joint, using a thermoelastic stress measurement method, wherein the frequency f of the repeated load and the plate width ratio R, which is the ratio of the minimum width of the plate material in the predetermined region to the maximum width of the plate material, are used, and the frequency f of the repeated load and the plate width ratio R are used. t By performing coupled finite element analysis of stress fields and temperature fields using the repeated load on each of the multiple numerical analysis models of the joint, which include those with different properties, the following equation (1) is obtained: stress σ from frequency f within the predetermined region cal The stress calculation formula for calculating the plate width ratio R is defined as follows: t A step to construct a stress calculation formula in advance for each step, and the constants a and b of the stress calculation formula are set to the plate width ratio R t Each item is organized according to the aforementioned plate width ratio R t A constant calculation formula construction step involves constructing a constant calculation formula in advance to calculate the constant a and the constant b from the joint to be measured, and the plate width ratio is R tIR The frequency f of the joint being measured IR The repeated load is applied, and the stress σ in the predetermined region of the joint to be measured is measured using the thermoelastic stress measurement method. IR A stress measurement step to measure the plate width ratio R, and the constant calculation formula to measure the plate width ratio R tIRBy substituting, the plate width ratio R tIR According to, the constants a and b are calculated, and by substituting the calculated constants a and b into the stress calculation formula, the plate width ratio R tIR A stress calculation formula derivation step for deriving the stress calculation formula according to, and the frequency f IR By substituting, the stress σ calIR is calculated, and a predetermined frequency f of 20 Hz or more is substituted into the derived stress calculation formula a By substituting, the stress σ cala is calculated, and the stress σ calIR For the stress σ cala A correction coefficient calculation step for calculating the correction coefficient c which is the ratio of, and the stress σ IR By multiplying by the correction coefficient c, a proper stress calculation step for calculating a proper stress corresponding to the actual stress in the predetermined region is provided, and a stress measurement method is provided. σ cal =a·f b ···(1) In the above formula (1), a and b are constants determined for each of the plate width ratios R t is a constant.

[0025] In the present invention, the "shearing direction" means a direction orthogonal to the overlapping direction (plate thickness direction) of two plate materials. The "repeated load" in the present invention may be a single-sided load which is either a tensile load or a compressive load, or a double-sided load which repeats a tensile load and a compressive load. In the case of a double-sided load, the average load may be either a tensile load or a compressive load. In the present invention, the "plate thickness" means the dimension in the overlapping direction of each plate material that is overlapped. In the present invention, the "stress" is a concept including not only the stress on the surface of the joint itself but also the temporal change of the stress. In the present invention, the "maximum width" and the "minimum width" mean the maximum value and the minimum value of the dimension in the plate width direction of the plate material, and the "plate width direction" means the direction orthogonal to the direction to which the repeated load is applied and the plate thickness direction. In the present invention, "substituting the plate width ratio R into the constant calculation formula" means inputting the value of the plate width ratio R into the plate width ratio R in the constant calculation formula. "Substituting the calculated constants a and b into the stress calculation formula" means inputting the calculated values of the constant a and the calculated value of the constant b into the constants a and b in Equation (1). "Substituting the frequency f into the derived stress calculation formula" means inputting the value of the frequency f into the frequency f in the derived stress calculation formula. "Substituting a predetermined frequency f of 20 Hz or more into the derived stress calculation formula" means inputting the value of the frequency f into the frequency f in the derived stress calculation formula. In the correction coefficient calculation step of the present invention, as the frequency f of the repeated load to be substituted into the stress calculation formula, either a set value or a measured value may be used.

[0026] According to the present invention, in the stress calculation formula construction step, a stress calculation formula for calculating the stress σ within a predetermined region on the surface of the joint from the frequency f of the repeated load is constructed in advance for each plate width ratio R of the joint. Next, in the constant calculation formula construction step, the constants a and b of the stress calculation formula are arranged for each plate width ratio R, and a constant calculation formula for calculating the constants a and b from the plate width ratio R is constructed in advance. Next, in the stress measurement step, a repeated load of frequency f is applied to the measurement target joint with a plate width ratio of R, and the stress σ within a predetermined region of the measurement target joint is measured using the thermoelastic stress measurement method. This stress σ is measured as a stress having a value smaller than the actual stress if the frequency f is a low frequency of about 5 Hz. ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​Therefore, according to the present invention, in the stress calculation formula derivation step, the plate width ratio R of the joint to be measured is added to the constant calculation formula. tIR By substituting this, the board width ratio R tIR The constants a and b are calculated accordingly. Then, by substituting the calculated constants a and b into the stress calculation formula, the plate width ratio R is calculated. tIR A stress calculation formula is derived accordingly. As a result, in the correction coefficient calculation step, the frequency f of the repeated load applied to the joint under measurement is added to the derived stress calculation formula. IR By substituting this, the stress σ calIR This stress σ can be calculated. calIR This is the stress σ measured by the thermoelastic stress measurement method. IR It can be expected to show a value equivalent to that. In addition, in the correction coefficient calculation step, a predetermined frequency f of 20 Hz or higher is added to the derived stress calculation formula. a By substituting this, the stress σ cala This stress σ can be calculated. cala It can be expected that this will show a value equivalent to the actual stress (stress equivalent to the actual stress that can be measured using strain gauges, etc.). Therefore, stress σ calIR Stress σ cala The ratio of stress σ measured in the stress step IR This can be calculated as a correction factor c. Finally, the stress σ measured in the stress measurement step IR By multiplying this by the correction coefficient c calculated as described above, the appropriate stress corresponding to the actual stress in a predetermined area on the surface of the joint to be measured is calculated. As described above, according to the present invention, in the stress calculation formula construction step, the stress calculation formula is set to the plate width ratio R t Each is pre-constructed, and in the constant calculation formula construction step, the constants a and b of this stress calculation formula are set to the plate width ratio R. t If we organize the data for each component and construct a constant calculation formula in advance, then in the stress measurement step, the plate width ratio of the joint being measured will be R tIR The frequency is f IR By applying a repeated load, the stress σ within a predetermined area on the surface of the joint to be measured is determined using the thermoelastic stress measurement method. IRWhen measuring, in the stress calculation formula derivation step, the plate width ratio R is used in the constant calculation formula. tIR By simply substituting, the board width ratio R tIR The constants a and b corresponding to the stress can be calculated efficiently. Therefore, in the stress calculation formula derivation step, by substituting the calculated constants a and b into the stress calculation formula, the plate width ratio R can be calculated efficiently. tIR A stress calculation formula is derived accordingly, and in the correction coefficient calculation step, the derived stress calculation formula is used with respect to the frequency f IR and a predetermined frequency f of 20 Hz or higher a By substituting this value, the correction coefficient c is calculated, and in the appropriate stress calculation step, the stress σ measured using the thermoelastic stress measurement method is used. IR By multiplying this by a correction factor c, it is possible to efficiently and accurately calculate the appropriate stress corresponding to the actual stress within a predetermined area on the surface of the joint being measured.

[0027] Furthermore, in this invention, if the constant calculation formula is constructed in advance by performing the stress calculation formula construction step only once and then the constant calculation formula construction step only once, then multiple joints to be measured (for example, plate width ratio R) can be measured. tIR or the frequency f of repeated loads IR When performing the stress calculation formula derivation step for multiple joints that are different from each other, the same constant calculation formula that has been constructed can be used repeatedly. In other words, when measuring the stress in a predetermined area of ​​multiple joints that are to be measured using the present invention, it is not necessary to perform the stress calculation formula construction step and the constant calculation formula construction step for each joint that is to be measured; they only need to be performed once in advance.

[0028] According to the inventors' findings, constant a and constant b are, respectively, the plate width ratio R t It can be approximated accurately by a power function of . In other words, in the present invention, preferably, the constant calculation formula is represented by the following formulas (2) and (3). a=s a ·R t ta ...(2) b=s b ·R t tb ...(3) Note that in equation (2) above, s a and ta are constants. In equation (3) above, s b And tb are constants.

[0029] The present invention is particularly suitable for use when the joint is a welded joint (such as an arc-welded joint or a spot-welded joint). However, the present invention is not limited to this, and can also be applied to a joint formed by joining two plate materials with bolts, for example.

[0030] The stress calculation formula construction step, constant calculation formula construction step, stress calculation formula derivation step, correction coefficient calculation step, and appropriate stress calculation step of the stress measurement method according to the present invention can be performed, for example, by a program installed on a computer. Accordingly, the present invention is also provided as a program for causing a computer to execute the stress calculation formula construction step, the constant calculation formula construction step, the stress calculation formula derivation step, the correction coefficient calculation step, and the appropriate stress calculation step, which are all part of the stress measurement method according to the present invention. [Effects of the Invention]

[0031] According to the present invention, when a shear load is repeatedly applied to a joint formed by overlapping and joining two plate materials in the thickness direction, the stress within a predetermined area on the surface of the joint can be efficiently and accurately measured regardless of the plate width ratio using a thermoelastic stress measurement method. [Brief explanation of the drawing]

[0032] [Figure 1] This example shows the results of measuring the stress distribution σIR within a predetermined region (the region near the weld) AS using the thermoelastic stress measurement method, after applying a repeated shear load P at a frequency of 5 Hz to an overlap fillet arc welded joint. [Figure 2]This example shows the results of calculating the stress σcal distribution within a predetermined region (the region near the weld) AS by performing coupled FEM analysis, using a numerical analysis model (1 / 2 symmetric model) corresponding to the same lap fillet arc welded joint as in Figure 1, under the condition of applying a repeated shear load P at a frequency of 5 Hz. [Figure 3] This example shows the results of calculating the stress distribution σa within a predetermined region (the region near the weld) AS by performing coupled FEM analysis, using a numerical analysis model (1 / 2 symmetric model) corresponding to the same lap fillet arc weld joint as in Figure 1, under the condition of applying a repeated shear load P at a frequency of 20 Hz. [Figure 4] This is a perspective view showing the outer diameter of a numerical analysis model (finite element analysis model) of a lap fillet arc welded joint used to investigate the effect of plate width ratio on stress. [Figure 5] Figure 4 shows the relationship between the frequency f calculated by coupled FEM analysis and the stress σcal within a predetermined region AS for each numerical analysis model. [Figure 6] This is a flowchart illustrating the steps involved in a stress measurement method according to one embodiment of the present invention. [Figure 7] An example of a numerical analysis model (finite element analysis model) for lap fillet arc welded joints is shown. [Figure 8] An example of the stress calculation formula calculated in step S1 of the stress calculation formula construction shown in Figure 6 is presented. [Figure 9] An example of a constant calculation formula calculated in step S2, shown in Figure 6, is presented. [Modes for carrying out the invention]

[0033] The following describes a stress measurement method according to one embodiment of the present invention, with reference to the attached drawings as appropriate, using the case where the joint to be measured for stress is a lap fillet arc welded joint as an example. Figure 6 is a schematic flowchart showing the steps of the stress measurement method according to this embodiment. Figure 7 shows an example of a numerical analysis model (finite element analysis model) of a lap fillet arc welded joint. Figure 7(a) is an element division diagram of the numerical analysis model, and Figure 7(b) is an element division diagram for a predetermined region AS of the numerical analysis model shown in Figure 7(a). The numerical analysis model shown in Figure 7 is a 1 / 2 symmetric model in which a plane of symmetry 10S is set at the center of the plate width direction (Z direction) of the plate materials 11 and 12 that constitute the joint 10.

[0034] The stress measurement method according to this embodiment is a method for measuring the stress in a predetermined area AS on the surface of a joint 10 (in the case of Figure 7, the area near the welded part 10A) when a repeated load P in the shear direction (X direction) is applied to a joint 10 formed by overlapping and joining two plate materials 11 and 12 in the plate thickness direction (Y direction) (in the case of Figure 7, by arc welding) using a fatigue testing machine or the like, using a thermoelastic stress measurement method. As shown in Figure 6, the stress measurement method according to this embodiment includes a stress calculation formula construction step S1, a constant calculation formula construction step S2, a stress measurement step S3, a stress calculation formula derivation step S4, a correction coefficient calculation step S5, and an appropriate stress calculation step S6. The stress calculation formula construction step S1, the constant calculation formula construction step S2, the stress calculation formula derivation step S4, the correction coefficient calculation step S5, and the appropriate stress calculation step S6 can be executed, for example, by a program installed on a computer. Each of the steps S1 to S6 will be described in order below.

[0035] <Stress calculation formula construction step S1> In stress calculation formula construction step S1, the joint 10 is as shown in Figure 7, and the frequency f of the repeated load P and the plate width ratio R of the plate members 11 and 12 are used. tFor each of the multiple numerical analysis models of the joint 10, which include those in which the ratio of the minimum width of the plates 11 and 12 in a predetermined region AS to the maximum width of the plates 11 and 12 differs from each other, a coupled finite element method (coupled FEM analysis) of the stress field and temperature field using repeated load P, simulating the thermoelastic stress measurement method, is performed. Note that the numerical analysis model shown in Figure 7 is the plate width ratio R t This is a numerical analysis model with a value of 0.4. The number of numerical analysis models used in stress calculation formula construction step S1 (frequency f and plate width ratio R) is as follows: t The number of combinations (where each combination is different from the others) should be kept to a minimum as long as it allows for the construction of a stress calculation formula with sufficient accuracy. The specific details of the coupled FEM analysis are the same as those described in Patent Document 7, so a detailed explanation is omitted here. Coupled FEM analysis can be performed using, for example, the general-purpose nonlinear finite element analysis program "Abaqus" manufactured by SIMULIA, but the present invention is not limited to this.

[0036] Then, in stress calculation formula construction step S1, the frequency f of the repeated load P and the plate width ratio R are used. t Based on the results of coupled FEM analysis performed on multiple numerical analysis models of the joint 10, each of which includes models with different properties, the stress σ within a predetermined region AS, expressed by the following equation (1), is obtained from the frequency f. cal The stress calculation formula for calculating the plate width ratio R t It is constructed for each case. Approximate calculations such as the least squares method can be used to construct the stress calculation formula. In addition, to construct the stress calculation formula, for example, the stress σ within a predetermined region AS is used. cal The maximum stress among them is used. σ cal =a·f b ...(1) In the above equation (1), a and b are the board width ratio R. t It is a constant that is determined for each instance.

[0037] Figure 8 shows an example of a stress calculation formula calculated in stress calculation formula construction step S1. The stress calculation formula shown in Figure 8 (dashed line shown in Figure 8) uses a total of 30 numerical analysis models, with six frequencies f = 1, 3, 5, 7, 10, and 20 Hz and five plate width ratios Rt = 1.0, 0.8, 0.6, 0.4, and 0.2, to calculate the plate width ratio R t This is the stress calculation formula constructed for each stage. As shown in Figure 8, the plate width ratio R t In either case, frequency f and stress σ cal It has a correlation with stress σ cal This can be accurately approximated by a power of frequency f. That is, the stress σ within a predetermined region, expressed by equation (1) above, is given by frequency f. cal It can be seen that a stress calculation formula can be constructed to accurately calculate the stress. As can be seen from Figure 8, the constants a and b in the stress calculation formula expressed in equation (1) above are the plate width ratio R t Each value is different.

[0038] <Constant calculation formula construction step S2> In step S2 of constructing the constant calculation formula, the constants a and b of the stress calculation formula represented by the above formula (1) are set to the plate width ratio R. t Organize each one, board width ratio R t We construct constant calculation formulas to determine constants a and b from this data. Specifically, in the constant calculation formula construction step S2, a constant calculation formula represented by equations (2) and (3) below is constructed. Approximation calculations such as the least squares method can be used to construct the constant calculation formula. a=s a ·R t ta ...(2) b=s b ·R t tb ...(3) Note that in equation (2) above, s a and ta are constants. In equation (3) above, s b And tb are constants.

[0039] Figure 9 shows an example of a constant calculation formula calculated in constant calculation formula construction step S2. Figure 9(a) is the constant calculation formula for constant a, and Figure 9(b) is the constant calculation formula for constant b. Figure 9 shows the five board width ratios R shown in Figure 8. t This constant calculation formula was constructed by organizing the five constants a and five constants b (shown as "●" in Figure 9) from the five stress calculation formulas constructed for each plate width ratio Rt. As shown in Figure 9, both constants a and b are related to the plate width ratio R t It is correlated with the constant a and constant b, and the plate width ratio R t It can be approximated accurately by a power function of . That is, the plate width ratio R, which is expressed by equations (2) and (3) above. t From this, we can see that we can construct constant calculation formulas for accurately calculating constants a and b.

[0040] <Stress measurement step S3> In stress measurement step S3, the plate width ratio of the joint 10 to be measured is R tIR The frequency f of the joint being measured IR A repeated load P is applied, and the stress σ within a predetermined region AS of the joint to be measured is measured using the thermoelastic stress measurement method. IR Measure the frequency f. IR The frequency f used to construct the stress calculation formula in stress calculation formula construction step S1 (in the example shown in Figure 8, f = 1, 3, 5, 7, 10, 20 Hz) can be a different value from the frequency f used to construct the stress calculation formula, but it may also be the same value. Also, the plate width ratio R tIR This is the board width ratio R used to construct the constant calculation formula in step S2 of the constant calculation formula construction. t (In the example shown in Figure 9, R t The values ​​can be different (e.g., 1.0, 0.8, 0.6, 0.4, 0.2), but they can also be the same. Specifically, in stress measurement step S3, an infrared imaging device positioned opposite the surface of the joint to be measured is used, and a fatigue testing machine or the like measures the frequency f IRA predetermined region AS of the joint to be measured is continuously imaged while a repeated shear load P is applied for a predetermined time. Preferably, a signal waveform corresponding to the temperature change caused by the thermoelastic effect to be measured is locked in from the image signal output from the infrared imaging device. This results in the stress σ within the predetermined region AS of the joint to be measured. IR It is possible to measure this. Note that the more specific details of the thermoelastic stress measurement method are publicly known, so a detailed explanation is omitted here.

[0041] <Stress calculation formula derivation step S4> In the stress calculation formula derivation step S4, the constant calculation formulas (equations (2) and (3)) constructed in the constant calculation formula construction step S2 are used, and the plate width ratio R of the joint to be measured is applied. tIR By substituting this, the board width ratio R tIR The constants a and b are calculated accordingly. That is, the board width ratio R in equations (2) and (3). t board width ratio R tIR By entering a value, the board width ratio R tIR The constants a and b are calculated accordingly. Next, in the stress calculation formula derivation step S4, the calculated constants a and b are substituted into the stress calculation formula (equation (1)) constructed in the stress calculation formula construction step S1, thereby determining the plate width ratio R tIR A stress calculation formula is derived accordingly. That is, by inputting the calculated constants a and b into the constants a and b of formula (1), the plate width ratio R is obtained. tIR A stress calculation formula is derived accordingly.

[0042] <Correction factor calculation step S5> In the correction coefficient calculation step S5, the stress calculation formula derived in the stress calculation formula derivation step S4 is used, and the frequency f of the repeated load applied to the joint to be measured is added. IR By substituting this, the stress σ calIR We calculate the frequency f in equation (1). IR The stress σ obtained by inputting a value σ cal The value of stress σ calIR The calculation is performed as follows. In addition, in the correction coefficient calculation step S5, a predetermined frequency f of 20 Hz or higher is added to the derived stress calculation formula.a By substituting this, the stress σ cala We calculate the frequency f in equation (1). a The σ obtained by inputting a value cal The value of stress σ cala It is calculated as follows. Then, in correction coefficient calculation step S5, stress σ calIR Stress σ cala The correction coefficient c, which is the ratio, is calculated.

[0043] <Step S6 for calculating appropriate stress> In the appropriate stress calculation step S6, the stress σ within a predetermined region AS of the joint to be measured, as measured in the stress measurement step S3, is calculated. IR By multiplying this by the correction coefficient c calculated in the correction coefficient calculation step S5, an appropriate stress corresponding to the actual stress within the predetermined region AS is calculated. For example, the stress σ within the predetermined region AS IR By multiplying the maximum stress by a correction factor c, the appropriate maximum stress value corresponding to the actual stress within the predetermined region AS is calculated.

[0044] According to the stress measurement method of this embodiment, in the stress calculation formula construction step S1, the stress calculation formula (formula (1)) is set to the plate width ratio R t Each is pre-constructed, and in the constant calculation formula construction step S2, the constants a and b of this stress calculation formula are set to the plate width ratio R. t If we organize the data for each condition and construct constant calculation formulas (Equations (2) and (3)) in advance, then in stress measurement step S3, the plate width ratio of the joint to be measured is R tIR The frequency is f IR By applying a repeated load, the stress σ within a predetermined region AS on the surface of the joint to be measured is determined using the thermoelastic stress measurement method. IR When measuring, in stress calculation formula derivation step S4, the plate width ratio R is added to the constant calculation formula. tIR By simply substituting, the board width ratio R tIR The constants a and b corresponding to the can be calculated efficiently. Therefore, in the stress calculation formula derivation step S4, by substituting the calculated constants a and b into the stress calculation formula, the plate width ratio R can be calculated efficiently. tIRA stress calculation formula is derived accordingly, and in the correction coefficient calculation step S5, the frequency f is applied to the derived stress calculation formula. IR and a predetermined frequency f of 20 Hz or higher a By substituting this value, the correction coefficient c is calculated, and in the appropriate stress calculation step S6, the stress σ measured using the thermoelastic stress measurement method is used. IR By multiplying by a correction factor c, it is possible to efficiently and accurately calculate the appropriate stress corresponding to the actual stress within a predetermined area AS on the surface of the joint being measured.

[0045] The following describes an example in which the stress measurement method according to this embodiment was implemented.

[0046] In this embodiment, the joint 10 used to measure stress has a plate thickness t of 1.4 mm, and a plate width ratio R. tIR A lap fillet arc welded joint was used, formed by arc welding two 590 MPa class steel plates, 11 and 12, with a pressure of 0.3, overlapping them in the thickness direction. Then, coupled FEM analysis was performed using a numerical analysis model of an overlapping fillet arc welded joint as shown in Figure 7.

[0047] First, in the stress calculation formula construction step S1 of this embodiment, the Young's modulus of the plate materials 11 and 12 is set to 205.9 GPa, the Poisson's ratio to 0.3, the initial temperature to 20°C, and the thermoelastic modulus to 3.14 e. -6 (e is the base of the natural logarithm), density is 7.8e -6 kg / mm 3 (e is the base of the natural logarithm), with a specific heat of 460 J / kg, a load difference (maximum load - minimum load) of 3.0 kN, and a stress ratio of 0.05, a repeated shear load P is applied to one end of the joint 10 (the front end shown in Figure 7(a)) (the other end is fixed), and the frequency Hz of the repeated load P is changed within the range of 1 to 20 Hz, under the conditions of plate width ratio R t For the numerical analysis models of each of the 10 joints with values ​​of =1.0, 0.8, 0.6, 0.4, and 0.2, coupled FEM analysis was performed, and a stress calculation formula represented by equation (1) was constructed. The stress calculation formula (plate width ratio R) constructed for each numerical analysis model tThe values ​​of constants a and b in the stress calculation formulas constructed for each were as follows: (1)R t Numerical analysis model with =1.0: a=93.291, b=0.3495 (2)R t Numerical analysis model with =0.8: a=111.43, b=0.34 (3)R t Numerical analysis model with =0.6: a=143.75, b=0.332 (4)R t Numerical analysis model with =0.4: a=203.66, b=0.3245 (5)R t Numerical analysis model with =0.2: a=338.69, b=0.3118 The five stress calculation formulas shown in Figure 8 above are stress calculation formulas that have the values ​​of the constants a and b described above.

[0048] In step S2 of constructing the constant calculation formula of this embodiment, the above constants a and b are used for the board width ratio R. t We organized the data and constructed constant calculation formulas represented by equations (2) and (3). The values ​​of the constants in the constructed constant calculation formula were as follows: s a =94.218, ta=-0.807, s b =0.3447, tb=0.0638 The constant calculation formula shown in Figure 9(a) above is the constant s mentioned above. a And it is a constant calculation formula that has the value of the constant ta. The constant calculation formula shown in Figure 9(b) above is the constant s b And it is a constant calculation formula that has a value for the constant tb.

[0049] In the stress measurement step S3 of this embodiment, a repeated shear load P with a load difference (maximum load - minimum load) of 2.6 kN and a stress ratio of 0.05 is applied to the plate width ratio R. tIR A joint 10 with a frequency f of the repeated load P is applied to the joint 10 with a frequency f of =0.3. IR Under conditions set to =3Hz, the stress σ within a predetermined region AS of the joint 10 was measured using the thermoelastic stress measurement method. IR The stress σ was measured. IRThe maximum stress among them was 360 MPa.

[0050] In the stress calculation formula derivation step S4 of this embodiment, the constant calculation formula (s) is expressed by equations (2) and (3). a =94.218, ta=-0.807, s b (=0.3447, tb=0.0638) with board width ratio R tIR By substituting =0.3, the board width ratio R tIR Calculate constants a and b according to =0.3, and the board width ratio R tIR A stress calculation formula corresponding to =0.3 was derived. The calculated values ​​of constant a and constant b were as follows. a = 248.941, b = 0.31921

[0051] In the correction coefficient calculation step S5 of this embodiment, the frequency f is applied to the derived stress calculation formula (a=248.941, b=0.31921). IR By substituting =3Hz, the stress σ calIR The frequency f is calculated and used in the derived stress calculation formula. a By substituting =20Hz, the stress σ cala The calculated stress σ was obtained. calIR and stress σ cala The values ​​were as follows: σ calIR =353.5MPa, σ cala = 647.7 MPa And the above stress σ calIR and stress σ cala The correction factor c was calculated from the following. The calculated value of the correction factor c was as follows: c = 1.832

[0052] In the appropriate stress calculation step S6 of this embodiment, the stress σ measured in the stress measurement step S3 is used. IR By multiplying =360MPa by a correction factor c=1.832, the appropriate stress of =659.5MPa, corresponding to the actual stress within the specified region AS, was calculated. Plate width ratio R tIRThe maximum stress within a predetermined region AS, calculated by performing static finite element method analysis (static FEM analysis) using a numerical analysis model of joint 10 with a stress of 0.3, is the actual stress σ a Therefore, σ a Since it was =677.4MPa, the appropriate stress =659.5MPa calculated in step S6 of the appropriate stress calculation in this embodiment is the actual stress σ a The error is 2.64% compared to 677.4 MPa, and the actual stress σ a It can be said that it was possible to accurately calculate the appropriate stress corresponding to the conditions. [Explanation of Symbols]

[0053] 10... Fittings 11, 12...Plate material AS...Specified area S1...Steps to construct the stress calculation formula S2... Step to construct a constant calculation formula S3... Stress measurement step S4...Step to derive stress calculation formula S5... Correction coefficient calculation step S6... Step for calculating appropriate stress

Claims

1. A method for measuring the stress in a predetermined area on the surface of a joint formed by overlapping and joining two plate materials in the thickness direction, when a repeated shear load is applied to the joint, using a thermoelastic stress measurement method, The frequency f of the repeated load and the plate width ratio R, which is the ratio of the minimum width of the plate material in the predetermined region to the maximum width of the plate material. ｔ By performing coupled finite element analysis of stress fields and temperature fields using the repeated load on each of the multiple numerical analysis models of the joint, which include those with different properties, the following equation (1) is obtained: stress σ from frequency f within the predetermined region ｃａｌ The stress calculation formula for calculating the plate width ratio R is defined as follows: ｔ Each step involves constructing a stress calculation formula in advance, The constants a and b in the stress calculation formula are set to the plate width ratio R ｔ Each item is organized, and the plate width ratio R ｔ A constant calculation formula construction step involves constructing a constant calculation formula in advance for calculating the constant a and the constant b from the above, The joint to be measured has a plate width ratio of R ｔＩＲ The frequency f of the joint being measured ＩＲ The repeated load is applied, and the stress σ in the predetermined region of the joint to be measured is measured using the thermoelastic stress measurement method. ＩＲ A stress measurement step to measure, By substituting the plate width ratio R into the constant calculation formula, ｔＩＲ the constants a and b corresponding to the plate width ratio R are calculated, and by substituting the constants a and b calculated into the stress calculation formula, ｔＩＲ a stress calculation formula derivation step of deriving the stress calculation formula corresponding to the plate width ratio R is performed, ｔＩＲ and the stress calculation formula corresponding to the plate width ratio R is derived. The stress calculation formula derived above is used with the frequency f ＩＲ By substituting this, the stress σ ｃａｌＩＲ The stress calculation formula derived is used to calculate a predetermined frequency f of 20 Hz or higher. ａ By substituting this, the stress σ ｃａｌａ The stress σ is calculated and ｃａｌＩＲ The stress σ against ｃａｌａ A correction coefficient calculation step that calculates a correction coefficient c which is the ratio, The aforementioned stress illustration ＩＲ A step to calculate appropriate stress by multiplying by the correction coefficient c, thereby calculating an appropriate stress corresponding to the actual stress within the predetermined region, A stress measurement method having the following characteristics. s ｃａｌ =a・f ｂ ・・・(1) In the above formula (1), a and b are the plate width ratio R. ｔ It is a constant that is determined for each instance.

2. The constant calculation formula is expressed by the following equations (2) and (3): The stress measurement method according to claim 1. a=s ａ ・R ｔ ｔａ ・・・(2) b=s ｂ ・R ｔ ｔｂ ・・・・(3) In addition, in the above equation (2), s ａ and ta are constants. In equation (3) above, s ｂ And tb are constants.

3. The aforementioned joint is a welded joint. The stress measurement method according to claim 1 or 2.

4. A program for causing a computer to perform the steps of constructing a stress calculation formula, constructing a constant calculation formula, deriving a stress calculation formula, calculating a correction coefficient, and calculating an appropriate stress, which are part of the stress measurement method according to claim 1 or 2.

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