Stress distribution measurement method and program

Abstract

To provide a method for efficiently and accurately measuring the stress distribution of a coupling.SOLUTION: A method for measuring stress distribution when a repeated load in a shearing direction is applied to a coupling 10 includes: a step S1 for performing coupled finite element method analysis of a plurality of numerical analysis models of couplings, some of which have different frequencies Hz of the repeated load and different board thickness t of a plate to establish an attenuation coefficient calculation formula in advance for calculating an attenuation coefficient Dhzi by entering the frequency Hz and the board thickness t; a step S2 for applying a repeated load of the frequency Hz' on the coupling to be measured with the board thickness t' and measuring the stress σi through the thermoelastic stress measurement method; and a step S3 for calculating an attenuation coefficient Dhzi based on the frequency Hz' and the board thickness t' by entering the frequency Hz' and the board thickness t' in the attenuation coefficient calculation formula, and multiplying the stress σi by an inverse of the attenuation coefficient Dhzi to calculate the proper stress σi' relative to the coupling to be measured.SELECTED DRAWING: Figure 6

Description

[Technical field]

[0001] The present invention relates to a method and a program for measuring, by using a thermoelastic stress measurement method, the stress distribution on the surface of a predetermined region of a joint (such as a welded joint) formed by overlapping and joining two plate materials in the plate thickness direction when a repeated load in the shear direction is applied to the joint. In particular, the present invention relates to a method and a program for efficiently and accurately measuring the stress distribution on the surface of a predetermined region of a joint by using a thermoelastic stress measurement method. [Background technology]

[0002] Joints (e.g., arc welded joints, spot welded joints, etc.) formed by overlapping and joining two sheets of plate material in the thickness direction are widely used in automobiles, social infrastructure facilities, buildings, etc. In order to maintain and manage the joints, it is important to evaluate their fatigue strength, etc., and for that purpose, it is important to evaluate the surface stress distribution that will be the starting point of fatigue fracture when repeated loads are applied to the joints.

[0003] Finite element method (hereinafter referred to as "FEM" (Finite Element Method)) analysis is sometimes used as a method for evaluating the stress distribution that occurs when a load is repeatedly applied to a test object such as a joint. However, since the numerical analysis model of FEM analysis is created by digitizing geometric information on a computer, it is difficult to accurately model complex shapes such as the welded part of a welded joint, for example, when the joint is a welded joint. Also, since the numerical analysis model of FEM analysis is divided into elements (meshes) such as hexahedrons, it may not be possible to reflect the subtle uneven shape of the welded part. Therefore, it may be difficult to accurately evaluate the stress distribution in the welded portion of a welded joint using only FEM analysis.

[0004] In view of this, a thermoelastic stress measurement method using an infrared imaging device (thermography) has been proposed as a method for non-contact measurement of the stress distribution occurring on the surface of an object to be measured (see, for example, Non-Patent Document 1). The thermoelastic stress measurement method utilizes the thermoelastic effect that occurs when the object to be measured undergoes adiabatic elastic deformation (heat is generated when compressive stress occurs, and heat is absorbed when tensile stress occurs), and measures the time change in the temperature distribution of the object to be measured (change in temperature distribution within a specified time) by continuously capturing images of the object to which a repeated load is applied using an infrared imaging device, and converts this measured time change in the temperature distribution into the time change in the stress distribution of the object to be measured (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 can be assumed), it is possible to measure the stress distribution after a specified time has passed by adding the time change in the stress distribution to this initial value.

[0005] When measuring the time change in the temperature distribution of the object using this thermoelastic stress measurement method, the heat (infrared rays) around the object may be reflected by the surface of the object and received by the infrared imaging device. In other words, the time change in the temperature distribution of the object measured using the infrared imaging device may include a change in the temperature distribution caused by factors other than the change in the temperature distribution caused by the thermoelastic effect (the change in the intensity of the infrared rays emitted from the object). Since the change in the temperature distribution caused by the thermoelastic effect is extremely small, if the reflectance of the infrared rays on the surface of the object is large, the change in the temperature distribution caused by the thermoelastic effect will be buried in the change in the reflection intensity of the infrared rays on the surface of the object, and there is a risk that the time change in the stress distribution of the object cannot be calculated accurately.

[0006] For this reason, in the technology described in Non-Patent Document 1, a signal waveform corresponding to the change in temperature distribution caused by the thermoelastic effect to be measured is locked in from the image signal output from the infrared imaging device. In other words, only a predetermined frequency component is 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 measured object and having the same frequency as the applied cyclic load is used. The image signal is synchronously detected by 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 signals in a narrow frequency band including the same frequency as the reference signal) are extracted, thereby improving the S / N ratio of the change in temperature distribution caused by the thermoelastic effect to be measured. Then, the time change in the temperature distribution of the measured object (the time change in the temperature of each pixel constituting the image captured by the infrared imaging device) is calculated according to the magnitude of the extracted image signal component and the correspondence relationship between the magnitude of the image signal component and the temperature stored in advance. Next, the time change in the stress distribution of the measured object is calculated based on the time change in the temperature of the measured object and a predetermined relational expression between the time change in temperature and the time change in stress.

[0007] In this way, by using the lock-in process, it is believed that in principle it is possible to accurately calculate the change in the stress distribution of the object to be measured over time, and therefore the stress distribution of the object to be measured. Furthermore, since the stress distribution of the object to be measured is calculated based on an image of the object to be measured that is actually captured by an infrared imaging device, it is also applicable to complex shapes such as welded parts.

[0008] However, when a repeated load in the shear direction is applied to a joint formed by overlapping and joining two plates in the plate thickness direction, bending stress acts near the joint (for example, the weld in the case of a welded joint), causing opposing stresses on both sides of the plate. 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 generated on the other side, and the two sides are affected by thermal diffusion, reducing the temperature change. Therefore, if the frequency of the repeated load is low, around 10 Hz, the measured stress distribution will be smaller than the stress distribution that actually occurs in the joint.

[0009] Although Patent Documents 1 to 4 propose methods for improving the measurement accuracy of the thermoelastic stress measurement method, they are unable to solve the above problems.

[0010] Patent Document 5 describes a method for calculating the stress (external stress) distribution in a joint (welded part) when a repeated load in the shear direction is applied to a joint (spot welded joint) formed by overlapping plate materials, by performing a coupled finite element analysis (coupled FEM analysis) of the stress field and temperature field using a maximum load (assumed maximum load) and a minimum load (assumed minimum load) of the repeated load, simulating a thermoelastic stress measurement method. Specifically, in the coupled FEM analysis described in Patent Document 5, after executing a stress analysis step, a heat flux calculation step and a heat transfer analysis step are repeatedly executed for a predetermined time (the same time as the predetermined time for actually continuously imaging a joint (spot-welded joint) using an infrared imaging device), and then a conversion step is executed. In the stress analysis step, a stress analysis is performed using the maximum load (assumed maximum load) and minimum load (assumed minimum load) of the repeated load, and the stress distribution of the numerical analysis model is calculated. In the heat flux calculation step, the heat flux is calculated using the stress distribution of the numerical analysis model calculated in the stress analysis step, the material properties of the joint (spot welded joint) (e.g., the thermoelastic coefficient, 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 a temperature distribution in the numerical analysis model is calculated. In the conversion step, the temperature (outer surface temperature) distribution of the joint (weld) is calculated based on the temperature distribution of the numerical analysis model after a predetermined time has elapsed, and this temperature distribution is converted into a stress (outer surface stress) distribution of the joint (weld). According to the coupled FEM analysis described in Patent Document 5, it is possible to calculate a stress (external stress) equivalent to the stress (external stress) of a joint (welded portion) measured using a thermoelastic stress measurement method. [Prior art documents] [Non-patent literature]

[0011] [Non-Patent Document 1] Tatsuya Yaoita and two others, "Stress measurement using infrared camera and prediction measurement of fatigue limit point", Society of Automotive Engineers of Japan Autumn Academic Conference, No.98-03, (2003) [Patent documents]

[0012] [Patent Document 1] JP 2018-179730 A [Patent Document 2] JP 2015-001392 A [Patent Document 3] JP 2016-024057 A [Patent Document 4] JP 2018-128431 A [Patent Document 5] Patent Publication No. 2022-032646 Summary of the Invention [Problem to be solved by the invention]

[0013] The present invention has been made to solve the problems of the conventional technology as described above, and has an object to provide a method and program for efficiently and accurately measuring, using a thermoelastic stress measurement method, the stress distribution on the surface of a specified region (e.g., near the joint) of a joint (such as a welded joint) formed by overlapping and joining two plate materials in the thickness direction when repeated loads in the shear direction are applied to the joint. [Means for solving the problem]

[0014] In order to solve the above problems, the present inventors have conducted extensive research with a focus on combining a thermoelastic stress measurement method with the coupled FEM analysis described in Patent Document 5. The details of the research conducted by the present inventors are described below.

[0015] By performing a coupled FEM analysis on the numerical analysis model of the joint, the stress σhz of each part i (e.g., each element constituting the numerical analysis model) in a specified region of the joint can be calculated. iIn this case, by performing a coupled FEM analysis while changing the frequency Hz of the repeated load in the shear direction applied to the joint, the stress σhz corresponding to each frequency Hz is calculated. i It is possible to calculate the stress σhz by performing this coupled FEM analysis. i is the stress σ of each part i measured using the thermoelastic stress measurement method i The value is equivalent to On the other hand, by performing a static finite element analysis (static FEM analysis) using the maximum load of the repeated shear load applied to the joint, the actual (ideal) stress σs of each part i within a specified area of ​​the joint can be calculated. i In this specification, the actual stress means a stress equivalent to an actual stress that can be measured using a strain gauge or the like. Alternatively, the actual stress σs i can also be calculated by performing a coupled FEM analysis with the frequency set to a high frequency of about 800 Hz. This is because the stress value calculated by performing a coupled FEM analysis with the frequency set to a high frequency of about 800 Hz is equivalent to the stress value calculated by performing a static FEM analysis. Therefore, the stress σhz corresponding to each frequency Hz i The actual stress σs i By dividing by , the actual stress σs i Stress σ i The attenuation coefficient Dhz of each part i represents the degree of attenuation of i Then, the stress σ i attenuation coefficient Dhz i By multiplying the inverse of i It is considered possible to calculate the appropriate stress for each part i according to the above.

[0016] FIG. 1 shows the stress σ in the region AS adjacent to the weld 10A when a cyclic load P of 10 Hz is applied to a lap fillet arc-welded joint corresponding to the numerical analysis model shown in FIG. 9 described later. i 4 shows an example of the distribution of the stress distribution measured by a thermoelastic stress measurement method. FIG. 2 shows the stress σhz in the region AS adjacent to the weld 10A under the condition of applying a repeated load P with a frequency of 10 Hz for the numerical analysis model shown in FIG. 9 described later. i An example of the distribution of calculated results by performing coupled FEM analysis is shown below. FIG. 3 shows the stress σs in the region AS adjacent to the weld 10A under the condition of applying a repeated load P with a frequency of 800 Hz for the numerical analysis model shown in FIG. 9 described later. i The following shows an example of the distribution of stress σs calculated by performing a coupled FEM analysis. i It was confirmed that the maximum stress in the distribution was equivalent to the maximum stress in the adjacent region AS of the weld 10A measured using a strain gauge. FIG. 4 shows the damping coefficient Dhz of the region AS adjacent to the weld 10A calculated from the results shown in FIG. 2 and FIG. i Shows. Figure 5 shows the stress σ measured using the thermoelastic stress measurement method shown in Figure 1. i The distribution of damping coefficient Dhz i 4 shows the stress distribution in the region AS adjacent to the weld 10A, calculated by multiplying the inverse of the distribution of

[0017] As can be seen by comparing Figures 1 and 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 condition of applying a repeated load P of 10 Hz, the same frequency as in the thermoelastic stress measurement method, are equivalent in value to each other. Furthermore, as can be seen by comparing Figures 2 and 3, the stress distribution calculated by performing coupled FEM analysis under the condition of applying a cyclic load P with a frequency of 10 Hz (Figure 2) is smaller than the stress distribution calculated by performing coupled FEM analysis under the condition of applying a cyclic load P with a frequency of 800 Hz (Figure 3). Furthermore, as can be seen by comparing Figs. 3 and 5, the stress σ measured using the thermoelastic stress measurement method i The distribution of damping coefficient Dhz iThe stress distribution calculated by multiplying the inverse of the distribution (Fig. 5) is equivalent to the stress distribution calculated by performing a coupled FEM analysis under the condition of applying a cyclic load P with a frequency of 800 Hz (Fig. 3). Therefore, the stress σ measured using the thermoelastic stress measurement method i The distribution of damping coefficient Dhz i By multiplying the inverse of the distribution of i It can be said that it is possible to accurately calculate an appropriate stress distribution according to the distribution of

[0018] However, in the above method, the damping coefficient Dhz of each portion i in a predetermined region (for example, a region AS in the vicinity of the welded portion 10A) for which an appropriate stress distribution is to be calculated is i must be calculated for each target frequency (Hz). For example, in the above example, the stress distribution was measured using the thermoelastic stress measurement method under the condition of applying a cyclic load with a frequency of 10 Hz, so the coupled FEM analysis was also performed under the condition of applying a cyclic load with the same frequency of 10 Hz, and the damping coefficient Dhz i However, if the stress distribution is measured using the thermoelastic stress measurement method under the condition of applying a cyclic load with a frequency of 20 Hz, the coupled FEM analysis should also be performed under the condition of applying a cyclic load with the same frequency of 20 Hz, and the damping coefficient Dhz i It becomes necessary to calculate In addition, according to the findings of the present inventors, the attenuation coefficient Dhz i Dhz also changes depending on the plate thickness t of the plate material that constitutes the joint. i must be calculated for each plate thickness t. For example, if the thermoelastic stress measurement method is used to measure the stress distribution of a joint with a plate thickness of 1.0 mm, the coupled FEM analysis must also be performed on a numerical analysis model with the same plate thickness of 1.0 mm, and the damping coefficient Dhz i However, if the stress distribution of a joint with a plate thickness of 2.0 mm is measured using the thermoelastic stress measurement method, the coupled FEM analysis is also performed on the same numerical analysis model with a plate thickness of 2.0 mm, and the damping coefficient Dhz i It becomes necessary to calculate This increases the calculation time cost and requires a huge amount of data storage capacity, which is inefficient.

[0019] Therefore, the inventors further conducted extensive research and found that by performing coupled FEM analysis on a plurality of numerical analysis models of joints, including those in which the frequency Hz of the cyclic load and the thickness t of the plate material are different from each other, the damping coefficient Dhz of each portion i can be calculated by inputting the frequency Hz of the cyclic load and the thickness t of the plate material. i It was found that it is possible to construct a damping coefficient calculation formula for calculating the damping coefficient. If the above damping coefficient calculation formula is constructed in advance, when applying a repeated load of frequency Hz' to a joint to be measured, which has a plate thickness of t', the damping coefficient Dhz corresponding to the frequency Hz' and plate thickness t' can be calculated simply by inputting the frequency Hz' and plate thickness t' into the damping coefficient calculation formula. i Therefore, the stress σ of each part i in a given region measured using the thermoelastic stress measurement method can be calculated efficiently. i , the calculated damping coefficient Dhz i By multiplying the reciprocal of σ, the appropriate stress σ for each part i of the joint being measured is obtained. i ' can be calculated efficiently and accurately.

[0020] The present invention has been completed based on the above findings of the present inventors. That is, in order to solve the above-mentioned problems, the present invention provides a method for measuring a stress distribution on the surface of a predetermined region of a joint formed by overlapping and joining two plate materials in the plate thickness direction, when a repeated load in a shear direction is applied to the joint, by using a thermoelastic stress measurement method, and by executing a coupled finite element analysis of a stress field and a temperature field using the repeated load for each of a plurality of numerical analysis models of the joint, including those having different frequencies Hz of the repeated load and plate thicknesses t of the plate materials, the method inputting the frequency Hz of the repeated load and the plate thickness t of the plate material, and measuring the stress σ of each portion i in the predetermined region measured using a thermoelastic stress measurement method for the actual stress. i The damping coefficient Dhz of each part i represents the degree of damping ia damping coefficient calculation formula construction step of constructing in advance a damping coefficient calculation formula for calculating a damping coefficient of the joint to be measured, the joint being a measurement target and having a plate thickness of the plate material of t', the repeated load of frequency Hz' is applied to the measurement target joint, and a stress σ of each portion i in the predetermined region of the measurement target joint is calculated by using a thermoelastic stress measurement method. i A stress distribution measurement step for measuring the frequency Hz' and the plate thickness t', and a damping coefficient Dhz corresponding to the frequency Hz' and the plate thickness t' by inputting the frequency Hz' and the plate thickness t' into the damping coefficient calculation formula. i Calculate the stress σ i to the damping coefficient Dhz i By multiplying the reciprocal of the stress σ of each part i corresponding to the actual stress of the joint to be measured, i and a proper stress distribution calculation step of calculating an appropriate stress distribution '.

[0021] In the present invention, the "shear direction" refers to a direction perpendicular to the overlapping direction (thickness direction) of two plate materials. The "repeated load" in the present invention may be a one-way load, which is either a tensile load or a compressive load, or may be an alternating load in which a tensile load and a compressive load are repeated. In the case of an alternating load, the average load may be either a tensile load or a compressive load. In the present invention, the "plate thickness" means the dimension of each plate material in the overlapping direction. In the present invention, the term "stress" is a concept that includes not only the stress itself on the surface of the joint, but also the change in stress over time. In the appropriate stress distribution calculation step of the present invention, the frequency Hz' of the repeated load and the plate thickness t' to be inputted into the damping coefficient calculation formula may be set values ​​or may be actually measured values.

[0022] According to the present invention, in the step of constructing a damping coefficient calculation formula, the frequency Hz of the repeated load and the thickness t of the plate material are input, and the stress σ of each part i in a predetermined region measured using a thermoelastic stress measurement method for the actual stress is calculated. i The attenuation coefficient Dhz of each part i represents the degree of attenuation of iA damping coefficient calculation formula for calculating the damping coefficient is constructed in advance. Next, in the stress distribution measurement step, a repeated load of frequency Hz' is applied to the joint to be measured, whose plate thickness is t', and the stress σ i Measure. Finally, in the appropriate stress distribution calculation step, the damping coefficient Dhz corresponding to the frequency Hz' and plate thickness t' is calculated by inputting the frequency Hz' and plate thickness t' into the damping coefficient calculation formula. i Calculate the stress σ i attenuation coefficient Dhz i By multiplying the reciprocal of σ, the appropriate stress σ for each part i according to the actual stress of the joint being measured is obtained. i ' is calculated. As described above, according to the present invention, if the damping coefficient calculation formula is previously constructed in the damping coefficient calculation formula construction step, the stress σ of each part i can be measured by using a thermoelastic stress measurement method in the stress distribution measurement step. i When measuring the frequency of repeated load Hz' and the thickness t' of the plate material, a coupled FEM analysis is performed to obtain the damping coefficient Dhz i There is no need to calculate the damping coefficient Dhz (just enter the frequency Hz' and plate thickness t' into the damping coefficient calculation formula) i Therefore, in the appropriate stress distribution calculation step, the stress σ measured using the thermoelastic stress measurement method is used. i , the calculated damping coefficient Dhz i By multiplying the reciprocal of σ, the appropriate stress σ for each part i of the joint being measured is obtained. i ' can be calculated efficiently and accurately.

[0023] In the present invention, if the damping coefficient calculation formula construction step is executed once to construct a damping coefficient calculation formula in advance, the same constructed damping coefficient calculation formula can be repeatedly used when executing the stress distribution measurement step and the appropriate stress distribution calculation step for a plurality of joints to be measured (for example, a plurality of joints to be measured having different frequencies Hz' of repeated loads or different plate thicknesses t' of plate materials). In other words, when measuring the stress distribution in a predetermined region of a plurality of joints to be measured according to the present invention, it is not necessary to execute the damping coefficient calculation formula construction step for the number of joints to be measured, and it is sufficient to execute it only once in advance.

[0024] Here, according to the findings of the present inventors, the attenuation coefficient Dhz of each part i i is a logarithmic function of the frequency of repeated load (Hz), regardless of the plate thickness (t) of the plate material. i It can be approximated as =a1·LN(Hz)+a2. Moreover, according to the findings of the present inventors, the variables a1 and a2 included in the above logarithmic function can be approximated by a linear function of the plate thickness t.

[0025] According to the findings of the inventors of the present invention, preferably, in the step of constructing a damping coefficient calculation formula, for each portion i in the predetermined region, the damping coefficient Dhz expressed by the following formula (1) is calculated for each frequency Hz of the repeated load and for each thickness t of the plate material. i A damping coefficient calculation procedure for calculating the damping coefficient Dhz of each part i calculated for each frequency Hz and plate thickness t i Based on the above, the damping coefficient Dhz i a first approximation formula derivation step of deriving a first approximation formula represented by the following formula (2) for each of the plate thicknesses t, which approximates a1, a2, and a3 included in the first approximation formula derived for each of the plate thicknesses t for each of the portions i, by a linear function of the plate thickness t. The second approximation formula derivation step of deriving second approximation formulas represented by the following formulas (3) and (4). The appropriate stress distribution calculation step includes a variable calculation step of calculating the variables a1 and a2 for each portion i of the joint to be measured by inputting the plate thickness t' of the plate material constituting the joint to be measured into the second approximation formula, and a variable calculation step of calculating the variables a1 and a2 for each portion i of the joint to be measured by inputting the variables a1 and a2 calculated in the variable calculation step and the frequency Hz' of the repeated load applied to the joint to be measured into the first approximation formula to calculate the damping coefficient Dhz of each portion i of the joint to be measured. i and a stress distribution measurement step for each part i. i By multiplying the inverse of the damping coefficient Dhzi calculated in the damping coefficient calculation procedure, the appropriate stress σ i and an appropriate stress distribution calculation procedure for calculating .sigma.'. Dhz i = σhz i / σs i (1) Dhz i = a1 LN(Hz) + a2 (2) a1 = b1 t + c1 (3) a2 = b2 t + c2 (4) In the above formula (1), σhz i means the stress of each part i calculated by performing coupled finite element method analysis on the numerical analysis model of the joint. i means the actual stress of each part i calculated by performing finite element analysis on the numerical analysis model of the joint. In the above formula (2), LN (Hz) means the natural logarithm of frequency Hz. In the above formula (3), b1 and c1 mean constants. In the above formula (4), b2 and c2 mean constants.

[0026] In the above-mentioned preferred method of the present invention, "inputting the plate thickness t' of the plate material constituting the joint to be measured into the second approximation formula" means inputting the value of t' into t in formulas (3) and (4). Also, "inputting the frequency Hz' of the repeated load applied to the joint to be measured into the first approximation formula" means inputting the value of Hz' into Hz in formula (2). According to a preferred method of the present invention, the first approximation formula (formula (2)) and the second approximation formula (formula (3) and formula (4)) are derived in advance, so that the appropriate stress σ of each portion i of the joint to be measured can be calculated. i ' can be calculated efficiently and accurately.

[0027] The present invention is particularly suitable for use when the joint is a welded joint (arc welded joint, spot welded joint, etc.). However, the present invention is not limited to this, and can also be applied to, for example, a joint formed by joining two plate materials together with bolts.

[0028] The step of constructing a damping coefficient calculation formula and the step of calculating an appropriate stress distribution included in the stress distribution measuring method according to the present invention can be executed by, for example, a program installed in a computer. Therefore, the present invention is also provided as a program for causing a computer to execute the damping coefficient calculation formula construction step and the appropriate stress distribution calculation step of the stress distribution measuring method according to the present invention. Effect of the Invention

[0029] According to the present invention, it is possible to efficiently and accurately measure the stress distribution on the surface of a specified area of ​​a joint formed by overlapping and joining two plate materials in the thickness direction when a repeated load in the shear direction is applied to the joint, using a thermoelastic stress measurement method. [Brief description of the drawings]

[0030] [Figure 1]An example of the results of applying a cyclic load P of 10 Hz to a lap fillet arc-welded joint corresponding to the numerical analysis model shown in Figure 9, and measuring the distribution of stress σi in the region AS adjacent to the weld 10A using a thermoelastic stress measurement method is shown. [Diagram 2] This shows an example of the results of calculating the distribution of stress σhzi in the region AS near the weld 10A by performing a coupled FEM analysis on the numerical analysis model shown in Figure 9 under the condition of applying a cyclic load P with a frequency of 10 Hz. [Diagram 3] This shows an example of the results of calculating the distribution of stress σsi in the region AS adjacent to the weld 10A by performing a coupled FEM analysis on the numerical analysis model shown in Figure 9 under the condition of applying a cyclic load P with a frequency of 800 Hz. [Figure 4] The damping coefficient Dhzi of the region AS in the vicinity of the welded portion 10A, calculated from the results shown in FIGS. [Diagram 5] The stress distribution in the region AS near the weld 10A is shown, which is calculated by multiplying the distribution of the stress σi measured using the thermoelastic stress measurement method shown in FIG. 1 by the inverse of the distribution of the damping coefficient Dhzi. [Figure 6] FIG. 2 is a flow chart illustrating steps of a stress distribution measuring method according to an embodiment of the present invention. [Figure 7] 7 is a flow chart specifically showing a procedure included in the damping coefficient calculation formula construction step S1 shown in FIG. 6. [Figure 8] 7 is a flow chart specifically showing a procedure of an appropriate stress distribution calculation step S3 shown in FIG. 6. [Figure 9] An example of a numerical analysis model (finite element analysis model) of a lap fillet arc welded joint is shown. [Figure 10] In the first approximate equation derivation procedure S12 shown in FIG. 7, an example of the damping coefficient Dhzmax calculated for each frequency Hz (1 Hz to 50 Hz) and plate thickness t (1.0 mm to 2.0 mm) and an example of the first approximate equation derived for each plate thickness t are shown. [Figure 11]In the second approximate formula derivation procedure S15 shown in FIG. 7, examples of variables a1 and a2 included in the first approximate formula derived for each plate thickness t (1.0 mm to 2.0 mm) and an example of the second approximate formula are shown. [Figure 12] An example of the stress distribution in a predetermined region (region in the vicinity of the welded portion 10A) AS of the joint to be measured, obtained by executing the appropriate stress distribution calculation procedure S33 shown in FIG. 8, is shown. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0031] Hereinafter, with reference to the attached drawings as appropriate, a stress distribution measuring method according to one embodiment of the present invention will be described, taking as an example a case in which the joint for measuring the stress distribution is a lap fillet arc welded joint. FIG. 6 is a flow diagram that shows the steps of the stress distribution measuring method according to the present embodiment. FIG. 7 is a flow diagram that shows in detail the procedure of the damping coefficient calculation formula construction step S1 shown in FIG. 6. FIG. 8 is a flow diagram that shows in detail the procedure of the appropriate stress distribution calculation step S3 shown in FIG. 6. FIG. 9 shows an example of a numerical analysis model (finite element analysis model) of a lap fillet arc welded joint. FIG. 9(a) is a perspective view showing the outer shape of the numerical analysis model, and FIG. 9(b) is an element division diagram for a predetermined area AS of the numerical analysis model shown in FIG. 9(a). In FIG. 9, the X direction indicates the direction (shear direction) in which a repeated load P is applied to a lap fillet arc welded joint (hereinafter simply referred to as a "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 a direction perpendicular to the X direction and the Y direction, 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 in the above-mentioned Figures 1 to 5 and the later-described Figure 12 are the same as those in the case shown in Figure 9. The numerical analysis model shown in Figure 9 is a half symmetrical model in which a symmetry plane 10S is set in the center of the plate materials 11 and 12 constituting the joint 10 in the plate width direction (Z direction).

[0032] The stress distribution measuring method according to this embodiment is a method for measuring, by using a thermoelastic stress measurement method, the stress distribution in a predetermined region AS of joint 10 (in the case shown in FIG. 9, a region adjacent to welded portion 10A) when a repeated load P in the shear direction (X direction) is applied to joint 10 formed by overlapping and joining two plate materials 11, 12 in the plate thickness direction (Y direction) (by arc welding in the case shown in FIG. 9) using a fatigue testing machine or the like. As shown in Fig. 6, the stress distribution measuring method according to this embodiment includes a damping coefficient calculation formula constructing step S1, a stress distribution measuring step S2, and an appropriate stress distribution calculating step S3. The damping coefficient calculation formula constructing step S1 and the appropriate stress distribution calculating step S3 can be executed by a program installed in a computer, for example. Each of steps S1 to S3 will be described in order below.

[0033] <Step S1 of constructing damping coefficient calculation formula> In the damping coefficient calculation formula construction step S1, a coupled finite element analysis (coupled FEM analysis) of the stress field and the temperature field using the repeated load P simulating the thermoelastic stress measurement method is performed for each of a plurality of numerical analysis models of the joint 10, including the joint 10 shown in FIG. 9, including those having different frequencies Hz of the repeated load P and different plate thicknesses t of the plate materials 11 and 12. In the same numerical analysis model, the plate thickness t of the plate material 11 and the plate thickness t of the plate material 12 are set to the same value. It is efficient to reduce the number of numerical analysis models (the number of different combinations of the frequency Hz and the plate thickness t) used in the damping coefficient calculation formula construction step S1 as much as possible, as long as the damping coefficient calculation formula can be constructed with high accuracy (the first and second approximation formulas described later can be derived with high accuracy). The specific content of the coupled FEM analysis is the same as the method described in Patent Document 5, so a detailed description thereof will be omitted here. In the damping coefficient calculation formula construction step S1, the frequency Hz of the cyclic load P and the thickness t of the plate materials 11 and 12 are input based on the results of performing a coupled FEM analysis on each of the multiple numerical analysis models of the joint 10, which includes models having different frequencies Hz of the cyclic load P and different thicknesses t of the plate materials 11 and 12, and the stress σ of each portion i in the predetermined region AS measured using a thermoelastic stress measurement method for the actual stress is calculated. i The attenuation coefficient Dhz of each part i represents the degree of attenuation of i A damping coefficient calculation formula is constructed to calculate

[0034] Hereinafter, the damping coefficient calculation equation construction step S1 will be described in more detail with reference to FIG. 7, the damping coefficient calculation formula establishment step S1 of this embodiment includes a damping coefficient calculation step S11, a first approximation formula derivation step S12, and a second approximation formula derivation step S13. Each of steps S11 to S13 will be described in order below.

[0035] [Damping coefficient calculation procedure S11] In the damping coefficient calculation procedure S11, for each portion i in the predetermined region AS (for example, each element constituting the numerical analysis model) (for all portions i in the predetermined region AS), a damping coefficient Dhz expressed by the following formula (1) is calculated for each frequency Hz of the repeated load P and the plate thickness t of the plate materials 11 and 12 (in other words, for each numerical analysis model of a plurality of numerical analysis models including those having different frequencies Hz of the repeated load P and different plate thicknesses t of the plate materials 11 and 12). i Calculate. Dhz i = σhz i / σs i (1) In the above formula (1), σhz i means the stress at each part i calculated by performing a coupled FEM analysis on the numerical analysis model of the joint 10. imeans the actual stress of each part i calculated by performing an FEM analysis (for example, a static FEM analysis or a coupled FEM analysis with the frequency Hz set to a high frequency of about 800 Hz) on the numerical analysis model of the joint 10. In this embodiment, the stress of each part calculated by performing a coupled FEM analysis with the frequency Hz set to 800 Hz is referred to as the actual stress σs i However, the present invention is not limited to this, and the stress of each part calculated by performing a coupled FEM analysis with a frequency Hz set in the range of 200 Hz to 1000 Hz, preferably in the range of 700 Hz to 1000 Hz, is used as the actual stress σs i By setting the frequency Hz within this range, a value equivalent to the stress value calculated by performing a static FEM analysis can be obtained, and the calculation time cost does not increase. Note that the FEM analysis (coupled FEM analysis, static FEM analysis) can be performed using, for example, the general-purpose nonlinear finite element analysis program "Abaqus" made by SIMULIA, but the present invention is not limited to this.

[0036] [Step S12 for deriving the first approximation equation] In the first approximation derivation procedure S12, the damping coefficient Dhz of each part i calculated for each frequency Hz and plate thickness t is i Based on the damping factor Dhz i A first approximation formula represented by the following formula (2), which approximates with a logarithmic function of the frequency Hz, is derived for each plate thickness t. The first approximation formula can be derived using an approximation calculation such as the least squares method. Dhz i = a1 LN(Hz) + a2 (2) In the above formula (2), LN (Hz) means the natural logarithm of the frequency Hz. FIG. 10 shows the damping coefficient Dhz calculated for each frequency Hz (1 Hz to 50 Hz) and plate thickness t (1.0 mm to 2.0 mm) in the first approximation formula derivation procedure S12. i 10) and an example of a first approximation formula derived for each plate thickness t (dashed line in FIG. 10). As can be seen from Figure 10, the damping coefficient Dhzi can be accurately approximated as a logarithmic function of the frequency of the repeated load (Hz), regardless of the plate thickness (t).

[0037] [Step S13 for deriving the second approximation equation] In the second approximation formula derivation procedure S13, for each portion i, the variables a1 and a2 included in the first approximation formula derived for each plate thickness t are approximated by a linear function of the plate thickness t to derive the second approximation formula represented by the following formulas (3) and (4). Approximation calculation such as the least squares method can be used to derive the second approximation formula. a1 = b1 t + c1 (3) a2 = b2 t + c2 (4) In the above formula (3), b1 and c1 are constants. In the above formula (4), b2 and c2 are constants. Figure 11 shows examples of variables a1 and a2 (indicated by "△" and "□" in Figure 11) included in the first approximate formula derived for each plate thickness t (1.0 mm to 2.0 mm) in the second approximate formula derivation procedure S13, and an example of the second approximate formula (indicated by the dashed line in Figure 11). As can be seen from FIG. 11, both the variables a1 and a2 can be accurately approximated by a linear function of the plate thickness t.

[0038] In the damping coefficient calculation formula construction step S1 of this embodiment, the damping coefficient calculation formula expressed by formulas (1) to (4) is constructed by executing the damping coefficient calculation procedure S11 to the second approximation formula derivation procedure S13 described above.

[0039] <Stress distribution measurement step S2> In the stress distribution measurement step S2, a repeated load P of frequency Hz' is applied to the joint 10 to be measured, which is a joint to be measured, and the plate thickness of the plate materials 11 and 12 is t', and the stress σ of each part i (all parts i in the predetermined area AS) in the predetermined area AS of the joint to be measured is measured using a thermoelastic stress measurement method. iThe frequency Hz' can be a value different from the frequency Hz used to construct the damping coefficient calculation formula in the damping coefficient calculation formula construction step S1, but it may be the same value. Similarly, the plate thickness t' can be a value different from the plate thickness t used to construct the damping coefficient calculation formula in the damping coefficient calculation formula construction step S1, but it may be the same value. Specifically, in the stress distribution measurement step S2, an infrared imaging device is used to continuously image a predetermined area AS of the joint to be measured, to which a repeated load P in the shear direction with a frequency Hz' is applied for a predetermined time by a fatigue testing machine or the like, using a device that faces the surface of the joint to be measured. Then, 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 makes it possible to measure the stress distribution in the predetermined area AS of the joint to be measured. Note that the specific details of the thermoelastic stress measurement method are publicly known, so a detailed description will be omitted here.

[0040] <Appropriate stress distribution calculation step S3> In the appropriate stress distribution calculation step S3, the frequency Hz' of the repeated load P applied to the joint to be measured and the plate thickness t' of the plate materials 11 and 12 constituting the joint to be measured are input into the damping coefficient calculation formula (formulas (1) to (4)) derived in the damping coefficient calculation formula construction step S1, thereby obtaining a damping coefficient Dhz according to the frequency Hz' and the plate thickness t'. i Then, the stress σ i attenuation coefficient Dhz i By multiplying the reciprocal of σ, the appropriate stress σ for each part i according to the actual stress of the joint being measured is obtained. i ' is calculated.

[0041] Hereinafter, the appropriate stress distribution calculation step S3 will be described in more detail with reference to FIG. 8, the appropriate stress distribution calculation step S3 of this embodiment includes a variable calculation step S31, a damping coefficient calculation step S32, and an appropriate stress distribution calculation step S33. Each of steps S31 to S33 will be described in order below.

[0042] [Variable calculation step S31] In the variable calculation step S31, the plate thickness t' of the plate materials 11, 12 constituting the joint to be measured is input to the second approximation formula (formula (3) and formula (4)). That is, the value of t' is input to t in formula (3) and formula (4). In this way, the variables a1 and a2 are calculated for each portion i of the joint to be measured.

[0043] [Damping coefficient calculation procedure S32] In the damping coefficient calculation procedure S32, the variables a1 and a2 calculated in the variable calculation procedure S31 and the frequency Hz' of the repeated load P applied to the joint to be measured are input to the first approximation formula (formula (2)). That is, the values ​​of the variables a1 and a2 calculated in the variable calculation procedure S31 are input to a1 and a2 in formula (2), and the value of Hz' is input to Hz in formula (2). As a result, the damping coefficient Dhz of each portion i of the joint to be measured is calculated. i Calculate.

[0044] In the variable calculation procedure S31 and the damping coefficient calculation procedure S32 described above, the only parameters that need to be input into the damping coefficient calculation formula consisting of equations (1) to (4) are the frequency Hz' of the repeated load P applied to the joint to be measured and the plate thickness t' of the plate materials 11 and 12 that make up the joint to be measured. By simply inputting these parameters into the damping coefficient calculation formula, the damping coefficient Dhz corresponding to the frequency Hz' and the plate thickness t' can be calculated. i can be efficiently calculated.

[0045] [Proper stress distribution calculation procedure S33] In the appropriate stress distribution calculation step S33, the stress σ of each part i measured in the stress distribution measurement step S2 is calculated. i , the damping coefficient Dhz calculated in the damping coefficient calculation step S32 i This multiplies the inverse of the stress σ for each part i of the joint to be measured. i ' is calculated. FIG. 12 shows an example of the stress distribution in a predetermined region (region in the vicinity of the welded portion 10A) AS of the joint to be measured, obtained by executing the appropriate stress distribution calculation procedure S33.

[0046] In the appropriate stress distribution calculation step S3 of this embodiment, the above-described variable calculation procedure S31 to appropriate stress distribution calculation procedure S33 are executed to calculate the appropriate stress σ of each portion i corresponding to the actual stress of the joint to be measured. i ' is calculated. As described above, in the variable calculation procedure S31 and the damping coefficient calculation procedure S32, the damping coefficient Dhz corresponding to the frequency Hz' and the plate thickness t' can be calculated simply by inputting the frequency Hz' and the plate thickness t' into the damping coefficient calculation formula. i In the proper stress distribution calculation step S33, the stress σ i attenuation coefficient Dhz i By multiplying the reciprocal of σ, the appropriate stress σ for each part i of the joint being measured is obtained. i ' can be calculated with high accuracy. Therefore, in the appropriate stress distribution calculation step S3 of this embodiment, the stress distribution in the predetermined area AS of the joint to be measured can be measured efficiently and accurately.

[0047] Hereinafter, an example in which the stress distribution measuring method according to this embodiment is carried out will be described.

[0048] In this example, a lap fillet arc-welded joint formed by overlapping and arc-welding plate materials 11 and 12, which are 590 MPa class steel plates having the same plate thickness t and plate width w of 25 mm, in the plate thickness direction, was used as the joint 10 for measuring the stress distribution. A coupled FEM analysis was then performed using the numerical analysis model of the lap fillet arc-welded joint shown in Figure 9. First, in the step S1 of constructing the damping coefficient calculation formula of this embodiment, the plate thickness t of the plate materials 11 and 12 was set to four types, 1.0 mm, 1.4 mm, 1.6 mm, and 2.0 mm. In addition, the Young's modulus of the plate materials 11 and 12 was set to 205.9 GPa, the Poisson's ratio was set to 0.3, the initial temperature was set to 20° C., and the thermoelastic coefficient was set to 3.14e -6 (e is the base of the natural logarithm), and the density is 7.8e -6 kg / mm 3(e is the base of the natural logarithm), the specific heat is 460 kJ / kg, the load difference (maximum load - minimum load) is 2.6 kN, and the stress ratio is 0.05. A repeated load P in the shear direction is applied to the joint 10, and the frequency Hz of the repeated load P is changed in the range of 1 to 50 Hz (however, the actual stress σs i When calculating, the frequency (Hz) was set to 800 Hz), and a first approximation formula (formula (2)) was derived for each plate thickness (t). The first approximation formula shown in FIG. 10 is the first approximation formula derived in this embodiment.

[0049] In the damping coefficient calculation formula construction step S1 of this embodiment, the second approximation formula (formula (3) and formula (4)) shown in Fig. 11 was derived. The values ​​of b1, b2, c1, and c2 shown in formula (3) and formula (4) differ for each part i, but for example, for the part where the maximum stress occurs, b1 = 0.058, b2 = 0.104, c1 = 0.054, and c2 = 0.163.

[0050] In the stress distribution measurement step S2 of this embodiment, a repeated load P in the shear direction with a load difference (maximum load - minimum load) of 2.6 kN and a stress ratio of 0.05 is applied to the joint 10 having the plate thickness t' of the plate materials 11 and 12 of 1.2 mm, and the stress σ of each portion i in the predetermined region AS of the joint 10 is measured using a thermoelastic stress measurement method under the condition that the frequency Hz' of the repeated load P is set to 7 Hz. i (External stress) was measured. Stress σ of each part i i The maximum stress was 150 MPa.

[0051] In the present embodiment, in the step S3 of calculating the appropriate stress distribution, a1 and a2 were calculated by inputting the plate thickness t'=1.2 mm into the second approximation formula (formulas (3) and (4)). The values ​​of a1 and a2 differ for each part i, but for example, for the part where the maximum stress occurs, a1=0.124 and a2=0.288. Furthermore, the calculated a1 and a2 (for example, for the part where the maximum stress occurs, a1=0.124 and a2=0.288) and the frequency Hz'=7 Hz were input into the first approximation formula (formula (2)), and the damping coefficient Dhz of each part i was calculated. i was calculated. Finally, in the appropriate stress distribution calculation step S3 of this embodiment, the stress σ of each part i measured in the stress distribution measurement step S2 is calculated. i , the calculated damping coefficient Dhz i By multiplying the inverse of i The stress distribution shown in FIG. 12 is calculated based on the stress σ i ' is the distribution.

[0052] As shown in FIG. 12, the stress σ i The maximum stress in the specified area AS of the joint 10 measured using a strain gauge was 271 MPa. As described above, the maximum stress measured in the stress distribution measurement step S2 is 150 MPa, which is smaller than the maximum stress of 271 MPa measured using a strain gauge. i It was confirmed that the maximum stress of 267 MPa in the test corresponds well with the maximum stress of 271 MPa measured using a strain gauge. [Explanation of symbols]

[0053] 10. Fittings 11, 12...Plate material AS...Specified area S1: Steps for constructing the damping coefficient calculation formula S2: Stress distribution measurement step S3: Calculation step of appropriate stress distribution

Claims

1. A method for measuring a stress distribution on a surface of a predetermined region of a joint formed by overlapping and joining two plate materials in the plate thickness direction and applying a repeated load in a shear direction to the joint, using a thermoelastic stress measurement method, comprising: A coupled finite element analysis of a stress field and a temperature field using the repeated load is performed for each of a plurality of numerical analysis models of the joint, including those having different frequencies Hz of the repeated load and different plate thicknesses t of the plate material. By inputting the frequency Hz of the repeated load and the plate thickness t of the plate material, the stress σ of each portion i in the specified region measured using a thermoelastic stress measurement method for the actual stress is calculated. ｉ The damping coefficient Dhz of each part i represents the degree of damping ｉ A damping coefficient calculation formula construction step of constructing a damping coefficient calculation formula in advance for calculating The repeated load having a frequency Hz' is applied to the joint to be measured, the joint being the object of measurement and having a plate thickness of t', and the stress σ of each portion i in the predetermined region of the joint to be measured is measured by using a thermoelastic stress measurement method. ｉ A stress distribution measurement step of measuring By inputting the frequency Hz' and the plate thickness t' into the damping coefficient calculation formula, the damping coefficient Dhz according to the frequency Hz' and the plate thickness t' is calculated. ｉ Calculate the stress σ ｉ to the damping coefficient Dhz ｉ By multiplying the reciprocal of the stress σ of each portion i of the joint to be measured according to the actual stress, ｉ An appropriate stress distribution calculation step for calculating '; The stress distribution measuring method includes the steps of:

2. The damping coefficient calculation formula construction step includes: For each portion i in the predetermined region, the damping coefficient Dhz is expressed by the following formula (1) for each frequency Hz of the repeated load and the plate thickness t of the plate material. ｉ A damping coefficient calculation procedure for calculating The damping coefficient Dhz of each portion i calculated for each frequency Hz and plate thickness t ｉ Based on this, the damping coefficient Dhz ｉ A first approximation formula deriving procedure for deriving a first approximation formula represented by the following formula (2), which approximates the frequency Hz with a logarithmic function, for each plate thickness t; A second approximation formula derivation step of deriving a second approximation formula represented by the following formulas (3) and (4) in which the variables a1 and a2 included in the first approximation formula derived for each of the plate thicknesses t are approximated by a linear function of the plate thickness t for each of the portions i; having The appropriate stress distribution calculation step includes: a variable calculation step of calculating the variables a1 and a2 for each portion i of the joint to be measured by inputting the plate thickness t' of the plate material constituting the joint to be measured into the second approximation formula; The variables a1 and a2 calculated in the variable calculation procedure and the frequency Hz' of the repeated load applied to the joint to be measured are input into the first approximation formula, whereby the damping coefficient Dhz of each portion i of the joint to be measured is calculated. ｉ A damping coefficient calculation procedure for calculating The stress σ of each portion i measured in the stress distribution measuring step ｉ The damping coefficient Dhz calculated in the damping coefficient calculation procedure ｉ By multiplying the reciprocal of the stress σ of each part i of the joint to be measured, ｉ and a proper stress distribution calculation procedure for calculating '; The stress distribution measuring method according to claim 1 . Dhz ｉ =σhz ｉ / σs ｉ ・・・(1) <h2 style=";text-align:left;direction:ltr">Dhz<h2 style=";text-align:left;direction:ltr"> ｉ <h2 style=";text-align:left;direction:ltr"> (I'm sorry, I'm sorry) a1=b1・t+c1...(3) a2=b2・t+c2...(4) In the above formula (1), σhz ｉ means the stress of each portion i calculated by performing a coupled finite element method analysis on the numerical analysis model of the joint. ｉ means the actual stress of each part i calculated by performing finite element analysis on the numerical analysis model of the joint. In the above formula (2), LN (Hz) means the natural logarithm of the frequency Hz. In the above formula (3), b1 and c1 mean constants. In the above formula (4), b2 and c2 mean constants.

3. The joint is a welded joint. The stress distribution measuring method according to claim 1 or 2.

4. 3. A program for causing a computer to execute the damping coefficient calculation formula construction step and the appropriate stress distribution calculation step of the stress distribution measuring method according to claim 1 or 2.

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