JP7568936B2 - Method for estimating thickness of spot welded joints - Google Patents

Description

The present invention relates to a method for estimating the thickness of a plate material at a welded portion of a spot-welded joint formed by spot welding overlapping plate materials, using the results of a so-called thermoelastic stress measurement method.

2. Description of the Related Art Spot welded joints formed by spot welding (resistance spot welding) overlapping steel plates or other plate materials are widely used as components for automobiles and home appliances because spot welding is highly productive and low cost.
The nugget (melted and solidified portion) of the welded portion of a spot welded joint is formed on the overlapping surface (inner surface) side of the overlapping plate materials. In the case of the welded portion of a spot welded joint, it is the inner surface side where the nugget is formed that is at risk of fracture due to stress concentration. However, it is not possible to inspect the quality of the welded portion by directly visually inspecting the nugget of the welded portion. In addition, the distance from the outer surface of the welded portion to the inner surface where the stress is concentrated, i.e., the thickness of the plate material at the welded portion, can change due to processing, etc., but this cannot be estimated by visually inspecting the welded portion from the outer surface.

2. Description of the Related Art Finite element method (hereinafter, occasionally referred to as "FEM") analysis is sometimes used as an inspection method (specifically, a stress evaluation method) for objects such as structures that cannot be visually inspected.
However, since the numerical analysis model of the FEM analysis is created by digitizing geometric information on a computer, it is difficult to accurately model a complex shape such as a nugget of a welded part of a spot-welded joint. Also, since the numerical analysis model of the FEM analysis is divided into elements (meshes) such as hexahedrons, it may not be possible to reflect shapes that have subtle changes, such as indentations that occur in parts of the welded part other than the nugget during spot welding (referred to as the "heat-affected zone" in this specification).
Therefore, it may be difficult to accurately evaluate the internal stress of the welded portion of a spot welded joint (the stress on the overlapping surface side of the plate materials) using only FEM analysis. In addition, even if FEM analysis is used, it is not possible to estimate the plate thickness of the plate material at the welded portion, which may change.

On the other hand, a thermoelastic stress measurement method using an infrared imaging device (thermography) has been proposed as a method for non-contact measurement of stress occurring in an object to be measured (see, for example, Non-Patent Document 1).
The thermoelastic stress measurement method utilizes the thermoelastic effect that a temperature change occurs when the object to be measured elastically deforms adiabatically, and measures the temperature change over time (temperature change within a specified time) of the object to be measured by continuously imaging the object to which a repeated load is applied using an infrared imaging device, and converts this measured temperature change over time into the stress change over time (stress change within a specified time) of the object to be measured. If the initial value of the stress is known (including not only cases where the stress is actually measured and known, but also cases where it can be assumed), the stress after the specified time has passed can be measured by adding the stress change over time to this initial value.

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

For this reason, in the technology described in Non-Patent Document 1, a signal waveform corresponding to a temperature change 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 repeated load to a measured object and having the same frequency as the applied repeated load is used. The image signal is synchronously detected by this reference signal, and only the image signal components in the frequency band corresponding to the reference signal (only the image signal components having the same frequency as the reference signal or only the image signal in a narrow frequency band including the same frequency as the reference signal) are extracted, thereby improving the S/N ratio of the temperature change caused by the thermoelastic effect to be measured. Then, the time change in temperature of the measured object (the time change in temperature of 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 correspondence relationship between the magnitude of the image signal components and the temperature stored in advance. Next, the time change in stress of the measured object is calculated based on the time change in temperature of the measured object and a predetermined relational expression between the time change in temperature and the time change in stress.

In this way, by using the lock-in process, it is believed that in principle it is possible to accurately calculate the change in stress of the object with time, and therefore the stress of the object. Furthermore, since the stress of the object is calculated based on an image of the object actually captured by an infrared imaging device, it is also applicable to complex shapes such as welded parts.
Therefore, when inspecting the welded portion of a spot welded joint, specifically when evaluating the internal stress of the welded portion, it is considered to use a thermoelastic stress measurement method to which lock-in processing is applied, rather than FEM analysis.

However, when using the thermoelastic stress measurement method to evaluate the internal stress of the welded part of a spot welded joint, the infrared imaging device images the outer surface of the welded part (the surface opposite the overlapping surfaces of the plate materials). Therefore, the stress that can be directly measured by the thermoelastic stress measurement method is the outer surface stress of the welded part (stress on the outer surface side), not the internal stress of the welded part. In addition, because the infrared imaging device images the outer surface of the welded part, it is not possible to directly estimate the thickness of the plate material at the welded part.

Patent documents 1 to 4 propose methods for improving the measurement accuracy of thermoelastic stress measurement, but they do not solve the above problems.

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)

JP 2018-179730 A JP 2015-001392 A JP 2016-024057 A JP 2018-128431 A

As described above, the present invention aims to provide a method that can estimate the thickness of the plate material at the welded part, among the problems that arise when using the thermoelastic stress measurement method to inspect the welded part of a spot welded joint, namely, that the internal stress of the welded part cannot be directly measured and that the thickness of the plate material at the welded part cannot be directly estimated.

In order to solve the above problems, the present inventors have conducted extensive research and have obtained the following findings (1) to (3).
(1) By performing a coupled finite element method analysis of stress field and temperature field simulating the thermoelastic stress measurement method using the maximum and minimum loads of repeated loads applied to the spot-welded joint for a numerical analysis model of a spot-welded joint, it is possible to calculate an outer surface stress σf equivalent to the outer surface stress of the weld measured by the thermoelastic stress measurement method. In other words, the measurement of the outer surface stress of the weld using the thermoelastic stress measurement method can be reproduced by the coupled finite element method analysis.
(2) When a coupled finite element analysis is performed by varying the thickness t of the plate material in the numerical analysis model and the assumed load difference ΔP, which is the difference between the maximum load (assumed maximum load) and the minimum load (assumed minimum load) of the repeated load set to be added to the numerical analysis model, to calculate the outer surface stress σf of the weld for each assumed load difference ΔP, for the same plate thickness t, the assumed load difference ΔP can be accurately approximated by a linear function of the outer surface stress σf, and the slope u of this linear function changes depending on the plate thickness t. The relationship between the slope u of this linear function and the plate thickness t of the plate material can be expressed by a relational expression such as an exponential function.
(3) From (1) and (2) above, by applying a cyclic load to the spot-welded joint to be evaluated and measuring the outer stress σir of the weld using a thermoelastic stress measurement method multiple times while changing the load difference ΔP', which is the difference between the maximum load and the minimum load of the cyclic load, the outer stress σir of the weld is measured for each load difference ΔP', and the load difference ΔP' is expressed as a linear function of the outer stress σir of the weld. Then, by calculating the slope u' of the linear function when the load difference ΔP' is expressed as a linear function of the outer stress σir of the weld, the thickness t' of the plate material at the weld of the spot-welded joint to be evaluated can be estimated using this slope u' and the above relational equation (2) (the relational equation between the slope u of the linear function and the thickness t of the plate material).

The present invention has been completed based on the above findings of the present inventors.
That is, in order to solve the above-mentioned problem, the present invention provides a method for estimating the plate thickness of a spot welded joint formed by spot welding overlapping plate materials, the method comprising the following steps (A) to (C):
(A) Procedure for deriving the relational equation: For multiple numerical analysis models of the spot welded joint in which the thickness t of the plate material is changed, a coupled finite element method analysis of the stress field and temperature field using the assumed maximum load and assumed minimum load of the repeated load in the shear direction applied to the spot welded joint is performed multiple times while changing the assumed load difference ΔP, which is the difference between the assumed maximum load and the assumed minimum load, to calculate the outer surface stress σf of the welded portion for each assumed load difference ΔP, and when the assumed load difference ΔP is expressed as a linear function of the outer surface stress σf of the welded portion, the slope u of the linear function is calculated for each thickness t of the plate material, and a relational equation between the slope u of the linear function and the thickness t of the plate material is derived.
(B) Outer surface stress measurement procedure: The step of applying the cyclic load to the spot welded joint to be evaluated and measuring the outer surface stress σir of the weld using a thermoelastic stress measurement method is repeated multiple times while changing the load difference ΔP', which is the difference between the maximum load and the minimum load of the cyclic load, thereby measuring the outer surface stress σir of the weld for each load difference ΔP'.
(C) Plate thickness calculation procedure: When the load difference ΔP′ is expressed as a linear function of the outer surface stress σir of the welded portion, the slope u′ of the linear function is calculated, and the slope u′ is input into the derived relational equation to calculate the plate thickness t′ of the plate material at the welded portion of the spot-welded joint to be evaluated.

In the present invention, the "thickness of the plate material" means the dimension in the overlapping direction of each stacked plate material on the side to which the thermoelastic stress measurement method is applied (the side facing the infrared imaging device used for the thermoelastic stress measurement method).
In the present invention, the "shear direction" means a direction perpendicular to the overlapping direction of the plate materials.
In the present invention, the "assumed maximum load" refers to the maximum load of the repeated load set to be applied to the numerical analysis model of the spot welded joint. It does not necessarily have to be the same value as the maximum load of the repeated load actually applied to the spot welded joint in the external stress measurement procedure. If the maximum load of the repeated load actually applied is unknown, the assumed maximum load may be set to any value.
In the present invention, the "assumed minimum load" means the minimum load of the repeated load set to be applied to the numerical analysis model of the spot welded joint. It does not necessarily have to be the same value as the minimum load of the repeated load actually applied to the spot welded joint in the external stress measurement procedure. If the minimum load of the repeated load actually applied is unknown, the assumed minimum load may be set to any value.
In the present invention, "external stress" refers to stress on the surface side opposite to the overlapping surface of the plate material. In addition, specifically, the "external stress of the welded portion" can be exemplified by stress in the heat-affected portion of the welded portion located at a position corresponding to the center of the nugget of the welded portion when viewed from the overlapping direction of the plate material. However, this is not limited thereto, and it is also possible to calculate stress in the heat-affected portion located at a position corresponding to the boundary between the nugget and the heat-affected portion of the welded portion, average stress in a predetermined portion on the outer surface side of the welded portion, etc.
In the present invention, the term "calculating the outer surface stress σf of the weld" refers to a concept including calculation of the outer surface stress of the weld as it is as well as calculation of the change in the outer surface stress of the weld over time.
In the present invention, the term "measuring the outer surface stress σir of the weld" refers to a concept including not only the measurement of the outer surface stress of the weld itself but also the measurement of the change in the outer surface stress of the weld over time.

According to the present invention, in the relational expression derivation procedure, a coupled finite element method analysis is performed multiple times with different assumed load differences ΔP for multiple numerical analysis models of spot-welded joints with different plate thicknesses t, thereby deriving a relational expression between the slope u of a linear function of the assumed load difference ΔP expressed as a linear function of the outer stress σf of the welded portion and the plate thickness t of the plate. Next, in the outer stress measurement procedure, a step of actually measuring the outer stress σir of the welded portion using a thermoelastic stress measurement method is performed multiple times with different load differences ΔP', thereby measuring the outer stress σir of the welded portion for each load difference ΔP'. Finally, in the plate thickness calculation procedure, a slope u' of the linear function of the load difference ΔP' expressed as a linear function of the outer stress σir of the welded portion actually measured in the outer stress measurement procedure is calculated, and the slope u' is input into the derived relational expression to calculate the plate thickness t' of the plate at the welded portion of the spot-welded joint to be evaluated.
As described above, according to the present invention, it is possible to calculate (estimate) the plate thickness t' of the plate material at the welded portion of a spot-welded joint by using the relational equation derived by coupled finite element method analysis and the outer surface stress σir of the welded portion of the spot-welded joint that is the subject of evaluation, which is actually measured by a thermoelastic stress measurement method.

In order to derive the relational expression, it is possible to prepare a plurality of test pieces having different thicknesses of the plate material, and perform the thermoelastic stress measurement method for each test piece by changing the load difference, but this would result in an increase in labor and cost for producing the test pieces and performing the thermoelastic stress measurement method. According to the present invention, the relational expression is derived by a coupled finite element method analysis, so such a problem does not occur. In the present invention, it is only necessary to perform the thermoelastic stress measurement method at least twice by changing the load difference ΔP' to calculate the gradient u' only for the spot welded joint to be evaluated, so that the labor and cost can be reduced.
In addition, in the present invention, if the relational equation is derived by executing the relational equation deriving procedure once, the derived relational equation can be repeatedly used when executing the external stress measurement procedure and the plate thickness calculation procedure for a plurality of evaluation objects. In other words, when estimating plate thicknesses at the welds of a plurality of evaluation objects according to the present invention, it is not necessary to execute the relational equation deriving procedure as many times as the number of evaluation objects, and it is sufficient to execute the relational equation deriving procedure only once in advance.

Here, in order to perform the coupled finite element method analysis executed in the relational equation derivation procedure of the present invention for a specified time period during which a repeated load is applied, it is necessary to repeat calculations for a specified time period for each cycle of the repeated load, which increases the calculation time and therefore poses the problem of increased costs.
Therefore, the inventors have conducted extensive research and have come to the conclusion that, in the case of elastic analysis of linear deformation, the change in stress over time caused by repeated loading hardly changes between cycles of the repeated loading, and that this fact can be utilized. Specifically, the analysis of the stress field is performed only once using the assumed maximum load and assumed minimum load of the repeated loading in one cycle as conditions, without repeating the calculation for each cycle of the repeated loading, and the change in stress over time calculated in this way is utilized in the analysis of the temperature field, thereby making it possible to quickly and easily calculate only the temperature change caused by the thermoelastic effect with sufficient accuracy.

The following preferred method has been completed based on the above findings of the present inventors.
That is, preferably, the coupled finite element method analysis performed in the relational equation deriving procedure includes a stress analysis step of performing a stress analysis using an assumed maximum load and an assumed minimum load of the repeated load for the numerical analysis model to calculate a stress distribution of the numerical analysis model, a heat flux calculation step of calculating a heat flux using the stress distribution of the numerical analysis model calculated in the stress analysis step, the material properties of the spot welded joint, and the frequency of the repeated load, and a heat transfer analysis step of performing a heat transfer analysis using the heat flux calculated in the heat flux calculation step to calculate a temperature distribution of the numerical analysis model, and further includes a conversion step of calculating a temperature distribution of the numerical analysis model after the predetermined time has elapsed by repeatedly executing the heat flux calculation step and the heat transfer analysis step for a predetermined time period during which the repeated load is applied, calculating an outer surface temperature of the weld based on the temperature distribution of the numerical analysis model after the predetermined time has elapsed, and converting the outer surface temperature of the weld into an outer surface stress σf of the weld.

In the above-mentioned preferred method, "calculating the outer surface temperature of the weld" is a concept that includes not only the calculation of the outer surface temperature of the weld itself, but also the calculation of the change in the outer surface temperature of the weld over time.
According to the above-mentioned preferred method, in the stress analysis step, a stress analysis is performed using an assumed maximum load and an assumed minimum load of a repeated load on a numerical analysis model of a spot welded joint, and a stress distribution of the numerical analysis model is calculated. This stress analysis step does not need to be performed repeatedly, and it is sufficient to perform it once using the assumed maximum load and the assumed minimum load of the repeated load.
Next, according to the above-mentioned preferred method, 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 spot-welded joint, and the frequency of the repeated load. Examples of the material properties of the spot-welded joint used in the heat flux calculation step include the thermoelastic coefficient, density, and specific heat of the spot-welded joint (plate material).
Next, according to the above-mentioned preferred method, 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.
Then, by repeatedly executing the above-mentioned heat flux calculation step and heat transfer analysis step for a predetermined time during which the repeated load is applied, it is possible to calculate the temperature distribution of the numerical analysis model after the predetermined time has elapsed.
Finally, according to the above-mentioned preferred method, in the conversion step, the outer surface temperature of the welded portion can be calculated based on the temperature distribution of the numerical analysis model after a predetermined time has elapsed, and the outer surface temperature of the welded portion can be converted into the outer surface stress σf of the welded portion. To convert the outer surface temperature of the welded portion into the outer surface stress σf, a known relational expression between temperature and stress may be used.

An example of the relational equation calculated in the relational equation derivation procedure is one in which the plate thickness t is expressed as an exponential function of the slope u of the linear function.

According to the present invention, it is possible to estimate the thickness of the plate material at the welded portion of a spot welded joint using the measurement results of the thermoelastic stress measurement method.

FIG. 2 is a flow chart illustrating a schematic procedure of a method for estimating a thickness of a spot-welded joint according to an embodiment of the present invention. An example of a numerical analysis model (finite element analysis model) of a spot welded joint is shown. FIG. 2 is a diagram showing an example of an outer surface stress σf calculated for each assumed load difference ΔP in the relational equation deriving step S1 shown in FIG. 1 . FIG. 2 is a diagram showing an example of a slope u of a linear function calculated for each thickness t of the plate material 11 in the relational equation deriving step S1 shown in FIG. 1 . FIG. 2 is a flow diagram showing an outline of a procedure for coupled finite element analysis executed in the relational equation deriving procedure S1. 1 shows an example of an outer surface stress distribution of a numerical analysis model obtained by performing a coupled finite element method analysis in an embodiment of the present invention. 1 shows an example of an outer surface stress distribution obtained by performing a thermoelastic stress measurement method in an embodiment of the present invention.

Hereinafter, a method for estimating thickness of a spot-welded joint according to one embodiment of the present invention (hereinafter, simply referred to as a "plate thickness estimation method") will be described with reference to the attached drawings as appropriate.
FIG. 1 is a flow diagram that shows a schematic procedure of the plate thickness estimation method according to the present embodiment. FIG. 2 shows an example of a numerical analysis model (finite element analysis model) of a spot welded joint. FIG. 2(a) is a perspective view showing half of the numerical analysis model, and FIG. 2(b) is an enlarged perspective view of the area surrounded by the dashed line A in FIG. 2(a). In FIG. 2, the X direction indicates the direction in which a repeated load is applied to the spot welded joint (shear direction). The Z direction indicates the overlapping direction of the plate materials of the spot welded joint. The Y direction indicates the direction in which a repeated load is applied to the spot welded joint and the direction perpendicular to the overlapping direction of the plate materials of the spot welded joint. FIG. 2(a) shows half of the numerical analysis model obtained by dividing the entire numerical analysis model by a plane that passes through the center of the weld and is parallel to the XZ plane.

As shown in FIG. 2 , the plate thickness estimation method according to the present embodiment is a method for estimating the plate thickness of the plate material at the welded portion 13 of the spot-welded joint 10 by applying repeated loads in a shear direction (X direction) using a fatigue testing machine or the like to a spot-welded joint 10 formed by spot welding overlapping plate materials 11, 12, and measuring the outer surface stress of the welded portion 13 of the spot-welded joint 10.
The outer surface stress of the welded portion 13 means, among the stresses occurring in the welded portion 13, the stress on the side of the surface (surface 11b of the plate material 11 and surface 12b of the plate material 12) opposite to the overlapping surface of the plate materials 11, 12 (surface 11a of the plate material 11 and surface 12a of the plate material 12, which are the opposing surfaces of the plate materials 11, 12). Specifically, an example of the outer surface stress of the welded portion 13 is the stress of a portion 111 or a portion 121 of the heat-affected zone of the welded portion 13, which is located at a position corresponding to a central portion 131 of the nugget 13a of the welded portion 13 when viewed from the overlapping direction (Z direction) of the plate materials 11, 12.
In this embodiment, in the external stress measurement procedure S2 described later, an infrared imaging device is disposed facing the surface (outer surface) of the plate material 11 to measure the external stress on the plate material 11 side of the welded portion 13 (for example, the stress of the portion 111 of the heat-affected zone of the welded portion 13), so the plate thickness t of the plate material 11 is used as the plate thickness of the plate material used in the relational expression derivation procedure S1 described later. In this case, the plate thickness of the plate material at the welded portion 13 calculated in the plate thickness calculation procedure S3 described later is the plate thickness t' of the plate material 11 at the welded portion 13. However, in the external stress measurement procedure S2 described later, it is also possible to dispose the infrared imaging device facing the surface (outer surface) of the plate material 12 to measure the external stress on the plate material 12 side of the welded portion 13. In this case, the thickness of the plate material used in the relational equation deriving procedure S1 described below is the thickness t of the plate material 12, and the thickness of the plate material at the welded portion 13 calculated in the thickness calculation procedure S3 described below is the thickness t' of the plate material 12 at the welded portion 13. In the example shown in Fig. 2, the thicknesses of the plate materials 11 and 12 in the numerical analysis model used in the relational equation deriving procedure S1 have the same value of t, but they can also be different values.

As shown in FIG. 1, the plate thickness estimation method according to this embodiment includes a relational equation deriving step S1, an outer surface stress measurement step S2, and a plate thickness calculation step S3. Each of steps S1 to S3 will be described below in order.

<Relational Equation Deriving Procedure S1>
In the relational equation derivation procedure S1 shown in FIG. 1, a coupled finite element analysis (coupled FEM analysis) of a stress field and a temperature field using an assumed maximum load and an assumed minimum load of repeated loads is performed on a numerical analysis model of a spot welded joint 10 as shown in FIG. 2.
Specifically, the coupled FEM analysis is performed multiple times for multiple numerical analysis models in which the plate thickness t of the plate material 11 is changed, while changing the assumed load difference ΔP, which is the difference between the assumed maximum load and the assumed minimum load, to calculate the outer surface stress σf of the welded portion 13 for each assumed load difference ΔP. The specific content of the coupled FEM analysis will be described later.

More specifically, in the relational equation deriving step S1, for a numerical analysis model having a certain plate thickness t, the outer surface stress σf of the welded portion 13 is calculated for each assumed load difference ΔP, and then, for a numerical analysis model having another plate thickness t, the outer surface stress σf of the welded portion 13 is calculated for each assumed load difference ΔP. The above steps are repeatedly executed for the numerical analysis models having all plate thicknesses t.
3 is a diagram showing an example of the outer surface stress σf calculated for each assumed load difference ΔP for a plurality of numerical analysis models with different plate thicknesses t. In the example shown in FIG. 3, the outer surface stress σf is calculated for each different assumed load difference ΔP for each numerical analysis model with plate thicknesses t = 0.8 mm, 1.2 mm, 1.6 mm, and 2.0 mm. As shown in FIG. 3, according to the knowledge of the inventors, for the same plate thickness t, the assumed load difference ΔP can be accurately approximated by a linear function of the outer surface stress σf, and it was found that the slope u of this linear function changes depending on the plate thickness t. That is, it was found that the following formula (1) is established.
ΔP=u・σf+v (1)
In the above formula (1), u and v represent predetermined constants.
As shown in FIG. 3, the slope u of the linear function increases as the plate thickness t increases.
The linear function of equation (1) that approximates the assumed load difference ΔP can be calculated by an approximation calculation such as the least squares method based on the outer surface stress σf calculated for each assumed load difference ΔP.

Next, in the relational equation derivation step S1, as shown in equation (1), when the expected load difference ΔP is expressed as a linear function of the outer surface stress σf of the welded portion 13, the slope u of the linear function is calculated for each plate thickness t of the plate material 11.
Fig. 4 is a diagram showing an example of the slope u of the linear function calculated for each thickness t of the plate material 11 in the relational equation derivation procedure S1. Specifically, Fig. 4 is a diagram showing the slope u of the linear function calculated for each thickness t of the plate material 11 using the data shown in Fig. 3. As shown in Fig. 4, according to the knowledge of the present inventors, it was found that the thickness t of the plate material 11 can be accurately approximated by an exponential function of the slope u of the linear function. That is, it was found that the following formula (2) holds.
t=c・e ^d・u ...(2)
In the above formula (2), c and d represent predetermined constants, and e represents the base of the natural logarithm.
Therefore, in the relational equation deriving step S1, equation (2) is derived as a relational equation between the slope u of the linear function and the plate thickness t of the plate material 11. Note that the exponential function of equation (2) that approximates the plate thickness t can be calculated by an approximation calculation such as the least squares method based on the slope u of the linear function calculated for each plate thickness t.

<External surface stress measurement procedure S2>
In the external stress measurement procedure S2 shown in Fig. 1, a repeated load is applied to the spot welded joint 10 to be evaluated, and the external stress σir of the welded portion 13 of the spot welded joint 10 to be evaluated is actually measured using a thermoelastic stress measurement method. Specifically, an infrared imaging device arranged opposite the surface (outer surface) of the plate material 11 is used to continuously image the surface (outer surface) of the plate material 11 including the welded portion 13 of the spot welded joint 10 to which a repeated load in the shear direction is applied for a predetermined time by a fatigue testing machine or the like. 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 distribution of the external stress in the imaged area of the spot welded joint 10 to be evaluated, and thus to measure the external stress σir of the welded portion 13.
In the outer stress measurement procedure S2, the step of measuring the outer stress σir of the welded portion 13 as described above is performed multiple times by changing the load difference ΔP', which is the difference between the maximum load and the minimum load of the repeated load, thereby measuring the outer stress σir of the welded portion 13 for each load difference ΔP'.
Since the specific details of the thermoelastic stress measurement method are publicly known, a detailed description thereof will be omitted here.

<Plate thickness calculation procedure S3>
In the plate thickness calculation step S3 shown in FIG. 1, when the load difference ΔP′ in the external stress measurement step S2 is expressed as a linear function of the external stress σir of the welded portion 13, the slope u′ of the linear function is calculated.
Specifically, in the same manner as in the step S1 of deriving the relational expression, the linear function of the formula (1) that approximates the assumed load difference ΔP is calculated, the following is calculated based on the outer surface stress σir measured for each load difference ΔP′ by the least squares method: By performing approximate calculations such as the above, the gradient u' of the linear function expressed by the following formula (1)' is calculated.
ΔP'=u'・σir+v'...(1)'
In the above formula (1)′, u′ and v′ represent predetermined constants.
In the external stress calculation step S2, when the external stress σir is measured only for two load differences ΔP′, the linear function is expressed by expressing each load difference ΔP′ and the external stress σir measured for each load difference ΔP′. It is calculated as a straight line connecting the two coordinate points.

Next, in the plate thickness calculation procedure S3, the slope u' calculated as described above is input into the relational equation (equation (2)) derived in the relational equation derivation procedure S1, thereby calculating the plate thickness t' of the plate material 11 at the welded portion 13 of the spot-welded joint 10 to be evaluated. Specifically, the value on the left side obtained by inputting u' instead of u on the right side of equation (2) is calculated as the plate thickness t'. That is, the plate thickness t' is calculated by the following equation (2)'.
t'=c・e ^d・u' ...(2)'

The specific contents of the coupled FEM analysis executed in the relational equation deriving step S1 will be described below.
5 is a flow diagram showing the procedure of the coupled FEM analysis executed in the relational equation deriving procedure S1. As shown in FIG. 5, the coupled FEM analysis executed in the relational equation deriving procedure S1 includes a stress analysis step S11, a heat flux calculation step S12, a heat transfer analysis step S13, and a conversion step S15. Each of steps S11 to S15 will be described below in order.

[Stress analysis step S11]
In the stress analysis step S11, a stress analysis is performed using an assumed maximum load and an assumed minimum load of the repeated load applied to the spot-welded joint 10 for a numerical analysis model of the spot-welded joint 10 as shown in Fig. 2, and a stress distribution in the numerical analysis model is calculated. In addition to the assumed maximum load and assumed minimum load of the repeated load applied to the spot-welded joint 10, the Young's modulus and Poisson's ratio of the plate materials 11, 12 and boundary conditions (symmetry conditions, constraint conditions, etc.) are used in this stress analysis.
Specifically, in the stress analysis step S11 of the present embodiment, the stress analysis is performed to calculate the change over time in the stress distribution of the numerical analysis model. In other words, the change over time Δσ in stress (also called the sum of principal stresses) is calculated for each element of the numerical analysis model.
As software for performing the stress analysis, for example, the general-purpose nonlinear finite element analysis program "Abaqus" manufactured by SIMULIA, Inc. can be suitably used, but the present invention is not limited to this. The calculated change in stress distribution over time of the numerical analysis model is used in the heat flux calculation step S12 described later, and may be stored in a storage medium such as a memory, a hard disk, or a CD-ROM provided in a computer for executing each of steps S11 to S15.

[Heat flux calculation step S12]
In the heat flux calculation step S12, the heat flux is calculated using the stress distribution (change in stress distribution over time) of the numerical analysis model calculated in the stress analysis step S11, the material properties of the spot welded joint 10 (e.g., the thermoelastic coefficient, density, and specific heat of the plate materials 11 and 12), and the frequency of the repeated load.
Specifically, in the heat flux calculation step S12 of this embodiment, first, a time change ΔT in temperature is calculated for each element of the numerical analysis model based on the following equation (3).
ΔT=-K・T・Δσ...(3)
In the above formula (3), ΔT is the change in temperature over time, K is the thermoelastic coefficient of the plate materials 11 and 12, Δσ is the change in stress over time, and T is the temperature of the numerical analysis model. When the heat flux calculation step S12 is executed for the first time, the ambient temperature (e.g., 20° C.) is input as the initial temperature in T.

Next, in a heat flux calculation step S12, a heat flux F is calculated for each element of the numerical analysis model based on the following formula (4) or (5).
F=-2・ΔT・ρ・Cp・Hz ...(4)
F=2・ΔT・ρ・Cp・Hz ...(5)
In the above formulas (4) and (5), F represents the heat flux, ρ represents the density of the plate materials 11 and 12, Cp represents the specific heat of the plate materials 11 and 12, and Hz represents the frequency of the repeated load. When the load changes in the compression direction, the above formula (4) is used, and when the load changes in the tension direction, the above formula (5) is used.
The software for executing the heat flux calculation step S12 can be created as a user subroutine of the general-purpose nonlinear finite element analysis program "Abaqus" manufactured by SIMULIA, for example, a program for executing the above equations (3) to (5). However, the present invention is not limited to this.

[Heat transfer analysis step S13]
In the heat transfer analysis step S13, a heat transfer analysis is performed using the heat flux F calculated in the heat flux calculation step S12, and a temperature distribution of the numerical analysis model is calculated. Specifically, in the heat transfer analysis step S13 of this embodiment, a heat transfer analysis is performed to calculate a change in temperature distribution over time in the numerical analysis model. In other words, a change in temperature over time ΔT is calculated for each element of the numerical analysis model.
Specifically, in addition to the heat flux F, the heat transfer analysis uses the temperature T of the numerical analysis model, and the convection heat transfer coefficients and emissivity of the plate materials 11 and 12. When the heat transfer analysis step S13 is executed for the first time, the ambient temperature (e.g., 20° C.) is input as the initial temperature in T.
As software for performing the heat transfer analysis, for example, the general-purpose nonlinear finite element analysis program "Abaqus" manufactured by SIMULIA Corporation can be suitably used, but the present invention is not limited to this.

Then, in the relational equation derivation procedure S1, the above-mentioned heat flux calculation step S12 and heat transfer analysis step S13 are repeatedly executed for a predetermined time (the same time as the predetermined time for continuously capturing images of the spot welded joint 10 using an infrared imaging device in the external stress measurement procedure S2). That is, in step S14 of FIG. 5, it is determined whether or not the predetermined time has elapsed, and if the predetermined time has not elapsed (if "No" in step S14 of FIG. 5), the heat flux calculation step S12 and heat transfer analysis step S13 are executed again. If the predetermined time has elapsed (if "Yes" in step S14 of FIG. 5), the calculations in the heat flux calculation step S12 and heat transfer analysis step S13 are terminated. This makes it possible to calculate the change over time in the temperature distribution of the numerical analysis model after the predetermined time has elapsed.

[Conversion step S15]
In the conversion step S15, the outer surface temperature of the welded portion 13 is calculated based on the temperature distribution (temporal change in temperature distribution) of the numerical analysis model after a predetermined time has elapsed. Then, this outer surface temperature of the welded portion 13 is converted into the outer surface stress σf of the welded portion 13. A known relational expression between temperature and stress may be used for the conversion into the outer surface stress σf.

By performing the coupled FEM analysis described above in the relational equation derivation procedure S1, it is possible to calculate the outer surface stress σf equivalent to the outer surface stress σir of the welded portion 13 measured using the thermoelastic stress measurement method in the outer surface stress measurement procedure S2.

According to the plate thickness estimation method of this embodiment described above, it is possible to calculate (estimate) the plate thickness t' of the plate material 11 at the welded portion 13 of the spot-welded joint 10 using the relational equation derived by the coupled FEM analysis and the outer surface stress σir of the welded portion 13 of the spot-welded joint 10, which is the object of evaluation, actually measured by a thermoelastic stress measurement method.
The plate thickness t' of the plate material 11 at the welded portion 13 estimated by the plate thickness estimation method according to the present embodiment is the distance from the outer surface 11b of the welded portion 13 to the inner surface 11a, which is the stress concentration site. For this reason, by applying the plate thickness estimation method according to the present embodiment not only to the spot-welded joint 10 but also to general plate materials, it is expected that the distance from the surface of the plate material to a defect present inside the plate material, which is the stress concentration site, can be estimated.

Hereinafter, an example in which the plate thickness estimation method according to this embodiment is executed will be described.
In this embodiment, a spot welded joint 10 formed by spot welding 590 MPa class steel plate plates 11 and 12 was evaluated, and a fatigue testing machine was used to apply a repeated load (tensile load) in the shear direction with a frequency of 7 Hz for a predetermined time (10 sec) to estimate the plate thickness t' of the plate material 11.

In this embodiment, in the relational expression derivation procedure S1, the assumed load difference ΔP of the repeated load was changed in the range of 0.5 kN to 1.7 kN for the plate thickness t = 0.8 mm, in the range of 0.8 kN to 2.6 kN for the plate thickness t = 1.2 mm, in the range of 1.1 kN to 3.5 kN for the plate thickness t = 1.6 mm, and in the range of 1.3 kN to 4.3 kN for the plate thickness t = 2.0 mm, as shown in Figure 2, and the outer surface stress σf of the welded portion 13 was calculated for each assumed load difference ΔP by performing a coupled FEM analysis. For each assumed load difference ΔP, the stress ratio R (R = assumed minimum load / assumed maximum load) was set to 0.05. The plate materials 11 and 12 each had a Young's modulus of 205.9 GPa and a Poisson's ratio of 0.3.
In the heat flux calculation step S12 of the coupled FEM analysis, the initial temperature of the numerical analysis model was set to 20° C., and the thermoelastic coefficient K of the plate materials 11 and 12 was set to 3.14e ⁻⁶ (e is the base of the natural logarithm). The density ρ of the plate materials 11 and 12 was set to 7.8e ⁻⁶ kg/mm ³ (e is the base of the natural logarithm), and the specific heat Cp of the plate materials 11 and 12 was set to 460 kJ/kg. Furthermore, when calculating the heat flux F, the above-mentioned formula (4) was used when the repeated load changed from the assumed maximum load to the assumed minimum load, and the above-mentioned formula (5) was used when the repeated load changed from the assumed minimum load to the assumed maximum load.
In the heat transfer analysis step S13 of the coupled FEM analysis, the initial temperature of the numerical analysis model was set to 20° C., the convection heat transfer coefficient of the plates 11 and 12 was set to 11.628 W/(m ² ·K), and the emissivity of the plates 11 and 12 was set to 0.8.
In the relational equation deriving procedure S1 of this embodiment, under the above-mentioned conditions, the slope u of the linear function when the assumed load difference ΔP is expressed as a linear function of the outer surface stress σf of the welded portion 13 is calculated for each thickness t of the plate material 11, and a relational equation between the slope u of the linear function and the thickness t of the plate material 11 is derived. Specifically, the values of the constants c and d in the above-mentioned equation (2) are derived. The derived values of the constants c and d are used in equation (2)' used in the plate thickness calculation procedure S3 of this embodiment described later.

Figure 6 shows an example of the outer surface stress distribution of the numerical analysis model obtained by performing a coupled FEM analysis in this embodiment. Specifically, Figure 6 shows the outer surface stress distribution when a maximum assumed load of repeated loads with a frequency of 7 Hz and an assumed load difference ΔP of 2.6 kN (stress ratio R = 0.05) is applied, and shows the outer surface stress distribution of half of the numerical analysis model obtained by dividing the entire numerical analysis model with a plate thickness t = 1.2 mm by a plane that passes through the center of the welded portion 13 and is parallel to the XZ plane. The outer surface stress σf of the welded portion 13 calculated based on the outer surface stress distribution of the numerical analysis model shown in Figure 6 was 135 MPa (compressive stress).

The example shown in Figure 3 above is the outer surface stress σf for each assumed load difference ΔP obtained by the relational equation derivation procedure S1 of this embodiment. Also, Figure 4 above shows the slope u of the linear function for each thickness t of the plate material 11 obtained by the relational equation derivation procedure S1 of this embodiment.

In this embodiment, in the external stress measurement procedure S2, as described above, a repeated load (tensile load) in the shear direction with a frequency of 7 Hz was applied to the spot welded joint 10 to be evaluated using a fatigue testing machine for a predetermined time (10 sec), and the external stress σir of the welded portion 13 was actually measured using a thermoelastic stress measurement method (with lock-in processing). The external stress σir was measured under two conditions of a load difference ΔP' of 2.0 kN (stress ratio R = 0.05) and 0.8 kN (stress ratio R = 0.05). When the load difference ΔP' = 2.0 kN, the external stress σir = 117 MPa, and when the load difference ΔP' = 0.8 kN, the external stress σir = 53 MPa.
FIG. 7 shows an example of an outer surface stress distribution obtained by performing a thermoelastic stress measurement method. Specifically, FIG. 7 shows an outer surface stress distribution obtained by performing a thermoelastic stress measurement method when a maximum load of a repeated load with a load difference ΔP′ of 2.6 kN (stress ratio R=0.05) is applied, as in the case of the coupled FEM analysis shown in FIG. 6. It can be seen that the outer surface stress distribution shown in FIG. 7 is a distribution that is close to the outer surface stress distribution of the numerical analysis model obtained by performing the coupled FEM analysis shown in FIG. 6. The outer surface stress σir calculated based on the outer surface stress distribution shown in FIG. 7 was 139 MPa (compressive stress), which was equivalent to the outer surface stress σf=135 MPa (compressive stress) calculated based on the outer surface stress distribution shown in FIG. 6.

In this embodiment, in the plate thickness calculation step S3, the load difference ΔP′ (ΔP′=2.0 kN, 0.8 kN) in the external stress measurement step S2 was expressed as a linear function of the external stress σir (σir=117 MPa, 53 MPa) of the welded portion 13, and the slope u′ of the linear function was calculated. Specifically, the slope u′ was calculated as the slope of a straight line connecting two points whose coordinates are each load difference ΔP′ and the external stress σir measured for each load difference ΔP′,
u'=(2.0-0.8)/(117-53)=0.01875
was obtained.
By substituting this u' into the right side of the above-mentioned equation (2)', the plate thickness t' becomes 1.22 mm.
Since the actual thickness of the plate material 11 at the welded portion 13 of the spot welded joint 10 being evaluated was 1.2 mm, the error was (1.22 - 1.2) / 1.2 x 100 ≒ 1.2%, and it was found that the thickness of the plate material 11 at the welded portion 13 could be estimated with high accuracy.

10: Spot welded joint 11, 12: Plate material 13: Welded part S1: Relational equation derivation procedure S2: Outer surface stress measurement procedure S3: Plate thickness calculation procedure

Claims (3)

A method for estimating a plate thickness of a plate material at a welded portion of a spot welded joint formed by spot welding overlapping plate materials, comprising:
a relational equation deriving step of: performing coupled finite element analysis of stress field and temperature field using assumed maximum load and assumed minimum load of repeated load in shear direction applied to the spot welded joint for a plurality of numerical analysis models of the spot welded joint in which the thickness t of the plate material is changed, and changing an assumed load difference ΔP, which is the difference between the assumed maximum load and the assumed minimum load, to calculate an outer surface stress σf of the welded portion for each assumed load difference ΔP; and calculating a slope u of the linear function when the assumed load difference ΔP is expressed as a linear function of the outer surface stress σf of the welded portion for each thickness t of the plate material, to derive a relational equation between the slope u of the linear function and the thickness t of the plate material;
an outer surface stress measurement procedure in which the step of applying the cyclic load to the spot-welded joint to be evaluated and measuring the outer surface stress σir of the welded portion using a thermoelastic stress measurement method is performed multiple times while changing a load difference ΔP′, which is the difference between a maximum load and a minimum load of the cyclic load, thereby measuring the outer surface stress σir of the welded portion for each load difference ΔP′;
A plate thickness calculation step of calculating a slope u' of a linear function of the load difference ΔP' expressed as a linear function of the outer surface stress σir of the welded portion, and inputting the slope u' into the derived relational expression to calculate a plate thickness t' of the plate material at the welded portion of the spot-welded joint to be evaluated.
A method for estimating plate thickness of a spot welded joint, comprising: The coupled finite element analysis performed in the procedure for deriving the relational equation is
a stress analysis step of performing a stress analysis using an assumed maximum load and an assumed minimum load of the repeated load on the numerical analysis model, and calculating a stress distribution of the numerical analysis model;
a heat flux calculation step of calculating a heat flux using the stress distribution of the numerical analysis model calculated in the stress analysis step, material properties of the spot welded joint, and a frequency of the repeated load;
a heat transfer analysis step of performing a heat transfer analysis using the heat flux calculated in the heat flux calculation step, and calculating a temperature distribution of the numerical analysis model,
by repeatedly executing the heat flux calculation step and the heat transfer analysis step for a predetermined time during which the repeated load is applied, a temperature distribution of the numerical analysis model after the predetermined time has elapsed is calculated;
The method further includes a conversion step of calculating an outer surface temperature of the welded portion based on a temperature distribution of the numerical analysis model after the predetermined time has elapsed, and converting the outer surface temperature of the welded portion into an outer surface stress σf of the welded portion.
The method for estimating a plate thickness of a spot welded joint according to claim 1. The relational equation calculated in the relational equation derivation procedure is an exponential function of the plate thickness t and the slope u of the linear function.
3. The method for estimating a plate thickness of a spot welded joint according to claim 1 or 2.

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