JP7469660B2 - Method for evaluating internal stress of spot welded joints and evaluation method for thermoelastic stress measurement - Google Patents

Description

The present invention relates to a method capable of evaluating the internal stress of a welded portion of a spot-welded joint using the measurement results of a so-called thermoelastic stress measurement method, and also to an evaluation method of the thermoelastic stress measurement method capable of easily evaluating the measurement results of the 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 weld of a spot welded joint is formed on the overlapping surface (inner surface) of the overlapping plate materials. In the case of the weld of a spot welded joint, the part on the inner surface where the nugget is formed is at risk of fracture due to stress concentration. However, it is not possible to inspect the quality of the weld by directly visually inspecting the nugget of the weld.

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 FEM numerical analysis model 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. In addition, since the FEM numerical analysis model 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 (stress on the overlapping surface side of the plate materials) of the weld of a spot-welded joint using only FEM analysis.

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 a measurement object (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, i.e., 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, it is believed that the lock-in process can, in principle, 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, the process can be applied to objects with complex shapes, such as welds.
Therefore, when inspecting the welded portion of a spot welded joint, specifically when evaluating the internal stress of the welded portion, it may be possible 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). This poses the problem that the stress that can be directly measured using the thermoelastic stress measurement method is the external stress of the welded part (stress on the outer surface), not the internal stress of the welded part.

As mentioned above, the temperature change caused by the thermoelastic effect is extremely small, and the plate thickness of the plate material of the spot welded joint is relatively small, so heat conduction to the periphery of the welded part is likely to occur. For this reason, the thermoelastic stress measurement method cannot accurately calculate the time change of temperature corresponding to the time change of the external stress actually generated in the welded part of the spot welded joint. According to the knowledge of the inventors, the smaller the frequency of the repeated load applied to the spot welded joint, the greater the effect of the above-mentioned heat conduction, and the worse the calculation accuracy of the time change of temperature corresponding to the time change of the external stress actually generated in the welded part. Specifically, the time change of temperature calculated corresponds to a value smaller than the time change of the external stress actually generated in the welded part. For this reason, there is a problem that the external stress measured by the thermoelastic stress measurement method is smaller than the external stress actually generated in 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

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 capable of evaluating the internal stress of a welded portion of a spot-welded joint using the measurement results of a thermoelastic stress measurement method . Another object of the present invention is to provide an evaluation method of the thermoelastic stress measurement method capable of easily evaluating the measurement results of the thermoelastic stress measurement method.

In order to solve the above problems, the present inventors have conducted extensive research and have obtained the following findings (1) to (4).
(1) By performing coupled finite element analysis of stress field and temperature field simulating the thermoelastic stress measurement method using the maximum and minimum loads of the repeated load applied to the spot welded joint for a numerical analysis model of the spot welded joint, it is possible to calculate an outer surface stress σhz equivalent to the outer surface stress of the weld measured by the thermoelastic stress measurement method. However, as with the thermoelastic stress measurement method, the outer surface stress σhz calculated by the coupled finite element analysis is affected by heat conduction according to the plate thickness t of the plate material of the spot welded joint and the frequency Hz of the repeated load applied to the spot welded joint.
(2) By performing a static finite element method analysis using the maximum load of the repeated load applied to the spot welded joint as the target of a numerical analysis model of the spot welded joint, it is possible to calculate an outer surface stress σf equivalent to the outer surface stress actually generated in the welded part. In addition, by performing a static finite element method analysis, it is possible to accurately calculate the ratio of the inner surface stress σi to the outer surface stress σf of the welded part (inner and outer stress ratio). However, the inner and outer stress ratio calculated by the static finite element method is affected by the plate thickness t of the plate material of the spot welded joint.
(3) From the above (1) and (2), by performing a static finite element method analysis and a coupled finite element method analysis on a numerical analysis model of a spot-welded joint, it is possible to derive a relational expression for estimating an inner stress σi of a weld calculated by performing a static finite element method analysis using the outer stress σhz of the weld calculated by performing the coupled finite element method analysis, the plate thickness t of the plate material, and the frequency Hz of the repeated load as input parameters. This relational expression is not easily affected by the complex shape of the weld and is not affected by the load value of the repeated load. In other words, even if it is difficult to accurately model the weld in the finite element method analysis, it is possible to derive a relational expression with high estimation accuracy.
(4) Therefore, by inputting the outer stress σir of the welded part of the spot-welded joint to be evaluated, measured using a thermoelastic stress measurement method, the plate thickness t of the plate material of the spot-welded joint to be evaluated, which can be known in advance, and the frequency Hz of the repeated load applied to the spot-welded joint to be evaluated, which can be known in advance, into the relational equation derived in (3) above (by inputting the outer stress σir of the welded part of the spot-welded joint to be evaluated, measured using a thermoelastic stress measurement method, instead of the outer stress σhz, which is an input parameter of the relational equation), the inner stress σi' of the welded part of the spot-welded joint to be evaluated can be calculated with the same accuracy as the inner stress actually occurring in the welded part.

The present invention has been completed based on the above findings of the present inventors.
In other words, in order to solve the above-mentioned problems, the present invention provides a method for evaluating the internal stress of a welded portion of a spot welded joint formed by spot welding overlapping plate materials when a repeated load in a shear direction is applied to the spot welded joint, the method comprising the following steps (A) to (C).
(A) Procedure for deriving the relational equation: A static finite element method analysis using the assumed maximum load of the repeated load and 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 are performed on a numerical analysis model of the spot welded joint, and a relational equation for estimating the internal stress σi of the welded portion calculated by performing a static finite element method analysis is derived using the outer surface stress σhz of the welded portion calculated by performing the coupled finite element method analysis, the plate thickness t of the plate material, and the frequency Hz of the repeated load as input parameters.
(B) Outer surface stress measurement procedure: The repeated load is applied to the spot welded joint to be evaluated, and the outer surface stress σir of the weld is measured using a thermoelastic stress measurement method.
(C) Inner surface stress calculation procedure: The outer surface stress σir of the welded portion of the spot welded joint to be evaluated measured in the outer surface stress measurement procedure, the plate thickness t of the plate material of the spot welded joint to be evaluated, and the frequency Hz of the repeated load in the shear direction applied to the spot welded joint to be evaluated are input into the relational equation derived in the relational equation derivation procedure to calculate the inner surface stress σi' of the welded portion of the spot welded joint to be evaluated.

In the present invention, the "shear direction" means a direction perpendicular to the overlapping direction of the plate materials.
In the present invention, "internal stress" refers to the stress on the overlapping surface side of the plate material. In addition, the "internal stress of the weld" can be specifically exemplified by the stress at the center of the nugget of the weld. However, this is not limited thereto, and it is also possible to calculate the stress at the boundary between the nugget and the heat-affected zone of the weld, the average stress at a specified portion on the internal side of the weld, etc.
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 "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, the "thickness of a plate material" means the dimension of each plate material in the overlapping direction.
In the present invention, the term "measuring the external stress of a weld" is a concept that includes not only the measurement of the external stress of a weld itself, but also the measurement of the change in the external stress of a weld over time.
In the present invention, the term "calculating the internal stress of a weld" is a concept that includes not only the calculation of the internal stress of a weld itself, but also the calculation of the change in the internal stress of a weld over time.
In the present invention, the plate thickness t of the plate material and the frequency Hz of the repeated load input to the relational expression in the procedure for calculating the internal stress may be set values or may be actual measured values.

According to the present invention, in the relational expression derivation procedure, a static finite element method analysis and a coupled finite element method analysis are performed to derive a relational expression for estimating an inner surface stress σi of a welded portion, using the outer surface stress σhz of the welded portion, the plate thickness t of the plate material, and the frequency Hz of the repeated load as input parameters. Next, in the outer surface stress measurement procedure, a repeated load is applied to the spot-welded joint to be evaluated, and the outer surface stress σir of the welded portion is actually measured using a thermoelastic stress measurement method. Finally, in the inner surface stress calculation procedure, the outer surface stress σir of the welded portion of the spot-welded joint to be evaluated, which is actually measured in the outer surface stress measurement procedure, the plate thickness t of the spot-welded joint to be evaluated, and the frequency Hz of the repeated load applied to the spot-welded joint to be evaluated are input into the relational expression derived in the relational expression derivation procedure, to calculate the inner surface stress σi' of the welded portion of the spot-welded joint to be evaluated.
As described above, according to the present invention, the inner surface stress σi' of the welded portion of a spot-welded joint can be calculated using the relational equation derived in the relational equation derivation procedure and the outer surface stress σir of the welded portion of the spot-welded joint that is the evaluation target actually measured in the outer surface stress measurement procedure. Since the plate thickness t of the plate material and the frequency Hz of the repeated load are input as input parameters into the relational equation, the influence of heat conduction due to the plate thickness t of the plate material and the frequency Hz of the repeated load is reduced, and the inner surface stress σi' of the welded portion can be calculated with high accuracy.

In addition, according to the present invention, the internal stress σi′ of the weld can be calculated without requiring the load values (maximum load, minimum load) of the cyclic load actually applied to the spot-welded joint to be evaluated, and therefore has the advantage of being applicable even when the load value of the cyclic load for the object to be evaluated is unknown.
Furthermore, according to the present invention, the outer surface stress σir of the weld of the spot-welded joint, which is the evaluation target, is used, which is actually measured using a thermoelastic stress measurement method (the finite element method analysis is used only when deriving the relational equation in the relational equation derivation procedure), so it has the advantage of being applicable to complex shapes that are difficult to model accurately, such as the weld of a spot-welded joint.

In addition, in the present invention, if the relational equation deriving procedure is performed once to derive the relational equation, the same derived relational equation can be repeatedly used when performing the outer surface stress measurement procedure and the inner surface stress calculation procedure for multiple evaluation objects. In other words, when evaluating the inner surface stress of the welds of multiple evaluation objects using the present invention, it is not necessary to perform the relational equation deriving procedure as many times as the number of evaluation objects, and it is sufficient to perform it 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 results in a problem of huge 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 derivation 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 on 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 Hz 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 during which the repeated load is applied, and calculating an outer surface temperature of the welded portion based on the 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 σhz of the welded portion.

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 Hz 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 σhz of the welded portion. To convert the outer surface temperature of the welded portion into the outer surface stress σhz, a known relationship between temperature and stress may be used.

In the present invention, specifically, the procedure for deriving the relational equation includes a first relational equation deriving step of calculating the outer surface stress σf and the inner surface stress σi of the welded portion by performing a static finite element method analysis on a plurality of the numerical analysis models in which the plate thickness t of the plate material is changed, calculating an inner and outer stress ratio Rt, which is the ratio of the inner surface stress σi to the outer surface stress σf of the welded portion, for each plate thickness t, and deriving a first relational equation in which the inner and outer stress ratio Rt is expressed as an exponential function of the plate thickness t; and performing a plurality of coupled finite element method analyses in which the frequency Hz of the repeated load is changed on a plurality of the numerical analysis models in which the plate thickness t of the plate material is changed. It is preferable that the method includes a second relational equation deriving step of calculating the outer surface stress σhz of the welded portion for each frequency Hz of the repeated load, calculating a stress conversion ratio Rhz, which is the ratio of the outer surface stress σf of the welded portion calculated by performing static finite element analysis to the outer surface stress σhz of the welded portion calculated by performing coupled finite element analysis, for each frequency Hz of the repeated load, and deriving a second relational equation in which the stress conversion ratio Rhz is expressed as a power function of the frequency Hz of the repeated load for each thickness t of the plate material, and a third relational equation deriving step of deriving a third relational equation in which the coefficient of the power function is expressed as a linear function of the thickness t of the plate material.

Specifically, the internal stress calculation procedure preferably includes a coefficient calculation step of calculating the coefficient of the power function by inputting the plate thickness t of the plate material of the spot welded joint to be evaluated into the third relational expression; a stress conversion ratio calculation step of calculating the stress conversion ratio Rhz by inputting the frequency Hz of the repeated load in the shear direction applied to the spot welded joint to be evaluated and the calculated coefficient of the power function into the second relational expression; an external stress correction step of multiplying the external stress σir of the welded portion of the spot welded joint to be evaluated measured in the external stress measurement procedure by the calculated stress conversion ratio Rhz to calculate a corrected external stress σf ' of the welded portion; an internal stress ratio calculation step of calculating the internal and external stress ratio Rt by inputting the plate thickness t of the plate material of the spot welded joint to be evaluated into the first relational expression; and an internal stress calculation step of multiplying the calculated corrected external stress σf ' by the calculated internal and external stress ratio Rt to calculate the internal stress σi ' of the welded portion.
In order to solve the above-mentioned problem, the present invention provides an evaluation method for a thermoelastic stress measurement method, which measures a time-varying temperature distribution of an object to be measured by continuously imaging the object to be measured using an infrared imaging device while applying a cyclic load to the object to be measured for a predetermined time, and converts the measured time-varying temperature distribution into a time-varying stress distribution of the object to be measured, the method comprising: a stress analysis step of performing a stress analysis using an assumed maximum load and an assumed minimum load of the cyclic load on a numerical analysis model of the object to be measured, and calculating a stress distribution of the numerical analysis model; a heat flow velocity calculation step of calculating a heat flow velocity using the stress distribution of the numerical analysis model calculated in the stress analysis step, material properties of the object to be measured, and a frequency of the cyclic load; and a heat transfer analysis step of performing a heat transfer analysis using the heat flow velocity calculated in the heat flow velocity calculation step, and calculating a temperature distribution of the numerical analysis model, the heat flow velocity calculation step and the heat transfer analysis step being repeatedly performed for the predetermined time during which the cyclic load is applied, thereby calculating a temperature distribution of the numerical analysis model after the predetermined time has elapsed.
In the evaluation method of the thermoelastic stress measurement method according to the present invention, it is preferable that the heat flow rate calculation step includes a step of calculating a change in temperature over time for each element of the numerical analysis model based on the following equation (5), and a step of calculating a heat flow rate for each element of the numerical analysis model based on the following equation (6) or (7).
ΔT=−K T Δσ (5)
F = -2 · ΔT · ρ · Cp · Hz ... (6)
F = 2 · ΔT · ρ · Cp · Hz ... (7)
In the above formula (5), ΔT represents the change in temperature over time, K represents the thermoelastic coefficient of the object to be measured, Δσ represents the change in stress over time, and T represents the temperature of the numerical analysis model.
In the above formulas (6) and (7), F is the heat flow rate, ρ is the density of the object to be measured, Cp is the specific heat of the object to be measured, and Hz is the frequency of the repeated load. When the load changes in the compression direction, the above formula (6) is used, and when the load changes in the tension direction, the above formula (7) is used.

According to the present invention, it is possible to evaluate the internal stress of the welded portion of a spot-welded joint using the measurement results of the thermoelastic stress measurement method. Also, according to the present invention, it is possible to easily evaluate the measurement results of the thermoelastic stress measurement method.

1 is a flow chart showing an outline of a procedure for evaluating an internal stress 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 flow chart specifically showing the contents of a relational equation deriving step S1 shown in FIG. 1 . FIG. 4 is a diagram showing an example of an internal and external stress ratio Rt calculated for each plate thickness t in the first relational expression derivation step S11 shown in FIG. 3. FIG. 4 is a diagram showing an example of a stress conversion ratio Rhz calculated for each frequency Hz of repeated load for a numerical analysis model having a certain plate thickness t in the second relational expression derivation step S12 shown in FIG. 3. 4 is a diagram showing an example of the relationship between the plate thickness t of the plate material in the numerical analysis model and the coefficients s1 and s2 of the power function of the second relational expression derived in the second relational expression derivation step S12 shown in FIG. 3 . FIG. FIG. 2 is a flow chart specifically showing the contents of an inner surface stress calculation procedure S3 shown in FIG. 1 . FIG. 4 is a flow chart showing an outline of a procedure of coupled finite element analysis executed in the second relational expression deriving step S12 shown in FIG. 3 . 1 shows an example of an outer surface stress distribution of a numerical analysis model obtained by performing a static finite element method analysis in an embodiment of the present invention. 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 outer surface stress distribution when a maximum load is applied, obtained by performing a thermoelastic stress measurement method in an embodiment of the present invention.

Hereinafter, a method for evaluating internal stress of a spot-welded joint according to one embodiment of the present invention (hereinafter, simply referred to as "internal stress evaluation method") will be described with reference to the attached drawings as appropriate.
FIG. 1 is a flow diagram showing a schematic procedure of the inner surface stress evaluation 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.

2, the method for evaluating the internal stress according to the present embodiment is a method for evaluating the internal stress of the welded portion 13 of the spot welded joint 10 formed by spot welding the overlapping plate materials 11 and 12 by applying repeated loads in the shear direction (X direction) using a fatigue testing machine or the like to the spot welded joint 10. The internal stress of the welded portion 13 means the stress on the overlapping surfaces of the plate materials 11 and 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 and 12) among the stresses generated in the welded portion 13. Specifically, the stress of the center portion 131 of the nugget 13a of the welded portion 13 can be exemplified as the internal stress of the welded portion 13. The external stress of the welded portion 13 means the stress on the surface opposite to the overlapping surfaces of the plate materials 11 and 12 (surface 11b of the plate material 11 and surface 12b of the plate material 12) among the stresses generated in the welded portion 13. Specifically, an example of the external stress of the welded portion 13 is the stress of the portion 111 or portion 121 of the heat-affected portion of the welded portion 13, which is located at a position corresponding to the center portion 131 of the nugget 13a of the welded portion 13 when viewed from the overlapping direction (Z direction) of the plate materials 11 and 12.

In this embodiment, in the external stress measurement procedure S2 described later, an infrared imaging device is placed opposite 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, so the plate thickness t of the plate material 11 is used as the plate thickness used in the relational equation derivation procedure S1 and the internal stress calculation procedure S3 described later. However, in the external stress measurement procedure S2 described later, an infrared imaging device can be placed opposite 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 plate thickness t of the plate material 12 is used as the plate thickness used in the relational equation derivation procedure S1 and the internal stress calculation procedure S3 described later. In the example shown in FIG. 2, the plate thicknesses t of the plates 11 and 12 are the same value, but they can also be different values.

As shown in FIG. 1, the method for evaluating inner surface stress according to this embodiment includes a relational equation deriving step S1, an outer surface stress measuring step S2, and an inner surface stress 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 static finite element method analysis (static FEM analysis) using an assumed maximum load of repeated loads and a coupled finite element method 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 are performed on a numerical analysis model of a spot welded joint 10 as shown in FIG. 2.
Then, in the relational equation derivation step S1, the outer surface stress σhz of the welded portion 13 calculated by executing the coupled FEM analysis, the plate thickness t of the plate material 11 (see FIG. 2A), and the frequency Hz of the repeated load are used as input parameters to derive a relational equation for estimating the inner surface stress σi of the welded portion 13. This relational equation is composed of first to third relational equations described below, an equation (Rt=σi/σf) defining an inner and outer stress ratio Rt described below, and an equation (Rhz=σf/σhz) defining a stress conversion ratio Rhz described below.

FIG. 3 is a flow chart specifically showing the contents of the relational expression deriving step S1.
3, the relational equation deriving procedure S1 of this embodiment includes a first relational equation deriving step S11, a second relational equation deriving step S12, and a third relational equation deriving step S13. Each of steps S11 to S13 will be described in order below.

[First relational equation derivation step S11]
In the first relational equation deriving step S11, a static FEM analysis using an assumed maximum load of the repeated load is performed on a plurality of numerical analysis models in which the plate thickness t of the plate material 11 is changed, thereby calculating the outer surface stress σf and the inner surface stress σi of the welded portion 13. Specifically, in addition to the assumed maximum 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 and 12, and boundary conditions (symmetry conditions, constraint conditions, etc.) are used in the static FEM analysis.
In this embodiment, a static FEM analysis is performed to calculate the change over time in stress distribution of a numerical analysis model of the spot-welded joint 10. In other words, the change over time in stress (also called the sum of principal stresses) is calculated for each element of the numerical analysis model. Then, the stress distribution after application of the expected maximum load is calculated by adding the change over time in the stress distribution to an initial value (e.g., 0) of the stress distribution, and the outer surface stress σf and inner surface stress σi of the welded portion 13 are calculated based on this calculated stress distribution.
As software for performing static FEM 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.

Next, in the first relational equation deriving step S11, the internal/external stress ratio Rt (Rt = σi/σf), which is the ratio of the internal stress σi to the external stress σf of the welded portion 13 calculated as described above, is calculated for each plate thickness t.
FIG. 4 is a diagram showing an example of the internal and external stress ratio Rt calculated for each plate thickness t. In the example shown in FIG. 4, the internal and external stress ratio Rt is calculated for each plate thickness t = 0.8 mm, 1.2 mm, 1.6 mm, and 2.0 mm. As shown in FIG. 4, according to the knowledge of the inventors, it was found that the internal and external stress ratio Rt can be accurately approximated by an exponential function of the plate thickness t. Therefore, in the first relational expression deriving step S11, based on the internal and external stress ratio Rt calculated for each plate thickness t, a first relational expression in which the internal and external stress ratio Rt is expressed as an exponential function of the plate thickness t is derived by an approximation calculation such as the least squares method. That is, the first relational expression represented by the following formula (1) is derived.
Rt = c1 · e ^{d1 · t} ... (1)
In the above formula (1), c1 and d1 are predetermined coefficients (constants), and e is the base of the natural logarithm.

[Step S12 for deriving the second relational expression]
In the second relational equation deriving step S12, a plurality of coupled FEM analyses are performed with different frequencies Hz of the repeated load for a plurality of numerical analysis models with different thicknesses t of the plate material 11, thereby calculating the outer surface stress σhz of the weld 13 for each frequency Hz of the repeated load. The specific content of the coupled FEM analysis performed in the second relational equation deriving step S12 will be described later.

Next, in the second relational expression derivation step S12, a stress conversion ratio Rhz (Rhz=σf/σhz), which is the ratio of the outer surface stress σf of the welded portion 13 calculated by performing static FEM analysis to the outer surface stress σhz of the welded portion 13 calculated by performing coupled FEM analysis, is calculated for each frequency Hz of the repeated load. Specifically, for a numerical analysis model of a certain plate thickness t, the stress conversion ratio Rhz is calculated for each frequency Hz of the repeated load, and then, for a numerical analysis model of another plate thickness t, the stress conversion ratio Rhz is calculated for each frequency Hz of the repeated load. The above procedure is repeatedly performed for the numerical analysis models of all plate thicknesses t.
FIG. 5 is a diagram showing an example of the stress conversion ratio Rhz calculated for each frequency Hz of the repeated load for a numerical analysis model with a certain plate thickness t. In the example shown in FIG. 5, for a numerical analysis model with a plate thickness t = 1.2 mm, the stress conversion ratio Rhz is calculated for each frequency Hz = 1 Hz, 3 Hz, 5 Hz, 7 Hz, 10 Hz, 15 Hz, 50 Hz, 100 Hz, 200 Hz, and 400 Hz. As shown in FIG. 5, according to the knowledge of the inventors, it was found that for any numerical analysis model with a plate thickness t, the stress conversion ratio Rhz can be accurately approximated by a power function of the frequency Hz of the repeated load. Therefore, in the second relational expression derivation step S12, based on the stress conversion ratio Rhz calculated for each frequency Hz of the repeated load, a second relational expression in which the stress conversion ratio Rhz is expressed as a power function of the frequency Hz of the repeated load is derived for each plate thickness t by an approximation calculation such as the least squares method. That is, the second relational expression represented by the following formula (2) is derived for each plate thickness t.
Rhz = s1 · Hz ^s2 ... (2)
In the above formula (2), s1 and s2 represent predetermined coefficients.

[Third relational expression derivation step S13]
FIG. 6 is a diagram showing an example of the relationship between the plate thickness t of the plate material 11 in the numerical analysis model and the coefficients s1 and s2 of the power function of the second relational expression derived in the second relational expression deriving step S12.
As shown in Fig. 6, according to the findings of the present inventors, it has been found that the coefficients s1 and s2 of the power function of the second relational expression can be accurately approximated by a linear function of the thickness t of the plate material 11. Therefore, in the third relational expression derivation step S13, a third relational expression in which the coefficients s1 and s2 of the power function are expressed by a linear function of the thickness t of the plate material 11 is derived by an approximation calculation such as the least squares method based on the values of the coefficients s1 and s2 corresponding to each plate thickness t (in the example shown in Fig. 6, the plate thicknesses t = 0.8 mm, 1.2 mm, 1.6 mm, and 2.0 mm). That is, the third relational expression represented by the following formulas (3) and (4) is derived.
s1=a1·t+b1... (3)
s2 = a2 · t + b2 ... (4)
In the above formula (3), a1 and b1 are predetermined coefficients (constants), and in the above formula (4), a2 and b2 are predetermined coefficients (constants).

In the relational equation deriving procedure S1 of this embodiment, the first relational equation to the third relational equation represented by the formulas (1) to (4) are derived by executing the first relational equation to the third relational equation, the formula (Rt=σi/σf) defining the internal/external stress ratio Rt, and the formula (Rhz=σf/σhz) defining the stress conversion ratio Rhz, which are relational equations for estimating the inner surface stress σi of the welded portion 13 calculated by executing a static FEM analysis using the outer surface stress σhz of the welded portion 13 calculated by executing a coupled FEM analysis, the plate thickness t of the plate material 11, and the frequency Hz of the repeated load as input parameters.
Specifically, coefficients s1 and s2 are calculated by inputting the plate thickness t, which is an input parameter, into the third relational expression. The coefficients s1 and s2 and the frequency Hz of the repeated load, which is an input parameter, are input into the second relational expression to calculate the stress conversion ratio Rhz. When the stress conversion ratio Rhz is multiplied by the external stress σhz of the welded portion 13, which is an input parameter, the external stress σf is calculated from the equation that defines the stress conversion ratio Rhz. On the other hand, the internal/external stress ratio Rt is calculated by inputting the plate thickness t, which is an input parameter, into the first relational expression. When the internal/external stress ratio Rt is multiplied by the external stress σf calculated as above, the internal stress σi is calculated from the equation that defines the internal/external stress ratio Rt. Therefore, the relational equation composed of the first to third relational equations, the equation defining the internal and external stress ratio Rt, and the equation defining the stress conversion ratio Rhz is a relational equation for estimating the internal stress σi of the welded portion 13 using the external stress σhz of the welded portion 13, the plate thickness t of the plate material 11, and the frequency Hz of the repeated load as input parameters.

<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 imaging area of the spot welded joint 10 to be evaluated, and thus to measure the external stress σir of the welded portion 13. Note that the specific content of the thermoelastic stress measurement method is publicly known, so a detailed description thereof will be omitted here.

<Inner surface stress calculation procedure S3>
1, the outer surface stress σir of the welded portion 13 of the spot-welded joint 10 to be evaluated measured in the outer surface stress measurement procedure S2, the plate thickness t of the plate material 11 of the spot-welded joint 10 to be evaluated, and the frequency Hz of the repeated load in the shear direction applied to the spot-welded joint 10 to be evaluated are input into the relational equation derived in the relational equation derivation procedure S1. In this way, the inner surface stress σi' of the welded portion 13 of the spot-welded joint 10 to be evaluated is calculated.

FIG. 7 is a flow chart specifically showing the contents of the inner surface stress calculation procedure S3.
7, the inner surface stress calculation procedure S3 of this embodiment includes a coefficient calculation step S31, a stress conversion ratio calculation step S32, an outer surface stress correction step S33, an inner/outer stress ratio calculation step S34, and an inner surface stress calculation step S35. Each of steps S31 to S35 will be described below in order.

[Coefficient calculation step S31]
In the coefficient calculation step S31, the plate thickness t of the plate material 11 of the spot welded joint 10 to be evaluated is input into the third relational equation (s1 = a1 · t + b1, s2 = a2 · t + b2) to calculate the coefficients s1 and s2 of the power function of the second relational equation.

[Stress conversion ratio calculation step S32]
In the stress conversion ratio calculation step S32, the frequency Hz of the repeated load in the shear direction applied to the spot welded joint 10 to be evaluated and the coefficients s1 and s2 of the power function calculated in the coefficient calculation step S31 are input into a second relational equation (Rhz = s1 · Hz ^s2 ) to calculate the stress conversion ratio Rhz.

[External surface stress correction step S33]
In the outer surface stress correction step S33, the outer surface stress σir of the welded portion 13 of the spot-welded joint 10 to be evaluated, measured in the outer surface stress measurement procedure S2, is multiplied by the stress conversion ratio Rhz calculated in the stress conversion ratio calculation step S32 to calculate a corrected outer surface stress σf' of the welded portion 13. The outer surface stress σir measured in the outer surface stress measurement procedure S2 may be a value smaller than the outer surface stress actually generated in the welded portion 13, but by multiplying by the stress conversion ratio Rhz, it is possible to calculate an outer surface stress σf' equivalent to the outer surface stress actually generated.

[Internal and external stress ratio calculation step S34]
In the internal/external stress ratio calculation step S34, the plate thickness t of the plate material 11 of the spot welded joint 10 to be evaluated is input into a first relational expression (Rt=c1·e ^{d1 ·t} ) to calculate the internal/external stress ratio Rt.

[Inner surface stress calculation step S35]
In the internal stress calculation step S35, the corrected external stress σf′ calculated in the external stress correction step S33 is multiplied by the internal/external stress ratio Rt calculated in the internal/external stress ratio calculation step S34 to calculate the internal stress σi′ of the welded portion 13. As described above, the external stress σf′ can be expected to be equivalent to the external stress that actually occurs, and therefore the internal stress σi′ calculated by multiplying it by the internal/external stress ratio Rt can also be expected to be equivalent to the internal stress that actually occurs.

In the inner surface stress calculation procedure S3 of this embodiment, the coefficient calculation step S31 to the inner surface stress calculation step S35 described above are executed to calculate the inner surface stress σi' of the welded portion 13. In other words, by inputting the outer surface stress σir of the welded portion 13 measured in the outer surface stress measurement procedure S2 instead of the outer surface stress σhz of the welded portion 13, which is one of the input parameters of the relational expressions (first relational expression to third relational expression, Rt = σi/σf, Rhz = σf/σhz) for estimating the inner surface stress σi of the welded portion 13, the inner surface stress σi' of the welded portion 13 can be calculated with high accuracy.
In the present embodiment, the inner stress calculation procedure S3 is performed in the order of coefficient calculation step S31, stress conversion ratio calculation step S32, outer surface stress correction step S33, inner and outer stress ratio calculation step S34, and inner stress calculation step S35, but the present invention is not limited to this. The inner stress calculation step S35 is performed last, and the coefficient calculation step S31, stress conversion ratio calculation step S32, and outer surface stress correction step S33 must be performed in this order. However, the inner and outer stress ratio calculation step S34 may be performed before the coefficient calculation step S31, between the coefficient calculation step S31 and the stress conversion ratio calculation step S32, or between the stress conversion ratio calculation step S32 and the outer surface stress correction step S33.

Hereinafter, the specific contents of the coupled FEM analysis executed in the second relational equation deriving step S12 of the relational equation deriving procedure S1 will be described.
8 is a flow diagram showing an outline of the procedure of the coupled FEM analysis executed in the second relational expression deriving step S12. As shown in FIG. 8, the coupled FEM analysis executed in the second relational expression deriving step S12 includes a stress analysis step S121, a heat flux calculation step S122, a heat transfer analysis step S123, and a conversion step S125. Each of steps S121 to S125 will be described in order below.

[Stress analysis step S121]
2, 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, and 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, 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 S121 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 S122 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 S121 to S125.

[Heat flux calculation step S122]
In the heat flux calculation step S122, 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 S121, 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 period Hz of the repeated load.
Specifically, in the heat flux calculation step S122 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 (5).
ΔT=−K T Δσ (5)
In the above formula (5), 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 S122 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 S122, a heat flux F is calculated for each element of the numerical analysis model based on the following formula (6) or (7).
F = -2 · ΔT · ρ · Cp · Hz ... (6)
F = 2 · ΔT · ρ · Cp · Hz ... (7)
In the above formulas (6) and (7), 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 (6) is used, and when the load changes in the tension direction, the above formula (7) is used.
The software for executing the heat flux calculation step S122 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 (5) to (7), but the present invention is not limited to this.

[Heat transfer analysis step S123]
In the heat transfer analysis step S123, a heat transfer analysis is performed using the heat flux F calculated in the heat flux calculation step S122, and a temperature distribution of the numerical analysis model is calculated. Specifically, in the heat transfer analysis step S123 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 S123 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.

In the relational equation derivation procedure S1 (second relational equation derivation step S12), the above heat flux calculation step S122 and heat transfer analysis step S123 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 S124 of FIG. 8, it is determined whether the predetermined time has elapsed, and if the predetermined time has not elapsed (if "No" in step S124 of FIG. 8), the heat flux calculation step S122 and heat transfer analysis step S123 are executed again. If the predetermined time has elapsed (if "Yes" in step S124 of FIG. 8), the calculations in the heat flux calculation step S122 and heat transfer analysis step S123 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 S125]
In the conversion step S125, 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 σhz of the welded portion 13. A known relational expression between temperature and stress may be used for the conversion into the outer surface stress σhz.

By performing the above-described coupled FEM analysis in the second relational equation derivation step S12 of the relational equation derivation procedure S1, it is possible to calculate the outer surface stress σhz equivalent to the outer surface stress σir of the welded portion 13 measured using a thermoelastic stress measurement method in the outer surface stress measurement procedure S2.
Therefore, the above-mentioned coupled FEM analysis can also be used as a method for evaluating the measurement results of the thermoelastic stress measurement method. The evaluation method of the thermoelastic stress measurement method is not limited to a spot-welded joint as a measurement object to which the thermoelastic stress measurement method is applied, and can be used for any measurement object such as other welded structures. Specifically, the above-mentioned stress analysis step S121 to heat transfer analysis step S123 are performed for a numerical analysis model of the measurement object (including repeatedly performing the heat flux calculation step S122 and the heat transfer analysis step S123 until a predetermined time has elapsed), thereby calculating the temperature distribution of the numerical analysis model of the measurement object, while actually measuring the temperature distribution of the measurement object using the thermoelastic stress measurement method (infrared imaging device), and comparing the two results, it is possible to evaluate the measurement results of the thermoelastic stress measurement method. In addition, by performing up to the conversion step S125, it is also possible to calculate the stress distribution of the numerical analysis model of the measurement object, while actually measuring the stress distribution of the measurement object using the thermoelastic stress measurement method, and comparing the two results, it is also possible to evaluate the measurement results of the thermoelastic stress measurement method.

According to the inner surface stress evaluation method of the present embodiment described above, it is possible to calculate the inner surface stress σi′ of the welded portion 13 of the spot-welded joint 10 by using the relational equation derived in the relational equation derivation procedure S1 and the outer surface stress σir of the welded portion 13 of the spot-welded joint 10 that is the evaluation target actually measured in the outer surface stress measurement procedure S2. Since the plate thickness t of the plate material 11 and the frequency Hz of the repeated load are input as input parameters into the relational equation, the influence of heat conduction due to the plate thickness t of the plate material 11 and the frequency Hz of the repeated load is reduced, and the inner surface stress σi′ of the welded portion 13 can be calculated with high accuracy.
In addition, according to the internal stress evaluation method of this embodiment, the internal stress σi′ of the welded portion 13 can be calculated without requiring the load value of the repeated load applied to the spot-welded joint 10 to be evaluated, and therefore has the advantage of being applicable even when the load value of the repeated load for the evaluation object is unknown.
Furthermore, according to the internal stress evaluation method of this embodiment, the external stress σir of the welded portion 13 of the spot-welded joint 10, which is the evaluation object actually measured using a thermoelastic stress measurement method, is used (FEM analysis is used only when deriving the relational equation in the relational equation derivation step S1), so it has the advantage of being applicable to complex shapes that are difficult to model accurately, such as the welded portion 13 of the spot-welded joint 10.

Below, we will explain an example of implementing the internal stress evaluation method according to this embodiment.

In this example, the spot welded joint 10 formed by spot welding plate materials 11 and 12, which are 590 MPa-class steel plates with a plate thickness t of 1.2 mm, was evaluated. A fatigue testing machine was used to apply repeated loads (tensile loads) in the shear direction under the conditions of maximum load: 2.736 kN, minimum load: 0.136 kN, and frequency Hz: 7 Hz for a specified time (10 sec), and the internal stress of the welded portion 13 was evaluated.

In this embodiment, in the first relational equation deriving step S11 of the relational equation deriving procedure S1, a static FEM analysis was performed using a maximum assumed load (2.736 kN, which is the same as the actual maximum load) for repeated loads for a plurality of numerical analysis models (four types of plate thicknesses t=0.8 mm, 1.2 mm, 1.6 mm, and 2.0 mm) as shown in Fig. 2, to calculate the outer surface stress σf and the inner surface stress σi of the weld 13. In the static FEM analysis, the Young's modulus of the plate materials 11 and 12 was set to 205.9 GPa, and the Poisson's ratio was set to 0.3.
FIG. 9 shows an example of the outer surface stress distribution of the numerical analysis model obtained by performing static FEM analysis in this embodiment. Specifically, FIG. 9 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 passing through the center of the welded portion 13 and 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 FIG. 9 was 457 MPa (compressive stress). In addition, the inner surface stress σi of the welded portion 13 calculated based on the inner surface stress distribution (not shown) of the numerical analysis model obtained by performing static FEM analysis was 1279 MPa (compressive stress). The outer surface stress σf calculated as described above was a value equivalent to the outer surface stress actually generated in the welded portion 13 measured using a strain gauge.
In the first relational expression deriving step S11, the internal and external stress ratio Rt (Rt = σi/σf) was calculated for each plate thickness t. The example shown in Fig. 4 above is the internal and external stress ratio Rt for each plate thickness t obtained in this embodiment. As a result, the first relational expression was derived in which the internal and external stress ratio Rt is expressed as an exponential function of the plate thickness t.

In this embodiment, in the second relational equation derivation step S12 of the relational equation derivation procedure S1, similarly to the first relational equation derivation step S11, multiple coupled FEM analyses were performed on multiple numerical analysis models (four types, plate thickness t = 0.8 mm, 1.2 mm, 1.6 mm, and 2.0 mm) as shown in Figure 2, with the frequency Hz of the repeated load changed in the range of 1 to 400 Hz, to calculate the outer surface stress σhz of the weld 13 for each frequency Hz of the repeated load.
In the heat flux calculation step S122 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 (6) was used when the repeated load changed from the assumed maximum load (2.736 kN, the same as the actual maximum load) to the assumed minimum load (0.136 kN, the same as the actual minimum load), and the above-mentioned formula (7) was used when the repeated load changed from the assumed minimum load to the assumed maximum load.
In the heat transfer analysis step S123 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 , and the emissivity of the plates 11 and 12 was set to 0.8.

FIG. 10 shows an example of the outer surface stress distribution of the numerical analysis model obtained by performing the coupled FEM analysis in this embodiment. Specifically, FIG. 10 shows the outer surface stress distribution when the assumed maximum load (2.736 kN) of the repeated load with a frequency of 7 Hz 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 passing through the center of the welded portion 13 and parallel to the XZ plane. It can be seen that the outer surface stress distribution shown in FIG. 10 has a smaller stress value than the outer surface stress distribution of the numerical analysis model obtained by performing the static FEM analysis shown in FIG. The outer surface stress σhz of the welded portion 13 calculated based on the outer surface stress distribution of the numerical analysis model shown in FIG. 10 was 135 MPa (compressive stress).
In the second relational expression deriving step S12, the stress conversion ratio Rhz (Rhz=σf/σhz), which is the ratio of the outer surface stress σf of the welded portion 13 calculated by performing the static FEM analysis to the outer surface stress σhz of the welded portion 13 calculated by performing the coupled FEM analysis, was calculated for each frequency Hz of the repeated load. The example shown in Fig. 5 above is the stress conversion ratio Rhz for each frequency Hz obtained in the case of the plate thickness t = 1.2 mm in this embodiment. As a result, the second relational expression in which the stress conversion ratio Rhz is expressed as a power function of the frequency Hz of the repeated load was derived.
Then, in the third relational equation deriving step S13 of the relational equation deriving procedure S1, a third relational equation was derived in which the coefficients s1 and s2 of the power function of the second relational equation were expressed as a linear function of the thickness t of the plate material 11. The above-mentioned Fig. 6 shows the relationship between the thickness t of the plate material 11 and the coefficients s1 and s2 of the power function used to derive the third relational equation of this embodiment.

In this embodiment, in the external stress measurement procedure S2, as described above, a fatigue testing machine was used to apply repeated loads (tensile loads) in the shear direction to the spot-welded joint 10 to be evaluated under conditions of maximum load: 2.736 kN, minimum load: 0.136 kN, and frequency: 7 Hz 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).
Fig. 11 shows the outer surface stress distribution when the maximum load was applied, which was obtained by performing the thermoelastic stress measurement method in this embodiment. It can be seen that the outer surface stress distribution shown in Fig. 11 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. 10. The outer surface stress σir calculated based on the outer surface stress distribution shown in Fig. 11 was 139 MPa (compressive stress).

In this embodiment, in the coefficient calculation step S31 of the internal stress calculation procedure S3, the plate thickness t of the plate material 11, ie, 1.2 mm, was input into the third relational expression to calculate the coefficient s1=4.99 and the coefficient s2=-0.20.
In the stress conversion ratio calculation step S32 of the inner surface stress calculation procedure S3, the stress conversion ratio Rhz = 3.4 was calculated by inputting the repeated load frequency Hz = 7 Hz, coefficient s1 = 4.99, and coefficient s2 = -0.20 into the second relational equation.
In the outer stress correction step S33 of the inner stress calculation procedure S3, the outer stress σir of the welded portion 13 = 139 MPa was multiplied by the stress conversion ratio Rhz = 3.4 to calculate the corrected outer stress σf' of the welded portion 13 = 473 MPa (compressive stress).
In the internal/external stress ratio calculation step S34 of the internal stress calculation procedure S3, the plate thickness t of the plate material 11 of 1.2 mm was input into the first relational expression to calculate the internal/external stress ratio Rt of 2.66.
In the inner surface stress calculation step S35 of the inner surface stress calculation procedure S3, the corrected outer surface stress σf′=473 MPa was multiplied by the inner/outer stress ratio Rt=2.66 to calculate the inner surface stress σi′=1258 MPa (compressive stress) of the welded portion 13.

As described above, the inner stress σi' of the welded portion 13 calculated in this embodiment is 1258 MPa, and if we assume that the inner stress σi = 1279 MPa calculated by static FEM analysis is the true value, the absolute value of the error ((σi' - σi)/σi x 100) is only 1.6%, so it is found that the inner stress σi' of the welded portion 13 of the spot welded joint 10 can be accurately evaluated using the measurement results of the thermoelastic stress measurement method.
After the above evaluation, the welded portion 13 of the spot-welded joint 10 to be evaluated in this example was cut and its cross section was observed, and it was found that the welded portion 13 had a relatively simple shape. Therefore, it is considered that there is no problem in assuming that the internal stress σi calculated by the static FEM analysis as described above is a true value.

10: Spot welded joint 11, 12: Plate material 13: Welded part S1: Procedure for deriving relational equation S2: Procedure for measuring outer surface stress S3: Procedure for calculating inner surface stress

Claims (6)

A method for evaluating an internal stress of a welded portion of a spot welded joint formed by spot welding overlapping plate materials when a repeated load in a shear direction is applied to the spot welded joint, comprising:
a relational equation derivation step of deriving a relational equation for estimating an inner surface stress σi of the welded portion calculated by performing a static finite element method analysis using an assumed maximum load of the repeated load and a coupled finite element method analysis of a stress field and a temperature field using an assumed maximum load and an assumed minimum load of the repeated load on a numerical analysis model of the spot welded joint, with the outer surface stress σhz of the welded portion calculated by performing the coupled finite element method analysis, the plate thickness t of the plate material, and the frequency Hz of the repeated load as input parameters;
an outer surface stress measurement procedure of applying the cyclic load to the spot welded joint to be evaluated and measuring an outer surface stress σir of the welded portion using a thermoelastic stress measurement method;
an inner surface stress calculation step of calculating an inner surface stress σ′ of the weld portion of the spot welded joint to be evaluated by inputting the outer surface stress σir of the weld portion of the spot welded joint to be evaluated measured in the outer surface stress measurement step, the plate thickness t of the plate material of the spot welded joint to be evaluated, and the frequency Hz of a repeated load in a shear direction applied to the spot welded joint to be evaluated into the relational equation derived in the relational equation derivation step.
A method for evaluating internal stress of a spot welded joint. 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, the material properties of the spot welded joint, and the frequency Hz 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 σhz of the welded portion.
The method for evaluating internal stress of a spot welded joint according to claim 1. The procedure for deriving the relational expression is as follows:
a first relational equation deriving step of calculating an outer surface stress σf and an inner surface stress σi of the welded portion by performing a static finite element method analysis on a plurality of the numerical analysis models in which the plate thickness t of the plate material is changed, and calculating an inner and outer stress ratio Rt, which is a ratio of the inner surface stress σi to the outer surface stress σf of the welded portion, for each plate thickness t, and deriving a first relational equation in which the inner and outer stress ratio Rt is expressed as an exponential function of the plate thickness t;
A second relational equation deriving step of calculating an outer surface stress σhz of the welded portion for each frequency Hz of the repeated load by performing a plurality of coupled finite element method analyses with a different frequency Hz of the repeated load for a plurality of the numerical analysis models in which the thickness t of the plate material is changed, and calculating a stress conversion ratio Rhz, which is the ratio of the outer surface stress σf of the welded portion calculated by performing a static finite element method analysis to the outer surface stress σhz of the welded portion calculated by performing the coupled finite element method analysis, for each frequency Hz of the repeated load, and deriving a second relational equation in which the stress conversion ratio Rhz is expressed as a power function of the frequency Hz of the repeated load for each thickness t of the plate material;
A third relational equation deriving step of deriving a third relational equation in which the coefficient of the power function is expressed as a linear function of the plate thickness t of the plate material.
3. The method for evaluating internal stress of a spot welded joint according to claim 1 or 2. The inner surface stress calculation procedure includes:
A coefficient calculation step of calculating a coefficient of the power function by inputting a plate thickness t of the plate material of the spot welded joint to be evaluated into the third relational expression;
A stress conversion ratio calculation step of calculating the stress conversion ratio Rhz by inputting the frequency Hz of a repeated load in a shear direction applied to the spot welded joint to be evaluated and the coefficient of the calculated power function into the second relational expression;
an outer surface stress correction step of multiplying the outer surface stress σir of the welded portion of the spot welded joint to be evaluated, measured in the outer surface stress measurement procedure, by the calculated stress conversion ratio Rhz to calculate a corrected outer surface stress σf' of the welded portion;
An internal and external stress ratio calculation step of calculating the internal and external stress ratio Rt by inputting the plate thickness t of the plate material of the spot welded joint to be evaluated into the first relational expression;
and an inner surface stress calculation step of multiplying the calculated corrected outer surface stress σf′ by the calculated internal and external stress ratio Rt to calculate an inner surface stress σi′ of the welded portion.
The method for evaluating internal stress of a spot welded joint according to claim 3. A method for evaluating a thermoelastic stress measurement method, comprising the steps of: applying a repeated load to an object to be measured for a predetermined period of time, continuously imaging the object using an infrared imaging device, measuring a change in temperature distribution over time in the object to be measured, and converting the measured change in temperature distribution over time into a change in stress distribution over time in the object to be measured, comprising:
a stress analysis step of performing a stress analysis using an assumed maximum load and an assumed minimum load of the repeated load on a numerical analysis model of the object to be measured, and calculating a stress distribution of the numerical analysis model;
a heat flow rate calculation step of calculating a heat flow rate using the stress distribution of the numerical analysis model calculated in the stress analysis step, the material properties of the object to be measured, and the frequency of the repeated load;
a heat transfer analysis step of performing a heat transfer analysis using the heat flow rate calculated in the heat flow rate calculation step, and calculating a temperature distribution in the numerical analysis model;
The heat flow rate calculation step and the heat transfer analysis step are repeatedly performed for a predetermined time during which the repeated load is applied, thereby calculating a temperature distribution in the numerical analysis model after the predetermined time has elapsed.
A method for evaluating a thermoelastic stress measurement method. The heat flow rate calculation step includes:
calculating a change in temperature over time for each element of the numerical analysis model based on the following formula (5);
Calculating a heat flow rate for each element of the numerical analysis model based on the following formula (6) or (7),
The evaluation method for thermoelastic stress measurement according to claim 5 .
ΔT=−K T Δσ (5)
F = -2 · ΔT · ρ · Cp · Hz ... (6)
F = 2 · ΔT · ρ · Cp · Hz ... (7)
In the above formula (5), ΔT represents the change in temperature over time, K represents the thermoelastic coefficient of the object to be measured, Δσ represents the change in stress over time, and T represents the temperature of the numerical analysis model.
In the above formulas (6) and (7), F is the heat flow rate, ρ is the density of the object to be measured, Cp is the specific heat of the object to be measured, and Hz is the frequency of the repeated load. When the load changes in the compression direction, the above formula (6) is used, and when the load changes in the tension direction, the above formula (7) is used.

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