JP7522354B2 - Crack state estimation method - Google Patents

Description

The present invention relates to a method for estimating the state of a crack (crack position, crack length) in a plate-like or tubular member having a crack on its inner surface. In particular, the present invention relates to a simple and versatile method for estimating the state of a crack.

In various types of mechanical structures, it is sometimes necessary to evaluate the fatigue strength when a component that constitutes the mechanical structure has a crack. Specifically, it may be necessary to evaluate whether or not a crack will grow under a load acting on the mechanical structure, and if growth is permitted, to evaluate the number of repeated load applications until the length (depth) of the crack reaches a critical length (i.e., the fatigue life) to evaluate the soundness of the mechanical structure.

In the above evaluation, it is necessary to know the state of the crack, that is, the position and length of the crack. However, if the crack is inside the mechanical structure (the inner surface of a component that constitutes the mechanical structure) and cannot be seen from the outside, the state of the crack cannot be known from the outside. For this reason, various non-destructive methods are sometimes used to detect the state of the crack. Specifically, methods are sometimes used in which ultrasonic waves, X-rays, infrared rays, etc. are irradiated to the mechanical structure, or a magnetic field, current, voltage, etc. are applied to the mechanical structure to detect the state of the crack by detecting the disturbance of the field (magnetic field, electric potential field, temperature field, etc.) caused by the presence of the crack. However, all of these methods have problems such as the need to use special equipment and the need to determine in advance the relationship between the disturbance of the field and the state of the crack.

On the other hand, methods have also been proposed for detecting the state of cracks based on the amount of deformation (strain) of a component caused by the application of an external force to the component (e.g., Non-Patent Documents 1 and 2).

Non-Patent Document 1 describes a method in which a strain gauge is attached to the back surface of the test piece facing the tip of the crack, compliance (deformation amount/load, the inverse of stiffness) is calculated from the relationship between the output (strain value) and the test force, and the crack length is calculated based on the relationship between this compliance and the crack length. This method is a technology that utilizes the fact that the stiffness of the test piece changes with the change in crack length, but the relationship between compliance and crack length is formulated individually for each type of test piece, and its application is limited to individual test pieces, resulting in a problem of lack of versatility.

Non-Patent Document 2 proposes a method for non-destructively detecting the occurrence and growth of internal cracks (increase in crack length) in spot welds of thin steel sheets based on the output of a strain gauge. However, as with Non-Patent Document 1, it is necessary to determine the relationship between strain and crack length in advance, which is problematic as it lacks versatility.

Non-Patent Document 3 proposes a method for approximately analyzing the effect of the presence or absence of a crack on compliance, and therefore bending moment, on a surface crack in a circular plate, and for obtaining the relationship between the crack length and the stress intensity factor. If viewed from a different perspective, the method described in Non-Patent Document 3 can also be applied to cracks that exist on the inner surface of a component, but it is less versatile because it only shows results for specific mechanical conditions and requires complex formulations for plate deflection, etc.

“Standard Test Method for Measurement of Fatigue Crack Growth Rates”, ASTM E647-15ε1, 2019, p.727, 748, 749 Hiroshi Abe and 1 other, "Nondestructive Detection Method of Fatigue Cracks in Spot Welded Joints", Proceedings of the Japan Welding Society, Vol. 4, No. 4, 1986, pp. 666-673 Hiroyuki Abe et al., "Bending of a Circular Plate with a Surface Crack on the Edge", Transactions of the Japan Society of Mechanical Engineers (Series A), Vol. 46, No. 401, 1980, pp. 34-42

The present invention was made to solve the problems of the conventional technology as described above, and aims to provide a simple and versatile method for estimating the state of a crack.

In order to solve the above problems, the present inventors have conducted extensive research. Since the presence of a crack and an increase in the length of the crack locally reduces the rigidity of a component, it is possible to quantitatively evaluate the state of the crack by evaluating the rigidity of the component. In addition, according to the theory of elastic deformation when an external force is applied to a component, the curvature of the shape of the component after deformation correlates with the rigidity of the component, and it is considered that the greater the absolute value of the curvature, the smaller the rigidity.
Therefore, the inventors focused on the outer surface shape that can be measured relatively easily and with high accuracy from the outer surface side of a component. Specifically, the inventors focused on measuring the outer surface shape after deformation occurs due to active application of an external force that does not damage the component, or the outer surface shape after deformation occurs due to an external force (residual stress) that occurs passively during an assembly process of a mechanical structure using the component. The inventors then found that if the curvature distribution of the outer surface shape is calculated based on the measured outer surface shape, the position of localized reduction in stiffness of the component, i.e., the position of a crack, can be estimated from the curvature distribution.

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 state of a crack in a member having an inner surface, the method comprising: a first step of measuring an outer surface shape of the member after deformation occurs due to application of an external force; a second step of calculating a curvature distribution of the outer surface shape based on the outer surface shape measured in the first step; a third step of identifying a position on the outer surface of the member where the absolute value of the curvature shows a maximum value in the curvature distribution calculated in the second step; a fourth step of estimating a position on the inner surface of the member opposite the position on the outer surface of the member identified in the third step as the position of the crack; a fifth step of determining a crack-affected range, which is a range of positions on the outer surface of the member where the presence of the crack affects the curvature in the curvature distribution calculated in the second step; a sixth step of estimating a curvature κ 0 in the case where the crack does not exist at the position on the outer surface of the member identified in the third step, based on the curvature distribution located outside the crack-affected range determined in the fifth step; and a curvature κ ₀ at which the absolute value shows a maximum value at the position on the outer surface of the member identified in the third step. a seventh step of calculating a ratio κ c /κ 0 between c and the curvature κ 0 estimated in the sixth step; an eighth step of estimating a remaining thickness tr of the member at the position of the crack estimated in the fourth step based on the ratio κ c /κ 0 calculated in the seventh step _and a _thickness t ₀ of _the member in the absence of the crack ; _and a _{ninth step of} estimating a length of the crack by subtracting the remaining thickness _tr estimated in the eighth step from the thickness t ₀ .

In the present invention, the "inner surface" refers to a surface of a member that cannot be seen from the outside, and the "outer surface" refers to a surface of the member that faces the "inner surface" and can be seen from the outside. When a member is plate-shaped, in the state of a mechanical structure assembled using this plate-shaped member, the surface that cannot be seen from the outside is the "inner surface", and the surface that can be seen from the outside is the "outer surface". When a member is tubular, the inner surface of the tubular member is literally the "inner surface", and the outer surface of the tubular member is the "outer surface".
In the present invention, the term "component having a crack on its inner surface" refers to a component in which the opening of the crack is present on the inner surface side.
In the present invention, the term "external force" is a concept including both an external force actively applied to a degree that does not damage a member, and an external force (residual stress) that occurs passively during an assembly process of a mechanical structure using the member. In addition, the "external force" is not particularly limited as long as it acts in a direction that expands the opening of a crack, and includes bending loads, tensile loads, and loads that are a mixture of these.

According to the method of the present invention, in the first step, the outer surface shape of a member after deformation caused by application of an external force is measured. The outer surface shape, i.e., the relationship between the in-plane position and the out-of-plane position on the outer surface of the member, can be measured relatively easily and with high accuracy from the outer surface side of the member by a known non-contact or contact shape measuring device. Examples of non-contact shape measuring devices include shape measuring devices that use a scanning optical one-dimensional distance meter using a laser or the like, optical two-dimensional distance meter, and optical three-dimensional shape measuring devices. Examples of contact shape measuring devices include a stylus-type three-dimensional shape measuring device.

In the method according to the present invention, in the second step, the curvature distribution of the outer surface shape, i.e., the relationship between the in-plane position on the outer surface of the component and the curvature at each position, is calculated based on the outer surface shape measured in the first step. The curvature distribution of the outer surface shape can be calculated, for example, by second-order differentiation of the out-of-plane position of the outer surface shape with respect to the in-plane position (for example, second-order differentiation with respect to a position in any one direction within the plane).

Furthermore, according to the method of the present invention, in the third step, a position (in-plane position) on the outer surface of the member where the absolute value of the curvature shows a maximum value in the curvature distribution calculated in the second step is identified. Since the absolute value of the curvature shows a maximum value at this identified position on the outer surface of the member, that is, the absolute value of the curvature is larger than that of the surrounding area, it is considered that the rigidity is small. Therefore, it can be considered that this identified position on the outer surface of the member corresponds to the position of the crack.
Therefore, according to the method of the present invention, in the fourth step, it is possible to estimate the position of the inner surface of the member that faces the identified position of the outer surface of the member as the position of the crack.

According to the first to fourth steps described above, the position of a crack present on the inner surface of any component can be easily estimated. However, it is difficult to estimate the length of a crack by only calculating the curvature distribution of the outer surface shape. This is because, in order to estimate the length of a crack using the curvature distribution of the outer surface shape as it is, it is necessary to know the relationship between the crack length and the curvature, but it is difficult to formulate this relationship for any mechanical condition.
Therefore, the inventors have further studied and found that it is useful to first estimate the curvature κ 0 in the case where no crack exists at the position of the outer surface of the member specified in the above-mentioned third step (the position of the outer surface corresponding to the position of the crack existing on the inner surface). This curvature κ ₀ can be estimated based on the curvature distribution located outside _the determined crack influence range, which is the range of positions of the outer surface of the member where the presence of a crack affects the curvature in the curvature distribution calculated in the second step. Next, the inventors have found that by calculating the ratio κ _c /κ ₀ between the curvature κ _c whose absolute value at the position of the outer surface of the member specified in the third step is a maximum value and the estimated curvature κ ₀ , the remaining thickness t _r of the member at the position of the crack can be accurately estimated based on this ratio κ _c /κ ₀ and the thickness t ₀ of the member in the case where no crack exists. If the remaining thickness t _r of the component at the crack location can be estimated, it is possible to estimate the length of the crack by subtracting the remaining thickness t _r from the thickness t ₀ of the component when the crack is not present.

According to the findings of the inventors mentioned above, in order to estimate the crack length in addition to the crack position, the above-mentioned fifth to ninth steps are necessary.

In the sixth step , "based on the curvature distribution located outside the crack influenced area" is a concept that includes not only the case where it is based on the entire curvature distribution located outside the crack influenced area, but also the case where it is based on a part of it.
As the inventors have discovered, the method according to the present invention makes it possible to estimate the remaining thickness t _r of the component at the position of the crack in the eighth step, and to use this to estimate the length of the crack in the ninth step.
The inventor's findings regarding the crack length will be described in detail later.

In the method according to the present invention , specifically, in the sixth step, it is considered that the curvature κ ₀ is estimated by extrapolating the curvature distribution located outside the crack affected area toward the position of the outer surface of the component identified in the third step.

In the method according to the present invention , specifically, in the eighth step, the remaining thickness _tr may be estimated by multiplying the cube root of the ratio κ _c /κ ₀ by the thickness t ₀ .

The present invention makes it possible to easily estimate the state of cracks present on the inner surface of any component.

1 is a diagram showing a schematic configuration of an apparatus for executing a crack state estimation method according to an embodiment of the present invention. FIG. 1 is a flow chart showing an outline of a procedure of an estimation method according to an embodiment of the present invention. FIG. 11 is an explanatory diagram illustrating the second to sixth steps of the estimation method according to one embodiment of the present invention. FIG. 2 is a diagram showing an example of an analytical model for performing finite element analysis in an embodiment of the present invention. 11 is a diagram showing the outer surface shape (amount of deformation of the outer surface) of a member after deformation calculated according to an embodiment of the present invention. FIG. FIG. 13 is a diagram showing a curvature distribution of an outer surface shape calculated according to an embodiment of the present invention. FIG. 1 is a diagram showing a summary of results of examples of the present invention.

Hereinafter, with reference to the accompanying drawings as appropriate, an embodiment of the present invention will be described, taking as an example a case in which a member having a crack on its inner surface is plate-shaped.
FIG. 1 is a diagram showing a schematic configuration of an apparatus for carrying out a crack state estimation method according to an embodiment of the present invention.

As shown in Fig. 1, a member S to which the crack state estimation method according to this embodiment (hereinafter, simply referred to as the "estimation method") is applied has a crack C on its inner surface S1. Although not shown in Fig. 1 for convenience, the member S is combined with other members to form a mechanical structure, and the inner surface S1 is not visible from the outside. The outer surface S2 of the member S is visible from the outside. The arrow X in Fig. 1 indicates the longitudinal direction of the member S, the arrow Y indicates the thickness direction, and the symbol Z indicates the width direction perpendicular to the longitudinal direction and the thickness direction.
As shown in FIG. 1, an apparatus 100 for executing the estimation method according to this embodiment includes a shape measuring apparatus 1 and a calculation apparatus 2.

The shape measuring device 1 is a device that measures the outer surface shape of a member S after deformation caused by application of an external force. The external force may be actively applied or passively generated. As the shape measuring device 1 of this embodiment, an optical two-dimensional distance meter using a light cutting method as a measurement principle is used. Specifically, the shape measuring device 1 of this embodiment includes a light source (not shown) that irradiates a linear laser light LL extending in the X direction, an imaging means (not shown) that images the outer surface S2 of the member S irradiated with the laser light LL, and an image processing means (not shown) that performs image processing on the image acquired by the imaging means to extract a pixel area corresponding to the laser light LL in the image, and calculates the shape (XY coordinates) of the outer surface S2 based on the position of the extracted pixel area. When it is necessary to measure the shape of a portion of the outer surface S2 outside the irradiation range of the laser light LL (when estimating the state of a crack present in a portion of the inner surface S1 facing the portion of the outer surface S2 outside the irradiation range of the laser light LL), the shape measuring device 1 may be moved in the longitudinal direction (X direction) of the member S so that the laser light LL is irradiated to different portions of the outer surface S2, and the outer surface shape may be measured for each moved position. Also, as necessary, the shape measuring device 1 may be moved in the width direction (Z direction) of the member S, and the outer surface shape may be measured for each moved position.
In this embodiment, as described above, an optical two-dimensional range finder is used as the shape measuring device 1, but the present invention is not limited to this. For example, it is also possible to use a shape measuring device that scans an optical one-dimensional range finder (a range finder that measures the Y coordinate) in the X direction, or an optical three-dimensional shape measuring device (a device that measures XYZ coordinates). It is also possible to use a contact type (e.g., a stylus type) three-dimensional shape measuring device.

The outer surface shape (shape of outer surface S2 (XY coordinates)) of component S measured by shape measuring device 1 is input to calculation device 2, and calculation device 2 is configured to perform the calculations described below (second step ST2 to ninth step ST9).
The calculation device 2 may be, for example, a general-purpose computer installed with a program for executing the calculations described below.

The estimation method according to this embodiment using the device 100 having the above configuration will be described below.
Fig. 2 is a flow diagram showing an outline of the procedure of the estimation method according to this embodiment. As shown in Fig. 2, the estimation method according to this embodiment includes a first step ST1 to a ninth step ST9. The first step ST1 to the fourth step ST4 are steps for estimating the position of the crack C, and the fifth step ST5 to the ninth step ST9 are steps for estimating the length of the crack C. Below, the steps for estimating the position of the crack C (the first step ST1 to the fourth step ST4) and the steps for estimating the length of the crack C (the fifth step ST5 to the ninth step ST9) will be described in order.

[Step of estimating the position of crack C]
When the crack C is present, the substantial thickness (residual thickness) of the member S is smaller than when the crack C is not present. Therefore, when an external force is applied to the member S, the member S locally bends near the position where the crack C exists. However, since the outer surface shape of the member S after deformation measured by the shape measuring device 1 is insensitive to the presence of the crack C, it is difficult to quantitatively and objectively determine the bending position based on the outer surface shape itself. In view of the fact that bending is caused by a local decrease in the rigidity of the member S, the present inventor has found that the bending position, i.e., the position of the crack C, can be accurately estimated by using a curvature distribution that is correlated with the rigidity of the member S and can be easily calculated from the outer surface shape of the member S.

<First step ST1>
In a first step ST1, the outer surface shape of the member S after deformation caused by the application of an external force is measured by the shape measuring device 1. The outer surface shape of the member S measured by the shape measuring device 1 (XY coordinates of the outer surface S2) is input to the calculation device 2.

<Second step ST2>
FIG. 3 is an explanatory diagram for explaining the second step ST2 to the sixth step ST6 of the estimation method according to this embodiment.
In the second step ST2, the calculation device 2 calculates the curvature distribution of the outer surface shape as shown in Fig. 3 based on the outer surface shape of the member S measured in the first step ST1. Specifically, the calculation device 2 calculates the curvature distribution in the X direction of the outer surface shape (the relationship between the X coordinate and the curvature at each X coordinate) by differentiating the Y coordinate of the outer surface shape of the member S (XY coordinate of the outer surface S2) twice with respect to the X coordinate.

<Third step ST3>
In the third step ST3, the calculation device 2 identifies the position on the outer surface of the member S where the absolute value of the curvature shows a maximum value in the curvature distribution calculated in the second step ST2. In the example shown in Fig. 3, the position (X coordinate) P of the outer surface S2 of the member S where the absolute value of the curvature shows a maximum value is identified.

<Fourth step ST4>
In a fourth step ST4, a position (X coordinate) P' (see FIG. 1) of the inner surface S1 of the member S opposite to the identified position P of the outer surface S2 of the member S is estimated to be the position of the crack C.

[Step of estimating the length of the crack C]
According to the theory of elastic deformation when an external force (e.g., bending load) is applied to the component S, the curvature of the outer surface shape of the component S after deformation is inversely proportional to the rigidity (bending rigidity) of the component S. Furthermore, when the component S is a plate-like component as in this embodiment, the rigidity is considered to be proportional to the cube of the thickness of the component S from the perspective of the second moment of area and the like. Therefore, if the curvature of the outer surface shape of the component S can be obtained, it may be possible to quantitatively estimate the remaining thickness of the component S at the position P' of the crack C, and therefore the length of the crack C. However, there are two problems to be solved in order to apply this perspective.
The first point is to quantify the correlation between the curvature of the outer surface shape of the member S and the rigidity of the member S. As described above, the curvature of the outer surface shape of the member S and the rigidity of the member S are inversely proportional to each other, but the proportionality coefficient is known only when the mechanical conditions are completely clear (the mechanical conditions are simple), and it is not possible to obtain a general-purpose solution for the complex mechanical conditions of an actual member S.
The second point is to quantify the correlation between the rigidity of the component S (the curvature of the outer surface shape) and the length of the crack C (the remaining thickness of the component S at the position P' of the crack C). The curvature at the position P of the outer surface S2 corresponding to the position P' of the crack C when a crack C exists is naturally different from the curvature of the outer surface shape of a component having a uniform thickness equal to the remaining thickness at the position P. This is because the mechanical conditions of the two are different. Therefore, it is not possible to directly obtain the remaining thickness of the component S, and therefore the length of the crack C, from the curvature of the outer surface shape of the component S.
Therefore, as a result of intensive research, the present inventors have found that the length of the crack C can be estimated with high accuracy by performing the fifth step ST5 to the ninth step ST9.

<Fifth step ST5>
In the fifth step ST5, the calculation device 2 determines the crack influence range (see Figure 3), which is the range of positions (X coordinates) on the outer surface S2 of the component S where the presence of the crack C affects the curvature in the curvature distribution calculated in the second step ST2.
When a crack C exists, the influence of the crack C on the curvature decreases with distance from the crack C, and the curvature eventually becomes equal to that when the crack C does not exist. Therefore, in this embodiment, the calculation device 2 determines the range of positions where the curvature almost does not change as the crack-influenced range, based on the position P corresponding to the position P' of the crack C. The crack-influenced range is determined according to the shape of the curvature distribution calculated in the second step ST2. Specifically, for example, the calculation device 2 calculates the distribution of the curvature change rate by first-order differentiation of the curvature distribution with respect to the X-coordinate, and determines the positions P1 and P2 (see FIG. 3) where the change rate is less than a predetermined threshold value (where the change in the curvature almost converges) as the outermost points of the crack-influenced range.

<Sixth step ST6>
In the sixth step ST6, the calculation device 2 estimates the curvature κ 0 in the case where the crack C does not exist at the position P on the outer surface S2 of the member S specified in the third step ST3, based on the curvature distribution located outside the crack-affected range determined in the fifth step ST5 (the curvature distribution surrounded by the dashed line OR in the example shown in FIG. 3, which is located at a position larger in the X coordinate than the crack-affected range). Specifically, in this embodiment, the calculation device 2 estimates the curvature _{κ 0 by} extrapolating the curvature distribution surrounded by the dashed line OR toward the position P. That is, based on the curvature distribution surrounded by the dashed line OR (the relationship between the X coordinate and the curvature at each X coordinate), the calculation device 2 approximates the relationship between the X coordinate and the curvature at each X coordinate with an appropriate function (an approximate straight line shown by a dashed line in the example shown in FIG. 3) using an approximation calculation such as the least squares method, and sets the value of the approximation function when the X coordinate is the position P as the curvature κ ₀ .

<Seventh step ST7>
In seventh step ST7, the calculation device 2 calculates a ratio κc/κ0 between the curvature _κc whose absolute value at the position P of the outer surface S2 of the member S specified in the third step ST3 is a maximum value and the curvature _κ0 estimated in the sixth step ST6. This ratio _κc / _κ0 is the relative curvature of the outer surface shape when the crack C exists, _and hereinafter this ratio _{κc / κ0} is appropriately referred to as the "non-dimensional curvature".
The reason for calculating the non-dimensional curvature κ _c /κ ₀ is as follows. As described in the second problem to be solved above, the mechanical conditions of a general member S are unknown, so the length of the crack C cannot be uniquely determined by the curvature κ _c alone. On the other hand, although the mechanical conditions cannot be clarified by the value of the curvature κ ₀ alone, the thickness t ₀ of the member S (thickness when the crack C does not exist, see FIG. 1) is known. Therefore, by taking the ratio between the curvature κ _c and the curvature κ ₀ , it is considered that the thickness of the member S that has changed, that is, the remaining thickness t _r (see FIG. 1), can be estimated after offsetting the influence of the mechanical conditions. Note that, as shown in the examples described later, the value of the curvature κ ₀ changes depending on the length of the crack C even if the structure of the member S and the external force applied are the same. This is because the mechanical conditions (deformation state near the crack C) differ depending on the length of the crack C, and it can be said that it is essential to introduce the non-dimensional curvature κ _c /κ ₀ to offset the influence of the mechanical conditions.

<Eighth step ST8>
In the eighth step ST8, the calculation device 2 estimates the remaining thickness t _r of the member S at the position P' of the crack C estimated in the fourth step ST4 based on the non-dimensional curvature κ _c /κ ₀ calculated in the seventh step ST7 and the thickness t ₀ of the member S when the crack C does not exist. The non-dimensional curvature κ _c /κ ₀ is a curvature of the outer surface shape relative to the case when the crack C does not exist. Therefore, based on the theory of elastic deformation, if it is considered that the non-dimensional curvature κ _c /κ ₀ is inversely proportional to the cube of the thickness of the member S, the thickness of the member S when the crack C exists, that is, the remaining thickness t r, can be estimated by comparing with the thickness t ₀ of the member S when the crack C does not exist. Specifically, in this embodiment, the calculation device 2 estimates the remaining thickness _{t r by} multiplying the cube root of the non-dimensional curvature κ _c /κ ₀ by the thickness t ₀ .
That is, the calculation device 2 estimates the remaining thickness _tr by the following formula (A).
t _r =t ₀・(κ _c /κ ₀ ) ^1/3・・(A)

<Ninth step ST9>
In a ninth step ST9, the calculation device 2 estimates the crack length _tc by subtracting the remaining thickness _tr estimated in the eighth step ST8 from the thickness _t0 .
That is, the calculation device 2 estimates the crack length _tc by the following formula (B).
t _c =t ₀ -t _r ...(B)

The estimation method according to the present embodiment described above solves the problem of unknown mechanical conditions by using the relative ratio of the curvatures of the outer surface shape (non-dimensional curvature κ _c /κ ₀ ) based on the thickness t ₀ of the member S when no crack C exists. In addition, this is a method for quantitatively estimating the effect of the crack C on the curvature distribution from the curvature distribution of the outer surface shape, and can accurately estimate the state of the crack C present on the inner surface S1 of the member S (the position and length of the crack C) from limited information, namely the outer surface shape of the member S. In this way, according to the estimation method according to the present embodiment, the state of the crack C in an arbitrary member S can be estimated non-destructively, simply, and with high accuracy, and the effect of quantitatively evaluating the effect of the crack C on the fatigue strength of the member S can also be obtained.

Below, we will explain examples in which the effectiveness of the crack state estimation method according to the present invention was verified using finite element analysis, to further clarify the features of the present invention.

As shown in FIG. 4, a finite element analysis was performed on a plate-like member S having a length (dimension in the X direction) of 20 mm, a thickness t ₀ (dimension in the Y direction) of 1.6 mm, and a crack C of length D at a distance L from one end (left end) in the X direction. A two-dimensional elastic analysis model was used as the analysis model, and plane strain elements were used as the elements of the analysis model. The element division was a lattice of 0.1 mm square. The nodes constituting the crack C were double nodes. The Young's modulus E of the material constituting the plate material was set to 206 [GPa], and the Poisson's ratio ν of the material was set to 0.3. The distance L was set to two conditions, 1 mm and 2 mm, and the length D was set to five conditions, 0 mm (no crack), 0.5 mm, 0.8 mm, 1.0 mm, and 1.2 mm.
Finite element analysis was performed on this analysis model under the condition that the left end of the member S was completely fixed and a load (bending load) of 500 N was applied to the other end (right end) of the member S in the negative Y direction (downward), and the outer surface shape of the member S after deformation (specifically, the deformation amount δ _y (x) of the outer surface S2, which is a function of the X coordinate) was calculated.

Although the crack C can be directly detected from the appearance if it is a single plate-like member S like the analysis model shown in Fig. 4, the purpose of this embodiment is to verify whether or not it is possible to estimate the state of the crack C (position of the crack C, length of the crack C) based on the shape (amount of deformation) of the outer surface S2 opposite to the inner surface S1 where the crack C exists. This embodiment simulates the deformation behavior of the member S on the side where the crack C exists in a mechanical structure (such as a spot welded portion) in which multiple plate-like members are stacked, and contributes to verifying whether or not the crack C on the inner surface S1 can be detected.
As described above, in the crack state estimation method according to the present invention, the curvature κ ₀ is estimated in the absence of the crack C (because the curvature in the absence of the crack C is not known for the member S constituting the actual mechanical structure), but in this embodiment, for comparison, an analysis in the absence of the crack C (D=0 mm) was also performed.
Furthermore, as described above, since the element division is in the form of a 0.1 mm square grid, the deformation amount δ _y (x) of the outer surface S2 is calculated as discrete data (values at each node constituting each element) related to the coordinate X. Even in measuring the outer surface shape of an actual member S, if a method for obtaining digital data is used, the measured outer surface shape will be discrete, but the measurement pitch can be set finely to a degree that satisfies the accuracy required for identifying the curvature κ _c and estimating the curvature κ ₀ .

FIG. 5 is a diagram showing the outer surface shape (deformation amount δ _y (x) of the outer surface S2) of the member S after deformation calculated by this embodiment. FIG. 5(a) shows the calculation result when L = 1 mm, and FIG. 5(b) shows the calculation result when L = 2 mm. In FIG. 5, the results calculated under each condition of D = 0 mm, 0.5 mm, 0.8 mm, 1.0 mm, and 1.2 mm are plotted with dots of different shapes. The vertical axis of FIG. 5 shows the non-dimensional deformation amount obtained by dividing the deformation amount δ _y (x) at each X coordinate by the deformation amount at the load position (the right end of the member S) where the deformation amount is maximum. Therefore, while the actually calculated deformation amount δ _y (x) is a negative value in the Y direction, the non-dimensional deformation amount shown in FIG. 5 is a positive value.
As shown in Figure 5, the deformation appears to bend near the position of crack C (position L = 1 mm in Figure 5(a) and position L = 2 mm in Figure 5(b)). However, the bending is unclear, especially when the length of crack C is small. For this reason, it is clear that it is difficult to clearly and quantitatively estimate the position of crack C based on the amount of deformation of the outer surface S2, i.e., the outer surface shape of the member S after deformation itself. Therefore, as described above, in the state estimation method of the present invention, the curvature distribution of the outer surface shape is calculated (second step ST2).

Fig. 6 is a diagram showing the curvature distribution of the outer surface shape calculated by this embodiment. Fig. 6(a) shows the calculation result when L = 1 mm, and Fig. 6(b) shows the calculation result when L = 2 mm. In Fig. 6, the results calculated under each condition of D = 0 mm, 0.5 mm, 0.8 mm, 1.0 mm, and 1.2 mm are plotted with dots of different shapes. Note that the vertical axis of Fig. 6 is a negative value, but this is because in this embodiment, the outer surface shape is a curve in the clockwise direction with respect to the positive side of the X direction (convex upward), and the curvature in this case is defined as a negative value.
The curvature distribution of the outer surface shape can be calculated by second-order differentiation of the Y coordinate with respect to the X coordinate of the outer surface shape of the member S. In this example, since the outer surface shape of the member S, i.e., the deformation amount δ _y (x), is calculated as discrete data, the first-order differentiation is calculated by the following formula (1), and the first-order differentiation is further calculated in the same manner to calculate the curvature distribution.
dδ _y (x _i )/dx _i = {δ _y (x _i+1 )−δ _y (x _i−1 )}/(x _i+1 −x _i−1 )...(1)
In the above formula (1), the subscript i indicates data at the i-th node from the fixed end (left end) of the member S.
As shown in Fig. 6, unlike Fig. 5, the absolute value of the curvature clearly shows a maximum value in the vicinity of the distance L from the fixed end of 1 mm and 2 mm. Therefore, it is possible to accurately estimate the position of the inner surface of the member S opposite the position (X coordinate) of the outer surface S2 of the member S where the absolute value of the curvature shows a maximum value as the position of the crack C. In this embodiment, it is considered that the positions of L = 1 mm and 2 mm are estimated to be the position of the crack C, and the length _tc of the crack C is estimated as described below.
In addition, when calculating the curvature distribution of the outer surface shape, the calculation method is not limited as long as the required accuracy can be ensured, such as, for example, appropriately performing a function approximation on discrete data and then performing a second-order differentiation of the function.

Next, in this embodiment, the crack-affected range defined as above was determined based on the curvature distribution of the outer surface shape shown in Fig. 6. In this embodiment, the distribution of the rate of change of the curvature was calculated by first-order differentiation of the curvature distribution with respect to the X coordinate in the same manner as in formula (1), and the position where this rate of change was less than a predetermined threshold value (approximately 5 x 10 ^-3 (1/mm ² )) (where the change in curvature nearly converges) was determined as the outermost point of the crack-affected range. Specifically, as shown in Fig. 6, the position of the outermost point of the crack-affected range (the outermost point on the positive side in the X direction) was the position of crack C + 2 mm.

Next, in this embodiment, the non-dimensional curvature κ _c /κ ₀ was calculated based on the curvature distribution of the outer surface shape and the crack-influenced range shown in Fig. 6. In this embodiment, as shown in Fig. 6, the curvature κ 0 was estimated by extrapolating the curvature distribution of the range OR, which is a range from the position of the crack C + 2 mm to the position of the crack C + 4 mm, among the curvature distributions located outside the crack-influenced range. Specifically, based on the curvature distribution of the range OR, an approximation was performed using the _least squares method with an approximation line expressed by the following formula (2), and the value on the vertical axis of the approximation line at the position of the crack C (L = 1 mm in Fig. 6(a) and L = 2 mm in Fig. 6(b)) was calculated as the curvature κ ₀ .
κ=ax+b...(2)
In the above formula (2), κ is the curvature [1/mm], and a and b are constants.
Then, the ratio κ _c /κ ₀ between the curvature κ _c at the position of the crack C and the curvature κ ₀ estimated as described above was calculated as a dimensionless curvature.
The method of determining the crack-affected range, the range of curvature distribution used for extrapolation, and its approximation function may be set according to appropriate conditions depending on the state of the curvature distribution.

Finally, in this embodiment, based on the calculated non-dimensional curvature κ _c /κ ₀ and the member thickness t ₀ = 1.6 mm, the remaining thickness _tr was estimated by the above-mentioned formula (A), and further, the length t _c of the crack C was estimated by the above-mentioned formula (B).

FIG. 7 is a diagram showing the results of this embodiment described above.
As shown in Fig. 7, the estimated curvature _κ0 varies depending on the actual crack length. That is, the curvature _κ0 is not a constant value, and does not match the curvature _κ0 in the analysis model without a crack (this curvature _κ0 is not an estimated value, but the curvature of the outer surface S2 calculated by finite element analysis). This is because the estimated curvature _κ0 represents the curvature of the outer surface S2 in a deformed state (which differs depending on the length of the crack C) at each crack C length.
As shown in FIG. 7, the estimated length _tc of the crack C is in good agreement with the actual length of the crack C set in the analysis model, confirming that the estimation method according to the present invention is valid.

1: Shape measuring device 2: Calculation device 100: Device S: Member S1: Inner surface S2: Outer surface C: Crack

Claims (3)

A method for estimating a state of a crack in a member having a crack on an inner surface, comprising the steps of:
A first step of measuring an outer surface shape of the member after deformation caused by application of an external force;
a second step of calculating a curvature distribution of the outer surface shape based on the outer surface shape measured in the first step;
a third step of identifying a position on the outer surface of the member where the absolute value of the curvature shows a maximum value in the curvature distribution calculated in the second step;
a fourth step of estimating the position of the inner surface of the member opposite the position of the outer surface of the member identified in the third step as the position of the crack;
a fifth step of determining a crack influence range, which is a range of positions on the outer surface of the component where the presence of the crack affects the curvature in the curvature distribution calculated in the second step;
A sixth step of estimating a curvature κ 0 in the case where the crack does not exist at the position of the outer surface of the component specified in the third step, based on the curvature distribution located outside the crack influence range determined in the fifth _step ;
a seventh step of calculating a ratio κ _c /κ ₀ between the curvature κ _c at the position of the outer surface of the member identified in the third step, the absolute value of which is a maximum value, and the curvature κ 0 estimated in the sixth _step ;
an eighth step of estimating a remaining thickness t r of the member at the position of the crack estimated in the fourth step based on the ratio κ _c /κ ₀ calculated in the seventh step and a thickness _{t 0} of the member in the absence of the crack ;
and a ninth step of estimating a length of the crack by subtracting the remaining thickness t _r estimated in the eighth step from the thickness t ₀ .
A method for estimating the state of a crack, comprising: In the sixth step, the curvature κ ₀ is estimated by extrapolating the curvature distribution located outside the crack influence range toward the position of the outer surface of the member identified in the third step.
The method for estimating a state of a crack according to claim 1 . In the eighth step, the remaining thickness t _r is estimated by multiplying the cube root of the ratio κ _c /κ ₀ by the thickness t ₀ .
3. The method for estimating a state of a crack according to claim 1 or 2 .

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