JP3167449B2 - Non-destructive inspection method of three-dimensional crack by DC potential difference method. - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a non-destructive inspection method for a structure such as a metal pipe or the like, and more particularly to a crack which has not been formed on the surface of a structure by using a potential difference method, that is, a buried crack or an inner or outer crack. The present invention relates to a nondestructive inspection method for detecting a crack exposed on a surface and quantifying a three-dimensional state of the crack.

[0002] When applying fracture mechanics to the evaluation of the remaining life of nuclear power / thermal power plants, petrochemical plants, etc., it is necessary to calculate fracture parameters such as stress intensity factor and J integral. At this time, it is important to non-destructively evaluate the size and shape of the crack in the structure together with the load condition. Non-destructive inspection technology by the potential difference method is one of the promising means.

When a current is applied to the surface of a structure, if a crack exists in the structure, the current distribution inside the structure is disturbed, and the potential difference distribution on the surface of the structure becomes abnormal. Non-destructive testing technology based on the potential difference method is based on this principle,
It measures the potential difference distribution on the surface of the structure, and indirectly detects the presence or absence of a crack in the structure and the state of the crack from the distribution.

The present invention provides an efficient technique for optimizing a three-dimensional crack virtually set in a structure in accordance with a measured potential difference distribution on the surface of the structure and quantifying it with a small error.

[0005]

2. Description of the Related Art Conventionally, as an example of evaluating the shape of a three-dimensional crack existing in a real structure by using a DC potential difference method, the following references (1), (2), and (3) show forests. And Kubo et al. The crack targeted in the above-mentioned research examples is a three-dimensional crack perpendicular to the measurement plane.
On the other hand, an existing crack has a three-dimensional shape with an arbitrary aspect ratio and is often inclined with respect to the measurement surface. However, there is no example in which such a general crack was quantitatively nondestructively evaluated by the DC potential difference method, and the solution of the problem was considered as a future subject.

Further, as shown in Reference (4), the present inventors first evaluated the shape of a slender three-dimensional crack having an aspect ratio close to zero by using the DC potential difference method. Is going. There, a two-dimensional solution derived by the potential singularity method is applied sequentially along the length of the crack,
By combining these results, the first approximation of the crack shape is evaluated. However, when the same method is applied to a disk-shaped crack having an aspect ratio close to 1, the evaluation result includes a large error. <References> (1) Hayashi and four others, Materials, 35-395 (198
6), 936, (2) Hayashi and four others, materials, 37-41
9 (1988), 964, (3) Kubo et al., 4 persons, Machine theory, 54-498, A (1988), 218, (4) Saka et al., 2 persons, nondestructive inspection, 38-10 (1989), 9
99,

[0007]

SUMMARY OF THE INVENTION The present invention provides a means for accurately and easily quantifying the state of a three-dimensional crack having an arbitrary aspect ratio and inclination buried in a structure or exposed on the surface. An object of the present invention is to realize a nondestructive inspection method using a potential difference method.

[0008]

According to the present invention, a three-dimensional crack having an arbitrary aspect ratio is virtually generated in a structure, and a potential difference distribution which will appear on the surface of the structure when measured by a potential difference method. Is calculated based on the virtual three-dimensional crack, while the potential difference distribution is actually measured on the structure surface,
The two potential difference distributions are compared, and the error is used to correct the state of the virtual three-dimensional crack, such as the shape and inclination, to determine the state of the virtual three-dimensional crack that minimizes the error. .

FIG. 1 is a diagram illustrating the principle of the present invention. In FIG. 1, reference numeral 1 denotes a structure to be evaluated, in which a part of a metal tube is cut away.

[0010] Reference numeral 2 denotes an example of a three-dimensional crack protruding from the back surface with respect to the measurement surface in the structure 1. In the figure, a and c indicate the aspect dimensions of the crack, and β indicates the inclination angle. Reference numeral 3 denotes a probe for measuring a potential difference. Here, it is simplified for convenience. The probe 3 is provided with current input / output terminals indicated by 4, 4 'and potential difference measurement terminals indicated by 5, 5'.

The current input / output terminals 4 and 4 'can be used separately from the probe 3 in addition to the fixed setting state in the probe 3 as shown in the figure.

The potential difference measuring terminals 5 and 5 'have a structure in which the relative distance is fixed and the potential difference measuring terminals 5 and 5' can move freely in a direction parallel to a line connecting the current input / output terminals 4 and 4 'or in a direction orthogonal to the line. .

Reference numeral 6 denotes a constant current source connected to the current input / output terminals 4, 4 '. Reference numeral 7 denotes a digital voltmeter connected to the potential difference measuring terminals 5 and 5 '. Reference numeral 8 denotes a data analyzer for evaluating a crack.

Reference numeral 9 denotes an actual potential difference distribution data storage unit that stores output data of the digital voltmeter 7 when an actual potential difference distribution is measured. Reference numeral 10 denotes a virtual three-dimensional crack generation unit that generates virtual three-dimensional crack data.

Reference numeral 11 denotes a virtual crack data storage unit for storing the generated virtual three-dimensional crack data. Reference numeral 12 denotes a virtual potential difference distribution calculation unit that calculates a potential difference distribution on the surface of the structure corresponding to the generated virtual three-dimensional crack data.

Reference numeral 13 denotes a virtual potential difference distribution data storage unit for storing virtual potential difference distribution data as a calculation result. 14
Is an error evaluation unit that compares the actual potential difference distribution data with the virtual potential difference distribution data to evaluate an error in the virtual potential difference distribution data.

15 instructs the virtual three-dimensional crack generation unit 10 to correct the virtual three-dimensional crack based on the magnitude of the error in the evaluation result, and furthermore, to the corrected virtual three-dimensional crack. An optimization control unit that optimizes a virtual three-dimensional crack by repeatedly executing calculation of a virtual potential difference distribution and evaluation of an error according to the distribution.

[0018]

The operation of FIG. 1 is performed as follows. First, the current input / output terminals 4 and 4 'and the potential difference measurement terminals 5 and 5' in the probe 3 are arranged in a line, and their relative positions are fixed to contact the surface of the structure. An electric current is passed through the structure 1 through 4, 4 '. The current input / output terminals 4, 4 'and the potential difference measuring terminals 5, 5' whose relative positions are fixed are roughly scanned on the surface of the structure, and the potential difference appearing on the surface is detected by the potential difference measuring terminals 5, 5 '. The measurement is performed by the total 7, and a portion showing an abnormality in the potential difference is found. Next, in the direction perpendicular to the longitudinal direction of the abnormal portion (the direction parallel to the crack length c in the three-dimensional crack 2 in FIG. 1), the current input / output terminal 4 is placed across the abnormal portion.
4 'is separated from the probe 3 by a sufficient distance, for example, and a current flows from the constant current source 6 into the structure 1 via the current input / output terminals 4, 4'. Next, the potential difference measurement terminals 5,
By fixing the relative position of 5 'and finely scanning the abnormal portion in the longitudinal direction and the direction perpendicular thereto, detailed potential difference distribution data near the crack can be obtained.

The potential difference distribution data actually measured in this way is stored in the actual potential difference distribution data storage unit 9. Next, processing for generating and optimizing a virtual three-dimensional crack is started.

The virtual three-dimensional crack generation unit 10 generates virtual three-dimensional crack data as an initial value and stores the data in the virtual crack data storage unit 11. The initial value of the virtual three-dimensional crack data can be set to a first-order approximation based on the actual potential difference distribution data stored in the actual potential difference distribution data storage unit 9.

The virtual potential difference distribution calculation unit 12 calculates a virtual potential difference distribution based on the data in the virtual crack data storage unit 11 according to a predetermined arithmetic expression, and stores the resulting data in the virtual potential difference distribution data storage unit 13. .

The error evaluator 14 compares the actual potential difference distribution data in the actual potential difference distribution data storage 9 with the virtual potential difference distribution data in the virtual potential difference distribution data storage 13.
Find the error.

The optimization control unit 15 instructs the virtual three-dimensional crack generation unit 10 to correct the virtual three-dimensional crack according to the magnitude of the error obtained by the error evaluation unit 14. The correction is performed based on a predetermined method. Based on the corrected virtual three-dimensional crack, the virtual potential difference distribution calculator 12 calculates the virtual potential difference distribution again, and the error evaluator 14 obtains the error. The optimization control unit 15 causes the correction of the virtual three-dimensional crack to be repeated until the error converges to the minimum value, and outputs the final result as the state value of the three-dimensional crack.

[0024]

Embodiments of the present invention will be described below. FIG.
3 shows a procedure for evaluating a three-dimensional crack by the method of one embodiment of the present invention.

Here, the problem of evaluating the shape of a semi-elliptical back surface crack or an elliptical burial crack existing in a flat plate as shown in FIG. The crack plane is perpendicular to the yz plane and parallel to or at an angle to the xy plane.

First, as shown in FIG. 1A, a probe 3 in which the relative positions of the current input / output terminals 4, 4 'and the potential difference measuring terminals 5, 5' are fixed is inspected on the measurement surface of the structure 1. Scan in the direction (z direction). At this time, the relationship between the center position of the probe 3 and the obtained potential difference in the vicinity of the crack is shown in FIG.
become that way. The center position α _m of the probe 3 at which the graph shows the maximum value substantially coincides with the position of the crack in the inspection direction. From this, the same position is taken as the approximate position in the inspection direction of the brought crack. In the measurement, a current is supplied in the z direction so as to be uniform in the x direction when there is no crack. Next, as shown in (c), the potential difference distribution in the z direction is measured at a plurality of points along the x direction such that the center position in the z direction of the potential difference measuring terminals 5 and 5 'coincides with the approximate position in the inspection direction. . The obtained voltage difference distribution of the position in the x direction is alpha _cc to the maximum value [(d) Reference. Further, as shown in (e), (c)
The potential difference distribution [(f)] in the z direction is measured on the line of x = α _{cc in} the same manner as in the above. As a result, a potential difference distribution on the crosshairs in the x and z directions near the crack is obtained. The inverse problem is solved by collating the finally obtained potential difference distribution with the analytically determined potential difference distribution ΔΦ _k for the three-dimensional crack in the data analyzer 8 using an optimization method. At this time, the following function F

[0027]

(Equation 1)

Is defined, and a crack shape that minimizes the function value is searched. Here, K represents the number of measurement points, and ΔΦ _mk represents a potential difference distribution obtained from the measurement. For optimization, Powell's conjugate direction method is used (for example, refer to the reference document “Sakawa, Optimization and Optimal Control, (1980), 50, Morikita Publishing”).

In performing the above-described evaluation procedure, it is necessary to calculate potential difference distributions for various three-dimensional cracks assumed in the virtual three-dimensional crack generation unit 10 in the data analysis device 8. It is desirable that this calculation can be performed as easily as possible. Methods for theoretically deriving the potential difference distribution on the measurement surface with an arbitrary three-dimensional crack include the finite element method, the boundary element method, the finite element method incorporating a line spring, a simple method that approximates the analytical solution, Singularity method. Finite element method and boundary element method are cracks of any shape,
Although it can handle members etc., the amount of data to be prepared is enormous,
There is a disadvantage that the calculation time is long. The calculation can be easily performed by the line spring method and the simple method, but there are limitations on the aspect ratio and types of cracks that can be handled.

On the other hand, the present inventors have previously proposed a potential singularity method for a two-dimensional crack. According to this method, it is possible to relatively easily find an accurate solution for a crack in a circular pipe (Ref. "Abe et al., Non-destructive inspection, 35-5 (1986), 326 ."reference).

In the present embodiment, the potential difference distribution on the measurement surface is derived by a method in which the potential singularity method is extended to a three-dimensional problem. Hereinafter, this analysis method will be described. Here, consider the problem of finding the potential difference distribution on the measurement surface when a uniform current is applied to a flat plate having a back surface crack or a buried crack as shown in FIG. In actual measurement, current is input and output from the measurement surface at points, but by sufficiently widening the interval between input and output terminals, the measured value and the theoretical value derived here are sufficient near the center between the input and output terminals to be measured. Matches. However, it is assumed that the spread of the plate in the x and z directions is infinite, and the measurement surface (surface ABCD) and the back surface (surface EF)
GH) is electrically insulated. Further, the shapes of the back surface crack and the buried crack are a semi-elliptic shape and an elliptical shape, respectively. As shown in FIGS. 4 (a) and 4 (b), the shape of the back surface crack is determined by the position α in the inspection direction, the angle β between the crack surface and the xy plane, and the lengths a and c. The shape is α, β, a,
c, defined by various quantities at position d in the thickness direction (y direction).

When a slit having a finite opening width is used instead of the crack, the electric field near the crack tip differs between the two. However, what is needed is not a potential field near the tip of the crack, but a potential field on the measurement surface. Furthermore, it has been confirmed by numerical experiments that there is no problem in accuracy if the slit width is made sufficiently smaller than the crack length. Therefore, the crack is replaced with a slit as shown in FIG. Here, the opening width of the slit is 2T. Note that, for the sake of convenience, the description that follows will focus on the problem directed to the back surface crack. The description of the problem of buried cracks will be made only when the description of both problems is different.

As shown in FIG. 6, the problem that a uniform current is applied to an infinite flat plate having a semi-elliptical slit is different from the problem that a uniform current is applied to an infinite flat plate having no slit.
[FIG. (A)] and a problem 2 in which a virtual slit is considered as the problem 1 and a problem 2 [FIG. Think about representing.

The potential distribution Φ ₁ of Problem 1 is expressed as follows, assuming that the value at the origin is zero. Φ ₁ = Uz (2) where U is the uniform current density in the z direction. As a coordinate system, a rectangular coordinate system in which the origin 0 is at the center of the back surface and the xz plane coincides with the back surface is considered.

Next, problem 2 will be described. Problem 2 is a problem 2-1 [FIG. 7A] in which a slit having current input / output exists in a semi-infinite body bounded by the xz plane as shown in FIG. 7 and a problem in the measurement plane ABCD. The problem 2-2 of the same magnitude as 2-1 and the application of a current in the opposite direction can be represented by the superposition of 2-2 [FIG. At this time, the current at the crack surface in Problem 2 is the superposition of the current at the crack surface in Problem 2-1 and the current caused on the virtual crack surface by the current input and output from the measurement surface ABCD in Problem 2-2. It is represented by

Consider problem 2-1. Here, in order to represent the input and output of the current on the slit surface, a three-dimensional double balloon having a streamline as shown in FIG. The strength of the double balloon is represented by b, and its position is represented by (x _0, y _0, z ₀ ).

The potential distribution φ _2-1 when a double balloon is present in a semi-infinite body bounded by the xz plane is represented by the y-axis at the mirror image position (x _0, −y _0, z ₀ ). By placing a double balloon having the same strength with a direction having an angle of π-θ as an axis, it is expressed as follows.

[0038]

(Equation 2)

It is well known that superimposing a uniform flow in the z-direction on a double blowout about the z-direction represents a flow around a sphere placed in a uniform fluid. . The radius of the sphere is then a function of the strength of the double blow and the current density of the uniform flow. Therefore, by distributing a three-dimensional double balloon in a semi-infinite body represented by the equation (3) on a plane as shown in FIG. Consider expressing a slit that exists in an infinite body. At this time, the direction of the axis of the double blowing is a direction perpendicular to the slit surface.

From this, the potential distribution Φ _2-1 representing the problem 2-1 is obtained.
Is obtained as follows.

[0041]

(Equation 3)

Here, A represents the area of the surface on which the double blowing is distributed. Consider the discretization of the integral in the above equation. First, A is divided into M rectangles. FIGS. 10 (a) and 10 (b) show examples of division for a back surface crack and a buried crack. As shown in the drawing, crack M ₁ is divided into xi] ₁ direction, and further M ₁ divides each xi] ₂ directions. Just each side of each divided rectangles, local coordinate system taken on the slit plane as in FIG. (Ξ _1, ξ ₂₎ and parallel to the xi] ₁ axis and xi] ₂ axis. Here, the quantities in the figure are defined as in the following equations.

[0043]

(Equation 4)

Here

[0045]

(Equation 5)

Next, in each division, the strength b of the double balloon is assumed to be constant, and the strength of the m-th division is represented by b ^m . A ^m Tosureba integrating a rectangular area of m th is discretized as follows.

[0047]

(Equation 6)

Where

[0049]

(Equation 7)

However, in the case of a back crack,

[0051]

(Equation 8)

In the case of a buried crack,

[0053]

(Equation 9)

On the other hand, it seems that it is difficult to analytically express the potential Φ _2-2 representing the problem 2-2. Therefore, a numerical solution method described below is introduced here. First, FIG.
The horizontal spread of the flat plate shown in FIG. However, the spread of the flat plate in the lateral direction is much larger than the plate thickness, and AB >> AE, AD >> AE.

Here, similar to the finite element method, three-dimensional element division is performed on the same plate, and considering the balance of each node,
Value Φ _{2-2i at} each node of potential distribution Φ _2-2 of Problem 2-2
The following equation is obtained with respect to

[0056]

(Equation 10)

Here, N represents the total number of nodes in the element division. A _2-2a (j, i) is the rigidity matrix of the present problem formulated by Laplace's equation, and q _j is the nodal current. The boundary conditions for this problem are as follows. First, AEFB and BF
GC, CGHD, and DHEA are considered to be electrically insulated because they are sufficiently separated from the slits represented by a set of double balloons. That is, q _j = 0 (11) Next, the boundary condition in the surface ABCD is assumed to be the same in magnitude as that of Problem 2-1 and a current in the opposite direction is loaded. That is, the current density q loaded on the same plane is:

[0058]

[Equation 11]

Here, n is an outward unit normal vector of the surface ABCD. In this case, it is considered that n = y. Further, the current applied to each node on the surface ABCD using q in the above equation is given by the following equation for each element.

[0060]

(Equation 12)

Here, the subscript e represents an element, and N
_r is the shape function, and ^Se is the surface A
Represents the area of the plane included in the BCD. Equation (13) is a local coordinate system taken in the element _{(η 1, η 2, η} 3) using the rewritten as follows. Here, the η _1, η _{2 and} η ₃ axes are parallel to the x, y and z axes, respectively, and η ₁ = ± 1 is the z of the element division.
The side parallel to the axis, η ₂ = 1 on plane ABCD, η ₃ = ±
1 represents a side parallel to the x-axis of the element division.

[0062]

(Equation 13)

Further, considering equations (7) and (12),

[0064]

[Equation 14]

[0065] In this case | J | is Yako bi Ann. In the present embodiment, the Gauss-Legendre four-point formula is applied when calculating the above equation. From the above, if the node current represented by the equation (15) is superimposed on all elements constituting the surface ABCD, the current at each node on the surface ABCD can be obtained as a boundary condition.

Finally, due to the nature of Problem 2-2, the surface EFGH is a boundary condition for electrical insulation. That is, q _j = 0 (16) As described above, the boundary condition of the problem 2-2 is:
All are given by nodal currents. From this, equation (10) can be transformed as follows,

[0067]

(Equation 15)

Further, by substituting equation (15) into the above equation, Φ _2-2i at each node is _obtained as follows.

[0069]

(Equation 16)

Here, A _2-2b (j, m) is an N-row × M-column matrix obtained by superimposing the portion in {} in equation (15) over the entire element division. Potential distribution [Phi _2-2 in which from an arbitrary point issues 2-2, can be used to shape functions N _r expressed as follows. Here, a 20-node isoparametric quadratic element is used.

[0071]

[Equation 17]

Here, i is the r of the element containing an arbitrary point.
Represents the second node number. From the above, problems 1, 2-1, and 2
By superimposing the expressions (2), (7), and (19) representing the potential distribution of −2, a uniform current is distantly applied to the flat plate having the back surface crack or the buried crack, which is the object of this embodiment. A potential distribution Φ at an arbitrary point when a load is applied is obtained as follows.

[0073]

(Equation 18)

In calculating the potential difference distribution using the equation (20), the division of the slit surface and the ratio element division between the slit width and the crack length are given as parameters in advance.

When the unknown function b ^m is obtained, the potential difference distribution can be calculated using the above equation. Consider a slit as shown in FIG. The double balloon is distributed from point P to Q in the figure.

The boundary conditions for determining the unknown function b ^m are as follows. That is, it is assumed that the slit surface is electrically insulated. Assuming that the normal vector on the slit plane is n _s , this condition is expressed as follows.

[0077]

[Equation 19]

Here, equation (20) is substituted into the above equation, and eventually the following equation is obtained as a boundary condition equation.

[0079]

(Equation 20)

Originally, the above boundary condition must be satisfied over the entire surface of the slit. However, in this solution, the same conditions are set as follows. In other words, the boundary conditions are M points regularly selected from points V to W on one side of the slit shown in FIG. 11 (points indicated by marks in FIG. 10).
It is assumed that the above holds. From this, the boundary condition expression shown in Expression (22) finally results in an M-element simultaneous equation relating to b ^m . Regarding the back crack, the coordinates (x _m,
y _m, z _m ) is as follows [see FIG. 10 (a)].

[0081]

(Equation 21)

Similarly, regarding the buried crack, FIG.
As shown in

[0083]

(Equation 22)

However,

[0085]

(Equation 23)

FIG. 12 shows an example of element division used by the present inventors in an experiment. As shown in FIG.
Division into three parts in the y direction. The parameters required for obtaining the potential difference distribution are: M ₁ = 4, T / a = 1.0 *
It was set to 10 ^-3 . It has been confirmed in advance that a sufficiently converged result can be obtained when using the above-described element division and parameters. The probe used had a current input / output terminal spacing of 4t (40mm) and a potential difference measuring terminal spacing of 1
t (10 mm), and the supplied current amount was 5 A.

The probe has a structure that can be moved very easily so that measurement operations at many points can be performed in a short time. Furthermore, by fixing the measurement terminals using springs, the measurement situation at each measurement position is made as uniform as possible.

FIG. 13 shows a test piece and the shape of a crack to be evaluated. The test piece is stainless steel (SUS304)
100 × 10 × 250 mm. Each test piece has a back surface crack at the center. As shown in the figure, three types of cracks are targeted. Indicates a crack having an aspect ratio close to 1, and indicates a crack having an aspect ratio close to zero. And are cracks perpendicular to the measurement plane, and are cracks inclined to the measurement plane. The crack is simulated by a slit (width 0.5 mm) created by electric discharge machining.

FIG. 14 shows the evaluation results of the obtained crack shapes. The solid line in the figure indicates the crack shape to be evaluated, and the broken line indicates the evaluated crack shape. The shapes of all cracks, that is, elongated cracks having an aspect ratio close to zero, and round cracks close to 1, including tilt, are well evaluated.

The embodiment described above deals with the case where the member having a crack is electrically uniform. However, many cracks occur in welds such as pipes and pressure vessels. It is conceivable that the electrical resistivity of the welded portion is different from that of the base material, and it cannot be said that the entire member is electrically uniform. There is also a non-uniform shape due to the build-up. Unless these effects are considered, it is difficult to accurately evaluate the crack shape.

Next, an embodiment for correcting the influence of the welded portion will be described. FIG. 15 exemplifies a cross section of a general welded portion having a build-up. FIG. 16 shows an evaluation procedure of an embodiment for a crack in a structure having such a weld. Here, the problem of evaluating the shape of a back surface crack or a buried crack existing in a flat plate as shown in the figure is dealt with. The back surface crack and the buried crack are semi-elliptical and disk-shaped, respectively, and are perpendicular to the yz plane and parallel to the xy plane or have a certain inclination angle. As shown in FIGS. 4 (a) and 4 (b), the shape of the back surface crack is represented by a position α in the inspection direction (z direction), an angle β formed between the crack surface and the xy plane, and lengths a and c.
Buried crack shape is α, β, a, c, thickness direction (y direction)
Is defined by various quantities at the position d.

In carrying out this procedure, the welding line is parallel to the x direction. In the measurement, when there is no crack near the weld, the direction parallel to the weld line (x direction)
The current is supplied in the z direction so as to be uniform. In the present embodiment, the approximate position of the crack in the inspection direction (z direction) is not estimated because the vicinity of the weld is targeted. The approximate position of the crack in the inspection direction is the center of the weld (z = 0). As shown in FIG. 16 (a), the z-direction position of the center of the potential difference measuring terminal coincides with the center of the welding line, and is perpendicular to the welding line at a plurality of points parallel to the welding line (x direction). The potential difference distribution in a different direction (z direction) is measured. The obtained voltage difference distribution shall be the position alpha _cc weld line parallel to the direction having the maximum value (x-direction) [FIG. (B) Reference. Note that the vertical axis ΔΦ represents a value obtained by rendering the obtained potential difference distribution non-dimensional by a potential difference obtained from a homogeneous member. Further, similarly as shown in FIG. 3C, the potential difference distribution [FIG. 3D] in the direction (z direction) perpendicular to the welding line is measured on the line of x = α _cc . A correction formula is applied to the measured potential difference distribution to remove the influence of the welded portion [FIG. As a result, a corrected potential difference distribution on the cross line in the direction parallel to the weld line near the crack (x direction) and in the direction perpendicular to the weld line (z direction) is obtained. Finally corrected potential difference distribution ΔΦ
_The inverse problem is solved by collating the _mk with the analytically determined potential difference distribution ΔΦ _k for the three-dimensional crack in the data analyzer using an optimization method. At this time, a function F as shown in Expression (1) is defined, and a crack shape that minimizes the function value is searched. It is to optimize use of the conjugate direction method of Powell.

The following equation is used as the correction equation.

[0094]

(Equation 24)

Here, w is the distance from the reference position of the test piece to the center position of the potential difference measuring terminal, and takes x or z. F (w) is higher than that of a homogeneous member without a weld by W
(w) shows the potential difference distribution obtained from a member having only a weld. Before using the equation (25), it is necessary to obtain F (w) and W (w) in the x and z directions in advance.

FIG. 17 shows the result of verification of the correction formula for the back surface crack of the welded portion from which the buildup has been removed. The solid line in the figure is the actual crack shape, the broken line is the crack shape evaluated by the conventional method using theoretical solutions for electrically homogeneous members without considering the effect of welds, and the dot-dash line is corrected. The evaluation result using the formula is shown. When the solid line and the dashed line are compared, it is understood that the effect of the welded part appears in the evaluation result. Although the positions of both crack tips are almost the same, it cannot be said that the inclination and length can be accurately evaluated. Therefore, it is necessary to correct the influence of the weld. Further, by comparing the solid line and the alternate long and short dash line, the effectiveness of the correction formula for the back surface crack from which the buildup has been removed can be seen. The dashed line almost overlaps the solid line.

Incidentally, the welded portion is accompanied by electrical inhomogeneity and shape inhomogeneity. The former is caused by the difference between the electric resistivity of the welded portion and the electric resistivity of the base material, and the latter is caused by the build-up. For accurate evaluation of cracks, it is essential to consider the effects of these two inhomogeneities. In addition, cracks generated in the welded portion include buried cracks in addition to backside cracks. From these points, it is not sufficient to verify the crack on the back surface only by removing the above-mentioned buildup. Here, the two-dimensional buried crack existing in the welded part having a built-up is taken up, and the correction formula is verified by numerical simulation.

In the numerical simulation, the potential difference distribution obtained by numerical calculation is used instead of the potential difference distribution on the measurement surface which is originally obtained from an experiment. A two-dimensional finite element method is used as a numerical calculation method. The elements used are 8-node isoparametric quadratic elements. In any case, the potential difference distribution obtained by calculation is rounded to a 4-digit value.

The crack material has an aspect ratio L / t = 12 as shown in FIG. Here, L is the length of the test piece.
At this aspect ratio, the influence of the end face of the cracked material can be ignored. The central part has a weld as shown in the figure. The height of the overlay at the center of the weld is 0.1 t. In the finite element analysis, the electric resistance ρ of the base metal was set at 1.0, and the resistivity of the weld was set at 1.1, targeting only the right half of the cracked material.
And Two types of buried cracks with different positions in the thickness direction,
Was targeted. Each crack shape is shown in the figure. As measurement conditions, the current input / output terminal interval W _I = 10 t and the potential difference measurement terminal interval W _p = 0.4 t.

FIGS. 19 and 20 show the correction results and the evaluation results. The solid line shows the potential difference distribution and the crack shape used for evaluation when there is no effect of the weld (the weld is replaced by the base metal), the broken line shows the potential before correction, and the one-dot chain line shows the potential difference calculated from the correction formula. The distribution and the evaluation results obtained from them are shown. From the figure, the solid line relatively well matches the one-dot chain line, and the validity of the correction method can be understood. Note that the solid line in FIG. 19 is a potential difference distribution obtained by theoretical analysis using the potential singularity method. For correction, F (w) and W (w)
Was calculated by finite element analysis. In the evaluation of the crack shape, the corrected shape matches well with the shape to be evaluated.

Next, an example of an experiment conducted to verify the effectiveness of the method for evaluating a three-dimensional crack present in a weld will be described. This experimental example is for a back surface crack.
In the experiment, a current of 5 A was supplied from a constant current source to the current input / output terminal of the probe, and input / output was performed at a plurality of points on the end face of the test piece so as to have a uniform current in the longitudinal direction of the crack. A reference resistor is placed between the test piece and the constant current source, and the voltage across the resistor is measured by a digital voltmeter to monitor the amount of current being supplied.

The potential difference is measured by inputting the output of the micro volt meter to the digital volt meter and reading the display of the digital volt meter. The distance between the potential difference measuring terminals is 10 mm.

FIG. 21 shows a test piece and a crack shape to be evaluated. In welding the test pieces, TIG welding is used. The test piece is stainless steel (SUS304)
100 × 14 × 250 mm. The test piece has a back surface crack at its center. As shown in the figure, three types of back surface cracks are targeted. The and cracks are cracks perpendicular to the measurement surface or cracks inclined to the measurement surface. The crack is simulated by a slit (width 0.5 mm) created by electric discharge machining.

FIG. 22 shows the experimental results. The solid line in the figure indicates the actual crack shape, and the dashed line indicates the evaluated crack shape. For any cracks, their shapes are well evaluated, including the inclination. From this, it can be seen that the high-precision evaluation method of the crack existing in the weld portion proposed in the present embodiment is effective.

[0105]

According to the present invention, it is possible to non-destructively and accurately evaluate a three-dimensional shape having an arbitrary aspect ratio and inclination of a buried crack or a back crack in a structure, which has been difficult in the past. Thus, the reliability of the structure can be significantly improved.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating the principle of the present invention.

FIG. 2 is an explanatory diagram of a crack evaluation procedure according to one embodiment of the present invention.

FIG. 3 is an explanatory diagram of an infinite flat plate having a crack for inputting and outputting a uniform current.

FIG. 4 is an explanatory diagram of a shape of a three-dimensional crack.

FIG. 5 is an explanatory diagram of a crack and a slit.

FIG. 6 is an explanatory diagram of an infinite flat plate having a slit for inputting and outputting a uniform current.

FIG. 7 is an explanatory diagram of an infinite flat plate having a slit with current input / output.

FIG. 8 is an explanatory diagram of a three-dimensional double balloon.

FIG. 9 is an explanatory diagram of a representation of a slit by a continuous distribution of three-dimensional double balloons.

FIG. 10 is an explanatory diagram of division of a plane for distributing double balloons.

FIG. 11 is an explanatory diagram of a boundary condition on a slit surface.

FIG. 12 is an explanatory diagram of an example of element division in an experiment.

FIG. 13 is an explanatory diagram of a test piece and a crack shape used in an experiment.

FIG. 14 is an explanatory diagram of an evaluation result of a crack shape.

FIG. 15 is an explanatory diagram of a cross section of a welding portion.

FIG. 16 is an explanatory diagram showing a procedure for evaluating a crack in an embodiment for correcting a welded portion.

FIG. 17 is an explanatory diagram of a verification result of a correction formula for a back surface crack from which a buildup is deleted.

FIG. 18 is an explanatory diagram of a crack material for verifying a correction equation by a numerical simulation.

FIG. 19 is an explanatory diagram of a correction result by numerical simulation of an object having a weld.

FIG. 20 is an explanatory diagram of an evaluation result of a target having a weld by numerical simulation.

FIG. 21 is an explanatory diagram of a test piece and a crack shape used in an experiment on an object having a weld.

FIG. 22 is an explanatory diagram of an evaluation result by an experiment of an object having a weld.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Structure to be evaluated 2 Three-dimensional crack 3 Probe 4, 4 'Current input / output terminal 5, 5' Potential difference measuring terminal 6 Constant current source 7 Digital voltmeter 8 Data analyzer 9 Actual potential difference distribution data storage unit 10 Virtual 3D crack generation unit 11 Virtual crack data storage unit 12 Virtual potential difference distribution calculation unit 13 Virtual potential difference distribution data storage unit 14 Error evaluation unit 15 Optimization control unit

Continuation of the front page (56) References JP-A-64-35357 (JP, A) JP-A-61-237045 (JP, A) JP-A-61-292546 (JP, A) Transactions A of the Japan Society of Mechanical Engineers, Vol. 55, No. 514 (1986-6), Nondestructive Inspection, 1301-1304, 38 (1989), No. 10, 909-916 (58) Fields investigated (Int. Cl. ⁷ , DB name) ) G01N 27/20 JICST file (JOIS)

Claims (1)

(57) [Claims] A current input / output terminal connected to a constant current source, a potential difference measuring terminal provided between the current input / output terminals, and a test target using the current input / output terminal and the potential difference measuring terminal. Using a data analyzer that analyzes potential difference data measured at multiple locations distributed two-dimensionally on the outer surface of the structure, quantifies the actual three-dimensional crack state in the structure by the potential difference method In the non-destructive inspection method, a state of a virtual three-dimensional crack having an arbitrary aspect ratio and an inclination that is buried or exposed on the surface without being attached to the surface in the structure is set in the data analyzer. Calculating a virtual potential difference distribution on the surface of the structure corresponding to the state of the virtual three-dimensional crack set above, and a virtual potential difference distribution on the surface of the obtained structure,
Compare the actual potential difference distribution based on the potential difference data on the surface of the structure measured using the current input / output terminal and the potential difference measuring terminal to determine an error in the virtual potential difference distribution, Based on the distribution error, the state of the set virtual three-dimensional crack is corrected, and the above-described processing is sequentially and repeatedly performed in a direction in which the error is minimized, thereby reducing the virtual three-dimensional crack. A non-destructive inspection method for a three-dimensional crack by a DC potential difference method, characterized by optimizing a state and quantitatively evaluating an actual three-dimensional crack state in a structure.