JPH06109684A - Method for non-destructive inspection of three-dimensional crack by dc potential difference method - Google Patents

Abstract

PURPOSE:To conduct determination of the sate of a three-dimensional crack accurately by virtually generating the three-dimensional crack inside a structure, calculating the potential difference distribution based on the virtual three-dimensional crack, actually measuring the potential difference distribution on the surface of the structure, comparing two potential differential distributions, and then obtaining error. CONSTITUTION:Current is allowed to flow from a constant current source 6 into a structure 1 via current input/output terminals 4 and 4'. The terminals 4 and 4' and potential difference measuring terminals 5 and 5' where the relative position is fixed are scanned on the surface of the structure, the potential difference is measured by a digital voltmeter 7, and a part indicating abnormality in the potential difference is detected. The data of a three-dimensional crack 2 is obtained by thinly scanning the longer and vertical directions of the abnormal site and then are stored in an actual potential difference distribution data storage part 9. A virtual three-dimensional crack generation part 10 generates data which become initial values and then stores them at a virtual crack data storage part 11. A virtual potential difference distribution calculation part 12 calculates the virtual potential distribution and then stores it at the virtual potential difference distribution data storage part 13. An error evaluation part 14 compares the actual potential difference distribution data with the virtual potential difference distribution data of the storage parts 9 and 13 and obtains error and then an optimization control part 15 instructs correction of cracks to the generation part 10.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for nondestructive inspection of a structure such as a metal circular tube, and in particular, a crack which is not exposed on the surface of the structure by using a potential difference method, that is, a buried crack or internal and external cracks. The present invention relates to a nondestructive inspection method for detecting a crack exposed on the surface and quantifying the three-dimensional state of the crack.

When applying fracture mechanics to residual life evaluation of nuclear / 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 nondestructively evaluate the size and shape of cracks in the structure as well as the load conditions. The non-destructive inspection technique by the potential difference method is one of the effective means.

When a current is applied on the surface of a structure, if a crack is present 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 inspection technology by the potential difference method is based on this principle,
The potential difference distribution on the surface of a structure is measured, and the presence or absence of a crack in the structure and the state of the crack are indirectly detected from the distribution.

The present invention provides an efficient technique for optimizing a three-dimensional crack virtually set in a structure according to the 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 an actual structure by using the DC potential difference method, the forest shown in the following references (1), (2) and (3) , Kubo and others. The crack targeted in the above-mentioned research examples is a three-dimensional crack perpendicular to the measurement surface.
On the other hand, a real 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 of quantitatively nondestructively evaluating such a general crack by the DC potential difference method, and it was considered to be a future task to solve the problem.

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

[0007]

DISCLOSURE OF THE INVENTION The present invention provides a means for quantifying a state of a three-dimensional crack embedded in a structure or exposed on the surface and having an arbitrary aspect ratio and inclination with high accuracy and easily. The purpose is to realize the non-destructive inspection method by the prepared 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 that will appear on the surface of the structure when measured by the potential difference method. Is calculated based on the virtual three-dimensional crack, while the potential difference distribution is actually measured on the surface of the structure,
These two potential difference distributions are compared, the state of the virtual three-dimensional crack such as the shape and inclination is corrected by the error, and the state of the virtual three-dimensional crack with the minimum error is obtained. .

FIG. 1 illustrates the principle of the present invention. In FIG. 1, reference numeral 1 denotes a structure to be evaluated, and here, a part of a metal circular pipe is cut away and shown.

Numeral 2 is an example of a three-dimensional crack extending on the back surface of the structure 1 with respect to the measurement surface. In the figure, a and c are the aspect dimensions of the crack, and β is the tilt angle. 3 is a probe for measuring a potential difference. Here, it is shown in a simplified manner for convenience. The probe 3 is provided with current input / output terminals denoted by 4,4 ′ and potential difference measurement terminals denoted by 5,5 ′.

The current input / output terminals 4 and 4'can be used not only in a fixed setting state in the probe 3 as shown in the drawing but also separately from the probe 3 for independent use.

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 parallel to a line connecting the current input / output terminals 4 and 4'or in a direction orthogonal to the line. .

A constant current source 6 is connected to the current input / output terminals 4 and 4 '. Reference numeral 7 is a digital voltmeter connected to the potential difference measuring terminals 5 and 5 '. Reference numeral 8 is a data analysis device for evaluating cracks.

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

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

A virtual potential difference distribution data storage unit 13 stores 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 and evaluates the error of the virtual potential difference distribution data.

The reference numeral 15 instructs the virtual three-dimensional crack generation unit 10 to correct the virtual three-dimensional crack on the basis of the magnitude of the error of the evaluation result, and the virtual three-dimensional crack generation unit 15 further receives the corrected virtual three-dimensional crack. This is an optimization control unit that optimizes the virtual three-dimensional crack by repeatedly executing the calculation of the virtual potential difference distribution and the evaluation of the 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 measuring terminals 5 and 5'in the probe 3 are arranged in a line, and the relative positions are fixed and brought into contact with the surface of the structure. A current is passed through the structure 1 via 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 ′ to obtain a digital voltage. It is measured by a total of 7 to find a site showing an abnormal potential difference. Next, in the direction perpendicular to the longitudinal direction of the abnormal part (the direction parallel to the crack length c in the three-dimensional crack 2 in FIG. 1), the current input / output terminals 4 are sandwiched across the abnormal part.
4'is removed from the probe 3, for example, and is placed at a sufficient distance from the probe 3, and a current flows from the constant current source 6 into the structure 1 through the current input / output terminals 4 and 4 '. Next, the potential difference measuring terminal 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 in the vicinity of 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, the process of 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 it in the virtual crack data storage unit 11. The initial value of the virtual three-dimensional crack data can be linearly set 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 evaluation section 14 compares the actual potential difference distribution data in the actual potential difference distribution data storage section 9 with the virtual potential difference distribution data in the virtual potential difference distribution data storage section 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 calculation unit 12 calculates the virtual potential difference distribution again, and the error evaluation unit 14 obtains the error. The optimization control unit 15 repeats the correction of the virtual three-dimensional crack until the error converges to the minimum value, and outputs the final result as the state value of the three-dimensional crack.

[0024]

EXAMPLES Examples of the present invention will be described below. Figure 2
3 shows a procedure for evaluating a three-dimensional crack according to the method of Example 1 of the present invention.

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

First, as shown in (a) of the figure, the 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 near the crack is (b) in the figure.
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 point, bring the same position to the approximate position in the crack inspection direction. 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 z-direction potential difference distribution is measured at a plurality of points along the x-direction so that the central z-direction positions of the potential-difference measuring terminals 5 and 5 ′ coincide with the approximate position in the inspection direction. . The position in the x direction where the potential difference distribution obtained here has the maximum value is α _cc [see (d)]. Further, as shown in (e), (c)
Similarly, the potential difference distribution [(f)] in the z direction is measured on the line of x = α _cc . After all, the potential difference distribution on the cross line in the x direction and the z direction near the crack is obtained. The finally obtained potential difference distribution is compared with the analytically determined potential difference distribution ΔΦ _k for the three-dimensional crack in the data analyzer 8 by using the optimization method to solve the inverse problem. At this time, the following function F

[0027]

[Equation 1]

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

To carry out the above-described evaluation procedure, it is necessary to calculate the potential difference distribution 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 be performed as easily as possible. The finite element method, the boundary element method, the finite element method incorporating a line spring, the simple method approximating the analytic solution, and the potential are theoretically derived for the potential difference distribution on the measurement surface with an arbitrary three-dimensional crack. There is a singularity method. The finite element method and the boundary element method are completely arbitrary shape cracks,
Although you can handle parts etc., the amount of data to prepare is huge,
It has the disadvantage of long calculation time. Although the line spring method and the simple method can easily perform calculations, 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, an accurate solution can be relatively easily obtained for a crack in a circular pipe (reference document "Abe et al., 2 persons, nondestructive inspection, 35-5 (1986), 326"). ."reference).

In this 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. The analysis method will be described below. Here, let us consider the problem of obtaining 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. 3 at a distance. In the actual measurement, the current is input and output at a point from the measurement surface, but by widening the I / O terminal interval sufficiently, the measured value and the theoretical value derived here are sufficient near the center between the input and output terminals. Matches However, assuming that the spread of the flat plate in the x and z directions is infinite, the measurement surface (surface ABCD) and the back surface (surface EF)
GH) is electrically insulated. The shapes of the back surface crack and the buried crack are semi-ellipsoidal and ellipsoidal, respectively. As shown in FIGS. 4 (a) and 4 (b), the shape of the back surface crack is 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 shapes are α, β, a,
It is defined by various amounts of c and position d in the plate thickness direction (y direction).

When a slit having a finite opening width is used instead of the crack, the electric field near the tip of the crack is different between the two. However, what is needed is not the electric field near the crack tip, but the electric 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, as shown in FIG. 5, the crack is replaced with a slit. Here, the opening width of the slit is 2T. For the sake of convenience, the description that follows will focus on the problem of backside cracks. The explanation of the buried crack problem will be given only if the explanations for both problems are different.

As shown in FIG. 6, the problem that a uniform current is applied to an infinite flat plate having a semi-ellipsoidal slit, and the problem 1 that a uniform current is applied to an infinite plate that does not have a slit 1
By superimposing [Figure (a)] and virtual slit in problem 1, problem 2 [diagram (b)] of the same size as problem 1 and the opposite direction current is applied on the slit surface. Think to represent.

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, consider 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.

Next, problem 2 will be described. Problem 2 is problem 2-1 [(a) in the same figure] in which a slit with current input and output exists in a semi-infinite body bounded by the xz plane as shown in FIG. It can be expressed by a superposition of problem 2-2 [(b) in the same figure] which has the same magnitude as 2-1 and is loaded with a reverse current. At this time, the current on the crack surface of Problem 2 is the superposition of the current on the virtual crack surface due to the current on the crack surface of Problem 2-1 and the current input / output from the measurement surface ABCD in Problem 2-2. It is represented by.

Consider problem 2-1. Here, a three-dimensional double blow-out having a streamline as shown in FIG. 8 and having a direction having an angle of θ with the y-axis is introduced in order to represent the input and output of the current on the slit surface. Let b be the strength of the double balloon and (x _0, y _0, z ₀ ) be its position.

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

[0038]

[Equation 2]

It is well known that, when a uniform flow in the z direction is superposed on a double blowout having an axis in the z direction, the flow represents a flow around a sphere placed in a uniform fluid. . The radius of the sphere is then a function of the double bubble strength and the current density of the uniform flow. Therefore, as shown in FIG. 9, the three-dimensional double balloons in the semi-infinite body represented by the equation (3) are distributed on the plane, so that the half of the current input / output on the surface of the problem 2-1. Consider representing a slit that exists in an infinite body. At this time, the axis of the double blow-out is set to the direction perpendicular to the slit surface.

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

[0041]

[Equation 3]

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

[0043]

[Equation 4]

Here

[0045]

[Equation 5]

Next, in each division, the strength b of the double balloon is constant, and the strength of the m-th division is represented by b ^m . If the area of the ^mth rectangle is A ^m , the integral is discretized as follows.

[0047]

[Equation 6]

Where

[0049]

[Equation 7]

However, in the case of a backside crack,

[0051]

[Equation 8]

In the case of a buried crack,

[0053]

[Equation 9]

On the other hand, it seems difficult to express the potential Φ _2-2 representing the problem 2-2 analytically. Therefore, here we introduce a numerical solution as described below. First, Fig. 7
The lateral expansion of the flat plate shown in (b) is finite. However, the lateral spread of the flat plate is much larger than the plate thickness, and AB >> AE and AD >> AE.

If three-dimensional element division is performed on the same plate as in the finite element method and the balance of each node is considered,
Value Φ _{2-2i at} each node of potential distribution Φ _{2-2 in} Problem 2-2
We obtain

[0056]

[Equation 10]

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

[0058]

[Equation 11]

Here, it is considered that n is an outward unit normal vector of the surface ABCD, and in this case, n = y. Further, the current loaded at 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 S ^e is the surface A among the surfaces forming the element.
It represents the area of the surface included in the BCD. Equation (13) is rewritten as follows using the local coordinate system (η _1, η _2, η ₃ ) taken in the element. However, 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 is on the plane ABCD, η ₃ = ±
1 represents a side parallel to the x-axis of element division.

[0062]

[Equation 13]

Further considering equations (7) and (12)

[0064]

[Equation 14]

Where | J | is the Jacobian. In this embodiment, the Gauss-Legendre four-point formula is applied to the calculation of the above equation. From the above, by superimposing the nodal currents represented by the equation (15) on all the elements constituting the surface ABCD, the currents at the respective nodes on the surface ABCD can be obtained as boundary conditions.

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

[0067]

[Equation 15]

By substituting the 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 overlapping the part in {} in the 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]

However, i is r of an element including an arbitrary point
Indicates the second node number. From the above, problems 1, 2-1, 2
By superimposing the equations (2), (7), and (19) representing the potential distribution of −2, a uniform current is applied to a flat plate having a back surface crack or a buried crack, which is a target in this embodiment, at a distance. The potential distribution Φ at an arbitrary point when loaded 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 of the slit width and the crack length are given as parameters in advance.

Once 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 balloons are distributed from points P to Q in the figure.

The boundary conditions for determining the unknown function b ^m are as follows. That is, the slit surface is electrically insulated. This condition is expressed as follows, where n _s is the normal vector on the slit surface.

[0077]

[Formula 19]

By substituting the equation (20) into the above equation, the following equation is finally obtained as a boundary condition equation.

[0079]

[Equation 20]

Originally, the above-mentioned boundary condition must be satisfied over the entire surface of the slit. However, in this solution, the same conditions are set as follows. That is, the boundary conditions are M points that are regularly selected in the range from points V to W on one side of the slit shown in FIG. 11 (points indicated by a mark in FIG. 10).
The above shall hold. From this, the boundary condition expression shown in the expression (22) is finally reduced to an M-element simultaneous equation with respect to b ^m . Regarding the backside crack, the coordinates of the same point (x _m,
y _m, z _m ) is taken as follows [see FIG. 10 (a)].

[0081]

[Equation 21]

Similarly, as for 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 inventors in experiments. As shown, the x and z directions are 10
Division, the y direction is divided into three. The parameters required to obtain 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 the above-described element division and the use of parameters are performed. The probe used had a current input / output terminal spacing of 4 t (40 mm) and a potential difference measurement terminal spacing of 1
t (10 mm), and the supplied current amount was 5 A.

The probe has a structure that can be moved extremely easily so that the measurement operation can be performed at a large number of points in a short time. Further, by fixing the measuring terminal by using a spring, the measuring situation at each measuring position is made as uniform as possible.

FIG. 13 shows the test piece and the crack shape to be evaluated. The test piece is stainless steel (SUS304)
It has a size of 100 × 10 × 250 mm. All the test pieces have a backside crack in the center thereof. As shown in the figure, three types of cracks are targeted. Indicates a crack whose aspect ratio is close to 1, and is a crack whose aspect ratio is close to zero. The cracks of and are cracks perpendicular to the measurement surface, and the cracks are inclined to the measurement surface. The cracks here are simulated by a slit (width 0.5 mm) created by electrical discharge machining.

FIG. 14 shows the evaluation result of the obtained crack shape. The solid line in the figure shows the crack shape that was the object of evaluation, and the broken line shows the evaluated crack shape. The shapes of all cracks, that is, elongated cracks with an aspect ratio close to zero to round cracks with an aspect ratio close to 1, are evaluated well.

The above-described embodiments deal with the case where the member having a crack is electrically homogeneous. However, many cracks occur in welds such as pipes and pressure vessels. It is considered that the electric resistivity of the welded portion is different from that of the base metal, and it cannot be said that the entire member is electrically homogeneous. There is also a non-uniform shape due to the buildup. Without considering these effects, it is difficult to evaluate the crack shape accurately.

Next, an embodiment for correcting the influence of the welded portion will be described. FIG. 15 exemplifies a cross section of a general weld having a buildup. FIG. 16 shows an evaluation procedure of an example for a crack in a structure having such a welded portion. Here, the problem of evaluating the shape of a back surface crack or a buried crack existing in a flat plate as illustrated is dealt with. The back surface crack and the buried crack have a semi-elliptic disk shape and a disk shape, 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 a position α in the inspection direction (z direction), an angle β between the crack surface and the xy plane, and lengths a and c.
The shape of the buried crack is α, β, a, c, and the plate thickness direction (y direction)
Shall be defined by the quantities at the position d.

In carrying out this procedure, the weld line is parallel to the x direction. When measuring, the direction parallel to the weld line (x direction) when there is no crack near the weld
The current is supplied in the z direction so that the current becomes uniform. In this embodiment, since the vicinity of the welded portion is targeted, the rough position of the crack in the inspection direction (z direction) is not estimated. 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 is made to coincide with the center of the welding line, and is perpendicular to the welding line at a plurality of points along the direction (x direction) parallel to the welding line. The potential difference distribution in different directions (z direction) is measured. The position in the direction (x direction) parallel to the welding line where the potential difference distribution obtained here has the maximum value is α _cc . [Refer to the same figure (b)].
The vertical axis ΔΦ represents a value obtained by making the obtained potential difference distribution dimensionless by the potential difference obtained from a homogeneous member. Further, as shown in FIG. 7C, similarly, on the line of x = α _cc , the potential difference distribution in the direction (z direction) perpendicular to the welding line [FIG. A correction formula is applied to the measured potential difference distribution to remove the influence of the welded portion [FIG. Eventually, the corrected potential difference distributions on the cross line in the direction parallel to the weld line (x direction) near the crack and in the direction perpendicular to the weld line (z direction) are obtained. Finally corrected potential difference distribution ΔΦ
_The inverse problem is solved by matching _mk and the potential difference distribution ΔΦ _k for the three-dimensional crack obtained analytically in the data analysis device by using the optimization method. At this time, a function F as shown in equation (1) is defined, and a crack shape that minimizes the function value is searched for. K represents the number of measurement points. Powell's conjugate direction method is used for optimization.

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 is x or z. F (w) is W
(w) shows the potential difference distribution obtained from the member having only the welded portion. In using 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 backside crack of the welded portion with the buildup removed. The solid line in the figure is the actual crack shape, the broken line is the crack shape evaluated by the method using the theoretical solution for the conventional electrically homogeneous member without considering the influence of the welded part, and the dashed-dotted line is the correction. The evaluation results using the formula are shown. When the solid line and the broken line are compared, it can be seen that the influence of the welded portion appears in the evaluation result. The positions of both crack tips are almost the same, but it cannot be said that the inclination and length can be evaluated accurately. Therefore, it is necessary to correct the influence of the welded portion. Furthermore, by comparing the solid line and the alternate long and short dash line, the effectiveness of the correction formula for the backside crack without the buildup can be seen. The alternate long and short dash line almost overlaps the solid line.

By the way, the welded portion is accompanied by electrical non-uniformity and non-uniform shape. The former is caused by the difference between the electrical resistivity of the weld and the electrical resistivity of the base metal, and the latter is caused by the buildup. In order to evaluate cracks with high accuracy, it is essential to consider the effects of these two inhomogeneities. In addition to backside cracks, cracks occurring in welds include buried cracks. From these points, it is not enough to verify the backside crack without the above-mentioned buildup. Here, the two-dimensional buried crack existing in the welded part with the build-up was taken up and the correction formula was verified by numerical simulation.

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

The crack material has an aspect ratio L / t = 12 as shown in FIG. However, L is the length of the test piece.
If the aspect ratio is about this level, the effect of the end surface of the cracked material can be ignored. The central portion has a welded portion as shown in the figure. The height of the buildup at the center of the weld is 0.1t. In the finite element analysis, only the right half of the cracked material was targeted and the electrical resistivity ρ of the base metal was 1.0 and the resistivity of the weld was 1.1.
And Two types of buried cracks with different positions in the thickness direction,
Was targeted. Each crack shape is shown in the figure. As the measurement conditions, the current input / output terminal interval W ₁ = 10t and the potential difference measurement terminal interval W _p = 0.4t.

The correction results and evaluation results are shown in FIGS. 19 and 20. The solid line shows the potential difference distribution when there is no influence of the welded part (the welded part was replaced by the base metal) and the crack shape to be evaluated, the broken line is before correction, and the dashed-dotted line is the potential difference calculated by the correction formula. The distributions and the evaluation results obtained from them are shown. From the figure, the solid line is relatively in good agreement with the alternate long and short dash line, which shows the validity of the correction method. The solid line in FIG. 19 represents the potential difference distribution obtained by theoretical analysis using the singularity method of potential. For correction, F (w) and W (w)
Were calculated by finite element analysis. In the evaluation of crack shape, the corrected shape is in good agreement with the shape evaluated.

Next, an example of an experiment conducted for verifying the effectiveness of the method for evaluating a three-dimensional crack existing in a weld will be described. This experimental example is for a backside crack.
In the experiment, a current of 5 A is supplied from a constant current source to the current input / output terminal of the probe, and input / output is performed at a plurality of points on the end surface of the test piece so that a uniform current is provided in the longitudinal direction of the crack. Install a reference resistor between the test piece and the constant current source, and measure the voltage across the resistor with a digital voltmeter to monitor the amount of current being supplied.

The potential difference is measured by inputting the output of the microvoltmeter to the digital voltmeter and reading the display of the digital voltmeter. The potential difference measurement terminal interval is 10 mm.

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

The experimental results are shown in FIG. The solid line in the figure shows the actual crack shape, and the alternate long and short dash line shows the evaluated crack shape. For all cracks, their shape including inclination is well evaluated. From this, it can be seen that the highly accurate evaluation method of cracks existing in the welded portion, which is proposed in this example, is effective.

[0105]

According to the present invention, it is possible to perform nondestructive and highly accurate evaluation of a three-dimensional shape having an arbitrary aspect ratio and inclination of a buried crack or a backside crack in a structure, which has been difficult in the past. Therefore, the reliability of the structure can be significantly improved.

[Brief description of 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 an embodiment of the present invention.

FIG. 3 is an explanatory diagram of an infinite plate having a crack in which a uniform current is input / output.

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 for inputting and outputting a current.

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

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

FIG. 10 is an explanatory diagram of division of a surface on which double balloons are distributed.

FIG. 11 is an explanatory diagram of boundary conditions 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 the experiment.

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

FIG. 15 is an explanatory view of a cross section of a welded portion.

FIG. 16 is an explanatory diagram showing a crack evaluation procedure of 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 with a padding removed.

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

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

FIG. 20 is an explanatory diagram of an evaluation result of a numerical simulation of an object having a welded portion.

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

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

[Explanation 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 analysis device 9 Real potential difference data storage unit 10 Virtual Three-dimensional 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

Claims (1)

[Claims] 1. A current input / output terminal connected to a constant current source, a potential difference measuring terminal provided between the current input / output terminals, and an inspection target using the current input / output terminal and the potential difference measuring terminal. Quantify the actual state of three-dimensional cracks in a structure by the potential difference method using a data analysis device that analyzes the potential difference data measured at multiple positions on the outer surface of the structure that are two-dimensionally distributed. In the non-destructive inspection method, a virtual three-dimensional crack state having an arbitrary aspect ratio and inclination which is not exposed on the surface in the structure and is buried or exposed on the surface is set in the data analysis device. , The virtual potential difference distribution on the structure surface corresponding to the state of the virtual three-dimensional crack set above, the virtual potential difference distribution on the structure surface obtained above,
By comparing with 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, the error of the virtual potential difference distribution is obtained, and the virtual potential difference obtained above is calculated. Based on the error in the distribution, the state of the virtual three-dimensional crack set as described above is corrected, and the above-described respective processes are sequentially and repeatedly executed in the direction in which the error is minimized to thereby create a virtual three-dimensional crack. A non-destructive inspection method for a three-dimensional crack by the direct current potential difference method, characterized by optimizing the state and quantitatively evaluating the state of the actual three-dimensional crack in the structure.