JPH0412412B2 - - Google Patents

Description

[Detailed description of the invention]

Technical Field The present invention uses an electronic computer to determine the position and shape of defects such as cracks and defects existing inside the fixed body by using an electronic computer to calculate the measured values obtained from the surface of the fixed body without destroying the fixed body. Regarding the computer-applied non-destructive measurement method for measuring internal defects through calculation processing, in particular, data on electrical potential or elastic compliance that can be measured on the surface of a constant body to be measured is analyzed using a new method to determine the target side. This system is designed to identify two-dimensional or three-dimensional defects existing inside the body as unknown free surfaces. Prior Art In general, nondestructively detecting cracks or defects inside structures and quantitatively measuring their position, shape, and dimensions is extremely important in evaluating the safety of equipment. It is. Conventionally, there are various non-destructive inspection methods used to detect cracks or defects inside such structures. It was used. However, all of these conventional inspection methods have the important problem that it is not always easy to quantitatively determine the location, shape, and dimensions of cracks or defects that exist inside structures, etc. with sufficient accuracy. There were flaws. The main cause of such defects with conventional inspection methods is that cracks or defects existing inside a structure, etc., have a so-called two-dimensional shape that is uniform in the thickness direction of a plate-like structure, for example. It is extremely rare for a crack or defect to have a three-dimensional shape, and conventionally it has been difficult to accurately measure the position and shape, especially the shape and dimensions, of cracks or defects in such a three-dimensional shape. This appears to be because the technology had not yet been established. Therefore, the development of a quantitative non-destructive inspection method that can be applied to such three-dimensional cracks and defects has become one of the extremely important issues in current technological development. On the other hand, the electrical potential method and the elastic compliance method, also called the potentiometric method or the electrical resistance method, respectively, have been widely used for measuring the length of two-dimensional cracks or defects as non-destructive testing methods. . Considering that these conventional electric potential method and elastic compliance method are extremely effective for highly accurate evaluation of the dimensions of two-dimensional cracks or defects,
If such a conventional and effective non-destructive testing method can be extended to the measurement of three-dimensional cracks or defects, it will be possible to quantify the position and shape of three-dimensional cracks or defects, which has been extremely difficult in the past. It is expected that this will become a promising measurement method. However, conventionally, it has not been possible to quantitatively measure the position and shape of a general three-dimensional crack or three-dimensional defect using the electric potential method or elastic compliance method, and it is still at the research and development stage. However, it seems that there is no prospect of success other than the method of the present invention described below. Purpose In view of the problems of the prior art described above, an object of the present invention is to eliminate the drawbacks and non-destructively increase the position and shape of three-dimensional cracks or defects existing inside the fixed body. The object of the present invention is to provide a non-destructive measuring method for internal defects that can accurately and quantitatively measure internal defects. Another object of the present invention is to use the electric potential method and the elastic compliance method, which have been proven to be effective for highly accurate quantitative measurement of the dimensions of two-dimensional cracks or defects mainly near the surface of a fixed object. The method is expanded and applied to the quantitative measurement of the position and shape of defects such as three-dimensional cracks and defects that exist inside the fixed body, and the internal defects can be detected by processing the measurement data using an electronic computer. It is an object of the present invention to provide a computer-applied non-destructive measurement method for internal defects that enables highly accurate non-destructive measurement. Summary of the Invention The computer-applied non-destructive internal defect measurement method according to the present invention includes a measurement technique based on electrical potential and elastic compliance that is effective for two-dimensional cracks or defects, and an inverse problem analysis based on boundary-type numerical analysis. A computer-applied electric potential tomography measurement method and a computer-applied elastic compliance tomography method that make it possible to quantitatively measure the position and shape of defects caused by three-dimensional cracks or defects by introducing and combining data analysis methods based on new principles. It is a comprehensive measurement method, and when a predetermined current or a predetermined mechanical load is applied to the target body, the measurement method is three-dimensionally arranged on the surface that covers at least a required part of the target body, In most cases, a boundary type is calculated by applying a computer to the measured values obtained by measuring the electric potential or elastic compliance that occurs at multiple points arranged three-dimensionally almost uniformly over almost the entire surface of the fixed object. By performing inverse problem analysis based on the numerical analysis of
The present invention is characterized in that the position and shape of a three-dimensional defect existing at least in the vicinity of the required portion inside the fixed body to be covered are quantitatively measured. In other words, the computer-applied non-destructive internal defect measurement method of the present invention uses a boundary element method, a boundary integral equation method, etc. for a group of measured values of electrical potential or elastic compliance at multiple points on the surface of a fixed body such as a structure. This is a new type of measurement method that performs data analysis by applying an inverse problem analysis method based on a boundary-type numerical analysis method, which is called a boundary-type numerical analysis method. This is a measurement method that is complementary or competitive with the quantitative evaluation method for three-dimensional cracks or three-dimensional defects used. Therefore, the measuring method of the present invention evaluates internal cracks based on the distribution of electric potential or elastic compliance appearing on the surface of the fixed object, and therefore, the measuring method of the present invention is not applicable to conventional medical technical fields. It can be considered to be theoretically and formally equivalent to the so-called X-ray CT method, that is, X-ray tomography used in It should also be called compliance CT crack shape and size measurement method. In general, boundary-type numerical analysis methods can be formulated using only the physical quantities at the boundary, so it is possible to formulate the boundary using only the physical quantities on the boundary, that is, the physical quantities on the surface of the target constant. An inverse problem analysis method that determines the unknown free boundary existing inside the side body, that is, the location of cracks or defects, that is, the physical quantity that appears on the surface due to the existence of internal cracks, etc. It is possible to construct an analytical method that analyzes the occurrence of cracks, etc., and conversely evaluates the presence of cracks, etc., as a cause. The above-mentioned electrical potential CT crack measurement method and elastic compliance CT crack measurement method according to the present invention are based on the application of such an inverse problem analysis method, and are based on a fundamentally new idea at least as a nondestructive measurement method for internal defects in structures. It can be considered as something. The measurement method of the present invention requires the use of a so-called computer to analyze the measurement data using the inverse problem analysis method, so the computer-aided measurement results can be easily post-processed by computer aids such as graphic display. Of course, it can be applied to Therefore, the measuring method of the present invention having such features is extremely useful as a non-destructive inspection method for cracks, defects, etc. inside structures, and
It is recognized as indispensable for material testing, especially strength tests that are affected by internal cracks and defects. It is also conceivable to incorporate the measuring device according to the present invention into a series of systems. EXAMPLES The present invention will be explained in detail below using examples with reference to the drawings. First, FIG. 1 shows a schematic configuration of an electrical potential CT crack measuring device as an example of a non-destructive measuring device for internal defects according to the method of the present invention. In the illustrated configuration example, a constant current of an appropriate magnitude is applied from a constant current power source 1 to a fixed body 4 that has cracks or the like inside, and the surface of the fixed body 4 is determined based on the constant current. The multi-point potentiometer 2 measures the distribution of electrical potential appearing at a large number of measurement points 5 set to be distributed almost uniformly. In the conventional electrical potential method, the object of measurement was a two-dimensional crack or three-dimensional defect near the surface of the fixed object, so the electric potential was measured only at a specific point on the surface of the fixed object or a measurement point in its vicinity. However, in the measuring method of the present invention, two-dimensional or three-dimensional cracks or defects existing inside the fixed body 4 are to be measured, so that the measurement method covers the entire surface of the fixed body 4. By measuring the electric potential values appearing at a large number of almost uniformly distributed measurement points, inputting the measured data into the data analysis computer 3, and performing the inverse problem analysis described above, cracks inside the fixed body can be detected. , quantitatively derive the position and shape of defects, etc.
It should be noted that the quantitative measurement itself by data analysis using a computer can be performed relatively easily as will be described later, and as mentioned above, post-processing such as graphical display of the measurement results using the computer 3 can also be performed easily. As I said. Here, to explain in more detail the above-mentioned inverse problem analysis method that forms the basis of the measurement method of the present invention, the electrical potential CT
In the crack measurement method, this inverse problem analysis is performed as follows. However, since the problem of electric potential boils down to a linear problem that satisfies Laplace's equation, if a boundary-type numerical analysis method called the boundary element method is based, it is possible to solve the problem using the electric potential and current density on the boundary. Can deal with problems. That is,
First, by comparing and contrasting the measured value of the electrical potential on the surface of the fixed body with the analytical value of the electrical potential in a state where there are no cracks or defects, the difference is found to determine the surface where the crack or defect exists, that is, the surface shown in the figure. Surface in the fixed body 4
Determine ABCD and make this surface the unknown boundary surface.
Note that boundary surfaces other than this unknown boundary surface that exist inside the to-be-side regular body, ie, the to-be-side regular body surface, are given boundary conditions in advance and are known. However, the internal unknown interface formed by a crack or defect
Regarding ABCD, it is unclear to what extent there is a crack or defect and the measured values are not continuous, and in what part there is no boundary and the measured values are continuous. Therefore, the boundary condition This means that it will not be possible to set . Such boundary problems with unknown conditions cannot be handled by conventional forward problem analysis methods such as the finite element method and the boundary element method, and constitute a kind of inverse problem. Regarding the unknown boundary surface obtained by numerical analysis of such an inverse problem, it can be said that the current density in the direction perpendicular to the surface of the space outside the fixed body is zero on the free surface formed by the surface of the fixed body on which the electric potential is measured. In addition to boundary conditions,
The electrical potential distribution on the surface is also known, and therefore measurements taken over the entire surface of the fixed object contain excess information caused by the presence of cracks or defects. Utilizing this fact, the unknown boundary surface can be identified. In reality, the cracks or defects that cause the distribution of electric potential measured on the surface of the target body to be expressed as a result may have any shape and size at any position inside the target body. Unknown cracks, defects, etc. can be identified by inverse analysis. On the other hand, in the elastic compliance CT crack measurement method, which is the other half of the measurement method of the present invention, the electrical current as the electrical load in the electrical potential CT crack measurement method described above is replaced with a mechanical load, and the electrical response is By replacing the electrical potential with elastic compliance as a mechanical response, unknown cracks and defects can be identified using the inverse problem analysis method in exactly the same manner as described above. That is, for example, when a load is applied to an appropriate part of the target body to cause elastic deformation, the elastic displacement, or elastic compliance, that appears on the surface of the target body is measured using a displacement meter such as a differential transformer. It turns out. Therefore, the problem of elastic deformation is also a typical linear problem, and in the same way as described above, inverse problem analysis based on the boundary type numerical analysis method can be applied. That is, by performing inverse problem analysis based on the measured values of elastic compliance, the position and shape of unknown cracks and defects can be identified. In addition, in any of the above-mentioned CT crack measurement methods, for surface cracks, surface defects, internal cracks, or internal defects where the crack or defect exists at a shallow position compared to the thickness of the target body, The lateral field can be regarded as a semi-infinite field and treated approximately. Therefore, as a measurement value to be subjected to numerical analysis, it is sufficient to obtain a measurement value of electric potential or elastic compliance on the fixed body surface on the side closer to the crack or defect. This makes it easier to apply the measuring method of the present invention. In general, the measurement technique for measuring the distribution of electric potential generated by passing a constant current through a part of a fixed object such as a member or structure has already been established and widely used as the so-called electric potential method. It is considered that the conventional measurement technique related to the measurement method of the present invention can be applied as is. That is, in the measurement method of the present invention, the measured value of the electrical potential on the surface of the fixed object is input into a computer along with data on the shape and dimensions of the fixed object, the current inflow position, and the amount of current, and the measurement is performed based on this information. Process the inverse problem analysis in the computer,
Identify the location and geometry of cracks or defects within the fixed body. Note that since the inverse problem analysis method based on the boundary type numerical analysis method is applied to the analysis of the information data, the analysis of the information data can be executed by a relatively small computer such as a personal computer. On the other hand, when elastic compliance is used as the measurement quantity, the position and shape of a crack or defect inside the fixed body can be measured using a similar procedure. In addition, if the location of the crack or defect is far away from the surface of the fixed object on which the electric potential or elastic compliance is to be measured, it is necessary to improve the measurement accuracy of the electric potential or elastic compliance and to measure the electric potential or elastic compliance efficiently and stably. The key point of measurement using the method of the present invention is that an appropriate inverse problem analysis method should be selected to perform appropriate data analysis. Next, an overview will be given of an analysis method for identifying an unknown free surface caused by a crack or a defect inside a fixed body to be covered, which forms the basis of the measurement method of the present invention. Generally, in the boundary element method, a solution is obtained by converting a governing differential equation into an equivalent boundary integral equation using the Gauss-Green theorem. On the other hand, in ordinary problems handled by the boundary element method, the second
As shown in the figure, the boundary Γ surrounding the region Ω consists of a boundary Γ ₁ whose potential value is known given the basic boundary conditions, and a flux q flowing into the boundary given the natural boundary conditions. consists of the known boundary Γ ₂ , and the unknown boundary values at these boundaries Γ ₁ and Γ ₂ , that is, the flux q on the boundary Γ ₁ and the potential value on the boundary Γ ₂ , can be calculated using the boundary integral equation described above. By solving, it can be determined from other known boundary conditions. However, in the problem targeted by the inverse problem analysis used in the measurement method of _the present invention, as shown in _FIG . There exists a boundary Γ ₀ where it is unknown whether there is a boundary, and both the potential value and the flux q on the boundary are unknown. Since such a boundary problem cannot be solved as it is, the boundary Γ ₂ obtained by measuring it using a conventionally well-known method
By solving the boundary integral equation using the above potential values together, the potential value and flux q on the boundary Γ ₀ can be obtained. It can be determined as a location where the condition of flux q=0 based on the free surface formed by the crack or defect is satisfied. Depending on the problem, it is also possible to determine the location of cracks or defects based on the potential value. As described above, as an example of data analysis for determining the location of cracks and defects inside the fixed body as an unknown free surface, for the sake of simplicity, we will consider the problem of two-dimensional electric potential. Note that once a data analysis method for a two-dimensional problem is known, it is easy to extend that analysis method to a three-dimensional problem and apply it in the same way. Generally, the governing equation within the region Q for the coordinate systems X ₁ and X ₂ is expressed as follows. ∇ ² φ=o (∇ ² = ∂ ² /∂X ² ₁ +∂ ² /∂ ² ₂ ) (1) Therefore, each boundary Γ ₀ , Γ ₁ , Γ ₂ with the following boundary condition (2) Consider the problem of the boundary Γ consisting of. Boundary Γ ₀ : Potential value = unknown flux q = ∂/∂n = unknown boundary Γ ₁ : Potential value = flux q = unknown boundary Γ ₂ : Potential value = flux q = q (2) Here, n is It is an outward unit normal on the boundary Γ, and the superscript bar in the symbol indicates that it is known. When both sides of the above equation (1) are multiplied by a weighting function ^* having a continuous second derivative within the region Q and integrated over the entire region Q, the following identity relation equation (3) is obtained. ∫〓∇ ²・^*・dΩ=o (3) On the other hand, according to Gauss's divergence theorem, the following equation
(4) is obtained. ∫〓(・∇ ² φ ^* − ^*・∇ ² )dΩ =∫〓(・q ^* − ^*・q)dΓ (4) Here q ^* ≡∂ ^* ／∂X _i・n _i ＝∂ ^* ／∂ n Next, assuming that the medium that has the same properties as the medium that fills the area Ω extends infinitely outside the area Ω, as shown in Figure 3, the unit concentration potential at a point a in the area Ω is Considering the potential change φ ^* (a, b) on another point b in the region Ω in the case where
(6) becomes. ∇ ^{2 *} (a, b) + δ (a, b) = o (6) where δ (a, b) is the Dirac delta function. Therefore, ^* (a, b) is the basic solution, and 2
For dimensional problems, it is given by the following equation (7). ^* (a,b)= ^* (r)=ln(1/r)/2π (7) Here, r is the distance between points a and b. Therefore, by substituting equation (7) and equation (3) into equation (4), the following integral equation (8) is obtained. (a)+∫Γ[q ^* (a, b)・(B) − ^* (a, b)・q(B)]・dΓ(B)=o (8) Here, a is the area Ω represents any point, B
represents an arbitrary point on the boundary Γ. Equation (8) above is an integral equation that relates the potential value at any point within the region Ω to the potential value and flux q on the boundary Γ, but as shown in Figure 3, The following equation (9) is obtained when an integral equation for moving an arbitrary point a to an arbitrary point A on the boundary Γ is obtained. C(A)・(A)+∫Γ[q ^* (A, B)・(B) − ^* (A, B)・q(B)]・dΓ(B) (9) Here, C(A ) is C=1/ when the boundary is smooth
It becomes 2. Next, when discretizing the above equation (9), the i-th node A _i on the boundary Γ coincides with point A, and the point B coincides with j
Assuming that the potential value and flux q are constant within the element, the following equation (10) is obtained. C _i・_i +Σq ^* ij・_j −Σ ^* ij・q _j =0 (10) Here, n is the total number of boundary elements, and ^* ij and ^* ij are given by the following equation (11). q ^* ij＝∫Γq ^* (A _i , B)・dΓ(B) ^* ij＝∫Γ ^* (A _i , B)・dΓ(B) (11) This equation (10) can be applied to all When expressed in terms of nodes, the following matrix representation of equation (12) is obtained. By solving this matrix equation (12), it is possible to identify the location of cracks and defects as unknown boundaries within the region. Now, as shown in Figure 4, the center line of the rectangular area
Assuming that there are free boundaries of a symmetrical crack on both sides of B′E, constant potential values φ = 1 and φ Suppose that the length a of the crack is identified based on the potential values on the sides AB' and C'D' of the quadrant AB'C'D' when given = -1, respectively. Accordingly, in such an inverse problem analysis, it is possible to analyze the above-mentioned quadrant area shown in shading in FIG. 4 due to the symmetry of the problem. Now, as shown in Figure 5, a rectangular area is created.
By dividing AB′C′D′ into boundary elements and giving the boundary conditions shown in Table 1, on the boundary AB′ and
Data on the potential value on C′D′ can be obtained by BEM analysis with the crack length a/W=1/2. The results of the analysis are shown in Table 2. Therefore, as can be seen from Table 2, the solution for flux q is on the order of 10 ^-6 to 10 ^-9 for element numbers 1 to 5,

【table】

Claims (1)

[Scope of Claims] 1. When a predetermined current or a predetermined mechanical load is applied to the object to be measured, it is arranged three-dimensionally on the surface covering at least a required part of the object to be measured, and at most, the Boundary-type numerical analysis using a computer for the measured values obtained by measuring the electric potential or elastic compliance that occurs at multiple points arranged almost uniformly three-dimensionally over almost the entire surface of the fixed object. A computer-applied internal defect detection method characterized by quantitatively measuring the position and shape of a three-dimensional defect existing at least in the vicinity of the required part inside the fixed body by performing an inverse problem analysis based on Destructive measurement method. 2. A computer-applied non-destructive measuring method for internal defects, wherein the defect is a crack or a defect in the measuring method according to claim 1. 3. In the measuring method according to claim 1 or 2, by applying a computer to identify a free surface existing inside the to-be-side fixed body based on the electric potential or the elastic compliance, A method for nondestructively measuring internal defects using a computer, characterized in that the inverse problem analysis is performed.