JP5602655B2 - Crack size estimation method - Google Patents

Description

  The present invention relates to a method for estimating the depth and surface length (hereinafter also referred to as “crack size”) of a crack on the inner surface of a structure generated by fatigue or stress corrosion cracking due to internal pressure in a nuclear power plant or the like.

  Conventionally, for example, a crack generated on the inner surface of a pipe is often detected by ultrasonic inspection. If the detected crack is small or if the amount of progress until the next inspection is expected to be small, it may continue to be used without being repaired. Then, the size of the crack is measured again at the next inspection, and the presence or absence of the progress of the crack and the validity of the progress prediction are confirmed. However, with ultrasonic measurement, the crack position on the inner surface of the pipe can be estimated, but the accuracy is poor in measuring the depth of the crack perpendicular to the plate surface, and when the plate thickness is thin, the crack depth is measured. Can not do it. Furthermore, it is said that the accuracy of crack depth measurement by the ultrasonic flaw detection method is several millimeters, and it is difficult to determine the presence or absence of crack growth and to measure the amount of progress.

  On the other hand, when the position where the crack is generated on the inner surface of the pipe is known in advance, a strain gauge is attached to the outer surface of the pipe where the crack is generated, and the change in strain at the position is measured. A method for estimating the depth is known (Patent Document 1, etc.). This method is based on the finding that when an internal crack occurs in a structure such as a cylinder and the crack progresses in the thickness direction, the strain on the outer surface of the position increases in proportion to the increase in the depth of the internal crack. Based on the relationship between the inner surface crack depth and the outer surface strain, the inner surface crack depth is estimated from the measured value of the outer surface strain. In Patent Document 1, the reason why the inner surface crack depth can be estimated from the measurement value of the outer surface strain is that when the load stress is constant and the inner surface crack depth is increased, the rigidity of the remaining portion decreases, so the outer surface strain is reduced. Is considered to increase (Patent Document 1, page 2, upper right column, lines 1 to 4).

JP-A-55-119041

  However, the method of estimating the crack depth on the inner surface of the tube by applying a strain gauge to the outer surface of the tube described above can identify the depth of the crack, but it spreads the crack toward the surface of the structure (surface length). ) Could not be identified at the same time.

  The main object of the present invention is to provide a crack size estimation method that can identify not only the depth of a crack but also the surface length of a crack on the inner surface of a structure that is under pressure.

  In order to achieve the above object, a crack size estimation method according to the present invention includes a first step of detecting a crack on the inner surface of a structure in advance, and a distortion of the detected outer surface of the structure on the outer surface of the crack. A second step of measuring with a plurality of strain gauges affixed, and a plurality of strain measurement values measured with the plurality of strain gauges, using a finite element analysis to determine the depth and surface length of the virtual crack on the inner surface of the virtual structure A third step of introducing a depth and a surface length of a virtual crack corresponding to each of the plurality of strain measurement values; A fourth step of graphing the relationship between the depth and surface length of the virtual crack corresponding to each of the measured values as a plurality of curves, and the depth and surface length of the intersection where the plurality of graphed curves intersect. By seeking Characterized in that it comprises a fifth step of estimating the depth and the surface length of the detected cracks, the.

  In the fifth step, a plurality of intersection points of the plurality of curves are selected, the depth and surface length of each intersection point are obtained for the plurality of intersection points, and as a sixth step, a weighting factor is calculated for the depth and surface length of each intersection point Preferably, the method further includes a step of deriving an average value in consideration of

  In addition, when the structure in which the crack is detected has a plate shape with a thickness t, the strain gauge preferably has a gauge length of 0.1 t or less.

As an analysis object, a cross section of a pipe (virtual structure) in which a semi-elliptical crack in the circumferential direction exists on the inner surface is shown, (a) is an axis perpendicular cross section, and (b) is an axis parallel cross section. As an analysis target, a cross section of a pipe (virtual structure) in which a semi-elliptical crack in the axial direction exists on the inner surface is shown, (a) is a cross section perpendicular to the axis, and (b) is a cross section parallel to the axis. It is the analysis image which divided the analysis object of Drawing 1 (A) into a mesh. It is the analysis image which divided the analysis object of Drawing 1 (B) into meshes. It is a graph which shows the relationship between the depth of a crack, the surface length of a crack, and the distortion in an outer surface regarding the circumferential strain of the analysis object of FIG. It is a graph which shows the relationship of the depth of a crack, the surface length of a crack, and the distortion in an outer surface regarding the axial distortion of the analysis object of FIG. 1 (A). It is a graph which shows the relationship between the depth of a crack, the surface length of a crack, and the distortion in an outer surface regarding the circumferential strain of the analysis object of FIG. 1 (B). It is a graph which shows the relationship between the depth of a crack, the surface length of a crack, and the distortion in an outer surface regarding the axial distortion of the analysis object of FIG. 1 (B). It is a strain distribution around the crack related to the analysis target in FIG. 1A, and is a graph showing the relationship between the distance from the crack center along the direction in which the crack extends and the strain (circumferential strain and axial strain). 1A is a graph showing strain distribution around a crack related to the analysis target in FIG. 1A and showing a relationship between a distance from a crack center and a strain (circumferential strain and axial strain) along a direction orthogonal to a direction in which the crack extends. is there. It is a strain distribution around the crack regarding the analysis target in FIG. 1B, and is a graph showing the relationship between the distance from the crack center along the extending direction of the crack and the strain (circumferential strain and axial strain). 1B is a graph showing the relationship between the strain (circumferential strain and axial strain) from the crack center along the direction perpendicular to the direction in which the crack extends, and the strain distribution around the crack related to the analysis target in FIG. is there. It is a graph which shows the relationship between the distance (x) from the crack center regarding the analysis object of FIG. It is a perspective view which shows the state which affixed several strain gauges with a partial expanded sectional view. It is a graph which shows the combination of the crack depth estimated from several strain gauges, and the surface length. Graph showing crack depth error (considering normal distribution error in strain gauge output) estimated from the combination of strain gauges in the circumferential direction and axial direction within the range of Lm in FIG. It is.

  An embodiment of a crack size estimation method according to the present invention will be described below with reference to FIGS.

  First, a structure having a crack is virtually modeled by CAD or the like, and a computer simulation analysis (finite element analysis) is performed on the virtual crack by a finite element method using the virtual structure as an analysis target.

  In the present embodiment, as shown in FIG. 1, the analysis object has semi-elliptical cracks 1 and 2 in the circumferential direction (FIG. 1 (a)) or axial direction (FIG. 1 (b)) on the inner surface. The tubes (virtual structures) 3 and 4 that receive the internal pressure (Pa) were used.

  The pipes 3 and 4 as virtual structures have an inner diameter (Ri) of 43.64 mm and a wall thickness (t) of 13.5 mm (a 4-inch pipe, corresponding to schedule number 160). The surface length (2c) of the crack (virtual crack) was set to t, 2t, and 4t with respect to the thickness (t) of the tubes 3 and 4, and the depth (a) was changed from 0 to 0.5t.

  As shown in FIG. 2, the finite element analysis was performed using mesh division with 20-node elements, and the elastic analysis was performed with the general-purpose code ABAQUS. In order to apply an internal pressure of 15 MPa including the crack surface and to consider the cap effect, an axial load corresponding to the internal pressure was applied to the pipe end. The Young's modulus was 180 GPa and the Poisson's ratio was 0.3.

  As a result of the above finite element analysis, FIG. 3 shows the case where the crack surface length (2c) is t, 2t, and 4t, respectively, at the depth (a / t) of the cracks 1 and 2 and the center position of the crack. The relationship with the distortion of the outer surface is shown.

3, the distortion shows the circumferential strain (circumferential strain) epsilon _theta axial strain (axial strain) epsilon _Z respectively. In FIG. 3, the relationship between the depth (a / t) and the strain at each surface length (2c) is represented by an approximate curve, but the plot interval of the depth (a / t) (FIG. 3). Then, 0.05) may be plotted more finely to display a graph as a set of points without using an approximate curve.

  The relationship between the crack surface length (2c), the crack depth (a / t), and the strain on the outer surface of the crack as described above is compiled into a database and stored in a storage device. In the present embodiment, for the sake of illustration, the crack surface length (2c) is set to three (2c = t, 2t, 4t). Increase the number and build a detailed database. FIG. 3 shows the relationship with only the strain on the outer surface of the tube at the center position of the crack. As will be described later, the finite element analysis is also performed on the strain on the outer surface of the tube at a plurality of positions separated from the center position of the crack. Database.

In FIG. 3, when there is no crack, that is, the circumferential strain ε _θ in the healthy part is 200 με, but the axial strain ε _Z is about 50 με. In either case, the strain monotonously decreases as the crack grows (crack progresses). For example, when the crack length (2c) is 2t (ie, c = 1t), the strain is reduced by 50 με or more when the crack depth is 0.5 t. In particular, the circumferential strain ε _θ of the axial crack is 100 με or more. It is falling. When the strain decreases by 100 με when the crack depth advances from 0 to 0.5 t, assuming that the strain detection sensitivity is 5 με, 0.5 t × (5/100) = 0.025 t (approximately 0.34 mm) Crack growth can be detected. However, as can be seen from FIG. 3, the change in strain depends on the shape of the crack (aspect ratio a / c), and the greater the crack surface length (c), the greater the change in strain. The analysis result that the strain decreases as the crack progresses is different from the conventional recognition (Patent Document 1).

  The strain distribution around the crack by the finite element analysis is shown in FIG. Both strains were the smallest on the outer surface of the crack center, and the sensitivity was greatest. In the direction along the crack surface, the strain greatly changed in the range of the crack length, and in the direction perpendicular to the crack surface in the range of the crack depth (0.5 t). In any crack direction and strain direction, the strain change is small in the range of about 0.1 t (1.35 mm) from the crack center. Therefore, the gauge length of the strain gauge is desirably 0.1 t or less.

  FIG. 5 shows the change in strain due to cracks in the circumferential direction of a / t = 0.5, c = t, and a / c = 0.5 (strain without cracks based on the calculation result by the finite element analysis. The amount of change from Since t = 13.5 mm, x = 13.5 mm (x is the distance in the crack length direction from the crack center) just corresponds to the end of the crack. The strain change due to the crack is observed in a wider range, and it can be seen that the change in the axial strain is larger.

  As described above, as the crack grows, the strain on the outer surface of the tube changes, but the change depends on the crack shape (aspect ratio). Therefore, it cannot be determined from a single strain change whether the crack has progressed in the depth direction or the surface direction.

  If the crack is assumed to be, for example, a semi-elliptical shape, the shape of the crack has two degrees of freedom, depth and length, and can be theoretically estimated from the outputs of at least two strain gauges. The crack shape is not limited to a semi-elliptical shape, and can be assumed to be various shapes such as a square shape, a semi-annular shape, and an irregular shape.

  As an example of an axial crack on the inner surface of the tube, as shown in FIG. 6, a plurality of strain gauges 5... 5 are installed on the outer surface of the semi-elliptical crack 2 at a predetermined interval (2 mm interval in the figure). Assuming that the depth (a) and the surface length (2c) of the crack 2 are identified as described below. Each of the strain gauges 5... 5 can measure and output strain in the circumferential direction and axial direction of the tube 4 (capable of measuring two orthogonal directions).

  The relationship between the depth and the surface length obtained from the output of the strain gauge at the center of the crack in FIG. 6, that is, the strain gauge with the distance X = 0 mm in FIG. 6, can be obtained using the database constructed previously. .

For example, referring to FIG. 3A, when the circumferential strain (ε _θ ) is 150 με, a = 0.5 at c = 1t, a≈0.46 at c = 2t, and a = 0.46 at c = 0.5t. > 0.5 (not shown). As described above, increasing the number of surface lengths (2c) in FIG. 3 (A) increases the number of curves displayed in FIG. 3 (A). The number of relationships increases. Using the graph in which the number of curves displayed in FIG. 3 is increased as described above, a graph in which a set of depth and surface length with respect to a certain strain value (circumferential strain and axial strain) is plotted is X = A plot group of 0 mm. In FIG. 7, c / t is plotted at intervals of 0.1.

  In the case of the distance X = 2 mm, 4 mm, and 6 mm in FIG. 6, the relationship between the depth and the surface length with respect to strain is plotted in FIG. The graph shown in FIG. 3 is a graph at the center of the crack, that is, when the distance X = 0 mm in FIG. 6 and is not shown, but is shown when the distance X = 2 mm, 4 mm, and 6 mm in FIG. The graph corresponding to 3 can be obtained from the finite element analysis when the database of the distance X = 0 is created.

  As described above, when the crack size is estimated from one strain gauge output, the depth and length of the crack are not uniquely determined, and have a combination of depth and surface length corresponding to the strain amount. As can be seen from FIG. 7, the relationship between the depth of the crack and the surface length draws a different curve depending on the position of the strain gauge. As shown in FIG. 7, all the curves intersect at a / t = 0.5 and c = t as calculation conditions. Therefore, by using the output of two strain gauges, two curves indicating the relationship between the crack depth and the surface length intersect at one point, and two kinds of parameters, the crack depth and the surface length, from the intersection point. Can be estimated.

  In actual measurement, the position of the crack is detected in advance by an ultrasonic flaw detection method or the like, and a plurality of strain gauges are attached to the outer surface of the detected crack structure at predetermined intervals. A known strain gauge can be used as the strain gauge. For example, a collective gauge in which five strain gauges are integrated at intervals of 2 mm is also commercially available, and this can also be used.

  In actual measurement, since there is a distortion measurement error, all the curves do not intersect at one point as shown in FIG. However, two strain gauges are selected from a plurality of strain gauges, and from the intersection of two curves indicating the correlation between the depth of the virtual crack and the surface length obtained from the two selected strain gauges, The depth and length can be determined, and the depth and surface length of the obtained virtual crack can be estimated as the actual crack depth and surface length. The strain gauge output can be monitored online, and the progress of the actual crack in the depth direction and the surface length direction can be monitored.

By changing the combination of two strain gauges selected from a plurality of strain gauges, a plurality of pairs of virtual crack depth and surface length can be estimated. The estimation accuracy can be improved by taking an average of the estimated depth and surface length of a plurality of sets of cracks. 8, with the circumferential direction and the axial strain gauges in the range of L _m as shown in FIG. 6 illustrates the error of crack depth is estimated from all of them combined. For example, when L _m = 4 mm, the estimation is performed using a total of six strain gauges in the circumferential and axial directions at x = 0, 2, and 4 mm.

  Here, assuming actual measurement, the error was given to all strain gauge outputs in a normal distribution having the standard deviation shown in the figure. FIG. 8 shows the error of the estimated value obtained from 1000 calculations with the strain gauge measurement error changed (filled plot in the figure).

When the standard deviation of the strain gauge error is 5 με, the crack depth estimation error decreases to L _m = 4 mm, but the error increases conversely. When the standard deviation of the error was 2 με, the error increased as the number of strain gauges increased. If the position where the strain gauge is attached is separated from the center of the crack, the amount of change in strain becomes smaller (sensitivity becomes worse), and the measurement accuracy decreases. Then, by using an estimated value using such a strain gauge with poor sensitivity (poor accuracy), the estimation error obtained from the average is reduced. Thus, when a simple average value of crack depths estimated from a plurality of strain gauges is used, the error cannot always be reduced even if the number of strain gauges is increased.

As shown in FIG. 8, when the number of strain gauges is simply increased, the error increases. Therefore, it is preferable not to use a simple average of the combinations of strain gauges but to consider the weight in the average. Specifically, using n gauges, a weight w ⁽ for a crack size (depth or surface length) a _est ^{(i, k)} estimated from a combination of two gauges i and k among them. ^{i, k)} is defined, and the crack size (depth or direction length) a _est is obtained by the following equation (1).

In this equation, the case where w ^{(i, k)} are all set to the same numerical value corresponds to the case where the above-described simple average is performed. For example, in FIG. 7, the axial strain curves almost coincide. In such a case, the intersecting point of the two curves is greatly shifted due to the strain gauge error, and the estimation accuracy tends to deteriorate. Conversely, a combination having a large angle at which two curves intersect reduces the error. In addition, when the magnitude of the strain change with respect to the crack size becomes small with respect to the measurement error, the estimation accuracy decreases.

As described above, the accuracy varies depending on the combination of strain gauges and the position where the gauges are attached. Therefore, by increasing the weight w ^{(i, k)} relative to an accurate estimated value, Improvements can be made.

Convergence calculation was performed to change the weight for each combination of strain gauges so that the error of the estimated crack depth estimated value a _est was reduced. Here, a combination of weighting factors that minimizes the influence of the strain gauge error was determined by trial and error by the Monte Carlo method that gives the error of the strain gauge as a random number.

  Then, combinations of weights as shown in Table 1 below were obtained.

This table shows the result when Lm = 6mm and the standard deviation of strain gauge error is 5με. However, the circumferential strain gauge at x = 6mm has all weights and is not used to estimate crack size. It will be. In many cases, the combination of the axial strain gauges and the combination of the circumferential strain gauges have zero weight. FIG. 8 shows an error in estimating the crack depth from the equation (1) using the weights thus obtained (open plot). By considering the weight, the identification error does not increase even if the number of strain gauges increases. It can be seen that the error is greatly reduced by increasing the number of gauges. However, the identification accuracy is about Lm = 12 mm, that is, saturated near the crack length. Thus, the error can be reduced by considering the weight.

  The present invention can be applied to all fields that may be used in a state where a crack exists on the inner surface of a structure, such as a nuclear power plant or an aircraft.

1 Circumferential crack 2 Axial crack 3, 4 Tube (structure)
5 Strain gauge

Claims (3)

A first step of detecting a crack on the inner surface of the structure in advance;
A second step of measuring strain detected on the outer surface of the crack structure by a plurality of strain gauges attached to the outer surface of the crack structure;
A plurality of strain measurement values measured by the plurality of strain gauges are introduced into a relationship obtained in advance for the depth and surface length of the virtual crack on the inner surface of the virtual structure and the strain on the outer surface of the virtual structure by finite element analysis. A third step of deriving a virtual crack depth and surface length corresponding to each of the plurality of strain measurements;
A fourth step of graphing the relationship between the virtual crack depth and the surface length corresponding to each of the plurality of strain measurements as a plurality of curves;
A fifth step of estimating the depth and surface length of the detected crack by determining the depth and surface length of the intersection where the plurality of graphed curves intersect;
The crack size estimation method characterized by including. In the fifth step, a plurality of intersections of the plurality of curves are selected, and for the plurality of intersections, a depth and a surface length of each intersection are obtained,
The crack size estimation method according to claim 1, further comprising a sixth step of deriving an average value in consideration of a weighting factor for the depth and the surface length of each intersection.   The crack size estimation method according to claim 1 or 2, wherein the structure in which the crack is detected has a plate shape with a thickness t, and the gauge length of the strain gauge is 0.1 t or less.