JP2001324431A - Method for detecting crack in plate-shaped member - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for detecting cracks in a plate-shaped member for continuously, easily and correctly detect cracks which occur in the periphery of the notch of the plate-shaped member by a minimum number of distortion gauges. SOLUTION: Distortion values in the radial direction, vertical distortion values in the circumferential direction which intersects the radial direction at right angles, shearing distortion values are each obtained by the distortion gauges 12, which is mounted at a plurality of locations on the periphery of the notch 16 of the plate-shaped member 11. A stress value corresponding to each measured distortion value is substituted into a stress state expression, which expresses a stress state obtained from the stress function of the periphery of the notch 16 of the plate-shaped member 11, in which the edge part of the notch 16 is a free boundary to determine the coefficient values of each expression. The occurrence of cracks in the plate-shaped member 11 is detected from the stress distribution as expressed by the coefficient values or stress state expressions obtained.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a plate-like member for detecting a crack generated from a notch when a load is applied to a plate-like mechanical part or a plate-like structure having a notch including an arc. It relates to a crack detection method.

[0002]

2. Description of the Related Art When an excessive load is applied to a plate-shaped machine part or a plate-shaped structure having a notch (for example, a circular hole or a semi-circular notch) including an arc which is unavoidable in structure. It is known that stress concentrates on that portion and cracks occur. However, the method of evaluating the strength of the material is incomplete, and human error during design cannot be completely prevented. It is necessary to carry out continuous inspections in this state, detect cracks that have occurred as soon as possible, and take countermeasures. As a method for detecting a crack, a method using a strain gauge, which is widely used as a means for measuring stress and strain, has been conventionally used. As a method, as shown in FIG. 7A, one or a plurality of strain gauges or a strain gauge 30 integrating the strain gauges is used.
Is attached to the periphery of the notch 32 of the member 31, a change in minute resistance due to a change in strain, or a disconnection of a strain gauge due to the occurrence of a crack is detected by a bridge box 33, and this output is amplified by an amplifier 34. Graph 35
Such as displaying it on the display.

[0003]

However, if it is not possible to limit the location of the crack in advance, the entire area (dangerous area) where a crack is likely to occur, such as a notch, is shown in FIG. As shown in (b), it is necessary to arrange a very large number of strain gauges 30, the operation becomes complicated, and a measuring instrument having a large number of measurement channels is required, which is not practical. In particular, large structures require so many strain gauges that implementation is virtually impossible. On the other hand, if the number of strain gauges is reduced, the possibility of overlooking a crack that has occurred is increased, and it cannot be used as a crack detection method. SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and detects a crack generated around a notch of a plate-like member continuously and easily and accurately with a minimum strain gauge. The aim is to provide a method.

[0004]

According to the present invention, there is provided a method of detecting a crack in a plate-like member having a notch including an arc, the method comprising the steps of:
The strain gauges attached at a plurality of locations around the notch of the plate-like member allow the respective strain values in the radial direction and the vertical strain values in the circumferential direction orthogonal to the respective strain values and the shear strain values (that is, the respective radial and Then, a stress value corresponding to each of the measured strain values is determined by calculating a stress value corresponding to each of the measured strain values of the plate-like member in which the edge of the notch is a free boundary. Substituting into a stress state equation representing a stress state obtained from a stress function around the notch, determining coefficient values of the respective equations, and determining the coefficient value or stress distribution represented by the stress state equation from the stress distribution represented by the stress state equation. It is configured to detect the occurrence of cracks. Here, each strain gauge is preferably a rosette-type strain gauge.

[0005] It is assumed that there is no object force near the bottom of the notch and the edge of the notch is a free boundary. When the stress component is obtained from the general stress function of the polar coordinate system and the free boundary condition is applied to the edge of the hole of radius r ₀ , the expression of the stress state of an arbitrary free hole plate including the multivalency of the displacement is given by (1) The stress state equation as shown in the equation is obtained. Here, the origin of the polar coordinate system is the center of the circular hole.

[0006]

(Equation 1)

The multivalency of displacement at θ = α is expressed by (2)
It looks like an expression. Here, ν is Poisson's ratio.

[0008]

(Equation 2)

[0009] Since the multivalency of the displacement is considered to represent a difference between the crack surfaces in addition to the intrinsic stress, in the equation (1) including the multivalency of the displacement in the determination of the boundary condition, the crack is found within the region. When present, the coefficient of multivalency changes significantly compared to when no crack is present. Therefore, the unknown coefficient of the equation (1) can be determined from the discrete stress value by the strain gauge near the notch bottom, and the crack can be detected based on the change of the obtained multivalent coefficient value. When the magnitude of the load changes, the coefficient of multivalency also changes in proportion to the magnitude of the load, so it is not possible to distinguish between a change due to the occurrence of a crack and a change due to a change in the load. for that reason,
The value of the square root of the sum of the squares of all the coefficients in Equation (1) is considered as an index of the strength of the stress field near the notch bottom, and this value is used to divide each multivalent coefficient into Equation (3). Cω, Cν, Cu shown
The crack that has occurred is detected using each of the above parameters.

[0010]

(Equation 3)

[0011]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Next, embodiments of the present invention will be described with reference to the accompanying drawings to provide an understanding of the present invention. Here, FIG. 1 is an explanatory view of an apparatus applied to a crack detecting method for a plate-like member according to the first and second embodiments of the present invention, and FIGS. FIG. 5 is an explanatory diagram showing a relationship between a multivalent Cω parameter and a crack length, and FIG. 6 is an explanatory diagram showing detection of a crack generated in a plate-like member from a stress distribution. .

As shown in FIG. 1, the first and second embodiments of the present invention
The apparatus 10 used in the method for detecting a crack in a plate-like member according to the embodiment of the present invention comprises a plate-like member 11 having a crack-formed circular edge.
A plurality of rosette-type strain gauges 12 attached to predetermined positions
And a bridge box 1 for processing the signal of the strain gauge 12
3, an amplifier 14 that converts the amount of distortion detected by the bridge box 13 into an electric signal and amplifies it, and an amplifier 1
And a computer 15 that performs A / D conversion on the signal amplified by the A / D converter 4 and performs signal processing. Hereinafter, these will be described in detail.

The plate-like member 11 is, for example, a plate-like mechanical part such as a cam, a stopper, and a large gear, a housing of the machine, and a plate-like structure such as a bridge. An arc-shaped notch 16 is formed. Since the notch 16 uses a stress function using polar coordinates in the calculation processing, it is sufficient to include a circular arc. For example, the notch 16 may be a semicircle as shown in FIG. The present invention can be applied to the case of an opening including an entire circular hole or an arc.

As the strain gauge 12, a rosette-type strain gauge capable of simultaneously measuring a strain value in a radial direction, a vertical strain value in a circumferential direction orthogonal to a radial direction, and a shear strain value is used. It may be a strain gauge. As shown in FIG. 1, if this strain gauge 12 is adhered in a fan shape at predetermined intervals, there is an advantage that the polar coordinate position where the strain gauge 12 is attached can be easily measured, but the polar coordinate position (r,
The strain gauge 12 may be attached to any position where θ) is clear.

The bridge box 13 has a well-known structure and detects a minute change in resistance of the strain gauge 12 and outputs a current or a voltage. The amplifier 14 amplifies this signal up to a voltage signal of a predetermined size that can easily process a small signal, includes an AD converter therein, and outputs it as a digital signal.

The computer 15 comprises a personal computer,
It has a first calculating means and a second calculating means for processing the input signal. The first calculating means is for obtaining the coefficient of the stress function as described above, and the second calculating means is for obtaining the stress distribution from the determined stress function.

Next, a method for detecting a crack in a plate-like member according to the first embodiment of the present invention using the apparatus 10 will be described. The crack detection method for a plate-like member according to the first embodiment of the present invention detects a crack generated from a change in a coefficient value of a stress state equation. With the center of the circular hole 18 having a radius of 1 formed in the plate-like member 17 as the origin, the horizontal direction is x-axis, x
FIG. 2 shows a case where a crack 19 is introduced rightward along the x-axis from the edge of the circular hole 18 with the direction perpendicular to the axis as the y-axis, and FIG. 3 shows a case where the crack 19 is introduced symmetrically. Show. The length of each of the cracks 19 was 0.512 with respect to the radius 1 of the circular hole 18. In addition, the load is a tensile stress (σξ = 1, ση = 1) in a direction perpendicular to the crack plane in the ξ-η plane which forms an angle of 45 ° with the xy plane,
Tensile stress in the direction of 5 ° (σ ＝= 1, ση = 0) and shear stress (σξ = 1, ση = -1) were applied to the surface along the crack surface, respectively. Detection of crack 18
(1) An equation in which n of the infinite series of the equation is taken up to 6, and a circular hole 18
The test was carried out using ten stress values at which the circumference of a circle having a radius of 1.5 from the center was almost equally divided. At this time, the stress value at the integration point of the finite element analysis was used instead of the measured data of the strain. For comparison, an unknown coefficient was determined in the same manner even when no crack 19 was present. Using the obtained coefficients, each of the multivalent parameters Cω, C
u and Cν were determined. Table 1 shows the obtained results.

[0018]

[Table 1]

When the crack 19 does not exist, each parameter of each multivalent coefficient has a value of about 10 ^-4 to 10 ^-3 . On the other hand, when the crack 19 shown in FIG.
As shown in Table 1, the rotational multi-value parameter Cω and the translational multi-value parameter Cv in the y-direction are applied to the tension in the direction perpendicular to the crack surface, while the translation-type multi-value parameter Cν is applied to the surface along the crack surface in the x-direction. When the multivalent parameter Cu is pulled in the direction of 45 ° to the crack surface, Cω, Cu, and Cν all have large values. However, when the crack 19 shown in FIG. 3 is bilaterally symmetric, only the rotation type multivalency parameter Cω in the vertical direction and the 45 ° direction tension becomes a large value as shown in Table 1. ing. This is because y in destruction mode I
The translational multivalence parameter Cν in the direction and the translational multivalence parameter Cu in the x direction in the fracture mode II have the same absolute value but different signs in the left and right cracks, and thus cancel each other out to zero. That's why. From the above results, it is considered that the crack 19 at the edge of the circular hole 18 can be detected even if the load condition changes to some extent from the change in the coefficient of multivalency of displacement. However, for a crack 19 generated at a symmetrical position under a shear load, the crack 19 cannot be detected by the multivalency coefficient.
However, when the load shifts to the shearing type, the direction of propagation of the crack changes in a direction perpendicular to the direction of the maximum principal stress, that is, in a direction forming 45 ° with the surface on which the shear load is applied. It is considered that a state in which a pure shear load is applied does not last for a long time. Therefore, it is considered that even when a pure shear load state occurs, the state shifts to the mode I, and an increase in the multivalency coefficient appears.

Next, the crack length which can be detected by this method will be described with reference to the embodiment of FIG. 4 as an example. As shown in FIG. 4, the center circular hole 21 having a radius of 1 formed in the plate member 20 having a width of 6 and having the origin as the origin, the horizontal direction is defined as the x-axis, and the direction perpendicular to the x-axis is defined as the y-axis. Cracks 22 of various lengths are introduced into the edge symmetrically along the x-axis, and a central circular hole 21 is formed.
Divide the circumference of the circle with a radius of 1.5 from the center of
The length of the crack 22 and the rotational multi-value parameter Cω when a uniform tensile load is applied by attaching a strain gauge 23 to a location
The relationship was investigated. The results obtained are shown in FIG. From FIG. 5, it can be seen that the rotation type multivalency parameter Cω rapidly increases with respect to the length of the crack 22, and the crack can be detected when the crack length becomes about 0.1.

Next, a method for detecting a crack in a plate-like member according to a second embodiment of the present invention using the apparatus 10 will be described. The crack detection method for a plate-like member according to the second embodiment of the present invention detects a change in stress distribution represented by a stress state equation. As shown in FIG. 1 and FIG. 6A, a plate-like member 11 having a semicircular notch 16 on one side is defined by an x-axis in the left-right direction from the center of the semicircle, and a y-axis is a direction perpendicular to the x-axis. ,
Apply a tensile load in the y-axis direction. The strain generated at this time is obtained by the strain gauge 12, and the measured strain value in the radial direction is obtained.
A stress value corresponding to each of the vertical strain value and the shear strain value in the circumferential direction orthogonal to the radial direction is calculated from the stress function around the notch 16 of the plate-shaped member 11 in which the edge of the notch 16 is a free boundary. The coefficient value of each equation is determined by substituting into the stress state equation representing the obtained stress state. When each coefficient is determined, the stress at an arbitrary position can be calculated using the stress state equation. Taking the intersection of the x-axis and the edge of the notch 16 as the origin, the relationship between the distance in the x-axis direction from the bottom of the notch and the generated stress, that is, the stress distribution, is a graph before the crack 24 occurs. 6 (b)
As shown in FIG. 7, the stress distribution is caused by the stress concentration due to the notch 16, and the stress becomes maximum at the notch bottom. On the other hand, for example, when the crack 24 occurs at the notch bottom along the x-axis, as shown in FIG.
Since no stress is transmitted at the crack 24, the distribution changes to a distribution in which a very large stress is generated at the tip of the crack 24. As described above, the largest difference in the stress distribution before and after the occurrence of the crack 24 is whether or not the stress at the edge of the notch 16 becomes maximum. Therefore, cracks can be detected by capturing characteristic changes in the generated stress distribution.

The embodiment of the present invention has been described above.
The present invention is not limited to this embodiment,
For example, although each strain gauge is independently adhered, a plurality of strain gauges, for example, 4 to 12 or more strain gauges may be integrated and used. In the above-described embodiment, the case of a circular hole has been described. Further, when detecting a crack by capturing a characteristic change in stress distribution, a crack generated at the notch bottom is taken as an example, but in the present invention, crack detection is performed in a region near the notch. Therefore, even if the maximum stress occurs at the notch edge other than the notch bottom and a crack occurs at that position,
Crack detection can be performed in exactly the same manner.

[0023]

In the method for detecting a crack in a plate-like member according to the first and second aspects of the present invention, the strain values in the radial direction and the strain values in the respective radial directions are measured by strain gauges attached to a plurality of locations around the notch in the plate-like member. The vertical strain value and the shear strain value in the circumferential direction orthogonal to are determined, and then the stress values corresponding to the measured strain values are calculated by calculating the stress values around the notch of the plate-like member where the edge of the notch is a free boundary. By substituting into the stress state equations representing the stress state obtained from the stress function, the coefficient values of each equation are determined, and from the obtained coefficient values or the stress distribution represented by the stress state equation, the occurrence of cracks in the plate-like member is determined. Since the detection is performed, the strain gauges are arranged only at the boundary of the dangerous area and the number of strain gauges is reduced, so that a wide area can be continuously measured and the crack that has occurred can be detected. In particular, in the method for detecting a crack in a plate-like member according to claim 2, since each strain gauge is a rosette-type strain gauge, a measurement error of a strain value at a position where the strain gauge is stuck is small and the strain gauge is generated. Cracks can be accurately detected.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram of an apparatus applied to a crack detecting method for a plate-like member according to first and second embodiments of the present invention.

FIG. 2 is an explanatory diagram of crack detection of a plate-like member having a notch formed therein.

FIG. 3 is an explanatory diagram of crack detection of a plate member having a notch formed therein.

FIG. 4 is an explanatory diagram of crack detection of a plate-like member having a notch formed therein.

FIG. 5 is an explanatory diagram showing a relationship between a multivalency parameter Cω and a crack length.

FIG. 6 is an explanatory diagram of detection of a crack generated in a plate member from a stress distribution.

FIG. 7 is an explanatory diagram of crack detection of a notch member according to a conventional example.

[Explanation of symbols]

10: device, 11: plate member, 12: strain gauge, 13:
Bridge box, 14: amplifier, 15: computer, 16: notch, 17: plate member, 18: circular hole, 1
9: crack, 20: plate member, 21: central hole, 22: crack, 23: strain gauge, 24: crack

 ────────────────────────────────────────────────── ─── Continued on the front page (72) Inventor Toru Aramaki Room 308, Building 4, Kaizuka Danchi, Higashi-ku, Fukuoka City F-term (reference) 2G061 BA03 CB01 EA04 EC02

Claims (2)

[Claims] 1. A method for detecting a crack in a plate-like member having a notch including a circular arc, wherein the strain gauges are attached to a plurality of locations around the notch of the plate-like member to detect the radial direction of the plate. A strain value and a vertical strain value and a shear strain value in a circumferential direction perpendicular to the strain value are determined.Then, a stress value corresponding to each of the measured strain values is calculated by using the plate whose edge of the notch is a free boundary. Substituting into a stress state equation representing the stress state obtained from the stress function around the notch of the shape member, determine the coefficient value of each equation, from the obtained coefficient value or the stress distribution represented by the stress state equation, A method for detecting a crack in a plate-like member, comprising detecting occurrence of a crack in the plate-like member. 2. The method for detecting cracks in a plate-like member according to claim 1, wherein each of the strain gauges is a rosette-type strain gauge.