Method for Determining Shape of Crack

The present invention relates to a method for determining a shape of crack, and more particularly to a method for determining a shape of crack using AE (acoustic emission) sensors which detect acoustic emissions produced when a metal is subjected to plastic deformation, shearing or friction.

An AE device which detects the occurrence of a crack developed in a metal by an AE sensor has been proposed. In a known AE device (disclosed in Japanese Published Examined Patent Application 53-21673), a number of AE sensors are mounted on a surface of a test object such as a vessel, crack is located based on signals from the AE sensors, and positions of source of acoustic emissions are indicated on an orthogonal coordinate. In case of fatigue crack, acoustic emissions developed by the friction of cracks previously developed under repetitive load, acoustic emissions developed by the shear of sheared ends and acoustic emissions developed by the plastic deformation ahead of the crack ends are mixed so that the AE signals distribute around the crack ends. It is, therefore, impossible to determine the shape of the crack.

It is an object of the present invention to determine the shape of the crack with a high accuracy.

The present invention is characterized by determining a crack source plane based on points of source of the acoustic emissions in the test object and determining the shape of the crack in the crack source plane based on a distribution of the points of source of the acoustic emissions.

The present invention will now be explained in conjunction with the accompanying drawings, in which:

FIG. 1 shows a system diagram of a crack end position detecting device to which a preferred embodiment of the present invention is applied;

FIG. 2 illustrates a mounting condition of AE sensors shown in FIG. 1 on a test object;

FIG. 3 shows waveforms of output signals produced from the AE sensors shown in FIG. 2;

FIGS. 4A, 4B and 4C show flow charts for operations carried out in a computer shown in FIG. 1;

FIG. 5 illustrates an approximated crack ends;

FIG. 6 shows a characteristic curve representing a relationship between a distance along a y.sub.o axis and the number of crack source points P.sub.n within a width of .DELTA.x.sub.om ;

FIG. 7 illustrates a process for determining a distribution of the crack source points, within a width of .DELTA.S normal to a curve S which envelopes the approximated crack ends; and

FIG. 8 illustrates a process for determining by a statistic analysis the crack ends based on the distribution of the crack source points.

Referring to FIG. 1 and FIG. 2, a preferred embodiment of the present invention is now explained. A crack shape detecting device 2 comprises a number of AE sensors 3, a computer 6 and a CRT display 7. Each of the AE sensors 3 is coupled to the computer 6 through a pre-amplifier 4 and a main amplifier 5. Numeral 8 denotes an I/O typewriter. The k number of AE sensors 3 are mounted at preselected positions on a surface of a test object such as a metal plate 1, as shown in FIG. 2. Symbols S.sub.1 -S.sub.8 represent the AE sensors 3. As shown in FIG. 2, coordinates of mounting positions of the AE sensors S.sub.1 -S.sub.4 in an orthogonal coordinate having x-axis, y-axis and z-axis are represented by (x.sub.1, y.sub.1, z.sub.1), (x.sub.2, y.sub.2, z.sub.2), (x.sub.3, y.sub.3, z.sub.3) and (x.sub.4, y.sub.4, z.sub.4), respectively.

The detection of the crack shape by the crack shape detecting device 2 is now explained in detail. Let us assume that a crack occurs at a point P.sub.n (x.sub.n, y.sub.n, z.sub.n) and acoustic emissions are generated therefrom. The acoustic emissions developed are detected by the AE sensors S.sub.1 -S.sub.8 which produce pulsive AE signals as shown in FIG. 3. Because of the difference of distances between the crack source point P.sub.n and the positions of the AE sensors S.sub.1 -S.sub.8, elapsed times t.sub.(k, n) measured from a reference time point t.sub.o to time points at which the AE signals are produced by the k (eight in FIG. 2) AE sensors are different as shown in FIG. 3. The AE signals produced by the AE sensors S.sub.1 -S.sub.8 are applied to the computer 6 via the preamplifiers 4 and the main amplifiers 5. An output from the computer 6 is displayed on the CRT display 7.

Referring to FIGS. 4A, 4B and 4C, the operation of the computer 6 is explained. The elapsed times t.sub.(k, n) from the reference time point t.sub.o to the time points at which the k AE sensors produce the output when the crack occurs at the point P.sub.n and the coordinates (x.sub.k, y.sub.k, z.sub.k) of the mounting positions of the AE sensors are inputted to the computer 6 (step 11). A time difference .DELTA.t.sub.(k, n) between the elapsed times of any two of the AE sensors is determined (step 12). For example, a time difference .DELTA.t.sub.(1, n) between the elapsed times of the AE sensors S.sub.1 and S.sub.2 is determined from [t.sub.(1, n) -t.sub.(2, n) ]. At a step 13, based on the time difference .DELTA.t.sub.(k, n) of the elapsed times, the crack source point P.sub.n is determined. More particularly, a difference between distances from any two of the AE sensors and the crack source point P.sub.n is given by v.multidot..DELTA.t.sub.(k,n), where v is a sound velocity in the test object. Accordingly, a coordinate (x.sub.n, y.sub.n, z.sub.n) of the crack source point is determined by resolving the following simultaneous equations: ##EQU1## where .DELTA.t.sub.(1,n) is a difference between the elapsed times for the AE sensors S.sub.1 and S.sub.2, .DELTA.t.sub.(2,n) is a difference between the elapsed times for the AE sensors S.sub.3 and S.sub.4, and .DELTA.t.sub.(3,n) is a difference between the elapsed times for the AE sensors S.sub.1 and S.sub.3. The preceding term and the succeeding term in the left side of the equation depend on the magnitude of the elapsed time t.sub.(k,n). If the elapsed time t.sub.(k,n) for the AE sensor (k) is shorter than the elapsed time t.sub.(k-1,n) for the AE sensor (k-1), the distance from the AE sensor (k) to the crack source point P.sub.n is to be subtracted from the distance from the AE sensor (k-1) to the crack source point P.sub.n. By resolving the above simultaneous equations, x.sub.n =a.sub.n, y.sub.n =b.sub.n and z.sub.n =c.sub.n are determined step (4). The x.sub.n =a.sub.n, y.sub.n =b.sub.n and z.sub.n =c.sub.n represent x, y and z axes positions of the crack source points P.sub.n. The coordinates (a.sub.n, b.sub.n, c.sub.n) of the crack source points P.sub.n are then stored (step 15). At a step 16, it is determined if the number n of the crack source points P.sub.n has reached a predetermined number u.sub.1. If the number n is smaller than the number u.sub.1, the steps 11-15 are repeated. If the number of the crack source points is small, a larger error will be included in determining crack end positions from the distribution of the crack source points.

When the number n reaches u.sub.1, an operation of a step 17 is carried out. A coordinate (a.sub.n, b.sub.n, c.sub.n) of a mean position derived by averaging the crack source points P.sub.n in three or more predetermined areas is substituted to the following equation (2);

to form simultaneous equations, which are then solved to determine an equation of a crack source plane P. Then, angles .theta. and .rho. between the (x, y) plane orthogonal to the z-axis and the crack source plane P are determined (step 18), where .theta. is the angle to the x-axis and .rho. is the angle to the y-axis. The coordinates (a.sub.n, b.sub.n, c.sub.n) of the crack source points P.sub.n are transformed to coordinates (a.sub.on, b.sub.on) of coordinate axes x.sub.o and y.sub.o on the crack source plane P (step 19). The transform is carried out in accordance with the following equations (3) and (4). A direction normal to the crack source plane P is a coordinate axis z.sub.o. Since the crack source points exist on the crack source plane P, z.sub.o is zero.

As shown in FIG. 5, the x.sub.o -axis is equi-divided, starting from a point of x.sub.o =0, into u.sub.2 segments each having a length .DELTA.x.sub.o (step 20). At a step 21, m is set to zero, and at a step 22, m is set to (m+1). At a step 23, the length .DELTA.x.sub.om is equi-divided along the y.sub.o -axis starting from a point of y.sub.o =0 into u.sub.3 segments each having a length .DELTA.y.sub.o. At a step 24, J is set to zero, and at a step 25, J is set to (J+1). The number of the crack source points P.sub.n in .DELTA.y.sub.oj is counted and stored (step 26). At a step 27, it is determined if j=u.sub.3. If j<u.sub.3, the steps 25 and 26 are repeated for the area .DELTA.y.sub.oj and the number of the crack source points P.sub.n in the area y.sub.oj is counted and stored. When j reaches u.sub.3 , the process moves to a step 28. As shown in FIG. 6, .DELTA.y.sub.oj which provides a maximum number of the crack source points P.sub.n in .DELTA.x.sub.om is selected and the position of .DELTA.y.sub.oj is stored (step 28). At a step 29, it is determined if m=u.sub.2. If m<u.sub.2, the steps 22, 23, 24, 25, 26, 27 and 28 are repeated. The positions of .DELTA.y.sub.oj each of which provides a maximum number of the crack source points P.sub.n in each .DELTA.x.sub.om are approximated crack end positions. If m reaches u.sub.2 at a step 29, the process moves to a step 30. A curve S (FIG. 5) which envelopes the approximated crack end positions of the respective .DELTA.x.sub.om is determined by a minimum square method. The curve S represents an approximated crack shape.

At those portions where an angle between a line tangential to the curve S and the y.sub.o -axis is small, the positions of the approximated crack ends determined by the above process include large errors. Accordingly, more exact crack end positions are determined in the following manner. The curve S is equi-divided into u.sub.4 segments each having a length .DELTA.S (step 31). At a step 32, f is set to zero, and at a step 33, f is set to (f+1). Lines r.sub.f and r.sub.(f-1) which pass through dividing points S.sub.f and S.sub.(f-1), respectively, on the curve S and are orthogonal to the curve S are determined (step 34). A distance .DELTA.S.sub.f between the lines S.sub.f and S.sub.(f-1) is equi-divided along the line r.sub.f into u.sub.5 segments each having a length .DELTA.r (step 35). At a step 36, g is set to zero, and at a step 37, g is set to (g+1). The number of the crack source points P.sub.n in the length .DELTA.r.sub.g is counted and stored (step 38). At a step 39, it is determined if g=u.sub.5. If g<u.sub.5, the steps 37 and 38 are repeated. If g=u.sub.5, the process moves to a step 40. The .DELTA.r.sub.g which provides a maximum number of the crack source points P.sub.n in the length .DELTA.S.sub.f is selected and the maximum number P.sub.fg of the crack source points P.sub.n is stored (step 40). In an outer region I and an inner region II (FIG. 7) with respect to the .DELTA.r.sub.g which provides the maximum number P.sub.fg in the length .DELTA.S.sub.f, a predetermined number (e.g. 15) of .DELTA.r.sub.g each having around P.sub.fg /2 crack source points P.sub.n are selected (step 41). Equations V.sub.f1 and V.sub.f2 (FIG. 8) which represent the relationships between positions W.sub.fg, along the line r.sub.f, of the .DELTA.r.sub.g selected from the outer region and the inner region, and the numbers of P.sub.n in the selected .DELTA.r.sub.g are determined (step 42). The number P.sub.fg /2 is placed in the equations V.sub.f1 and V.sub.f2 to determine the linear positions W.sub.fg1 and W.sub.fg2 corresponding to the number P.sub.fg /2 (step 43). The crack end position W.sub.fgo in the direction of the line r.sub.f is determined from the following equation (5) (step 45).

The operation in the steps 41 to 45 determines a statistical representative value (one half of half value width) based on statistical analysis. The position W.sub.fgo of the crack end in the direction of the line r.sub.f is shown in FIG. 8. In accordance with the above process, the position W.sub.fgo of the crack end in the direction of the line r.sub.f can be determined with a high accuracy. A coordinate (x.sub.of, y.sub.of) of the crack end position W.sub.fgo with respect to the coordinates x.sub.o and y.sub.o is stored (step 46). At a step 47, it is determined if f=u.sub.4. If f<u.sub.4, the steps 33-47 are repeated. When f reaches u.sub.4, the process moves to a step 48. At the step 48, the crack end positions W.sub.fgo for the respective .DELTA.S.sub.f are connected to define the crack shape. A signal representing the crack shape is applied to the display 7 (step 49). The display 7, when it receives the crack shape signal, displays the crack shape on a screen by an X-Y plotter. In this manner, the crack shape can be non-destructively determined with a high accuracy.

By displaying on the display 7 the crack end positions stored in the step 46, the crack end positions can be determined. It is also possible to indicate the positions on a sheet by a printer instead of the display 7.

By periodically sampling the output signals from the AE sensors, determining the crack shape by the process described above and comparing it with a previously determined crack shape, it is possible to determine a process of crack.

In the embodiment explained above, the approximated crack shape is determined based on the positions of .DELTA.y.sub.oj which provide the maximum numbers of the crack source points P.sub.m in .DELTA.x.sub.om alternatively, the approximated crack shape may be determined based on the statistical representative values described above. In this case, instead of the step 28 in the embodiment described above, the steps 40-46 are carried out. In the steps 40-46, S is substituted by x.sub.o, r is substituted by y.sub.o, f is substituted by m and g is substituted by j. A formula of a curve S derived by connecting W.sub.mjo of the respective .DELTA.x.sub.om is defined. This method of determining the approximated crack shape improves the accuracy of determining the crack shape.

When the crack exists within the metal plate 1 without opening to the surface of the metal plate 1 as shown in FIG. 2, a peak number, instead of the maximum number of the crack source points P.sub.n is used. That is, the maximum number in the steps 28, 30 and 40 is substituted by the peak number. In this manner a crack shape of closed loop such as ellipsoidal shape which exists within the metal plate 1 can be determined with a high accuracy. Since the maximum number is the largest one among the peak numbers, only one exists in the length .DELTA.x.sub.om. In the closed loop crack, there are two y.sub.oj positions which provide peak numbers of the crack source points P.sub.n in the length .DELTA.x.sub.om. Accordingly, when only the .DELTA.y.sub.oj position which provides the maximum number of the crack source points P.sub.n in the length .DELTA.x.sub.om, the crack shape cannot be accurately determined.

In the embodiment described above, by omitting the steps 31-48 and displaying the shape of the curve S determined at the step 30 on the display 7, the crack shape of the test object can be determined. Again, in this case, the detection accuracy of the crack shape is improved if the curve S is determined using the statistical representative values.

The present invention is applicable to the test object of tubular shape or other complex shape. The present invention is also applicable to the detection of the crack shape developed in a vessel or pipe mounted in an assembled plant.

In accordance with the present invention, the shape of the crack which exists inside the test object can be non-destructively detected with a high accuracy.