JP5339253B2 - X-ray stress measurement method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a measurement method with higher accuracy, which solves the problem in a conventional area detector type triaxial stress measurement method. <P>SOLUTION: In the method, triaxial stress components are measured on the basis of a diffraction ring obtained by irradiating a specimen with X rays. In a first embodiment, diffraction rings are respectively obtained by conducting oblique X ray irradiation operations in four incident directions (&phiv;<SB>0</SB>=0&deg;, 90&deg;, 180&deg; and 270&deg;), and (&sigma;<SB>x</SB>-&sigma;<SB>z</SB>) and &tau;<SB>yz</SB>are determined in the case of &phiv;<SB>0</SB>=(0&deg;, 180&deg;), and (&sigma;<SB>y</SB>-&sigma;<SB>z</SB>) and &tau;<SB>xz</SB>are determined in the case of &phiv;<SB>0</SB>=(90&deg;, 270&deg;), and &tau;<SB>xy</SB>&sigma;<SB>z</SB>is determined from these diffraction rings, thereby obtaining six triaxial stress components. In a second embodiment, diffraction rings are respectively obtained by conducting a vertical incidence operation and two oblique incidence operations of &phiv;<SB>0</SB>=(0&deg;, 90&deg;), and &tau;<SB>xz</SB>and &tau;<SB>yz</SB>are determined in the case of the vertical incidence, and (&sigma;<SB>x</SB>-&sigma;<SB>z</SB>) and &tau;<SB>xy</SB>are determined in the case of &phiv;<SB>0</SB>=0&deg;, and (&sigma;<SB>y</SB>-&sigma;<SB>z</SB>) and &tau;<SB>xy</SB>are determined in the case of &phiv;<SB>0</SB>=90&deg;, and &sigma;<SB>z</SB>is determined from these diffraction rings, thereby obtaining six triaxial stress components. <P>COPYRIGHT: (C)2011,JPO&amp;INPIT

Description

  The present invention relates to an X-ray stress measurement method for measuring stress (especially triaxial stress) existing in an object by irradiating the object with X-rays.

  The X-ray stress measurement method is a method for obtaining the state of stress in a material from information of diffraction when a material (particularly a crystalline material such as a metal) is irradiated with X-rays. In the X-ray stress measurement method, the fact that the lattice spacing changes due to the stress is used, the change is obtained by measuring the relationship between the angle and intensity of the diffracted X-ray, and the strain and stress are calculated.

Since the X-ray stress measurement method is a method of measuring the surface portion of the test object, the plane stress theory is usually applied and the plane stress measurement method is used.
Further, it is known that a triaxial stress remains in a ground steel material or the like due to a strong deformation in a specific direction applied by a tool during grinding (for example, Non-Patent Document 1). Such). The triaxial stress has a component (components in the x-axis and y-axis directions) along the surface (xy plane) of the test object and a component in the direction perpendicular to the surface (z-axis direction). This is a stress state that simultaneously includes stress in a three-dimensional direction.
Another technique of a method of measuring triaxial stress by X-ray irradiation (X-ray triaxial stress measurement method) has been proposed by Dolle et al.

However, since the measurement method of Dale et al. Uses a total of six strain lattice distributions (sin ² Ψ diagram), there is a problem that measurement and analysis require a complicated apparatus and a great amount of measurement time. This method does not cause any particular problems when performed in the laboratory, but is difficult to apply at construction sites, sites where specimens are laid, production lines, etc. where relatively quick measurement work is required. It is.

In order to solve the problems of the conventional X-ray stress measurement method as described above, the present inventor analyzed the entire information of the diffraction ring obtained by irradiating X-rays by an area detector such as an imaging plate (IP) or CCD. The X-ray plane stress measurement method (Patent Document 1) and the X-ray triaxial stress measurement method (Non-Patent Document 1) used for the above are proposed, and the waste of measurement and analysis is reduced. Hereinafter, the X-ray triaxial stress measurement method described in Non-Patent Document 1 will be referred to as a conventional area detector X-ray triaxial stress measurement method.
In the conventional area detector type triaxial stress measurement method, for example, if the central angle of the diffraction ring is analyzed at intervals of 1 degree, a total of 360 lattice strains are obtained from the entire diffraction ring, so that six triaxial stresses are obtained. Sufficient data is obtained for component determination.

Next, the measurement principle of the conventional area detector X-ray triaxial stress measurement method will be described.
In consideration of on-site measurement and practicality, it is desirable to avoid the use of absolute values of diffraction data that are easily affected by the setting of the sample, and to use relative changes as much as possible. From this point, in the following description, a triaxial stress measurement method through relative change of diffraction data, such as a plane stress measurement method (sin ² Ψ method) will be described.

Most of the metal materials actually used are aggregates of fine crystal grains, and when irradiated with X-rays, diffracted X-rays are generated according to the Bragg condition of the following formula (1).
[Formula (1)]

Here, d is the lattice spacing, θ is the Bragg angle, λ is the X-ray wavelength, and n is the diffraction order. Hereinafter, n = 1 is used.
Diffracted X-rays are generated so as to form a side surface of a cone whose apex is an irradiation point (measurement point that is the target of X-ray irradiation). Are measured.
In the measurement method of Dale et al., Θ is determined through measurement of the diffraction intensity distribution at one end of the diffraction ring and used for stress calculation.
On the other hand, in the conventional triaxial stress measurement method of the area detector method, the diffraction ring radius R is first obtained as shown in FIG. 8, and then the Bragg angle θ (unit: radians) is obtained using the following equation (2). Get.
[Formula (2)]

Here, C _L is the distance between the X-ray irradiation point and the detector.

The value of the Bragg angle θ obtained as described above is an average value for a group of lattice planes contributing to diffraction. From the differentiation of the above equation (1), the relationship between the longitudinal strain ε in the normal direction of the lattice plane and the Bragg angle θ is derived as in the following equation (3).
[Formula (3)]

Here, [Delta] d is, the amount of change in lattice spacing d, i.e., the value of the undistorted when d is taken as d _0, a [Delta] d = d-d _0.
Δθ is Δθ = θ−θ _0, where the amount of change in the Bragg angle θ, that is, the value of θ when there is no strain is θ ₀ .

Next, as shown in FIG. 9, a coordinate system xyz is set at the irradiation point on the surface of the test object, and each stress in the triaxial direction at the origin (= irradiation point) (ie, stress σ _x , y in the x-axis direction). Axial stress σ _y and z-axis direction stress σ _z ) and respective shear stresses (τ _xy , τ _xz , τ _yz ) are expressed by the following equation (4). Note that τ _xy represents the stress that causes the displacement of the xy plane, and similarly, τ _xz represents the stress that causes the displacement of the xz plane, and τ _yz represents the stress that causes the displacement of the yz plane. Yes.
[Formula (4)]

When the strain obtained by using the above equation (3) from the position where the central angle of the diffraction ring is _α is written as εα, the following equation (5) is established for the stress of the above equation (4).
[Formula (5)]

Here, E is a longitudinal elastic constant, and v is a Poisson's ratio (both are diffraction elastic constants).

The above equation (5) is a basic equation of the conventional area detector type triaxial stress measurement method. N ₁ ~n ₃ in formula is the direction cosine of epsilon _alpha relative to the sample coordinate system, respectively represented by the following formula (6).
[Formula (6)]

here,
η is the complementary angle [(π / 2) −θ] of the Bragg angle θ,
Ψ ₀ is the angle between the normal to the surface of the specimen at the measurement point and the incident beam,
φ ₀ is an angle formed by the projection of the incident beam on the surface of the test object and the x axis.

As shown in FIG. 8, in the diffractive ring for any φ ₀ ,
ε _α : strain in the central angle α direction,
ε _{π + α} : strain in the direction where the central angle differs from ε _α by π,
ε− _α : strain in the central angle−α direction,
ε _π-α: consider the central angle strain only different directions [pi relative _{epsilon-.alpha.,} seeking a ₁ ~a ₃ represented by the following formula (7) using these.
[Formula (7)]

Substituting the above equation (5) into the above equation (7), the following equation (8) is obtained when φ ₀ = 0 °.
[Formula (8)]

Here, Φ and Ψ are as shown in the following equation (9).
[Formula (9)]

From the above equation (8), it is found that a ₁ and a ₂ are linear with respect to cos α and sin α, respectively. The slope of each straight line is expressed by the following equation (10).
[Formula (10)]

Next, for each of the above formulas (10), ψ ₀ > 0 (that is, incident from a direction inclined to φ ₀ = 0 °) and ψ ₀ <0 (that is, φ in the direction opposite to the former) ₀ = incident from the direction inclined to the 180 ° side) and the deviation are obtained and expressed as b _{1 to} b ₄ as in the following equation (11).
[Formula (11)]
Substituting the above equation (10) into the above equation (11) and rearranging, the following equation (12) is obtained when φ ₀ = 0 °.
[Formula (12)]

From the above equation (12), all the shear stress components (τ _xy , τ _xz , τ _yz ) and the stress relational expression (σ _x −σ _z ) of the x-axis and z-axis are obtained.

On the other hand, the relationship of the following equation (13) relating to the stress relationship equation (σ _y −σ _z ) of the y-axis and the z-axis is obtained from Φ in the above equations (8) and (9).
[Formula (13)]

Here, Φ is an inclination when a ₃ in the above equation (7) obtained by ε _α is linearly approximated to cos ² α, and can be obtained by measurement.
Since (σ _x −σ _z ) and τ _{xz on} the right side of the above equation (13) are already known from the above equation (12), from the above equation (13) and Φ, (σ _y −σ _z ) Can be determined.

In order to clarify the normal stress component σ _z , the relationship of the following equation (14) derived from the above equation (5) is used.
[Formula (14)]

Here, X is expressed as the following equation (15).
[Formula (15)]

As shown in the above equation (15), X is composed of only the stress component and the known number found so far, and the value is determined by calculation. Therefore, if the obtained X is substituted into the above equation (14), E and v are already known, so σ _z is determined.
Such sigma _z is one from one sigma _z 360 pieces of data obtained from the whole diffraction rings are obtained, in consideration of the influence of the variation, it is preferable to employ an average value thereof.
From σ _z and the already obtained stress relational expressions (σ _x −σ _z ) and (σ _y −σ _z ), σ _x and σ _y are determined. As a result, six triaxial stress components ( σ _x , σ _y , σ _z , τ _xy , τ _yz , τ _xz ) are all known.

The above is the principle of determining the triaxial stress component in the conventional triaxial stress measurement method of the area detector method.
However, when the present inventor examined the triaxial stress measurement method by the conventional area detector method in detail, it was newly found that the measurement accuracy may be insufficient. According to the inventor's research, it has been found that the measurement accuracy for the σ _y component is particularly low in the above-described conventional method. The cause of this is thought to be that due to the Poisson effect, the effect of σ _y is hardly reflected in the radius change of the diffraction ring measured from only φ ₀ = 0 ° and 180 ° directions, thereby lowering the measurement sensitivity. It is done.

JP-A-2005-241308

"Sasaki, T. and Hirose, Y., X-Ray Triaxial Stress Analysis Using Whole Diffraction Ring Detected with Imaging Plate, Transactions of the Japan Society of Mechanical Engineers, Series A, Vol. 61, No.590 (1995), pp 2288-2295. "

  An object of the present invention is to solve the above-described problems of the conventional area detector type triaxial stress measurement method and to provide a more accurate measurement method.

The present invention has been made to solve this problem, and has the following features.
(1) An X-ray stress measurement method for measuring stress existing in a test object based on a diffraction ring obtained by irradiating the test object with X-rays,
The measurement points on the surface of the test object are irradiated with X-rays in the four incident directions s1, s2, s3, and s4 defined in (A) below, and a diffraction ring is obtained for each.
From the set of diffraction rings in the incident directions s1 and s3, at least a relational expression (σ _x −σ _z ) of stress in the x-axis and z-axis directions and a shear stress τ _yz are obtained.
From the set of diffraction rings in the incident directions s2 and s4, at least a relational expression (σ _y −σ _z ) of stress in the y-axis and z-axis directions and a shear stress τ _xz are obtained,
A shear stress τ _xy is obtained from one or both of the set of diffraction rings in the incident directions s1 and s3 and the set of diffraction rings in the incident directions s2 and s4,
The stress σ _z in the z-axis direction is obtained from the relational expression of stress obtained as described above and the shear stress, and these are used to obtain six triaxial stress components σ _x , σ _y , σ _z , τ _xy , τ _yz , τ _xz. X-ray stress measurement method characterized by obtaining.
(A) Four incident directions s1, s2, s3, and s4 that are inclined by a predetermined incident angle Ψ ₀ from the normal of the surface of the test object at the measurement point and head toward the measurement point. Are defined on the surface of the test object, and when these incident directions are projected onto the surface of the test object, the projections of the incident directions s1 and s3 coincide with the x axis and face each other, and the incident direction s2 The four incident directions s1, s2, s3, and s4 are in such a positional relationship that the projections of s4 and s4 coincide with the y-axis and face each other.
(2) One of the shear stress τ _xy obtained from each of the pair of diffractive rings in the incident directions s1 and s3 and the pair of diffractive rings in the incident directions s2 and s4 is determined as the shear stress τ _xy. The X-ray stress measurement method according to the above (1), wherein the value is an average value of both values or both values.
(3) The X-ray stress measurement method according to (1) or (2) above, wherein the test object is a wheel or roller made of a polycrystalline substance, or a rail made of a polycrystalline substance.
(4) An X-ray stress measurement method for measuring stress existing in a test object based on a diffraction ring obtained by irradiating the test object with X-rays,
The measurement points on the surface of the test object are irradiated with X-rays in the three incident directions t1, t2, and t3 defined in the following (B), and a diffraction ring is obtained for each.
From the diffraction ring in the incident direction t1, shear stresses τ _xz and τ _yz are obtained,
From the diffraction ring in the incident direction t2, the relational expression (σ _x −σ _z ) of the stress in the x-axis and z-axis directions and the shear stress τ _xy are obtained, and
From the diffraction ring in the incident direction t3, the relational expression (σ _y −σ _z ) of the stress in the x-axis and z-axis directions and the shear stress τ _xy are obtained,
The stress σ _z in the z-axis direction is obtained from the relational expression of the shear stress and the stress obtained as described above, and with these, six triaxial stress components σ _x , σ _y , σ _z , τ _xy , τ _yz , τ _{xz are obtained.} X-ray stress measurement method characterized by obtaining.
(B) An incident direction t1 toward the measurement point along the normal line of the surface of the test object at the measurement point, and two incident directions t2 and t3 that are inclined from the normal line by a predetermined incident angle ψ ₀ toward the measurement point. Are incident directions t1, t2, and t3, and the incident directions t2 and t3 define xy coordinates orthogonal to the measurement point on the surface of the test object, and project these incident directions on the surface of the test object. Sometimes the three incident directions t1, t2, and t3 are in such a positional relationship that the projection in the incident direction t2 coincides with the x-axis and the projection in the incident direction t3 coincides with the y-axis.
(5) shear stress tau the _xy, an average value of the shear stress tau _xy obtained respectively from the diffraction ring in the direction of incidence t2 and t3, the (4) X-ray stress measuring method described.
(6) In carrying out the X-ray stress measurement method, first, X-ray irradiation in the incident direction t1 is performed on the measurement point on the surface of the test object, and the shear stress τ _xz obtained from the diffraction ring is obtained. _{Alternatively} , the X-ray stress measurement method according to (5), wherein the state of stress inside the test object is determined based on the shear stress τ _yz .

As described above, in the conventional triaxial stress measurement method using the area detector method, only a pair of incident directions that are symmetric with respect to the normal of the surface of the test object at the measurement point are used. As shown in FIG. 9, when the pair of incident directions are projected onto the surface of the test object, they coincide with the x-axis of the xy orthogonal coordinates defined on the surface of the test object at the measurement point (the projection direction is the same). It can also be considered to be the x-axis), the directions facing each other. That is, when one of a pair of projections in the incident direction is a direction of φ ₀ = 0 ° as a reference direction, the other is a direction of φ ₀ = 180 °. Hereinafter, the original oblique incident direction is also distinguished from the incident direction of φ ₀ = 0 °, the incident direction of φ ₀ = 180 °, and the like using the direction projected on the surface of the test object.

In the triaxial stress measurement by X-ray irradiation in two directions located on opposite sides as shown in FIG. 9, an effective stress calculation result is given for strain data rounded off to the order of 10 ⁻⁷ to 10 ^−6. For data including more errors than that (for example, data rounded off to the order of 10 ⁻⁵ ), the stress calculation error increases centering on the σ _y component, and for example 45 % Error may be reached.
As described above, because of the Poisson effect, the effect of σ _y is difficult to be reflected in the radius change of the diffraction ring due to X-ray irradiation from the directions of φ ₀ = 0 ° and φ ₀ = 180 °. This is probably because the measurement sensitivity is lowered.

On the other hand, in the first aspect of the measurement method of the present invention, as in (A) above, two conventional incident directions s1 (direction of φ ₀ = 0 °) and s3 (φ ₀ = 180 °) In addition to the incident direction s2 (direction of φ ₀ = 90 °) and s4 (direction of φ ₀ = 270 °), each diffraction ring obtained by irradiation from a total of four directions. To determine the triaxial stress measurement.
At this time, the measurement is not simply performed from multiple directions, but at least (σ _x −σ _z ) and τ _yz are obtained from a set of diffraction rings in the incident directions a1 and a3, and at least (σ _y− σ _z ) and τ _xz are obtained from a set of diffraction rings with incident directions a2 and a4, and are used to set a new stress and a relational set σ _z and (σ _x −σ _z ). , (Σ _y −σ _z ), τ _xy , τ _xz , τ _yz , from which six triaxial stress components σ _x , σ _y , σ _z , τ _xy , τ _yz , τ _xz are obtained. ing.
As a result, the stress calculation result within the practical range is given to the strain data rounded off to 10 ⁻⁷ to 10 ⁻⁶ , and the error is 10% even to the data rounded off to 10 ^−5. It was found that the error stayed on the table and there were fewer errors than the conventional method.

In the second aspect of the measurement method of the present invention, triaxial stress measurement is determined using each diffraction ring obtained by X-ray irradiation in three incident directions.
These three incident directions are, as described in (B) above, incident direction t1 (hereinafter also referred to as a normal incident direction) toward the measurement point along the normal of the surface of the test object at the measurement point. 2), two incident directions t2 (φ ₀ = 0 ° direction) and t3 (φ ₀ = 90 ° direction) that are inclined from the normal by a predetermined incident angle Ψ ₀ toward the measurement point. is there.
As a result, it was found that all triaxial stress components can be determined from the three diffraction rings, and measurement accuracy exceeding the first aspect is obtained, and in particular, measurement accuracy of σ _y is improved.

Furthermore, in the second aspect of the measurement method of the present invention, only normal incidence is performed first, and the state of stress inside the test object is determined based on the shear stress τ _xz and τ _yz obtained from the diffraction ring. Propose to do.
The method of judging the state of stress inside the test object only by normal incidence of X-rays is simple and completely different from the conventional method in which X-ray stress measurement is mainly performed obliquely. However, the unique stress caused by rolling contact on a rail or the like has a special significance as a method for roughly determining the state.
Therefore, for example, for a long section of a railroad rail, vertical irradiation of X-rays is performed first to make a general determination of internal stress, and a part requiring reexamination is found. It is also possible to perform detailed triaxial stress measurement by performing oblique irradiation.
In addition, by measuring the shear stress τ _xz in a railroad rail, it is possible to detect the initial deterioration state of the rail and the occurrence of cracks, which is effective as a reference for the rail inspection method.

FIG. 1 is a diagram for explaining the configuration of an X-ray stress measurement method according to the present invention. FIG. 1 (a) shows a first aspect of the present invention, and FIG. 1 (b) shows a second aspect of the present invention. Show. FIGS. 2A to 2C show the strain ε _α and the stresses σ _y and τ _xz τ _{yz at} oblique incidence (φ ₀ = 0 °, 90 °) and normal incidence (Ψ ₀ = 0 °). It is a graph which shows a relationship. 3 was obtained by sequentially analysis calculation (incident direction φ ₀ = ₀ °, the inclination Ψ ₀ = 30 °) is a graph showing the epsilon _alpha distribution for X-ray irradiation at. FIG. 4 is a graph showing stress calculation results in the simulation of Example 1 of the present invention. FIG. 5 is a photograph showing an example of a measured diffraction ring image in Example 2 of the present invention. FIG. 6 is an a ₁ diagram obtained by diffraction of a rail sample in Example 2 of the present invention. FIG. 7 is a diagram comparing the stress components obtained when the conventional area detector type triaxial stress measurement method and the first and second aspects of the measurement method of the present invention are applied to the measurement data. is there. FIG. 8 is a diagram for explaining the positional relationship between the area detector and the test object, the diffraction ring (Debye-Scherrer ring), and the definition of four strains used for stress calculation in the conventional area detector method. . FIG. 9 is a diagram for explaining a method of measuring a diffraction ring in a conventional area detector.

First, the first aspect of the X-ray stress measurement method of the present invention (also referred to as the first method of the present invention) will be described.
The first aspect of the present invention has at least the following operations.
First, as shown in FIG. 1A, the measurement points on the surface of the test object are irradiated with X-rays in the four incident directions s1, s2, s3, and s4 defined in (A) above. Each obtains a diffractive ring.
Here, when the four incident directions s1, s2, s3, and s4 are projected onto the surface of the test object, the incident directions s1 and s3 correspond to the xy coordinates on the test object surface orthogonal to the measurement point. The projections coincide with the x axis and face each other, and the projections in the incident directions s2 and s4 coincide with the y axis and face each other. That is, when the incident direction s1 is the reference direction and φ ₀ = 0 °, the incident direction s3 is φ ₀ = 180 °, and the incident direction s2 is φ ₀ = 90 with respect to these s1 and s3. When the direction is °, the incident direction s4 is a direction of φ ₀ = 270 °.

Next, from the set of diffraction rings in the incident directions s1 and s3 and the set of diffraction rings in the incident directions s2 and s4, stresses and stress relational expressions σ _z , (σ _x −σ _z ), (σ _y− σ _z ), τ _xy , τ _xz , τ _yz are obtained.
The calculation method itself for obtaining the set of stress from the set of diffraction rings in the incident directions s1 and s3 is the same as the conventional triaxial stress measurement method of the area detector method.
On the other hand, a method for obtaining a stress set from a set of diffraction rings in the incident direction s2 (φ ₀ = 90 °) and s4 (φ ₀ = 270 °) is basically the same as the conventional method. In this case, the following equation (16) is obtained from the equations (5) to (7) as an equation corresponding to the equation (10).
[Formula (16)]

When the stress component is obtained by substituting the above equation (16) into b _{1 to} b ₄ of the above equation (11), τ _yz , (σ _y −σ _z ), τ _xz as shown in the following equation (17). , Τ _xy is obtained.
[Formula (17)]
Similarly to the conventional method, (σ _x −σ _z ), (σ _y −σ _z ), and τ _xz can be determined by the above equations (13) and (14), and τ _xy can also be determined.

As described above, from the set of diffraction rings in the incident directions s1 and s3 and the set of diffraction rings in the incident directions s2 and s4, the relational expression of stress and stress, that is, σ _z , (σ _x −σ _z ), (Σ _y −σ _z ), τ _xy , τ _xz , τ _yz .
In the present invention, the stress obtained from the set of diffraction rings in the incident directions s1 and s3 is adopted for at least (σ _x −σ _z ) and τ _yz out of the stress included in each stress set. For at least (σ _y −σ _z ) and τ _xz , the stress obtained from the set of diffraction rings in the incident directions s2 and s4 is adopted, and these are combined to [(σ _x −σ _z ), (σ _y −σ _z ), σ _z , τ _xy , τ _yz , τ _xz ], from which six triaxial stress components σ _x , σ _y , σ _z , τ _xy , τ _yz , τ _xz Ask.
As a result, the stress (σ _y −σ _z ) and τ _xz obtained from the set of diffraction rings in the incident directions s2 and s4 newly added in the present invention are used in the calculation, and the measurement accuracy is improved.

In the first aspect of the present invention, four-direction diffraction ring measurement is required, which is twice as much as the two-direction measurement in the conventional area detector triaxial stress measurement method shown in FIG. However, the measurement accuracy of σ _y can be improved, and the measurement accuracy of σ _x and σ _z affected by the measurement accuracy can also be expected.

As the shear stress τ _xy, any of the set of diffraction rings in the incident directions s1 and s3 and τ _xy obtained from the set of diffraction rings in the incident directions s2 and s4 may be adopted. It is preferable to use the average value of the obtained τ _xy .
Also, σ _z is determined from each point on the diffraction ring using the stress component obtained up to this point. Since 360 σ _z are obtained from 360 ° to the entire circumference of the diffraction ring, it is preferable to obtain an average value and improve the reliability.

Next, a second aspect of the X-ray stress measurement method according to the present invention will be described.
In the second aspect of the present invention, as shown in FIG. 1 (b), X is measured in the three incident directions t1, t2, and t3 defined in (B) above with respect to the measurement points on the surface of the test object. Irradiate a line to obtain a diffractive ring for each. When the incident direction t1 is a direction of φ ₀ = 0 ° or 180 °, the incident direction t3 is a direction of φ ₀ = 90 ° or 270 °, but a combination of them makes the incident direction t1 φ ₀ = 0 °. This is equivalent to a combination in which t3 is a direction of φ ₀ = 90 °.

In the second mode, the pair of s1 (φ ₀ = 0 °) and s3 (φ ₀ = 180 °), s2 (φ ₀ = 90 °) and s4 (φ ₀ = 270 °) in the first mode Instead of using X-ray irradiation from the opposite direction, such as a pair of diffractors, a diffractive ring obtained by making X-rays incident in the normal direction of Ψ ₀ = 0 ° is used instead. The number of measurements is reduced.

In the second embodiment, the calculation method for obtaining the stress from the diffraction ring of the X-ray irradiation by the three incident directions is as follows.
In the case where X-rays are vertically incident (when Ψ ₀ = 0), the two expressions in the above expression (10) are respectively the following two expressions (18).
[Formula (18)]
From the above equations, shear stresses τ _xz and τ _yz are obtained as in the following equation (19).
[Formula (19)]

The present inventor has conducted extensive research and found that the influence of τ _xz and τ _{yz on} the diffraction ring shape is greatest when Ψ ₀ = 0, and is therefore the optimum condition for stress measurement. In this regard, a phi ₀ direction will be described later in the descriptions of the change in strain epsilon _alpha.
When τ _xz is obtained, when Ψ ₀ ≠ 0, that is, in oblique irradiation in the direction of t2, σ _x −σ _z is obtained from the first expression of the above expression (10) as the following expression (20). ([Psi] ₀ is the most accurate when it is 45 [deg.], And the accuracy decreases when it approaches _{0 [} deg.] And 90 [deg.]).
[Formula (20)]

Similarly, when τ _yz obtained from the second equation of the above equation (19) is used, in the oblique irradiation in the direction of t2, from the first equation of the above equation (16), σ _y −σ _z is expressed by the following equation ( 21).
[Formula (21)]

Next, for τ _xy , the relationship of a ₂ at φ ₀ = 0 ° and φ ₀ = 90 ° is used. That is, since τ _xz and τ _yz are already obtained from the equation (19), the relationship of the following equation (22) is obtained from the second equations of the equations (10) and (16).
[Formula (22)]
Regarding τ _xy , the calculation accuracy of the two equations (22) is equivalent, and any of the above may be used, but reliability is improved by averaging both.
From the above results, σ _z can be determined using the above formula (14), as in the first aspect of the present invention. When σ _z is obtained, σ _x and σ _y are immediately determined from the values of (σ _x −σ _z ) and (σ _y −σ _z ), and six triaxial stress components σ _x and σ _{y are obtained.} , Σ _z , τ _xy , τ _yz , τ _xz are obtained.
In the second aspect of the present invention, as is clear from FIG. 1B, three-direction diffraction ring measurement is performed, and there is an advantage that the diffraction ring measurement is smaller in one direction than the first aspect described above. .

Here, a phi ₀ direction, the change in strain epsilon _alpha explained.
As shown in the following formula (23), the distribution of ε _{α in} the entire circumference of the diffraction ring when only σ _y (for example, 100 MPa) acts, and the influence of φ _{0 on} the distribution are shown in the graph of FIG. Shown in the figure. The calculation conditions are the same as in the simulation described later (including the case where the X-ray incident angle Ψ ₀ is 30 ° and Ψ ₀ = 0 in the second mode).
[Formula (23)]

As shown in the graph of FIG. 2 (a), the variation width of the epsilon _alpha is greater at φ ₀ = 90 °, shows about 8.2 times the time of φ ₀ = ₀ °. Further, φ ₀ = 0 ° exhibits a slightly more complicated change than φ ₀ = 90 °.
Therefore, when measuring σ _y , it can be seen that it is more advantageous to use a strain distribution of φ ₀ = 90 °.

Similarly to the above, τ _xz is examined assuming the following equation (24).
[Formula (24)]

FIG. 2B shows ε _α with respect to τ _xz . variation of epsilon _alpha at φ ₀ = 90 ° becomes about 1.75 times in the case of φ ₀ = ₀ °, and when to measure tau _xz should be used strain distribution of φ ₀ = 90 ° I can say that.
As shown in FIG. 2B, in the case of normal incidence (Ψ ₀ = 0 °), it is 2.0 times that when φ ₀ = 0 °, and when φ ₀ = 90 °. It can be seen that the strain change is 1.15 times, which is advantageous for measurement.

Similarly to the above, τ _yz is examined on the assumption of the following formula (25).
[Formula (25)]

As shown in FIG. 2C, a tendency similar to that in the case of τ _xz is observed, and ε _α at φ ₀ = 0 ° is approximately 1.75 times larger than ε _α at φ ₀ = 90 °. I understand. Therefore, it is desirable to use the condition of φ ₀ = 0 ° for the inverse analysis with respect to τ _yz .
The point that the sensitivity is highest in the case of normal incidence is also the same as τ _xz (φ ₀ = 2.0 times in the 90 ° direction and 1.15 times in the φ ₀ = 0 direction).

The test object to which the measurement method of the present invention is applied is not particularly limited as long as it is made of a polycrystalline material (for example, metal, ceramics, specific plastic, etc.). Triaxial stress is applied to articles that are repeatedly subjected to rolling contact, such as rollers (especially their outer peripheral surfaces), rails, bearings, etc., and to ground parts and materials with precipitated phases. The utility of the present invention to measure becomes significant.
The stress measurement method of the present invention has a step of obtaining triaxial stress, and can be called an X-ray triaxial stress measurement method. Good.

In the second aspect of the present invention, as described in the description of the effect of the invention, only normal incidence is performed first, and the stress inside the test object is based on the shear stress τ _xz and τ _yz obtained from the diffraction ring. Determine the state. This determination method has a special significance for the determination of the stress caused by rolling contact on a rail or the like and the presence or absence of fatigue.
Stresses generated in articles such as railroad rails that undergo rolling contact are special, and in particular, the properties of shear stress τ _xz and τ _yz are unique.
The initial crack of rolling contact fatigue is generated by the shear stress τ _xz . The shear stress changes from negative to positive as the wheel passes. On the other hand, the sign of other stress components does not change even when the wheels pass.
Further, the shear stress τ _xz is maximized not in the contact surface but in the interior. On the other hand, other stress components become maximum at the contact surface.
When the plane stress is measured by a conventionally known stress measurement method for an article subjected to such rolling contact, σ _x −σ _z = 0, σ _x − in the triaxial stress state and the pseudohydrostatic pressure state. σ _z = 0. In other words, even if σ _x , σ _y , and σ _z have significant values, the method of measuring only plane stress gives zero stress and misunderstands that there is no stress and there is no danger. There is a possibility that.
On the other hand, if the method of the present invention is applied to the surfaces of rails, wheels, etc., the correct residual stress can be obtained with higher accuracy.

In addition, if only normal incidence is performed in the second aspect of the present invention, the evaluation of the special shear stress τ _xz in the rolling contact can be easily and effectively known, and further detailed inspection is performed. It is possible to determine whether or not it should be.
The method of performing the normal incidence only, obtaining the shear stress τ _xz from the resulting diffraction ring, and evaluating the internal stress of the test object is not only as part of the second aspect of the present invention, It can also be regarded as an independent X-ray stress measurement method.

The aspect of the measuring apparatus for carrying out the X-ray triaxial stress measurement method according to the present invention is not particularly limited, and X-ray irradiation from the direction necessary for the measurement method and the diffraction ring generated thereby can be analyzed. And means.
X-rays used for irradiation may be characteristic X-rays used in a conventionally known X-ray stress measurement method, and examples thereof include CrKα characteristic X-rays by an X-ray tube having a Cr target.

The means for analyzing the diffraction ring is not particularly limited. For example, the diffraction ring is generally detected by an area detector such as an imaging plate, a CCD (charge coupled device), a semiconductor detector, or a C-Mos image sensor. An apparatus for analysis is preferable.
As described in Patent Document 1, the imaging plate once accumulates X-ray energy and then captures an entire image of the diffraction ring using a photostimulable luminescence phenomenon in which fluorescence is generated by excitation with light. A sensor, for example, formed by applying a fine crystal of a stimulable phosphor such as BaFBr: Eu ^{2+ on} the surface of a plastic film, and when X-rays enter the X-ray Energy is stored.
As shown in FIG. 1, a through-hole through which an X-ray irradiation tube passes is usually formed at the center of the imaging plate, and a characteristic X-ray is irradiated from there to a measurement point to form a diffraction ring. The reflected X-rays that have returned in this way are configured to receive light around them.

  A CCD, a semiconductor detector, a C-Mos image sensor, or the like can obtain an output signal for image data of a diffraction ring that can be subjected to image processing and arithmetic processing by a computer. On the other hand, a recording medium such as an imaging plate is used together with a reading device (imaging plate reader) for reading a diffraction ring image recorded on the plate. The reader scans and irradiates excitation light such as a He-Ne laser on the imaging plate, amplifies the fluorescence generated from the X-ray energy accumulation portion in the imaging plate by a photomultiplier tube, The apparatus is configured to read the diffraction ring image by measuring the intensity, and an output signal for the image data of the diffraction ring is obtained through the reading device.

  When analyzing the distortion on the diffraction ring shown in FIG. 8, it is preferable to finely decompose the entire circumference of the diffraction ring to obtain more data. For example, the angle α interval is set to 1 °, It is a preferred embodiment to obtain a total of 360 data over the circumference.

The apparatus configuration for holding the imaging plate, the CCD, etc. at a predetermined angle with respect to the surface of the test object is one that can achieve the incident direction required in the first and second aspects of the present invention. Just make it.
Prepare only one pair of imaging plate and collimator located in the center of the plate and change the arrangement position to the required incident direction, that is, use one set for multi-directional measurement. It may be configured to perform, and for the four directions of the first aspect and the three directions of the second aspect, a set corresponding to all necessary irradiation directions may be prepared, As an intermediate configuration between these, only a configuration position that can be used in combination may be used.

The angle of oblique irradiation to the measurement point on the surface of the test object (that is, the angle Ψ ₀ of the inclination from the normal line at the measurement point) refers to the irradiation angle in the triaxial stress measurement method by the conventional area detector method described above. It's okay.
[Psi ₀ is most preferably 45 °, in the case of other [psi ₀ becomes ^{_{Ψ 0 = 45 (sin 2 Ψ}} 0) for the case of ° fold measurement sensitivity (accuracy). When ψ ₀ <45 °, the closer ψ ₀ is to 0 °, the less the influence of X-ray absorption and the better a diffractive ring can be obtained. When 45 ° <ψ ₀ , the depth of X-ray penetration can be reduced when ψ ₀ approaches 90 °, which is suitable for measurement of the surface portion.

Example 1
In this example, the result of simulation is shown for verification of the stress measurement method (first aspect, second aspect) according to the present invention. The simulation does not use an actual test object and X-rays, but can be sufficiently shown as an example.
Further, the principle of the triaxial stress component determination using the area detector type triaxial stress measurement method described in Non-Patent Document 1 (that is, in the description of the prior art, using equations (1) to (15)). The results of the triaxial stress measurement method (hereinafter referred to as “conventional method”) are also shown and compared with the first and second aspects of the present invention.

〔Calculation condition〕
First, a simple stress component such as the following equation (21) was assumed.
[Formula (21)]

Next, assuming the measurement of 211 diffraction of steel (ferrite) by irradiation with CrKα ray, which is a standard characteristic X-ray, the following calculation conditions were set.
Material: Steel (ferrite)
Young's modulus: 206.0 (GPa)
Poisson's ratio: 0.28
Miller index of diffraction surface (hkl): 211
Diffraction angle without stress: 156.4 (degrees)
X-ray incident angle (angle between normal) Ψ ₀ : 30.0 (degrees), 0.0 (degrees)
Distance between material and detector: 100.0 (mm)
Number of strains ε _α used for calculation: 360
Angle α interval (interval): 1.0 (degrees)

In this way, the strain ε _α on the diffraction ring was determined by 1 degree with respect to the angle α. This ε _α is virtually regarded as measurement data, and the above-described stress calculation methods are applied to verify whether the stress value can be correctly back-analyzed.
3 was obtained by sequentially analysis computation (the incident beam of azimuth (φ ₀ = ₀ °, and is a graph showing the epsilon _alpha distribution for X-ray irradiation at Ψ ₀ = 30 °). In Fig. Rounds the strain to the 10 ^-7 digit (graph line indicated by a dashed line), 10 ^-6 digit (graph line indicated by a solid line), 10 ^-5 digit (graph line indicated by a one-dot chain line), respectively. In this simulation, mixing of the measurement error assumed in actual measurement was simply simulated by changing the rounding digit in this way.

Comparison of results The obtained stress calculation results are shown in the graphs of FIGS. The black bar graph represents the first mode, and the broken bar graph represents the second mode. In addition, in the same graph, the stress measurement result by the conventional method is also shown by a shaded bar graph.
FIG. 4A shows the stress calculation result for the data rounded to the 10 ⁻⁷ digit, FIG. 4B shows the stress calculation result for the data rounded to the 10 ⁻⁶ digit, and FIG. ) ^Shows the stress calculation results for the data rounded to the nearest 10 ^-5 .
In the case of using strain data rounded off to a relatively high precision of 10 ⁻⁷ shown in FIG. 4A (hereinafter referred to as 10 ⁻⁷ data), the direction of the incident beam is φ ₀ = 0 °, 180 The conventional method is 0.02 to 0.36% error range, the first embodiment of the method of the present invention is 0.0 to 0.05%, the second embodiment of the method of the present invention is 0.09 to It becomes 0.47%, and it can be seen that the three methods are sufficiently accurate in actual use.
Next, in the stress calculation result for the data rounded off to the 10 ⁻⁶ digit shown in FIG. 4B (hereinafter referred to as “10 ⁻⁶ data”), the conventional method has an error range of 0.19 to 3.5%. The first embodiment of the method has an error range of 0.19 to 0.65%, and the second embodiment of the method of the present invention has an error range of 0.83 to 3.8%. It has been found that the measurement accuracy of the first aspect is sufficiently high.
Further, in the stress calculation result for the data rounded to the 10 ⁻⁵ digit shown in FIG. 4C (hereinafter referred to as “10 ⁻⁵ data”), the conventional method has an error range of 0.6 to 46.0%. The first embodiment of the method had an error range of 0.56 to 2.7%, and the second embodiment of the method of the present invention had an error range of 1.8 to 16.0%. In 10 ⁻⁵ data, the error of σ _y by the conventional method is significant. The second method is relatively accurate for all stress components.

As described above, when measurement data (ε _α ) with higher accuracy than 10 ⁻⁶ data is obtained, both the conventional method and the method of the present invention provide stress accuracy within the practical range, but the variation in ε _α is 10 ^As we approached ^-5 data, the error of σ _{y in} the conventional method was found to increase. In the latter case, it has been found that the error can be greatly suppressed by using the first or second aspect of the present invention.
The reason why the measurement accuracy of the conventional method is low is thought to be because sensitivity reduction due to the Poisson effect occurred in the stress component related to the direction orthogonal to the X-ray incident direction. On the other hand, in the first or second aspect of the present invention, since diffraction data of φ ₀ = 90 ° is used, it is considered that relatively good accuracy was obtained.
In any calculation result, the first aspect of the present invention shows the most accurate result, but the stress determination accuracy varies to some extent depending on the initial value and calculation conditions.

Example 2
In this example, a rail used on a conventional line and replaced by maintenance is used as a test object.
The measurement accuracy was compared by applying the first and second aspects of the conventional method and the method of the present invention.
The rail of the test object is a part of a 60 kg normal rail defined in JIS E 1101. Its standard chemical composition and mechanical properties are as follows.
Carbon (C): 0.63-0.75 (% by weight)
Silicon (Si): 0.15 to 0.30 (% by weight)
Manganese (Mn): 0.70 to 1.10 (% by weight)
Phosphorus (P): Less than 0.030 (% by weight) Sulfur (S): Less than 0.025 (% by weight) Tensile strength: 800 (MPa) or more A plastic flow of the metal structure is formed near the contact surface), and triaxial residual stress is observed when X-ray stress measurement is performed.
In this example, the top of the rail was cut so as to be a sample having a dimension of [10 mm in depth from the rail surface and 10 mm in the longitudinal direction of the original rail] so that it could be set in the experimental apparatus, and then the tread. X-ray measurement was performed on the center point.

The sample was cut into a slice shape (thickness: 10 mm, length: 165 mm) by an automatic sawing machine, and then cooled to a width of 10 mm in the longitudinal direction of the rail while cooling with a precision cutting machine. . At that time, consideration was given to the application of residual stress to the rail tread during the cutting process. The measurement result is considered to correspond to the result of superimposing the local residual stress formed immediately below the rail tread by the rolling contact with the wheel and the stress release by cutting.
The main X-ray conditions are as follows.
Characteristic X-ray: CrKα
Miller index (hkl) of diffraction surface: αFe-211
X-ray tube voltage: 30 (kV)
X-ray tube current: 10 (mA)
Collimator diameter: 1 (mm)
X-ray incident angle Ψ ₀ : 30 (degrees) on the sample
X-ray incident angle on Fe powder: 0 (degrees)
Distance between sample and detector: 100 (mm)
Distance between Fe powder and detector: 43 (mm)

A 127 mm × 127 mm imaging plate (IP) was used for the diffraction ring measurement.
Each pixel constituting the diffraction ring image is, by design, a square having a side of 100 μm, and approximately 1000 pixels (1 million pixels in total) both vertically and horizontally. The luminance resolution of each pixel is 8 bits.
The processing method of the diffraction ring image is the same as the conventional method.
In the sample coordinate system, the X-ray irradiation point at the center of the tread surface of the rail was set as the origin, and the longitudinal side (traveling direction) of the rail was set to the x axis (φ ₀ = 0 °).

Measurement Results FIGS. 5A to 5E show examples of measured diffraction ring images. In both cases, the inner diffraction ring is 211 diffraction of the reference material (annealed steel), and the next is 211 diffraction of the rail sample. Furthermore, the weak diffraction outside thereof is 220 diffraction of the reference material.
The diffraction intensity distribution in the radial direction was determined from the measured diffraction ring image.
Next, for the diffraction of the rail sample, the peak position was determined by the half-width midpoint method, and then the a ₁ diagram was obtained. An example thereof is shown in the graph of FIG.

FIG. 7 is a diagram comparing the stress components obtained when the conventional method and the first and second aspects of the measurement method of the present invention are applied to the measurement data. The results of (σ _x −σ _z ) and (σ _y −σ _z ) are shown. The black bar graph represents the first embodiment, the broken bar graph represents the second embodiment, and the shaded bar graph represents the stress component of the conventional method.
As shown in FIG. 7, with respect to the shear stress, almost the same consistent tendency is shown in any of the measurement methods. On the other hand, with respect to normal stress, particularly σ _y and (σ _y −σ _z ), the results of the conventional method show a tendency different from the results of the measurement method of the present invention.

The comparison result for each stress calculation method is almost similar to the tendency of FIG. 4C in the simulation of the first embodiment. It is surmised that this cause is related to the difference in strain sensitivity due to the Poisson effect. The error of (σ _y −σ _z ) affects the determination of σ _z and also affects the subsequent determination of σ _x .
On the other hand, in the first and second aspects of the measuring method of the present invention, such influence is reduced by using diffraction ring data in the direction of φ ₀ = 90 °.
The difference in stress value between the first and second aspects of the measurement method of the present invention was relatively small, but both used diffraction data with different X-ray penetration depths, and each measurement result was Depending on the stress state, it may be possible that they do not exactly match. That is, in the first mode, the four types of incident angles Ψ ₀ are all the same, but in the second mode, data of Ψ ₀ = 0 ° is used in part. For this reason, the measurement range in the material differs depending on the difference in the X-ray penetration depth due to Ψ ₀ together with the influence of the experimental error at Ψ ₀ = 0.

  It is considered that Hertz contact stress is generated on the rail top surface, a stress gradient is generated in the vicinity of the top surface including the X-ray penetration depth region, and the residual stress state is also affected. One of the causes of errors in the stress calculation results of both methods may be due to the difference in the X-ray penetration depth.

In the second aspect of the present invention, τ _xz and τ _yz are obtained from the diffraction ring with normal incidence (Ψ ₀ = 0), and oblique incidence (Ψ ₀ = 30 °, φ ₀ = 0 °, φ ₀ = 90 °). ) Can be determined from (σ _x −σ _z ) and (σ _y −σ _z ), respectively. On the other hand, in the first aspect, a total of two sets of (φ ₀ = 0 °, φ ₀ = 180 °) and (φ ₀ = 90 °, φ ₀ = 270 °) are combined. Similar stress components are determined by using a diffraction ring. As a result, a new error may occur due to an increase in the calculation process.
Thus, for use of each aspect, an appropriate selection is required according to the measurement accuracy of the diffraction ring and the degree of the stress gradient.

Through the numerical simulation of Example 1 and the actual measurement of Example 2, it was confirmed that the measurement method according to the present invention was theoretically correct. In addition, when the accuracy of the lattice strain ε _α is 10 ⁻⁶ data (strain data rounded to the nearest 10 ⁻⁶ ), correct results can be obtained using either the first or second mode. Turned out to be.
The conventional method uses diffractive rings from two directions, the first mode uses four directions, and the second mode uses diffractive rings from three directions. Therefore, when the accuracy of the lattice strain epsilon _alpha is high, the measured quantity less conventional method is practically effective.
However, when the accuracy of the lattice strain was lower than 10 ⁻⁶ data, it was recognized that an error tends to appear in the stress component σ _y acting in the direction orthogonal to the X-ray incident direction due to the Poisson effect. In order to avoid this influence, it is necessary to apply the first and second aspects of the present invention using measurement data in the direction of φ ₀ = 90 °.

Further, in the second aspect of the present invention, it is possible to reduce the required diffraction ring data by one direction while maintaining the features of the first aspect. Therefore, a reduction in measurement time can be expected, and an effect is expected in the triaxial stress measurement in the field measurement such as a laying rail.
In the second mode, only the normal incidence measurement is performed alone in advance, so that the outline of the internal stress of the entire test object and the location that requires a detailed inspection can be obtained. You can find out at

In addition, there are many steel materials in outdoor structures that require on-site measurement, and the inside contains ferrite and cementite. For this reason, microscopic additional stress due to the difference in elastic constants between the two phases is generally generated, and even if the macroscopic stress is a uniaxial stress or a plane stress state, the microscopic scale is in a triaxial stress state.
In such a case, the stress by the diffraction method is a phase stress composed of the sum of the macroscopic average stress (macro stress) and the above-described microscopic interaction stress (micro stress). Therefore, there is a possibility that the necessity of triaxial stress analysis is not limited in X-ray stress measurement of steel materials. In particular, when crystal grains become finer, it is said that the influence of triaxial stress is likely to appear in the X-ray penetration depth range.
The method shown in the present invention is a relatively practical evaluation method for such a case.

According to the present invention, the measurement accuracy for the σ _y component, which is cited as a problem in the conventional method, that is, the conventional triaxial stress measurement method of the area detector method, is improved, and X-rays are applied to an article subjected to rolling contact such as a rail. The usefulness of the triaxial stress measurement method became higher. In addition, the state of the shear stress τ _xy can be easily known by performing vertical X-ray irradiation on a rail or the like.

Claims (6)

An X-ray stress measurement method for measuring stress existing in a test object based on a diffraction ring obtained by irradiating the test object with X-rays,
The measurement points on the surface of the test object are irradiated with X-rays in the four incident directions s1, s2, s3, and s4 defined in (A) below, and a diffraction ring is obtained for each.
From the set of diffraction rings in the incident directions s1 and s3, at least a relational expression (σ _x −σ _z ) of stress in the x-axis and z-axis directions and a shear stress τ _yz are obtained.
From the set of diffraction rings in the incident directions s2 and s4, at least a relational expression (σ _y −σ _z ) of stress in the y-axis and z-axis directions and a shear stress τ _xz are obtained,
A shear stress τ _xy is obtained from one or both of the set of diffraction rings in the incident directions s1 and s3 and the set of diffraction rings in the incident directions s2 and s4,
The stress σ _z in the z-axis direction is obtained from the stress relational expression and the shear stress obtained as described above, and six triaxial stress components σ _x , σ _y , σ _z , τ _xy , τ _yz , τ _xz are obtained from these. X-ray stress measurement method characterized by obtaining.
(A) Four incident directions s1, s2, s3, and s4 that are inclined by a predetermined incident angle Ψ ₀ from the normal of the surface of the test object at the measurement point and head toward the measurement point. Are defined on the surface of the test object, and when these incident directions are projected onto the surface of the test object, the projections of the incident directions s1 and s3 coincide with the x axis and face each other, and the incident direction s2 The four incident directions s1, s2, s3, and s4 are in such a positional relationship that the projections of s4 and s4 coincide with the y-axis and face each other. The shear stress τ _xy is a value of one of the shear stress τ _xy obtained from both the pair of diffraction rings in the incident directions s1 and s3 and the pair of diffraction rings in the incident directions s2 and s4, Or the X-ray-stress measuring method of Claim 1 made into the average value of both values.   The X-ray stress measurement method according to claim 1 or 2, wherein the test object is a wheel or roller made of a polycrystalline material, or a rail made of a polycrystalline material. An X-ray stress measurement method for measuring stress existing in a test object based on a diffraction ring obtained by irradiating the test object with X-rays,
The measurement points on the surface of the test object are irradiated with X-rays in the three incident directions t1, t2, and t3 defined in the following (B), and a diffraction ring is obtained for each.
From the diffraction ring in the incident direction t1, shear stress τ _xz and τ _yz are obtained,
From the diffraction ring in the incident direction t2, the relational expression (σ _x −σ _z ) of the stress in the x-axis and z-axis directions and the shear stress τ _xy are obtained, and
From the diffraction ring in the incident direction t3, the relational expression (σ _y −σ _z ) of the stress in the x-axis and z-axis directions and the shear stress τ _xy are obtained,
The stress σ _z in the z-axis direction is obtained from the relational expression of the shear stress and the stress obtained as described above, and with these, six triaxial stress components σ _x , σ _y , σ _z , τ _xy , τ _yz , τ _{xz are obtained.} X-ray stress measurement method characterized by obtaining.
(B) An incident direction t1 toward the measurement point along the normal line of the surface of the test object at the measurement point, and two incident directions t2 and t3 that are inclined from the normal line by a predetermined incident angle ψ ₀ toward the measurement point. Are incident directions t1, t2, and t3, and the incident directions t2 and t3 define xy coordinates orthogonal to the measurement point on the surface of the test object, and project these incident directions on the surface of the test object. Sometimes the three incident directions t1, t2, and t3 are in such a positional relationship that the projection in the incident direction t2 coincides with the x-axis and the projection in the incident direction t3 coincides with the y-axis. The shear stress tau _xy, the average value of the resulting shear stress tau _xy respectively from the diffraction ring in the direction of incidence t2 and t3, X-ray stress measuring method according to claim 4, wherein. When performing the X-ray stress measurement method, X-ray irradiation in the incident direction t1 is first performed on the measurement point on the surface of the test object, and the shear stress τ _xz or shear stress obtained from the diffraction ring is obtained. The X-ray stress measurement method according to claim 5, wherein the state of stress inside the test object is determined based on τ _yz .