Method for analyzing triaxial shear stress components

Abstract

Determine the shear stress components in the three axes. [Solution] In stress measurement using the X-ray diffraction phenomenon, the angle of the X-rays incident on the object is set to 38.0 degrees, and measurements are taken from 2 to 16 directions at a single measurement point. The stress and shear stress measurement data, along with the average of two stresses and shear stresses measured at 180 degrees apart, are plotted with stress on the X-axis and shear stress on the Y-axis. The shear stress component in the three axes is then determined as the difference between two stresses at 180 degrees apart. Alternatively, the angle of the X-rays incident on the object is set to 31.7 degrees, and measurements are taken from 2 to 16 directions at a single measurement point. The stress and shear stress measurement data, along with the average of two stresses and shear stresses measured at 180 degrees apart, are plotted with stress on the X-axis and shear stress on the Y-axis. The shear stress component in the three axes is then determined as the difference between the average of two stress values ​​at 180 degrees apart and each measured value.

Description

Technical Field

[0001] The present invention relates to a method for analyzing triaxial shear stress components from measurement results of plane stresses and shear stresses in multiple directions in the field of stress measurement using X-ray diffraction.

Background Art

[0002] According to Patent No. 7513234, for a plurality of sets of stress values and shear stress values obtained by measuring the stress at a point on a plane from a plurality of directions, the stress value is plotted on the X-axis and the shear stress value is plotted on the Y-axis. For two measurement points that differ by 180 degrees, an average is obtained and the stress value is plotted on the X-axis and the shear stress value is plotted on the Y-axis in the same manner. Next, the Mohr's stress circle is determined so that the distance between the circular orbit and the measurement point or the average measurement point is minimized, and the principal stresses are determined at the two intersections of the circular orbit and the stress axis, so that the principal stresses can be determined. Here, it is known that the difference in stress and the difference in shear stress between two measurement points that differ by 180 degrees, for example, 0 and 180 degrees, 45 and 225 degrees, 9 and 270 degrees, 135 and 315 degrees, are proportional to the triaxial shear stress components (Non-Patent Document 1). That is, according to Patent No. 7513234, it has become possible to display a length proportional to the triaxial shear stress component on the drawing. Generally, the stress difference between two measurement points that differ by 180 degrees is the projection of the triaxial shear stress component, but depending on the measurement conditions, the ratio of the stress difference between two measurement points that differ by 180 degrees and the triaxial shear stress component changes, so although it was known that there was a triaxial shear stress component, it could not be quantitatively determined.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Non-Patent Documents

[0004]

Non-Patent Document 1

[0005] The challenge is to enable the determination of the triaxial shear stress component [MPa] by using measurement conditions such that, in a graph plotting stress values ​​on the X-axis and shear stress on the Y-axis according to Patent No. 7513234, the ratio of the stress difference [MPa] between two measurement points separated by 180 degrees and the triaxial shear stress component [MPa] is 1:1 or 2:1. In the case of 1:1, the triaxial shear stress component [MPa] is obtained as the stress difference [MPa] between the two measurement points separated by 180 degrees. In the case of 2:1, the triaxial shear stress component [MPa] is obtained as the average of the two measurement points separated by 180 degrees and the stress difference [MPa] between each measurement point. [Means for solving the problem]

[0006] In this invention, as described in Patent No. 7513234, the incident angle ψ0 of the X-rays is set to 38.0 degrees, where tan(2ψ0)=4, as a condition for X-ray stress measurement. This ensures that the ratio of the stress difference [MPa] between two measurement points separated by 180 degrees to the triaxial shear stress component [MPa] is 1:1, so that the stress difference between two measurement points separated by 180 degrees matches the triaxial shear stress component. Alternatively, by setting the angle to 31.7 degrees, where tan(2ψ0)=2, the ratio of the stress difference [MPa] between two measurement points separated by 180 degrees to the triaxial shear stress component [MPa] is 2:1, so that the stress difference [MPa] between two measurement points separated by 180 degrees is twice the triaxial shear stress component [MPa]. This corresponds to the average point of the two measurement points separated by 180 degrees and the stress difference at each measurement point. According to Non-Patent Literature 1, the X-ray incidence angle for stress measurement is ψ0, the direction of the stress measured on the plane is θ, and the stress obtained from the cosα and sinα diagrams of the measuring instrument is s(θ), and the shear stress is t(θ). s(θ) and t(θ) are numerical values ​​output from the measuring instrument. If the direction perpendicular to the object being measured, i.e., the normal direction of the measurement plane, is the Z direction, then the three-axis shear stress τz(θ) is [s(θ) - s(θ+180)]tan(2ψ0) / 4. Therefore, when tan(2ψ0)=4, τz(θ) is equal to [s(θ)- s(θ+180)], and the stress difference between s(θ) and s(θ+180) coincides with the triaxial shear stress τz(θ). When tan(2ψ0)=2, τz(θ) becomes [s(θ)- s(θ+180)] / 2, and the stress difference between s(θ) and s(θ+180) coincides with twice the triaxial shear stress τz(θ). In other words, the difference between the average of s(θ) and s(θ+180) and s(θ) or s(θ+180) coincides with the triaxial shear stress τz(θ). In this way, by setting the incident angle of the X-rays to 38.0 degrees or 31.7 degrees, the stress difference between two measurement points, or half of that difference, can be determined as the triaxial shear stress component. This allows for a quantitative comparison of the triaxial shear stress component and principal stresses on a graph. Figure 4 explains the case where the stress in the θ direction σ(θ) = 100 MPa and the triaxial shear stress τz(θ) = 100 MPa. When the X-ray incidence angle ψ0 = 38.0 degrees and tan(2ψ0) = 4 (vertical striped circle), s(θ) = 50 MPa and s(θ + 180) = 150 MPa are measured. Therefore, the triaxial shear stress τz(θ) = 100 MPa can be obtained as the stress difference between s(θ) and s(θ + 180). See the vertical striped circle. Next, when the X-ray incidence angle ψ0 = 31.7 degrees and tan(2ψ0) = 2 (horizontal striped circle), the measured values ​​are s(θ) = 0 [MPa] and s(θ + 180) = 200 [MPa]. Therefore, the triaxial shear stress τz(θ) = 100 [MPa] can be found as half the stress difference between s(θ) and s(θ + 180), that is, the difference between the average point of s(θ) and s(θ + 180) and s(θ) or s(θ + 180). The measurement points are shown as horizontal striped circles, and the average point is shown as a hollow circle. If 0-180 degrees is the X direction, then τz(0) = τxz, and if 90-270 degrees is the Y direction, then τz(90) = τyz. [Effects of the Invention]

[0007] According to Patent No. 7513234, on a graph plotting stress values ​​on the X-axis and shear stress on the Y-axis, the stress difference between two measurement points separated by 180 degrees, or half of that difference, can be determined as the shear stress components in three axes. Therefore, principal stress, stress and shear stress in the XY direction, and shear stress in the z-axis direction can be quantitatively compared on the same graph, enabling visual evaluation of measurement accuracy. As an unwritten rule in the measurement industry, a 10% error in measurements is acceptable. Therefore, the acceptable range of the incident angle is 37.2 to 38.6 degrees if a 10% error is allowed for the triaxial shear stress component and principal stress at an incident angle of 38.0 degrees, and 30.5 to 32.8 degrees if a 10% error is allowed for the triaxial shear stress component and principal stress at an incident angle of 31.7 degrees. [Brief explanation of the drawing]

[0008] [Figure 1] Mohr's stress circle estimation results and triaxial shear stress, illustrating the first embodiment of the present invention, with an X-ray incidence angle of 38.0 degrees. [Figure 2] Coordinate system in embodiments of the present invention [Figure 3] Mohr's stress circle estimation results and triaxial shear stress, showing a second embodiment of the present invention, with an X-ray incidence angle of 31.7 degrees. [Figure 4]Relationship between the stress difference [MPa] and the ratio of the triaxial shear stress component [MPa] at two measurement points with an X-ray incidence angle of 38.0 degrees and 31.7 degrees, where the two measurement points are 180 degrees apart. [Modes for carrying out the invention]

[0009] A first embodiment of the present invention will be described with reference to Figure 1. With an X-ray incidence angle of 38.0 degrees, stress measurements are performed in eight directions: 0, 45, 90, 135, 180, 225, 270, and 315 degrees, and measured stress and shear stress values ​​are obtained. The average is calculated for two measurement points that differ by 180 degrees, such as 0 and 180 degrees, 45 and 225 degrees, 90 and 270 degrees, and 135 and 315 degrees. Four average points are obtained from the eight measurements, and then these eight measurement points and the four average points are plotted with stress values ​​on the X-axis and shear stress values ​​on the Y-axis. Mohr's stress circle trajectory is determined so that the distance between the measurement average points and the circular trajectory is minimized. The principal stress is the stress value at the two intersection points of the circle and the X-axis. In this embodiment, the maximum principal stress is 54 MPa at an angle of approximately 170 degrees, and the minimum principal stress is -115 MPa at an angle of approximately 80 degrees. [Figure 1] The stress differences between 0 and 180 degrees, 45 and 225 degrees, 90 and 270 degrees, and 135 and 315 degrees represent the three-axis shear stress components. In Figure 1, as an example, the stress difference between the measurement points at 0 and 180 degrees represents the three-axis shear stress component τz(0) ~9. Because shear stress components of the same scale can be compared with principal stresses, Mohr circle radii, etc., the magnitude of the shear stress components affecting the measurement can be visually compared. Next, a second embodiment of the present invention will be described with reference to Figure 3. With an X-ray incidence angle of 31.7 degrees, stress measurements are performed in eight directions: 0, 45, 90, 135, 180, 225, 270, and 315 degrees, and measured stress and shear stress values ​​are obtained. The average is calculated for two measurement points that differ by 180 degrees, such as 0 and 180 degrees, 45 and 225 degrees, 90 and 270 degrees, and 135 and 315 degrees. Four average points are obtained from the eight measurements, and then these eight measurement points and the four average points are plotted with stress values ​​on the X-axis and shear stress values ​​on the Y-axis. Mohr's stress circle trajectory is determined so that the distance between the average points and the circular trajectory is minimized. The principal stress is the stress value at the two intersection points of the circle and the X-axis. In this embodiment, the maximum principal stress is 33 MPa at an angle of approximately 170 degrees, and the minimum principal stress is -114 MPa at an angle of approximately 80 degrees [Figure 3]. The stress difference between the average point and the measurement point at 0 and 180 degrees, 45 and 225 degrees, 90 and 270 degrees, and 135 and 315 degrees represents the triaxial shear stress components. In Figure 3, as an example, the stress difference between the average point and the 0-degree measurement point, or the stress difference between the average point and the 180-degree measurement point, represents the triaxial shear stress component τz(0) ~9. Because shear stress components of the same scale can be compared with principal stresses, Mohr circle radii, etc., the magnitude of the shear stress components affecting the measurement can be visually compared. [Industrial applicability]

[0010] It is used for stress analysis of objects that have undergone machining or grinding processes, where three-axis shear stress components are expected to be generated. [Explanation of Symbols]

[0011] • Estimated Mohr stress circle • Plotting of measurement points for each angle (circular) • Average score of measurement points at 180 degrees apart (circular frame) • A polygon formed by connecting the average points of measurement points that are 180 degrees apart. • Stress axis [unit: MPa] • Shear stress axis [unit: MPa] • Estimated point of maximum principal stress: Rectangular frame • Minimum principal stress estimation point: Rectangular frame Shear stress in the measurement direction and the z-axis (normal to the measurement surface) direction.

Claims

[Claim 1] In a stress measurement method utilizing the diffraction phenomenon of X-rays, the triaxial shear stress is determined from the measured stress and shear stress in multiple directions at a single measurement point. The angle of the X-rays incident on the sample is set to 38.0 degrees (37.2 degrees to 38.6 degrees with a 10% error tolerance). Stress and shear stress measurement data in 2 to 16 directions, and data obtained by averaging two stress and shear stress measurements taken at 180-degree intervals, are plotted with stress on the X-axis and shear stress on the Y-axis. The difference between the two stress values ​​at 180-degree intervals is used as the triaxial shear stress component to determine the triaxial shear stress component. Alternatively, by setting the angle of the X-ray incident on the object to be measured to 31.7 degrees (30.5 to 32.8 degrees with a 10% error tolerance), the stress and shear stress measurement data in 2 to 16 directions, and the averaged stress and shear stress data for measurements with a 180-degree difference in orientation are plotted with stress values ​​on the X-axis and shear stress values ​​on the Y-axis. The triaxial shear stress component is then determined by taking half the difference between two stress values ​​with a 180-degree difference, i.e., the difference between the average value of two stress values ​​with a 180-degree difference and each measured value, as the triaxial shear stress component. This is the characteristic method for analyzing the triaxial shear stress component.

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