Method for determining principal stress from measurement results of multi-directional stresses and shear stress

Abstract

To solve the problem that calculating principal stresses based on measured stress values sometimes produces results greatly different from the actual state due to measurement errors.SOLUTION: In stress measurement utilizing an X-ray diffraction phenomenon, stresses and shear stresses measured from 2 to 16 directions at one measurement point are plotted in a stress-shear stress space, Mohr's stress circle is determined by a least-squares method so that the sum of distances of points on one of a circular locus and on a circle is minimized, and principal stresses are determined at intersections with stress axes.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for determining principal stresses from measurements of stresses and shear stresses in multiple directions. [Background technology]

[0002] In stress measurements using X-ray diffraction, when estimating the principal stress in a stress field, a method has traditionally been used to calculate the principal stress from stress in three directions, but depending on the degree of error in the stress value, the calculated results can be inaccurate. With the conventional method, valid calculation results could only be obtained in cases close to an ideal plane stress field. Furthermore, no information about the degree of error could be obtained. Below, we will explain the conventional method of estimating principal stresses using Figure 2. This is the case where principal stresses are calculated from the stress values ​​at 0, 45, and 90 degrees. σ0, σ45, and σ90 are the stress values ​​at 0, 45, and 90 degrees, respectively. Using this, C (the stress value at the center of Mohr's stress circle) and R (the radius of Mohr's stress circle) are found, and the principal stresses σ1 and σ2 are calculated.

[0003] Several methods have been proposed to calculate the principal stress and its direction from stress values ​​measured in multiple directions, and all of them are equally effective when measurement errors are not included. However, actual measurements contain errors, and when calculating principal stress using stress measurements, the errors can sometimes result in results that differ significantly from the actual situation.

[0004] Mohr's stress circle is a circle that shows that the relationship between stress and shear stress found in X-ray stress measurements and materials mechanics textbooks is the Mohr's stress circle orbit. (Non-Patent Documents 1 and 2) Until now, it has been used to illustrate stress calculation results. The reason is that, of the stresses and shear stresses that make up Mohr's stress circle, there was no way to measure shear stress, and measured shear stress was never used for Mohr's stress circle. In 2012, an X-ray stress measurement device using a 2D detector was developed, making it possible to measure shear stress, and measured shear stress values ​​can now be used to estimate Mohr's stress circle and principal stresses. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] "Revised X-Ray Stress Measurement Methods" edited by the Japan Society for Materials Science, published by Yokendo, 1990 [Non-patent document 2] Keisuke Tanaka et al., "X-ray Evaluation of Residual Stress," Yokendo Publishing, 2006 Summary of the Invention [Problem to be solved by the invention]

[0006] Several methods have been proposed for calculating principal stresses and their directions from stress values ​​measured in multiple directions, and all of them are equally effective when measurement errors are not included. However, actual measurements contain errors, and calculations using actual measurements can result in results that differ significantly from the actual situation due to the influence of these errors. The purpose of this invention is to solve this problem of inappropriate calculated values ​​and to estimate more appropriate principal stresses. [Means for solving the problem]

[0007] This invention provides a method for highly accurate estimation of principal stress using stress and shear stress values ​​measured in stress measurements utilizing X-ray diffraction. Stress and shear stress values ​​measured at a single measurement point from 2 to 16 directions are used. First, measurements are performed from 2 to 16 directions at a single point using a measuring device that outputs both stress and shear stress using a 2D detector. For example, measurements are performed in three directions (0, 45, and 90 degrees) or four directions (0, 45, 90, and 135 degrees). When triaxial stress occurs, measurements are performed in six directions (0, 45, 90, 180, 225, and 270 degrees) or eight directions (0, 45, 90, 135, 180, 225, 270, and 315 degrees). The number of measurements is adjusted according to the stress conditions. In other words, when the stress field is closer to a plane, sufficient accuracy can be achieved with fewer directions, but when errors from a plane stress field, such as triaxial stress, are large, measurements in more directions are required. Although the accuracy improves with more measurements, the measurement cost also increases, so the practical number of measurements is about 16 at most.

[0008] Next, plot the measured data on the X axis for stress value and on the Y axis for shear stress value. Also, by averaging two measurement points in opposite directions that are 180 degrees apart, such as 0 and 180 degrees, 45 and 225 degrees, 90 and 270 degrees, or 135 and 315 degrees, errors due to the influence of triaxial stress components can be reduced.

[0009] Third, estimate the Mohr's stress circle orbit that passes near each measurement point. There are two methods for estimating the Mohr's stress circle. (1) Determine the center and radius of the circle that minimizes the sum of the distances between each measurement point and the Mohr's stress circle orbit, i.e., determine the circle that minimizes the sum of the distances between each measurement point and the nearest point on the Mohr's stress circle orbit. (2) Determine the center of the circle that minimizes the sum of the distances between each measurement point and the center of the circle, and then determine the circle that minimizes the sum of the distances between each measurement point and the point on the full circular orbit. The two intersections of the estimated circle and the stress X-axis become the principal stresses.

[0010] The above solution works as follows: Stress at one point is measured from multiple directions to obtain multiple sets of stress and shear stress values. These multiple sets of stress and shear stress values ​​are plotted on a plane with the X and Y axes, respectively. The influence of errors can be reduced or cancelled out by determining Mohr's stress circle using the least squares method and determining the principal stress at the two intersections of the circular orbit and the stress axis. In addition, the degree of error at the measurement point can be visually confirmed from the positional relationship between the plot of each measurement point and Mohr's stress circle.

[0011] As described above, the present invention can reduce or cancel the influence of errors when determining the principal stresses. Furthermore, the degree of the errors can be visually confirmed from the positional relationship between the plots of each measurement point and the Mohr's stress circle. [Effects of the Invention]

[0012] The influence of measurement errors can be reduced or cancelled out by measuring stress at one point from multiple directions, plotting the results in stress and shear stress space, determining Mohr's stress circle using the least squares method, and determining the principal stress at the point where it intersects with the stress axis.The degree of error can also be visually confirmed from the positional relationship between the plots of each measurement point and Mohr's stress circle. [Brief explanation of the drawings]

[0013] [Figure 1] Mohr's stress circle estimation results and measurement points showing the first embodiment of the present invention [Figure 2] Principal stress calculation method of prior art invention [Figure 3] Mohr's stress circle estimation results and measurement points showing the second embodiment of the present invention [Figure 4] Mohr's stress circle estimation results and measurement points showing the third embodiment of the present invention DETAILED DESCRIPTION OF THE INVENTION

[0014] A first embodiment of the present invention will be described with reference to Figure 1. This figure illustrates measurement points and Mohr's stress circle when the error is small. Stress measurements are performed in eight directions, including 0, 45, 90, 135, 180, 225, 270, and 315 degrees, to obtain measured values ​​of stress and shear stress. The average is calculated for two measurement points that are 180 degrees apart, such as 0 and 180 degrees, 45 and 225 degrees, 90 and 270 degrees, and 135 and 315 degrees. Four average points are calculated from the eight measurements, and then these average measurement points are plotted as stress values ​​on the X axis and shear stress values ​​on the Y axis.

[0015] [Table 1] @0001

[0016] Furthermore, the Mohr's stress circle orbit is determined so that the sum of the distances between the measurement average point and the closest point on the circular orbit is minimized. The principal stresses are the stress values ​​at the two intersections of the circle and the X axis. In this example, the maximum principal stress is -69 MPa and the angle is approximately 45 degrees, while the minimum principal stress is -969 MPa and the angle is approximately 135 degrees.

[0017] Next, a second embodiment of the present invention will be described with reference to Figure 3. This is a case where some data contains errors, but the errors are mitigated by Mohr's stress circle. Stress measurements are performed in eight directions, including 0, 45, 90, 135, 180, 225, 270, and 315 degrees, to obtain measured values ​​of stress and shear stress. The average is calculated for two measurement points in opposite directions that are 180 degrees apart, such as 0 and 180 degrees, 45 and 225 degrees, 90 and 270 degrees, and 135 and 315 degrees. Four average points are calculated from the eight measurements, and then these average points are plotted as stress values ​​on the X axis and shear stress values ​​on the Y axis.

[0018] [Table 2] @0002

[0019] Furthermore, the Mohr's stress circle orbit is determined so that the sum of the distances between the Mohr's stress circle orbit and the average point is minimized. The principal stresses are the stress values ​​at the two intersections of the circle and the X-axis. In this example, the angles for the maximum and minimum principal stresses are 45° and 135°. In Example 2, only the data at 135° and 315° have a concave polygon, resulting in a large error. However, this does not significantly affect the Mohr's stress circle or the maximum and minimum principal stresses. This means that the 135° and 315° angles and their average point, which have a large error, are far from the Mohr's stress circle orbit, while the other average points are close to the Mohr's stress circle orbit. In other words, the influence of the measurement at 135° and 315°, which has a large error, is mitigated. In the conventional method, when data near 135° is included in the calculation, the error becomes large, but this does not have a significant effect in the present invention.

[0020] Finally, a third embodiment of the present invention will be described with reference to Fig. 4. This is an example in which stress can be estimated even in a direction that cannot be physically measured using Mohr's stress circle analysis. When measuring stress in a T-joint weld, the joint gets in the way in the direction parallel to the weld line (set at 0 degrees), making it physically impossible to measure the stress near the weld line. In this case, from the measurement results at 45 degrees, 90 degrees, and 135 degrees, which are measurable, Mohr's stress circle is calculated so that the sum of the distances between the orbit of Mohr's stress circle and the average point is minimized. By determining the stress in the direction parallel to the weld line, the stress can be estimated from the measurement points at 45 degrees, 90 degrees, and 135 degrees on Mohr's stress circle. [Industrial Applicability]

[0021] This method can estimate the appropriate principal stress and its direction in stress analysis based on measurement values ​​that contain errors. It can also estimate stress in directions that cannot be measured directly due to the shape of the object, contributing to the evaluation of the safety of structures, etc. [Explanation of symbols]

[0022] Estimated Mohr's stress circle Plot of measurement points for each angle Circular Average point of 180 degree different measurement points Circular frame A polygon connecting the average points of measurement points that are 180 degrees apart Stress axis [unit: MPa] Shear stress axis [unit: MPa] Maximum principal stress estimated point Rectangular frame Minimum principal stress estimated point Rectangular frame

Claims

[Claim 1] In stress measurement utilizing the diffraction phenomenon of X-rays, this is a method for estimating principal stress from the measurement results of stress and shear stress in multiple directions at one measurement point, characterized in that the measurement data of stress and shear stress in 2 to 16 directions or the average data thereof are plotted with stress on the X axis and shear stress on the Y axis, and the Mohr's stress circle orbit that minimizes the total distance between the measurement points and the Mohr's stress circle orbit is determined by the least squares method, and the principal stress is determined from the intersection of the Mohr's stress circle orbit and the X-axis stress axis.

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