An amorphous residual stress measurement method based on X-ray diffraction technology
By using an X-ray diffraction-based method, the expression for the residual stress of amorphous materials was derived and combined with measurements from strain gauges and X-ray diffractometers, thus solving the problem of the inability to measure the residual stress of amorphous materials and achieving accurate measurement of the stress in amorphous materials.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN INST OF TECH
- Filing Date
- 2023-07-13
- Publication Date
- 2026-07-31
AI Technical Summary
Existing X-ray diffraction methods can only measure the residual stress of crystalline materials, and cannot effectively measure the residual stress of amorphous materials.
Based on X-ray diffraction technology, by deriving the expression for the residual stress of amorphous materials, the full width at half maximum (FWHM) of the amorphous materials is measured using a strain gauge and an X-ray diffractometer in the θ-2θ scanning mode with an offset angle. A scatter plot is then drawn and linear fitting is performed to calculate the residual stress of the amorphous materials.
It enables accurate measurement of residual stress in amorphous materials and allows determination of stress type and magnitude by observing changes in the full width at half maximum (FWHM).
Smart Images
Figure CN116818168B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of residual stress measurement, specifically relating to a method for measuring residual stress based on X-ray diffraction of typical amorphous spectral lines. Background Technology
[0002] As is well known, residual stress is a very important physical quantity. Measuring residual stress plays a crucial role in both industrial production and scientific research. Although various measurement methods exist, including destructive methods such as mechanical drilling, slab cutting, and layer-by-layer milling, and non-destructive testing methods such as X-ray diffraction, neutron diffraction, and ultrasonic testing, X-ray diffraction, based on Hooke's law, remains the most widely used. As a method for characterizing macroscopic residual stress, X-ray diffraction is based on the principle that the lattice strain caused by a given stress state is consistent with the macroscopic strain calculated according to elasticity theory. The lattice strain state can be measured by X-ray diffraction, allowing the macroscopic residual stress to be calculated by measuring the changes in the lattice. After decades of development, X-ray diffraction equipment and technology have greatly improved, and X-ray diffraction has become an important means of residual stress measurement, widely applied in scientific research and production practices across various fields.
[0003] Currently, X-ray diffraction (XRD) can only measure residual stress in crystalline materials. During XRD, crystalline materials produce diffraction peaks corresponding to different diffraction planes. When macroscopic residual stress exists in the material, it alters the interplanar spacing within the crystal. When this change satisfies Bragg's equation, the diffraction peak positions will shift to a certain extent. The degree of peak shift is proportional to the magnitude of the residual stress. By measuring the change in the diffraction peak positions, residual strain can be obtained, and the residual stress value can be calculated using Hooke's law.
[0004] For amorphous materials, X-ray spectra only show typical diffuse peaks, known as amorphous envelopes, lacking a lattice and thus unable to characterize residual strain caused by lattice changes under stress. However, a key characteristic of amorphous structures is the regular arrangement of atoms within a few atomic spacings around any given atom, i.e., short-range order. The average atomic displacement can be calculated using the radial distribution function. The presence of residual stress in amorphous materials leads to changes in the average atomic displacement; therefore, the degree to which atoms actually deviate from their average positions can characterize the residual stress in amorphous materials. Summary of the Invention
[0005] The purpose of this invention is to address the limitation of existing X-ray diffraction stress measurement methods, which can only be applied to crystalline materials, and to provide a method for measuring residual stress in amorphous materials.
[0006] The present invention provides a method for measuring amorphous residual stress based on X-ray diffraction (X-ray diffraction spectroscopy) technology, which is implemented according to the following steps:
[0007] I. Based on the principles of elasticity and Hooke's law, the expression for the residual stress σ′ in amorphous materials is derived as follows:
[0008]
[0009] In the formula: E is the Young's modulus of the amorphous material, ν is the Poisson's ratio, FWHM is the full width at half maximum (FWHM) of the amorphous peak, and ψ is the angle between the incident ray and the normal to the surface of the amorphous material.
[0010] II. The stress magnitude σ of multiple amorphous material standard samples was measured using a strain gauge. Then, the full width at half maximum (FWHM) of the amorphous material standard samples was obtained using an X-ray diffractometer in θ-2θ scanning mode with an offset angle. 2 A scatter plot was drawn with ψ as the x-axis and the full width at half maximum (FWHM) of the amorphous diffraction peak as the y-axis. Then, a linear fit was performed, and the slope of the fitted line was... Will Substituting into formula (1), the residual stress σ of the amorphous material standard sample is calculated. φ ′, thereby determining the stress measurement coefficient The expression for the residual stress σ of the corrected amorphous material is shown in Equation (2);
[0011]
[0012] 3. Using an X-ray diffractometer in the θ-2θ scanning mode of the bias angle, the full width at half maximum (FWHM) of the amorphous diffraction peaks of the amorphous material under test in multiple different ψ orientations is measured in the plane of measurement direction.
[0013] IV. Based on the ψ angle selected in step three, and the measured full width at half maximum (FWHM) of the amorphous diffraction peak, using sin 2 Using ψ as the x-axis and the full width at half maximum (FWHM) of the amorphous diffraction peak as the y-axis, a scatter plot was drawn, and then a linear fit was performed. The slope of the fitted line is then...
[0014] V. The result obtained in step four Substituting into formula (2), the residual stress of the amorphous material can be calculated.
[0015] This invention, through measurement and calibration of amorphous oxides such as SiO2, derives a universal formula for the amorphous residual stress X-ray diffraction method. This formula can be obtained through FWHM-sin 2 The sign of the slope of the straight line ψ is used to determine whether the residual stress is tensile or compressive, and the magnitude of the stress value is obtained by the magnitude of the slope of the straight line. Attached Figure Description
[0016] Figure 1 The following are X-ray diffraction patterns of SiO2 amorphous material under different compressive stresses in the examples.
[0017] Figure 2 The image shows the XRD stress measurement of amorphous materials under a known standard stress state.
[0018] Figure 3 The above are amorphous diffraction peak curves with different ψ orientations obtained in step three of the embodiment.
[0019] Figure 4 FWHM-sin for different samples 2 ψ-line slope measurement diagram;
[0020] Figure 5 This is a schematic diagram of macroscopic stress measurement in crystalline materials. Detailed Implementation
[0021] Specific Implementation Method 1: This implementation method of the present invention, based on X-ray diffraction technology (X-ray diffraction spectroscopy), for measuring amorphous residual stress is carried out according to the following steps:
[0022] I. Based on the principles of elasticity and Hooke's law, the expression for the residual stress σ′ in amorphous materials is derived as follows:
[0023]
[0024] In the formula: E is the Young's modulus of the amorphous material, ν is the Poisson's ratio, FWHM is the full width at half maximum (FWHM) of the amorphous peak, and ψ is the angle between the incident ray and the normal to the surface of the amorphous material.
[0025] II. The stress magnitude σ of multiple amorphous material standard samples was measured using a strain gauge. Then, the full width at half maximum (FWHM) of the amorphous material standard samples was obtained using an X-ray diffractometer in θ-2θ scanning mode with an offset angle. 2 A scatter plot was drawn with ψ as the x-axis and the full width at half maximum (FWHM) of the amorphous diffraction peak as the y-axis. Then, a linear fit was performed, and the slope of the fitted line was... Will Substituting into formula (1), the residual stress σ of the amorphous material standard sample is calculated. φ ′, thereby determining the stress measurement coefficient The expression for the residual stress σ of the corrected amorphous material is shown in Equation (2);
[0026]
[0027] 3. Using an X-ray diffractometer in the θ-2θ scanning mode of the bias angle, the full width at half maximum (FWHM) of the amorphous diffraction peaks of the amorphous material under test in multiple different ψ orientations is measured in the plane of measurement direction.
[0028] IV. Based on the ψ angle selected in step three, and the measured full width at half maximum (FWHM) of the amorphous diffraction peak, using sin 2 Using ψ as the x-axis and the full width at half maximum (FWHM) of the amorphous diffraction peak as the y-axis, a scatter plot was drawn, and then a linear fit was performed. The slope of the fitted line is then...
[0029] V. The result obtained in step four Substituting into formula (2), the residual stress of the amorphous material can be calculated.
[0030] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that 4 to 10 amorphous material standard samples are selected in step two.
[0031] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 2 in that 5 to 8 amorphous material standard samples are selected in step 2.
[0032] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the range of ψ azimuth angle selection in step three is 0° to 30°.
[0033] Specific Implementation Method 5: This implementation method differs from Specific Implementation Method 4 in that the selection range of the azimuth angle ψ in step 3 is 0° to 10°.
[0034] Example: This example demonstrates an amorphous residual stress measurement method based on X-ray diffraction technology, implemented according to the following steps:
[0035] I. Based on the principles of elasticity and Hooke's law, the expression for the residual stress σ′ in amorphous materials is derived as follows:
[0036]
[0037] In the formula: E is the Young's modulus of the amorphous material, ν is the Poisson's ratio, FWHM is the full width at half maximum (FWHM) of the amorphous peak, and ψ is the angle between the incident ray and the normal to the surface of the amorphous material.
[0038] II. The stress magnitude σ of multiple amorphous material standard samples was measured using a strain gauge. Then, the full width at half maximum (FWHM) of the amorphous material standard samples was obtained using an X-ray diffractometer in θ-2θ scanning mode with an offset angle. The correspondence between the amorphous material standard samples and the X-ray amorphous residual stress measurements is as follows: Figure 2As shown, the half-peak bandwidth of the amorphous material standard sample is incorporated into formula (1) to calculate the residual stress σ′ of the amorphous material standard sample, thereby determining the stress measurement coefficient k = 4 * 10. -3 The expression for the residual stress σ of the amorphous material after correction is shown in formula (2);
[0039]
[0040] III. Using an X-ray diffractometer in θ-2θ scanning mode with a bias angle, the full width at half maximum (FWHM) of the amorphous diffraction peaks of the amorphous material under test at multiple different ψ orientations was measured in the measurement direction plane. The ψ orientation angles were selected as 0°, 1°, 2°, 3°, 4°, and 5°, and the corresponding FWHM measurements were 4.82, 4.81, 4.70, 4.41, 4.43, and 4.30, respectively. Figure 3 As shown;
[0041] IV. Based on the ψ angle selected in step three, and the measured full width at half maximum (FWHM) of the amorphous diffraction peak, using sin 2 Using ψ as the x-axis and the full width at half maximum (FWHM) of the amorphous diffraction peak as the y-axis, a scatter plot was drawn, and then a linear fit was performed. The slope of the fitted line is then... The slope of the straight line is -55.07.
[0042] V. The result obtained in step four Substituting into formula (2), the residual stress of the amorphous material can be calculated.
[0043] The derivation principle of the expression for the residual stress σ′ of the amorphous material in step one of this embodiment is as follows.
[0044] Figure 5 This is a schematic diagram of macroscopic stress measurement in crystalline materials. The residual stress σ to be measured is established. φ With strain ε in a certain spatial orientation φψ The relationship between these factors is key to solving stress measurement problems. Strain can be characterized by the rate of change of the average atomic displacement, i.e., the rate of change of the half-maximum width. The stress in the normal direction of the free surface of an object is zero. When the stress gradient within the object along the direction perpendicular to the surface is extremely small, and the X-ray penetration depth is also very small, the measurement area approximately satisfies a plane stress state. Based on the principles of elasticity and Hooke's law in three dimensions, the stress expression for continuous, homogeneous, and isotropic crystalline materials is derived as follows:
[0045]
[0046] Where σ φ ψ is the stress magnitude of the crystalline material, ψ is the angle between the sample surface normal and the diffracting crystal plane, and φ is the σ φ With σX The angle between the two α and β is E, where E is the Young's modulus of the crystalline material and ν is Poisson's ratio.
[0047] When the sample is amorphous, strain can be characterized by the rate of change of the average atomic displacement, i.e., the rate of change of the full width at half maximum (FWHM). Typically, XRD measures out-of-plane strain, while the calculated stress is in-plane. That is, when the in-plane strain decreases, the out-of-plane strain caused by the in-plane strain must increase. Therefore, a "-" sign must be introduced into the measurement formula.
[0048]
[0049] Where σ′ is the stress magnitude of the amorphous material, ψ is the angle between the incident ray and the normal to the surface of the amorphous material, E is the Young's modulus of the amorphous material, and ν is the Poisson's ratio.
[0050] Since the unit of half-peak width (FWHM) is angle (°), it should be changed to radians, so the stress constant should be multiplied by π / 180.
[0051]
[0052] In step five of this embodiment, the Young's modulus E of SiO2 is found to be 71.7 GPa and the Poisson's ratio ν is 0.16. Substituting these values into formula (2), the residual stress of the amorphous material can be calculated to be 237.5 MPa. Since the stress is positive, it represents tensile stress.
[0053] This embodiment focuses on SiO2 amorphous material, measuring the X-ray diffraction pattern under applied stress, such as... Figure 1 As shown, it is clearly observed that the full width at half maximum (FWHM) of the X-ray amorphous peak decreases with increasing compressive stress and increases with increasing tensile stress. Therefore, this variation in the FWHM reflects the characteristics of residual stress in amorphous materials and can be used to measure the residual stress of amorphous materials. It is particularly important to emphasize that amorphous materials are isotropic and do not exhibit preferred orientation; therefore, the X-ray diffraction stress measurement formula for crystalline materials is more applicable to amorphous materials.
Claims
1. A method of measuring amorphous residual stress based on X-ray diffraction technique, characterized by The method for measuring amorphous residual stress is implemented according to the following steps: I. The expression of residual stress of amorphous material is derived according to the principle of elasticity and three-dimensional Hooke's law as follows: σres = -σ0 + σ0 (1 - v) （1） wherein: E is the Young's modulus of the amorphous material, is the Poisson's ratio, FWHM is the full width at half maximum of the amorphous diffraction peak, is the angle between the incident ray and the normal to the surface of the amorphous material; 2. The stress magnitude of multiple amorphous material standard samples was measured using a strain gauge, and then X-ray diffractometer was used at an offset angle. In scanning mode, the full width at half maximum (FWHM) of the amorphous diffraction peaks of the amorphous material standard was obtained. A scatter plot was created with the full width at half maximum (FWHM) of the amorphous diffraction peaks on the x-axis and the full height at half maximum (FWHM) on the y-axis. A linear fit was then performed, and the slope of the fitted line was... ,Will Substituting into formula (1), the residual stress of the amorphous material standard sample is calculated. This allows for the determination of the stress measurement coefficient k, and the correction of the residual stress in the amorphous material. The expression for is shown in formula (2); （2） III. Using an X-ray diffractometer at an offset angle In scanning mode, the amorphous material under test is measured in multiple different directions within the measurement direction plane. Full width at half maximum (FWHM) of the amorphous diffraction peak at the angle; IV. Based on the selection made in step three The angle, and the measured full width at half maximum (FWHM) of the amorphous diffraction peak, to Plot a scatter plot with the full width at half maximum (FWHM) of the amorphous diffraction peaks on the x-axis and the full height at half maximum (FWHM) on the y-axis. Then, perform a linear fit, and the slope of the fitted line is... ; V. The result obtained in step four Substituting into formula (2), the residual stress of the amorphous material can be calculated.
2. The method for measuring amorphous residual stress based on X-ray diffraction technology according to claim 1, characterized in that... In step two, 4 to 10 amorphous material standard samples are selected.
3. The method for measuring amorphous residual stress based on X-ray diffraction technology according to claim 2, characterized in that... In step two, select 5 to 8 amorphous material standard samples.
4. The method for measuring amorphous residual stress based on X-ray diffraction technology according to claim 1, characterized in that... In step three The angle can be selected from 0° to 30°.
5. The method for measuring amorphous residual stress based on X-ray diffraction technology according to claim 4, characterized in that... In step three The angle can be selected from 0° to 10°.