Bearing ring heat treatment residual stress testing method based on FIB-DIC ring core milling technology

Abstract

The invention discloses a bearing ring heat treatment residual stress testing method based on an FIB-DIC ring core milling technology, and belongs to the field of stress testing. The method comprises the steps of sample preparation, mark point deposition and image acquisition, ring core milling and in-situ monitoring, DIC analysis and residual stress calculation. According to the invention, the FIB-DIB ring core milling technology is creatively and systematically applied to the stress test of the secondary surface of the bearing ring roller path, and a set of complete and reusable test process is constructed by optimizing platinum mark point deposition and ring core geometric parameters and adopting open source DIC software (such as Ncorr) to carry out strain analysis. The method inherits the core advantages that the FIB-DIC technology is ultrahigh in spatial resolution and does not need a stress-free reference sample, the pertinence and feasibility of the method in engineering practice are enhanced through process optimization, and direct and reliable microcosmic data support is provided for precise regulation and control and product quality evaluation of the bearing heat treatment process.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of stress testing, and particularly relates to a bearing ring heat treatment residual stress testing method based on FIB-DIC ring core milling technology. BACKGROUND

[0002] As the core transmission component of aero-engines, high-end CNC machine tools and other equipment, the service performance and reliability of bearing rings directly depend on the microstructure and stress state after heat treatment. Taking 8Cr4Mo4V high-temperature bearing steel as an example, during quenching and tempering, due to the significant difference in thermal expansion coefficient and phase volume change between the tempering martensite matrix and primary carbides (such as VC and M2C), the second type of residual stress will be generated in the micro regions such as the carbide / matrix interface. According to the stability theory of bearing contact fatigue, this kind of micro stress, especially tensile stress concentration, will significantly increase the strain amplitude of the raceway subsurface, promote the formation of plastic deformation and white etching area, thereby becoming the source of fatigue crack initiation and sharply shortening the service life of the bearing. Therefore, accurately characterizing the residual stress at the micro scale (especially at the specific phase interface) after heat treatment is an urgent need for optimizing the process and improving the reliability of bearings.

[0003] At present, the testing methods for residual stress have obvious limitations when applied to this micro scene. (1) Macro method (such as X-ray diffraction method): its measurement area is much larger than the grain size, only the macro average stress can be obtained, and the stress gradient in the micron level near the interface cannot be captured, and the spatial resolution is insufficient. (2) Traditional nanoindentation method (such as Suresh, Lee model): although it has micron-level resolution, its core model must rely on the load-displacement curve of the stress-free sample as a reference. However, for high-hardness bearing steel, the stress-free sample needs to be prepared by long-time high-temperature annealing, which will cause the coarsening of carbides and the softening of the matrix, resulting in the mismatch of the microstructure between the reference sample and the sample to be tested, introducing unavoidable systematic errors, and the process is complicated. (3) Emerging FIB-DIC ring core method: although it can theoretically achieve high-precision measurement of micron / submicron stress, the existing technical solutions mostly focus on the principle of the method, and for the specific component of bearing ring with high-hardness and multi-phase structure, its testing adaptability has not been perfected, which is not conducive to the promotion of the testing of the second type of residual stress of bearing rings. SUMMARY

[0004] The purpose of the present application is to solve the above technical bottlenecks existing in the background art, and provide a bearing ring heat treatment micro residual stress testing method based on FIB-DIC ring core milling technology. The FIB-DIB ring core milling technology is creatively applied to the stress testing of the bearing ring raceway subsurface, and a complete and reusable testing process is constructed by optimizing the platinum marker point deposition, the ring core geometric parameters and using the open source DIC software (such as Ncorr) for strain analysis. The method not only inherits the core advantages of FIB-DIC technology such as ultra-high spatial resolution and no need for stress-free reference sample, but also enhances its pertinence and feasibility in engineering practice through process optimization, thereby providing direct and reliable micro data support for realizing precise control of bearing heat treatment process and product quality evaluation.

[0005] To achieve the above purpose, the technical solutions adopted by the present application are as follows:

[0006] A bearing ring heat treatment residual stress testing method based on FIB-DIC ring core milling technology, the method comprises the following steps: sample preparation, marker point deposition and image acquisition, ring core milling and in-situ monitoring, DIC analysis and residual stress calculation.

[0007] Further, the method specifically comprises:

[0008] Step 1: Sample preparation: use a wire cutting device to cut a small sample from a bearing ring that has undergone complete heat treatment along the circumferential direction of the raceway, ensuring that the sampling position accurately includes the raceway bottom contact area; grind the cut sample and then finely polish it to obtain a mirror surface that meets the testing requirements; before testing, use acetone and alcohol to clean the sample with ultrasonic waves and dry it;

[0009] Step 2: Marker point deposition: place the prepared sample into a dual-beam electron microscope and determine the specific micro area to be tested, such as the interface near the primary carbide and the tempered martensite matrix; then, use a focused ion beam for key in-situ deposition, first inject an organic platinum gas with a lower ion beam current to deposit a thin and dense platinum adhesion layer in the test area; then, continue to deposit platinum using a higher ion beam current, form a lattice arrangement of platinum marker points in the center of the test area by controlling the beam spot, and simultaneously deposit a ring-shaped platinum protective layer around the marker point area;

[0010] Step 3: Image Acquisition, Core Milling, and In-situ Monitoring: After deposition, the first image of the test area before core milling is acquired using a SEM electron beam. Switching to ion beam mode, the outer side of the platinum protective layer is sequentially core-milled using FIB. The inner diameter of the core is consistent with the inner diameter of the protective ring, and the milling depth is 0.5 μm each time. An ion beam current of 30 keV and 1.2 nA is used for processing. After each milling, the second image of the test area is immediately acquired in-situ using a SEM electron beam until the total core depth reaches the diameter of the core, to ensure that the stress is fully released.

[0011] Step 4: DIC Analysis: Import the first and second images obtained in Step 3 into the open-source DIC analysis software Ncorr. Set the sub-region size to 41 pixels × 41 pixels, the step size to 3-5 pixels, and the strain window to 15 × 15 data points. The software calculates the displacement field relative to the first image for each milling stage using a digital image correlation algorithm. Based on the displacement field data, it calculates the strain relaxation amount of the ring core region in the X and Y directions. and ;

[0012] Step 5: Residual Stress Calculation: Calculate the residual stress based on elasticity theory, and determine the strain release amount at each milling depth. Fit the normalized depth (H / D, where H is the milling depth and D is the inner diameter of the ring core) and extrapolate to an infinite depth (H / D → The fully released strain Δεx is obtained. ∞ and Δεy ∞ According to Hooke's Law, the residual stress is calculated; the residual stress distribution at a specific microscopic location at the bottom of the bearing raceway can be directly obtained using this method.

[0013] Further, step one specifically involves: selecting materials for the bearing race that allow for the control of microstructure and residual stress through heat treatment, such as 8Cr4Mo4V, high-carbon chromium bearing steel (GCr15), carburized bearing steel (20CrMoNi), and high-temperature bearing steel (W18Cr4V). The heat treatment process for the bearing race is as follows: vacuum austenitizing at 1080℃~1100℃ for 30~40 minutes, followed by quenching in high-pressure nitrogen at 0.4MPa~0.6MPa to room temperature, and finally tempering three times at 550℃~560℃, holding at that temperature for 2~2.5 hours each time before air cooling; precisely cutting samples from the circumference of the bearing raceway using wire cutting to ensure that the test area includes the bottom contact area of ​​the raceway; cold mounting the samples, grinding them sequentially with 400# to 2000# sandpaper, and fine polishing them with diamond polishing compound to obtain a smooth test surface; and ultrasonically cleaning and drying the samples with acetone and alcohol before testing.

[0014] Further, step two specifically involves: placing the prepared sample into the sample chamber of a dual-beam scanning electron microscope (SEM-FIB), observing and locating the microscopic region to be tested in electron beam mode, such as near the interface between primary carbides and tempered martensite matrix. Switching to focused ion beam (FIB) mode, a thin platinum adhesion layer is first deposited on the selected circular region to be tested with a diameter of 15-25 μm; then, deposition continues using a 1.2 nA beam current, controlling the beam spot to form platinum markers arranged in a lattice at the center of the region, with a marker diameter of 100 nm-120 nm and a spacing of 200-300 nm. Simultaneously, a complete annular platinum protective layer of a specific thickness is deposited around this region. The inner diameter of this protective ring is the inner diameter of the subsequent ring core, with an inner diameter of 10 μm-20 μm and a width of 2 μm-5 μm.

[0015] Further, step three specifically involves: after deposition, acquiring a high-resolution first image (reference image) of the test area before core milling in electron beam mode, with an accelerating voltage of 5kV and a working distance of 5mm; switching to ion beam mode to perform core milling on the outer side of the platinum protective ring, using beam current parameters of 30keV and 1.2nA, with a milling depth of 0.5μm each time; immediately switching back to electron beam mode to acquire a second image (deformed image) of the test area in situ after each milling, with the parameters of the image acquisition during milling being consistent with the parameters of the first image before milling, repeating this process until the depth of the ring diameter reaches 20μm.

[0016] Furthermore, in step four, the sub-region size is set to 41 pixels × 41 pixels, the step size is 3 to 5 pixels, and the strain window is 15 × 15 data points.

[0017] Furthermore, in step five, the in-plane residual stress is calculated using the following three formulas.

[0018]

[0019]

[0020]

[0021] in, The main function used for fitting, The relaxation strain is the stress at which residual stress is completely released, and z is the normalized depth corresponding to each milling step. Let be the in-plane residual stress in the x-direction of the region to be measured, v be the Poisson's ratio of the material, and E be the Young's modulus of the material. For the fully released strain in the x-direction of the region to be measured, The strain in the y-direction of the region to be measured is the fully released strain. Let be the in-plane residual stress in the y-direction of the region to be measured. These three formulas (including corresponding formulas) The calculation formula and strain-stress derivation formula are specific applications of Hooke's Law in the calculation of in-plane residual stress. They are derived based on the core principle of Hooke's Law (stress is proportional to strain) and combined with the elastic mechanical properties of bearing ring materials. They are not the original general formula of Hooke's Law.

[0022] This invention fully utilizes the precision machining capabilities of FIB and the full-field deformation measurement capabilities of DIC. Compared with existing bearing ring residual stress testing technologies, it achieves direct, accurate, and visual measurement of microscopic residual stress, and has the following significant effects:

[0023] (1) Direct and absolute measurement of microscopic residual stress is achieved: This invention directly releases the residual stress in the test area through physical milling, and accurately measures the resulting strain relaxation using DIC technology, thereby directly calculating the residual stress value according to Hooke's law. This method fundamentally avoids the dependence of traditional indirect measurement methods such as nanoindentation on stress-free samples, as well as the systematic errors caused by the difference in microstructure between the reference sample and the test sample, and achieves absolute measurement of residual stress, resulting in more direct and reliable results.

[0024] (2) It possesses micron / submicron level spatial resolution, enabling precise location and quantification of stress concentration: Thanks to the nanometer-level processing precision of FIB and the resolution capability of DIC for submicron level image displacement, the effective spatial resolution of this method can reach below 300 nanometers. This allows the method to not only measure the average stress inside the grain, but also to accurately locate key microscopic features such as primary carbide interfaces and grain boundaries, and clearly characterize the residual stress gradient and concentration phenomena around them, providing unprecedented detail for understanding the origin of stress.

[0025] (3) It realizes visualization and in-situ measurement of specific micro-regions, providing intuitive basis for guiding process optimization: This invention combines a SEM / FIB dual-beam system, which can intuitively select specific areas to be measured under a high-magnification microscope and perform in-situ processing and measurement. By analyzing the stress value differences at different micro-locations, the correspondence between "microstructure and residual stress" can be directly established, thereby providing clear and accurate data support and improvement direction for the optimization of heat treatment processes. Attached Figure Description

[0026] Figure 1 A diagram showing the sampling location and shape of the FIB-DIC sample;

[0027] Figure 2 Image showing the location and depositional effect of speckled deposits near the primary carbide interface;

[0028] Figure 3Topographic images of the ring core at different milling depths;

[0029] Figure 4 For different milling depths Strain distribution diagram;

[0030] Figure 5 For different milling depths Strain distribution diagram;

[0031] Figure 6 To fit the strain release plot using the master function. Detailed Implementation

[0032] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0033] This invention provides a method for directly measuring the residual stress at the microscale of bearing rings after heat treatment using FIB (Fixed Ink Blasting) ring milling combined with DIC (Diverterless Conversion) technology. The method involves using FIB technology to precisely prepare a ring core and marking points in the microscopic region to be measured, releasing the residual stress through ring core milling, and then using DIC technology to accurately measure the strain field resulting from the stress release, thereby directly calculating the residual stress value.

[0034] Example 1: Microscopic residual stress test at the carbide interface

[0035] This embodiment details the specific implementation process of testing the microscopic residual stress at the interface between primary carbides and the matrix in the 8Cr4Mo4V bearing ring using the FIB-DIC ring milling method.

[0036] The test object was an 8Cr4Mo4V bearing ring that had undergone heat treatment including vacuum austenitization at 1090℃ for 30 minutes, quenching under 0.5MPa high-pressure nitrogen to room temperature, and three tempering processes at 560℃ (each holding time 2.5 hours). Considering the requirements of the dual-beam electron microscope equipment regarding sample size and shape, the sample was machined as follows: Figure 1 As shown, a 5mm thick arc-shaped sample was first cut from the bearing race using wire EDM. Because the raceway shape restricts the rolling of the bearing race to the bottom, affecting the FIB machining and SEM image acquisition results, the raceway area was preserved on the arc-shaped sample. Cutting was then performed approximately 0.1mm from the bottom, resulting in a FIB-DIC ring-core milled sample. The sample was then ground and polished to a mirror finish using 500#~2000# sandpaper, followed by ultrasonic cleaning with acetone and alcohol, and then dried.

[0037] The prepared sample was placed in the sample chamber of a Thermo Scientific dual-beam scanning electron microscope, and the primary carbide region to be measured was observed and located in electron beam mode (accelerating voltage 5 kV, working distance 5 mm). Figure 2 As shown, a large primary carbide with a size of approximately 18 μm was selected, and a circular test region with a diameter of 20 μm was defined in the matrix region at its edge. Switching to focused ion beam mode (accelerating voltage 30 kV), Pt gas was first injected using a 30 pA beam current, and a platinum adhesion layer was formed after 60 seconds of deposition. Subsequently, a 1.2 nA beam current was used to continue deposition for 120 seconds, forming platinum markers (approximately 100 nm in diameter, with a spacing of 250 nm between adjacent dots) arranged in an 8×8 lattice at the center of the test region. At the same time, a 2 μm wide annular platinum protective layer was deposited around this region.

[0038] After deposition, a high-resolution reference image of the test area before core milling was acquired in electron beam mode. Figure 3 The accelerating voltage was 5kV, and the working distance was 5mm. Switching to ion beam mode, the outer core of the platinum guard ring was milled. The inner diameter of the core was set to 20μm, and the outer diameter to 24μm. Beam current parameters of 30keV and 1.2nA were used, with a milling depth of 1μm per milling pass. SEM images were acquired in situ at milling depths of 0μm, 4μm (H / D=0.2), and 8μm (H / D=0.4), respectively. Figure 3 After each milling operation, the system immediately switches back to electron beam mode to acquire a second image (deformed image) of the area under test in situ. The parameters for image acquisition during the milling process are consistent with the parameters for the first image before milling. The entire milling process is performed a total of 20 times, with a total depth of 20 μm.

[0039] The acquired image sequences were imported into the open-source DIC analysis software Ncorr, with the sub-region size set to 41 pixels × 41 pixels, the step size to 5 pixels, and the strain window to 15 × 15 data points. The strain in the ring core region at different normalization depths was analyzed. and distributed( Figure 4 , Figure 5 The results show that the strain release gradually increases with increasing milling depth, stabilizing after H / D > 0.2, indicating that residual stress is fully released. Based on the strain magnitude of each sub-region of the analysis area after each milling step, the average strain of the analysis area is calculated as the strain release obtained in that analysis step. The strain release is then compared with the normalized depth using a function...

[0040]

[0041] Perform fitting ( Figure 6 ), where z = H / 0.42D, extrapolation yields the fully released strain: = 0.692×10 -3 , =-0.916×10 -3 .

[0042] According to Hooke's Law, using the formula

[0043]

[0044]

[0045] Calculate the residual stress, where E = 203 GPa and ν = 0.3. The calculated residual stress at the carbide interface is: = -91 MPa (compressive stress). = 155 MPa (tensile stress). The results indicate that there is significant micro-stress concentration at the carbide / matrix interface, and it exhibits anisotropic characteristics.

[0046] Example 2: Microscopic Residual Stress Test Inside Grains

[0047] This embodiment tests samples from the same heat-treated batch as in Example 1, but the test area is selected as the internal region of the grains far from any second phase, in order to compare the stress state at different microscopic locations.

[0048] The sample preparation process was exactly the same as in Example 1. Under SEM, a region within a grain with no obvious microscopic features was selected, and platinum markers and a protective ring were deposited using the same parameters. The ring core dimensions were also 20 μm inner diameter and 24 μm outer diameter. The same core milling procedure was performed, with a cumulative milling depth of 20 μm, and SEM images were recorded at each milling depth.

[0049] DIC analysis showed that the strain release distribution in this region was uniform, and the release degree was significantly lower than that in Example 1. The variation of strain release with milling depth was similar to that in Example 1, stabilizing after H / D > 0.2. The fully released strain obtained by fitting was: = 0.152×10 -3 , =-0.198×10 -3 .

[0050] The calculated residual stress value is: = -20 MPa, = 26 MPa. The results show that the residual stress value is significantly reduced and uniformly distributed inside the grains unaffected by the second phase, and the stress state is dominated by low tensile stress, proving that the method can effectively distinguish between micro-stress concentration regions and stress uniform regions.

[0051] Example 3: Microscopic Residual Stress Testing in Multi-Carbide Regions

[0052] In this embodiment, another bearing ring that has undergone the same heat treatment process was tested. A region containing multiple small nascent carbides was selected for testing to evaluate the stress distribution characteristics under the complex microstructure.

[0053] Sample preparation and testing parameters were the same as in Example 1. After depositing a platinum marker array and an annular protective layer in the selected multi-carbide region, ring milling and image acquisition were performed. DIC analysis showed that due to the presence of multiple carbides, the strain release distribution exhibited obvious spatial fluctuation characteristics, but the overall trend with milling depth was consistent with the previous two examples.

[0054] The fully released strain was obtained through data fitting: = 0.384×10 -3 , = -0.512×10 -3 The calculated residual stress value is: = -51 MPa, = 87 MPa.

[0055] The results show that in regions with multiple stress concentration sources, the residual stress value in the matrix lies between the high-stress region at the interface in Example 1 and the low-stress region inside the grains in Example 2. Furthermore, due to the superposition of stress fields from different carbides, the stress distribution exhibits significant spatial inhomogeneity. This reflects the complex distribution of microscopic residual stress in multiphase materials and verifies the effectiveness of this method in assessing complex microscopic stress fields.

Claims

1. A method for testing residual stress in bearing rings after heat treatment based on FIB-DIC ring milling technology, characterized in that: The method includes: sample preparation, marker deposition and image acquisition, ring core milling and in-situ monitoring, DIC analysis and residual stress calculation.

2. The method for testing residual stress in bearing rings after heat treatment based on FIB-DIC ring milling technology according to claim 1, characterized in that: The method is specifically as follows: Step 1: Sample preparation: Use a wire cutting device to cut a small sample from the fully heat-treated bearing ring along the circumference of the raceway, ensuring that the sampling position accurately includes the bottom contact area of ​​the raceway; grind the cut sample and then finely polish it to obtain a mirror surface that meets the test requirements; before the test, use acetone and alcohol to ultrasonically clean the sample and then dry it. Step 2: Marker deposition: The prepared sample is placed in a dual-beam electron microscope to determine the specific micro-region to be measured. In-situ deposition is performed using a focused ion beam. First, a platinum adhesion layer is deposited in the region to be measured. Then, platinum is deposited again using a higher ion beam current. By controlling the beam spot to form a lattice of platinum markers in the center of the region to be measured, a ring-shaped platinum protective layer is deposited around the marker area. Step 3: Image Acquisition, Core Milling, and In-situ Monitoring: After deposition, the first image of the test area before core milling is acquired using a SEM electron beam; switch to ion beam mode and use FIB to perform successive core milling on the outer side of the platinum protective layer, with the inner diameter of the core consistent with the inner diameter of the protective ring; immediately after each milling, the second image of the test area is acquired in-situ using a SEM electron beam until the total core depth reaches the diameter of the core, to ensure that stress is fully released; Step 4: DIC Analysis: Import the first and second images obtained in Step 3 into the open-source DIC analysis software Ncorr. The software calculates the displacement field relative to the first image for each milling stage using digital image correlation algorithms. Based on the displacement field data, the strain relaxation amounts in the X and Y directions of the ring core region are calculated. and ; Step 5: Residual Stress Calculation: Calculate the residual stress based on elasticity theory, and determine the strain release amount at each milling depth. Fit the normalized depth (H / D, where H is the milling depth and D is the inner diameter of the ring core) and extrapolate to an infinite depth (H / D → The fully released strain Δεx is obtained. ∞ and Δεy ∞ According to Hooke's Law, the residual stress is calculated; the residual stress distribution at a specific microscopic location at the bottom of the bearing raceway can be directly obtained using this method.

3. The method for testing residual stress in bearing rings after heat treatment based on FIB-DIC ring milling technology according to claim 1, characterized in that: Step one specifically involves: selecting a material for the bearing race that allows for the control of microstructure and residual stress through heat treatment; the heat treatment process for the bearing race is as follows: vacuum austenitizing at 1080℃~1100℃ for 30~40 minutes, followed by quenching in high-pressure nitrogen at 0.4MPa~0.6MPa to room temperature, and finally tempering three times at 550℃~560℃, holding at that temperature for 2~2.5 hours each time, followed by air cooling; precisely cutting samples from the circumference of the bearing raceway using wire cutting to ensure that the test area includes the bottom contact area of ​​the raceway; grinding the samples sequentially with 400# to 2000# sandpaper, and then finely polishing them with diamond polishing compound to obtain a smooth test surface; and ultrasonically cleaning and drying the samples with acetone and alcohol before testing.

4. The method for testing residual stress in bearing rings after heat treatment based on FIB-DIC ring milling technology according to claim 1, characterized in that: Step two specifically involves: placing the prepared sample into the sample chamber of a dual-beam scanning electron microscope (SEM-FIB), observing and locating the microscopic region to be measured in electron beam mode, switching to focused ion beam (FIB) mode, first depositing a thin platinum adhesion layer on the selected circular region to be measured with a diameter of 15~25μm; then continuing deposition using a 1.2nA beam current, by controlling the beam spot to form platinum markers arranged in a lattice at the center of the region, with a marker diameter of 100nm~120nm and a spacing of 200~300nm, and simultaneously depositing a complete annular platinum protective layer of a specific thickness around the region, the inner diameter of which is the inner diameter of the subsequent ring core, the inner diameter of which is 10μm~20μm and the width of which is 2μm~5μm.

5. The method for testing residual stress in bearing rings after heat treatment based on FIB-DIC ring milling technology according to claim 1, characterized in that: Step three specifically involves: after deposition, acquiring a high-resolution first image (reference image) of the test area before core milling in electron beam mode, with an accelerating voltage of 5kV and a working distance of 5mm; switching to ion beam mode to perform core milling on the outer side of the platinum protective ring, using beam current parameters of 30keV and 1.2nA, with a milling depth of 0.5μm each time; immediately switching back to electron beam mode after each milling operation to acquire a second image (deformed image) of the test area in situ, with the parameters of the image acquisition during milling being consistent with the parameters of the first image before milling, repeating this process until the depth of the ring diameter reaches 20μm.

6. The method for testing residual stress in bearing rings after heat treatment based on FIB-DIC ring milling technology according to claim 1, characterized in that: In step four, the sub-region size is set to 41 pixels × 41 pixels, the step size is 3 to 5 pixels, and the strain window is 15 × 15 data points.

7. The method for testing residual stress in bearing rings after heat treatment based on FIB-DIC ring milling technology according to claim 1, characterized in that: In step five, the in-plane residual stress is calculated using the following three formulas. in, The main function used for fitting, The relaxation strain is the stress at which residual stress is completely released, and z is the normalized depth corresponding to each milling step. Let be the in-plane residual stress in the x-direction of the region to be measured, v be the Poisson's ratio of the material, and E be the Young's modulus of the material. This represents the fully released strain in the x-direction of the region to be measured. The strain in the y-direction of the region to be measured is the fully released strain. Let be the in-plane residual stress in the y-direction of the region to be measured.

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