CN111751035A - Residual stress analysis method and application - Google Patents
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- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
- G01L5/0047—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes measuring forces due to residual stresses
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Abstract
The invention discloses a residual stress analysis method and application, and belongs to the technical field of optical measurement mechanics and microelectronic devices. The analysis method comprises the steps of matching an image before cutting with an image after cutting, and calculating released residual stress by combining a corresponding calculation formula. The method can be applied to measurement and analysis of the surface residual stress of metal and non-metal materials, and can also be used for measurement and analysis of the surface residual stress of the ultra-thin oriented silicon steel sheet and non-metal materials.
Description
Technical Field
The invention relates to a stress analysis method, belongs to the technical field of optical measurement mechanics and microelectronic devices, and particularly relates to a residual stress analysis method and application.
Background
Residual stress is of great concern both in the scientific research field and in industrial production. In the traditional industrial field, the macro structural member is often subjected to strong thermal mismatch and plastic deformation in the casting and processing production process, so that internal stress is caused, and the influence of residual stress on the fatigue life and the fracture strength of the macro structural member is very important. In the study of micro-mechanical structure and material, the residual stress has a profound influence, and the effect can be attributed to the influence on point, line and plane structures. For example, in a micro electro mechanical system, residual stress is introduced in the etching and deposition processes, and problems such as pre-deformation and even inaccurate dimension are often caused; at Nb3In the Sn superconducting wire, the critical current is sharply reduced and even the wire fails due to residual stress; during the coating process of the sheet structure, residual stress is often introduced due to lattice mismatch, which causes significant warpage. Of course, in some cases, residual stresses may also be beneficial. For example, in the semiconductor industry, the concept of strain engineering has been developed to greatly improve the performance of diodes by exploiting the effect of stress on carrier concentration.
In order to reduce the adverse effect of the residual stress and exert the advantages of the residual stress, the method has important significance for measuring and analyzing the residual stress. Currently, the residual stress analysis techniques can be mainly classified into the following categories: diffraction method, stress relief method, and physical quantity conversion method. The diffraction method reflects the size or relative change of the internal interplanar spacing of the material through an X-ray or neutron diffraction spectrum so as to invert the stress, but the method is only suitable for crystalline materials and is not applicable to amorphous materials.
Physical quantity conversion methods include mechanical and non-mechanical methods. For example, a typical representation of the mechanical method is an indentation method, and the non-mechanical method includes stress analysis using an acoustic field, a magnetic field, and the like.
The stress relief method is to estimate the original stress state by measuring the deformation before and after removing a part of the material at the stress application position. The method is not only suitable for measuring macroscopic residual stress, but also suitable for measuring microscopic residual stress, and is suitable for various different materials.
Since the film failure is often a local failure, the micro-domain residual stress measurement is of great importance. The focused ion beam system with micro-nano processing capability is combined with an optical measurement method, so that the possibility of measuring the residual stress of a micro-area is provided. Sabate et al, n.sabate, d.vogel et al, journal of microelectromechanical systems,2007, reported measuring the residual stress of suspended beam films by using focused ion beams to drill or notch the film surface in combination with digital image correlation; korsunsky, A.Korsunsky, M.Sebastiani et al surface and Coatings Technology,2020 reports measuring residual stress of films using focused ion beam machining of ring grooves in conjunction with digital image correlation. The drilling or grooving method causes strain concentration in the etched area, and the ring-core method releases strain more uniformly, which is the best choice for releasing residual stress.
The displacement or strain caused by residual stress release is measured by using a digital image correlation method, and the surface images of the test piece before and after drilling or grooving need to be recorded, but the damage to the edge region morphology is serious in the micro-processing process of the focused ion beam, the gray scale morphology of the surface of the test piece is also influenced, and the calculation accuracy of the digital image correlation method is obviously influenced.
The Chinese invention patent application (application publication No. CN 110110390A, application publication date: 2019-08-09) discloses a strain testing method based on three-dimensional geometric shape matching, wherein the surface of a tested sample is processed to form a surface shape with a micron-sized roughness structure, micron-sized three-dimensional shape data of a surface investigation region of the tested sample is obtained by sampling, and three-dimensional shape information of the surface investigation region of the tested sample is continuously measured until a test is stopped in the process that the tested sample is deformed by bearing external force and is respectively marked as M1、M2、…、MnFor the recorded three-dimensional shape data M0、M1、…、MnProcessing is carried out, and the strain of the surface investigation region of the tested sample is calculated; can be matched according to geometric shape data when a photo without a sample surface deformation process or the definition of the photo is not enoughThe strain distribution of the sample surface is obtained by analysis, and the method is a new way for strain measurement different from the traditional digital speckle image analysis method. The method has the advantages of being independent of whether images exist or whether the images are clear, but has the defects that the analysis precision of the local micro-area strain is not high enough and the method is not suitable for small strain analysis caused by residual stress release compared with the method.
Disclosure of Invention
In order to solve the technical problems, the invention discloses a residual stress analysis method and application thereof, and the method not only can be applied to the measurement and analysis of the surface residual stress of metal and non-metal materials, but also can be applied to the test and analysis of the surface residual stress of ultra-thin oriented silicon steel sheets and non-metal materials.
In order to achieve the purpose, the invention discloses a residual stress analysis method, which comprises the following steps:
1) preparing a sample wafer and determining a position to be analyzed of the residual stress on the surface of the sample wafer;
2) obtaining the 2D initial gray level image M of the position to be analyzed0；
3) Processing an annular groove at the position to be analyzed by adopting a plasma beam to obtain a 2D gray image M in the annular groove1；
4) For the images M before and after processing0、M1Matching analysis is carried out, and the specific analysis process is as follows:
4.1) image preprocessing: removing image M1And the image M is taken of unreliable data points on the annular groove1Dispersed as N evenly distributed subimages m1,nN is any natural number from 1 to N;
4.2) image matching analysis: with said image M1Sub-image m of1,1The middle part pixel point is used as the starting point Q of analysis1,1And with said image M0Performing matching analysis to find the image M0Corresponding sub-image m0,1And said sub-image m0,1Is starting point Q of0,1；
4.3) calculating the subimage m0,1And (4) treating residual stress: due to the fact thatResidual stress is released in the sub-image m0,1Main strain of1And2the following mathematical relationship is satisfied:
and is1The included angle between the X-axis and the X-axis satisfies the following mathematical relation:
the released residual stress sigma can be calculated according to Hooke's law1And σ2：
Wherein E is the elastic modulus of the material, and mu is the Poisson's ratio of the material;
4.4) calculating other sub-images m0,nRelaxed strain and relaxed residual stress at the site;
5) to M0The residual stresses calculated from the analysis of each sub-image are averaged to obtain an average residual stress released from the cutting region of the plasma beam.
Further, u isx、uy、vx、vyAlso satisfies the subimage m1,1The pixel point (x) to which it belongsi，yi) And sub-image m0,1Matching pixel points (x)i’，yi') an error function Er (u)0,v0,ux,uy,vx,vy) And the error function Er satisfies the following mathematical relation:
Er＝∑i(g0(xi’,yi’)-g1(xi,yi))2；
wherein, g0(xi’,yi') is a subimage m0,1Pixel point (x)i’，yi') gray value, g1(xi,yi) As sub-image m1,1Middle pixel (x)i，yi) The gray value of (a);
u0、v0is 0, ux、uy、vx、vy1, and solving the parameter u through optimization0、v0、ux、uy、vx、vySo that the error function Er tends to be minimal.
Further, the sub-image m1,1The pixel point (x) to which it belongsi，yi) And sub-image m0,1Matching pixel points (x)i’，yi') the matching process is as follows:
suppose a sub-image m1,1、m0,1The gray distribution of (a) satisfies a first order transformation relationship, and the mathematical relationship is as follows:
wherein (x) in the above mathematical relation0，y0) Is a starting point Q1,1(u) coordinates of0，v0) Is a starting point Q0,1And the starting point Q1,1Relative coordinate of (1), Δ xi、ΔyiAs sub-image m1,1The pixel point (x) to which it belongsi，yi) And the starting point Q1,1Pixel point (x)0，y0) Relative position therebetween, then (x)i’，yi') is a pixel point (x)i，yi) At m0,1The matching point in (1).
Further, m1,1Neutral starting point Q1,1(x0，y0) At m0,1The corresponding starting point in (2) is Q0,1Has the coordinates of (x)0+u0，y0+v0)。
Further, in step 4.1), the image M is removed1The process of unreliable data points on the annular groove comprises setting the diameter of the inner boundary of the annular groove as D and the radius of the influence range of the plasma beam as R, M1The effective data point of (a) is the region enclosed after the boundary in the annular groove has been shifted by R, i.e. M1Has a diameter of (D-2R).
Further, in the step 3), the depth of the annular groove is larger than 10 micrometers, and the diameter D of the inner boundary of the annular groove is 10-20 micrometers.
Furthermore, each sub-image comprises 5-30 evenly distributed pixel points.
Further, the radius of each sub-image is r, and the distance between adjacent sub-images is d.
Further, image M0And image M1Is obtained by means of scanning and/or optical photography.
In order to better achieve the technical purpose of the invention, the invention also discloses the application of the residual stress analysis method on the surfaces of metal and non-metal materials.
Has the advantages that:
the analysis method designed by the invention can be applied to measurement and analysis of residual stress on the surfaces of metal and non-metal materials. Meanwhile, the method can be used for testing and analyzing the residual stress on the surfaces of the ultra-thin oriented silicon steel sheet and the non-metallic material, and is a beneficial supplement of residual stress analysis methods such as an X-ray diffraction method and the like.
Drawings
FIG. 1 is a 2D grayscale image of an example design coupon;
FIG. 2 is a 2D grayscale image of the sample wafer of FIG. 1 after circular cutting;
FIG. 3 is a selected and segmented image of the internal circle of FIG. 2;
FIG. 4 is an image of the post-cut strain distribution of FIG. 1;
fig. 5 is a graph of the principal strain distribution of fig. 1 after cutting.
Detailed Description
Because the thin steel plates such as oriented silicon steel sheets and the like and non-metallic materials are limited by material structures and dimension specifications, the residual stress can not be measured by adopting a full-release method, an indentation strain method and a drilling method, and also can not be measured by adopting an X-ray diffraction method, wherein the oriented silicon steel sheets belong to large-grain materials, most of the non-metallic materials belong to non-polycrystalline materials, and the two types of materials can not be subjected to residual stress analysis by using the X-ray diffraction method. Based on the limitations of the method, the invention provides a residual stress analysis method and application.
Firstly, the invention discloses a residual stress analysis method, which comprises the following steps:
1) preparing a sample wafer and determining a position to be analyzed of the residual stress on the surface of the sample wafer;
2) obtaining the 2D gray level image M of the position to be analyzed0(ii) a The image may be obtained by scanning and/or by optical photography;
3) processing an annular groove at the position to be analyzed by adopting a plasma beam to obtain a 2D gray image M in the annular groove1(ii) a The image may be obtained by scanning and/or by optical photography; the depth of the annular groove is more than 10 micrometers, and the diameter D of the inner boundary of the annular groove is 10-20 micrometers;
4) for the images M before and after processing0、M1Matching analysis is carried out, and the specific analysis process is as follows:
4.1) image preprocessing: removing image M1The specific removing process comprises setting the diameter of the inner boundary of the annular groove as D and the radius of the influence range of the plasma beam as R and M1The effective data point of (a) is the region enclosed after the boundary in the annular groove has been shifted by R, i.e. M1Has a diameter of (D-2R).
And the image M is processed1Dispersed as N evenly distributed subimages m1,nN is any natural number from 1 to N; e.g. comprising sub-images m1,1Sub-image m1,2Sub-image m1,3Sub-image m1,4Sub-image m1,5A, a sub-imagem1,N(ii) a The radius of each sub-image is r, 5-30 pixel points are included in the radius r range, r can be larger if strain distribution is uniform, the distance between adjacent sub-images is d, and the adjacent sub-images can be partially overlapped;
4.2) image matching analysis: with said image M1Sub-image m of1,1The middle part pixel point is used as the starting point Q of analysis1,1And with said image M0Matching analysis is carried out, and the specific matching process is as follows:
find the image M0Corresponding sub-image m0,1And said sub-image m0,1Is starting point Q of0,1(ii) a The specific matching process is as follows:
suppose a sub-image m1,1、m0,1The gray distribution of (a) satisfies a first order transformation relationship, and the mathematical relationship is as follows:
wherein (x) in the above mathematical relation0，y0) Is a starting point Q1,1(u) coordinates of0，v0) Is a starting point Q0,1And the starting point Q1,1Relative coordinate of (1), Δ xi、ΔyiAs sub-image m1,1The pixel point (x) to which it belongsi，yi) And the starting point Q1,1Pixel point (x)0，y0) Relative position therebetween, then (x)i’，yi') is a pixel point (x)i，yi) At m0,1The matching point of (1); then m is1,1Neutral starting point Q1,1(x0，y0) At m0,1The corresponding starting point in (2) is Q0,1Has the coordinates of (x)0+u0，y0+v0)。
Suppose u isx、uy、vx、vyAlso satisfies the subimage m1,1The pixel point (x) to which it belongsi，yi) And sub-image m0,1Matching pixel points (x)i’，yi') an error function Er (u)0,v0,ux,uy,vx,vy) And the error function Er satisfies the following mathematical relation:
Er＝∑i(g0(xi’,yi’)-g1(xi,yi))2；
wherein, g0(xi’,yi') is a subimage m0,1Pixel point (x)i’，yi') gray value, g1(xi,yi) As sub-image m1,1Middle pixel (x)i，yi) The gray value of (a);
u0、v0is 0, ux、uy、vx、vy1, and solving the parameter u through optimization0、v0、ux、uy、vx、vySo that the error function Er tends to be minimal.
4.3) calculating the subimage m0,1And (4) treating residual stress: due to residual stress release in sub-image m0,1Main strain of1And2the following mathematical relationship is satisfied:
and is1The included angle between the X-axis and the X-axis satisfies the following mathematical relation:
the released residual stress sigma can be calculated according to Hooke's law1And σ2：
Wherein E is the elastic modulus of the material, and mu is the Poisson's ratio of the material;
4.4) calculating other sub-images m0,nRelaxed strain and relaxed residual stress at the site;
5) to M0The residual stresses calculated from the analysis of each sub-image are averaged to obtain an average residual stress released from the cutting region of the plasma beam.
For better explanation of the above analysis method, the following detailed description is made with reference to specific application scenarios.
Example 1
The embodiment discloses a method for analyzing residual stress on a coated metal surface, which comprises the following steps:
1) preparing a coated sample for analysis, the dimensions 25mm x 35mm x 0.5 mm;
2) placing the sample wafer on a plasma beam cutting objective table for fixing, and obtaining a 2D gray image M of the middle part of the sample wafer0See fig. 1;
3) processing an annular groove at the analysis position by adopting a plasma beam, wherein the depth of the annular groove is 10 mu M, and a camera acquires a processed gray level image M in situ1See fig. 2;
4) remove M1The effective data in the inner circular range is divided into subimages by the image data close to the annular cutting groove, which is shown in figure 3;
5) for the images M before and after processing0、M1Performing first-order affine transformation matching analysis, and calculating the strain of each sub-image due to residual stress release after cutting, as shown in fig. 4 and 5;
6) the residual stress of the sub-image is calculated.
The principal strain in the middle of the sample due to residual stress in the examples:
1＝0.00028，2＝-0.00004，；
the elastic modulus E of the base material is 205Gpa, the Poisson ratio mu is 0.3,the released residual stress sigma can be calculated according to Hooke's law1And σ2：
Wherein E is the elastic modulus of the material, and mu is the Poisson's ratio of the material;
and additionally, taking the strain of other 3 measuring points and the strain average value of all measuring points in the area to calculate the released residual stress:
the calculation result of the area average strain is more consistent with the actual residual stress distribution condition of the material. The main reason for the large difference of the calculated residual stress of different measuring points on the surface of the material is that the thickness unevenness and the internal gaps of the coating affect the actual strain distribution of the surface after the residual stress is released.
The analysis method designed by the invention can also be applied to other non-metallic materials, the specific analysis process is consistent with that described above, and the detailed description of the invention is omitted.
Claims (10)
1. A residual stress analysis method is characterized by comprising the following steps:
1) preparing a sample wafer and determining a position to be analyzed of the residual stress on the surface of the sample wafer;
2) obtaining the 2D gray level image M of the position to be analyzed0；
3) Processing an annular groove at the position to be analyzed by adopting a plasma beam to obtain a 2D gray image M in the annular groove1；
4) For the images M before and after processing0、M1Matching analysis is carried out, and the specific analysis process is as follows:
4.1) image preprocessing: removing image M1And the image M is taken of unreliable data points on the annular groove1Dispersed as N evenly distributed subimages m1，nN is any natural number from 1 to N;
4.2) image matching analysis: with said image M1Sub-image m of1，1The middle part pixel point is used as the starting point Q of analysis1，1And with said image M0Performing matching analysis to find the image M0Corresponding sub-image m0，1And said sub-image m0，1Is starting point Q of0，1；
4.3) calculating the subimage m0，1And (4) treating residual stress: due to residual stress release in sub-image m0，1Main strain of1And2the following mathematical relationship is satisfied:
and is1The included angle between the X-axis and the X-axis satisfies the following mathematical relation:
the released residual stress sigma can be calculated according to Hooke's law1And σ2：
Wherein E is the elastic modulus of the material, and mu is the Poisson's ratio of the material;
4.4) calculating other sub-images m0，nOfReleasing the strain and the released residual stress;
5) to M0The residual stresses calculated from the analysis of each sub-image are averaged to obtain an average residual stress released from the cutting region of the plasma beam.
2. The residual stress analysis method according to claim 1, wherein u is the same as ux、uy、vx、vyAlso satisfies the subimage m1，1The pixel point (x) to which it belongsi，yi) And sub-image m0，1Matching pixel points (x)i’，yi') an error function Er (u)0，v0，ux，uy，vx，vy) And the error function Er satisfies the following mathematical relation:
Er＝∑i(g0(xi’，yi’)-g1(xi，yi))2；
wherein, g0(xi’，yi') is a subimage m0，1Pixel point (x)i’，yi') gray value, g1(xi，yi) As sub-image m1，1Middle pixel (x)i，yi) The gray value of (a);
u0、v0is 0, ux、uy、vx、vy1, and solving the parameter u through optimization0、v0、ux、uy、vx、vySo that the error function Er tends to be minimal.
3. The residual stress analysis method according to claim 2, wherein the sub-image m1，1The pixel point (x) to which it belongsi，yi) And sub-image m0，1Matching pixel points (x)i’，yi') the matching process is as follows:
suppose a sub-image m1，1、m0，1The gray distribution of (A) satisfies a first order transformation relation, a mathematical relationThe formula is as follows:
wherein (x) in the above mathematical relation0，y0) Is a starting point Q1，1(u) coordinates of0，v0) Is a starting point Q0，1And the starting point Q1，1Relative coordinate of (1), Δ xi、ΔyiAs sub-image m1，1The pixel point (x) to which it belongsi，yi) And the starting point Q1，1Pixel point (x)0，y0) Relative position therebetween, then (x)i’，yi') is a pixel point (x)i，yi) At m0，1The matching point in (1).
4. The residual stress analysis method according to claim 3, wherein m is m1，1Neutral starting point Q1，1(x0，y0) At m0，1The corresponding starting point in (2) is Q0，1Has the coordinates of (x)0+u0，y0+V0)。
5. The residual stress analysis method according to any one of claims 1 to 3, wherein in step 4.1), the image M is removed1The process of unreliable data points on the annular groove comprises setting the diameter of the inner boundary of the annular groove as D and the radius of the influence range of the plasma beam as R, M1The effective data point of (a) is the region enclosed after the boundary in the annular groove has been shifted by R, i.e. M1Has a diameter of (D-2R).
6. The residual stress analysis method according to any one of claims 1 to 3, wherein in the step 3), the depth of the annular groove is greater than 10 micrometers, and the diameter D of the inner boundary of the annular groove is 10 to 20 micrometers.
7. The residual stress analysis method according to any one of claims 1 to 3, wherein each sub-image comprises 5 to 30 uniformly distributed pixel points.
8. The residual stress analysis method according to claim 7, wherein the radius of each sub-image is r, and the distance between adjacent sub-images is d.
9. Method for residual stress analysis according to claim 1 or 2 or 3 or 8, characterized in that the image M is an image M0And image M1Is obtained by means of scanning and/or optical photography.
10. Use of the residual stress analysis method according to claim 1 on the surfaces of metallic and non-metallic materials.
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