CN110110390B - Strain testing method based on three-dimensional geometric shape matching - Google Patents

Abstract

The invention discloses a strain testing method based on three-dimensional geometric shape matching, which comprises the steps of processing the surface of a tested sample to form a surface shape with a micron-sized roughness structure, sampling to obtain micron-sized three-dimensional shape data of a tested sample surface investigation region, continuously measuring the three-dimensional shape information of the tested sample surface investigation region until the test is stopped in the process that the tested sample bears external force and deforms, and respectively marking as M ₁ 、M ₂ 、…、M _n For the recorded three-dimensional shape data M ₀ 、M ₁ 、…、M _n Processing is carried out, and the strain of the surface investigation region of the tested sample is calculated; the strain distribution of the surface of the sample can be obtained according to the matching analysis of the geometric shape data when the picture of the deformation process of the surface of the sample does not exist or the definition of the picture is not enough, and the method is a new way for carrying out strain measurement different from the traditional digital speckle image analysis method.

Description

Strain testing method based on three-dimensional geometric shape matching

Technical Field

The invention belongs to the technical field of strain measurement, and particularly relates to a strain testing method based on three-dimensional geometric shape matching.

Background

At present, the strain test method based on image analysis generally comprises the following processes: processing the surface of a sample to form a random speckle pattern with higher resolution, deforming the sample under the condition of auxiliary illumination, continuously photographing by using a calibrated single-lens or multi-lens camera to obtain continuous photos of the sample in the deformation process, carrying out image analysis on the photos, firstly dispersing an original image into micro-surfaces according to a certain method, then carrying out identification and matching on subsequent images so as to track the position information of each micro-surface in the deformation process of the sample, and calculating the strain of the corresponding surface part of the sample according to the position information of the micro-surfaces so as to obtain the information of the strain distribution of the surface of the sample along with the change of time. The strain test analysis method based on image analysis requires a clear picture of the deformation process of the tested object, and the integrity and continuity of image detail information on the picture determine the accuracy of analysis.

Although the method based on image similarity analysis is widely applied to the measurement of the surface strain of the material, when the image analysis method cannot be used (no image or image with insufficient clarity), the deformation process of the sample surface is difficult to measure and analyze, and the strain process inside the object is difficult to obtain through the image analysis of the surface if the image analysis method is desired.

Disclosure of Invention

The invention aims to provide a strain testing method based on three-dimensional geometric shape matching independent of image quality aiming at the defects of the traditional detection method.

In order to achieve the purpose, the invention designs a strain testing method based on three-dimensional geometric shape matching, which comprises the following steps:

1) Processing the surface of a tested sample to form a surface topography with a micron-scale roughness structure;

2) Sampling to obtain micron-sized three-dimensional shape data of the inspected area on the surface of the tested sample, and recording the data as M ₀ ，M ₀ Three-dimensional topography data of a surface investigation region of a sample to be measured at an initial time, M ₀ A plurality of three-dimensional data points P containing the peak/valley height information of the surface investigation region of the tested sample ₀ (X _i ，Y _i ，Z _i ) Forming;

3) When the sample is subjected to external forceContinuously measuring the three-dimensional topography information of the surface investigation region of the measured sample in the deformation process until the test is stopped, measuring the three-dimensional topography data of the surface investigation region of the measured sample according to a sampling time interval delta t after the initial moment, and respectively marking as M ₁ 、M ₂ 、…、M _n ；

4) For the three-dimensional shape data M recorded in the step 2) and the step 3) ₀ 、M ₁ 、…、M _n Carrying out treatment;

4a) For recorded three-dimensional shape data M ₀ 、M ₁ 、…、M _n Fitting to obtain a projection point, a projection height and a normal vector of each point on the respective median plane;

4b) For three-dimensional shape data M ₀ 、M ₁ 、…、M _n The projection height of each point in the image on the respective median plane is normalized;

5) Calculating the strain of the inspected area on the surface of the tested sample

The deformation of the inspected area on the surface of the tested sample is corresponding to the change of the median plane in space, and M is used ₀ Dividing the virtual grid by the median plane Q, and analyzing the subsequent M by correlation matching ₁ 、M ₂ …、M _n Finding out the corresponding position of each node of the virtual grid on each median plane, and then calculating the strain of the surface investigation area of the sample to be measured according to the side length change of a triangle formed by the nodes of the virtual grid and the assumption of uniform strain.

Further, in the step 3), the maximum strain generated by the next three-dimensional shape data in the two adjacent three-dimensional shape data compared with the previous three-dimensional shape data is not more than 5%.

Further, in the step 4 a), the specific process is as follows:

4a1) Calculating M ₀ Each point P on ₀ (X _i ，Y _i ，Z _i ) Projection point Q on median plane Q ₀ (x _i ，y _i ，z _i ) And a projection height h ₀ (x _i ，y _i ，z _i ) Wherein, P ₀ (X _i ，Y _i ，Z _i ) The nearby median plane Q adopts a binomial expression:

z＝f(x,y)＝ax ² +by ² +cxy+d

to P ₀ (X _i ，Y _i ，Z _i ) Fitting for three-dimensional data points in a region with a center and a radius of R, P ₀ (X _i ，Y _i ，Z _i ) The projection height on the median plane Q satisfies:

wherein (x, y, z) ∈ z = f (x, y), (x) _i ，y _i ，z _i ) Is the projection point Q at which the formula (1) takes the minimum value ₀ Coordinates;

point Q ₀ (x _i ，y _i ，z _i ) The normal vector at (a) is:

4a2) Calculating M according to the fitting method of the step 4a 1) ₁ 、M ₂ 、…、M _n The projection point coordinates, the projection heights and the normal vectors of each point on the respective median plane;

further, in the step 4 b), the specific process is as follows:

4b1) Will M ₀ All of (1) h ₀ (x _i ，y _i ，z _i ) Sorting according to the sequence from big to small, and taking the average value of the first m as the maximum value h _max The average of the last m is taken as the minimum value h _min According to

Carrying out normalization processing to obtain each projection point Q ₀ (x _i ，y _i ，z _i ) Normalized height value g of ₀ (x _i ，y _i ，z _i ) Wherein, when g ₀ (x _i ，y _i ，z _i )>When 1, order

4b2) Calculating M according to the normalization method of the step 4b 1) ₁ 、M ₂ 、…、M _n The normalized height value of the projection height of each point in the image;

further, in the step 5), the specific process is as follows:

5a)M ₀ the median plane Q divides the virtual grid into M ₀ Upper by projection point Q ₀ (x _i ，y _i ，z _i ) The formed middle level surface Q is subdivided into small square areas of L multiplied by L,

5b) Determining M ₀ And M ₁ Feature data point set for matching analysis

Let P (x) ₀ ,y ₀ ,z ₀ ) Is M ₀ One of N nodes on median plane Q, taken as P (x) ₀ ,y ₀ ,z ₀ ) The projection data points (including more than 4 peak-valley height data points) with the center and the radius within the range of rho are calculated according to the normalized height value g ₀ (x _i ,y _i ,z _i ) Sorting from big to small, taking the top J ₁ (J ₁ Not less than 2) and the rearmost J ₂ (J ₂ Not less than 2) data to form a feature data point set P of matching analysis ₀ ＝{P _0,1 ，P _0,2 ，…,P _0,j ，…,P _0,J }(J＝J ₁ +J ₂ ≥4)；

Let M ₁ Neutral P (x) ₀ ,y ₀ ,z ₀ ) The matched point is at P' (x) ₀ ’,y ₀ ’,z ₀ ') near, take P' (x) ₀ ’,y ₀ ’,z ₀ ') as a center and having a radius of ρ ' (ρ '>ρ) in terms of normalized height value g ₁ (x _k ,y _k ,z _k ) Sorting from big to small, and taking the top K ₁ (K ₁ ≥J ₁ ) And finallyK of noodles ₂ (K ₂ ≥J ₂ ) The data form a characteristic data point set P of matching analysis ₁ ＝{P _1,1 ，P _1,2 ，…,P _1,k ，…,P _1,K }，K＝K ₁ +K ₂ ；

5c) Matching according to the characteristic data points in step 5 b)

According to M ₀ And M ₁ Respectively constructing feature vector sets U and V by using middle feature data points _L Further constructing data sets U' and V to facilitate matching analysis _L '; the elements in U' are the same as V _L ' the elements in the above are compared and analyzed (considering normalized height values of two end points of the vector, the length of the vector and the position relationship between the vectors), and each data set V is found _L Best matching subset of V of' Zhou and U _L ", and then from all V _L Find the best matching subset of "(L = 1-K) to get M ₁ Set of best matching points P in (1) ₁ ’＝{P _1,1 ’，P _1,2 ’，…,P _1,j ’，P _1,J ’}；

5d) Coordinate computation of grid nodes

According to the corresponding relation of the matching points, adopting first-order affine transformation:

wherein (x) _i ,y _i ,z _i ) Is P ₀ Coordinates of the midpoint, (x) _i ’,y _i ’,z _i ') is P ₁ ' in corresponds to (x) _i ,y _i ,z _i ) U, v, w are nodes P (x) ₀ ,y ₀ ,z ₀ ) Δ x, Δ y, Δ z are points (x) _i ,y _i ,z _i ) And P (x) ₀ ,y ₀ ,z ₀ ) The first order linear system of equations can be obtained:

solving the system of equations can yield

Is the optimal solution of M ₁ Neutralization of P (x) ₀ ,y ₀ ,z ₀ ) Corresponding node P' (x) ₀ ’,y ₀ ’,z ₀ ') coordinates are:

5e) According to the matched node pair P (x) ₀ ,y ₀ ,z ₀ ) And P' (x) ₀ ’,y ₀ ’,z ₀ ') respectively obtaining M by the method of steps 5 b) to 5 d) by diverging to the neighboring nodes around ₁ Neutral M ₀ Virtual grid node coordinates matched with other grid nodes;

5f) Obtaining M according to the method of steps 5 b) to 5 e) ₂ 、…、M _n Corresponding virtual grid node coordinates in (1);

5g) And calculating the grid strain, wherein the strain of the virtual grid is calculated according to the side length change of the triangle and the assumption of uniform strain.

Further, in the step 5 a), the specific dividing method includes:

get M ₀ All of Q on ₀ (x _i ，y _i ，z _i ) Mean value of coordinates of

And average of normal vectors

Taking a straight line as a parameter>

Parallel to the straight lineTwo perpendicular sets of planes, the spacing distance between each set of planes is L (L)<2 rho), the two groups of planes intersect with the median plane Q, and the median plane Q is cut into N ₀ In each L multiplied by L area, the intersection point of the intersection line of the two groups of planes and the middle plane Q is a node of the virtual grid, and the number of the nodes is N.

Further, in the step 5 c), the specific process is as follows:

5c1) With P ₀ ＝{P _0,1 ，P _0,2 ，…,P _0,j ，…,P _0,J Constructing a vector set with the 1 st point as a starting point

J-1 vector sets U are sorted from large to small according to vector length, an included angle alpha between each vector in U and the first vector is calculated, and a new data set U '= { U' for matching analysis is obtained ₁ ，U ₂ ，…，U _j ，…，U _J-1 }, each sub-element U _j Including the starting point P of the vector _s End point P _e Length of vector L _j Angle alpha between vectors _j I.e. U _j ＝{P _s ，P _e ，L _j ，α _j }；

5c2) With P ₁ ＝{P _1,1 ，P _1,2 ，…,P _1,k ，…,P _1,K Constructing a vector set with the L-th point as a starting point

L is not equal to K, K-1, and the vector set V has K different types _L (ii) a Vector set V _L Sorting according to the vector length from large to small, and calculating V _L The included angle beta between each vector and the first vector is obtained to obtain a new data set V for matching analysis _L ’＝{V _L,1 ，V _L,2 ，…，V _L,k ，…，V _L,K-1 V, each sub-element V _L,k Including the starting point P of the vector _s ', end point P _e ', vector length L _k ' vector included angle beta _k I.e. V _L,k ＝{P _s ’，P _e ’，L _k ’，β _k }；

5c3) Will U' = { U ₁ ，U ₂ ，…，U _j ，…，U _J-1 Each of the elements U _j Same as V _L ’＝{V _L,1 ，V _L,2 ，…，V _L,k ，…，V _L,K-1 Carry out matching analysis on the elements in the sequence, if the element U is in the sequence _j ＝{P _s ，P _e ，L _j ，α _j And element V _L,k ＝{P _s ’，P _e ’，L _k ’，β _k The following conditions are satisfied:

(1-μ)|g ₀ (P _s )|<|g ₀ (P _s )-g ₁ (P′ _s )|<(1+μ)|g ₀ (P _s )|

(1-μ)|g ₀ (P _e )|<|g ₀ (P _e )-g ₁ (P′ _e )|<(1+μ)|g ₀ (P _e )|

(1-μ)L _j <|L _j -L _k ′|<(1+μ)L _j

(1-μ)α _j <|α _j -β _k |<(1+μ)α _j

wherein mu = 0.03-0.10

Then consider U _j And V _L,k Similarly, let e _j ＝|g ₀ (P _e )-g ₁ (P′ _e ) If else, continue to use U _j And V _L,k The latter elements are compared if at V _L ' found in and U _j Similar elements continue to compare U _j+1 And V _L The remaining elements of 'until all elements of U' are at V _L ' find similar elements, let the found subset elements be V _L ”，

Otherwise, consider V _L 'there are no subset elements similar to U';

5c4) Repeating the steps 5c 2) and 5c 3) until U' is constructed with all V of different starting points L _L ' complete search comparison, choose E _L Smallest subset element V _L "makeFor optimum results, P is thereby obtained ₀ ＝{P _0,1 ，P _0,2 ，…,P _0,j ，…,P _0,J } set of matching points P ₁ ’＝{P _1,1 ’，P _1,2 ’，…,P _1,j ’，P _1,J ’}。

Further, in the step 5 g), the specific calculation process is as follows:

A. b and C are three adjacent nodes on the grid, A ', B ' and C ' are three nodes after deformation, wherein ≈ BAC = theta, B ' A ' C ' = theta ',

then strain epsilon _x 、ε _y 、γ _xy The calculation formula of (c) is:

/>

principal strain epsilon ₁ 、ε ₂ Respectively as follows:

the strain of the virtual grid nodes adopts the strain average value of the surrounding virtual triangular grid.

Compared with the prior art, the invention has the following beneficial effects: the strain testing method based on three-dimensional geometric shape matching can obtain the strain distribution of the surface of a sample according to the matching analysis of geometric shape data when the picture of the deformation process of the surface of the sample does not exist or the definition of the picture is not enough, and is a new way for carrying out strain measurement different from the traditional digital speckle image analysis method.

Drawings

FIG. 1 is a three-dimensional topography information data diagram of a surface observation area of a measured sample;

fig. 2 is a schematic diagram of uniform deformation of a triangular mesh.

Detailed Description

The invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings and specific examples, which are not intended to limit the invention.

The invention provides a strain testing method based on three-dimensional geometric shape matching, which comprises the following steps:

1) Processing the surface of a tested sample to form a surface appearance with a micron-scale roughness structure;

the surface of the tested sample can be treated by adopting methods such as mechanical, chemical corrosion or spraying;

2) Obtaining micron-sized three-dimensional shape data of the surface investigation region of the tested sample by adopting laser interference or other methods, and recording as M ₀ ，M ₀ Three-dimensional topography data of a surface investigation region of a sample to be measured at an initial time, M ₀ A plurality of three-dimensional data points P containing the peak/valley height information of the examined area on the surface of the tested sample ₀ (X _i ，Y _i ，Z _i ) The structure is shown in figure 1;

3) Continuously measuring the three-dimensional morphology information of the surface investigation region of the sample to be measured by adopting methods such as laser interference and the like in the process that the sample to be measured bears the external force and deforms until the test is stopped, measuring the three-dimensional morphology data of the surface investigation region of the sample to be measured according to the sampling time interval delta t after the initial moment, and respectively marking as M ₁ 、M ₂ 、…、M _n And the maximum strain generated by comparing the next three-dimensional shape data with the previous three-dimensional shape data in the two adjacent three-dimensional shape data is not more than 5%;

4) For the three-dimensional shape data M recorded in the step 2) and the step 3) ₀ 、M ₁ 、…、M _n Carrying out treatment;

4a) For recorded three-dimensional shape data M ₀ 、M ₁ 、…、M _n Fitting to obtain the projection point, the projection height and the normal vector of each point on the respective median plane, and the specific process is as follows:

4a1) Calculating M ₀ Each point P on ₀ (X _i ，Y _i ，Z _i ) Projection point Q on median plane Q ₀ (x _i ，y _i ，z _i ) And projectionHeight h ₀ (x _i ，y _i ，z _i ) Wherein P is ₀ (X _i ，Y _i ，Z _i ) The nearby median plane Q adopts a binomial expression:

z＝f(x，y)＝ax ² +by ² +cxy+d

to P ₀ (X _i ，Y _i ，Z _i ) Fitting three-dimensional data points in a region with a center and a radius of R, P ₀ (X _i ，Y _i ，Z _i ) The projection height on the median plane Q satisfies:

/>

wherein (x, y, z) ∈ z = f (x, y), (x) _i ，y _i ，z _i ) Is the projection point Q which makes formula (1) take the minimum value ₀ Coordinates;

point Q ₀ (x _i ，y _i ，z _i ) The normal vector at (a) is:

4a2) Calculating M according to the fitting method of the step 4a 1) ₁ 、M ₂ 、…、M _n The projection point coordinates, the projection height and the normal vector of each point on the respective median plane;

4b) For three-dimensional shape data M ₀ 、M ₁ 、…、M _n The projection height of each point on the respective median plane is normalized, and the specific process is as follows:

4b1) Will M ₀ All of (1) h ₀ (x _i ，y _i ，z _i ) Sorting according to the sequence from big to small, taking the average value of the first m as the maximum value h _max The average of the last m is taken as the minimum value h _min According to

Carrying out normalization processing to obtain each projection point Q ₀ (x _i ，y _i ，z _i ) Normalized height value g of ₀ (x _i ，y _i ，z _i ) Wherein, when g ₀ (x _i ，y _i ，z _i )>When 1, order

4b2) Calculating M according to the normalization method of step 4b 1) ₁ 、M ₂ 、…、M _n The normalized height value of the projection height of each point in the image;

5) Calculating the strain of the inspected area on the surface of the tested sample

The deformation of the inspected area on the surface of the tested sample is corresponding to the change of the median plane in space, and M is used ₀ Dividing the virtual grid by the median plane Q, and analyzing the virtual grid in the subsequent M by correlation matching ₁ 、M ₂ …、M _n Finding the corresponding position of each node of the virtual grid on each median plane, and then calculating the strain of the surface investigation region of the tested sample by the side length change of a triangle formed by the nodes of the virtual grid and the assumption of uniform strain, wherein the specific process comprises the following steps:

5a)M ₀ the median plane Q divides the virtual grid into M ₀ Upper projected point Q ₀ (x _i ，y _i ，z _i ) The formed median plane Q is subdivided into small L multiplied by L square areas, and the specific division method is as follows:

get M ₀ All of Q of ₀ (x _i ，y _i ，z _i ) Mean value of coordinates of

And average of normal vectors

Taking a straight line as a parameter>

Two mutually perpendicular sets of planes parallel to the line, the planes of each set being spaced apart by a distance L (L)<2 ρ) of the two sets of planes intersect the median plane Q, cutting the median plane Q into N ₀ Each region with the size of L multiplied by L, the intersection point of the intersection line of the two groups of planes and the middle plane Q is a node of the virtual grid, and the number of the nodes is N;

5b) Determining M ₀ And M ₁ Feature data point set for matching analysis

Let P (x) ₀ ,y ₀ ,z ₀ ) Is M ₀ One of N nodes on median plane Q, taken as P (x) ₀ ,y ₀ ,z ₀ ) The projection data points (including more than 4 peak-valley height data points) with the center and the radius within the range of rho are calculated according to the normalized height value g ₀ (x _i ,y _i ,z _i ) Sorting from big to small, taking the top J ₁ (J ₁ Not less than 2) and the rearmost J ₂ (J ₂ Not less than 2) data to form a feature data point set P of matching analysis ₀ ＝{P _0,1 ，P _0,2 ，…,P _0,j ，…,P _0,J }(J＝J ₁ +J ₂ ≥4)；

TABLE 1M ₀ Characteristic data points of (1) for matching analysis

Matching data points

P 0,1

P 0,2

…

P 0,j

…

P 0,J

Point coordinates

(x 1 ,y 1 ,z 1 )

(x 1 ,y 1 ,z 1 )

…

(x j ,y j ,z j )

…

(x J ,y J ,z J )

Height value

g 0 (x 1 ,y 1 ,z 1 )

g 0 (x 1 ,y 1 ,z 1 )

…

g 0 (x j ,y j ,z j )

…

g 0 (x J ,y J ,z J )

Let M ₁ Neutral P (x) ₀ ,y ₀ ,z ₀ ) The matched point is at P' (x) ₀ ’,y ₀ ’,z ₀ ') near, take P' (x) ₀ ’,y ₀ ’,z ₀ ') as a center and a radius of ρ ' (ρ '>ρ) of the projected data points in accordance with the normalized height value g ₁ (x _k ,y _k ,z _k ) Sorting from big to small, and taking the top K ₁ (K ₁ ≥J ₁ ) Last and last K ₂ (K ₂ ≥J ₂ ) The data form a characteristic data point set P of matching analysis ₁ ＝{P _1,1 ，P _1,2 ，…,P _1,k ，…,P _1,K }，K＝K ₁ +K ₂ ；

TABLE 2M ₁ Characteristic data points of (1) for matching analysis

Matching data points

P 1,1

P 1,2

…

P 1,k

…

P 1,K

Point coordinates

(x 1 ’,y 1 ’,z 1 ’)

(x 2 ’,y 2 ’,z 2 ’)

…

(x k ’,y k ’,z’ k )

…

(x K ’,y K ’,z K ’)

Height value

g 1 (x 1 ’,y 1 ’,z 1 ’)

g 1 (x 2 ’,y 2 ’,z 2 ’)

…

g 1 (x k ’,y k ’,z’ k )

…

g 1 (x K ’,y K ’,z K ’)

5c) Matching according to the characteristic data points in step 5 b)

According to M ₀ And M ₁ Respectively constructing feature vector sets U and V by using middle feature data points _L Further constructing data sets U' and V to facilitate matching analysis _L '; the elements in U' are the same as V _L ' the elements in the above are compared and analyzed (considering normalized height values of two end points of the vector, the length of the vector and the position relationship between the vectors), and each data set V is found _L Best matching subset of V of' Zhou and U _L ", then from all V _L (L = 1-K) to find the best matching subset, resulting in M ₁ Set of best matching points P in (1) ₁ ’＝{P _1,1 ’，P _1,2 ’，…,P _1,j ’，P _1,J ' }, the specific process is as follows:

5c1) With P ₀ ＝{P _0,1 ，P _0,2 ，…,P _0,j ，…,P _0,J Constructing a vector set with the 1 st point as a starting point

J-1 vector sets U are sorted from large to small according to vector length, an included angle alpha between each vector in U and the first vector is calculated, and a new data set U' = for matching analysis is obtained{U ₁ ，U ₂ ，…，U _j ，…，U _J-1 }, each sub-element U _j Including the starting point P of the vector _s End point P _e Length of vector L _j Angle alpha between vectors _j I.e. U _j ＝{P _s ，P _e ，L _j ，α _j }；

5c2) With P ₁ ＝{P _1,1 ，P _1,2 ，…,P _1,k ，…,P _1,K Constructing a set of vectors starting at the L-th point in the equation

L is not equal to K, K-1, and has K different vector sets V _L (ii) a Set of vector quantities V _L Sorting according to the vector length from large to small, and calculating V _L The included angle beta between each vector and the first vector is obtained to obtain a new data set V for matching analysis _L ’＝{V _L,1 ，V _L,2 ，…，V _L,k ，…，V _L,K-1 V, each sub-element V _L,k Including the starting point P of the vector _s ', end point P _e ', vector length L _k ' vector included angle beta _k I.e. V _L,k ＝{P _s ’，P _e ’，L _k ’，β _k }；

5c3) Will U' = { U = ₁ ，U ₂ ，…，U _j ，…，U _J-1 Each of the elements U _j Same V _L ’＝{V _L,1 ，V _L,2 ，…，V _L,k ，…，V _L,K-1 Carry out matching analysis on the elements in the sequence, if the element U is in the sequence _j ＝{P _s ，P _e ，L _j ，α _j And element V _L,k ＝{P _s ’，P _e ’，L _k ’，β _k The following conditions are satisfied:

(1-μ)|g ₀ (P _s )|<|g ₀ (P _s )-g ₁ (P′ _s )|<(1+μ)|g ₀ (P _s )|

(1-μ)|g ₀ (P _e )|<|g ₀ (P _e )-g ₁ (P′ _e )|<(1+μ)|g ₀ (P _e )|

(1-μ)L _j <|L _j -L _k ′|<(1+μ)L _j

(1-μ)α _j <|α _j -β _k |<(1+μ)α _j

wherein mu = 0.03-0.10

Then consider U _j And V _L,k Similarly, let e _j ＝|g ₀ (P _e )-g ₁ (P′ _e ) If else, continue to use U _j And V _L,k The latter elements are compared if at V _L ' found in and U _j Similar elements continue to compare U _j+1 And V _L The remaining elements of 'until all elements of U' are at V _L ' find similar elements, let the found subset element be V _L ”，

Otherwise, consider V _L 'there are no subset elements similar to U';

5c4) Repeating the steps 5c 2) and 5c 3) until U' is constructed with all V of different starting points L _L ' complete search comparison, select E _L Smallest subset element V _L "as an optimal result, thereby obtaining P ₀ ＝{P _0,1 ，P _0,2 ，…,P _0,j ，…,P _0,J } set of matching points P ₁ ’＝{P _1,1 ’，P _1,2 ’，…,P _1,j ’，P _1,J ’}；

5d) Coordinate computation of grid nodes

According to the corresponding relation of the matching points, adopting first-order affine transformation:

wherein (x) _i ,y _i ,z _i ) Is P ₀ Coordinates of the midpoint, (x) _i ’,y _i ’,z _i ') is P ₁ ' in corresponds to (x) _i ,y _i ,z _i ) U, v, w are the coordinates of the matching point of (c), and u, v, w are the node P (x) ₀ ,y ₀ ,z ₀ ) Δ x, Δ y, Δ z are points (x) _i ,y _i ,z _i ) And P (x) ₀ ,y ₀ ,z ₀ ) The first order linear system of equations can be obtained:

solving the system of equations can yield

Is the optimal solution of, then M ₁ Neutral P (x) ₀ ,y ₀ ,z ₀ ) Corresponding node P' (x) ₀ ’,y ₀ ’,z ₀ ') coordinates are:

5e) According to the matched node pair P (x) ₀ ,y ₀ ,z ₀ ) And P' (x) ₀ ’,y ₀ ’,z ₀ ') respectively obtaining M by the method of steps 5 b) to 5 d) by diverging to the neighboring nodes around ₁ Neutral M ₀ Virtual grid node coordinates matched with other grid nodes;

5f) Obtaining M according to the method of steps 5 b) to 5 e) ₂ 、…、M _n Corresponding virtual grid node coordinates in (1);

5g) Calculating the grid strain, wherein the strain of the virtual grid is calculated according to the side length change of the triangle and the assumption of uniform strain, and the specific calculation process is as follows:

as shown in fig. 2, a, B and C are three adjacent nodes on the grid, a ', B ' and C ' are three nodes after deformation, wherein ≈ BAC = θ, and ≈ B ' a ' C ' = θ ',

then strain epsilon _x 、ε _y 、γ _xy The calculation formula of (2) is as follows: />

Principal strain epsilon ₁ 、ε ₂ Respectively as follows:

the strain of the virtual grid nodes adopts the strain average value of the surrounding virtual triangular grid.

Claims (8)

1. A strain testing method based on three-dimensional geometric shape matching is characterized by comprising the following steps: the strain testing method comprises the following steps:

1) Processing the surface of a tested sample to form a surface appearance with a micron-scale roughness structure;

2) Sampling to obtain micron-sized three-dimensional shape data of the inspected area on the surface of the tested sample, and recording the data as M ₀ ，M ₀ Three-dimensional topography data of a surface investigation region of a sample to be measured at an initial time, M ₀ A plurality of three-dimensional data points P containing the peak/valley height information of the examined area on the surface of the tested sample ₀ (X _i ，Y _i ，Z _i ) Forming;

3) Continuously measuring the three-dimensional topography information of the surface investigation region of the measured sample in the process that the measured sample bears external force and deforms until the test is stopped, measuring the three-dimensional topography data of the surface investigation region of the measured sample according to a sampling time interval delta t after the initial moment, and respectively recording as M ₁ 、M ₂ 、…、M _n ；

4) For the three-dimensional shape data M recorded in the step 2) and the step 3) ₀ 、M ₁ 、…、M _n Carrying out treatment;

4a) For recorded three-dimensional shape data M ₀ 、M ₁ 、…、M _n Fitting to obtain the projection point, the projection height and the normal direction of each point on the respective median planeA vector;

4b) For three-dimensional shape data M ₀ 、M ₁ 、…、M _n The projection height of each point in the image on the respective median plane is normalized;

5) Calculating the strain of the inspected area on the surface of the tested sample

The deformation of the inspected area on the surface of the tested sample is corresponding to the change of the median plane in space, and M is ₀ Dividing the virtual grid by the median plane Q, and analyzing the subsequent M by correlation matching ₁ 、M ₂ …、M _n Finding out the corresponding position of each node of the virtual grid on each median plane, and then calculating the strain of the surface investigation area of the sample to be measured according to the side length change of a triangle formed by the nodes of the virtual grid and the assumption of uniform strain.

2. The strain testing method based on three-dimensional geometric shape matching according to claim 1, characterized in that: in the step 3), the maximum strain generated by the next three-dimensional shape data in the two adjacent three-dimensional shape data compared with the previous three-dimensional shape data is not more than 5%.

3. The strain testing method based on three-dimensional geometric shape matching according to claim 1, characterized in that: in the step 4 a), the specific process is as follows:

4a1) Calculating M ₀ Each point P on ₀ (X _i ，Y _i ，Z _i ) Projection point Q on median plane Q ₀ (x _i ，y _i ，z _i ) And a projection height h ₀ (x _i ，y _i ，z _i ) Wherein P is ₀ (X _i ，Y _i ，Z _i ) The nearby median plane Q adopts a binomial expression:

z＝f(x,y)＝ax ² +by ² +cxy+d

to P ₀ (X _i ，Y _i ，Z _i ) Fitting three-dimensional data points in a region with a center and a radius of R, P ₀ (X _i ，Y _i ，Z _i ) The projection height on the median plane Q satisfies:

wherein (x, y, z) ∈ z = f (x, y), (x) _i ，y _i ，z _i ) Is the projection point Q at which the formula (1) takes the minimum value ₀ Coordinates;

point Q ₀ (x _i ，y _i ，z _i ) The normal vector at (a) is:

4a2) Calculating M according to the fitting method of the step 4a 1) ₁ 、M ₂ 、…、M _n The projection point coordinates, the projection height and the normal vector of each point on the respective median plane.

4. The strain testing method based on three-dimensional geometric shape matching according to claim 1, characterized in that: in the step 4 b), the specific process is as follows:

4b1) Will M ₀ All of (1) h ₀ (x _i ，y _i ，z _i ) Sorting according to the sequence from big to small, and taking the average value of the first m as the maximum value h _max And the average value of the last m is taken as the minimum value h _min According to

Carrying out normalization processing to obtain each projection point Q ₀ (x _i ，y _i ，z _i ) Normalized height value g of ₀ (x _i ，y _i ，z _i ) Wherein, when g ₀ (x _i ，y _i ，z _i )>When 1, order

4b2) Calculating M according to the normalization method of step 4b 1) ₁ 、M ₂ 、…、M _n The normalized height value of the projection height of each point in the image.

5. The strain testing method based on three-dimensional geometric shape matching according to claim 1, characterized in that: in the step 5), the specific process is as follows:

5a)M ₀ the median plane Q divides the virtual grid into M ₀ Upper by projection point Q ₀ (x _i ，y _i ，z _i ) The formed middle level surface Q is subdivided into small square areas of L multiplied by L,

5b) Determining M ₀ And M ₁ Feature data point set for matching analysis

Let P (x) ₀ ,y ₀ ,z ₀ ) Is M ₀ One of N nodes on the median plane Q is taken as P (x) ₀ ,y ₀ ,z ₀ ) As a central projection data point with a radius within a range of rho according to a normalized height value g ₀ (x _i ,y _i ,z _i ) Sorting from big to small, and taking the front J ₁ (J ₁ Not less than 2) and the last J ₂ (J ₂ Not less than 2) data to form a feature data point set P of matching analysis ₀ ＝{P _0,1 ，P _0,2 ，…,P _0,j ，…,P _0,J }(J＝J ₁ +J ₂ ≥4)；

Let M ₁ Neutral P (x) ₀ ,y ₀ ,z ₀ ) The matched point is at P' (x) ₀ ’,y ₀ ’,z ₀ ') near, take P' (x) ₀ ’,y ₀ ’,z ₀ ') as a center and a radius of ρ ' (ρ '>ρ) of the projected data points in accordance with the normalized height value g ₁ (x _k ,y _k ,z _k ) Sorting from big to small, and taking the top K ₁ (K ₁ ≥J ₁ ) Last and last K ₂ (K ₂ ≥J ₂ ) The data form a characteristic data point set of matching analysisP ₁ ＝{P _1,1 ，P _1,2 ，…,P _1,k ，…,P _1,K }，K＝K ₁ +K ₂ ；

5c) Matching according to the characteristic data points in step 5 b)

According to M ₀ And M ₁ Constructing feature vector sets U and V respectively by middle feature data points _L Further constructing data sets U' and V to facilitate matching analysis _L '; the elements in U' are the same as V _L ' the elements in the data set are compared and analyzed to find each data set V _L Best matching subset of V of' Zhou and U _L ", then from all V _L Find the best matching subset of "(L = 1-K) to get M ₁ Best matching point set P in (1) ₁ ’＝{P _1,1 ’，P _1,2 ’，…,P _1,j ’，P _1,J ’}；

5d) Coordinate computation of grid nodes

According to the corresponding relation of the matching points, adopting first-order affine transformation:

wherein (x) _i ,y _i ,z _i ) Is P ₀ Coordinates of the midpoint, (x) _i ’,y _i ’,z _i ') is P ₁ In corresponds to (x) _i ,y _i ,z _i ) U, v, w are the coordinates of the matching point of (c), and u, v, w are the node P (x) ₀ ,y ₀ ,z ₀ ) Δ x, Δ y, Δ z are points (x) _i ,y _i ,z _i ) And P (x) ₀ ,y ₀ ,z ₀ ) The first order linear system of equations can be obtained:

solving the system of equations can yield

Is the optimal solution of, then M ₁ Neutralization of P (x) ₀ ,y ₀ ,z ₀ ) Corresponding node P' (x) ₀ ’,y ₀ ’,z ₀ ') coordinates are:

5e) According to the matched node pair P (x) ₀ ,y ₀ ,z ₀ ) And P' (x) ₀ ’,y ₀ ’,z ₀ ') respectively obtaining M by the method of steps 5 b) to 5 d) by diverging to the neighboring nodes around ₁ Neutralizing M ₀ Virtual grid node coordinates matched with other grid nodes;

5f) Determining M according to the method of steps 5 b) to 5 e) ₂ 、…、M _n Corresponding virtual grid node coordinates in (1);

5g) And calculating the grid strain, wherein the strain of the virtual grid is calculated according to the side length change of the triangle and the assumption of uniform strain.

6. The strain testing method based on three-dimensional geometric shape matching according to claim 5, characterized in that: in the step 5 a), the specific division method is as follows:

get M ₀ All of Q on ₀ (x _i ，y _i ，z _i ) Mean value of coordinates of

And average of normal vectors

Taking a straight line as a parameter>

Two mutually perpendicular sets of planes parallel to the line, the planes of each set being spaced apart by a distance L (L)<2 ρ) of the two sets of planes intersect the median plane Q, cutting the median plane Q into N ₀ And in each L multiplied by L-sized area, the intersection point of the intersection line of the two groups of planes and the middle plane Q is a node of the virtual grid, and the number of the nodes is N.

7. The strain testing method based on three-dimensional geometric shape matching according to claim 5, characterized in that: in the step 5 c), the specific process is as follows:

5c1) With P ₀ ＝{P _0,1 ，P _0,2 ，…,P _0,j ，…,P _0,J Constructing a vector set with the 1 st point as a starting point

J-1 vector sets U are sorted from large to small according to vector length, an included angle alpha between each vector in U and the first vector is calculated, and a new data set U '= { U' for matching analysis is obtained ₁ ，U ₂ ，…，U _j ，…，U _J-1 }, each sub-element U _j Including the starting point P of the vector _s End point P _e Length of vector L _j Angle alpha between vectors _j I.e. U _j ＝{P _s ，P _e ，L _j ，α _j }；

5c2) With P ₁ ＝{P _1,1 ，P _1,2 ，…,P _1,k ，…,P _1,K Constructing a set of vectors starting at the L-th point in the equation

L is not equal to K, K-1, and has K different vector sets V _L (ii) a Set of vector quantities V _L Sorting according to the vector length from large to small, and calculating V _L The included angle beta between each vector and the first vector is obtained to obtain a new data set V for matching analysis _L ’＝{V _L,1 ，V _L,2 ，…，V _L,k ，…，V _L,K-1 V, each sub-element V _L,k Including the starting point P of the vector _s ', end point P _e ', vector length L _k ' vector included angle beta _k I.e. V _L,k ＝{P _s ’，P _e ’，L _k ’，β _k }；

5c3) Will U' = { U = ₁ ，U ₂ ，…，U _j ，…，U _J-1 Each of the elements U _j Same as V _L ’＝{V _L,1 ，V _L,2 ，…，V _L,k ，…，V _L,K-1 Carry out matching analysis on the elements in the sequence, if the element U is in the sequence _j ＝{P _s ，P _e ，L _j ，α _j And element V _L,k ＝{P _s ’，P _e ’，L _k ’，β _k The following conditions are satisfied:

(1-μ)|g ₀ (P _s )|<|g ₀ (P _s )-g ₁ (P′ _s )|<(1+μ)|g ₀ (P _s )|

(1-μ)|g ₀ (P _e )|<|g ₀ (P _e )-g ₁ (P′ _e )|<(1+μ)|g ₀ (P _e )|

(1-μ)L _j <|L _j -L _k ′|<(1+μ)L _j

(1-μ)α _j <|α _j -β _k |<(1+μ)α _j

wherein mu = 0.03-0.10

Then consider U _j And V _L,k Similarly, let e _j ＝|g ₀ (P _e )-g ₁ (P′ _e ) If else, continue to use U _j And V _L,k The latter elements are compared if at V _L ' found in and U _j Similar elements continue to compare U _j+1 And V _L The remaining elements of 'until all elements of U' are at V _L ' find similar elements, let the found subset element be V _L ”，

Otherwise, consider V _L ' there is no subset element similar to UA peptide;

5c4) Repeating the steps 5c 2) and 5c 3) until U' is constructed with all V of different starting points L _L ' complete search comparison, select E _L Smallest subset element V _L "as an optimal result, thereby obtaining P ₀ ＝{P _0,1 ，P _0,2 ，…,P _0,j ，…,P _0,J Set of matching points P of ₁ ’＝{P _1,1 ’，P _1,2 ’，…,P _1,j ’，P _1,J ’}。

8. The strain testing method based on three-dimensional geometric shape matching according to claim 5, characterized in that: in the step 5 g), the specific calculation process is as follows:

A. b and C are three adjacent nodes on the grid, A ', B ' and C ' are three nodes after deformation, wherein ≈ BAC = theta, B ' A ' C ' = theta ',

then strain epsilon _x 、ε _y 、γ _xy The calculation formula of (2) is as follows:

principal strain epsilon ₁ 、ε ₂ Respectively as follows:

the strain of the virtual grid nodes adopts the strain average value of the surrounding virtual triangular grid.

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