Full-field strain measurement method of crack discontinuity region based on error control

Abstract

The present invention provides a full-field strain measurement method for a crack discontinuity zone based on error control. The method divides an unstable zone into a plurality of continuous sub-zones according to the error, and then calculates the displacement and strain of each sub-zone respectively, thereby effectively reducing the calculation result error of the crack zone and improving the calculation accuracy of the full-field strain measurement. That is, the calculation problem of the discontinuous boundary near the crack during the cracking process of the measured object can be handled more accurately, thereby making the calculation result of the crack zone boundary more accurate, and being able to more accurately extract the discontinuous discontinuity surface of the crack zone.

Description

Technical Field

[0001] The invention relates to an application field of digital image correlation method, and in particular to a full-field strain measurement method of a crack discontinuity zone based on error control. Background Art

[0002] With the continuous advancement of optical technology, optical measurement has the advantages of non-contact, full-field, high spatial resolution and high precision. Traditional strain measurement requires the experimenter to accurately judge the patch position and perform operations such as affixing strain gauges. Optical strain measurement is gradually replacing traditional strain measurement. The experimental data obtained is more convenient and comprehensive, and the strain information obtained is more accurate and complete.

[0003] Digital image correlation (DIC) is one of the main methods for optically measuring strain fields and has been widely used in material experiments. However, this method still has many problems that need to be further optimized, such as fluctuations in illumination intensity, various noises during image acquisition, and rounding errors in image pixel integerization and calculation procedures, which will affect the measured displacement and strain fields.

[0004] The displacement accuracy of the DIC method compiled by related literature or reported by commercial software is usually between ±0.02 and ±0.1 pixels. Due to the low accuracy, it is impossible to directly calculate the strain through DIC difference. The existing technology proposes a full-field strain solution method using local least squares fitting, which can effectively suppress noise and thus improve the accuracy of strain measurement.

[0005] However, when processing the crack area, the above-mentioned prior art, since the deformation is no longer continuous, if the local least squares fitting method is still used for solving, the discontinuous data will be over-smoothed, thereby causing an increase in the error of the calculation result at the crack boundary position. Summary of the invention

[0006] The object of the present invention is to provide a full-field strain measurement method for a crack discontinuity zone based on error control, aiming to reduce the calculation result error in the crack area and improve the calculation accuracy of the full-field strain measurement.

[0007] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0008] A full-field strain measurement method for a crack discontinuity region based on error control, using a digital correlation method, wherein the image of the object to be measured before being deformed by a load is called a reference image, and the image after deformation is called a current image, is characterized in that it includes the following steps:

[0009] Step S, determining whether a displacement mutation occurs in the displacement field of the current image relative to the reference image;

[0010] Step A, when the displacement field does not have a sudden change, the region where the displacement field does not have a sudden change is a stable region, and the strain field is calculated using the local least squares method for the stable region;

[0011] Step B: when a sudden displacement occurs in the displacement field, the region where the sudden displacement field is located is an unstable region, the unstable region is divided into a plurality of continuous sub-regions according to the error, and then the displacement and strain are calculated for each sub-region respectively.

[0012] The above technical solution can be improved as follows:

[0013] As an improvement, the step S comprises the following steps:

[0014] Step S1, taking any point P(x, y) of the reference image and determining a region radius m;

[0015] Step S2: select an area with a size of A displacement field as the region And according to the current image, the region Perform displacement smoothing fitting on the points in the image to determine the discrete x-direction displacement data and discrete y-direction displacement data of each point;

[0016] Step S3, in the area A circular sub-region Ω is selected from the discrete x-direction displacement data and the discrete y-direction displacement data, and a displacement error of each point in the circular sub-region Ω is calculated;

[0017] Step S4, giving a first threshold δ 0 , determine whether the displacement error is less than the first threshold value. If so, it is considered that the displacement field does not have a sudden displacement change. If not, it is considered that the displacement field has a sudden displacement change.

[0018] As a further improvement, the step B comprises the following steps:

[0019] Step B1, using a one-dimensional local least square method for the points in the unstable region to obtain an x-direction displacement error and a y-direction displacement error;

[0020] Step B2, given a second threshold, the x-direction displacement error and the y-direction displacement error of the point are compared with the second threshold respectively, if they are higher than the second threshold, the area where the point is located is an invalid area, if they are lower than the second threshold, the area where the point is located is a valid area;

[0021] Step B3, performing displacement smoothing fitting on the points in the effective area, and calculating the strain field of each point in the effective area.

[0022] Compared with the prior art, the above technical solution has the following beneficial effects:

[0023] By dividing the unstable area into several continuous sub-areas according to the error, and then calculating the displacement and strain of each sub-area respectively, the calculation result error of the crack area is effectively reduced, and the calculation accuracy of the full-field strain measurement is improved. That is, the calculation problem of the discontinuous boundary near the crack during the cracking process of the measured object can be handled more accurately, so that the calculation result of the crack area boundary is more accurate, and the discontinuous discontinuity surface of the crack area can be extracted more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 Schematic diagram of local data points for calculating displacement field using the least squares method;

[0025] Figure 2 Schematic diagram of calculation of data points for full-field strain measurement of crack discontinuity region based on error control;

[0026] Figure 3 Comparison of strain results calculated by different methods in uniaxial tension test;

[0027] Figure 4 Comparison of absolute strain errors between the traditional method and the optimized method in uniaxial tensile tests. DETAILED DESCRIPTION

[0028] The present invention provides a full-field strain measurement method for a crack discontinuity zone based on error control. The specific steps of the measurement method are as follows.

[0029] Step S, determining whether a displacement mutation occurs in the displacement field of the current image relative to the reference image.

[0030] Step S specifically includes the following steps:

[0031] Step S1, taking any point P(x, y) of the reference image and determining a region radius m;

[0032] Specifically, to solve the deformation of any point (x, y) in the reference image, it can be measured by calculating the deformation of a sub-region centered on the point. Assuming that the region radius is m, the sub-region centered on the point occupies s = (2m+1) × (2m+1) pixels.

[0033] Step S2: select an area with a size of A displacement field as the region And according to the current image, the region Perform displacement smoothing fitting on the points in the image to determine the discrete x-direction displacement data and discrete y-direction displacement data of each point;

[0034] Specifically, the displacement smoothing fitting function uses a two-dimensional first-order polynomial. For any point (x, y) in the sub-region, we have

[0035]

[0036]

[0037] Where Δx=xx i , Δy=yy j ,(x i ,y j ) is the coordinate of the center point of the sub-region, a 0 、a 1 、a 2 、b 0 、b 1 、b 2 are the coefficients of the fitting polynomial to be determined, and are the discrete x- and y-direction displacement data points.

[0038] Step S3, in the area A circular sub-region Ω is selected from the discrete x-direction displacement data and the discrete y-direction displacement data, and a displacement error of each point in the circular sub-region Ω is calculated;

[0039] Specifically, the region size is selected as In order to reduce the excessive influence of boundary data on central data, Select a circular sub-region in like Figure 1 shown.

[0040] Step S4, given a first threshold, determines whether the displacement error is less than the first threshold, if so, it is considered that no displacement mutation occurs in the displacement field, if not, it is considered that a displacement mutation occurs in the displacement field.

[0041] Specifically, the displacement error is expressed using the 1-norm as follows:

[0042]

[0043]

[0044] However, the actual region boundary may be an arbitrary line or a surface, such as Figure 2 As shown, the calculated δu is calculated according to the given first threshold δ 0It is divided into three areas, two stable areas and one unstable area.

[0045] Due to different external environments, factors such as noise and window size are different, the first threshold δ 0 Usually, 2 to 4 times the average value of all data within a certain percentage (such as the first 50%, sorted from small to large) of the error displacement field δu can be selected.

[0046] Step A, when the displacement field does not have a sudden change, the region where the displacement field does not have a sudden change is a stable region, and the strain field is calculated using the local least squares method for the stable region;

[0047] Step B: when a sudden displacement occurs in the displacement field, the region where the sudden displacement field is located is an unstable region, the unstable region is divided into a plurality of continuous sub-regions according to the error, and then the displacement and strain are calculated for each sub-region respectively.

[0048] The above step B specifically includes the following steps:

[0049] Step B1, using a one-dimensional local least square method for the points in the unstable region to obtain an x-direction displacement error and a y-direction displacement error;

[0050] Specifically, the two-dimensional local least squares method is transformed into a one-dimensional local least squares method in two directions, as follows: Figure 2 The calculation formulas for displacement and displacement error are as follows:

[0051]

[0052]

[0053]

[0054]

[0055] Step B2: give a second threshold αδ 0 / N Ω , comparing the x-direction displacement error and the y-direction displacement error of the point with the second threshold value respectively, if they are higher than the second threshold value, the area where the point is located is an invalid area, and if they are lower than the second threshold value, the area where the point is located is a valid area;

[0056] Specifically, δu x and δu y The second threshold is used to divide the area again, and the unstable boundary area is determined by the second threshold, that is, to distinguish the effective area from the invalid area, and the formulas (5) and (6) are used for fast fitting. When the displacement error is greater than the second threshold αδ 0 / NΩ (α is a coefficient, ranging from 1 to 2 according to different external environments, N Ω The points (the total number of points in the circular sub-area) are removed, and the area composed of the removed points is the invalid area, and the rest are the valid areas.

[0057] like Figure 2 As shown, area 1 and area 2 are valid areas, area 3 is the boundary between areas 1 and 2, and area 3 may be a line or an area with width (with multiple cracks or discontinuous areas), which is an invalid area.

[0058] Step B3, performing displacement smoothing fitting on the points in the effective area, and calculating the strain field of each point in the effective area.

[0059] Specifically, after the area is divided, the calculation is as follows Figure 2 When the area 2 shown is taken, the valid pixel points in the circular window are calculated, such as Figure 2 The square points in the lower half are shown, and points in the effective area or stable area are added to compensate for the noise caused by the reduction of effective points. The closer the added points are to the calculation points, the better, and they are within the diameter of the sub-area. The calculation of area 1 is similar to that of area 2, that is, the effective pixel points in the circular window are taken for calculation, such as Figure 2 The valid points in the upper area 1 are shown, and points in the valid area or stable area are also added to compensate for the noise influence caused by the reduction in the number of valid points. The added points are as close to the calculation points as possible and are within the diameter range of the sub-area.

[0060] In order to improve the calculation accuracy of the discontinuous area and reduce noise, the displacement smoothing fitting function of the unstable area is described by a two-dimensional quadratic polynomial as follows:

[0061] u(Δx, Δy)=a 0 +a 1 Δx+a 2 Δy+a 3 ΔxΔy+a 4 Δx 2 +a 5 Δy 2 (9)

[0062] v(Δx, Δy) = b 0 +b 1 Δx+b 2 Δy+b 3 ΔxΔy+b 4 Δx 2 +b 5 Δy 2 (10)

[0063] After the area is divided, the strain field in area 3 is no longer calculated because the strain field error is large. The strain fields in areas 1 and 2 can be effectively calculated. Since the strain field of an arbitrary point can be calculated from multiple points near it, the point with the smallest error is selected for calculation, and its strain expression is:

[0064]

[0065]

[0066]

[0067] The following uniaxial tension model experiment verifies the effectiveness of the present invention. The plane size of the uniaxial tension model is 201 mm × 247 mm (X × Y), and the load is along the X direction. The image region (ROI) size of the calculation is set to 201 pixels × 201 pixels, where the circular sub-regions for displacement calculation and stress calculation are:

[0068]

[0069] That is, a circular sub-region with a radius of 15 pixels (recorded as 31 pixels × 31 pixels), and a calculation step of 1 pixel. The first threshold is obtained by calculation as follows:

[0070]

[0071] The second threshold is as follows:

[0072] αδ 0 / N Ω =0.0027mm(α=1);

[0073] Finally, by comparing the strain results calculated by theoretical calculation, traditional DIC method and optimized DIC method, Figure 3 and Figure 4 As shown in the figure, the optimization method is very close to the results of theoretical calculation. Compared with the traditional DIC calculation method, it greatly reduces the calculation error and improves the calculation accuracy of the crack discontinuity zone.

Claims

1. A full-field strain measurement method for a crack discontinuity region based on error control, using digital correlation method processing, the image of the object to be measured before being loaded and deformed is called the reference image, and the image after deformation is called the current image, characterized in that: The steps include: Step S, determining whether a displacement mutation occurs in the displacement field of the current image relative to the reference image; Step A, when the displacement field does not have a sudden change, the region where the displacement field does not have a sudden change is a stable region, and the strain field is calculated using the local least squares method for the stable region; Step B, when a sudden displacement occurs in the displacement field, the region where the sudden displacement field is located is an unstable region, the unstable region is divided into a plurality of continuous sub-regions according to the error, and the displacement and strain are calculated for each of the sub-regions respectively; The step S comprises the following steps: Step S1, taking any point P(x, y) of the reference image and determining a region radius m; Step S2: select an area with a size of A displacement field as the region And according to the current image, the region Perform displacement smoothing fitting on the points in the image to determine the discrete x-direction displacement data and discrete y-direction displacement data of each point; Step S3, in the area A circular sub-region Ω is selected from the discrete x-direction displacement data and the discrete y-direction displacement data, and a displacement error of each point in the circular sub-region Ω is calculated; Step S4, given a first threshold, determining whether the displacement error is less than the first threshold, if so, it is considered that the displacement field does not have a sudden displacement change, if not, it is considered that the displacement field has a sudden displacement change; The step B comprises the following steps: Step B1, using a one-dimensional local least square method for the points in the unstable region to obtain an x-direction displacement error and a y-direction displacement error; Step B2, given a second threshold, the x-direction displacement error and the y-direction displacement error of the point are compared with the second threshold respectively, if they are higher than the second threshold, the area where the point is located is an invalid area, if they are lower than the second threshold, the area where the point is located is a valid area; Step B3, performing displacement smoothing fitting on the points within the effective area, and calculating the strain field of each point within the effective area; In the step S1, the deformation of a sub-region centered on the point is calculated. If the region radius is m, the sub-region centered on the point occupies s=(2m+1)×(2m+1) pixels; In step S2, the displacement smoothing fitting function adopts a two-dimensional first-order polynomial. For any point (x, y) in the sub-region, there is Where Δx=xx i , Δy=yy j ,(x i ,y j ) is the coordinate of the center point of the sub-region, a0, a1, a2, b0, b1, b2 are the coefficients of the fitting polynomial to be calculated, and are the discrete x- and y-direction displacement data points; In step S3, the size of the selected area is In the area Select a circular subregion in: In step S3, the displacement error is expressed using the 1-norm as follows: The calculated δ u According to the given first threshold δ0, it is divided into three regions, two stable regions and one unstable region; In step B1, the two-dimensional local least squares method is transformed into a one-dimensional local least squares method in two directions, and the calculation formulas for displacement and displacement error are as follows: In step B2, the second threshold is αδ0 / N Ω , where α is a coefficient, ranging from 1 to 2 according to different external environments, N Ω is the total number of points in the circular sub-region, and δu x and δu y The second threshold is used to divide the area again, and the unstable boundary area is determined by the second threshold, that is, to distinguish the effective area from the invalid area, and the formulas (5) and (6) are used for fast fitting. When the displacement error is greater than the second threshold αδ0 / N Ω The points are removed, and the area formed by the removed points is the invalid area, and the rest are the valid area; In step B3, the displacement smoothing fitting function of the unstable region is described by a two-dimensional quadratic polynomial as follows: u(Δx,Δy)=a0+a1Δx+a2Δy+a3ΔxΔy+a4Δx 2 +a5Δy 2 (9);v(Δx,Δy)=b0+b1Δx+b2Δy+b3ΔxΔy+b4Δx 2 +b5Δy 2 (10)。

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