A method for determining uniform extension strain limit diagram of thin plates

Abstract

The invention discloses a method for determining a uniform extension strain limit diagram of a thin plate, comprising pre-test processing, sample loading, strain identification point positioning, strain identification point strain output, strain-time curve drawing, non-uniform deformation critical moment determination, equivalent plastic strain calculation, true strain ratio fitting, uniform extension strain limit diagram drawing, repeating the steps to obtain (r, ε) of the remaining samples. eq ) and plotted in the FLD diagram; at the same time, the (r, ε eq ) take the average value (r, ε eq ) avg Plotted in the FLD diagram and connected. It conforms to the physical meaning of uniform and non-uniform deformation, rather than relying on experience or phenomenology to approximate, and more accurately characterizes the material properties; this method can evaluate the uniform deformation of the material including the strain path from the (-0.5,1) strain ratio, and the evaluation is more comprehensive, which can reflect the uniform deformation capabilities of different materials under different strain paths.

Description

Technical Field

[0001] The invention belongs to the technical field of cold forming of metal plates, and in particular relates to a method for determining a uniform extension strain limit diagram of a thin plate. Background Art

[0002] In engineering applications, thin plates need to be processed into parts of different shapes. This process is the forming process of thin plates. Formability is the key performance of thin plate machinability. The uniform elongation of thin plates is one of the important mechanical properties for evaluating the formability of materials. The larger the uniform elongation, the better the formability. Thin plate forming goes through elastic deformation, uniform plastic deformation and non-uniform plastic deformation stages from the beginning to fracture. Generally speaking, the uniform elongation A in the tensile test is used in engineering. gt To characterize the ability of a material to deform uniformly, such as Figure 1 As shown, the maximum load F in the tensile test max The corresponding engineering strain.

[0003] Uniform elongation of uniaxial tension A gt It is an important indicator for evaluating the formability of materials. However, with the emergence of new materials, the same A gt However, the materials show different formability during processing and forming, so the uniform elongation A of a single uniaxial stretch is used. gt There are limitations in using the maximum load value to evaluate the uniform deformation capacity of materials. There are mainly three problems: 1) Using the maximum load value to distinguish between uniform and non-uniform plastic deformation is limited. The concept of uniform plastic deformation is that under the same strain path loading, the plastic strain in the region is the same, otherwise it is non-uniform plastic deformation. The strain value corresponding to the maximum tensile load cannot be explained in a physical sense as the transformation of uniform deformation into non-uniform deformation; 2) Material forming is a complex strain process, which includes multiple strain paths (such as plane strain, biaxial tension and the states between them). Uniaxial tension is only one of the strain paths. If the uniaxial tension data is used to evaluate the whole The whole process is not rigorous enough and it is biased, especially with the current development and application of a large number of new materials. The organization of the material determines the different formability under different strain states. Therefore, it is necessary to comprehensively evaluate the uniform plastic deformation of the material; 3) The strain state of uniaxial tension is relatively simple, and there is a linear relationship between the load and stress values. The maximum load value can correspond to the (non-)uniform deformation. Under relatively complex strain states, the maximum load cannot reflect the boundary between uniform and non-uniform materials, and the stress value under complex strain states cannot be directly measured. Therefore, it is temporarily impossible to judge the uniform strain capacity of the material under other strain paths through the traditional maximum load. Summary of the invention

[0004] To overcome A gtIn order to solve the problem of accuracy in evaluating uniform elongation and its limitation of not being able to characterize uniform deformation capacity under different strain paths, the present invention proposes a more accurate and complete method for determining uniform elongation strain limit diagram of thin plates, which is suitable for evaluating uniform elongation of metal plates less than 3 mm under different strain paths.

[0005] To achieve the above object, a method for determining the forming limit of a thin plate based on time and position correlation is as follows:

[0006] 1) Pre-test treatment

[0007] Take p kinds of samples with different geometrical dimensions, and each sample has q pieces. Grid processing is performed on the surfaces of all samples, and the grid form matches the DIC measurement system.

[0008] 2) Loading the sample

[0009] The first specimen was loaded. During the loading process, the DIC measurement system was used to take photos of the deformation process of the first specimen. The photos at each moment were recorded, and the strain cloud map of the deformation surface of the first specimen at each moment was obtained. The first moment photo without deformation was recorded as stage-0, the second moment photo after loading was recorded as stage-1, the third moment photo was recorded as stage-2, and so on. When macroscopic cracks visible to the naked eye appeared, the loading test was stopped, and the last moment photo was recorded as stage-m, where m is a natural number.

[0010] 3) Strain identification point positioning

[0011] In the m strain cloud maps in step 2), find the fracture photo stage-n when the first specimen begins to crack, and 1<n<m, then trace back to the photo stage-n-1 at the previous moment of the fracture photo stage-n; record the point O where the principal strain is the largest in the crack area and the direction θ of the crack opening on the photo stage-n-1; then trace the point O back to the photo stage-0 at the first moment, make a cross-sectional line passing through the point O and perpendicular to the direction θ of the crack opening on the photo stage-0 at the first moment, and finally set z strain identification points on the cross-sectional line with the point O as the starting point on the photo stage-0 at the first moment;

[0012] 4) Strain output at strain identification point

[0013] Record the principal strain ε1, secondary strain ε2 and time t corresponding to the z strain identification points and point O in the photo at each moment in step 3), and calculate the thickness direction strain ε3 corresponding to the z strain identification points and point O in the photo at each moment by the volume invariance principle;

[0014] 5) Strain-time curve drawing

[0015] According to the thickness direction strain ε3 and time t corresponding to each strain identification point in the photo at each moment obtained in step 4), the ε3-t curve of each strain identification point is drawn. At the same time, according to the thickness direction strain ε3 and time t corresponding to point O in the photo at each moment obtained in step 4), the ε3-t curve of point O is drawn, and a total of z+1 ε3-t curves are obtained;

[0016] 6) Determination of critical moment of non-uniform deformation

[0017] When the difference between the minimum and maximum values ​​of the thickness strain ε3 at the z strain identification points and point O at the same time is 1-3%, it is considered that the sheet metal begins to undergo non-uniform deformation. The moment t i is the critical moment of uniform deformation and non-uniform deformation; at the same time, point O is at t i The principal strain ε1 and the secondary strain ε2 at the moment are recorded as the uniform limiting strain of the first specimen under the strain ratio r;

[0018] 7) Equivalent plastic strain ε eq Calculation

[0019] In order to fully characterize the deformability of the sheet metal, the equivalent plastic strain ε eq Represents the arrival time t i The plastic strain magnitude at point O;

[0020] 8) Fitting of the true strain ratio r

[0021] Fitting point O in the time region (0, t i )’s ε2-ε1 curve is linearly fitted with its slope k, which is recorded as the true strain ratio r;

[0022] 9) Draw a uniform extension strain limit diagram

[0023] The true strain ratio r calculated in step 8) and the ε calculated in step 7) are eq As a set of data (r, ε eq )1 is plotted in the figure, the X coordinate is the true strain ratio r, and the ordinate Y is the equivalent plastic strain value ε eq ;

[0024] 10) Repeat steps 2) to 9) to obtain the (r, ε) of the second to p×q groups of samples. eq ) and plotted in the FLD diagram; at the same time, the (r, ε eq ) take the average value (r, ε eq ) avg Draw in FLD diagram and connect the lines.

[0025] Furthermore, in the step 1), P is 5-10, and q is 3-5.

[0026] Furthermore, in the step 2), the frequency of taking pictures is 10 to 20 Hz.

[0027] Furthermore, in the step 3), z is 3 to 8, and the distance between each strain identification point is 1 mm or 2 mm, the distance between points close to point O is 1 mm, and the distance between points far from point O is 2 mm.

[0028] Furthermore, in step 4), the calculation formula (1) of the thickness direction strain ε3 is as follows:

[0029] ε1+ε2+ε3=0 (1).

[0030] Further, in step 7), ε eq Calculate using formula 2:

[0031]

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1) The boundary between uniform and inhomogeneous deformation has a clear calculation process, which conforms to the physical meaning of uniform and inhomogeneous deformation, rather than relying on experience or phenomenology to approximate, and more accurately characterizes the material properties;

[0034] 2) This method can evaluate the uniform deformation of the material including the strain path from the (-0.5, 1) strain ratio. The evaluation is more comprehensive and can reflect the uniform deformation capabilities of different materials under different strain paths.

[0035] 3) This method does not require measuring stress values ​​or maximum stress, but uses the strain bifurcation at different points to define the non-uniform plastic deformation of the material, thus avoiding the problem that stress values ​​cannot be measured directly. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a typical tensile curve for thin plates;

[0037] Figure 2 Schematic diagram of the geometric shape of the "dog bone" specimen;

[0038] Figure 3 This is a schematic diagram of the location of the strain points of the present invention;

[0039] Figure 4 It is the uniform equivalent plastic strain limit diagram of the present invention;

[0040] Figure 5 It is a photo of stage-617 in the embodiment;

[0041] Figure 6It is a photo of stage-616 in the embodiment;

[0042] Figure 7 It is a strain identification point positioning diagram in the embodiment;

[0043] Figure 8 Determine the boundary between uniform and non-uniform in the embodiment;

[0044] Fig. 9 It is a schematic diagram for determining the strain ratio in the embodiment;

[0045] Fig.10 It is the uniform extension strain limit diagram of QP980 in the embodiment. DETAILED DESCRIPTION

[0046] The present application is further described in detail below in conjunction with the accompanying drawings. The test part of the present invention meets the requirements of ISO12004-2 standard. The loading system is carried out on an Erichsen forming tester or a tensile testing machine. The strain path of uniaxial tension or approximate uniaxial tension can be carried out on a tensile testing machine, and other strain paths are carried out on an Erichsen forming tester. The strain measurement system of the present invention is an optical non-contact strain measurement system of DIC technology, which can realize online real-time measurement of the primary and secondary strains of the sheet material. Each frame of the sample during deformation is recorded by a high-speed camera, and the strain distribution of each image in the deformation is obtained by calibration and calculation, and then the strain value of any position in the photo at each moment can be obtained.

[0047] The sample of the present invention is a "dog bone" shaped sample, such as Figure 2 The specimen shown includes large rectangular blocks at two ends and a small rectangular block in the middle. The small rectangular block in the middle is coaxially arranged with the large rectangular blocks at two ends, and the small rectangular block and the large rectangular block are connected by an arc surface transition. The length of the small rectangular block is c, the width is a, the width of the large rectangular block is b, the radius of the arc is R, and the total length of the specimen is d. For strain paths with a strain ratio r greater than 0, rectangular specimens can also be used.

[0048] In order to fully reflect the uniform deformation capacity of the material in each strain path, the geometric size types of the specimens are 5 to 10, and must include three typical states of uniaxial tension, plane strain and biaxial tension, with 3 to 5 valid specimens of each geometric size.

[0049] The method for determining the uniform extension strain limit diagram of the thin plate of the present invention is as follows:

[0050] 1) Pre-test treatment

[0051] Take p kinds of specimens with different geometric sizes, and each kind of specimen has q pieces. In order to obtain the strain of the specimens during the deformation process, the surfaces of all specimens are processed. The surfaces of the specimens are printed with speckle spraying (virtual grid) or electro-etching grids, and the form of the grid matches the DIC measurement system; P is 5-10 and q is 3-5.

[0052] 2) Loading the sample

[0053] The first specimen is loaded on a tensile machine or an Erichsen forming test machine. During the loading process, the DIC measurement system is used to take photos of the deformation process of the first specimen, record the photos at each moment, and obtain the strain cloud map of the deformation surface of the first specimen at each moment. The first moment photo without deformation is recorded as stage-0, the second moment photo after loading is recorded as stage-1, the third moment photo is recorded as stage-2, and so on. When a macro crack visible to the naked eye appears, the loading test is stopped, and the last moment photo is recorded as stage-m, where m is a natural number. The frequency of taking photos is 10 to 20 Hz.

[0054] 3) Strain identification point positioning

[0055] In the m strain cloud maps in step 2), find the fracture photo stage-n when the first specimen begins to crack, and 1<n<m, then trace back to the photo stage-n-1 at the previous moment of the fracture photo stage-n; record the point O where the principal strain in the crack area is the largest on the photo stage-n-1 (point O is the strain extreme point of the strain cloud map of the photo stage-n-1) and the direction θ of the crack opening; then trace point O back to the photo stage-0 at the first moment, make a cross-sectional line passing through point O and perpendicular to the crack opening direction θ on the photo stage-0 at the first moment, and the angle of the cross-sectional line is θ+90°, and finally set z strain identification points on the cross-sectional line with point O as the starting point on the photo stage-0 at the first moment, and z is 3 to 8, such as Figure 3 As shown, the distance between each identification point is 1mm or 2mm. In principle, the distance between points close to point O is 1mm, and the distance between points far away from point O is 2mm.

[0056] 4) Strain output at strain identification point

[0057] The principal strain ε1, secondary strain ε2 and time t corresponding to the z strain identification points and point O in the photo at each moment in step 3) are recorded, and the thickness direction strain ε3 corresponding to the z strain identification points and point O in the photo at each moment is calculated by the volume invariance principle. The calculation formula (1) of the thickness direction strain ε3 is as follows:

[0058] ε1+ε2+ε3=0 (1).

[0059] 5) Strain-time curve drawing

[0060] According to the thickness direction strain ε3 and time t corresponding to each strain identification point in the photo at each moment obtained in step 4), the ε3-t curve of each strain identification point is drawn. At the same time, according to the thickness direction strain ε3 and time t corresponding to point O in the photo at each moment obtained in step 4), the ε3-t curve of point O is drawn, and a total of z+1 ε3-t curves are obtained; according to the z+1 ε3-t curves, it is found that the ε3-t curves of the z strain identification points and the ε3-t curve of point O are completely overlapped at the beginning of the thickness strain. With the increase of plastic deformation, when the first specimen enters the dispersed instability, the ε3-t curves of the z strain identification points and the ε3-t curve of point O begin to diverge, and the thickness direction strain ε3 value of point O is the largest, and the thickness direction strain ε3 value of the strain identification point farther away from point O is smaller.

[0061] 6) Determination of critical moment of non-uniform deformation

[0062] The difference between the thickness direction strain ε3 values ​​of the z strain identification points and point O increases with time. When the difference between the minimum and maximum values ​​of the thickness direction strain ε3 of the z strain identification points and point O at the same time is 1-3%, it is considered that the sheet metal begins to undergo non-uniform deformation. The moment t i is the critical moment of uniform deformation and non-uniform deformation, and point O is at t i The principal strain ε1 and secondary strain ε2 at the moment are recorded as the uniform limiting strain of the first specimen under the strain ratio r (i.e., strain path).

[0063] 7) Equivalent plastic strain ε eq Calculation

[0064] In order to fully characterize the deformability of the sheet metal, the equivalent plastic strain ε eq Represents the arrival time t i The plastic strain magnitude at point O, ε eq Calculate using formula 2.

[0065]

[0066] 8) Fitting of the true strain ratio r

[0067] The strain ratio obtained by the "dog bone" test specimen described above is only a theoretical value and the true strain ratio needs to be measured. i )’s ε2-ε1 curve is linearly fitted with its slope k, and the slope k is recorded as the true strain ratio r.

[0068] 9) Draw a uniform extension strain limit diagram

[0069] The true strain ratio r calculated in step 8) and the ε calculated in step 7) are eq As a set of data (r, ε eq )1 is plotted in the figure, the X coordinate is the true strain ratio r, and the ordinate Y is the equivalent plastic strain value ε eq .

[0070] 10) Repeat steps 2) to 9) to obtain the (r, ε) of the second to p×q groups of samples. eq ) and plotted in the FLD diagram; at the same time, the (r, ε eq ) take the average value (r, ε eq ) avg Draw it in the FLD diagram and connect it, such as Figure 4 shown.

[0071] The present invention proposes a method for determining the uniform extension strain limit diagram of a thin plate, and proposes a method for evaluating the uniform extension strain limit diagram of a thin plate under various strain paths and its determination method, respectively overcoming the above-mentioned defects of using the strain corresponding to the maximum load of uniaxial tension to evaluate the uniform plastic deformation ability of the material. In view of the first defect in the background technology, the method monitors the strain values ​​of different regions in the plate surface online in real time, makes a relationship between the strain ε and the time t, and takes the moment when the theoretically same strain point bifurcates as the boundary of the uniform and non-uniform plastic deformation of the plate, and uses the equivalent plastic strain value ε at this moment as the boundary of the uniform and non-uniform plastic deformation of the plate. eq To evaluate the uniform plastic deformation capability of materials, it is consistent with the concept of (non-uniform) deformation in a physical sense, rather than a phenomenological approximation to characterize the uniform deformation capability of materials; for the second defect in the background technology, this method uses specimens of different geometric sizes to simulate strain paths of different strain ratios r (= secondary strain ε2 / primary strain ε1) during loading, and the plastic strain ratio r range is (-0.5, 1), and finally obtains the limit equivalent plastic strain value when non-uniform changes occur under different strain ratios; for the third defect in the background technology, whether non-uniform plastic deformation occurs is determined by the difference in stress boundary values ​​of different points in the region, so no load value is required, nor is it necessary to measure and calculate stress values, and only the strain change can be monitored online in real time through the DIC (Digital Image Correlation) method.

[0072] The method is introduced by taking 980MPa grade ultra-high strength steel as an example. The parameters of 980MPa grade ultra-high strength steel are shown in Table 1.

[0073] Table 1

[0074] <![CDATA[R p0.2 / MPa]]> <![CDATA[R m / MPa]]> <![CDATA[A gt ]]> n r 698 1047 0.16 0.179 1.020

[0075] All tests were conducted using Figure 2The “dog bone” specimens were tested and five specimen sizes were used as shown in Table 2.

[0076] Table 2 Five specimen sizes

[0077] size 1# 2# 3# 4# 5# a / mm 20 65 85 100 170 b / mm 60 100 120 160 170 c / mm 30 30 30 0 - d / mm 170 170 170 170 170 R / mm 30 30 30 30 -

[0078] There are five sample sizes, 3 samples of each size are taken, and the surface of 15 samples is sprayed with white background and black spots. Sample 1# is tested on a tensile testing machine, and samples 2 to 5# are tested on an Erichsen forming testing machine. The tensile chuck speed of sample 1# is 5mm / min, and the punch speed of samples 2 to 5# is 1mm / s.

[0079] Load the first sample 1# on the tensile machine until a macroscopic crack visible to the naked eye appears and then stop the loading test; find the fracture photo of the first sample when cracks begin to appear in the strain cloud diagram, such as Figure 5 As shown, then go back to the photo of the last moment of the fracture photo Figure 6 As shown in the figure; the strain cloud diagram of the photo taken at the last moment of the fracture photo and the location of its cross-section line and strain identification point are shown in the figure. Figure 7 As shown, the crack initiation position O, crack direction and cross-section line are determined. Going back to the first undeformed photo, points 2mm, 4mm and 6mm away from point O in the direction of the cross-section line are selected and recorded as O1, O2 and O3 respectively.

[0080] The relationship between the output O1, O2, O3 principal strain, secondary strain and time is shown in Table 3.

[0081] Table 3

[0082]

[0083] The relationship between the thickness strain and time ε3-t of the three strain identification points and point O is plotted in one graph ( Figure 8 As shown in Figure 3, at 80s, the principal strains of the four strain identification points showed obvious bifurcation, and this moment was defined as the dividing moment between uniform and non-uniform strains.

[0084] Calculate the true strain ratio r of the specimen, as Fig. 9 As shown, the ratio k of the secondary strain to the primary strain of the sample is -0.478, so the strain ratio of the sample is r=k=-0.478.

[0085] Calculate the equivalent uniform plastic strain of the specimen,

[0086] One point of the uniform extension strain limit diagram of this specimen is (-0.478, 0.132).

[0087] Repeat the above process for other samples, and remove the average value of the same samples to obtain the uniform extension strain limit diagram of QP980, as shown in Fig.10 shown.

Claims

1. A method for determining a uniform extension strain limit diagram of a thin plate, characterized in that: The determination method is as follows: 1) Pre-test treatment Take p kinds of samples with different geometrical dimensions, and each sample has q pieces. Grid processing is performed on the surfaces of all samples, and the grid form matches the DIC measurement system. 2) Loading the sample The first specimen was loaded. During the loading process, the DIC measurement system was used to take photos of the deformation process of the first specimen. The photos at each moment were recorded, and the strain cloud map of the deformation surface of the first specimen at each moment was obtained. The first moment photo without deformation was recorded as stage-0, the second moment photo after loading was recorded as stage-1, the third moment photo was recorded as stage-2, and so on. When macroscopic cracks visible to the naked eye appeared, the loading test was stopped, and the last moment photo was recorded as stage-m, where m is a natural number. 3) Strain identification point positioning In the m strain cloud maps in step 2), find the fracture photo stage-n when the first specimen begins to crack, and 1<n<m, then trace back to the photo stage-n-1 at the previous moment of the fracture photo stage-n; record the point O where the principal strain is the largest in the crack area and the direction θ of the crack opening on the photo stage-n-1; then trace the point O back to the photo stage-0 at the first moment, make a cross-sectional line passing through the point O and perpendicular to the direction θ of the crack opening on the photo stage-0 at the first moment, and finally set z strain identification points on the cross-sectional line with the point O as the starting point on the photo stage-0 at the first moment; 4) Strain output at strain identification point Record the principal strain ε1, secondary strain ε2 and time t corresponding to the z strain identification points and point O in the photo at each moment in step 3), and calculate the thickness direction strain ε3 corresponding to the z strain identification points and point O in the photo at each moment by the volume invariance principle; 5) Strain-time curve drawing According to the thickness direction strain ε3 and time t corresponding to each strain identification point in the photo at each moment obtained in step 4), the ε3-t curve of each strain identification point is drawn. At the same time, according to the thickness direction strain ε3 and time t corresponding to point O in the photo at each moment obtained in step 4), the ε3-t curve of point O is drawn, and a total of z+1 ε3-t curves are obtained; 6) Determination of critical moment of non-uniform deformation When the difference between the minimum and maximum values ​​of the thickness strain ε3 at the z strain identification points and point O at the same time is 1-3%, it is considered that the sheet metal begins to undergo non-uniform deformation. The moment t i is the critical moment of uniform deformation and non-uniform deformation; at the same time, point O is at t i The principal strain ε1 and the secondary strain ε2 at the moment are recorded as the uniform limiting strain of the first specimen under the strain ratio r; 7) Equivalent plastic strain ε eq Calculation In order to fully characterize the deformability of the sheet metal, the equivalent plastic strain ε eq Represents the arrival time t i The plastic strain magnitude at point O; 8) Fitting of the true strain ratio r Fitting point O in the time region (0, t i )’s ε2-ε1 curve is linearly fitted with its slope k, which is recorded as the true strain ratio r; 9) Draw a uniform extension strain limit diagram The true strain ratio r calculated in step 8) and the ε calculated in step 7) are eq As a set of data (r, ε eq )1 is plotted in the figure, the X coordinate is the true strain ratio r, and the ordinate Y is the equivalent plastic strain value ε eq ; 10) Repeat steps 2) to 9) to obtain the (r, ε) of the second to p×q groups of samples. eq ) and plotted in the FLD diagram; at the same time, the (r, ε eq ) take the average value (r, ε eq ) avg Draw in FLD diagram and connect the lines.

2. The method for determining the uniform extension strain limit diagram of a thin plate according to claim 1, characterized in that: In the step 1), P is 5-10, and q is 3-5.

3. The method for determining the uniform extension strain limit diagram of a thin plate according to claim 1, characterized in that: In the step 2), the frequency of taking pictures is 10 to 20 Hz.

4. The method for determining the uniform extension strain limit diagram of a thin plate according to claim 1, characterized in that: In the step 3), z is 3 to 8, and the distance between each strain identification point is 1 mm or 2 mm, the distance between points close to point O is 1 mm, and the distance between points far from point O is 2 mm.

5. The method for determining uniform extension strain limit diagram of a thin plate according to claim 1, characterized in that: In step 4), the calculation formula (1) of the thickness direction strain ε3 is as follows: ε1+ε2+ε3=0 (1).

6. The method for determining the uniform extension strain limit diagram of a thin plate according to claim 1, characterized in that: In the step 7), ε eq Calculate using formula 2:

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