Measurement method of local plastic strain tensor of short fiber reinforced composites

Abstract

The present invention relates to the technical field of material plastic deformation measurement, and in particular to a method for measuring the local plastic strain tensor of a short fiber reinforced composite material, comprising: obtaining a sample to be measured and determining a region to be measured, and determining the orientation of each short fiber in the region to be measured in a measurement coordinate system; determining three strain principal axes of the region to be measured based on the orientations of all short fibers in the region to be measured, and establishing a strain principal axis coordinate system; in the established strain principal axis coordinate system, calculating the principal strain based on the orientation distribution of all short fibers in the region to be measured; rotating the principal strain to the measurement coordinate system, and obtaining the strain tensor measured in the measurement coordinate system. The present invention can realize simple and reliable measurement and characterization of the local plastic strain performance of short fiber reinforced composite materials.

Description

Technical Field

[0001] The present invention relates to the technical field of material plastic deformation measurement, and in particular to a method for measuring the local plastic strain tensor of a short fiber reinforced composite material, a computer device and a computer-readable storage medium. Background Art

[0002] Plastic deformation refers to the irreversible deformation of a material after it is subjected to a load. By utilizing the room temperature or high temperature plasticity of the material, the material can be processed into components of various shapes through extrusion, forging, blow molding, etc. Deformation localization is a common phenomenon during the plastic deformation of materials. Specifically, it is manifested as the difference in the size and direction of plastic deformation of various parts of the material due to the differences in material organization, stress state, damage conditions, and constraint conditions during the plastic deformation process. Plastic deformation localization will cause uneven distribution of the material's organization and performance after plastic processing, resulting in substandard component performance or unexpected failure during service. Therefore, accurately characterizing the local plastic deformation of the material has significant practical significance. The local plastic strain of the material is usually characterized in the form of a strain tensor. The strain tensor is a second-order tensor that requires four components (two normal strain components and two shear strain components) in a two-dimensional plane and nine components (three normal strain components and six shear strain components) in a three-dimensional space.

[0003] Short fiber reinforced composite materials refer to composite materials obtained by adding hard short fibers to a relatively soft matrix. The matrix material can be metal, resin or ceramic. Compared with the matrix material, short fiber reinforced composite materials have better room temperature and high temperature strength and good deformation ability. They have been widely used in the fields of automobiles, sports equipment and aerospace. Studying the plastic deformation properties of short fiber reinforced composite materials is helpful for the research and development and production of different components.

[0004] At present, the main method used to characterize the local plastic strain performance of materials is the digital image correlation (DIC) method. The DIC method relies on one or more cameras to record the entire deformation process of the component, and obtains the two-dimensional or three-dimensional plastic deformation information of the component by tracking the movement of the prefabricated speckle on the surface of the component. It has the characteristics of large field of view, high accuracy and good quantitativeness. However, the DIC method has very strict requirements and limited measurement. Summary of the invention

[0005] The purpose of the present invention is to provide a method for measuring the local plastic strain tensor of short fiber reinforced composite materials with fewer restrictions and higher precision to address at least some of the above-mentioned deficiencies, so as to achieve simple and reliable measurement and characterization of the local plastic strain performance of short fiber reinforced composite materials.

[0006] In order to achieve the above object, the present invention provides a method for measuring the local plastic strain tensor of a short fiber reinforced composite material, comprising:

[0007] Obtain a sample to be measured and determine a region to be measured, and determine the orientation of each short fiber in the region to be measured in a measurement coordinate system; wherein the sample is taken from a short fiber reinforced composite material after plastic deformation, and the region to be measured is a local region of the sample where the strain tensor needs to be measured;

[0008] Based on the orientations of all the short fibers in the area to be tested, three strain principal axes of the area to be tested are determined, and a strain principal axis coordinate system is established;

[0009] In the established strain principal axis coordinate system, the principal strain is calculated based on the directional distribution of all short fibers in the area to be measured;

[0010] The principal strain is rotated to the measurement coordinate system to obtain the strain tensor measured in the measurement coordinate system.

[0011] Optionally, the area to be tested contains at least 50 short fibers.

[0012] Optionally, the determining the orientation of each short fiber in the area to be tested includes:

[0013] The EBSD method or the X-ray tomography method is used to perform pointing measurement on each short fiber in the area to be measured.

[0014] Optionally, determining three strain principal axes of the area to be measured based on the orientations of all short fibers in the area to be measured and establishing a strain principal axis coordinate system includes:

[0015] The directions of all the short fibers in the area to be measured are represented as particles on a unit sphere; wherein the mass of the particle is 1 / n, n is the total number of short fibers in the area to be measured, the location of the particle is the projection of the directions of the short fibers on the unit sphere, and the center of the unit sphere is at the origin of the measurement coordinate system;

[0016] Based on all the mass points, determining the moment of inertia matrix of the mass point group corresponding to the area to be measured;

[0017] Based on the moment of inertia matrix, the corresponding three eigenvalues ​​and the eigenvectors corresponding to each eigenvalue are solved, and the directions indicated by the three eigenvectors are respectively the directions of the three principal strain axes of the area to be measured;

[0018] The strain principal axis coordinate system is established based on the three eigenvectors obtained by solving the problem.

[0019] Optionally, the calculating the principal strain based on the directional distribution of all short fibers in the area to be measured in the established strain principal axis coordinate system includes:

[0020] In the strain principal axis coordinate system, determining the directional distribution of all short fibers in the test area after the actual plastic deformation occurs;

[0021] Constructing a probability density function of the directional distribution of all short fibers in the test area after plastic deformation occurs; wherein the probability density function takes the deformation ratio in the direction of each strain principal axis as a parameter, and assumes that before plastic deformation occurs, the directional distribution of all short fibers in the test area obeys random distribution;

[0022] The parameters in the probability density function are estimated based on the directional distribution of all the short fibers in the test area after the actual plastic deformation, so as to obtain the deformation ratio of the test area in the direction of each strain principal axis;

[0023] The principal strain is determined according to the deformation ratio of the measured area in the direction of each strain principal axis.

[0024] Optionally, the probability density function is expressed as:

[0025]

[0026] Among them, α, β and γ represent the inclination angles of the short fiber about the principal plane v1v2, principal plane v2v3 and principal plane v3v1 after plastic deformation, respectively, v1, v2 and v3 represent the three strain principal axes, respectively, α', β' and γ' represent the inclination angles of the short fiber about the principal plane v1v2, principal plane v2v3 and principal plane v3v1 before plastic deformation, respectively, a, b and c represent the deformation ratios in the directions of the strain principal axes v1, v2 and v3, respectively, and a×b×c=1, f'(α'), g'(β') and h'(γ') represent the probability density of the inclination angles of α', β' and γ' before plastic deformation, respectively, satisfying the following expressions:

[0027]

[0028] f(α), g(β) and h(γ) represent the probability density of the tilt angles α, β and γ after plastic deformation, respectively.

[0029] Optionally, the parameters in the probability density function are estimated based on the directional distribution of all short fibers in the test area after the actual plastic deformation, so as to obtain the deformation ratio of the test area in each strain principal axis direction, including:

[0030] The maximum likelihood estimation method is used to establish the likelihood function of the probability density f(α), g(β) and h(γ) according to the directional distribution of all short fibers in the test area after the actual plastic deformation. The expression is:

[0031]

[0032] Among them, L α (a,b,|α1,...,α n )、L β (b,c,|β1,...,β n ) and L γ (c,a,|γ1,...,γ n ) are the likelihood functions of probability densities f(α), g(β) and h(γ) respectively; (α i ,β i ,γ i ) represents the orientation of the i-th short fiber after plastic deformation;

[0033] Make equivalent substitutions, let a = st / r 3 , b = rt / s 3 And c = rs / t 3 , and then the three-way comprehensive likelihood function is obtained, the expression is:

[0034]

[0035] By obtaining the maximum value of the three-directional comprehensive likelihood function, the maximum likelihood estimation values ​​of r, s and t are determined, and then the deformation ratios a, b and c in the directions of the main strain axes are obtained;

[0036] According to the magnifications a, b and c, the principal strain of the measured area is obtained. Among them, ε1=a-1, ε2=b-1, and ε3=c-1.

[0037] Optionally, the strain tensor expression determined in the measurement coordinate system is:

[0038]

[0039] Where V = [v1 v2 v3], v1, v2 and v3 represent the three strain principal axes in the measurement coordinate system, represents the principal strain of the measured area.

[0040] The present invention also provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the method for measuring the local plastic strain tensor of the short fiber reinforced composite material described in any one of the above items are implemented.

[0041] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the method for measuring the local plastic strain tensor of a short fiber reinforced composite material described in any one of the above items are implemented.

[0042] The above-mentioned technical scheme of the present invention has the following advantages: The present invention provides a method for measuring the local plastic strain tensor of a short fiber reinforced composite material, a computer device and a computer-readable storage medium. The present invention calculates the strain tensor of the local deformation of the material by statistically analyzing the rearrangement of the short fiber orientation during the plastic deformation process. Compared with previous methods, this method can give the local plastic strain tensor of any area on the surface or inside of the short fiber reinforced composite material without relying on the observation of the deformation process, and fully describe the plastic deformation of the local area. It can be used to quantitatively measure the local deformation of the material after plastic forming or load-bearing deformation, and provide a basis for the evolution of material structure properties after plastic forming or component failure analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic diagram of the steps of a method for measuring the local plastic strain tensor of a short fiber reinforced composite material in an embodiment of the present invention;

[0044] Figure 2 The short fiber orientation result measured by the EBSD method in the embodiment of the present invention is shown;

[0045] Figure 3 The directional results of the short fibers converted to the strain principal axis coordinate system in the embodiment of the present invention are shown;

[0046] Figure 4(a) to Figure 4(c) The figure shows the results of fitting the short fiber orientation distribution in the three strain principal axis directions using the maximum likelihood estimation method in the embodiment of the present invention. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] As mentioned above, the current method for characterizing the local plastic strain properties of materials is mainly the digital image correlation (DIC) method. Although the method of measuring the local plastic deformation of materials using the DIC method has high accuracy and good quantitative results, it has the following defects:

[0049] The DIC method relies on the complete tracking of speckles during the deformation process. When the deformation process cannot be observed or the speckles on the surface of the component are destroyed during the plastic deformation process, the material deformation cannot be measured by the DIC method.

[0050] The speckle required by the DIC method can only be applied to the surface of the material, and the camera cannot observe the internal conditions of the component, so it can only track on the surface of the component; the deformation component perpendicular to the surface can only be estimated by the volume conservation principle, and the accuracy of the result cannot be guaranteed; and when it is necessary to obtain the internal plastic deformation of the component for organizational analysis or failure analysis, it cannot provide effective information;

[0051] The resolution of the DIC method is limited by the camera resolution and the size of the component. When the size of the tested component exceeds 10 cm, the resolution of the DIC method is difficult to exceed 1 mm. For larger components, the resolution of the DIC method will gradually decrease as the size of the component increases.

[0052] In summary, the DIC method requires a complete observation of the plastic deformation process. At the same time, it cannot accurately characterize the internal deformation or off-plane deformation of the material, and the spatial resolution of the measurement decreases rapidly as the size of the tested component increases. These defects are caused by the measurement principle of the DIC method and cannot be eliminated by changing the calculation method or improving the observation accuracy.

[0053] In view of this, the present invention proposes to calculate the local deformation tensor of the material by statistically analyzing the rearrangement of short fibers during the deformation process, so as to accurately and effectively describe the plastic deformation of the local area of ​​the short fiber reinforced composite material without relying on the observation of the deformation process.

[0054] like Figure 1 As shown, a method for measuring the local plastic strain tensor of a short fiber reinforced composite material (hereinafter referred to as the method of the present invention) provided in an embodiment of the present invention comprises:

[0055] Step 100, obtain the sample to be measured and determine the area to be measured, and determine the orientation of each short fiber in the area to be measured in the measurement coordinate system; wherein the sample is taken from a short fiber reinforced composite material after plastic deformation, and the area to be measured is a local area in the sample where the strain tensor needs to be measured.

[0056] The measurement coordinate system is an artificially selected reference coordinate system. For example, the measurement coordinate system can be set according to the shape of the sample. The orientation of the short fiber is the spatial direction of the long axis of the short fiber. The size of the area to be measured can be smaller than the sample size. Usually, the sample size is preferably several millimeters to tens of millimeters, and the area to be measured can be tens of microns to hundreds of microns.

[0057] Step 102: based on the orientations of all the short fibers in the area to be measured, three strain principal axes corresponding to the area to be measured are determined, and a corresponding strain principal axis coordinate system is established.

[0058] Determine the three strain principal axes of the area to be tested, that is, determine the main deformation direction of the area to be tested. The main deformation direction includes three unit vectors corresponding to the three strain principal axes. The area to be tested has only normal strain components but no shear strain components relative to the three strain principal axes.

[0059] Step 104 , in the established strain principal axis coordinate system, the principal strain is calculated based on the directional distribution of all short fibers in the area to be measured.

[0060] In this step, the orientation results of the short fibers measured in the measurement coordinate system are converted to the strain principal axis coordinate system, and then the orientation distribution of all short fibers is counted to determine the orientation distribution of the short fibers in order to calculate the principal strain, that is, to calculate the strain tensor in the strain principal axis coordinate system. The strain tensor is in the form of a 3×3 matrix. In the strain principal axis coordinate system, the non-diagonal elements of the principal strain are all 0. Calculating the principal strain first can effectively reduce the amount of subsequent calculations.

[0061] Step 106 , rotating the calculated principal strain to the measurement coordinate system, and finally obtaining the strain tensor measured in the measurement coordinate system.

[0062] In this step, the principal strains obtained are rotated to obtain the strain tensor relative to the observer, thereby characterizing the local plastic strain of the short fiber reinforced composite material.

[0063] To ensure that the measurement results are statistical, optionally, at least 50 short fibers are included in the area to be measured determined in step 100. The size of the area to be measured can be determined with reference to the density and size of the short fibers, and is usually between 100 μm and 1 mm.

[0064] Optionally, in step 100, determining the orientation of each short fiber in the area to be measured in the measurement coordinate system includes:

[0065] Pointing measurements are performed on each short fiber in the area to be measured using the EBSD method or the X-ray tomography method.

[0066] When the EBSD method is used for measurement, the measurement area is a two-dimensional cross section, and accordingly, the shape of the sample is usually taken as a cube. For short fibers whose long axis direction has a clear correlation with the crystallographic direction, such as TiB whiskers or SiC whiskers, the EBSD method can be used to calibrate the orientation of the short fibers on the cross section to be measured. Taking TiB whiskers as an example, the

[010] crystal direction is the long axis direction of the whisker. By calibrating the spatial orientation of the

[010] crystal direction of each whisker by the EBSD method, the spatial orientation of the TiB whiskers in the area can be obtained.

[0067] When using X-ray tomography for measurement, the measurement area is a three-dimensional volume, and accordingly, the shape of the sample is usually taken as a cylinder. For materials with obvious density differences between the short fiber reinforcement and the matrix, such as SiC whisker reinforced aluminum-based composites, the X-ray tomography method can be used to measure the orientation of the short fibers in the measured volume. When using the X-ray tomography method for measurement, the spatial distribution of the short fibers is first reconstructed by a three-dimensional reconstruction method, and then the tensor form moment of inertia of each short fiber about its center of mass is calculated. The direction of the minimum principal value of the moment of inertia is the long axis direction of the short fiber.

[0068] It should be noted that the EBSD method or the X-ray tomography method is not the only technology for measuring the orientation of short fibers in the test area. Step 100 can also be measured by referring to other methods for determining the orientation of short fibers in the prior art. Accordingly, when obtaining the sample to be measured, the shape of the sample needs to be adjusted according to the actual situation to ensure that the measurement area contains enough short fibers.

[0069] Optionally, step 102 further includes:

[0070] Step 102-1, the directions of all short fibers in the area to be measured are represented as particles on the unit sphere; wherein the mass of the particle is 1 / n, n is the total number of short fibers in the area to be measured, the position of the particle is the projection of the direction of the short fiber on the unit sphere, and the center of the unit sphere is at the origin of the measurement coordinate system.

[0071] Assume the unit sphere in the measurement coordinate system: 2 +y 2 +z 2 =1, the position of the particle (x, y, z), represents the coordinates of the projection point of the directional measurement result of the short fiber corresponding to the particle on the unit sphere.

[0072] Step 102-2: Based on all the mass points, determine the moment of inertia matrix of the mass point group corresponding to the area to be measured.

[0073] Furthermore, it is assumed that the coordinates of the projection point of the i-th short fiber in the test area on the unit sphere are (x i ,y i ,z i ), i = 1, .., n, then the moment of inertia matrix I of the mass group corresponding to all short fibers in the region is expressed as:

[0074]

[0075] Step 102 - 3 , based on the moment of inertia matrix, solve the corresponding three eigenvalues ​​and the eigenvector corresponding to each eigenvalue, the directions indicated by the three eigenvectors are the directions of the three principal strain axes of the area to be measured.

[0076] Solving the linear algebraic equation: Iv=λv, we can obtain the eigenvalues ​​and eigenvectors corresponding to the moment of inertia matrix I, where I is the moment of inertia matrix, v is an arbitrary three-dimensional column vector of unit length, and λ is an arbitrary constant.

[0077] Step 102-4, establishing a strain principal axis coordinate system based on the three eigenvectors obtained by solving.

[0078] After obtaining the three eigenvalues ​​corresponding to the moment of inertia matrix I, they can be denoted as λ1, λ2 and λ3 from small to large. These three eigenvalues ​​are the three principal values ​​of the moment of inertia of the particle group. Their corresponding eigenvectors v1, v2 and v3 represent the main directions of the moment of inertia of the particle group, and also represent the main deformation directions of the plastic strain in the area. That is, under the measurement coordinate system, the three coordinate axes of the strain principal axis coordinate system can be denoted as v1, v2 and v3 respectively.

[0079] In the above embodiment, the present invention adopts a method of abstracting the direction of short fibers as particles on a unit sphere, and determines the overall direction of the short fibers in the test area by obtaining the main direction of the moment of inertia of the particle group, thereby quickly and accurately obtaining the main deformation direction of the area.

[0080] Optionally, step 104 includes:

[0081] Step 104 - 1 : determining the directional distribution of all short fibers in the test area after the actual plastic deformation in the strain principal axis coordinate system.

[0082] In this step, the short fiber corresponding to the coordinate (x i ,y i ,z i ) Left multiply matrix [v1 v2 v3] -1 To obtain its coordinates in the strain principal axis coordinate system (x i ',y i ',z i '), and then the inclination angle of each short fiber with respect to each principal plane is obtained according to the following expression:

[0083]

[0084] Among them, α i , β i and γ i They represent the inclination angles of the i-th short fiber about the principal plane v1v2 formed by the strain principal axis v1 and the strain principal axis v2, the principal plane v2v3 formed by the strain principal axis v2 and the strain principal axis v3, and the principal plane v3v1 formed by the strain principal axis v3 and the strain principal axis v1; (α1, β1, γ1),…, (α i ,β i ,γi ),…,(α n ,β n ,γ n ) is used to indicate the directional distribution of all short fibers in the tested area after actual plastic deformation, which has been transformed to the strain principal axis coordinate system.

[0085] Step 104-2, constructing a probability density function of the directional distribution of all short fibers in the test area after plastic deformation; wherein the probability density function takes the deformation ratio in each strain principal axis direction as a parameter, and assumes that before plastic deformation occurs, the directional distribution of all short fibers in the test area obeys a random distribution.

[0086] In this step, it is assumed that the area to be tested is deformed to a, b and c times of its original size in the strain principal axes v1, v2 and v3 directions respectively. Since plastic deformation does not change the material density, a×b×c=1. At this time, if the orientation of a short fiber before plastic deformation can be expressed as (α', β', γ'), then its orientation after plastic deformation (α, β, γ) can be determined by the following set of equations:

[0087]

[0088] Assuming that before plastic deformation occurs, the directional distribution of all short fibers in the test area obeys random distribution, the following expression is satisfied:

[0089]

[0090] Where f'(α'), g'(β') and h'(γ') represent the probability density of plastic deformation with front tilt angles of α', β' and γ', respectively.

[0091] Therefore, the expression of the probability density function with the deformation ratio in each strain principal axis direction as a parameter after plastic deformation is obtained:

[0092]

[0093] Among them, v1, v2 and v3 represent three strain principal axes, (α', β', γ') represent the orientation of the short fibers before plastic deformation, (α, β, γ) represent the orientation of the short fibers after plastic deformation, α and α' represent the inclination angles of the short fibers (long axis direction) before and after plastic deformation with respect to the principal plane v1v2 formed by the strain principal axes v1 and v2, β and β' represent the inclination angles of the short fibers (long axis direction) before and after plastic deformation with respect to the strain principal axes v2 and v3, respectively. The inclination angle of the principal plane v2v3, γ and γ' respectively represent the inclination angle of the principal plane v3v1 formed by the short fiber (in the long axis direction) before and after plastic deformation with respect to the strain principal axes v3 and v1, a represents the deformation ratio in the direction of the strain principal axis v1, b represents the deformation ratio in the direction of the strain principal axis v2, and c represents the deformation ratio in the direction of the strain principal axis v3; f(α), g(β) and h(γ) respectively represent the probability density of inclination angles of α, β and γ after plastic deformation.

[0094] Step 104 - 3 , estimating the parameters in the probability density function based on the directional distribution of all short fibers in the test area after the actual plastic deformation, and obtaining the deformation ratio of the test area in each strain principal axis direction.

[0095] Step 104 - 4 , determining the strain tensor in the strain principal axis coordinate system according to the deformation ratio of the measured area in the directions of each strain principal axis.

[0096] Optionally, step 104-3 further includes:

[0097] The maximum likelihood estimation method is used to establish the likelihood function of the probability density f(α), g(β) and h(γ) according to the directional distribution of all short fibers in the test area after the actual plastic deformation. The expression is:

[0098]

[0099] Among them, L α (a,b,|α1,...,α n )、L β (b,c,|β1,...,β n ) and L γ (c,a,|γ1,...,γ n ) are the likelihood functions of the probability densities f(α), g(β) and h(γ) in the three strain principal axis directions respectively; (α i ,β i ,γ i ) represents the orientation of the i-th short fiber after plastic deformation, α i , β i and γ iThey represent the inclination angles of the short fiber about the principal plane v1v2, principal plane v2v3 and principal plane v3v1 after plastic deformation, respectively. The set {(α i ,β i ,γ i )} i＝1,…,n It is used to indicate the directional distribution of all short fibers in the tested area after the actual plastic deformation occurs;

[0100] Since a×b×c=1, make an equivalent substitution and let a=st / r 3 , b = rt / s 3 And c = rs / t 3 , so that the likelihood function implies this condition, multiply the likelihood functions of the three direction components and take the logarithm, and then we can get the three-direction comprehensive likelihood function, which is expressed as:

[0101]

[0102] By obtaining the maximum value of the above three-directional comprehensive likelihood function, the maximum likelihood estimation values ​​of r, s and t can be determined, and then the deformation magnifications a, b and c in the directions of the main strain axes can be obtained; wherein, the method for obtaining the maximum value of the three-directional comprehensive likelihood function can be various optimization methods such as Newton iteration method and gradient descent method, which will not be further limited here;

[0103] According to the deformation ratios a, b and c in the three strain principal axis directions, the principal strain of the measured area can be obtained, that is, the strain tensor in the strain principal axis coordinate system. Among them, ε1=a-1, ε2=b-1, and ε3=c-1.

[0104] Optionally, in step 106, the strain tensor measured in the measurement coordinate system is obtained, and the expression is:

[0105]

[0106] v1, v2 and v3 represent the three principal strain axes in the measurement coordinate system. Represents the principal strain in the measured area.

[0107] In a specific embodiment, the present invention also verifies the above method. Since rolling deformation has the characteristic of uniform deformation distribution, the difference between the overall deformation and the local deformation is small, which is suitable for verifying the accuracy of the present invention. Therefore, the present invention uses the TiB whisker reinforced TA15-based composite material with a rolling deformation of 60% at 910°C as an example for testing. The original size of the composite material before rolling deformation is φ60mm×40mm. After rolling, the plate-shaped material obtained is 130mm long in the long axis direction, 70mm wide in the short axis direction, and 16mm high, that is, the length direction is elongated by 117%, the width direction is elongated by 17%, and the thickness direction is reduced by 60% due to rolling.

[0108] The deformation of the TiB whisker reinforced TA15-based composite material is measured using the method for measuring the local plastic strain tensor of the short fiber reinforced composite material provided by the present invention. The specific process is as follows:

[0109] In step 100, since the short fibers in the composite material have a clear crystal orientation, namely the

[010] direction of the TiB whiskers, the EBSD method is used to measure the orientation of the short fibers. During the measurement, a sample is taken from the center of the plate-like material obtained after rolling (referred to as the rolled plate) for measurement. When the measurement coordinate system is selected, the measurement viewing angle coincides with the short axis direction of the rolled plate, recorded as the Z axis; the long axis direction of the rolled plate is located in the vertical direction of the measurement viewing angle, recorded as the Y axis; the thickness direction of the rolled plate is located in the horizontal direction of the measurement viewing angle, recorded as the X axis. The measured orientation of the TiB short fibers is projected onto the unit sphere, and the result is as follows: Figure 2 As shown, Figure 2 The sphere surrounded by the dotted line is the unit sphere, and each point represents the direction of a short fiber. It can be seen that the points are concentrated in the Y direction, followed by the Z direction, and the least in the X direction, which means that the short fibers tend to point to the tensile direction of plastic deformation and away from the compression direction of plastic deformation.

[0110] In step 102, the deformation principal direction of the area to be measured is calculated. In this embodiment, 146 short fibers are actually measured. Therefore, there are 146 mass points on the unit sphere, and the mass of each mass point is 1 / 146. The moment of inertia matrix of the point group can be calculated as:

[0111]

[0112] After obtaining the three eigenvalues ​​corresponding to the moment of inertia matrix I, they are recorded as λ1, λ2 and λ3 from small to large, and the corresponding eigenvectors v1, v2 and v3. The main deformation direction is obtained based on the eigenvectors of the moment of inertia matrix:

[0113]

[0114] In step 104, Figure 2The point group in is rotated from the measurement coordinate system to the strain principal axis coordinate system. The result after rotation is as follows Figure 3 As shown in Figure 1, it can be seen that the most concentrated direction of the short fibers is rotated to the v1 direction, the second most concentrated direction is rotated to the v2 direction, and the most sparse direction is rotated to the v3 direction. After the short fiber orientation is counted and fitted by maximum likelihood estimation, the distribution of short fiber orientations in the three strain principal axis directions and the fitting results of the distribution are shown in Figure 1. Figure 4(a) to Figure 4(c) As shown, the ordinate is the frequency of the corresponding inclination angle value. Figure 4 (a) shows the distribution and fitting results of the short fiber orientation in the v1 direction, Figure 4 (b) shows the distribution and fitting results of the short fiber orientation in the v2 direction, and Figure 4 (c) shows the distribution and fitting results of the short fiber orientation in the v3 direction. It can be seen that the method of the present invention can well fit the actual distribution of the short fibers. The ratio parameters a, b and c determined by fitting are 2.15, 1.24 and 0.38 respectively.

[0115] In step 106, the strain tensor in the measurement coordinate system is finally obtained as:

[0116]

[0117] [v1 v2 v3] T is the transpose of [v1 v2 v3].

[0118] The method of the present invention calculates that the rolling amount of the rolled plate in the thickness direction is 61%, the elongation in the length direction is 114%, and the elongation in the width direction is 24%. The calculated results are equivalent to the actual deformation, indicating that the method of the present invention has good measurement accuracy.

[0119] In particular, in some preferred embodiments of the present invention, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the method for measuring the local plastic strain tensor of the short fiber reinforced composite material described in any of the above embodiments are implemented.

[0120] In some other preferred embodiments of the present invention, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the method for measuring the local plastic strain tensor of the short fiber reinforced composite material described in any of the above embodiments are implemented.

[0121] A person of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment method can be implemented by instructing related hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the process of the embodiment of the method for measuring the local plastic strain tensor of the short fiber reinforced composite material, which will not be repeated here.

[0122] In summary, the present invention provides a method for measuring the local plastic strain tensor of a short fiber reinforced composite material, a computer device and a computer readable storage medium. The present invention is based on the rotation of short fibers caused by plastic deformation. First, the three-dimensional orientation of the short fibers in the local area is measured, and then statistical analysis is performed to obtain the main deformation direction of the area and the tensile and compressive deformation in the direction, and the two are combined to obtain the plastic strain tensor of the area. The short fiber reinforced composite material is composed of hard short fibers and a soft matrix, wherein the short fiber reinforcement can be crystalline TiB whiskers, SiC whiskers, or amorphous glass short fibers, chopped carbon short fibers, etc., and its orientation distribution should be approximately random; the matrix can be metals and alloys such as titanium, aluminum, iron, etc. that can be used as structural materials, or resins, ceramics, etc.

[0123] Compared with the prior art, the method of the present invention has at least the following advantages:

[0124] The present invention uses the direction of short fibers to judge the plastic deformation of composite materials. It is not necessary to record the state of the component during deformation. It is only necessary to sample and measure the local area of ​​interest in the material after deformation. The final result can be obtained based on the statistics of the spatial orientation of the short fibers in the sample. Therefore, the cost of setting up the test bench is saved, the amount of data required for local plastic deformation measurement is reduced, and the limitation of process observation on plastic deformation means is avoided.

[0125] The present invention uses the EBSD method or the X-ray tomography method to determine the orientation of the short fibers. Since the orientation of the short fibers is three-dimensional information, the present invention can calculate the three-dimensional plastic strain tensor without estimating a certain direction. Compared with the DIC method, the present invention has better accuracy when calculating the three-dimensional strain.

[0126] The samples of the EBSD method and the X-ray tomography method can be taken from any position in the component. Therefore, the present invention can judge the three-dimensional deformation at any position of the component, intuitively characterize the spatial distribution of plastic deformation inside the component, and is not limited to the surface of the component. It does not need to be estimated by finite element simulation and other methods, and has good reliability.

[0127] The present invention abstracts the orientation of the short fibers as particles distributed on a unit sphere, and determines the principal axis of the plastic strain of the material by obtaining the moment of inertia of the particles. This step simplifies the independent components in the plastic strain tensor into three principal strain components, greatly reducing the complexity of subsequent calculations.

[0128] The present invention adopts the maximum likelihood estimation method to calculate the principal strain, and constructs likelihood functions with the same form for the three principal strain components respectively, so as to ensure that the calculation errors in different directions are at the same level. By using the parameters r, s, and t to replace the original parameters a, b, and c through equal transformation, it is ensured that the calculation results satisfy the volume conservation law.

[0129] The spatial resolution of the method of the present invention depends on the size of the short fibers, which can usually reach 0.05 mm to 0.1 mm. For common micron-sized short fiber reinforced metal matrix composites, the spatial resolution of the method of the present invention can reach up to 0.05 mm, and this resolution is not affected by other factors such as component size. When used to characterize the local plastic deformation of large components, the method of the present invention has a spatial resolution much higher than that of the DIC method.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for measuring the local plastic strain tensor of a short fiber reinforced composite material, characterized in that: include: Obtain a sample to be measured and determine a region to be measured, and determine the orientation of each short fiber in the region to be measured in a measurement coordinate system; wherein the sample is taken from a short fiber reinforced composite material after plastic deformation, and the region to be measured is a local region of the sample where the strain tensor needs to be measured; Based on the orientation of all the short fibers in the area to be tested, three strain principal axes of the area to be tested are determined, and a strain principal axis coordinate system is established, including: The directions of all the short fibers in the area to be measured are represented as particles on a unit sphere; wherein the mass of the particle is 1 / n, n is the total number of short fibers in the area to be measured, the location of the particle is the projection of the directions of the short fibers on the unit sphere, and the center of the unit sphere is at the origin of the measurement coordinate system; Based on all the mass points, determining the moment of inertia matrix of the mass point group corresponding to the area to be measured; Based on the moment of inertia matrix, the corresponding three eigenvalues ​​and the eigenvectors corresponding to each eigenvalue are solved, and the directions indicated by the three eigenvectors are respectively the directions of the three principal strain axes of the area to be measured; The strain principal axis coordinate system is established based on the three eigenvectors obtained by solving the problem; In the established strain principal axis coordinate system, the principal strain is calculated based on the directional distribution of all short fibers in the test area, including: In the strain principal axis coordinate system, determining the directional distribution of all short fibers in the test area after the actual plastic deformation occurs; Constructing a probability density function of the directional distribution of all short fibers in the test area after plastic deformation occurs; wherein the probability density function takes the deformation ratio in the direction of each strain principal axis as a parameter, and assumes that before plastic deformation occurs, the directional distribution of all short fibers in the test area obeys random distribution; The parameters in the probability density function are estimated based on the directional distribution of all the short fibers in the test area after the actual plastic deformation, so as to obtain the deformation ratio of the test area in the direction of each strain principal axis; Determining the principal strain according to the deformation ratio of the measured area in the direction of each strain principal axis; The principal strain is rotated to the measurement coordinate system to obtain the strain tensor measured in the measurement coordinate system.

2. The method for measuring the local plastic strain tensor of a short fiber reinforced composite material according to claim 1, characterized in that: The area to be tested contains at least 50 short fibers.

3. The method for measuring the local plastic strain tensor of a short fiber reinforced composite material according to claim 1, characterized in that: Determining the orientation of each short fiber in the area to be tested includes: The EBSD method or the X-ray tomography method is used to perform pointing measurement on each short fiber in the area to be measured.

4. The method for measuring the local plastic strain tensor of a short fiber reinforced composite material according to claim 1, characterized in that: The expression of the probability density function is: Among them, α, β and γ represent the inclination angles of the short fiber about the principal plane v1v2, principal plane v2v3 and principal plane v3v1 after plastic deformation, respectively, v1, v2 and v3 represent the three strain principal axes, respectively, α', β' and γ' represent the inclination angles of the short fiber about the principal plane v1v2, principal plane v2v3 and principal plane v3v1 before plastic deformation, respectively, a, b and c represent the deformation ratios in the directions of the strain principal axes v1, v2 and v3, respectively, and a×b×c=1, f'(α'), g'(β') and h'(γ') represent the probability density of the inclination angles of α', β' and γ' before plastic deformation, respectively, satisfying the following expressions: f(α), g(β) and h(γ) represent the probability density of the tilt angles α, β and γ after plastic deformation, respectively.

5. The method for measuring the local plastic strain tensor of a short fiber reinforced composite material according to claim 4, characterized in that: The parameters in the probability density function are estimated based on the directional distribution of all short fibers in the test area after the actual plastic deformation, and the deformation ratio of the test area in each strain principal axis direction is obtained, including: The maximum likelihood estimation method is used to establish the likelihood function of the probability density f(α), g(β) and h(γ) according to the directional distribution of all short fibers in the test area after the actual plastic deformation. The expression is: Among them, L α (a,b,α1,...,α n )、L β (b,c,|β1,...,β n ) and L γ (c,a,γ1,...,γ n ) are the likelihood functions of probability densities f(α), g(β) and h(γ) respectively; (α i ,β i ,γ i ) represents the orientation of the i-th short fiber after plastic deformation; Make equivalent substitutions, let a = st / r 3 , b = rt / s 3 And c = rs / t 3 , and then the three-way comprehensive likelihood function is obtained, the expression is: By obtaining the maximum value of the three-directional comprehensive likelihood function, the maximum likelihood estimation values ​​of r, s and t are determined, and then the deformation ratios a, b and c in the directions of the main strain axes are obtained; According to the magnifications a, b and c, the principal strain of the measured area is obtained. Among them, ε1=a-1, ε2=b-1, and ε3=c-1.

6. The method for measuring the local plastic strain tensor of a short fiber reinforced composite material according to claim 1, characterized in that: The strain tensor expression measured in the measurement coordinate system is: Where V = [v1 v2 v3], v1, v2 and v3 represent the three strain principal axes in the measurement coordinate system, represents the principal strain of the measured area.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the method for measuring the local plastic strain tensor of the short fiber reinforced composite material according to any one of claims 1 to 6 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for measuring the local plastic strain tensor of a short fiber reinforced composite material according to any one of claims 1 to 6 are implemented.

Images