Method for measuring defect density of a metallic material

Abstract

The application provides a kind of metal material defect density measurement method, it is related to the technical field of metal material defect density quantitative analysis regulation material performance.This method includes six steps of establishing original data set, preprocessing original data, judging grain boundary existence, calculating elastic distortion tensor, calculating dislocation density and calculating dislocation density.Compared with the traditional microdefect organization analysis method, this method first introduces Lie algebra mathematical tool to quantitatively analyze the rotation characteristics and structure of dislocation such as Frank vector, breaks through the existing material defect density measurement method and the difficulty in accurately describing and calculating the rotation vector, proposes a differential calculation method for the rotation vector, and quantifies the microdefects such as dislocation and dislocation by combining the EBSD data of the metal material to be measured, which provides an important reference for analyzing the influence of crystal defects such as dislocation on material performance.

Description

Technical Field

[0001] This invention relates to the technical field of quantitative analysis of defect density in metallic materials to regulate material properties, and specifically to a method for measuring the defect density of metallic materials. Background Technology

[0002] Crystal defects, such as dislocations, are widely present in metals and play a crucial role in determining the mechanical properties of materials. By adjusting the structure and density of defects within the crystal, the mechanical properties of metals and alloys can be improved through machining and other methods. For example, work hardening, a common engineering practice, is one of the most effective methods to improve the strength of metallic materials. Its solution lies in increasing the dislocation density of the crystal during cold working, thereby increasing the material's strength. In physical metallurgy and materials science, information about defect structures is crucial for establishing the fundamental relationship between microstructure, processing, and properties, all of which require quantitative methods to determine defect characteristics. Currently, there is no precise quantitative calculation method for dislocations because there is a lack of mathematical tools to describe the rotational characteristics and structure of this crystal defect. This also leads to the lack of consideration for dislocations in existing analyses of the impact of crystal defects on material properties. Therefore, how to quantitatively analyze dislocations in metallic materials and thus comprehensively analyze the impact of crystal defects on material properties is a pressing technical challenge that needs to be addressed. Summary of the Invention

[0003] To address the aforementioned technical challenges, this invention provides a method for measuring the defect density of metallic materials.

[0004] A method for measuring the defect density of metallic materials, characterized by comprising the following steps:

[0005] Step 1: Establish the original dataset 1 for the target metallic material's test area;

[0006] To collect the required data for EBSD experiments on the test area of ​​the target metallic material, the number of data points in the EBSD map of the test area is defined as N, where the information of any data point is represented by orientation parameters and position parameters.

[0007] The number of data points N satisfies: 10 ≤ N ≤ 10000000 and N is an integer.

[0008] The information for any point is: orientation parameters, using three Euler angles, which are (α... i ,β i ,γ i ), with position parameter (x i ,y i ), where i satisfies: 1≤i≤N and i is an integer.

[0009] The data point information in the EBSD map of the area to be tested is then defined as dataset 1, which is: {(x1,y1,α1,β1,γ1), (x2,y2,α2,β2,γ2)…(x N ,y N ,α N ,β N ,γ N )}.

[0010] Step 2: Preprocess Dataset 1;

[0011] Select the orientation parameter (α) of any point in dataset 1 from step 1. i ,β i ,γ i The rotation matrix g of the point is obtained by calculating the following formulas (1), (2), (3) and (4). i ;

[0012]

[0013]

[0014]

[0015]

[0016] Among them, g i Defined as a rotation matrix at a point.

[0017] Defined as a point Euler angle α i The corresponding matrix representation,

[0018] Defined as a point Euler angle β i The corresponding matrix representation,

[0019] Defined as a point Euler angle γ i The corresponding matrix representation;

[0020] For all points in dataset 1, calculate according to formulas (1), (2), (3), and (4) to obtain dataset 2, which is: {(x1,y1,g1), (x2,y2,g2)…(x N ,y N ,g N )}.

[0021] Select the rotation matrix g of any point in dataset 2 i Because of g i ∈ SO(3) group, therefore g can be obtained through logarithmic mapping. i Corresponding Lie algebra The rotation vector ω at any point can then be calculated using the following formulas (5) and (6). i ;

[0022]

[0023]

[0024] in, Defined as g i The corresponding Lie algebra,

[0025] ω i Defined as a rotation vector,

[0026] ∨ is defined as satisfying The symbols for operations;

[0027] After calculating all points in dataset 2 according to formulas (5) and (6), dataset 3 is obtained. Dataset 3 is: {(x1,y1,ω1), (x2,y2,ω2)…(x N ,y N ,ω N )};.

[0028] Step 3: Determine if there are grain boundaries around the point;

[0029] Select the rotation matrix g of any point in dataset 2 i The rotation matrix of the point and the four points surrounding it is denoted as g. j Where j is any one of i-1, i+1, ih or i+h, h is the ratio of the x-direction length of the EBSD data map to the scan step size, and M is defined as... ij Let M be the grain boundary determination variable, and when M ij =1 indicates the presence of a grain boundary, M ij =0 means there are no grain boundaries, then M ij It is obtained by calculation using formulas (7), (8), (9) and (10);

[0030] q ij =g j g i -1 (7)

[0031] ω ij =(q ij ) ∨ (8)

[0032] δ ij =|ω ij | (9)

[0033]

[0034] Where, q ij Defined as the orientation difference matrix between the selected point and its surrounding points.

[0035] ω ij Defined as orientation difference matrix q ij The corresponding rotation vector,

[0036] δ ij Defined as rotation vector ω ij The corresponding orientation difference angle, in radians;

[0037] After calculating all points in dataset 2 according to formulas (7), (8), (9), and (10), dataset 4 is finally obtained. Dataset 4 is {(x1, y1, M... 1j ), (x2,y2,M 2j )…(x N ,y N M Nj )}.

[0038] Step 4: Calculate the elastic torsion tensor K ie ;

[0039] Select the rotation vector ω of any point in dataset 3 i Define the elastic torsion tensor at any point as K. ie Then K ie We obtain the following formulas (11), (12), (13), (14), and (15):

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] in, Defined as a gradient computation notation containing a Lie algebra structure.

[0046] Defined as the derivative sign along the x-axis for structures containing Lie algebras.

[0047] Defined as the derivative symbol along the y-axis for structures containing Lie algebras.

[0048] Defined as the derivative sign along the z-axis containing Lie algebraic structures.

[0049] [] represents the bracket operator.

[0050] In formulas (13), (14) and (15) and The calculation uses the five-point method, and M is set. ij Points with a value of 0 participate in the elastic torsion tensor K. ie Calculation;

[0051] After performing calculations on all points in dataset 3 according to formulas (11), (12), (13), (14), and (15), dataset 5 is obtained. Dataset 5 is {(x1, y1, K} 1e ), (x2,y2,K 2e )…(x N ,y N ,K Ne )}.

[0052] Step 5: Calculate the dislocation density tensor α i ;

[0053] Select the elastic torsion tensor K at any point in dataset 5 from step 4. ie Define the dislocation density tensor at any point as α i Then α i It is obtained from the following formula (16):

[0054] α i =tr(K ie )I-(K ie ) t (16)

[0055] Where I is the identity matrix,

[0056] tr is the trace notation for a matrix.

[0057] t is the matrix transpose symbol;

[0058] Perform calculations on all points in dataset 5 according to formula (16) to obtain dataset 6, which is {(x1,y1,α...} 1 ), (x2,y2,α 2 )…(xN , y N ,α N )}.

[0059] Step 6: Calculate the dislocation density tensor θ i ;

[0060] Select the elastic torsion tensor K at any point in dataset 5 from step 4. ie Define the dislocation density tensor at any point as θi θ i It is obtained from the following formulas (17) and (18);

[0061]

[0062]

[0063] in, Defined as a curl calculation notation containing a Lie algebra structure;

[0064] Dataset 7 is obtained by calculating all points in dataset 5 according to formulas (17) and (18). Dataset 7 is {(x1,y1,θ...} 1 ), (x2,y2,θ 2 )…(x N ,y N ,θ N )}.

[0065] Furthermore, the position of the point mentioned in step 3 relative to the four surrounding points is as follows: the four points are located sequentially to the left, right, up, and down of the point.

[0066] Furthermore, the specified value described in formula (10) is radian.

[0067] Furthermore, N is 100 ≤ N ≤ 1000000.

[0068] Furthermore, the metal material is an iron alloy, magnesium alloy, or aluminum alloy.

[0069] Furthermore, the iron alloy is a ferrosilicon alloy, a ferromanganese alloy, a ferrochrome alloy, a ferronickel alloy, or a ferrotitanium alloy.

[0070] Furthermore, the magnesium alloy is a magnesium-aluminum alloy, a magnesium-manganese alloy, or a magnesium-zinc-zirconium alloy.

[0071] Furthermore, the aluminum alloy is one of the 1-9 series aluminum alloys.

[0072] Furthermore, the titanium alloy is: titanium-aluminum alloy, titanium-tin alloy, titanium-zirconium alloy, or titanium-vanadium alloy.

[0073] The beneficial effects of adopting the technical solution of this invention are as follows:

[0074] This invention, for the first time, introduces the mathematical tools of Lie algebras and EBSD data to describe the rotational properties and structure of dislocations, a crystal defect. It proposes a differential calculation method for rotational vectors, such as the Frank vector representing dislocations. This method not only clearly and intuitively represents the rotational properties of the rotational vectors but also facilitates the superposition and differential operations of these vectors. Compared to traditional methods for measuring the defect density of metallic materials, which lack quantitative analysis of dislocations, resulting in an incomplete analysis of the relationship between material properties and crystal defects, the method provided in this invention enables simultaneous quantitative analysis of both dislocations and dislocations—two widely existing defects in crystals. This establishes a more accurate and comprehensive measurement method for the defect density of metallic materials, providing a new perspective and more complete support for studying the relationship between material properties and crystal defects, and also offering important reference for the field of materials testing. Attached Figure Description

[0075] Figure 1 This is a flowchart illustrating the overall process of a method for measuring the defect density of metallic materials according to the present invention.

[0076] Figure 2 This is an image of EBSD data collected from the test area in Embodiment 1 of the present invention;

[0077] Figure 3 This is a schematic diagram of the grain boundary structure of the test region in Embodiment 1 of the present invention;

[0078] Figure 4 This is a schematic diagram of the dislocation density distribution in the test area of ​​Embodiment 1 of the present invention, with units of 1 / μm. (a) shows the total dislocation density distribution, and (b), (c), (d), (e), and (f) represent the dislocation density tensor α, respectively. i 12 components 21 components 13 portions 23 portions and 33 components Distribution diagram;

[0079] Figure 5 This is a schematic diagram of the anisotropy density distribution in the test area of ​​Embodiment 1 of the present invention, with units of rad / μm. 2 (a) is a schematic diagram of the total dislocation density distribution, and (b), (c) and (d) are the dislocation density tensors θ, respectively. i 13 components 23 portions and 33 components Distribution diagram;

[0080] Figure 6 This is an image of EBSD data collected from the test area in Embodiment 2 of the present invention;

[0081] Figure 7 This is a schematic diagram of the grain boundary structure of the test region in Embodiment 2 of the present invention;

[0082] Figure 8 This is a schematic diagram of the dislocation density distribution in the test area of ​​Embodiment 2 of the present invention, with units of 1 / μm. Among them, (a) is a schematic diagram of the total dislocation density distribution, and (b), (c), (d), (e), and (f) are the dislocation density tensors α, respectively. i 12 components 21 components 13 portions 23 portions and 33 components Distribution diagram;

[0083] Figure 9 This is a schematic diagram of the anisotropy density distribution in the test area of ​​Embodiment 2 of the present invention, with units of rad / μm. 2 (a) is a schematic diagram of the total dislocation density distribution, and (b), (c) and (d) are the dislocation density tensors θ, respectively. i 13 components 23 portions and 33 components Distribution diagram;

[0084] Figure 10 This is a diagram of EBSD data collected from the test area in Embodiment 3 of the present invention;

[0085] Figure 11 This is a schematic diagram of the grain boundary structure of the test region in Embodiment 3 of the present invention;

[0086] Figure 12 This is a schematic diagram of the dislocation density distribution in the test area of ​​Embodiment 3 of the present invention, with units of 1 / μm. (a) shows the total dislocation density distribution, and (b), (c), (d), (e), and (f) represent the dislocation density tensor α, respectively. i 12 components 21 components 13 portions 23 portions and 33 components Distribution diagram;

[0087] Figure 13 This is a schematic diagram of the anisotropy density distribution in the test area of ​​Embodiment 3 of the present invention, with units of rad / μm. 2 (a) is a schematic diagram of the total dislocation density distribution, and (b), (c) and (d) are the dislocation density tensors θ, respectively. i 13 components 23 portions and 33 components Distribution diagram. Detailed Implementation

[0088] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0089] Example 1

[0090] A method for measuring the defect density of a metallic material includes the following steps:

[0091] Step 1: Establish the original dataset 1 for the target metallic material's test area;

[0092] In this embodiment, a metallographic sample was prepared using commercially available AZ31 magnesium alloy. An EBSD experiment was performed on a region of the metallographic sample that clearly displayed its microstructure to collect the necessary data. The resulting EBSD data image is shown below. Figure 2 Define the number of data points in the EBSD map of the area to be tested as N, and the number of data points in the resulting data map is N = 65455. Use orientation parameters and position parameters to define the information of any point in the data map.

[0093] The arbitrary point information is defined as follows: Orientation parameters: using three Euler angles, which are (α... i ,β i ,γ i ), with position parameter (x i ,y i ), where i satisfies: 1≤i≤65455 and i is an integer.

[0094] The data point information in the EBSD map of the area to be tested is then defined as dataset 1, which is: {(x1,y1,α1,β1,γ1),(x2,y2,α2,β2,γ2)…(x 65455 ,y 65455 ,α 65455 ,β 65455 ,γ 65455 )}.

[0095] Step 2: Preprocess Dataset 1;

[0096] In this embodiment, x from dataset 1 42313 =26.55, y 42313 Taking the point α = 23.85 as an example, read the orientation information (α) at ​​this point. 42313 ,β 42313 ,γ 42313 The value is (42.462, 153.72, 18.015). The rotation matrix corresponding to this point can be calculated using formulas (1), (2), (3), and (4).

[0097]

[0098]

[0099]

[0100]

[0101] Among them, g i Defined as a rotation matrix at a point.

[0102] Defined as a point Euler angle α i The corresponding matrix representation,

[0103] Defined as a point Euler angle β i The corresponding matrix representation,

[0104] Defined as a point Euler angle γ i The corresponding matrix representation;

[0105] The remaining points in dataset 1 are calculated using formulas (1), (2), (3), and (4) to obtain dataset 2 as: {(x1,y1,g1),(x2,y2,g2)…(x 65455 ,y 654555 ,g 65455 )}.

[0106] Then take x from dataset 2 42313 =26.55, y 42313 Taking the value of 23.85 as an example, read its rotation matrix. The rotation vector of this point is calculated using formulas (5) and (6).

[0107]

[0108]

[0109] in, Defined as g i The corresponding Lie algebra,

[0110] ω i Defined as a rotation vector,

[0111] ∨ is defined as satisfying The symbols for operations;

[0112] After performing the same calculations on the remaining points in dataset 2 according to formulas (5) and (6), dataset 3 is obtained as: {(x1,y1,ω1),(x2,y2,ω2)…(x 65455 ,y 654555 ,ω65455 )}.

[0113] Step 3: Determine if there are grain boundaries around the point;

[0114] In this embodiment, x from dataset 2 is still used as an example. 42313 =26.55, y 42313 Taking the point = 23.85 as an example, the rotation matrix for the surrounding 4 points is g. j Where j is any one of 42312, 42314, 42048 or 42578, and the specified value is... The radian value is then calculated using formulas (7), (8), (9), and (10) to obtain the grain boundary determination variable M at this point. 42313j =1;

[0115] q ij =g j g i -1 (7)

[0116] ω ij =(q ij ) ∨ (8)

[0117] δ ij =|ω ij | (9)

[0118]

[0119] Where, q ij Defined as the orientation difference matrix between the selected point and its surrounding points.

[0120] ω ij Defined as orientation difference matrix q ij The corresponding rotation vector,

[0121] δ ij Defined as rotation vector ω ij The corresponding orientation difference angle, in radians;

[0122] Calculated M 42313j =1, and all of the above values ​​for j hold true, indicating that there are grain boundaries between this point and its surrounding points. After calculating the remaining points in dataset 2 according to formulas (7), (8), (9), and (10), dataset 4 is obtained as: {(x1,y1,M 1j ),(x2,y2,M 2j )…(x 65455 ,y 65455 M 65455j Select the grain boundary determination variable M from dataset 4. ij Value and location information (x) i,y i The grain boundary diagram of the test region of the sample can be drawn using MATLAB software (see...). Figure 3 Furthermore, it can determine whether each point crosses a grain boundary with its surrounding points, which is helpful for subsequent calculations of dislocation and dislocation density.

[0123] Step 4: Calculate the elastic torsion tensor K ie ;

[0124] In this embodiment, x from dataset 3 is used as an example. 42313 =26.55, y 42313 Taking the point = 23.85 as an example, read the rotation matrix for this point. From formulas (11), (12), (13), (14) and (15), we obtain its

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] in, Defined as a gradient computation notation containing a Lie algebra structure.

[0131] Defined as the derivative sign along the x-axis for structures containing Lie algebras.

[0132] Defined as the derivative symbol along the y-axis for structures containing Lie algebras.

[0133] Defined as the derivative sign along the z-axis containing Lie algebraic structures.

[0134] [] represents the bracket operator.

[0135] In formulas (13), (14) and (15) and The calculation uses the five-point method, and M is set. ij Points with a value of 0 participate in the elastic torsion tensor K. ie Calculation;

[0136] For the elastic torsion tensor K obtained at each point in this embodiment ieSince the data measured by the EBSD experiment only pertains to a single cross-section of the sample, it cannot display information about the portion perpendicular to the sample cross-section, i.e., it cannot display information about the z-axis direction. Therefore, the tensor K to be calculated... ie The three components in the z-axis direction are missing, namely... and Three parts, and in the dislocation density tensor and These four components and the dislocation density tensor and The calculation of these six components requires and Since it consists of three parts, it cannot be derived. When the experiment can provide three-dimensional orientation and position information of the sample, the method provided by this invention can calculate all components of the dislocation and orientation density tensor.

[0137] After performing the same calculations on the remaining points in dataset 3 according to formulas (11), (12), (13), (14), and (15), dataset 5 is obtained as: {(x1,y1,K 1e ), (x2,y2,K 2e )…(x 65455 ,y 65455 ,K 65455e )}.

[0138] Step 5: Calculate the dislocation density tensor α i ;

[0139] In this embodiment, x from dataset 5 42313 =26.55, y 42313 Taking the point 23.85 as an example, read the elastic torsion tensor at this point. The dislocation density tensor is obtained from formula (16).

[0140] α i =tr(K ie )I-(K ie ) t (16)

[0141] Where I is the identity matrix,

[0142] tr is the trace notation for a matrix.

[0143] t is the matrix transpose symbol;

[0144] For the dislocation density tensor α at each point obtained in this embodiment i Due to tensor K ie The sample lacks three components perpendicular to its cross-section. and Therefore, only the dislocation density tensor can be obtained. and These five components.

[0145] After performing the same calculations on the remaining points in dataset 5 according to formula (16), dataset 6 is obtained as: {(x1,y1,α 1 ), (x2,y2,α 2 )…(x 65455 ,y 65455 ,α 65455 )}, select the dislocation density tensor α for each point in dataset 6 i Value and location information (x) i ,y i Based on the principle that the total dislocation density equals the sum of the squares of each of the sub-square dislocation density components, the total dislocation density and the distribution of each component in the test region of the sample can be plotted using MATLAB software (see...). Figure 4 ).

[0146] Step 6: Calculate the dislocation density tensor θ i ;

[0147] In this embodiment, x from dataset 5 is still used as an example. 42313 =26.55, y 42313 Taking the point 23.85 as an example, read the elastic torsion tensor at this point. Its dislocation density tensor is obtained from formulas (17) and (18).

[0148]

[0149]

[0150] in, Defined as a curl calculation notation containing a Lie algebra structure;

[0151] For the dislocation density tensor θ at each point obtained in this embodiment i Due to tensor K ie The sample lacks three components perpendicular to its cross-section. and Therefore, only the displaced density tensor can be obtained. and These three components.

[0152] After performing the same calculations on the remaining points of dataset 5 according to formulas 17) and (18), dataset 7 is obtained as: {(x1,y1,θ 1 ), (x2,y2,θ 2 )…(x 65455 ,y65455 ,θ 65455 )}, select the dislocation density tensor θ for each point in dataset 7 i Value and location information (x) i ,y i Based on the principle that the total dislocation density equals the sum of the squares of the dislocation density components, MATLAB software can be used to plot the total dislocation density and the distribution of each component in the test area of ​​the sample (see...). Figure 5 ).

[0153] Based on AERomanov's 2002 formula σ=λGθ proposed in his study of dislocation structures in deformable materials and Taylor's formula... Where σ is the material strength, λ is the geometric factor related to dislocation, G is the shear modulus of the material, δ is the geometric factor related to dislocation, and b is the Burgers vector; it can be seen that dislocation density and dislocation density jointly affect the material strength. Therefore, the method for measuring metal defect density provided by the present invention can simultaneously calculate dislocation and dislocation densities, thereby predicting and controlling the material properties. The dislocation density tensor α at all points of the AZ31 magnesium alloy sample selected in Example 1 is... i Take the average value α ave1 = 0.0255, dislocation density tensor θ i Take the average value θ ave1 =0.0172, and the yield strength σ1 of the commercial AZ31 magnesium alloy in this embodiment was measured to be 259.388 MPa.

[0154] Commercial AZ31 alloy α as described in Example 1 ave1 and α ave1 As a standard, when metallic materials are processed, the density of dislocations and faults within the material is changed, and therefore the strength of the material also changes accordingly.

[0155] Example 2

[0156] A method for measuring the defect density of a metallic material includes the following steps:

[0157] Step 1: Establish the original dataset 1 for the target metallic material's test area;

[0158] In this embodiment, a metallographic sample was prepared from a commercially available AZ31 magnesium alloy annealed at 300°C for 1 hour. An EBSD experiment was performed on a region of this metallographic sample that clearly showed the defect structure, and the resulting EBSD data is shown in the figure below. Figure 6 Define the number of data points in the EBSD map of the area to be tested as N, and the number of data points in the resulting data map is N = 24702. Use orientation parameters and position parameters to define the information of any point in the data map.

[0159] The arbitrary point information is defined as follows: Orientation parameters: using three Euler angles, which are (α... i ,β i ,γ i ), with position parameter (x i ,y i ), where i satisfies: 1≤i≤24702 and i is an integer.

[0160] The data point information in the EBSD map of the area to be tested is then defined as dataset 1, which is: {(x1,y1,α1,β1,γ1),(x2,y2,α2,β2,γ2)…(x 24702 ,y 24702 ,α 24702 ,β 24702 ,γ 24702 )}.

[0161] Step 2: Preprocess Dataset 1;

[0162] In this embodiment, x from dataset 1 10952 =7.35, y 10952 Taking the point α = 11.85 as an example, read the orientation information (α) at ​​this point. 10952 ,β 10952 ,γ 10952 The value is (38.623, 154.07, 56.299). The rotation matrix corresponding to this point can be calculated using formulas (1), (2), (3), and (4).

[0163]

[0164]

[0165]

[0166]

[0167] Among them, g i Defined as a rotation matrix at a point.

[0168] Defined as a point Euler angle α i The corresponding matrix representation,

[0169] Defined as a point Euler angle β i The corresponding matrix representation,

[0170] Defined as a point Euler angle γ i The corresponding matrix representation;

[0171] The remaining points in dataset 1 are calculated using formulas (1), (2), (3), and (4) to obtain dataset 2 as: {(x1,y1,g1),(x2,y2,g2)…(x 24702 ,y 247025 ,g 24702 )}.

[0172] Then take x from dataset 2 10952 =7.35, y 10952 Taking the value of 11.85 as an example, read its rotation matrix. The rotation vector of this point is calculated using formulas (5) and (6).

[0173]

[0174]

[0175] in, Defined as g i The corresponding Lie algebra,

[0176] ω i Defined as a rotation vector,

[0177] ∨ is defined as satisfying The symbols for operations;

[0178] After performing the same calculations on the remaining points in dataset 2 according to formulas (5) and (6), dataset 3 is obtained as: {(x1,y1,ω1),(x2,y2,ω2)…(x 24702 ,y 247025 ,ω 24702 )}.

[0179] Step 3: Determine if there are grain boundaries around the point;

[0180] In this embodiment, x from dataset 2 is still used as an example. 10952 =7.35, y 10952 Taking the point = 11.85 as an example, the rotation matrix for the surrounding 4 points is g. j Where j is any one of 10951, 10953, 10814 or 11090, and the specified value is... The radian value is then calculated using formulas (7), (8), (9), and (10) to obtain the grain boundary determination variable M at this point. 10952j =1;

[0181] q ij =g j g i -1 (7)

[0182] ω ij =(q ij ) ∨ (8)

[0183] δ ij =|ψ ij | (9)

[0184]

[0185] Where, q ij Defined as the orientation difference matrix between the selected point and its surrounding points.

[0186] ω ij Defined as orientation difference matrix q ij The corresponding rotation vector,

[0187] δ ij Defined as rotation vector ω ij The corresponding orientation difference angle, in radians;

[0188] Calculated M 10952j =1, and all of the above values ​​for j hold true, indicating that there are grain boundaries between this point and its surrounding points. After calculating the remaining points in dataset 2 according to formulas (7), (8), (9), and (10), dataset 4 is obtained as: {(x1,y1,M 1j ),(x2,y2,M 2j )…(x 24702 ,y 24702 M 24702j Select the grain boundary determination variable M from dataset 4. ij Value and location information (x) i ,y i The grain boundary diagram of the test region of the sample can be drawn using MATLAB software (see...). Figure 7 Furthermore, it can determine whether each point crosses a grain boundary with its surrounding points, which is helpful for subsequent calculations of dislocation and dislocation density.

[0189] Step 4: Calculate the elastic torsion tensor K ie ;

[0190] In this embodiment, x from dataset 3 is used as an example. 10952 =7.35, y 10952 Taking the point = 11.85 as an example, read the rotation matrix for this point. From formulas (11), (12), (13), (14) and (15), we obtain its

[0191]

[0192]

[0193]

[0194]

[0195]

[0196] in, Defined as a gradient computation notation containing a Lie algebra structure.

[0197] Defined as the derivative sign along the x-axis for structures containing Lie algebras.

[0198] Defined as the derivative symbol along the y-axis for structures containing Lie algebras.

[0199] Defined as the derivative sign along the z-axis containing Lie algebraic structures.

[0200] [] represents the bracket operator.

[0201] In formulas (13), (14) and (15) and The calculation uses the five-point method, and M is set. ij Points with a value of 0 participate in the elastic torsion tensor K. ie Calculation;

[0202] For the elastic torsion tensor K obtained at each point in this embodiment ie Since the data measured by the EBSD experiment only pertains to a single cross-section of the sample, it cannot display information about the portion perpendicular to the sample cross-section, i.e., it cannot display information about the z-axis direction. Therefore, the tensor K to be calculated... ie The three components in the z-axis direction are missing, namely... and Three parts, and in the dislocation density tensor and These four components and the dislocation density tensor and The calculation of these six components requires and Since it consists of three parts, it cannot be derived. When the experiment can provide three-dimensional orientation and position information of the sample, the method provided by this invention can calculate all components of the dislocation and orientation density tensor.

[0203] After performing the same calculations on the remaining points in dataset 3 according to formulas (11), (12), (13), (14), and (15), dataset 5 is obtained as: {(x1,y1,K 1e), (x2,y2,K 2e )…(x 24702 ,y 24702 ,K 24702e )}.

[0204] Step 5: Calculate the dislocation density tensor α i ;

[0205] In this embodiment, x from dataset 5 10952 =7.35, y 10952 Taking the point 11.85 as an example, read the elastic twist tensor at this point. The dislocation density tensor is obtained from formula (16).

[0206] α i =tr(K ie )I-(K ie ) t (16)

[0207] Where I is the identity matrix,

[0208] tr is the trace notation for a matrix.

[0209] t is the matrix transpose symbol;

[0210] For the dislocation density tensor α at each point obtained in this embodiment i Due to tensor K ie The sample lacks three components perpendicular to its cross-section. and Therefore, only the dislocation density tensor can be obtained. and These five components.

[0211] After performing the same calculations on the remaining points in dataset 5 according to formula (16), dataset 6 is obtained as: {(x1,y1,α 1 ), (x2,y2,α 2 )…(x 24702 ,y 24702 ,α 24702 )}, select the dislocation density tensor α for each point in dataset 6 i Value and location information (x) i ,y i Based on the principle that the total dislocation density equals the sum of the squares of each of the sub-square dislocation density components, the total dislocation density and the distribution of each component in the test region of the sample can be plotted using MATLAB software (see...). Figure 8 ).

[0212] Step 6: Calculate the dislocation density tensor θ i ;

[0213] In this embodiment, x from dataset 5 is still used as an example. 10952 =7.35, y 10952 Taking the point 11.85 as an example, read the elastic twist tensor at this point. Its dislocation density tensor is obtained from formulas (17) and (18).

[0214]

[0215] in, Defined as a curl calculation notation containing a Lie algebra structure;

[0216] For the dislocation density tensor θ at each point obtained in this embodiment i Due to tensor K ie The sample lacks three components perpendicular to its cross-section. and Therefore, only the displaced density tensor can be obtained. and These three components.

[0217] After performing the same calculations on the remaining points of dataset 5 according to formulas 17) and (18), dataset 7 is obtained as: {(x1,y1,θ 1 ), (x2,y2,θ 2 )…(x 24702 ,y 24702 ,θ 24702 )}, select the dislocation density tensor θ for each point in dataset 7 i Value and location information (x) i ,y i Based on the principle that the total dislocation density equals the sum of the squares of the dislocation density components, MATLAB software can be used to plot the total dislocation density and the distribution of each component in the test area of ​​the sample (see...). Figure 9 ).

[0218] Calculate the dislocation density α in the material sample selected in Example 2. i The average value α ave2 = 0.0062, dislocation density tensor θ i The average value θ ave2 =0.0051, and the measured yield strength σ2 of this material is 241.511 MPa. Compared with the material selected in Example 1, α ave2 <α ave1 θ ave2 <θ ave1 Since σ2 < σ1, it can be seen that the processing method in Example 2 will reduce the dislocation and fault density of the alloy material, which will lead to a decrease in the strength of the material.

[0219] Example 3

[0220] A method for measuring the defect density of a metallic material includes the following steps:

[0221] Step 1: Establish the original dataset 1 for the target metallic material's test area;

[0222] In this embodiment, a metallographic specimen was prepared from a commercially available AZ31 magnesium alloy stretched to 13.5% strain along the TD direction at room temperature. An EBSD experiment was performed on a region of this metallographic specimen that clearly showed the defect microstructure, and the resulting EBSD data is shown in the figure below. Figure 10 Define the number of data points in the EBSD map of the area to be tested as N, and the number of data points in the resulting data map is N = 76473. Use orientation parameters and position parameters to define the information of any point in the data map.

[0223] The arbitrary point information is defined as follows: Orientation parameters: using three Euler angles, which are (α... i ,β i ,γ i ), with position parameter (x i ,y i ), where i satisfies: 1≤i≤76473 and i is an integer,

[0224] The data point information in the EBSD map of the area to be tested is then defined as dataset 1, which is: {(x1,y1,α1,β1,γ1),(x2,y2,α2,β2,γ2)…(x 76473 ,y 76473 ,α 76473 ,β 76473 ,γ 76473 )}.

[0225] Step 2: Preprocess Dataset 1;

[0226] In this embodiment, x from dataset 1 25266 =10.05, y 25266 Taking the point = 12.9 as an example, read the orientation information (α) at ​​this point. 25266 ,β 25266 ,γ 25266 The value is (110.55, 161.15, 41.422). The rotation matrix corresponding to this point can be calculated using formulas (1), (2), (3), and (4).

[0227]

[0228]

[0229]

[0230]

[0231] Among them, g i Defined as a rotation matrix at a point.

[0232] Defined as a point Euler angle α i The corresponding matrix representation,

[0233] Defined as a point Euler angle β i The corresponding matrix representation,

[0234] Defined as a point Euler angle γ i The corresponding matrix representation;

[0235] The remaining points in dataset 1 are calculated using formulas (1), (2), (3), and (4) to obtain dataset 2 as: {(x1,y1,g1),(x2,y2,g2)…(x 76473 ,y 76473 ,g 76473 )}.

[0236] Then take x from dataset 2 25266 =10.05, y 25266 Taking the point = 12.9 as an example, read its rotation matrix. The rotation vector of this point is calculated using formulas (5) and (6).

[0237]

[0238]

[0239] in, Defined as g i The corresponding Lie algebra,

[0240] ω i Defined as a rotation vector,

[0241] ∨ is defined as satisfying The symbols for operations;

[0242] After performing the same calculations on the remaining points in dataset 2 according to formulas (5) and (6), dataset 3 is obtained as: {(x1,y1,ω1),(x2,y2,ω2)…(x 76473 ,y 76473 ,ω 76473 )}.

[0243] Step 3: Determine if there are grain boundaries around the point;

[0244] In this embodiment, x from dataset 2 is still used as an example. 25266 =10.05, y 25266 Taking the point = 12.9 as an example, the rotation matrix for the surrounding 4 points is g. j Where j is any one of 25265, 25267, 24973 or 25559, and the specified value is... The radian value is then calculated using formulas (7), (8), (9), and (10) to obtain the grain boundary determination variable M at this point. 25266j =1;

[0245] q ij =g j g i -1 (7)

[0246] ω ij =(q ij ) ∨ (8)

[0247] δ ij =|ω ij | (9)

[0248]

[0249] Where, q ij Defined as the orientation difference matrix between the selected point and its surrounding points.

[0250] ω ij Defined as orientation difference matrix q ij The corresponding rotation vector,

[0251] δ ij Defined as rotation vector ω ij The corresponding orientation difference angle, in radians;

[0252] Calculated M 25266j =1, and all of the above values ​​for j hold true, indicating that there are grain boundaries between this point and its surrounding points. After calculating the remaining points in dataset 2 according to formulas (7), (8), (9), and (10), dataset 4 is obtained as: {(x1,y1,M 1j ),(x2,y2,M 2j )…(x 76473 ,y 76473 M 76473j Select the grain boundary determination variable M from dataset 4. ij Value and location information (x) i ,y iThe grain boundary diagram of the test region of the sample can be drawn using MATLAB software (see...). Figure 11 Furthermore, it can determine whether each point crosses a grain boundary with its surrounding points, which is helpful for subsequent calculations of dislocation and dislocation density.

[0253] Step 4: Calculate the elastic torsion tensor K ie ;

[0254] In this embodiment, x from dataset 3 is used as an example. 25266 =10.05, y 25266 Taking the point = 12.9 as an example, read the rotation matrix for this point. From formulas (11), (12), (13), (14) and (15), we obtain its

[0255]

[0256]

[0257]

[0258]

[0259]

[0260] in, Defined as a gradient computation notation containing a Lie algebra structure.

[0261] Defined as the derivative sign along the x-axis for structures containing Lie algebras.

[0262] Defined as the derivative symbol along the y-axis for structures containing Lie algebras.

[0263] Defined as the derivative sign along the z-axis containing Lie algebraic structures.

[0264] [] represents the bracket operator.

[0265] In formulas (13), (14) and (15) and The calculation uses the five-point method, and M is set. ij Points with a value of 0 participate in the elastic torsion tensor K. ie Calculation;

[0266] For the elastic torsion tensor K obtained at each point in this embodiment ie Since the data measured by the EBSD experiment only pertains to a single cross-section of the sample, it cannot display information about the portion perpendicular to the sample cross-section, i.e., it cannot display information about the z-axis direction. Therefore, the tensor K to be calculated...ie The three components in the z-axis direction are missing, namely... and Three parts, and in the dislocation density tensor and These four components and the dislocation density tensor and The calculation of these six components requires and Since it consists of three parts, it cannot be derived. When the experiment can provide three-dimensional orientation and position information of the sample, the method provided by this invention can calculate all components of the dislocation and orientation density tensor.

[0267] After performing the same calculations on the remaining points in dataset 3 according to formulas (11), (12), (13), (14), and (15), dataset 5 is obtained as: {(x1,y1,K 1e ), (x2,y2,K 2e )…(x 76473 ,y 76473 ,K 76473e )}.

[0268] Step 5: Calculate the dislocation density tensor α i ;

[0269] In this embodiment, x from dataset 5 25266 =10.05, y 25266 Taking the point = 12.9 as an example, read the elastic torsion tensor at this point. The dislocation density tensor is obtained from formula (16).

[0270] α i =tr(K ie )I-(K ie ) t (16)

[0271] Where I is the identity matrix,

[0272] tr is the trace notation for a matrix.

[0273] t is the matrix transpose symbol;

[0274] For the dislocation density tensor α at each point obtained in this embodiment i Due to tensor K ie The sample lacks three components perpendicular to its cross-section. and Therefore, only the dislocation density tensor can be obtained. and These five components.

[0275] After performing the same calculations on the remaining points in dataset 5 according to formula (16), dataset 6 is obtained as: {(x1,y1,α 1 ), (x2,y2,α 2 )…(x 76473 ,y 76473 ,α 76473 )}, select the dislocation density tensor α for each point in dataset 6 i Value and location information (x) i ,y i Based on the principle that the total dislocation density equals the sum of the squares of each of the sub-square dislocation density components, the total dislocation density and the distribution of each component in the test region of the sample can be plotted using MATLAB software (see...). Figure 12 ).

[0276] Step 6: Calculate the dislocation density tensor θ i ;

[0277] In this embodiment, x from dataset 5 is still used as an example. 25266 =10.05, y 25266 Taking the point = 12.9 as an example, read the elastic torsion tensor at this point. Its dislocation density tensor is obtained from formulas (17) and (18).

[0278]

[0279]

[0280] in, Defined as a curl calculation notation containing a Lie algebra structure;

[0281] For the dislocation density tensor θ at each point obtained in this embodiment i Due to tensor K ie The sample lacks three components perpendicular to its cross-section. and Therefore, only the displaced density tensor can be obtained. and These three components.

[0282] After performing the same calculations on the remaining points of dataset 5 according to formulas (17) and (18), dataset 7 is obtained as: {(x1,y1,θ 1 ), (x2,y2,θ 2 )…(x 76473 ,y 76473 ,θ 76473 )}, select the dislocation density tensor θ for each point in dataset 7 i Value and location information (x) i,y i Based on the principle that the total dislocation density equals the sum of the squares of the dislocation density components, MATLAB software can be used to plot the total dislocation density and the distribution of each component in the test area of ​​the sample (see...). Figure 13 ).

[0283] Calculate the dislocation density tensor α in the material sample selected in Example 3. i The average value α ave3 = 0.0496, dislocation density tensor θ i The average value θ ave3 =0.0387, and the measured yield strength σ3 of this material is 279.739 MPa. Compared with the material selected in Example 1, α ave3 >α ave1 θ ave3 >θ ave1 σ3>σ1, meaning that the dislocation and fault density of the alloy material is increased after processing in Example 3, and the strength of the material is also increased as a result.

[0284] Traditional dislocation density calculation methods based on KAM diagrams were proposed by Marion Calcagnotto et al. in 2010 in their study of orientation gradients and geometrically necessary dislocations in ultrafine grains. Unlike the dislocation density calculation method provided in this invention, traditional methods calculate the average value of the local orientation difference in the selected region using KAM diagrams. ave Then by formula The dislocation density is calculated, where ρ is defined as the dislocation density, μ is the EBSD experimental scan step size, and b is the Burgers vector of the dislocation. Compared with the metal defect density measurement method provided by this invention, firstly, traditional methods do not consider the rotational characteristics and structure of the rotational vector representing orientation when calculating orientation difference, resulting in errors in the differential calculation of orientation difference and thus lacking accuracy in the calculation of dislocation density. The dislocation density calculation method provided by this invention takes into account the rotational vector representing orientation more completely, deriving a differential calculation method that reflects its rotational characteristics and structure. Secondly, traditional methods cannot calculate the specific components of the dislocation density tensor, thus failing to quantify the individual densities of edge dislocations and screw dislocations. The method provided by this invention can calculate the specific components of the dislocation density tensor, enabling more refined quantitative calculations of any component in the dislocation. Finally, existing technologies do not disclose the calculation method and related parameters for dislocation density, while the metal defect density measurement method provided by this invention can simultaneously calculate the densities of both dislocations and dislocations in metallic materials, providing support for a more comprehensive study of the impact of defects on material properties. The method provided by this invention can not only simultaneously detect the density of dislocations and dislocations in metallic materials, enabling more accurate quantitative calculation of material defect density, but also provide early warning for whether metallic materials can be successfully industrialized. Specifically, when the density of dislocations and dislocations in the tested metallic material differs significantly from the standard values ​​for commercial materials, it can promptly indicate which processing technology is more suitable for industrialization. Furthermore, in the field of materials testing, the calculation of the density of dislocations and dislocations can reveal whether the material's performance meets the specified requirements.

[0285] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for measuring the defect density of metallic materials, characterized in that: Includes the following steps: Step 1: Establish the original dataset 1 for the target metallic material's test area; The required data are collected by performing EBSD experiments on the test area of ​​the target metallic material. The number of data points in the EBSD image of the test area is defined as follows: The information of any data point is represented by orientation parameters and position parameters; The number of data points satisfy: and It is an integer. The information for any data point is: orientation parameters, using three Euler angles, which are... The position parameters are ,in satisfy: and It is an integer. The data point information in the EBSD map of the area to be tested is then defined as dataset 1. Dataset 1 is: ; Step 2: Preprocess Dataset 1; Select the orientation parameter of any data point in dataset 1 from step 1. The rotation matrix of the point can be calculated using the following formulas (1), (2), (3) and (4). ; in, Defined as a rotation matrix at a point. Defined as a one-point Euler angle The corresponding matrix, Defined as a one-point Euler angle The corresponding matrix, Defined as a one-point Euler angle The corresponding matrix; Calculate all points in dataset 1 according to formulas (1), (2), (3), and (4) to obtain dataset 2, which is: ; Select the rotation matrix of any data point in dataset 2 ,because The group, therefore, can be obtained through the logarithmic mapping. Corresponding Lie algebra Then, the rotation vector of any data point can be calculated using the following formulas (5) and (6). ; in, Defined as The corresponding Lie algebra, Defined as a rotation vector, Defined as satisfying The symbols for operations; After calculating all points in dataset 2 according to formulas (5) and (6), dataset 3 is obtained, which is: ; Step 3: Determine if there are grain boundaries around the point; Select the rotation matrix of any data point in dataset 2 The rotation matrix of the given point and the four points surrounding it is denoted as follows: The rotation matrix of any one of the four points is denoted as... ,in for or Any one of them, EBSD data graph x The ratio of directional length to scan step size, and defined. For grain boundary determination variables, and when This indicates the presence of grain boundaries. This indicates the absence of grain boundaries. It is obtained by calculation using formulas (7), (8), (9) and (10); in, Defined as the orientation difference matrix between the selected point and its surrounding points. Defined as orientation difference matrix The corresponding rotation vector, Defined as a rotation vector The corresponding orientation difference angle, in radians; After calculating all points in dataset 2 according to formulas (7), (8), (9), and (10), dataset 4 is finally obtained. Dataset 4 is... ; Step 4: Calculate the elastic torsion tensor ; Select the rotation vector of any data point in dataset 3 Define the elastic twist tensor of any data point as: ,but We obtain the following formulas (11), (12), (13), (14) and (15): in, Defined as a gradient computation notation containing a Lie algebra structure. Defined as an edge containing Lie algebra structure The sign of differentiation in the axial direction. Defined as an edge containing Lie algebra structure The sign of differentiation in the axial direction. Defined as an edge containing Lie algebra structure The sign of differentiation in the axial direction. For Lip bracket operators, In formulas (13), (14) and (15) The calculation uses the five-point method and sets... Points participating in the elastic twist tensor Calculation; After performing calculations on all points in dataset 3 according to formulas (11), (12), (13), (14), and (15), dataset 5 is obtained. Dataset 5 is... ; Step 5: Calculate the dislocation density tensor ; Select any data point from dataset 5 in step 4. Elastic twist tensor Define the dislocation density tensor of any data point as ,but It is obtained from the following formula (16): in, It is the identity matrix. tr is the trace notation for a matrix. t is the matrix transpose symbol; Perform calculations on all points in dataset 5 according to formula (16) to obtain dataset 6, which is... ; Step 6: Calculate the dislocation density tensor ; Select any data point from dataset 5 in step 4. Elastic twist tensor Define the disorientation density tensor of any data point as , It is obtained from the following formulas (17) and (18); in, Defined as a curl calculation notation containing a Lie algebra structure; Dataset 7 is obtained by calculating all points in dataset 5 according to formulas (17) and (18). Dataset 7 is... .

2. The method for measuring the defect density of metallic materials according to claim 1, characterized in that: The position of the point mentioned in step 3 relative to the four surrounding points is as follows: the four points are located to the left, right, up, and down of the point in sequence.

3. The method for measuring the defect density of metallic materials according to claim 1, characterized in that: The specified value described in formula (10) is radian.

4. The method for measuring the defect density of metallic materials according to claim 1, characterized in that: The aforementioned for .

5. A method for measuring the defect density of a metallic material according to any one of claims 1-4, characterized in that: The metal material is an iron alloy, magnesium alloy, aluminum alloy, or titanium alloy.

6. The method for measuring the defect density of a metallic material according to claim 5, characterized in that: The iron alloy is a silicon-iron alloy, a manganese-iron alloy, a chromium-iron alloy, a nickel-iron alloy, or a titanium-iron alloy.

7. The method for measuring the defect density of a metallic material according to claim 5, characterized in that: The magnesium alloy is a magnesium-aluminum alloy, a magnesium-manganese alloy, or a magnesium-zinc alloy.

8. The method for measuring the defect density of a metallic material according to claim 5, characterized in that: The aluminum alloy mentioned is any one of the 1-9 series aluminum alloys.

9. The method for measuring the defect density of a metallic material according to claim 5, characterized in that: The titanium alloy mentioned is: titanium-aluminum alloy, titanium-tin alloy, titanium-zirconium alloy, or titanium-vanadium alloy.

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