Neutron diffraction testing method and system for hexagonal intergranular stress

Abstract

The application provides a neutron diffraction testing method and system for hexagonal intergranular stress, comprising the following steps: S1, determining the composition phase and crystal structure type of a material to be tested, and detecting the texture of the material to be tested; S2, determining the texture component to be tested and the crystal face to be tested of a three-dimensional internal stress field, and calculating the specific direction relationship between the crystal face to be tested of the texture component to be tested and the sample to be tested; S3, neutron diffraction data acquisition, obtaining neutron diffraction signals of all corresponding crystal faces to be tested; and S4, calculating the three-dimensional internal stress field of different texture components of the material. The application solves the short board of the detection of the three-dimensional internal stress field of different texture components of the hexagonal system, and provides effective technical guidance for the testing of the third-order stress tensor of different texture components of hexagonal system alloys such as magnesium, titanium and zirconium.

Description

Technical Field

[0001] This invention relates to the field of crystal material texture measurement technology, specifically to a neutron diffraction testing method and system for intergranular stress in hexagonal crystal systems. Background Technology

[0002] The three-dimensional internal stress field at the grain scale within a material has a certain influence on the evolution of its microstructure, and thus affects the macroscopic properties of polycrystalline materials. However, most neutron diffraction measurements of internal stress in polycrystalline materials are limited to strain testing on different crystal planes along the loading direction and perpendicular to the tensile direction. This method cannot distinguish between grain families with different orientations, and the strain values ​​obtained are only the normal strain in that direction. Therefore, a method is needed to test the third-order stress tensor of a grain family with a specific orientation.

[0003] The existing technology (the strain orientation distribution function method is disclosed in Acta Materialia, April 2002, pp. 1717-1734; the grain orientation method is disclosed in Acta Materialia, January 2010, pp. 499-509) allows for the detection and analysis of the three-dimensional internal stress field of different texture components in a material. However, all the methods mentioned in the above-mentioned scientific papers and patents are limited to the third-order stress test of cubic crystal systems, and do not cover the stress test of other more common hexagonal crystal systems.

[0004] Patent document CN104764758B discloses a neutron diffraction measurement method for measuring the internal texture of a crystal using a robotic arm. This method utilizes a programmable robotic arm as a sample stage, offering greater flexibility compared to Euler rings. A serial cable connects the robotic arm to a computer for data acquisition. However, this invention does not address the limitation of detecting the three-dimensional internal stress field of different texture components in a hexagonal crystal system. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the purpose of this invention is to provide a neutron diffraction test method and system for intergranular stress in hexagonal crystal systems.

[0006] A neutron diffraction testing method for intergranular stress in a hexagonal crystal system, provided by the present invention, includes:

[0007] Step S1: Determine the constituent phases and crystal structure type of the material to be tested, and detect the texture of the material to be tested;

[0008] Step S2: Determine the texture component to be tested and its crystal plane to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal plane to be tested and the sample to be tested for the texture component to be tested.

[0009] Step S3: Neutron diffraction data acquisition, obtaining neutron diffraction signals for all corresponding crystal planes to be measured;

[0010] Step S4: Calculate the three-dimensional internal stress field of the material for different texture components.

[0011] Preferably, in step S1:

[0012] Determine the constituent phases and crystal structure type of the material to be tested, determine whether the material to be tested is a single-phase or multi-phase material and the crystal structure type of each phase, and determine the crystal planes of the material to be tested by neutron diffraction.

[0013] The experimental design for detecting the texture of the material under test and the three-dimensional internal stress field of different texture components of the material under test is based on the texture information of the material under test.

[0014] Preferably, in step S2:

[0015] Determine the texture components to be tested and their crystal planes to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal planes to be tested and the sample to be tested for the texture components to be tested.

[0016] Based on the texture information of the material to be tested and the research requirements, the texture component (hkil) [uvtw] to be tested for the three-dimensional internal stress field to be detected is selected, and the volume fraction of this texture component is not less than 5%.

[0017] Based on the texture component to be measured, determine the target crystal plane (HKIL) of the texture component to be measured, detect the three-dimensional internal stress field of the texture component, and detect its Q linearly independent crystal plane strains, where Q≥10;

[0018] Based on the target crystal plane (HKIL) of the texture component to be measured, calculate the orientation of the target crystal plane relative to the sample. The normal direction ND, the rolling direction RD, and the transverse direction TD are the three unit directions in the sample coordinate system. The angle between the normal direction n of the measured crystal plane (HKIL) and the ND direction is defined as χ. The angle between the projection of the crystal plane normal direction n onto the TD-RD plane and the RD direction is defined as χ. horn;

[0019] For a cubic crystal system, for the texture component (hkl)[uvw], the normal of its crystal plane (hkl) is parallel to the ND direction, and the crystal direction of [uvw] is parallel to the RD direction. included angle The angle between the projection of the normal n of the crystal plane under test onto the plane perpendicular to the (hkl) direction and the direction (uvw) is used to represent this. Therefore, the orientation of the test crystal plane (HKL) relative to the sample is determined for the texture component (hkl) [uvw].

[0020] In the hexagonal crystal system, the crystal plane indices and crystal direction indices defined in the hexagonal crystal system are transformed into a cubic coordinate system, and then the orientation of the test crystal plane (HKL) relative to the sample is calculated using the calculation methods for the cubic crystal system. Define the corresponding cubic coordinate system, using the cubic coordinate system defined within the hexagonal crystal system: For any crystal plane index or crystal direction index (HKIL) of the hexagonal crystal system hex In the defined cubic coordinate system, its equivalent crystal plane indices or crystal direction indices are:

[0021] (HKL) cub =T h-c (HKIL) hex

[0022] Where (100), (010), and (001) represent unit vectors in cubic coordinates, and the subscript cub indicates the cubic coordinate system. and Let represent a vector within the hexagonal crystal system, with the subscript hex indicating the hexagonal crystal system; γ is the ratio of the crystal constants c and a in the hexagonal crystal system, i.e., γ = c / a; a cubic coordinate system is defined within the hexagonal crystal system. The vector is defined as a (100) unit vector in cubic coordinates; T h-c The transformation matrix is ​​for the two coordinate systems. The transformation matrix differs for crystal plane indices and crystal direction indices. For crystal plane indices, the transformation matrix is:

[0023]

[0024] For crystal orientation indices, the transformation matrix is:

[0025]

[0026] The target crystal plane (HKIL) and the target texture component (hkil) [uvtw] are transformed into a cubic crystal system, and then the orientation of the target crystal plane (HKIL) relative to the sample is solved for the target texture component (hkil) [uvtw].

[0027] Preferably, in step S3:

[0028] The interplanar spacing d of the target crystal plane (HKIL) based on the determined target texture component (hkil) [uvtw] is... (HKIL) And the incident neutron wavelength λ, using Bragg's diffraction law 2d (HKIL) sinθ (HKIL)=nλ to calculate the diffraction angle 2θ (HKIL) Move the detector to the designated 2θ (HKIL) Angle; n is any integer;

[0029] Based on the determined texture component (hkil) [uvtw], the direction of the test crystal plane (HKIL) relative to the sample. Rotate the Euler ring to the corresponding position, set the measurement duration or neutron count according to the signal-to-noise ratio requirements, and detect the neutron diffraction signal;

[0030] Repeat step S3 to obtain the neutron diffraction signals of all the corresponding Q crystal planes to be tested. If an in-situ neutron diffraction experiment is to be carried out, repeat step S3 after the in-situ loading conditions reach the set value.

[0031] Preferably, in step S4:

[0032] Step S4.1: Calculate the three-dimensional internal stress field of the texture component in the crystal coordinate system;

[0033] The diffraction data of the target crystal plane (HKIL) based on the determined texture component (hkil) [uvtw] are selected and fitted to obtain the diffraction angle 2θ. (HKIL) The strain ε of the crystal plane is obtained based on the change in diffraction angle. hkil :

[0034]

[0035] Where, ε (HKIL) Let θ be the lattice strain of the HKIL crystal plane. (HKIL)，0 The diffraction angle corresponding to the HKIL crystal plane in a stress-free state;

[0036] Three-dimensional internal stress field of texture components Represented using a second-order stress tensor:

[0037]

[0038] For the cubic crystal system, the three-dimensional stress field of the (HKL) crystal plane strain and the texture component has the following relationship:

[0039]

[0040] x, y, and z are the cosine values ​​of the angles between the (HKL) crystal plane normal and the three unit vectors of the coordinate axes, respectively. The superscript c represents the (HKL) crystal plane strain ε of the corresponding texture component obtained in the crystal coordinate system. HKL Based on equation (3), Q six-variable linear equations are established. These equations are overdetermined and do not have analytical solutions. The least squares solutions of the six strain tensor components are obtained using the multiple linear regression method. The solution is:

[0041] ε=(M T M) -1 M T b (4)

[0042] in,

[0043]

[0044] b=(ε hkl，1 , ε hkl，2 , …, ε hkl，p , …, ε hkl，Q )

[0045] The subscripts 1, 2, ..., p, ..., Q represent the test crystal plane numbers, and a total of Q crystal planes were tested;

[0046] The second-order stress tensor σ is calculated using the constitutive relationship between stress and strain. c :

[0047]

[0048] in, This is the stiffness coefficient matrix of the material;

[0049] The hexagonal crystal system's plane coefficients (HKIL) hex Transform to cubic coordinates (HKL) using formula (1). cub Then, construct the second-order stress tensor according to the cubic crystal system method;

[0050] Step S4.2: Construct the second-order stress tensor based on the second-order strain tensor in crystal coordinates:

[0051] According to the generalized Hooke's law Where C ijkl Let be the stiffness matrix of the crystal; Hooke's law is written as:

[0052]

[0053] Among them, C 66 =(C 11 -C 12 ) / 2;

[0054] Step S4.3: Transform the second-order stress tensor of the crystal coordinate system to the sample coordinate system;

[0055] The second-order stress tensor σ obtained in the crystal coordinate system {C} c Transform to the sample coordinate system {S}.

[0056] σ s =Gσc G T

[0057] The transformation matrix G is related to the texture component to be measured. For a cubic crystal system, for any texture component (hkl)[uvw) cub The transformation matrix G is:

[0058]

[0059] in, g is the inverse of the transformation matrix;

[0060] The texture component to be tested (hkil) [uvtw] hex The texture components (hkl)[uvw) in cubic coordinates are converted using formula (1). cub Then, the transformation matrix is ​​used to transform the sample coordinate system to obtain the second-order stress tensor of the texture component, that is, the three-dimensional internal stress field of the texture component.

[0061] A neutron diffraction testing system for intergranular stress in a hexagonal crystal system, provided by the present invention, comprises:

[0062] Module M1: Determines the constituent phases and crystal structure type of the material under test, and detects the texture of the material under test;

[0063] Module M2: Determine the texture component to be tested and its crystal plane to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal plane to be tested and the sample to be tested for the texture component to be tested;

[0064] Module M3: Neutron diffraction data acquisition, obtaining neutron diffraction signals of all corresponding crystal planes to be measured;

[0065] Module M4: Calculates the three-dimensional internal stress field of materials with different texture components.

[0066] Preferably, in module M1:

[0067] Determine the constituent phases and crystal structure type of the material to be tested, determine whether the material to be tested is a single-phase or multi-phase material and the crystal structure type of each phase, and determine the crystal planes of the material to be tested by neutron diffraction.

[0068] The experimental design for detecting the texture of the material under test and the three-dimensional internal stress field of different texture components of the material under test is based on the texture information of the material under test.

[0069] Preferably, in module M2:

[0070] Determine the texture components to be tested and their crystal planes to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal planes to be tested and the sample to be tested for the texture components to be tested.

[0071] Based on the texture information of the material to be tested and the research requirements, the texture component (hkil) [uvtw] to be tested for the three-dimensional internal stress field to be detected is selected, and the volume fraction of this texture component is not less than 5%.

[0072] Based on the texture component to be measured, determine the target crystal plane (HKIL) of the texture component to be measured, detect the three-dimensional internal stress field of the texture component, and detect its Q linearly independent crystal plane strains, where Q≥10;

[0073] Based on the target crystal plane (HKIL) of the texture component to be measured, calculate the orientation of the target crystal plane relative to the sample. The normal direction ND, the rolling direction RD, and the transverse direction TD are the three unit directions in the sample coordinate system. The angle between the normal direction n of the measured crystal plane (HKIL) and the ND direction is defined as χ. The angle between the projection of the crystal plane normal direction n onto the TD-RD plane and the RD direction is defined as χ. horn;

[0074] For a cubic crystal system, for the texture component (hkl)[uvw], the normal of its crystal plane (hkl) is parallel to the ND direction, and the crystal direction of [uvw] is parallel to the RD direction. included angle The angle between the projection of the normal n of the crystal plane under test onto the plane perpendicular to the (hkl) direction and the direction (uvw) is used to represent this. Therefore, the orientation of the test crystal plane (HKL) relative to the sample is determined for the texture component (hkl) [uvw].

[0075] In the hexagonal crystal system, the crystal plane indices and crystal direction indices defined in the hexagonal crystal system are transformed into a cubic coordinate system, and then the orientation of the test crystal plane (HKL) relative to the sample is calculated using the calculation methods for the cubic crystal system. Define the corresponding cubic coordinate system, using the cubic coordinate system defined within the hexagonal crystal system: For any crystal plane index or crystal direction index (HKIL) of the hexagonal crystal system hex In the defined cubic coordinate system, its equivalent crystal plane indices or crystal direction indices are:

[0076] (HKL) cub =T h-c (HKIL) hex

[0077] Where (100), (010), and (001) represent unit vectors in cubic coordinates, and the subscript cub indicates the cubic coordinate system. and Let represent a vector within the hexagonal crystal system, with the subscript hex indicating the hexagonal crystal system; γ is the ratio of the crystal constants c and a in the hexagonal crystal system, i.e., γ = c / a; a cubic coordinate system is defined within the hexagonal crystal system. The vector is defined as a (100) unit vector in cubic coordinates; T h-c The transformation matrix is ​​for the two coordinate systems. The transformation matrix differs for crystal plane indices and crystal direction indices. For crystal plane indices, the transformation matrix is:

[0078]

[0079] For crystal orientation indices, the transformation matrix is:

[0080]

[0081] The target crystal plane (HKIL) and the target texture component (hkil) [uvtw] are transformed into a cubic crystal system, and then the orientation of the target crystal plane (HKIL) relative to the sample is solved for the target texture component (hkil) [uvtw].

[0082] Preferably, in module M3:

[0083] The interplanar spacing d of the target crystal plane (HKIL) based on the determined target texture component (hkil) [uvtw] is... (HKIL) And the incident neutron wavelength λ, using Bragg's diffraction law 2d (HKIL) sinθ (HKIL) =nλ to calculate the diffraction angle 2θ (HKIL) Move the detector to the designated 2θ (HKIL) Angle; n is any integer;

[0084] Based on the determined texture component (hkil) [uvtw], the direction of the test crystal plane (HKIL) relative to the sample. Rotate the Euler ring to the corresponding position, set the measurement duration or neutron count according to the signal-to-noise ratio requirements, and detect the neutron diffraction signal;

[0085] Repeat module M3 to obtain neutron diffraction signals for all the corresponding Q crystal planes to be tested. If an in-situ neutron diffraction experiment is to be carried out, repeat module M3 once the in-situ loading conditions reach the set value.

[0086] Preferably, in module M4:

[0087] Module M4.1: Calculates the three-dimensional internal stress field of the texture component in crystal coordinates;

[0088] The diffraction data of the target crystal plane (HKIL) based on the determined texture component (hkil) [uvtw] are selected and fitted to obtain the diffraction angle 2θ. (HKIL) The strain ε of the crystal plane is obtained based on the change in diffraction angle. hkil :

[0089]

[0090] Where, ε (HKIL) Let θ be the lattice strain of the HKIL crystal plane. (HKIL)，0 The diffraction angle corresponding to the HKIL crystal plane in a stress-free state;

[0091] Three-dimensional internal stress field of texture components Represented using a second-order stress tensor:

[0092]

[0093] For the cubic crystal system, the three-dimensional stress field of the (HKL) crystal plane strain and the texture component has the following relationship:

[0094]

[0095] x, y, and z are the cosine values ​​of the angles between the (HKL) crystal plane normal and the three unit vectors of the coordinate axes, respectively. The superscript c represents the (HKL) crystal plane strain ε of the corresponding texture component obtained in the crystal coordinate system. HKL Based on equation (3), Q six-variable linear equations are established. These equations are overdetermined and do not have analytical solutions. The least squares solutions of the six strain tensor components are obtained using the multiple linear regression method. The solution is:

[0096] ε=(M T M) -1 M T b (4)

[0097] in,

[0098]

[0099] b=(ε hkl，1 , ε hkl，2 , …, ε hkl，p , …, ε hkl，Q )

[0100] The subscripts 1, 2, ..., p, ..., Q represent the test crystal plane numbers, and a total of Q crystal planes were tested;

[0101] The second-order stress tensor σ is calculated using the constitutive relationship between stress and strain. c :

[0102]

[0103] in, This is the stiffness coefficient matrix of the material;

[0104] The hexagonal crystal system's plane coefficients (HKIL) hex Transform to cubic coordinates (HKL) using formula (1). cub Then, construct the second-order stress tensor according to the cubic crystal system method;

[0105] Module M4.2: Constructing a second-order stress tensor based on the second-order strain tensor in crystal coordinates:

[0106] According to the generalized Hooke's law Where C ijkl Let be the stiffness matrix of the crystal; Hooke's law is written as:

[0107]

[0108] Among them, C 66 =(C 11 -C 12 ) / 2;

[0109] Module M4.3: Transforms the second-order stress tensor from the crystal coordinate system to the sample coordinate system;

[0110] The second-order stress tensor σ obtained in the crystal coordinate system {C} c Transform to the sample coordinate system {S}.

[0111] σ s =Gσ c G T

[0112] The transformation matrix G is related to the texture component to be measured. For a cubic crystal system, for any texture component (hkl)[uvw) cub The transformation matrix G is:

[0113]

[0114] in, g is the inverse of the transformation matrix;

[0115] The texture component to be tested (hkil) [uvtw] hex The texture components (hkl)[uvw) in cubic coordinates are converted using formula (1). cub Then, the transformation matrix is ​​used to transform the sample coordinate system to obtain the second-order stress tensor of the texture component, that is, the three-dimensional internal stress field of the texture component.

[0116] Compared with the prior art, the present invention has the following beneficial effects:

[0117] This invention addresses the shortcomings in detecting the three-dimensional internal stress field of different texture components in hexagonal crystal systems, and provides effective technical guidance for testing the third-order stress tensor of different texture components in hexagonal crystal alloys such as magnesium, titanium, and zirconium. Attached Figure Description

[0118] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0119] Figure 1 This is the procedure for third-order stress neutron diffraction testing in a hexagonal crystal system. Detailed Implementation

[0120] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0121] Example 1:

[0122] This invention develops a method for detecting the three-dimensional internal stress field of grain families with different texture orientations in hexagonal polycrystalline materials using neutron diffraction technology. This method extends the grain orientation analysis method, which was originally only applicable to cubic crystal systems, to hexagonal crystal systems through coordinate transformation, ultimately realizing a method for detecting the three-dimensional internal stress field of different texture components in hexagonal crystal systems using neutron diffraction.

[0123] This invention extends grain orientation analysis by incorporating the symmetry difference between hexagonal and cubic crystal systems. A transformation matrix is ​​used to project the indices of the hexagonal crystal system onto a cubic coordinate system, thus extending grain orientation analysis to the hexagonal crystal system. This provides effective and reliable methodological support for testing the third-order internal stress tensor of different texture components in metals such as magnesium, titanium, and zirconium, inorganic non-metallic materials such as silicon carbide, and many other hexagonal crystal systems. When an application server switches over, information on business items that cannot be processed normally within the time window is provided to the business platform for post-processing.

[0124] The present invention provides a neutron diffraction testing method for intergranular stress in hexagonal crystal systems, such as... Figure 1 As shown, it includes:

[0125] Step S1: Determine the constituent phases and crystal structure type of the material to be tested, and detect the texture of the material to be tested;

[0126] Specifically, in step S1:

[0127] Determine the constituent phases and crystal structure type of the material to be tested, determine whether the material to be tested is a single-phase or multi-phase material and the crystal structure type of each phase, and determine the crystal planes of the material to be tested by neutron diffraction.

[0128] The experimental design for detecting the texture of the material under test and the three-dimensional internal stress field of different texture components of the material under test is based on the texture information of the material under test.

[0129] Step S2: Determine the texture component to be tested and its crystal plane to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal plane to be tested and the sample to be tested for the texture component to be tested.

[0130] Specifically, in step S2:

[0131] Determine the texture components to be tested and their crystal planes to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal planes to be tested and the sample to be tested for the texture components to be tested.

[0132] Based on the texture information of the material to be tested and the research requirements, the texture component (hkil) [uvtw] to be tested for the three-dimensional internal stress field to be detected is selected, and the volume fraction of this texture component is not less than 5%.

[0133] Based on the texture component to be measured, determine the target crystal plane (HKIL) of the texture component to be measured, detect the three-dimensional internal stress field of the texture component, and detect its Q linearly independent crystal plane strains, where Q≥10;

[0134] Based on the target crystal plane (HKIL) of the texture component to be measured, calculate the orientation of the target crystal plane relative to the sample. The normal direction ND, the rolling direction RD, and the transverse direction TD are the three unit directions in the sample coordinate system. The angle between the normal direction n of the measured crystal plane (HKIL) and the ND direction is defined as χ. The angle between the projection of the crystal plane normal direction n onto the TD-RD plane and the RD direction is defined as χ. horn;

[0135] For a cubic crystal system, for the texture component (hkl)[uvw], the normal of its crystal plane (hkl) is parallel to the ND direction, and the crystal direction of [uvw] is parallel to the RD direction. included angle The angle between the projection of the normal n of the crystal plane under test onto the plane perpendicular to the (hkl) direction and the direction (uvw) is used to represent this. Therefore, the orientation of the test crystal plane (HKL) relative to the sample is determined for the texture component (hkl) [uvw].

[0136] In the hexagonal crystal system, the crystal plane indices and crystal direction indices defined in the hexagonal crystal system are transformed into a cubic coordinate system, and then the orientation of the test crystal plane (HKL) relative to the sample is calculated using the calculation methods for the cubic crystal system. Define the corresponding cubic coordinate system, using the cubic coordinate system defined within the hexagonal crystal system: For any crystal plane index or crystal direction index (HKIL) of the hexagonal crystal system hex In the defined cubic coordinate system, its equivalent crystal plane indices or crystal direction indices are:

[0137] (HKL) cub =T h-c (HKIL) hex

[0138] Where (100), (010), and (001) represent unit vectors in cubic coordinates, and the subscript cub indicates the cubic coordinate system. and Let represent a vector within the hexagonal crystal system, with the subscript hex indicating the hexagonal crystal system; γ is the ratio of the crystal constants c and a in the hexagonal crystal system, i.e., γ = c / a; a cubic coordinate system is defined within the hexagonal crystal system. The vector is defined as a (100) unit vector in cubic coordinates; T h-c The transformation matrix is ​​for the two coordinate systems. The transformation matrix differs for crystal plane indices and crystal direction indices. For crystal plane indices, the transformation matrix is:

[0139]

[0140] For crystal orientation indices, the transformation matrix is:

[0141]

[0142] The target crystal plane (HKIL) and the target texture component (hkil) [uvtw] are transformed into a cubic crystal system, and then the orientation of the target crystal plane (HKIL) relative to the sample is solved for the target texture component (hkil) [uvtw].

[0143] Step S3: Neutron diffraction data acquisition, obtaining neutron diffraction signals for all corresponding crystal planes to be measured;

[0144] Specifically, in step S3:

[0145] The interplanar spacing d of the target crystal plane (HKIL) based on the determined target texture component (hkil) [uvtw] is... (HKIL)And the incident neutron wavelength λ, using Bragg's diffraction law 2d (HKIL) sinθ (HKIL) =nλ to calculate the diffraction angle 2θ (HKIL) Move the detector to the designated 2θ (HKIL) Angle; n is any integer;

[0146] Based on the determined texture component (hkil) [uvtw], the direction of the test crystal plane (HKIL) relative to the sample. Rotate the Euler ring to the corresponding position, set the measurement duration or neutron count according to the signal-to-noise ratio requirements, and detect the neutron diffraction signal;

[0147] Repeat step S3 to obtain the neutron diffraction signals of all the corresponding Q crystal planes to be tested. If an in-situ neutron diffraction experiment is to be carried out, repeat step S3 after the in-situ loading conditions reach the set value.

[0148] Step S4: Calculate the three-dimensional internal stress field of the material for different texture components.

[0149] Specifically, in step S4:

[0150] Step S4.1: Calculate the three-dimensional internal stress field of the texture component in the crystal coordinate system;

[0151] The diffraction data of the target crystal plane (HKIL) based on the determined texture component (hkil) [uvtw] are selected and fitted to obtain the diffraction angle 2θ. (HKIL) The strain ε of the crystal plane is obtained based on the change in diffraction angle. hkil :

[0152]

[0153] Where, ε (HKIL) Let θ be the lattice strain of the HKIL crystal plane. (HKIL)，0 The diffraction angle corresponding to the HKIL crystal plane in a stress-free state;

[0154] Three-dimensional internal stress field of texture components Represented using a second-order stress tensor:

[0155]

[0156] For the cubic crystal system, the three-dimensional stress field of the (HKL) crystal plane strain and the texture component has the following relationship:

[0157]

[0158] x, y, and z are the cosine values ​​of the angles between the (HKL) crystal plane normal and the three unit vectors of the coordinate axes, respectively. The superscript c represents the (HKL) crystal plane strain ε of the corresponding texture component obtained in the crystal coordinate system. HKL Based on equation (3), Q six-variable linear equations are established. These equations are overdetermined and do not have analytical solutions. The least squares solutions of the six strain tensor components are obtained using the multiple linear regression method. The solution is:

[0159] ε=(M T M) -1 M T b (4)

[0160] in,

[0161]

[0162] b=(ε hkl，1 , ε hkl，2 , …, ε hkl，p , …, ε hkl，Q )

[0163] The subscripts 1, 2, ..., p, ..., Q represent the test crystal plane numbers, and a total of Q crystal planes were tested;

[0164] The second-order stress tensor σ is calculated using the constitutive relationship between stress and strain. c :

[0165]

[0166] in, This is the stiffness coefficient matrix of the material;

[0167] The hexagonal crystal system's plane coefficients (HKIL) hex Transform to cubic coordinates (HKL) using formula (1). cub Then, construct the second-order stress tensor according to the cubic crystal system method;

[0168] Step S4.2: Construct the second-order stress tensor based on the second-order strain tensor in crystal coordinates:

[0169] According to the generalized Hooke's law Where C ijkl Let be the stiffness matrix of the crystal; Hooke's law is written as:

[0170]

[0171] Among them, C 66 =(C 11 -C 12 ) / 2;

[0172] Step S4.3: Transform the second-order stress tensor of the crystal coordinate system to the sample coordinate system;

[0173] The second-order stress tensor σ obtained in the crystal coordinate system {C} c Transform to the sample coordinate system {S}.

[0174] σ s =Gσ c G T

[0175] The transformation matrix G is related to the texture component to be measured. For a cubic crystal system, for any texture component (hkl)[uvw) cub The transformation matrix G is:

[0176]

[0177] in, g is the inverse of the transformation matrix;

[0178] The texture component to be tested (hkil) [uvtw] hex The texture components (hkl)[uvw) in cubic coordinates are converted using formula (1). cub Then, the transformation matrix is ​​used to transform the sample coordinate system to obtain the second-order stress tensor of the texture component, that is, the three-dimensional internal stress field of the texture component.

[0179] Example 2:

[0180] Example 2 is a preferred embodiment of Example 1, and is used to illustrate the present invention in more detail.

[0181] The present invention also provides a neutron diffraction testing system for intergranular stress in hexagonal crystal systems. The neutron diffraction testing system for intergranular stress in hexagonal crystal systems can be implemented by executing the process steps of the neutron diffraction testing method for intergranular stress in hexagonal crystal systems. That is, those skilled in the art can understand the neutron diffraction testing method for intergranular stress in hexagonal crystal systems as a preferred embodiment of the neutron diffraction testing system for intergranular stress in hexagonal crystal systems.

[0182] A neutron diffraction testing system for intergranular stress in a hexagonal crystal system, provided by the present invention, comprises:

[0183] Module M1: Determines the constituent phases and crystal structure type of the material under test, and detects the texture of the material under test;

[0184] Specifically, in module M1:

[0185] Determine the constituent phases and crystal structure type of the material to be tested, determine whether the material to be tested is a single-phase or multi-phase material and the crystal structure type of each phase, and determine the crystal planes of the material to be tested by neutron diffraction.

[0186] The experimental design for detecting the texture of the material under test and the three-dimensional internal stress field of different texture components of the material under test is based on the texture information of the material under test.

[0187] Module M2: Determine the texture component to be tested and its crystal plane to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal plane to be tested and the sample to be tested for the texture component to be tested;

[0188] Specifically, in module M2:

[0189] Determine the texture components to be tested and their crystal planes to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal planes to be tested and the sample to be tested for the texture components to be tested.

[0190] Based on the texture information of the material to be tested and the research requirements, the texture component (hkil) [uvtw] to be tested for the three-dimensional internal stress field to be detected is selected, and the volume fraction of this texture component is not less than 5%.

[0191] Based on the texture component to be measured, determine the target crystal plane (HKIL) of the texture component to be measured, detect the three-dimensional internal stress field of the texture component, and detect its Q linearly independent crystal plane strains, where Q≥10;

[0192] Based on the target crystal plane (HKIL) of the texture component to be measured, calculate the orientation of the target crystal plane relative to the sample. The normal direction ND, the rolling direction RD, and the transverse direction TD are the three unit directions in the sample coordinate system. The angle between the normal direction n of the measured crystal plane (HKIL) and the ND direction is defined as χ. The angle between the projection of the crystal plane normal direction n onto the TD-RD plane and the RD direction is defined as χ. horn;

[0193] For a cubic crystal system, for the texture component (hkl)[uvw], the normal of its crystal plane (hkl) is parallel to the ND direction, and the crystal direction of [uvw] is parallel to the RD direction. included angle The angle between the projection of the normal n of the crystal plane under test onto the plane perpendicular to the (hkl) direction and the direction (uvw) is used to represent this. Therefore, the orientation of the test crystal plane (HKL) relative to the sample is determined for the texture component (hkl) [uvw].

[0194] In the hexagonal crystal system, the crystal plane indices and crystal direction indices defined in the hexagonal crystal system are transformed into a cubic coordinate system, and then the orientation of the test crystal plane (HKL) relative to the sample is calculated using the calculation methods for the cubic crystal system. Define the corresponding cubic coordinate system, using the cubic coordinate system defined within the hexagonal crystal system: For any crystal plane index or crystal direction index (HKIL) of the hexagonal crystal system hex In the defined cubic coordinate system, its equivalent crystal plane indices or crystal direction indices are:

[0195] (HKL) cub =T h-c (HKIL) hex

[0196] Where (100), (010), and (001) represent unit vectors in cubic coordinates, and the subscript cub indicates the cubic coordinate system. and Let represent a vector within the hexagonal crystal system, with the subscript hex indicating the hexagonal crystal system; γ is the ratio of the crystal constants c and a in the hexagonal crystal system, i.e., γ = c / a; a cubic coordinate system is defined within the hexagonal crystal system. The vector is defined as a (100) unit vector in cubic coordinates; T h-c The transformation matrix is ​​for the two coordinate systems. The transformation matrix differs for crystal plane indices and crystal direction indices. For crystal plane indices, the transformation matrix is:

[0197]

[0198] For crystal orientation indices, the transformation matrix is:

[0199]

[0200] The target crystal plane (HKIL) and the target texture component (hkil) [uvtw] are transformed into a cubic crystal system, and then the orientation of the target crystal plane (HKIL) relative to the sample is solved for the target texture component (hkil) [uvtw].

[0201] Module M3: Neutron diffraction data acquisition, obtaining neutron diffraction signals of all corresponding crystal planes to be measured;

[0202] Specifically, in module M3:

[0203] The interplanar spacing d of the target crystal plane (HKIL) based on the determined target texture component (hkil) [uvtw] is... (HKIL)And the incident neutron wavelength λ, using Bragg's diffraction law 2d (HKIL) sinθ (HKIL) =nλ to calculate the diffraction angle 2θ (HKIL) Move the detector to the designated 2θ (HKIL) Angle; n is any integer;

[0204] Based on the determined texture component (hkil) [uvtw], the direction of the test crystal plane (HKIL) relative to the sample. Rotate the Euler ring to the corresponding position, set the measurement duration or neutron count according to the signal-to-noise ratio requirements, and detect the neutron diffraction signal;

[0205] Repeat module M3 to obtain neutron diffraction signals for all the corresponding Q crystal planes to be tested. If an in-situ neutron diffraction experiment is to be carried out, repeat module M3 once the in-situ loading conditions reach the set value.

[0206] Module M4: Calculates the three-dimensional internal stress field of materials with different texture components.

[0207] Specifically, in module M4:

[0208] Module M4.1: Calculates the three-dimensional internal stress field of the texture component in crystal coordinates;

[0209] The diffraction data of the target crystal plane (HKIL) based on the determined texture component (hkil) [uvtw] are selected and fitted to obtain the diffraction angle 2θ. (HKIL) The strain ε of the crystal plane is obtained based on the change in diffraction angle. hkil :

[0210]

[0211] Where, ε (HKIL) Let θ be the lattice strain of the HKIL crystal plane. (HKIL)，0 The diffraction angle corresponding to the HKIL crystal plane in a stress-free state;

[0212] Three-dimensional internal stress field of texture components Represented using a second-order stress tensor:

[0213]

[0214] For the cubic crystal system, the three-dimensional stress field of the (HKL) crystal plane strain and the texture component has the following relationship:

[0215]

[0216] x, y, and z are the cosine values ​​of the angles between the (HKL) crystal plane normal and the three unit vectors of the coordinate axes, respectively. The superscript c represents the (HKL) crystal plane strain ε of the corresponding texture component obtained in the crystal coordinate system. HKL Based on equation (3), Q six-variable linear equations are established. These equations are overdetermined and do not have analytical solutions. The least squares solutions of the six strain tensor components are obtained using the multiple linear regression method. The solution is:

[0217] ε=(M T M) -1 M T b (4)

[0218] in,

[0219]

[0220] b=(ε hkl，1 , ε hkl，2 , …, ε hkl，p , …, ε hkl，Q )

[0221] The subscripts 1, 2, ..., p, ..., Q represent the test crystal plane numbers, and a total of Q crystal planes were tested;

[0222] The second-order stress tensor σ is calculated using the constitutive relationship between stress and strain. c :

[0223]

[0224] in, This is the stiffness coefficient matrix of the material;

[0225] The hexagonal crystal system's plane coefficients (HKIL) hex Transform to cubic coordinates (HKL) using formula (1). cub Then, construct the second-order stress tensor according to the cubic crystal system method;

[0226] Module M4.2: Constructing a second-order stress tensor based on the second-order strain tensor in crystal coordinates:

[0227] According to the generalized Hooke's law Where C ijkl Let be the stiffness matrix of the crystal; Hooke's law is written as:

[0228]

[0229] Among them, C 66 =(C 11 -C 12 ) / 2;

[0230] Module M4.3: Transforms the second-order stress tensor from the crystal coordinate system to the sample coordinate system;

[0231] The second-order stress tensor σ obtained in the crystal coordinate system {C} c Transform to the sample coordinate system {S}.

[0232] σ s =Gσ c G T

[0233] The transformation matrix G is related to the texture component to be measured. For a cubic crystal system, for any texture component (hkl)[uvw) cub The transformation matrix G is:

[0234]

[0235] in, g is the inverse of the transformation matrix;

[0236] The texture component to be tested (hkil) [uvtw] hex The texture components (hkl)[uvw) in cubic coordinates are converted using formula (1). cub Then, the transformation matrix is ​​used to transform the sample coordinate system to obtain the second-order stress tensor of the texture component, that is, the three-dimensional internal stress field of the texture component.

[0237] Example 3:

[0238] Example 3 is a preferred example of Example 1, and is used to illustrate the present invention in more detail.

[0239] This invention analyzes the differences in crystal symmetry and anisotropy between hexagonal and cubic crystal systems, and derives a transformation matrix that converts the Miller-Bravais crystal planes and crystal orientation indices commonly used in hexagonal crystal systems to cubic coordinates, thus extending the crystal orientation analysis method, which is only applicable to cubic crystal systems, to hexagonal crystal systems.

[0240] This invention combines grain orientation and texture analysis methods to develop a neutron diffraction-based simultaneous detection method for texture and the three-dimensional internal stress field of different texture components. The specific detection method is as follows:

[0241] Step 1: Determine the constituent phases and crystal structure type of the material to be tested. Determine whether the material to be tested is a single-phase or multi-phase material and the crystal structure type of each phase, and then determine the crystal planes of the material to be tested by neutron diffraction.

[0242] Step 2: Detect the texture of the material under test. The experimental design for the three-dimensional internal stress field of different texture components of the material under test is based on the texture information of the material under test. The texture of the material can be detected according to the national standard "Non-destructive Testing of Material Texture - Neutron Detection Method" (GB / T 40307-2021).

[0243] Step 3: Determine the texture component to be tested and its crystal plane to be tested in the three-dimensional internal stress field to be tested, and calculate the specific directional relationship between the crystal plane to be tested and the sample to be tested for the texture component to be tested.

[0244] Step 3.1: Based on the texture information of the material to be tested obtained in Step 2 and the research requirements, select the texture component (hkil) [uvtw] to be tested for the three-dimensional internal stress field. The volume fraction of this texture component should not be less than 5%.

[0245] Step 3.2: Based on the texture component to be measured determined in Step 3.1, determine the target crystal plane (HKIL) of the texture component. To detect the three-dimensional internal stress field of the texture component, it is necessary to detect the strain of its Q (Q≥10) linearly independent crystal planes. The selected crystal planes should satisfy the following conditions: their crystal plane indices should be as small as possible, and their structure factor |F... HKIL | 2 The condition is not zero, and it is best to have a certain crystal representativeness. For example, the basic crystal planes of the hexagonal crystal system (0002), prism (10-10), (11-20), etc. can be selected, or the characteristic slip planes and slip directions of the crystal can be selected for research.

[0246] Step 3.3: Based on the target crystal plane (HKIL) of the texture component to be measured determined in Step 3.2, calculate the direction (χ, φ) of the target crystal plane relative to the sample. The normal direction ND, the rolling direction RD, and the transverse direction TD are the three unit directions in the sample coordinate system. The angle between the normal direction n of the target crystal plane (HKIL) and the ND direction is defined as χ, and the angle between the projection of the normal direction n of the crystal plane in the TD-RD plane and the RD direction is defined as φ.

[0247] For a cubic crystal system, for the texture component (hkl)[uvw], the normal of its crystal plane (hkl) is parallel to the ND direction, and the crystal plane [uvw] is parallel to the RD direction. Therefore, the included angle χ can be expressed as the angle between the normal n of the crystal plane to be measured (i.e., [HKL]) and the (hkl) direction, which is... The included angle φ can be represented by the angle between the projection of the normal n of the crystal plane to be measured onto the plane perpendicular to the (hkl) direction and the direction (uvw), which is... This allows us to determine the orientation (χ, φ) of the test crystal plane (HKL) of the texture component (hkl) [uvw] relative to the sample.

[0248] However, in the hexagonal crystal system, due to differences in crystal symmetry and coordinate definition, the calculated directions (χ, φ) cannot be calculated as in the cubic crystal system. Therefore, it is necessary to transform the crystal plane indices and crystal direction indices defined in the hexagonal crystal system into the cubic coordinate system, and then use the calculation methods of the cubic crystal system to calculate the direction (χ, φ) of the measured crystal plane (HKL) relative to the sample. To transform the crystal plane and crystal direction indices in the hexagonal crystal system, a corresponding cubic coordinate system needs to be defined. Here, the widely used cubic coordinate system definition within the hexagonal crystal system is adopted: For any crystal plane index or crystal direction index (HKIL) of the hexagonal crystal system hex In the defined cubic coordinate system, its equivalent crystal plane indices or crystal direction indices are:

[0249] (HKL) cub =T h-c (HKIL) hex

[0250] Among them, T h-c Here are the transformation matrices for the two coordinate systems. It's important to note that the transformation matrices differ for crystal plane indices and crystal direction indices. For crystal plane indices, the transformation matrix is:

[0251]

[0252] For crystal orientation indices, the transformation matrix is:

[0253]

[0254] Therefore, the crystal plane to be measured (HKIL) and the texture component to be measured (hkil) [uvtw] are used with formula (HKL). cub =T h-c (HKIL) hex The crystal system is transformed to cubic, and then the direction (χ, φ) of the target crystal plane (HKIL) of the target texture component (hkil) [uvtw] relative to the sample is solved.

[0255] Step 4: Neutron diffraction data acquisition.

[0256] Step 4.1: The interplanar spacing d of the target crystal plane (HKIL) of the target texture component (hkil) [uvtw] determined in steps 3.1 and 3.2. (HKIL) And the incident neutron wavelength λ, using Bragg's diffraction law 2d (HKIL) sinθ (HKIL) =nλ to calculate the diffraction angle 2θ (HKIL) Move the detector to the designated 2θ (HKIL) horn.

[0257] Step 4.2: Based on the direction (χ, φ) of the target crystal plane (HKIL) of the texture component (hkil) [uvtw] determined in Step 3.3 relative to the sample, rotate the Euler ring to the corresponding position, set the measurement duration or neutron count according to the signal-to-noise ratio requirements, and detect the neutron diffraction signal.

[0258] Step 5: Repeat step 4 to obtain the neutron diffraction signals of all corresponding Q crystal planes to be tested. If conducting an in-situ neutron diffraction experiment, repeat step 4 after the in-situ loading conditions reach the set values.

[0259] Step 6: Calculate the three-dimensional internal stress field of the material for different texture components.

[0260] Step 6.1: Calculate the three-dimensional internal stress field of the texture component in the crystal coordinate system.

[0261] The diffraction data of the target crystal plane (HKIL) of the target texture component (hkil) [uvtw] determined in step 3.3 are selected and fitted to obtain the diffraction angle 2θ. (HKIL) The strain ε of the crystal plane is obtained based on the change in diffraction angle. hkl :

[0262]

[0263] The three-dimensional internal stress field of the texture component can be represented by a second-order stress tensor:

[0264]

[0265] For the cubic crystal system, the three-dimensional stress field of the (HKL) crystal plane strain and the texture component has the following relationship:

[0266]

[0267] x, y, and z are the cosine values ​​of the angles between the (HKL) crystal plane normal and the three unit vectors of the coordinate axes, respectively. The (HKL) crystal plane strain ε of the corresponding texture components obtained in steps 4 and 5 is then used. HKL Based on equation (3), Q six-variable linear equations are established. These equations are overdetermined and do not have analytical solutions. The least squares solutions of the six strain tensor components are obtained using the multiple linear regression method. (Strain tensor) The solution is:

[0268] ε=(M T M) -1 M T b#(4)

[0269] in,

[0270]

[0271] b=(ε hkl，1 , ε hkl，2 , …, ε hkl，p , …, ε hkl，Q )

[0272] The second-order stress tensor is calculated using the constitutive relationship between stress and strain:

[0273]

[0274] in, This is the stiffness coefficient matrix of the material.

[0275] However, formula (4) does not hold true for the hexagonal crystal system because the three coordinate axes of the hexagonal crystal system do not satisfy the requirement that they are mutually perpendicular and all are of unit length. Therefore, it is necessary to use the hexagonal crystal plane coefficient (HKIL). hex Transform to cubic coordinates (HKL) using formula (1). cub Then, the second-order stress tensor is constructed using the cubic crystal system method.

[0276] Step 6.2: Construct the second-order stress tensor based on the second-order strain tensor in the crystal coordinate system.

[0277] According to the generalized Hooke's law Where C ijkl This represents the stiffness matrix of the crystal. According to the definition of the cubic coordinate system within the hexagonal crystal system in step 3.3, Hooke's law can be written as:

[0278]

[0279] Among them, C 66 =(C 11 -C 12 ) / 2.

[0280] Step 6.3: Transform the second-order stress tensor of the crystal coordinate system to the sample coordinate system.

[0281] The second-order stress tensor σ obtained in the crystal coordinate system {C} c Transform to the sample coordinate system {S}.

[0282] σ s =Gσ c G T

[0283] The transformation matrix G is related to the texture components to be measured. For the cubic crystal system, the transformation matrix G is:

[0284]

[0285] in,

[0286] Similarly, the transformation matrix G is not suitable for the hexagonal crystal system, therefore the texture component to be measured (hkil)[uvtw) needs to be considered. hex The texture components (hkl)[uvw) in cubic coordinates are converted using formula (1). cub Then, a transformation matrix is ​​used for transformation. This yields the second-order stress tensor of the texture component in the sample coordinate system, i.e., the three-dimensional internal stress field of the texture component.

[0287] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0288] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A neutron diffraction method for measuring intergranular stress in a hexagonal crystal system, characterized in that, include: Step S1: Determine the constituent phases and crystal structure type of the material to be tested, and detect the texture of the material to be tested; Step S2: Determine the texture component to be tested and its crystal plane to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal plane to be tested and the sample to be tested for the texture component to be tested. In step S2: Determine the texture components to be tested and their crystal planes to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal planes to be tested and the sample to be tested for the texture components to be tested. Based on the texture information of the material to be tested and the research requirements, the texture components of the three-dimensional internal stress field to be detected are selected. The volume fraction of this texture component is not less than 5%; Determine the crystal plane to be measured for the texture component to be measured. The three-dimensional internal stress field of the texture component is detected, and the strain of its Q linearly independent crystal planes is detected, where Q≥10; Based on the crystal plane of the texture component to be measured Calculate the orientation of the crystal plane to be tested relative to the sample. The normal direction ND, rolling direction RD, and transverse direction TD are the three unit directions in the sample coordinate system, representing the crystal plane to be measured. normal direction The angle between the ND direction and the ND direction is defined as follows: Crystal plane normal The angle between the projection in the TD-RD plane and the RD direction is defined as follows: horn; For cubic crystal systems, the texture component In terms of its crystal plane The normal direction is parallel to the ND direction. The crystal orientation is parallel to the RD direction. included angle Using the normal of the crystal plane under test Perpendicular to Projection on the plane of direction and direction The included angle represents, ; This determines the texture components to be measured. The crystal plane to be tested relative to the direction of the sample ; In the hexagonal crystal system, the crystal plane indices and crystal direction indices defined in the hexagonal crystal system are transformed into cubic coordinates, and then the calculation methods for the cubic crystal system are used to calculate the crystal plane to be measured. relative to the direction of the sample Define the corresponding cubic coordinate system, using a cubic coordinate system within the hexagonal crystal system: , , For any crystal plane index or crystal direction index of the hexagonal crystal system In the defined cubic coordinate system, its equivalent crystal plane indices or crystal direction indices are: Where (100), (010) and (001) represent unit vectors in cubic coordinates, and the subscripts are... Represents a cubic coordinate system. , and The subscript represents a vector in the hexagonal crystal system. Indicates hexagonal crystal system; is the ratio of the crystal constant c to a in the hexagonal crystal system, i.e. Define a cubic coordinate system within the hexagonal crystal system, and then... A vector is defined as a (100) unit vector in a cubic coordinate system; The transformation matrix is ​​for the two coordinate systems. The transformation matrix differs for crystal plane indices and crystal direction indices. For crystal plane indices, the transformation matrix is: For crystal orientation indices, the transformation matrix is: The crystal plane to be tested The texture component to be tested Transform to a cubic crystal system and then solve for the texture components to be measured. The crystal plane to be tested relative to the direction of the sample ; Step S3: Neutron diffraction data acquisition, obtaining neutron diffraction signals for all corresponding crystal planes to be measured; In step S3: Based on the determined texture components to be measured The crystal plane to be tested interplanar spacing and the wavelength of the incident neutron Using Bragg's law of diffraction The diffraction angle was calculated. Move the detector to the designated location horn; It can be any integer; Based on the determined texture components to be measured The crystal plane to be tested relative to the direction of the sample Rotate the Euler ring to the corresponding position, set the measurement duration or neutron count according to the signal-to-noise ratio requirements, and detect the neutron diffraction signal; Repeat step S3 to obtain the neutron diffraction signals of all the corresponding Q crystal planes to be tested. If an in-situ neutron diffraction experiment is carried out, repeat step S3 after the in-situ loading conditions reach the set value. Step S4: Calculate the three-dimensional internal stress field of the material with different texture components; In step S4: Step S4.1: Calculate the three-dimensional internal stress field of the texture component in the crystal coordinate system; Select based on the determined texture components to be measured The crystal plane to be tested The diffraction data were fitted to obtain the diffraction angle. The strain of the crystal plane can be determined based on the change in diffraction angle. : （1） in, crystal plane lattice strain, crystal plane The diffraction angle corresponding to the stress-free state; Three-dimensional internal stress field of texture components Represented using a second-order stress tensor: （2） For cubic crystal systems The three-dimensional stress field of crystal plane strain and texture components has the following relationship: （3） , , They are respectively The cosine of the angle between the crystal plane normal and the three unit vectors of the coordinate axes, where the superscript 'c' indicates the corresponding texture component obtained in the crystal coordinate system. Crystalline strain Based on equation (3), Q six-variable linear equations are established. These equations are overdetermined and do not have analytical solutions. The least squares solutions of the six strain tensor components are obtained using the multiple linear regression method. The solution is: （4） in, The subscripts 1, 2, ..., p, ..., Q represent the test crystal plane numbers, and a total of Q crystal planes were tested; The second-order stress tensor is calculated using the constitutive relationship between stress and strain. : （5） in, This is the stiffness coefficient matrix of the material; The crystal plane coefficients in the hexagonal crystal system Transform to cubic coordinates using formula (1) Then, construct the second-order stress tensor according to the cubic crystal system method; Step S4.2: Construct the second-order stress tensor based on the second-order strain tensor in crystal coordinates: According to the generalized Hooke's law ,in Let be the stiffness matrix of the crystal; Hooke's law is written as: in, ; Step S4.3: Transform the second-order stress tensor of the crystal coordinate system to the sample coordinate system; crystal coordinate system The second-order stress tensor obtained from the solution Transform to sample coordinate system , Wherein, the transformation matrix It depends on the texture component being measured. For a cubic crystal system, for any texture component... Transformation matrix for: （6） in, , ; It is the inverse of the transformation matrix; The texture component to be tested The texture components are converted to cubic coordinates using formula (1). Then, the transformation matrix is ​​used to transform the sample coordinate system to obtain the second-order stress tensor of the texture component, that is, the three-dimensional internal stress field of the texture component.

2. The neutron diffraction testing method for intergranular stress in a hexagonal crystal system according to claim 1, characterized in that, In step S1: Determine the constituent phases and crystal structure type of the material to be tested, determine whether the material to be tested is a single-phase or multi-phase material and the crystal structure type of each phase, and determine the crystal planes of the material to be tested by neutron diffraction. The experimental design for detecting the texture of the material under test and the three-dimensional internal stress field of different texture components of the material under test is based on the texture information of the material under test.

3. A neutron diffraction testing system for intergranular stress in hexagonal crystal systems, characterized in that, include: Module M1: Determines the constituent phases and crystal structure type of the material under test, and detects the texture of the material under test; Module M2: Determine the texture component to be tested and its crystal plane to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal plane to be tested and the sample to be tested for the texture component to be tested; In module M2: Determine the texture components to be tested and their crystal planes to be tested in the three-dimensional internal stress field to be detected, and calculate the specific directional relationship between the crystal planes to be tested and the sample to be tested for the texture components to be tested. Based on the texture information of the material to be tested and the research requirements, the texture components of the three-dimensional internal stress field to be detected are selected. The volume fraction of this texture component is not less than 5%; Determine the crystal plane to be measured for the texture component to be measured. The three-dimensional internal stress field of the texture component is detected, and the strain of its Q linearly independent crystal planes is detected, where Q≥10; Based on the crystal plane of the texture component to be measured Calculate the orientation of the crystal plane to be tested relative to the sample. The normal direction ND, rolling direction RD, and transverse direction TD are the three unit directions in the sample coordinate system, representing the crystal plane to be measured. normal direction The angle between the ND direction and the ND direction is defined as follows: Crystal plane normal The angle between the projection in the TD-RD plane and the RD direction is defined as follows: horn; For cubic crystal systems, the texture component In terms of its crystal plane The normal direction is parallel to the ND direction. The crystal orientation is parallel to the RD direction. included angle Using the normal of the crystal plane under test Perpendicular to Projection on the plane of direction and direction The included angle represents, This determines the texture components to be measured. The crystal plane to be tested relative to the direction of the sample ; In the hexagonal crystal system, the crystal plane indices and crystal direction indices defined in the hexagonal crystal system are transformed into cubic coordinates, and then the calculation methods for the cubic crystal system are used to calculate the crystal plane to be measured. relative to the direction of the sample Define the corresponding cubic coordinate system, using a cubic coordinate system within the hexagonal crystal system: , , For any crystal plane index or crystal direction index of the hexagonal crystal system In the defined cubic coordinate system, its equivalent crystal plane indices or crystal direction indices are: Where (100), (010) and (001) represent unit vectors in cubic coordinates, and the subscripts are... Represents a cubic coordinate system. , and The subscript represents a vector in the hexagonal crystal system. Indicates hexagonal crystal system; is the ratio of the crystal constant c to a in the hexagonal crystal system, i.e. Define a cubic coordinate system within the hexagonal crystal system, and then... A vector is defined as a (100) unit vector in a cubic coordinate system; The transformation matrix is ​​for the two coordinate systems. The transformation matrix differs for crystal plane indices and crystal direction indices. For crystal plane indices, the transformation matrix is: For crystal orientation indices, the transformation matrix is: The crystal plane to be tested The texture component to be tested Transform to a cubic crystal system and then solve for the texture components to be measured. The crystal plane to be tested relative to the direction of the sample ; Module M3: Neutron diffraction data acquisition, obtaining neutron diffraction signals of all corresponding crystal planes to be measured; In module M3: Based on the determined texture components to be measured The crystal plane to be tested interplanar spacing and the wavelength of the incident neutron Using Bragg's law of diffraction The diffraction angle was calculated. Move the detector to the designated location horn; It can be any integer; Based on the determined texture components to be measured The crystal plane to be tested relative to the direction of the sample Rotate the Euler ring to the corresponding position, set the measurement duration or neutron count according to the signal-to-noise ratio requirements, and detect the neutron diffraction signal; Repeat module M3 to obtain the neutron diffraction signals of all the corresponding Q crystal planes to be tested. If an in-situ neutron diffraction experiment is carried out, repeat module M3 when the in-situ loading conditions reach the set value. Module M4: Calculates the three-dimensional internal stress field of a material with different texture components; In module M4: Module M4.1: Calculates the three-dimensional internal stress field of the texture component in crystal coordinates; Select based on the determined texture components to be measured The crystal plane to be tested The diffraction data were fitted to obtain the diffraction angle. The strain of the crystal plane can be determined based on the change in diffraction angle. : （1） in, crystal plane lattice strain, crystal plane The diffraction angle corresponding to the stress-free state; Three-dimensional internal stress field of texture components Represented using a second-order stress tensor: （2） For cubic crystal systems The three-dimensional stress field of crystal plane strain and texture components has the following relationship: （3） , , They are respectively The cosine of the angle between the crystal plane normal and the three unit vectors of the coordinate axes, where the superscript 'c' indicates the corresponding texture component obtained in the crystal coordinate system. Crystalline strain Based on equation (3), Q six-variable linear equations are established. These equations are overdetermined and do not have analytical solutions. The least squares solutions of the six strain tensor components are obtained using the multiple linear regression method. The solution is: （4） in, The subscripts 1, 2, ..., p, ..., Q represent the test crystal plane numbers, and a total of Q crystal planes were tested; The second-order stress tensor is calculated using the constitutive relationship between stress and strain. : （5） in, This is the stiffness coefficient matrix of the material; The crystal plane coefficients in the hexagonal crystal system Transform to cubic coordinates using formula (1) Then, construct the second-order stress tensor according to the cubic crystal system method; Module M4.2: Constructing a second-order stress tensor based on the second-order strain tensor in crystal coordinates: According to the generalized Hooke's law ,in Let be the stiffness matrix of the crystal; Hooke's law is written as: in, ; Module M4.3: Transforms the second-order stress tensor from the crystal coordinate system to the sample coordinate system; crystal coordinate system The second-order stress tensor obtained from the solution Transform to sample coordinate system , Wherein, the transformation matrix It depends on the texture component being measured. For a cubic crystal system, for any texture component... Transformation matrix for: （6） in, , ; It is the inverse of the transformation matrix; The texture component to be tested The texture components are converted to cubic coordinates using formula (1). Then, the transformation matrix is ​​used to transform the sample coordinate system to obtain the second-order stress tensor of the texture component, that is, the three-dimensional internal stress field of the texture component.

4. The neutron diffraction testing system for intergranular stress in a hexagonal crystal system according to claim 3, characterized in that, In module M1: Determine the constituent phases and crystal structure type of the material to be tested, determine whether the material to be tested is a single-phase or multi-phase material and the crystal structure type of each phase, and determine the crystal planes of the material to be tested by neutron diffraction. The experimental design for detecting the texture of the material under test and the three-dimensional internal stress field of different texture components of the material under test is based on the texture information of the material under test.

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