Method for predicting slippage transmission probability of different crystal systems

Abstract

The invention discloses a method for predicting slippage transmission probabilities of different crystal systems. Aiming at a scene in which dislocation needs to pass through a grain boundary and is reconstructed in alien system slip transfer, a rotational symmetry operation matrix group of two crystal systems and variant orientation of each slip system are constructed, the minimum angle of crystal grains rotating to generate a parallel slip system of the alien system is calculated, and the smaller the value is, the larger the slip transfer probability is. According to the method, crystal system limitation is broken through, typical crystal system combinations such as face-centered cubic, body-centered cubic and close-packed hexagonal are compatible, and activation and transmission difficulty of dislocation slippage at the allomorphic system crystal boundary is quantified by constructing a joint matching criterion that the normal direction and the slippage direction of a slippage face are parallel. The method is suitable for complex systems such as a heterojunction interface, and a crystallographic basis is provided for inhibiting microcrack initiation.

Description

Technical Field

[0001] This invention belongs to the field of basic materials science and relates to a method for predicting the slip transfer probability of different crystal systems. Background Technology

[0002] In metallic materials, the long-range disorder of atomic arrangement at grain boundaries due to differences in crystal structure leads to dislocation slip propagation mechanisms that differ from those at homocrystalline grain boundaries. At interfaces caused by differences in crystal structure, dislocation slip vectors undergo a reconstruction process, and their propagation behavior is influenced by multiple factors, including differences in lattice parameters, interface coherence, and slip system matching. Existing slip propagation prediction models (such as geometric propagation factor N and orientation compatibility factor m') are based on the assumption of homocrystalline grain boundaries, making it difficult to adapt to the complexity of slip propagation at heterocrystalline grain boundaries. They fail to consider the order of activation difficulty of slip systems in different crystal systems caused by orientation relationships, thus limiting their predictive ability for slip propagation behavior at high interface energy grain boundaries. Therefore, establishing slip propagation prediction models compatible with multiple crystal systems and analyzing the activation and reconstruction mechanisms of slip systems at heterocrystalline interfaces is a key technical challenge for overcoming the synergistic improvement of strength and plasticity in heterocrystalline polycrystalline materials. Summary of the Invention

[0003] To address the aforementioned technical problems, a method for predicting the slip transfer probability of different crystal systems is proposed, the specific scheme of which is as follows:

[0004] A method for predicting the slip transfer probability of different crystal systems includes the following steps:

[0005] Calculate the minimum rotation angle required for the first grain to rotate to form a parallel slip system with the second grain, which has a different crystal system.

[0006] "Parallel" means that the normals to the slip planes and the slip directions of the two grains are parallel;

[0007] The term "parallel slip system" includes a specific slip system or a range of specific slip systems;

[0008] The minimum rotation angle is defined as the slip orientation difference between different crystal systems, and the smaller the value, the greater the probability of slip propagation.

[0009] A preferred embodiment of the method for predicting the probability of slip transfer in different crystal systems is that the calculation process of the minimum rotation angle includes:

[0010] Step 1. The rotation of grains and the transformation of the crystal lattice are regarded as the rotation and transformation of coordinate axes;

[0011] Establish the sample coordinate system as bv0, the crystal coordinate system of the first grain as bv1, and the crystal coordinate system of the second grain as bv2. The slip coordinate systems of the two grains are bv1_1 and bv2_1, respectively, and bv0, bv1_1, and bv2_1 are all orthogonal coordinate systems. Use the superscript of the matrix to indicate the crystal system or the crystal system transformation order, and the index in the subscript of the matrix indicates that it is a set of matrices.

[0012] Step 2. Parallel slip systems of different crystal systems are represented as follows:

[0013]

[0014] In the formula, The row basis vectors of the sample coordinate axes; and These are the transformation matrices from the sample coordinate system to its crystal coordinate system, i.e., the crystal orientation matrices of the two grains; and These are the rotational symmetry operation matrix groups for the crystal systems to which the first and second grains belong, respectively; and These are all the transformation matrices of the two grains from the crystal coordinate system to their respective slip coordinate systems; The matrix represents the rotation matrix performed on the basis vectors of the sample coordinate system to produce the aforementioned parallel slip system between the two grains; in the subscripts, a and b are the number of rotational symmetry operation matrices of the two grain crystal systems, and m and n are the number of slip variants of all / part of the slip system of the two grain crystal systems.

[0015] Step 3. Formula The transformed expression is:

[0016]

[0017] Step 4. Based on Rodriguez's formula and the properties of the rotation matrix, the rotation angle is determined by... The trace is used to calculate the result, and the formula is:

[0018]

[0019] In the formula, the rotation angle The minimum value min{ This refers to the slip orientation difference between different crystal systems.

[0020] In a preferred embodiment of the method for predicting the probability of slip transfer in different crystal systems, the rotational symmetry operation matrix group does not include reflection and inversion operations.

[0021] The preferred embodiment of the method for predicting the probability of slip transfer in different crystal systems is that the coordinate axes of the slip system are composed of the slip plane normal vector, the slip direction vector, and another direction vector located in the slip plane and perpendicular to the slip direction.

[0022] The preferred embodiment of the method for predicting the probability of slip transfer in different crystal systems is that the crystal system includes any two different combinations of cubic, hexagonal, tetragonal, trigonal, orthorhombic, monoclinic and triclinic crystal systems.

[0023] Beneficial effects: This method proposes a slip propagation prediction model compatible with polycrystalline system differences. By calculating the minimum rotation angle of grain orientation, the slip plane normal and slip direction are made approximately parallel on both sides of the grain boundary, thereby quantifying the geometric matching degree of slip propagation. Its technical advantages are reflected in: (1) breaking through the crystal system limitations of traditional methods, and being compatible with combination systems of typical crystal systems such as face-centered cubic, body-centered cubic, and hexagonal close-packed; (2) characterizing the difficulty of dislocation activation and reconstruction at heterocrystalline grain boundaries through the joint matching criterion of slip plane normal and slip direction; (3) establishing a quantitative index of slip propagation probability, providing a calculable mechanical basis for the microstructure design of heterojunctions. This method is applicable to complex systems such as heterocrystalline composite materials and heterojunction interfaces, providing theoretical support for controlling the uniformity of dislocation movement at grain boundaries and suppressing microcrack initiation. Attached Figure Description

[0024] Figure 1 This is a grain orientation distribution diagram of the titanium alloy in Example 1;

[0025] Figure 2 This is a diagram showing the slip trace distribution of titanium alloy grains in Example 1;

[0026] Figure 3 This is a grain orientation distribution diagram of the titanium alloy in Example 2;

[0027] Figure 4 This is a diagram showing the slip trace distribution of titanium alloy grains in Example 2;

[0028] Figure 5 Grain orientation distribution diagram of titanium alloy in Example 3;

[0029] Figure 6 This is a distribution diagram of the slip traces of titanium alloy grains in Example 3. Detailed Implementation

[0030] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples; the following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0031] Example 1

[0032] Taking the slip transfer between the α2 phase of the hexagonal close-packed crystal system and the B2 phase of the body-centered cubic crystal system in titanium alloy (Ti2AlNb) as an example, the slip transfer probability prediction method for different crystal systems of the present invention is used for calculation:

[0033] Step 1. Grain rotation and lattice transformation can be viewed as rotation and transformation of coordinate axes. An orthogonal coordinate system is established using three unit vectors: the slip plane normal, the slip direction, and another direction perpendicular to the slip direction on the plane. For ease of description, the sample coordinate system is defined as bv0, the two grain crystal coordinate systems as bv1 and bv2, and the two grain slip coordinate systems as bv1_1 and bv2_1, where bv0, bv1_1, and bv2_1 are all orthogonal coordinate systems. Superscripts in matrices indicate the crystal system or crystal system transformation order, while subscripts indicate a set of matrices.

[0034] Step 2. Parallel slip systems of different crystal systems can be represented as:

[0035]

[0036] In the formula, is the basis vector of the sample coordinate axes. and These are the transformation matrices from the sample coordinate axes to the crystal coordinate axes, i.e., the crystal orientation matrices of the two grains, which can be determined by the grain Euler angles in Table 1. and It is the rotational symmetry operation matrix group of the crystal system in which the two grains are located (excluding reflection and inversion). For details of body-centered cubic and hexagonal close-packed crystals, please refer to Tables 2 and 3. and These are all the transformation matrices from the crystal axes of the two grains to their respective slip system axes, as shown in Tables 4 and 5. This refers to the rotation matrix performed on the basis vectors of the sample coordinate system to produce the aforementioned parallel slip system between the two grains.

[0037] Table 1 Figure 1 and Figure 2 Euler angles of each grain

[0038]

[0039] Table 2. Set of rotational symmetry operation matrices for body-centered cubic crystal systems

[0040]

[0041] Table 3. Set of rotational symmetry operation matrices for hexagonal close-packed crystal systems

[0042]

[0043] Step 3. Formula The transformation yields:

[0044]

[0045] Step 4. Based on Rodriguez's formula and the properties of the rotation matrix, the rotation angle can be determined by... The trace is used to calculate the result, and the formula is:

[0046]

[0047] In the formula, the rotation angle The minimum value min{ This refers to the slip orientation difference between different crystal systems. Based on Figure 1 The orientation and boundaries of each grain are analyzed, and the slip orientation difference between adjacent grains is calculated. Figure 2 The distribution of slip traces among the grains can determine whether slip transfer has occurred within a grain group, as shown in Table 6. Given the diversity of grain slip systems and the complexity of slip system matching between grains with different orientations, traditional methods struggle to predict slip transfer. The statistical prediction accuracy of this invention reaches 82.35%, fully demonstrating its innovation and practicality.

[0048] Table 4. Set of all transformation matrices from crystal axes to slip system axes in body-centered cubic grains.

[0049]

[0050] Table 5. Set of all transformation matrices from the grain axis to the slip system axis of hexagonal close-packed grains.

[0051]

[0052] Table 6 shows the slip orientation differences of each group of grains in Table 1.

[0053]

[0054] Example 2

[0055] Taking the slip transfer between the α phase of the hexagonal close-packed crystal system and the β phase of the body-centered cubic crystal system in titanium alloy (TB18) as an example, the slip transfer probability prediction method for different crystal systems of the present invention is used for calculation:

[0056] Step 1. Grain rotation and lattice transformation can be viewed as rotation and transformation of coordinate axes. An orthogonal coordinate system is established using three unit vectors: the slip plane normal, the slip direction, and another direction perpendicular to the slip direction on the plane. For ease of description, the sample coordinate system is defined as bv0, the two grain crystal coordinate systems as bv1 and bv2, and the two grain slip coordinate systems as bv1_1 and bv2_1, where bv0, bv1_1, and bv2_1 are all orthogonal coordinate systems. Superscripts in matrices indicate the crystal system or crystal system transformation order, while subscripts indicate a set of matrices.

[0057] Step 2. Parallel slip systems of different crystal systems can be represented as:

[0058]

[0059] In the formula, is the basis vector of the sample coordinate axes. and These are the transformation matrices from the sample coordinate axes to the crystal coordinate axes, i.e., the crystal orientation matrices of the two grains, which can be determined by the grain Euler angles in Table 7. and It is the rotational symmetry operation matrix group of the crystal system in which the two grains are located (excluding reflection and inversion). For details of body-centered cubic and hexagonal close-packed crystals, please refer to Tables 2 and 3. and These are all the transformation matrices from the crystal axes of the two grains to their respective slip system axes, as shown in Tables 4 and 5. This refers to the rotation matrix performed on the basis vectors of the sample coordinate system to produce the aforementioned parallel slip system between the two grains.

[0060] Table 7 Figure 3 and Figure 4 Euler angles of each grain

[0061]

[0062] Step 3. Formula The transformation yields:

[0063]

[0064] Step 4. Based on Rodriguez's formula and the properties of the rotation matrix, the rotation angle can be determined by... The trace is used to calculate the result, and the formula is:

[0065]

[0066] In the formula, the rotation angle The minimum value min{ This refers to the slip orientation difference between different crystal systems. Based on Figure 3 The orientation and boundaries of each grain are analyzed, and the slip orientation difference between adjacent grains is calculated. Figure 4 The distribution of slip traces among the grains can determine whether slip transfer has occurred within a grain group, as shown in Table 8. Given the diversity of grain slip systems and the complexity of slip system matching between grains with different orientations, traditional methods struggle to predict slip transfer. The prediction results of this invention are highly consistent with experimental phenomena, fully demonstrating its innovation and practicality.

[0067] Table 8 shows the slip orientation differences of each group of grains in Table 7.

[0068]

[0069] Example 3

[0070] Taking the slip transfer between the orthorhombic O phase and the body-centered cubic B2 phase in titanium alloy (Ti2AlNb) as an example, the slip transfer probability prediction method for different crystal systems of the present invention is used for calculation. Since the slip transfer occurs during room temperature tensile testing, the slip system of the O phase almost only initiates {010}. <100> and {1-10} <110> Therefore, the specific slip system range of the orthorhombic crystal system in this example is {010}. <100> and {1-10} <110> :

[0071] Step 1. Grain rotation and lattice transformation can be viewed as rotation and transformation of coordinate axes. An orthogonal coordinate system is established using three unit vectors: the slip plane normal, the slip direction, and another direction perpendicular to the slip direction on the plane. For ease of description, the sample coordinate system is defined as bv0, the two grain crystal coordinate systems as bv1 and bv2, and the two grain slip coordinate systems as bv1_1 and bv2_1, where bv0, bv1_1, and bv2_1 are all orthogonal coordinate systems. Superscripts in matrices indicate the crystal system or crystal system transformation order, while subscripts indicate a set of matrices.

[0072] Step 2. Parallel slip systems of different crystal systems can be represented as:

[0073]

[0074] In the formula, is the basis vector of the sample coordinate axes. and These are the transformation matrices from the sample coordinate axes to the crystal coordinate axes, i.e., the crystal orientation matrices of the two grains, which can be determined by the grain Euler angles in Table 9. and It is the rotational symmetry operation matrix group of the crystal system in which the two grains are located (excluding reflection and inversion). For details of body-centered cubic and orthorhombic crystal systems, please refer to Table 2 and Table 9. and These are all the transformation matrices from the crystal axes of the two grains to their respective slip system axes, as shown in Tables 4 and 10. This refers to the rotation matrix performed on the basis vectors of the sample coordinate system to produce the aforementioned parallel slip system between the two grains.

[0075] Table 9 Figure 5 and Figure 6 Euler angles of each grain

[0076]

[0077] Table 10 Set of rotational symmetry operation matrices for orthorhombic crystal systems

[0078]

[0079] Table 11 Orthorhombic crystal system grain axes to {010} <100> and {1-10} <110> The set of all transformation matrices of the slip system axis

[0080]

[0081] Step 3. Formula The transformation yields:

[0082]

[0083] Step 4. Based on Rodriguez's formula and the properties of the rotation matrix, the rotation angle can be determined by... The trace is used to calculate the result, and the formula is:

[0084]

[0085] In the formula, the rotation angle The minimum value min{ This refers to the slip orientation difference between different crystal systems. Based on Figure 5 The orientation and boundaries of each grain are analyzed, and the slip orientation difference between adjacent grains is calculated. Figure 6 The distribution of slip traces among the grains can determine whether slip transfer has occurred within a grain group, as shown in Table 11. Given the diversity of grain slip systems and the complexity of slip system matching between grains with different orientations, traditional methods struggle to predict slip transfer. The prediction results of this invention are highly consistent with experimental phenomena, fully demonstrating its innovation and practicality.

[0086] Table 12 shows the slip orientation differences of each group of grains in Table 8.

[0087]

[0088] The above embodiments are only for illustrating the technical concept and specific calculation method of the present invention, and are not intended to limit the ideas of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention, such as the selection of other alloy systems, should be included within the protection scope of the present invention.

Claims

1. A method for predicting the slip transfer probability of different crystal systems, characterized in that, Includes the following steps: Calculate the minimum rotation angle required for the first grain to rotate to form a parallel slip system with the second grain, which has a different crystal system. "Parallel" means that the normals to the slip planes and the slip directions of the two grains are parallel; The term "parallel slip system" includes a specific slip system or a range of specific slip systems; The minimum rotation angle is defined as the slip orientation difference between different crystal systems, and the smaller the value, the greater the probability of slip propagation.

2. The method for predicting the probability of slip transfer in different crystal systems according to claim 1, characterized in that, The calculation process for the minimum rotation angle includes: Step 1. The rotation of grains and the transformation of the crystal lattice are regarded as the rotation and transformation of coordinate axes; Establish the sample coordinate system as bv0, the crystal coordinate system of the first grain as bv1, and the crystal coordinate system of the second grain as bv2. The slip coordinate systems of the two grains are bv1_1 and bv2_1, respectively, and bv0, bv1_1, and bv2_1 are all orthogonal coordinate systems. Use the superscript of the matrix to indicate its crystal system or crystal system transformation order, and the index in the subscript of the matrix indicates that it is a set of matrices. Step 2. Parallel slip systems of different crystal systems are represented as follows: In the formula, The row basis vectors of the sample coordinate axes; and These are the transformation matrices from the sample coordinate system to its crystal coordinate system, i.e., the crystal orientation matrices of the two grains; and These are the rotational symmetry operation matrix groups for the crystal systems to which the first and second grains belong, respectively; and These are all the transformation matrices of the two grains from the crystal coordinate system to their respective slip coordinate systems; The matrix represents the rotation matrix performed on the basis vectors of the sample coordinate system to produce the aforementioned parallel slip system between the two grains; in the subscripts, a and b are the number of rotational symmetry operation matrices of the two grain crystal systems, and m and n are the number of slip variants of all / part of the slip system of the two grain crystal systems. Step 3. Formula The transformed expression is: Step 4. Based on Rodriguez's formula and the properties of the rotation matrix, the rotation angle is determined by... The trace is used to calculate, and the formula is: In the formula, the rotation angle The minimum value min{ This refers to the slip orientation difference between different crystal systems.

3. The method for predicting the probability of slip transfer in different crystal systems according to claim 2, characterized in that, The rotationally symmetric operation matrix group does not include reflection and inversion operations.

4. The method for predicting the probability of slip transfer in different crystal systems according to claim 2, characterized in that, The coordinate axes of the sliding system are composed of the normal vector of the sliding surface, the sliding direction vector, and another direction vector located in the sliding surface and perpendicular to the sliding direction.

5. The method for predicting the probability of slip transfer in different crystal systems according to claim 1, characterized in that, The crystal system includes any two different combinations of cubic, hexagonal, tetragonal, trigonal, orthorhombic, monoclinic, and triclinic crystal systems.

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