A method for predicting orthorhombic martensite variant selection of a metastable beta titanium alloy

Abstract

The application discloses a metastable beta titanium alloy orthorhombic martensite variant selection prediction method, and belongs to the technical field of titanium alloy phase change analysis and structure regulation, and comprises the following steps: acquiring the parent phase beta orientation, main twin crystal information, load, crystal lattice and elastic parameters of the metastable beta titanium alloy to be analyzed; calculating a deformation distortion tensor based on Burgers relationship and PTMC to construct a candidate variant branch set; establishing a main twin crystal local coordinate system and equivalently taking the main twin crystal as an inclusion; calculating a local stress tensor based on Eshelby theory and Mura-Cheng solution; calculating basic and local interaction work based on a macroscopic applied stress tensor, the local stress tensor and the deformation distortion tensor; sorting the basic and local interaction work, determining the local dominant candidate after sorting, and further determining a dominant main variant or a habit plane branch, so that the variant selection of the orthorhombic martensite in the twin crystal dominant deformation can be quantitatively predicted, and a theoretical basis is provided for structure evolution and performance optimization.

Description

Technical Field

[0001] This application relates to the field of phase transformation analysis and microstructure control technology of titanium alloys, and in particular to a method for predicting the selection of orthogonal martensite variants in metastable β titanium alloys. Background Technology

[0002] Metastable β-titanium alloys can undergo microstructural evolution behaviors such as deformation twinning and stress-induced martensitic transformation during deformation, among which {332} <113> β Twins and orthorhombic martensite are typical deformation products. After the formation of the main twins, the microstructure of the material may continue to evolve during subsequent deformation processes, accompanied by the formation of subsequent deformation products such as orthorhombic martensite; this evolution process is closely related to the microstructure regulation and performance optimization of metastable β-titanium alloys.

[0003] In existing technologies, studies on phase transformation variants of titanium alloys can typically identify the orientation relationship between the parent and daughter phases, distinguish and calibrate variants, and conduct preliminary analysis based on macroscopic external loads. For twinning-related issues, existing technologies have also been developed to study specific microstructure phenomena using crystallographic analysis or local stress field analysis.

[0004] However, for the question of how the subsequent deformation products of metastable β-titanium alloys continue to evolve during twin-dominated deformation, existing technologies are still mainly at the level of phenomenon description or qualitative explanation. There is a lack of a quantitative analysis method that can combine the construction of crystallographic candidate variants with the calculation of local stress fields induced by the main twins. Therefore, it is difficult to conduct a unified analysis and prediction of the continuous evolution of the associated orthorhombic martensite and its variant selection behavior.

[0005] Therefore, it is necessary to propose a new analysis and prediction method to quantitatively analyze the continuous evolution behavior of subsequent deformation products under local stress during twin-dominated deformation in metastable β-titanium alloys, and to provide technical support for related microstructure control and performance optimization. Summary of the Invention

[0006] To address the aforementioned shortcomings in the prior art, this application provides a method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys. This method solves the problem that the prior art lacks a quantitative analysis method that combines crystallographic candidate variant construction with the calculation of local stress fields induced by the principal twin, making it difficult to uniformly analyze and predict the continuous evolution of associated orthogonal martensite and its variant selection behavior during the twin-dominated deformation process of metastable β-titanium alloys.

[0007] To achieve the aforementioned objectives, the technical solution adopted in this application is as follows: This application provides a method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys, including: S1: Obtain the crystallographic orientation information of the parent phase β, the crystallographic information of the principal twin, the information of the applied load, the information of the lattice parameters, and the information of the elastic parameters of the metastable β titanium alloy to be analyzed; S2: Based on the orientation information of the parent phase β crystallography, combined with the Burgers orientation relationship and the martensitic phase transformation crystallography theory PTMC, a candidate variant branch set consisting of multiple candidate orthogonal martensitic principal variants and habit plane branches is constructed, and the deformation distortion tensor corresponding to each candidate variant branch is calculated. S3: Establish a local coordinate system for the main twin based on the twin plane normal and twin shear direction, and in the local coordinate system, the main twin is equivalent to a thin plate-like or flattened ellipsoidal inclusion body; S4: Based on the positional relationship between the associated orthogonal martensite and the main twin, the formation state of the associated orthogonal martensite is divided, and the local stress tensor inside and outside the main twin is calculated based on Eshelby theory and Mura–Cheng external field analytical solution. S5: Establish the macroscopic external stress tensor based on the external load information, and calculate the interaction work of the foundation and the interaction work of the local forces based on the macroscopic external stress tensor, the local stress tensor and the deformation distortion tensor. S6: Sort the basic interaction work and local interaction work of each candidate variant branch, determine the candidate variant branch whose local interaction work is within the preset dominant sorting range as the local dominant candidate, and determine the dominant principal variant or dominant habit surface branch of the associated orthogonal martensite according to the change of the local dominant candidate relative to the basic interaction work sorting.

[0008] Furthermore, the external load information includes the loading direction and stress state; the lattice parameter information includes the lattice constants of the β parent phase and orthorhombic martensite; and the elastic parameter information includes the elastic stiffness tensor, elastic compliance tensor, or equivalent elastic constants of the β parent phase.

[0009] Further, S2 includes: S201: Based on the Burgers orientation relationship between the parent β phase and orthorhombic martensite, construct equivalent candidate orthorhombic martensite principal variants; S202: Based on the martensitic phase transformation crystallography theory PTMC, two conjugate habit plane branches, the corresponding habit plane normal and shear direction are solved for each candidate orthogonal martensite principal variant, resulting in a candidate variant branch set composed of multiple candidate orthogonal martensite principal variants and habit plane branches. S203: Calculate the deformation gradient tensor corresponding to each candidate variant branch. The calculation formula is as follows:

[0010] In the formula, For the first The deformation gradient tensor of each candidate variant branch For unit tensors, For macroscopic shape strain amplitude, and These represent the first and second digits in the β-parent phase crystallographic reference frame, respectively. The unit vectors of the macroscopic shear direction and habit surface normal of each candidate variant branch, with superscript... Represents the physical quantities associated with candidate martensitic variant branches. Represents the vector tensor product; S204: Based on the deformation gradient tensor, calculate the deformation distortion tensor corresponding to each candidate variant branch. The calculation formula is as follows:

[0011] In the formula, For the first The deformed distortion tensor of each candidate variant branch.

[0012] Furthermore, the principal twin's local coordinate system satisfies: x The 0-axis is parallel to the direction of the principal twin shear. η 1. z The 0-axis is parallel to the principal twin plane. K 1's normal direction y The 0-axis is perpendicular to the direction of the twin shear. η 1 and twin plane K 1. A plane formed by normals; The sheet-like or flattened ellipsoidal inclusion has a first characteristic dimension and a second characteristic dimension located within the twin plane, and a third characteristic dimension along the normal of the twin plane, wherein the third characteristic dimension is smaller than the first characteristic dimension and the second characteristic dimension.

[0013] Further, S4 includes: S401: In the β-parent phase crystallographic reference frame, the deformation gradient tensor of the principal twin is defined and calculated as follows:

[0014] In the formula, The deformation gradient tensor of the main twin. For twin shear rate, and The superscripts represent the unit vectors of the twinning shear direction and the twin plane normal in the crystallographic coordinate system of the β parent phase, respectively. This represents physical quantities related to the principal twin; S402: The deformation gradient tensor of the principal twin is converted into effective intrinsic strain, and the calculation formula is as follows:

[0015] In the formula, To effectively adapt to intrinsic strain, superscript For transpose; S403: Based on the positional relationship between the associated orthorhombic martensite and the main twin, the formation state of the associated orthorhombic martensite is divided into the formation state inside the main twin and the near-field formation state outside the main twin. S404: For the associated orthorhombic martensite formed within the main twin, the local stress tensor within the main twin is calculated using Eshelby theory. The calculation formula is as follows:

[0016]

[0017]

[0018] In the formula, The main twin is subject to constrained strain inside. For Eshelby tensors, For elastic strain, For internal local stress tensor, Let be the elastic stiffness tensor of the β phase; S405: For the associated orthorhombic martensite formed in the near-field region outside the main twin, the local stress tensor outside the main twin is calculated using the Mura–Cheng external field analytical solution. The calculation formula is as follows:

[0019] In the formula, For any external evaluation point The local stress tensor of the principal twin at that location. The kernel function of the outer field of the ellipsoidal inclusion body is related to the location of the evaluation point, the geometric parameters of the inclusion body, and its orientation.

[0020] Furthermore, the near-field formation state of the main twin includes the formation state near the wide face of the main twin and the formation state near the leading edge of the main twin; For the formation state of the main twin broad face, one or more surface nearest evaluation points are set along the direction of the main twin broad face; for the formation state of the main twin front edge, one or more evaluation points are set along the parameterized path from the center of the main twin broad face to the front edge region, and the continuous evolution trend of the associated orthorhombic martensite is characterized by the ranking of the local interaction work at different evaluation points through continuous evaluation.

[0021] Further, S5 includes: A macroscopic applied stress tensor is established based on the applied load information. The macroscopic applied stress tensor is then used to perform a tensor double dot product calculation with the deformation distortion tensor of each candidate variant branch to obtain the fundamental interaction work of each candidate variant branch. The calculation formula is as follows:

[0022] In the formula, For the first The fundamental interaction work of each candidate variant branch. For macroscopic applied stress tensor, superscript Represents a physical quantity under macroscopic external stress; The local interaction work of each candidate variant branch is obtained by performing a tensor double dot product calculation on the local stress tensors inside and outside the principal twin and the deformation distortion tensors of each candidate variant branch. The calculation formula is as follows:

[0023] In the formula, For the first Local interaction work of each candidate variant branch It is the local stress tensor inside or outside the main twin; Among them, when the candidate variant is formed inside the main twin, Take the local stress tensor inside the principal twin When candidate variants form in the near-field region outside the master twin, Take the local stress tensor outside the principal twin .

[0024] The beneficial effects of this application are: This application provides a method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys. Based on input crystallographic information, material parameters, and loading conditions, it calculates and predicts the preferred trends of candidate variant branches, thus providing a theoretical basis and methodological support for the microstructure evolution and performance optimization of metastable β-titanium alloys and other alloys exhibiting deformation-induced phase transformation characteristics. This method establishes a quantitative correlation between crystallographic constraints, local stress redistribution induced by principal twins, and the selection behavior of associated orthogonal martensite variants. It can transform microstructure observation results into a computable ranking of candidate variant branches, significantly improving the quantification and repeatability of variant selection analysis. By uniformly adopting a two-layer driving force criterion combining fundamental interaction work and local interaction work, this method can uniformly compare and rank candidate variants formed inside and outside the near-field region of the principal twin within the same computational framework, enhancing the consistency and operability of the method. Furthermore, this application does not regard the associated orthogonal martensite as a simple uniform response to applied stress, but can accurately characterize the influence of the local stress field induced by the principal twin on the selection of variants of subsequent deformation products, providing a reliable calculation basis for the microstructure control of metastable β titanium alloys. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.

[0026] Figure 1 This is a flowchart illustrating a method for predicting orthogonal martensite variants in metastable β-titanium alloys, provided in an embodiment of this application.

[0027] Figure 2 This is a schematic diagram of the crystallographic construction of a candidate orthorhombic martensite principal variant provided in an embodiment of this application.

[0028] Figure 3 This is a schematic diagram of a principal twin local coordinate system and a geometric model of an ellipsoidal inclusion body provided in an embodiment of this application.

[0029] Figure 4 This is a schematic diagram of a surface nearest neighbor evaluation path in a master twin wide-face proximity state provided in an embodiment of this application.

[0030] Figure 5 This is a schematic diagram of a parameterized evaluation path extending from the center of the wide face to the leading edge in the vicinity of the main twin front, provided for an embodiment of this application.

[0031] Figure 6 This is a schematic diagram showing the continuous distribution of local interaction work of candidate variant branches along the scan path in a state of proximity to the main twin broad facet, as provided in an embodiment of this application.

[0032] Figure 7 This is a schematic diagram illustrating the continuous evolution of the angle parameter of the local interaction work of a candidate variant branch in the vicinity of the principal twin front in an embodiment of this application. Detailed Implementation

[0033] To make the technical solution, implementation method, and beneficial effects of the present invention clearer, the present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are only used to illustrate the technical solution of the present invention and are not intended to limit the scope of protection of the present invention. Unless otherwise stated, the material system, twin type, lattice parameters, elastic parameters, inclusion body geometric ratio, evaluation path parameters, and reference stress amplitude in the embodiments are all exemplary parameters, and those skilled in the art can make corresponding adjustments according to the material to be analyzed and the experimental conditions.

[0034] It should be noted that, in this application, the material to be analyzed is not limited to a metastable β-titanium alloy with a specific composition. As long as the material can undergo β-phase twinning and orthorhombic martensitic phase transformation during deformation, the method of this invention can be implemented based on the crystallographic orientation information of its parent phase β, the crystallographic information of the principal twin, lattice parameters, elastic parameters, and external load information. The principal twin can be equivalent to a thin sheet, a flattened ellipsoid, or other inclusion body model that can characterize the difference between the wide facet and the thickness direction of the twin, depending on its actual morphology; the geometric parameters of the inclusion body can be determined by experimental observation, image measurement, empirical setting, or parametric scanning.

[0035] Example 1: This application provides an analysis and prediction method for variant selection during the continuous evolution of associated orthorhombic martensite in metastable β-titanium alloys based on crystallography-local stress field coupling. This embodiment uses Ti–12Mo metastable β-titanium alloy as an example to illustrate the implementation process of the method. It should be understood that the method is not limited to Ti–12Mo alloys, but can also be applied to other metastable β-titanium alloy systems capable of undergoing β-phase twinning deformation and α'' martensite (orthorhombic martensite) phase transformation. In this embodiment, the β-parent phase lattice constant, α'' martensite lattice constant, and β-parent phase elastic constant are obtained from experimental measurements, literature, or database parameters; for ease of explanation, the following parameters are used in this embodiment: β-parent phase lattice constant a β =3.2792 Å, orthogonal α'' martensite lattice constant a α'' =3.0787 Å, b α'' =4.9198 Å and c α'' =4.6329 Å; β parent phase elastic constant C 11 =118.5787 GPa, C 12 =116.2173 GPa, C 44 =39.3580 GPa. The above parameters are used as inputs for candidate variant construction and calculation of the local stress field induced by the principal twin.

[0036] This method can be found in Figure 1 ,include: S1: Obtain the crystallographic orientation information of the parent phase β, the crystallographic information of the principal twin, the information of the applied load, the information of the lattice parameters, and the information of the elastic parameters of the metastable β titanium alloy to be analyzed.

[0037] In one embodiment of this application, the crystallographic orientation information of the β parent phase and the crystallographic information of the principal twin are obtained by electron backscatter diffraction (EBSD) technology, preferably orientation data continuously acquired by in-situ tensile EBSD technology; the applied load information includes the loading direction and stress state; the lattice parameter information includes the lattice constants of the β parent phase and α'' martensite; the elastic parameter information includes the elastic stiffness tensor, elastic compliance tensor, or elastic constants obtained from their equivalents of the β parent phase. Orientation information is continuously collected during the tensile process to characterize the formation and evolution of the associated α'' martensite after the principal twin activation during continued deformation. Combining pole figure analysis, trace analysis, and Burgers orientation relationship identification results, it can be seen that: the associated α'' formed near the wide face of the principal twin corresponds to the CV3 principal variant; the associated α'' formed near the leading edge of the principal twin corresponds to CV4 (…). The associated α'' formed inside the main twin corresponds to the CV4(+) and CV3 branches. The above experimental observations are only used as a basis for verifying and comparing the model calculation results in this embodiment, and are not necessary input conditions for implementing the method of this invention.

[0038] S2: Based on the crystallographic orientation information of the parent phase β, combined with the Burgers orientation relation and the martensitic phase transformation crystallography theory PTMC, a candidate variant branch set consisting of multiple candidate α'' martensite principal variants and habit plane branches is constructed, and the deformation distortion tensor corresponding to each candidate variant branch is calculated.

[0039] Further, S2 includes: S201: Based on the Burgers orientation relationship between the parent phase β phase and orthogonal α'' martensite, construct an equivalent candidate α'' martensite main variant.

[0040] S202: Based on the martensitic phase transformation crystallography theory PTMC, two conjugate habit plane branches, the corresponding habit plane normal and shear direction are solved for each candidate α'' martensitic principal variant, resulting in a candidate variant branch set composed of multiple candidate α'' martensitic principal variants and habit plane branches.

[0041] S203: Calculate the deformation gradient tensor corresponding to each candidate variant branch. The calculation formula is as follows:

[0042] In the formula, For the first The deformation gradient tensor of each candidate variant branch For unit tensors, For macroscopic shape strain amplitude, and These represent the first and second digits in the β-parent phase crystallographic reference frame, respectively. The unit vectors of the macroscopic shear direction and habit surface normal of each candidate variant branch, with superscript... Represents the physical quantities associated with candidate martensitic variant branches. This represents the vector tensor product.

[0043] S204: Based on the deformation gradient tensor, calculate the deformation distortion tensor corresponding to each candidate variant branch. The calculation formula is as follows:

[0044] In the formula, For the first The deformed distortion tensor of each candidate variant branch.

[0045] In one embodiment of this application, based on the Burgers orientation relationship between orthogonal α'' martensite and the parent body-centered cubic β phase, six crystallographically equivalent α'' principal variants are constructed. The Burgers orientation relationship is as follows: for any candidate α'' martensite principal variant, its

[100] α''

[010] α'' and

[001] α'' A set corresponding to the β parent phase , and The crystal orientation, controlled by the crystallographic symmetry of the β parent phase, yields six crystallographically equivalent α'' principal variants, such as... Figure 2 As shown. Further combining the martensitic phase transformation crystallography theory PTMC, using type I {111} α'' Twins are used as lattice-invariant shearing, and two conjugate habit plane branches are solved for each principal variant, thus forming twelve candidate variant branches.

[0046] Taking CV1 as an example, the macroscopic shape strain amplitudes of its two representative habit surface branches m The average value is approximately 0.1295, representing the intrinsic lattice-invariant shear amplitude. m 1 is approximately 0.0092; the principal strains corresponding to the three principal axes of the orthogonal α'' martensite are respectively λ 1= 6.11%, λ 2 = 6.09% and λ 3= 0.10%. For the first Each candidate variant branch has a deformation gradient tensor. and deformation distortion tensor Calculated according to the foregoing definition in this application.

[0047] S3: Establish a local coordinate system for the main twin based on the twin plane normal and twin shear direction, and in the local coordinate system, the main twin is equivalent to a thin plate-like or flattened ellipsoidal inclusion.

[0048] In one embodiment of this application, {332} is selected. <113> β The twin is used as a representative principal twin object. Based on the twin plane normal and twinning shear direction of the principal twin, a local coordinate system for the principal twin is introduced. x 0– y 0– z 0, where, x The 0-axis is parallel to the twin shear direction. η 1, z The 0-axis is parallel to the twin plane. K 1 normal direction, y The 0 axis is perpendicular to the axis formed by... η 1 and K A plane formed by 1 normal direction, such as Figure 3 As shown. The local coordinate system of the principal twin is used to determine the geometric orientation of the equivalent inclusion, establish the external near-field evaluation path of the principal twin, and realize the coordinate transformation between the local stress tensor and the parent phase β crystallographic reference system. The local stress tensor is transformed to a reference coordinate system consistent with the candidate variant branch deformation distortion tensor through a coordinate transformation matrix, ensuring that the tensor double dot product in the interaction work calculation has a consistent coordinate reference. For a representative principal twin, the normal to the twin plane is taken. Twin shear direction Theoretical twin shear rate γ =0.3536, superscript This represents the physical quantities associated with the principal twin. For other twinning systems, a corresponding local coordinate system for the principal twin can be established based on the normal to the twin plane and the twinning shear direction.

[0049] In this embodiment, to simulate the lamellar geometry of the main twin, the main twin can be equivalent to a lamellar or flattened ellipsoidal inclusion. Here, the main twin is approximately equivalent to an axisymmetric flattened ellipsoidal inclusion. Its first and second characteristic dimensions a1 and a2 within the twin's wide plane are located within the twin's wide plane, and the third characteristic dimension a3 in the thickness direction is along the normal to the twin plane, and a3 is smaller than a1 and / or a2. In a preferred embodiment, a1 = a2 and a1 and a2 are much larger than a3 to characterize the flattened geometry of the main twin. Here, a1 = a2 and a3 / a1 = 0.01 are taken. This geometric ratio is only used to illustrate the calculation process of this embodiment and does not constitute a limitation on the geometric ratio of the inclusion.

[0050] S4: Based on the positional relationship between the associated α'' martensite and the main twin, the formation state of the associated α'' martensite is divided into the formation state inside the main twin and the near-field formation state outside the main twin. The local stress tensor inside and outside the main twin is calculated based on Eshelby theory and Mura–Cheng external field analytical solution.

[0051] In one embodiment of this application, the deformation gradient tensor of the principal twin in the β-parent phase crystallographic reference frame is... Determined by the twin shear direction and the twin plane normal, and further converted into effective intrinsic strain. As a unified input for calculating the local stress field inside Eshelby and the local stress field outside Mura–Cheng, the calculation formula is as follows:

[0052]

[0053] In the formula, The deformation gradient tensor of the main twin. For twin shear rate, and These represent the unit vectors of the twinning shear direction and the twin plane normal in the β-parent phase crystallographic coordinate system, respectively. To effectively adapt to intrinsic strain, superscript For transpose, superscript This represents physical quantities related to the principal twin.

[0054] Based on the positional relationship of the associated α'' martensite relative to the main twin, the formation state of the associated α'' martensite is divided into the formation state inside the main twin and the near-field formation state outside the main twin. For the associated α'' martensite formed inside the main twin, the local stress tensor inside the main twin is calculated using Eshelby theory. The calculation formula is as follows:

[0055]

[0056]

[0057] In the formula, The main twin is subject to constrained strain inside. For Eshelby tensors, For elastic strain, For internal local stress tensor, Let be the elastic stiffness tensor of the β phase.

[0058] For the associated α'' martensite formed in the near-field region outside the main twin, the local stress tensor outside the main twin is calculated using the Mura–Cheng external field analytical solution. The calculation formula is as follows:

[0059] In the formula, For any external evaluation point The local stress tensor of the principal twin at that location. The kernel function of the outer field of the ellipsoidal inclusion body is related to the location of the evaluation point, the geometric parameters of the inclusion body, and its orientation. Figure 4 The surface nearest neighbor evaluation path under the wide-area proximity state is shown, where, The positional parameters are along the broad plane of the principal twin. For points on the broad surface of the ellipsoid, It is the outward normal (unit vector). As the outer evaluation point, , The outward offset distance along the outward normal is used to ensure that the evaluation point is located in the near-field region outside the containing body and does not fall on the boundary of the containing body. In one embodiment, , Note: Based on The approximation of an oblate spheroid approximates the middle part of the main twin's broad face as a straight interface. and fix the height on its outside. Evaluation was performed by scanning along the width direction.

[0060] Figure 5 The parametric path extending from the center of the broad face to the front is shown in the state of proximity to the front, where (a) is the overall path diagram. x 0 z (a) is a section 0), and (b) is a magnified view of the local vector relationship (dashed box area). Points on the surface of an ellipsoid To describe x 0 z Angular parameters of the position of the elliptical surface within section 0. It is the outward normal (unit vector). As the outer evaluation point, .

[0061] Preferably, for the region adjacent to the wide facet of the main twin, a surface nearest neighbor scanning path is set along the direction of the wide facet of the twin; for the region adjacent to the leading edge of the main twin, a scanning path is set along the local coordinate system of the main twin. x 0 z A parameterized path is set from the center of the twin broad face to the leading edge of the 0 section to obtain the local stress tensor at different evaluation points.

[0062] S5: Establish a macroscopic external stress tensor based on the external load information. Perform tensor double dot product calculation on the macroscopic external stress tensor and the deformation distortion tensor of each candidate variant branch to obtain the basic interaction work of each candidate variant branch. Perform tensor double dot product calculation on the local stress tensor inside and outside the main twin and the deformation distortion tensor of each candidate variant branch to obtain the local interaction work of each candidate variant branch.

[0063] S6: Sort the basic interaction work and local interaction work of each candidate variant branch respectively, and determine the candidate variant branch whose local interaction work ranking is within the preset dominant ranking range as the local dominant candidate. Based on the change of the local dominant candidate relative to the basic interaction work ranking, determine the dominant variant and / or dominant habit surface branch, thereby realizing the analysis and prediction of variant selection behavior in the continuous evolution of the associated α'' martensite.

[0064] In one embodiment of this application, the driving force analysis of the candidate α'' martensite variant is performed using a "basic + local + comprehensive judgment" approach. Before calculating the interaction work, the macroscopic applied stress tensor, the principal twin-induced local stress tensor, and the deformation distortion tensor of the candidate variant branch are transformed into the same reference coordinate system, which is the β parent phase crystallographic reference system, the sample reference system, or the principal twin local reference system.

[0065] First, establish the macroscopic external stress tensor based on the external load information. Based on this, the fundamental interaction work of each candidate variant branch under macroscopic external stress is calculated. The calculation formula is:

[0066] In the formula, For the first The fundamental interaction work of each candidate variant branch, superscript It represents a physical quantity under macroscopic external stress.

[0067] In this embodiment, to obtain the preferred trend of candidate variant branches under a given loading mode, 100 MPa is used as an exemplary reference stress amplitude to calculate the foundation interaction work. Since the relative order of foundation interaction work under the same loading mode does not change with linear scaling of the stress amplitude, the reference stress amplitude does not represent the actual martensitic triggering stress, nor does it constitute a limitation on the stress range to which this invention is applicable.

[0068] The fundamental interaction work of each candidate variant branch under macroscopic applied stress is shown in Table 1. As can be seen from the table, when the external β matrix is ​​taken as the parent phase reference frame, CV4( The fundamental interaction work between CV4(+) and CV4(+) is approximately 5.99 MJ / m. 3 and 5.89 MJ / m 3 It is higher than 0.18 MJ / m³ of CV3(+). 3 and CV3 ( 0.21 MJ / m 3 When β inside the principal twin is taken as the parent phase reference system, CV5(+) and CV5( The fundamental interaction work is approximately 5.15 MJ / m. 3 and 4.68 MJ / m 3 However, the CV4(+) and CV3 branches related to the experimental observations do not dominate when considering only macroscopic applied stress. Therefore, relying solely on the macroscopic applied stress basis is insufficient to explain the aforementioned experimentally observed selection results of the associated α'' martensite variants.

[0069] Table 1. Work of fundamental interactions of candidate variant branches under macroscopic applied stress

[0070] For the proximity state of the main twin broad face, a surface nearest neighbor evaluation path is set on the outer side of the main twin broad face, such as... Figure 4 As shown. Generally, the wide face is adjacent to the evaluation point. Defined as:

[0071] in, The positional parameters are along the broad plane of the principal twin. For the surface points on the broad surface of the flattened ellipsoid, To correspond to the outer normal, δ A small positive offset is set along the outer normal to ensure that the evaluation point is located in the near-field region outside the inclusion body and does not fall on the boundary of the inclusion body.

[0072] In this embodiment, based on a3 / a1 The approximation of a flattened ellipsoidal thin plate (1) approximates the middle of the main twin's broad face as a flat interface. This approximation simplifies the evaluation path setting for the region adjacent to the broad face; in other embodiments, evaluation points adjacent to the broad face can also be determined directly based on the flattened ellipsoidal surface equation and its outward normal. In the local coordinate system of the principal twin x 0– y 0– z In 0, the equivalent flat width surface is taken as: z 0=a3 Wide surface points Approximately expressed as:

[0073] Corresponding outer evaluation points Take as:

[0074] in, s / a1∈[ [0.9, 0.9]. This range is used to avoid the leading edge of the flattened ellipsoid and characterize the nearby region in the middle of the broad face; in other embodiments, it can be adjusted according to the actual size of the principal twin and evaluation requirements. The range of values ​​for .

[0075] Secondly, take the center position of the wide side. s / a1=0 was used as a representative evaluation point, and the local stress field outside the principal twin at this point was obtained based on the analytical solution of the Mura–Cheng external field. The local interaction work was calculated for each of the 12 candidate variant branches. The calculation formula is:

[0076] In the formula, For the first Local interaction work of each candidate variant branch This refers to the local stress tensor inside or outside the main twin, where, when the candidate variant forms inside the main twin, Take the local stress tensor inside the principal twin When candidate variants form in the near-field region outside the master twin, Take the local stress tensor outside the principal twin .

[0077] Table 2 shows the local interaction work of each candidate variant branch at this representative evaluation point. As can be seen from the numerical patterns in Table 2, the CV3(+) branch has the highest local interaction work at this representative evaluation point, approximately 7.39 MJ / m. 3 CV3( The branch is approximately 7.28 MJ / m 3 The CV6(+) branch is approximately 6.53 MJ / m 3 CV1( The branch is approximately 6.37 MJ / m 3 Based on the fundamental results in Table 1, it can be seen that although the CV3 branch is not dominant under macroscopic external stress, it becomes preferred in the wide-face proximity state due to the local stress field induced by the principal twins. This comprehensive judgment is consistent with the CV3 principal variant corresponding to the interface-associated α'' identified in the aforementioned experiments.

[0078] Table 2. Proximity to the main twin broad face. s Local interaction work of candidate variant branches at the evaluation point / a1=0

[0079] For the state adjacent to the broad face of the principal twin, it can also be along Figure 4 The path shown is in s / a1∈[ Continuous sampling was performed within the range of 0.9, 0.9 to obtain the distribution of local interaction work and the change in the preferred order at different evaluation points. The continuous distribution of local interaction work of candidate variant branches along the scanning path in the state of proximity to the main twin broad face is shown in the figure. Figure 6 As shown, (a) represents the "+" branch for each candidate variant, and (b) represents the "+" branch for each candidate variant. "Branch. Under the conditions of this embodiment, along the scanning path, the CV3(+) branch maintains a high local interaction work in the left half of the main twin broad face and near the center, while the CV6( The CV6(+) and CV6(+) branches exhibit a competitive preference trend in some right-hand intervals. This allows for the output of a continuous variation relationship between the "evaluation point location and local interaction work ranking," which can be used to analyze the local preference trend during the continuous evolution of associated α'' martensite in the vicinity of the main twin broad face.

[0080] For the state near the principal twin front, adopt Figure 5 The parameterized path shown is used for evaluation. Preferably, it is along the principal twin local coordinate system. x 0 z A parametric evaluation path is set from the center of the wide face to the leading edge of the 0 section, where the ellipsoidal surface points Defined as:

[0081] in, To describe x 0– z Angular parameters of the position of the elliptical surface within section 0; when =0° corresponds to the center surface point of the wide face. =90° corresponds to the frontal surface point.

[0082] Corresponding outward normal Determined by the geometric relations of the oblate spheroid, for an oblate spheroid containing a body that satisfies the following equation:

[0083] Its in x 0– z Unit outward normal within section 0 It can be represented as:

[0084] Then the evaluation point of the frontier Defined as:

[0085] In this embodiment, the region closest to the leading edge is taken. =90° is used as a representative evaluation point. In actual calculations, it can be selected based on numerical stability. Angles of 90° or less are used as the nearest neighbor evaluation points for the leading edge. The local stress field outside the principal twin at this point is calculated using the Mura–Cheng external field analytical solution, and the local interaction work of the candidate α'' martensite variant branches is further calculated. .

[0086] The local interaction work of each candidate variant branch at this representative evaluation point is shown in Table 3. From the numerical patterns in Table 3, it can be seen that at this location, CV4( The highest value was achieved by the branch, approximately 243.12 MJ / m². 3 The CV4(+) branch is the second largest, at approximately 192.89 MJ / m². 3 The remaining candidate branches are all lower than the aforementioned two. Combining the basic results in Table 1, it can be seen that CV4 ( Under macroscopic external stress, CV4 has shown a high preference trend, and is further promoted by the local stress field induced by the main twin in the vicinity of the main twin front. Therefore, comprehensive judgment indicates that CV4( The branching is a dominant variant branch in the vicinity of the main twin front. This result corresponds to the aforementioned experimentally identified front-associated α'' CV4( The branches match.

[0087] Table 3 Proximity to the principal twin front Local interaction work of candidate variant branches at the 90° evaluation point

[0088] For the state near the principal twin front, it can also be along Figure 5 The parameter path is continuously sampled to obtain the continuous evolution results of the local interaction work of each candidate variant branch under different angular parameters. The continuous evolution of the local interaction work of the candidate variant branches along the angular parameters in the state near the principal twin front is as follows: Figure 7 As shown, (a) represents the "+" branch for each candidate variant, and (b) represents the "+" branch for each candidate variant. "Branch. Under the conditions of this embodiment, as the evaluation position gradually moves from the center of the main twin broad face to the region very close to the leading edge, the local interaction work of the CV4 system branch gradually increases, wherein CV4 ( The branch exhibits the highest local preference tendency in the region very close to the leading edge. This continuous evolution result indicates that the variant selection behavior of the associated α'' martensite in the vicinity of the main twin leading edge is related to the evaluation position.

[0089] For the internal state of the principal twin, the local stress tensor inside the principal twin is calculated using Eshelby theory. Based on this, the local interaction work of each candidate variant branch is calculated. The local interaction work of each candidate variant branch within the main twin state is shown in Table 4. The numerical patterns in Table 4 show that both candidate branches CV3 and CV4 exhibit significant local preference, with a local interaction work of approximately 24 MJ / m. 3 The remaining candidate branches are mostly negative. Combined with the basic results in Table 1, it can be seen that the CV4(+) and CV3 branches are not dominant when only macroscopic external stress is considered, but they are re-selected as preferred candidates under the influence of local stress fields within the main twin. This comprehensive judgment result is consistent with the CV4(+) and CV3 branches corresponding to the associated α'' within the main twin identified in the aforementioned experiments.

[0090] Table 4. Local interaction work of candidate variant branches in the internal state of the principal twin.

[0091] To facilitate intuitive explanation, the comparison between experimental observation results and model comprehensive judgment results under different formation states is shown in Table 5. Table 5 shows that: for the state adjacent to the broad face of the main twin, experimental observation corresponds to the CV3 system variant, while the model comprehensive judgment also indicates that the CV3 system branch is preferred; for the state adjacent to the leading edge of the main twin, experimental observation corresponds to CV4 (… ) branch, and the model's overall judgment also indicates that CV4 ( The preferred variant is CV4(+) or CV3. For the internal state of the main twin, experimental observations showed that the CV4(+) and CV3 branches were the most preferred. The model's overall assessment also indicated that the CV4(+) and CV3 branches were highly preferred candidates. The above comparative results demonstrate that, under the material parameters, main twin geometry model, and loading conditions used in this embodiment, the method of this invention can provide dominant variant branch judgment results that are consistent with experimental observations.

[0092] Table 5. Comparison of experimental observation results and model comprehensive judgment results under different formation states.

[0093] As can be seen from the above embodiments, this invention does not treat the associated α'' martensite as a uniform response determined solely by macroscopic applied stress. Instead, by introducing a principal twin-induced local stress field, and based on the coupling of crystallographic candidate variant construction and local stress field calculation, it performs a unified analysis and prediction of variant selection behavior during the continuous evolution of subsequent deformation products. This method can not only provide the basic preference trend of candidate variant branches under macroscopic applied stress, but also characterize the rearrangement, amplification, or re-screening effect of the principal twin-induced local stress field on the preference order of candidate variant branches.

[0094] It should be noted that those skilled in the art will recognize that the embodiments described herein are for the purpose of helping readers understand the principles of this application, and should be understood as not limiting the scope of protection of this application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this application without departing from the essence of this application, and these modifications and combinations are still within the scope of protection of this application.

Claims

1. A method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys, characterized in that, include: S1: Obtain the crystallographic orientation information of the parent phase β, the crystallographic information of the principal twin, the information of the applied load, the information of the lattice parameters, and the information of the elastic parameters of the metastable β titanium alloy to be analyzed; S2: Based on the orientation information of the parent phase β crystallography, combined with the Burgers orientation relationship and the martensitic phase transformation crystallography theory PTMC, a candidate variant branch set consisting of multiple candidate orthogonal martensitic principal variants and habit plane branches is constructed, and the deformation distortion tensor corresponding to each candidate variant branch is calculated. S3: Establish a local coordinate system for the main twin based on the twin plane normal and twin shear direction, and in the local coordinate system, the main twin is equivalent to a thin plate-like or flattened ellipsoidal inclusion body; S4: Based on the positional relationship between the associated orthogonal martensite and the main twin, the formation state of the associated orthogonal martensite is divided, and the local stress tensor inside and outside the main twin is calculated based on Eshelby theory and Mura–Cheng external field analytical solution. S5: Establish the macroscopic applied stress tensor based on the applied load information, and calculate the interaction work between the foundation and the local interaction work based on the macroscopic applied stress tensor, the local stress tensor and the deformation distortion tensor. S6: Sort the basic interaction work and local interaction work of each candidate variant branch, determine the candidate variant branch whose local interaction work is within the preset dominant sorting range as the local dominant candidate, and determine the dominant principal variant or dominant habit surface branch of the associated orthogonal martensite according to the change of the local dominant candidate relative to the basic interaction work sorting.

2. The method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys according to claim 1, characterized in that, The external load information includes the loading direction and stress state; the lattice parameter information includes the lattice constants of the β parent phase and orthorhombic martensite; the elastic parameter information includes the elastic stiffness tensor, elastic compliance tensor, or equivalent elastic constants of the β parent phase.

3. The method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys according to claim 1, characterized in that, The S2 includes: S201: Based on the Burgers orientation relationship between the parent β phase and orthorhombic martensite, construct equivalent candidate orthorhombic martensite principal variants; S202: Based on the martensitic phase transformation crystallography theory PTMC, two conjugate habit plane branches, the corresponding habit plane normal and shear direction are solved for each candidate orthogonal martensite principal variant, resulting in a candidate variant branch set composed of multiple candidate orthogonal martensite principal variants and habit plane branches. S203: Calculate the deformation gradient tensor corresponding to each candidate variant branch. The calculation formula is as follows: In the formula, For the first The deformation gradient tensor of each candidate variant branch For unit tensors, For macroscopic shape strain amplitude, and These represent the first and second digits in the β-parent phase crystallographic reference frame, respectively. The unit vectors of the macroscopic shear direction and habit surface normal of each candidate variant branch, with superscript... Represents the physical quantities associated with candidate martensitic variant branches. Represents the vector tensor product; S204: Based on the deformation gradient tensor, calculate the deformation distortion tensor corresponding to each candidate variant branch. The calculation formula is as follows: In the formula, For the first The deformed distortion tensor of each candidate variant branch.

4. The method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys according to claim 1, characterized in that, The principal twin's local coordinate system satisfies: x The 0-axis is parallel to the direction of the principal twin shear. η 1. z The 0-axis is parallel to the principal twin plane. K 1's normal direction y The 0-axis is perpendicular to the direction of the twin shear. η 1 and twin plane K 1. A plane formed by normals; The sheet-like or flattened ellipsoidal inclusion has a first characteristic dimension and a second characteristic dimension located within the twin plane, and a third characteristic dimension along the normal of the twin plane, wherein the third characteristic dimension is smaller than the first characteristic dimension and the second characteristic dimension.

5. The method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys according to claim 3, characterized in that, The S4 includes: S401: In the β-parent phase crystallographic reference frame, the deformation gradient tensor of the principal twin is defined and calculated as follows: In the formula, The deformation gradient tensor of the main twin. For twin shear rate, and The superscripts represent the unit vectors of the twinning shear direction and the twin plane normal in the crystallographic coordinate system of the β parent phase, respectively. This represents physical quantities related to the principal twin; S402: The deformation gradient tensor of the principal twin is converted into effective intrinsic strain, and the calculation formula is as follows: In the formula, To effectively adapt to intrinsic strain, superscript For transpose; S403: Based on the positional relationship between the associated orthorhombic martensite and the main twin, the formation state of the associated orthorhombic martensite is divided into the formation state inside the main twin and the near-field formation state outside the main twin. S404: For the associated orthorhombic martensite formed within the main twin, the local stress tensor within the main twin is calculated using Eshelby theory. The calculation formula is as follows: In the formula, The main twin is subject to constrained strain inside. For Eshelby tensors, For elastic strain, For internal local stress tensor, Let be the elastic stiffness tensor of the β phase; S405: For the associated orthorhombic martensite formed in the near-field region outside the main twin, the local stress tensor outside the main twin is calculated using the Mura–Cheng external field analytical solution. The calculation formula is as follows: In the formula, For any external evaluation point The local stress tensor of the principal twin at that location. The kernel function of the outer field of the ellipsoidal inclusion body is related to the location of the evaluation point, the geometric parameters of the inclusion body, and its orientation.

6. The method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys according to claim 5, characterized in that, The near-field formation state of the main twin includes the formation state near the wide face of the main twin and the formation state near the leading edge of the main twin. For the formation state of the main twin broad face, one or more surface neighbor evaluation points are set along the direction of the main twin broad face; for the formation state of the main twin front edge, one or more evaluation points are set along the parameterized path from the center of the main twin broad face to the front edge region, and the continuous evolution trend of the associated orthorhombic martensite is characterized by the ranking of the local interaction work at different evaluation points through continuous evaluation.

7. The method for predicting the selection of orthogonal martensite variants in metastable β-titanium alloys according to claim 6, characterized in that, The S5 includes: A macroscopic applied stress tensor is established based on the applied load information. The macroscopic applied stress tensor is then used to perform a tensor double dot product calculation with the deformation distortion tensor of each candidate variant branch to obtain the fundamental interaction work of each candidate variant branch. The calculation formula is as follows: In the formula, For the first The fundamental interaction work of each candidate variant branch. For macroscopic applied stress tensor, superscript Represents a physical quantity under macroscopic external stress; The local interaction work of each candidate variant branch is obtained by performing a tensor double dot product calculation on the local stress tensors inside and outside the principal twin and the deformation distortion tensors of each candidate variant branch. The calculation formula is as follows: In the formula, For the first Local interaction work of each candidate variant branch It is the local stress tensor inside or outside the main twin; Among them, when the candidate variant is formed inside the main twin, Take the local stress tensor inside the principal twin When candidate variants form in the near-field region outside the master twin, Take the local stress tensor outside the principal twin .

Images