A method for accurately calculating the orientation relationship and the beta-ti grain orientation before phase transition in titanium and its alloys

Abstract

The application relates to the technical field of metal material development, in particular to a method for accurately calculating the orientation relationship and the beta-Ti grain orientation before phase change in titanium and its alloy. The method is based on the principle of minimizing the average orientation difference between the theoretical orientation and the measured orientation of all alpha-Ti variants generated by the phase change of the same original beta-Ti grain, and directly determines the optimal solution through mathematical optimization. The application adopts a suitable mathematical calculation method, so that the average value of the deviation angle between the measured orientation and the theoretical orientation of all alpha variants transformed from the same beta-Ti grain is minimized, thereby accurately calculating the beta-Ti grain orientation and the orientation relationship in the phase change process.

Description

Technical Field

[0001] This invention relates to the field of metal material development technology, and in particular to a method for accurately calculating the orientation relationship and β-Ti grain orientation before phase transformation in titanium and its alloys. Background Technology

[0002] The properties of titanium and titanium alloys are highly dependent on their microstructure, and one of the core characteristics of this microstructure is the orientation of the α phase (hexagonal close-packed) formed during the low-temperature transformation of the high-temperature β phase (body-centered cubic) and the grain boundary features formed between them. During this transformation, the α phase formed maintains a certain orientation relationship with the high-temperature β phase; ideally, this is a Burgers orientation relationship ((110)β / / (0001)α, <111> β / / <11-20>α). However, due to the presence of phase transformation stress, the actual orientation relationship deviates from the ideal Burgers orientation relationship. This fundamentally determines the possible orientation of the α variant, the grain boundary characteristics formed by two adjacent variants, the morphological distribution of the α variant, and its interface structure with the residual β phase, thus having a decisive impact on the material's strength, plasticity, toughness, and fatigue properties. Therefore, accurately calculating and mastering this orientation relationship is the foundation for realizing the directional design and performance optimization of titanium alloy microstructure.

[0003] On the other hand, a fundamental prerequisite and challenge for achieving the aforementioned "directional design" of the microstructure lies in the precise prediction and control of the crystallographic orientation of the parent phase β-titanium before the transformation. This is because the orientation of the β-phase directly determines the type, spatial orientation, and relative distribution of the α-transformation resulting from the phase transformation based on the corresponding orientation relationship. Currently, process development largely relies on empirical "trial and error" and tedious subsequent microstructural characterization, lacking the ability to proactively and quantitatively calculate and predict the initial β-phase orientation and its evolutionary behavior during subsequent phase transformations under given processing conditions. Patent application number 202310947971.6 discloses "a method for reconstructing the original β-Ti grain orientation before phase transformation." While it can calculate the β-Ti grain orientation, the accuracy is insufficient because it relies heavily on the accuracy of manual sampling. Furthermore, it cannot calculate the orientation relationship during the phase transformation process. Therefore, a more accurate method capable of precisely calculating the orientation relationship is needed. This results in the inability to accurately establish a reliable and quantitative positive prediction chain from initial process parameters to initial β-phase orientation, and then to the final microstructure and properties. This lack of capability severely restricts the R&D efficiency and performance ceiling of advanced titanium alloys, leading to low efficiency in microstructure control, unstable performance improvement, and difficulty in achieving an optimal balance of strength, toughness, and plasticity. 1. Blindness in organizational design: Any attempt to improve strength and toughness by controlling phase transition to obtain a specific α-Ti morphology (such as fine lamellars or specific textures) lacks precise guidance because it cannot anchor the initial β-Ti grain orientation, and the process development falls into a "trial and error" cycle.

[0004] 2. Inaccurate performance prediction: Performance simulations based on the final microstructure are significantly less accurate and universal because they fail to trace back to the orientation of the original β-Ti grains.

[0005] 3. Inefficient process control: For processes such as forging, rolling and heat treatment that aim to obtain ideal β-Ti grains and α variant orientations, there is a lack of tools to calculate the β-Ti grain orientation during processing, making the direction of process optimization unclear.

[0006] Therefore, developing a reliable method to accurately calculate or determine the orientation of β-Ti grains and their orientation relationship during subsequent α-phase transformation, either before phase transformation or during the process design stage, has become an urgent need to break through the bottleneck in titanium alloy R&D and achieve integrated and precise control of material "design-preparation-performance". This invention addresses this core technological gap by providing a method that can accurately calculate the orientation relationship and pre-phase transformation β-Ti grain orientation in titanium and its alloys without relying on the presence of residual β-Ti microstructure, laying a crucial technological foundation for the directional design and intelligent manufacturing of high-performance titanium alloys. Summary of the Invention

[0007] The purpose of this invention is to provide a method for accurately calculating the orientation relationship and β-Ti grain orientation before phase transformation in titanium and its alloys. This method overcomes the shortcomings of existing methods for determining β-Ti grain orientation and proposes a method for accurately calculating the orientation relationship. By employing appropriate mathematical calculation methods, the average value of the deviation angle between the measured and theoretical orientations of all α variants transformed from the same β-Ti grain is minimized, thereby accurately calculating the β-Ti grain orientation and the orientation relationship during the phase transformation process.

[0008] To achieve the above objectives, the present invention employs the following technical solution: A method for accurately calculating the orientation relationship and β-Ti grain orientation before phase transformation in titanium and its alloys is based on the principle of minimizing the average orientation difference between the theoretical and measured orientations of all α-Ti variants generated by the phase transformation of the same original β-Ti grain, and the optimal solution is directly determined through mathematical optimization. The specific operating steps are as follows: Step 1) Using polar chart or The range belonging to the same β-Ti grain is determined by pole figure or direct visual observation, and the orientation data of the α-Ti phase transformation products derived from it are obtained, assuming that the number of orientation points is N; Step 2) Calculate the first step using the following formula (1). Theoretical and experimental orientations of α-Ti variants Orientation difference matrix between : = / (1); Step 3) Calculate the first step using the following formula (2). Orientation difference between theoretical and measured orientations of α-Ti variants : (2); Step 4) Calculate the average orientation difference between the theoretical and measured orientations of all α-Ti phase transformation products belonging to the same β-Ti grain phase transformation using the following calculation formula (3). : (3); Step 5) Iteratively solve using an optimization algorithm, when The orientation matrix corresponding to reaching the global minimum. With orientation matrix This refers to the precise β→α orientation relationship and the orientation of β-Ti grains before the phase transformation; in The first representing β-Ti grains One equivalent orientation transformation matrix; , These represent the first and second grains of α-Ti. The and the first There are several equivalent orientation transformation matrices. See Table 1 for details. Table 1 Equivalent matrices for cubic and hexagonal systems Furthermore, the method is applicable to all covariant phase transformation processes in titanium-based metals or alloys that follow or are close to the Burgers relation.

[0009] Furthermore, the method is applied to phase transformation product regions including solidified products, forged products, hot-rolled products, cold-rolled products, heat-treated products, weld heat-affected zones, and welds. The method of this invention can be applied simultaneously to deformable structures (such as plastically deformed structures) and non-deformable structures (such as as-cast structures).

[0010] Furthermore, the method exhibits high precision and good accuracy, with a minimum accuracy of 1e-12°. The method of this invention has a wide range of applications and can still accurately calculate even when significant variant selection occurs in the tissue.

[0011] Furthermore, when calculating the orientation of β-Ti grains, the present invention can also obtain the morphological characteristics and size information of β-Ti grains before phase transformation.

[0012] Compared with existing technologies, the beneficial effects of this invention are: 1) Accurate calculation of β-Ti grain orientation before phase transformation and orientation relationship during phase transformation is achieved. The calculated β-Ti grain orientation and orientation relationship during phase transformation have extremely high accuracy, reaching 12 decimal places.

[0013] 2) The calculation of β-Ti grain orientation and orientation relationship during phase transformation does not depend on the residual β-Ti structure. Even when there is no residual β-Ti structure, the calculation of orientation relationship and β-Ti grain orientation during phase transformation can still be successfully performed.

[0014] 3) It has few limitations on the conditions of use and can be used for deformed structures. This method has wide adaptability and wide application. It can perform orientation calculation and orientation relationship calculation for local micro-regions and β-Ti grains with severe variant selection.

[0015] 4) Since this invention is based on the orientation relationship existing in the phase transformation process, it is applicable to all covariant phase transformation processes; it can be applied to the calculation of orientation relationship and β-Ti grain orientation in the phase transformation process of all forged products, hot-rolled products, cold-rolled products, heat-treated products, heat-affected zones after welding, and welds.

[0016] 5) The present invention can further obtain information on the original β-Ti grain morphology and size; the method can be used for the covariant phase transformation process of all hexagonal metallic materials.

[0017] 6) The method of this invention is rigorous in principle. It performs global optimization by minimizing the average orientation difference, thereby achieving high-precision reconstruction of the orientation and orientation relationship of β-Ti grains. The calculation process is direct, avoiding the complex indirect conversion and multiple cross-products in the prior art. At the same time, the method does not depend on specific pole figure features, has a wide range of applications, and has good versatility and practicality for various titanium alloy systems and microstructures. Attached Figure Description

[0018] Figure 1 This is the utilization of phase transition products in Embodiment 1 of the present invention. The BC (BandContrast) diagram of the phase transformation products of the original β-Ti grains when the pole figure is used to calculate the orientation relationship and the orientation of the original β-Ti grains.

[0019] Figure 2In Example 1, based on the orientation relationships calculated in Table 1 and the original β-Ti grain orientation, 24 variants of the phase transformation products were theoretically generated. A superimposed comparison of the pole figure and the actual pole figure measured experimentally.

[0020] Figure 3 This is the second embodiment of the invention utilizing phase transition products. The BC (BandContrast) diagram of the phase transformation products of the original β-Ti grains when the pole figure is used to calculate the orientation relationship and the orientation of the original β-Ti grains.

[0021] Figure 4 In Example 2, based on the orientation relationships calculated in Table 1 and the original β-Ti grain orientation, 24 variants of the generated phase transformation products were theoretically derived. A superimposed comparison of the pole figure and the actual pole figure measured experimentally.

[0022] Figure 5 This is the utilization of phase transition products in Embodiment 3 of the present invention. The BC (BandContrast) diagram of the phase transformation products of the original β-Ti grains when the pole figure is used to calculate the orientation relationship and the orientation of the original β-Ti grains.

[0023] Figure 6 In Example 3, based on the orientation relationship calculated in Table 1 and the original β-Ti grain orientation, 24 variants of the phase transformation products were theoretically generated. A superimposed comparison of the pole figure and the actual pole figure measured experimentally.

[0024] Figure 7 This is the utilization of phase transition products in Embodiment 4 of the present invention. The BC (BandContrast) diagram of the phase transformation products of the original β-Ti grains when the pole figure is used to calculate the orientation relationship and the orientation of the original β-Ti grains.

[0025] Figure 8 In Example 4, based on the orientation relationships calculated in Table 1 and the original β-Ti grain orientation, 24 variants of the generated phase transformation products were theoretically derived. A superimposed comparison of the pole figure and the actual pole figure measured experimentally.

[0026] Figure 9 This is the application of phase transition products in Embodiment 5 of the present invention. The BC (BandContrast) diagram of the phase transformation products of the original β-Ti grains when the pole figure is used to calculate the orientation relationship and the orientation of the original β-Ti grains.

[0027] Figure 10In Example 5, based on the orientation relationships calculated in Table 1 and the original β-Ti grain orientation, 24 variants of the phase transformation products were generated theoretically. A superimposed comparison of the pole figure and the actual pole figure measured experimentally. Detailed Implementation

[0028] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0029] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0030] The components of the embodiments of the invention described and shown in the accompanying drawings can typically be arranged and designed in numerous different configurations. Therefore, the following detailed description of the embodiments of the invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention.

[0031] In the following examples, the experimental titanium material used was forged TC4 titanium alloy. The β-phase transformation temperature was measured to be approximately 970℃ by metallographic method. The specific composition (mass fraction, %) was: Al: 5.90%, V: 3.98%, Fe: 0.07%, C: 0.011%, N: 0.002%, O: 0.051%, and the plate thickness was 12mm. Four small cube samples of 10mm×8mm×6mm were cut from the billet. They were placed in a vacuum tube furnace and heated to different temperatures. After holding at these temperatures for 60min, they were either air-cooled (1100℃ in Example 1, 1060℃ in Example 2) or water-quenched (980℃ in Example 3, 940℃ in Example 4) to room temperature. Next, mechanical grinding was performed sequentially using 400#, 800#, 1200#, and 2000# sandpaper. Following this, micron-level chromium oxide polishing paste was used for mechanical polishing until the surface was smooth and free of scratches. Electrolytic polishing was then performed in a 10% perchloric acid + 90% ethanol solution at 25V and a current maintained at approximately 0.5 mA for 30-40 seconds. After polishing, EBSD experiments were conducted on a ZEISS Sigma 360 field emission scanning electron microscope equipped with an Oxford Symmetry S3-EBSD probe. The accelerating voltage was 20V, the tilt angle was 70°, and the step size was 0.1 μm. The EBSD data were processed using HKL Channel 5 software after scanning. Example 1:

[0032] The heating temperature was 1100℃. After cooling, coarse, interwoven lamellar α phases and residual β phases between the lamellars were obtained, which is a typical covariant phase transformation structure after high-temperature β-region heat treatment.

[0033] A method for accurately calculating the orientation relationship and β-Ti grain orientation before phase transformation in titanium and its alloys, the specific operation steps of which are as follows: Step 1) Using polar chart or The polarimetric diagram or direct visual observation determines the range belonging to the same β-Ti grain, and the orientation data of the α-Ti phase transformation product derived from it are obtained, assuming the number of orientation points is N; Step 2) Calculate the first... Theoretical and experimental orientations of α-Ti variants Orientation difference matrix between Step 3) Calculate the first step using formula (2). Orientation difference between theoretical and measured orientations of α-Ti variants Step 4) Calculate the average orientation difference between the theoretical and measured orientations of all α-Ti phase transformation products belonging to the same β-Ti grain using the following calculation formula (3). Step 5) Iteratively solve using an optimization algorithm, when The orientation matrix corresponding to reaching the global minimum. With orientation matrix This refers to the precise β→α orientation relationship and the orientation of β-Ti grains before the phase transformation.

[0034] Figure 1 As in Example 1 The BC diagram of the phase transformation products of the original β-Ti grains before phase transformation obtained by pole figure reconstruction; Table 1 shows the orientation relationship calculated by the method of the present invention, as well as the orientation of the original β-Ti grains, with an accuracy of 12 decimal places; Figure 2 This is based on the orientation relationship and β-Ti grain orientation calculated in Example 1, from which the theoretical basis for 24 variants is derived. Extreme graphs, and reality Overlay comparison of polar charts. Figure 2 The results show that the pole positions of the theoretical pole figure and the actual pole figure are in high agreement, which intuitively verifies the accuracy of the orientation relationship and the original β-Ti grain orientation calculated in Table 1, and further confirms the scientificity and reliability of the orientation relationship and the original β-Ti grain orientation calculation method proposed in this invention. This fully demonstrates the correctness and accuracy of the method of this invention in calculating the orientation relationship during the phase transformation and the original β-Ti grain orientation before the phase transformation. Example 2:

[0035] The heating temperature was 1060°C. After cooling, lamellar α tissue with residual β was obtained, and the lamellars were arranged in bundles. Compared with Example 1, the α lamellars were significantly thinner.

[0036] A method for accurately calculating the orientation relationship and β-Ti grain orientation before phase transformation in titanium and its alloys, the specific operation steps of which are as follows: Step 1) Using polar chart or The polarimetric diagram or direct visual observation determines the range belonging to the same β-Ti grain, and the orientation data of the α-Ti phase transformation product derived from it are obtained, assuming the number of orientation points is N; Step 2) Calculate the first... Theoretical and experimental orientations of α-Ti variants Orientation difference matrix between Step 3) Calculate the first step using formula (2). Orientation difference between theoretical and measured orientations of α-Ti variants Step 4) Calculate the average orientation difference between the theoretical and measured orientations of all α-Ti phase transformation products belonging to the same β-Ti grain using the following calculation formula (3). Step 5) Iteratively solve using an optimization algorithm, when The orientation matrix corresponding to reaching the global minimum. With orientation matrix This refers to the precise β→α orientation relationship and the orientation of β-Ti grains before the phase transformation.

[0037] Figure 3 As in Example 2 The BC diagram of the phase transformation products of the original β-Ti grains before phase transformation obtained by pole figure reconstruction; Table 1 shows the orientation relationship calculated by the method of the present invention, as well as the orientation of the original β-Ti grains, with an accuracy of 12 decimal places; Figure 4 Based on the orientation relationship and β-Ti grain orientation calculated in Example 2, the theoretical basis for 24 variants was derived. Extreme graphs, and reality The superimposed comparison of the pole figures shows that the pole positions of the theoretical and actual pole figures are highly consistent, intuitively verifying the accuracy of the orientation relationship and the original β-Ti grain orientation calculated in Table 1. This further confirms the scientific validity and reliability of the orientation relationship and original β-Ti grain orientation calculation method proposed in this invention. This fully demonstrates the correctness and accuracy of the method of this invention in calculating the orientation relationship during the phase transformation and the original β-Ti grain orientation before the phase transformation. Example 3:

[0038] The heating temperature is 980℃, slightly higher than the β phase transformation temperature. After water cooling, a diffusionless shear phase transformation occurs to obtain extremely fine acicular / lamellar martensite α (α'), with a large number of significantly refined strip bundles densely interwoven.

[0039] A method for accurately calculating the orientation relationship and β-Ti grain orientation before phase transformation in titanium and its alloys, the specific operation steps of which are as follows: Step 1) Using polar chart or The polarimetric diagram or direct visual observation determines the range belonging to the same β-Ti grain, and the orientation data of the α-Ti phase transformation product derived from it are obtained, assuming the number of orientation points is N; Step 2) Calculate the first... Theoretical and experimental orientations of α-Ti variants Orientation difference matrix between Step 3) Calculate the first step using formula (2). Orientation difference between theoretical and measured orientations of α-Ti variants Step 4) Calculate the average orientation difference between the theoretical and measured orientations of all α-Ti phase transformation products belonging to the same β-Ti grain using the following calculation formula (3). Step 5) Iteratively solve using an optimization algorithm, when The orientation matrix corresponding to reaching the global minimum. With orientation matrix This refers to the precise β→α orientation relationship and the orientation of β-Ti grains before the phase transformation.

[0040] Figure 5 As in Example 3 The BC diagram of the phase transformation products of the original β-Ti grains before phase transformation obtained by pole figure reconstruction; Table 1 shows the orientation relationship calculated by the method of the present invention, as well as the orientation of the original β-Ti grains, with an accuracy of 12 decimal places; Figure 6 Based on the orientation relationship and β-Ti grain orientation calculated in Example 3, the theoretical basis for 24 variants was derived. Extreme graphs, and reality The superimposed comparison of the pole figures shows that the pole positions of the theoretical and actual pole figures are highly consistent, intuitively verifying the accuracy of the orientation relationship and the original β-Ti grain orientation calculated in Table 1. This further confirms the scientific validity and reliability of the orientation relationship and original β-Ti grain orientation calculation method proposed in this invention. This fully demonstrates the correctness and accuracy of the method of this invention in calculating the orientation relationship during the phase transformation and the original β-Ti grain orientation before the phase transformation. Example 4:

[0041] The heating temperature was 940℃, which was in the α+β phase region. A large number of equiaxed α phases were retained. After water cooling, a coexistence structure of equiaxed α and acicular martensite α (α') was obtained, and the size of α' was smaller than that under the single-phase region cooling condition in Example 4.

[0042] A method for accurately calculating the orientation relationship and β-Ti grain orientation before phase transformation in titanium and its alloys, the specific operation steps of which are as follows: Step 1) Using polar chart or The polarimetric diagram or direct visual observation determines the range belonging to the same β-Ti grain, and the orientation data of the α-Ti phase transformation product derived from it are obtained, assuming the number of orientation points is N; Step 2) Calculate the first... Theoretical and experimental orientations of α-Ti variants Orientation difference matrix between Step 3) Calculate the first step using formula (2). Orientation difference between theoretical and measured orientations of α-Ti variants Step 4) Calculate the average orientation difference between the theoretical and measured orientations of all α-Ti phase transformation products belonging to the same β-Ti grain using the following calculation formula (3). Step 5) Iteratively solve using an optimization algorithm, when The orientation matrix corresponding to reaching the global minimum. With orientation matrix This refers to the precise β→α orientation relationship and the orientation of β-Ti grains before the phase transformation.

[0043] Figure 7 As in Example 4 The BC diagram of the phase transformation products of the original β-Ti grains before phase transformation obtained by pole figure reconstruction; Table 1 shows the orientation relationship calculated by the method of the present invention, as well as the orientation of the original β-Ti grains, with an accuracy of 12 decimal places; Figure 8 These are the theoretical results of 24 variants derived from the orientation relationship and β-Ti grain orientation calculated based on Example 4. Extreme graphs, and reality The superimposed comparison of the pole figures shows that the pole positions of the theoretical and actual pole figures are highly consistent, intuitively verifying the accuracy of the orientation relationship and the original β-Ti grain orientation calculated in Table 1. This further confirms the scientific validity and reliability of the orientation relationship and original β-Ti grain orientation calculation method proposed in this invention. This fully demonstrates the correctness and accuracy of the method of this invention in calculating the orientation relationship during the phase transformation and the original β-Ti grain orientation before the phase transformation. Example 5:

[0044] In the following examples, the experimental titanium material used was forged TA2 pure titanium, with the following composition (mass fraction, %): Fe: 0.045%, C: 0.02%, N: 0.011%, H: 0.0006%, O: 0.081%, Ti: Bal. The β-phase transformation temperature was measured to be approximately 885℃ by metallographic method. A 12mm thick plate was used. A small cube sample (10mm × 8mm × 6mm) was cut from the blank and heated to 920℃ in a vacuum tube furnace, then slowly cooled to room temperature. Next, it was mechanically ground sequentially with 400#, 800#, 1200#, and 2000# sandpaper, followed by mechanical polishing with micron-level chromium oxide polishing paste until the surface was bright and scratch-free. Finally, electrolytic polishing was performed in a 10% perchloric acid + 90% ethanol solution at a voltage of 25V and a current maintained at approximately 0.5 mA for 30-40 seconds. After polishing, EBSD experiments were performed on a ZEISS Sigma 360 field emission scanning electron microscope equipped with an Oxford Symmetry S3-EBSD probe. The accelerating voltage was 20V, the tilt angle was 70°, and the step size was 0.15μm. After scanning, the EBSD data were processed using HKL Channel 5 software.

[0045] A method for accurately calculating the orientation relationship and β-Ti grain orientation before phase transformation in titanium and its alloys, the specific operation steps of which are as follows: Step 1) Using polar chart or The polarimetric diagram or direct visual observation determines the range belonging to the same β-Ti grain, and the orientation data of the α-Ti phase transformation product derived from it are obtained, assuming the number of orientation points is N; Step 2) Calculate the first... Theoretical and experimental orientations of α-Ti variants Orientation difference matrix between Step 3) Calculate the first step using formula (2). Orientation difference between theoretical and measured orientations of α-Ti variants Step 4) Calculate the average orientation difference between the theoretical and measured orientations of all α-Ti phase transformation products belonging to the same β-Ti grain using the following calculation formula (3). Step 5) Iteratively solve using an optimization algorithm, when The orientation matrix corresponding to reaching the global minimum. With orientation matrix This refers to the precise β→α orientation relationship and the orientation of β-Ti grains before the phase transformation.

[0046] Figure 9 As in Example 5 The BC diagram of the phase transformation products of the original β-Ti grains before phase transformation obtained by pole figure reconstruction; Table 1 shows the orientation relationship calculated by the method of the present invention, as well as the orientation of the original β-Ti grains, with an accuracy of 12 decimal places; Figure 10 Based on the orientation relationship and β-Ti grain orientation calculated in Example 5, the theoretical basis for 24 variants was derived. Polar charts, and reality The superimposed comparison of the pole figures shows that the pole positions of the theoretical and actual pole figures are highly consistent, intuitively verifying the accuracy of the orientation relationship and the original β-Ti grain orientation calculated in Table 1. This further confirms the scientific validity and reliability of the orientation relationship and original β-Ti grain orientation calculation method proposed in this invention. This fully demonstrates the correctness and accuracy of the method of this invention in calculating the orientation relationship during the phase transformation and the original β-Ti grain orientation before the phase transformation.

[0047] The method of this invention can accurately calculate the orientation relationship during the phase transformation process and the original β-Ti grain orientation before the phase transformation, with a calculation accuracy of up to 12 decimal places. Table 2 shows the results obtained by calculating the orientation relationship and original β-Ti grain orientation of Examples 1 to 5 using the method of this invention.

[0048] Table 2 It should be noted that the calculation process of this invention does not depend on the presence of the β-Ti phase, and the method of this invention can also be applied to all covariant phase transformation processes in other metallic materials that follow or are close to the Burgers relationship. The metallic materials mentioned include titanium-based metals or alloys, zirconium (Zr) and its alloys, hafnium (Hf) and its alloys, or other metallic materials with a hexagonal crystal structure. Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for accurately calculating the orientation relationship and pre-phase transformation β-Ti grain orientation in titanium and its alloys, characterized in that, Based on the principle of minimizing the average orientation difference between the theoretical and measured orientations of all α-Ti variants generated by the phase transformation of the same original β-Ti grain, the optimal solution is directly determined through mathematical optimization. The specific operating steps are as follows: Step 1) Using polar chart or The range belonging to the same β-Ti grain is determined by pole figure or direct visual observation, and the orientation data of the α-Ti phase transformation products derived from it are obtained, assuming that the number of orientation points is N; Step 2) Calculate the first step using the following formula. Theoretical and experimental orientations of α-Ti variants Orientation difference matrix between : = / ； Step 3) Calculate the first step using the following formula. Orientation difference between theoretical and measured orientations of α-Ti variants : ； Step 4) Calculate the average orientation difference between the theoretical and measured orientations of all α-Ti phase transformation products originating from the same β-Ti grain using the following formula. : ； Step 5) Iteratively solve using an optimization algorithm, when The orientation matrix corresponding to reaching the global minimum. With orientation matrix This refers to the precise β→α orientation relationship and the orientation of β-Ti grains before the phase transformation; in The first representing β-Ti grains One equivalent orientation transformation matrix; , These represent the first and second grains of α-Ti. The and the first Equivalent orientation transformation matrices.

2. The method for accurately calculating the orientation relationship and β-Ti grain orientation before phase transformation in titanium according to claim 1, characterized in that, The method is applicable to all covariant phase transformation processes in titanium-based metals or alloys that follow or are close to the Burgers relation.

3. The method for accurately calculating the orientation relationship and pre-phase transformation β-Ti grain orientation in titanium and its alloys according to claim 1, characterized in that, The method is applied to solidified products, forged products, hot-rolled products, cold-rolled products, heat-treated products, weld heat-affected zones, and phase transformation product regions of welds.

4. The method for accurately calculating the orientation relationship and pre-phase transformation β-Ti grain orientation in titanium and its alloys according to claim 1, characterized in that, The method has an accuracy of at least 1e-12°.

5. The method for accurately calculating the orientation relationship and pre-phase transformation β-Ti grain orientation in titanium and its alloys according to claim 1, characterized in that, When calculating the orientation of β-Ti grains, the morphological characteristics and size information of β-Ti grains before phase transformation are further obtained.

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