A yield strength calculation method based on titanium alloy microstructure morphology of mesh organization

Abstract

The present application relates to the technical field of titanium alloy material engineering, and particularly relates to a yield strength calculation method based on the microstructure of titanium alloy with basket weave structure. The yield strength of titanium alloy with basket weave structure is divided into matrix strength, solid solution strengthening effect, grain boundary strengthening effect, dislocation strengthening effect and alpha phase precipitation strengthening effect. The present application innovatively designs a more accurate alpha phase precipitation strengthening model, and designs a circumscribed rectangle length-width statistical method and a phase microstructure weighting algorithm based on area for auxiliary statistics. The traditional method converts lamellar alpha phase into an equal-area circle to consider the strengthening effect. The present application fits the lamellar alpha phase into a long-axis rectangular part and a short-axis two-semicircle part. Compared with the traditional method, the yield strength calculation method based on the microstructure of titanium alloy with basket weave structure in the present application is more close to the actual situation, the statistical method is more accurate and reliable, the result has a smaller error with the actual result, and can be used in the engineering technical fields of titanium alloy microstructure design and performance control.

Description

Technical Field

[0001] This invention relates to the field of titanium alloy materials engineering technology, specifically to a method for calculating the yield strength of titanium alloys based on the microstructure of a basket-like structure. This method can be used in engineering technology fields such as titanium alloy microstructure design and performance control. Background Technology

[0002] Titanium alloys are widely used in aerospace, aviation, and shipbuilding due to their excellent specific strength, corrosion resistance, and high-temperature resistance. As structural materials, the strength of titanium alloys is a key performance indicator, and their microstructure is a crucial factor determining this strength. Accurately predicting the yield strength of titanium alloys based on their microstructure can guide the design and fabrication of novel titanium alloys. However, existing strength calculations based on microstructure all have significant errors, and there is currently no accurate theoretical calculation model. The fundamental reason is the inability to accurately calculate the influence of lamellar α on the overall strength. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the yield strength of a basket-structured titanium alloy. This method calculates the yield strength by statistically analyzing and predicting the microstructure characteristics of the basket-structured titanium alloy, and has high accuracy.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A method for calculating the yield strength of titanium alloys based on the microstructure of basket-like structures includes the following steps:

[0006] Step 1: Calculate the solid solution strengthening effect based on the elemental composition of the titanium alloy;

[0007] Step 2: Calculate the grain boundary strengthening effect based on the average grain size of the original β grains;

[0008] Step 3: Calculate the dislocation strengthening effect based on the alloy dislocation density;

[0009] Step 4: Calculate the α-phase reinforcement effect based on the α-phase ratio, size, and aspect ratio of the basket;

[0010] Step 5: Obtain the alloy matrix strength based on the critical decomposition shear stress of pure titanium;

[0011] Step 6: Based on the calculation results of steps 1 to 5, add them together to obtain the alloy yield strength.

[0012] The method for calculating the yield strength of titanium alloys based on basket microstructure, in step 1, uses the dislocation-solute interaction equation to calculate the solid solution strengthening effect:

[0013]

[0014] In the formula, x i B is the concentration of solute i (at.%). i λ is the strengthening coefficient of solute i, M is the Taylor factor, μ is the solute shear modulus, and λ is the intensification factor of solute i. i Let be the mismatch coefficient of component i, and R be a parameter based on the Seitz radius of the solute atom.

[0015] The method for calculating the yield strength of titanium alloys based on basket structure microstructure, in step 2, uses the Hall-Petch formula to calculate the grain boundary strengthening effect:

[0016]

[0017] In the formula, k is a constant related to the matrix material; for titanium alloys, the constant k = 750 MPa·μm. 1 / 2 d represents the β grain size.

[0018] The method for calculating the yield strength of titanium alloys based on basket microstructure, in step 3, uses the Bailey-Hirsch formula and the Williamson-Hall formula to calculate the dislocation strengthening effect.

[0019]

[0020] In the formula, α is the dislocation interaction constant, M is the Taylor factor, G is the shear modulus, b is the Burgers vector, ρ is the dislocation density, E is the elastic modulus, v is the Poisson's ratio, and ε is the microstrain.

[0021] The method for calculating the yield strength of titanium alloys based on basket structure microstructure, in step 4, uses a modified Orowan formula to calculate the dislocation strengthening effect:

[0022]

[0023] In the formula, M is Taylor factor, G is shear modulus, b is Burgers vector, A is lamellar aspect ratio, δ is lamellar width, f is phase ratio, r0 is dislocation loop radius, and v is Poisson's ratio.

[0024] In the method for calculating the yield strength of titanium alloys based on the microstructure of the basket structure, step 4 uses ImagePro Plus software to measure the phase morphology data.

[0025] In the method for calculating the yield strength of titanium alloys based on the microstructure of the basket structure, in step 4, at least 200 effective phases of each phase morphology data need to be statistically analyzed.

[0026] The yield strength calculation method based on the microstructure of the basket structure titanium alloy described above uses the circumscribed rectangle method to measure the length and width of the α phase in step 4. The circumscribed rectangle measurement methods under different interlacing conditions are: (a) circumscribed rectangle of a single lamellar α phase without interlacing, and circumscribed rectangle of a simply interlaced lamellar α phase; (b) circumscribed rectangle of a complex closed loop formed by lamellar α phase.

[0027] The yield strength calculation method based on the microstructure of the basket-shaped titanium alloy uses the area-weighted method to calculate the aspect ratio in step 4.

[0028] In the method for calculating the yield strength of titanium alloys based on the microstructure of the basket structure, the matrix strength of the alloy in step 5 is taken as 180 MPa for pure titanium.

[0029] The advantages and beneficial effects of this invention are:

[0030] 1. This invention divides the yield strength of basket-structured titanium alloys into matrix strength, solid solution strengthening effect, grain boundary strengthening effect, dislocation strengthening effect and α phase precipitation strengthening effect. Based on existing theories, the Orowan model is improved to more accurately calculate the strength contribution of lamellar α phase.

[0031] 2. This invention innovatively designs a more accurate α-phase precipitation enhancement model, and designs a statistical method for the length and width of the circumscribed rectangle and a phase morphology weighting algorithm based on area to assist in statistics and further improve the accuracy of calculation.

[0032] 3. Traditional methods convert the lamellar α phase into circles of equal area to account for the strengthening effect. This invention fits the lamellar α phase to a rectangular portion along the long axis and two semicircular portions along the short axis. Compared to traditional methods, this invention's model is closer to reality, the statistical method is more accurate and reliable, and the results have smaller errors compared to reality. Furthermore, this invention also demonstrates a certain degree of accuracy when statistically analyzing other titanium alloy microstructures containing lamellar features. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the XRD data in Example 1. In the figure, the horizontal axis 2θ represents the diffraction angle (degree), and the vertical axis Intensity represents the relative intensity (au).

[0034] Figure 2 The diagrams show the schematics and operational procedures of the external rectangle method. Specifically: (a) is a schematic diagram of the external rectangle method for non-interlaced or simply interlaced lamellae; (b) is a schematic diagram of the external rectangle method for interlaced lamellae, with the following markings: 1. Lamellar α phase; 2. Rectangle, using an external rectangle to replace the interlaced blocking effect of multiple interconnected α phases; (c) is a schematic diagram of measuring primary α lamellae using the external rectangle method; and (d) is a schematic diagram of measuring secondary α lamellae using the external rectangle method.

[0035] Figure 3 The following are metallographic data used in Example 1 for statistical analysis of microstructure morphology. Among them: (a) 100x metallographic statistical analysis of β phase size; (b) 1000x metallographic statistical analysis of primary α phase proportion; (c) 5000x metallographic statistical analysis of primary α phase length and width; (d) 10000x metallographic statistical analysis of secondary α phase proportion; (e) 20000x metallographic statistical analysis of secondary α phase length and width.

[0036] Figure 4 The figures show the raw XRD data from Example 1. In the figure, the horizontal axis 2θ represents the diffraction angle (degree), and the vertical axis Intensity represents the relative intensity (au).

[0037] Figure 5 The following are metallographic data used in Example 2 for statistical analysis of microstructure morphology. Among them: (a) 100x metallographic statistical analysis of β phase size; (b) 1000x metallographic statistical analysis of primary α phase proportion; (c) 5000x metallographic statistical analysis of primary α phase length and width; (d) 10000x metallographic statistical analysis of secondary α phase proportion; (e) 20000x metallographic statistical analysis of secondary α phase length and width.

[0038] Figure 6 The figures show the raw XRD data from Example 2. In the figure, the horizontal axis 2θ represents the diffraction angle (degree), and the vertical axis Intensity represents the relative intensity (au).

[0039] Figure 7 The following are metallographic data used in Example 3 for statistical analysis of microstructure morphology. Among them: (a) 100x metallographic statistical analysis of β phase size; (b) 1000x metallographic statistical analysis of primary α phase proportion; (c) 5000x metallographic statistical analysis of primary α phase length and width; (d) 10000x metallographic statistical analysis of secondary α phase proportion; (e) 20000x metallographic statistical analysis of secondary α phase length and width.

[0040] Figure 8 The figures show the raw XRD data from Example 3. In the figure, the horizontal axis 2θ represents the diffraction angle (degree), and the vertical axis Intensity represents the relative intensity (au). Detailed Implementation

[0041] In practical implementation, this invention proposes a method for calculating the yield strength of titanium alloys based on the microstructure of the basket structure. The calculation method includes the following steps:

[0042] Step 1: Calculate the solid solution strengthening effect based on the elemental composition of the titanium alloy.

[0043] Step 2: Calculate the grain boundary strengthening effect based on the average grain size of the original β grains.

[0044] Step 3: Calculate the dislocation strengthening effect based on the alloy dislocation density.

[0045] Step 4: Calculate the α-phase reinforcement effect based on the α-phase ratio, size, and aspect ratio of the basket.

[0046] Step 5: Obtain the alloy matrix strength based on the critical decomposition shear stress of pure titanium.

[0047] Step 6: Based on the calculation results of steps 1 to 5, add them together to obtain the alloy yield strength.

[0048] In step 1, the elemental composition is determined according to a preset elemental structure. The weight percentage is converted into atomic concentration, and the solid solution strengthening effect is calculated using the dislocation-solute interaction equation.

[0049]

[0050] In the formula, σ ss For solid solution strengthening effect (MPa), x i B is the concentration of solute i (at.%). i Let be the strengthening coefficient of solute i (MPa·at). -2 / 3 M is the Taylor factor, μ is the solute shear modulus (GPa), and λ is the solute shear modulus. i Let R be the mismatch coefficient of component i, and R be a parameter based on the Seitz radius of the solute atom. As shown in Table 1, the specific alloying elements and their corresponding strengthening coefficients are as follows:

[0051] Table 1. Alloying elements and their corresponding B i value

[0052]

[0053] Step 2 requires the preparation of high-quality metallographic images to ensure the presence of multiple complete and clear β grains in the field of view. Magnifications of 50x and 100x are recommended. The β grains are then converted into equal-area circles using the equal-area method, and the diameter of these circles is considered the average grain diameter. The grain boundary strengthening effect is calculated using the Hall-Petch formula.

[0054]

[0055] In the formula, σ GB The strength of the grain boundary is expressed in MPa, where k is a constant related to the matrix material; for titanium alloys, the constant k = 750 MPa·μm. 1 / 2 d represents the β grain size (μm).

[0056] Step 3 uses Jade software to process XRD data, performing noise reduction and flattening on the raw data, marking elements and corresponding peak values, and then using Jade's built-in half-peak method to perform multi-peak fitting calculations to obtain micro-strain. The XRD data after Jade data processing is shown below. Figure 1Young's modulus, shear modulus, and Poisson's ratio data were obtained through thermophysical property testing, with the average of at least three parallel sample data taken as the final result. The dislocation strengthening effect was calculated using the Bailey-Hirsch and Williamson-Hall formulas.

[0057]

[0058] In the formula, σ DS The dislocation strengthening effect is given by α, the dislocation interaction constant is given by M, the Taylor factor is given by G, the shear modulus is given by GPa, b is the Burgers vector, and ρ is the dislocation density (1 / m). 2 E is the elastic modulus (GPa), v is Poisson's ratio, and ε is microstrain.

[0059] Step 4 requires the preparation of high-quality metallographic samples. SEM images are taken at magnifications ranging from 1000x to 20000x, ensuring clear visibility of phase interfaces at each magnification. Image Pro Plus software is used to statistically analyze the microstructure morphology in the SEM images. The area method is used to determine the ratio of primary and secondary α phases; the circumscribed rectangle method is used to determine the aspect ratio of each primary and secondary phase layer, and an area-weighted algorithm is used to obtain the average aspect ratio. Each statistical analysis requires data from at least 200 layers.

[0060] like Figure 2The diagram illustrates the circumscribed rectangle measurement method. Considering that secondary α-lamellae are connected end-to-end, forming a closed loop, the dislocation loop mechanism within the closed loop is ineffective; and that secondary phases are generally small with many connections between them, making it difficult and inaccurate to statistically analyze individual α-lamellae. To improve the accuracy of the calculation results, the blocking effect of the secondary α-lamellae morphology on dislocation motion should be statistically analyzed, rather than simply the length and width of each phase. Based on this, this invention proposes the circumscribed rectangle method to measure the blocking effect of the secondary α-lamellae morphology on dislocation motion, that is, using the length and width of the circumscribed rectangle instead of the length and width of multiple interconnected α-phases. Figures (a)-(b) are schematic diagrams of the circumscribed rectangle measurement method under different interlacing conditions, namely: (a) circumscribed rectangle 2 of a single lamellar α phase 1 without interlacing, and circumscribed rectangle 2 of a simply interlaced lamellar α phase 1; (b) circumscribed rectangle 2 of a complex closed loop formed by lamellar α phase 1; Figure (c) is a schematic diagram of the circumscribed rectangle measurement method for primary lamellar phases, which includes non-interlaced lamellar phases and circumscribed rectangles as well as simply interlaced lamellar phases and circumscribed rectangles. Primary lamellar phases mostly exist independently or are simply connected between lamellar phases. The actual fitting process principle is shown in (a); Figure (d) is a schematic diagram of the circumscribed rectangle measurement method for secondary lamellar phases, which includes interlaced lamellar phases and circumscribed rectangles. The interlacing of secondary phases is complex. Interlaced lamellar phases and corresponding circumscribed rectangles are marked with short bars and rectangles of the same color. The actual fitting process principle is shown in (b). It should be noted that this circumscribed rectangle method has high accuracy in replacing a small number of layers (2 to 5). When there are a large number of interconnected layers (more than 10), it is necessary to manually separate these layers into multiple smaller layer combinations. This is mainly because the circumscribed rectangle method is significantly less effective at blocking dislocations when replacing a large number of interconnected layers.

[0061] When processing the length and width data of lamellae, many small-area phasors have very small widths and aspect ratios closer to spherical shapes. Simple averaging methods are often overly influenced by these phasors. Based on this, this invention proposes an area-based length and width weighted algorithm: for the length and width data of each lamellae, the length and width data of that lamellae are weighted according to the proportion of the lamellae area to the total area of ​​the primary or secondary α-phase, and then statistical calculations are performed. That is, the length and width of each lamellae are multiplied by the proportion of that lamellae to the same type of lamellae, and these calculation results are summed to obtain the final statistical result. This algorithm takes into account each lamellae well and ensures the accuracy of the statistical data.

[0062] After data processing, the improved Orowan formula was used to calculate the dislocation strengthening effect, specifically primary α strengthening and secondary α strengthening. The primary α strengthening coefficient was set to 0.1, and the secondary α strengthening coefficient was set to 1.

[0063]

[0064] In the formula, σ αα represents the strengthening effect of the α phase (MPa), M is the Taylor factor, G is the shear modulus (GPa), b is the Burgers vector, A is the aspect ratio of the lamellar layer, δ is the lamellar width (m), f is the phase ratio, r0 is the dislocation loop radius (m), and v is the Poisson's ratio.

[0065] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0066] Example 1:

[0067] Titanium alloys with the following chemical composition were prepared by weight percentage:

[0068] Al: 5.5%, Mo: 3%, Cr: 2%, V: 2%, Sn: 1.5%, Zr: 1.5%, Fe: ≤0.1%, O: ≤0.1%, balance Ti.

[0069] This alloy requires electrode pressing, ingot melting, ingot blanking, and forging. The hot deformation process parameters for forging are 15°C above the phase transformation point and 35% hot deformation. The subsequent heat treatment parameters are 880°C / 2h / AC (air cooling) + 650°C / 4h / AC.

[0070] Samples were taken 1 cm below the surface of the forging to prepare metallographic specimens, XRD specimens, elastic modulus specimens, and tensile specimens, and the microstructure was obtained as follows: Figure 3 XRD data such as Figure 4 The elastic modulus data are shown in Table 2.

[0071] Table 2. Young's modulus, shear modulus, and Poisson's ratio of three parallel samples from Example 1.

[0072]

[0073] Based on the preset elemental composition, the alloying elements calculated as weight percentages are converted into atomic percentages, and the solid solution strengthening effect is calculated using the dislocation-solute interaction equation:

[0074]

[0075] In the formula, x i B is the concentration of solute i (at.%). i Let be the strengthening coefficient of solute i (MPa·at). -2 / 3 M is the Taylor factor, μ is the solute shear modulus (GPa), and λ is the solute shear modulus. i Let R be the mismatch coefficient of component i, and R be a parameter based on the Seitz radius of the solute atom. Solute enhancement coefficient B i See Table 1.

[0076] The calculated solid solution strengthening effect is 225.3913 MPa.

[0077] The area of ​​β grains in the low-magnification microstructure was statistically analyzed and converted into a circle using the equal area method to obtain the diameter of the equivalent circle. The grain boundary strengthening effect was calculated using the Hall-Petch formula.

[0078]

[0079] In the formula, k is a constant related to the matrix material; for titanium alloys, the constant k = 750 MPa·μm. 1 / 2 d represents the β grain size.

[0080] The calculated equivalent circle diameter is 455.61 μm, and the grain boundary strengthening effect is 35.137 MPa.

[0081] The raw XRD data were denoised and flattened, and the corresponding peak values ​​were calibrated. Microstrain was calculated using Jade's built-in half-peak method through multi-peak fitting. The calculation process is as follows: Figure 1 Data such as the elastic modulus were obtained through sample testing, and the average value of at least three parallel sample data was taken as the final result. The dislocation strengthening effect was calculated using the Bailey-Hirsch formula and the Williamson-Hall formula.

[0082]

[0083] In the formula, α is the dislocation interaction constant, M is the Taylor factor, G is the shear modulus (GPa), b is the Burgers vector, and ρ is the dislocation density (1 / m). 2 E is the elastic modulus (GPa), v is Poisson's ratio, and ε is microstrain.

[0084] Calculations show that the microstrain is 0.0049 and the dislocation density is 2.858 × 10⁻⁶. 15 The dislocation strengthening effect is 303.96378 MPa.

[0085] Image Pro Plus software was used to statistically analyze the microstructure morphology of metallographic images. The area method was used to determine the ratio of primary and secondary α phases. The bounding rectangle method (using the aspect ratio of the smallest bounding rectangle instead of the aspect ratio of layers at complex overlap locations) was used to determine the aspect ratio of each primary and secondary phase layer. An area-weighted algorithm was then used to obtain the average aspect ratio. More than 200 phase data points were analyzed each time. After data processing, a modified Orowan formula was used to calculate the dislocation strengthening effect, calculating primary and secondary α strengthening separately. The primary α strengthening coefficient was set to 10, and the secondary α strengthening coefficient was set to 1000.

[0086]

[0087] In the formula, M is Taylor factor, G is shear modulus (GPa), b is Burgers vector, A is lamellar aspect ratio, δ is lamellar width (m), f is phase ratio, r0 is dislocation loop radius (m), and v is Poisson's ratio.

[0088] Statistical analysis showed that the proportion of primary α cells was 51.32%, with a width of 2.5791 × 10⁻⁶. -6 m, length-to-width ratio is 5.39424; secondary α ratio is 9.816%, width is 1.2×10 -7 m, with an aspect ratio of 4.075. The calculated primary α enhancement effect is 12.6497 MPa, and the secondary α enhancement effect is 218.9788 MPa.

[0089] The strength of the alloy matrix is ​​taken as 180 MPa for pure titanium.

[0090] Adding the calculated solid solution strengthening, grain boundary strengthening, dislocation strengthening, primary α strengthening, secondary α strengthening, and matrix strength, we obtain the predicted yield strength of 976.12 MPa in this embodiment.

[0091] A tensile specimen was taken at the same location, and the yield strength was measured to be 978 MPa.

[0092] The calculated strength in this embodiment has an error of -0.192% compared to the actual strength, proving that the calculation method and results in this embodiment are accurate and reliable.

[0093] Example 2:

[0094] Titanium alloys with the following chemical composition were prepared by weight percentage:

[0095] Al: 5.5%, Mo: 3.5%, Cr: 2%, V: 2%, Sn: 1.5%, Zr: 1.5%, Fe: ≤0.1%, O: ≤0.1%, balance Ti.

[0096] This alloy requires electrode pressing, ingot melting, ingot blanking, and forging processes. The hot deformation process parameters for forging are 15°C above the phase transformation point and 35% hot deformation. The subsequent heat treatment parameters are 880°C / 2h / AC + 650°C / 4h / AC.

[0097] Samples were taken 1 cm below the surface of the forging to prepare metallographic specimens, XRD specimens, elastic modulus specimens, and tensile specimens, and the microstructure was obtained as follows: Figure 5 XRD data such as Figure 6 The elastic modulus data are shown in Table 3.

[0098] Table 3. Young's modulus, shear modulus, and Poisson's ratio of three parallel samples from Example 2.

[0099]

[0100]

[0101] Based on the preset elemental composition, the alloying elements calculated as weight percentages are converted into atomic percentages, and the solid solution strengthening effect is calculated using the dislocation-solute interaction equation:

[0102]

[0103] In the formula, x i B is the concentration of solute i (at.%). i Let be the strengthening coefficient of solute i (MPa·at). -2 / 3 M is the Taylor factor, μ is the solute shear modulus (GPa), and λ is the solute shear modulus. i Let R be the mismatch coefficient of component i, and R be a parameter based on the Seitz radius of the solute atom. Solute enhancement coefficient B i See Table 1.

[0104] The calculated solid solution strengthening effect is 226.5344 MPa.

[0105] The area of ​​β grains in the low-magnification microstructure was statistically analyzed and converted into a circle using the equal area method to obtain the diameter of the equivalent circle. The grain boundary strengthening effect was calculated using the Hall-Petch formula.

[0106]

[0107] In the formula, k is a constant related to the matrix material; for titanium alloys, the constant k = 750 MPa·μm. 1 / 2 d represents the β grain size.

[0108] The calculated equivalent circle diameter is 350.49 μm, and the grain boundary strengthening effect is 40.061 MPa.

[0109] The raw XRD data were denoised and flattened, and the corresponding peak values ​​were calibrated. Microstrain was calculated using multi-peak fitting with Jade's built-in half-peak method. Data such as the elastic modulus were obtained through specimen testing, with the average of at least three parallel specimens used as the final result. The dislocation strengthening effect was calculated using the Bailey-Hirsch and Williamson-Hall formulas.

[0110]

[0111] In the formula, α is the dislocation interaction constant, M is the Taylor factor, G is the shear modulus (GPa), b is the Burger vector, and ρ is the dislocation density (1 / m). 2E is the elastic modulus (GPa), v is Poisson's ratio, and ε is microstrain.

[0112] The calculated microstrain is 0.0047, and the dislocation density is 2.613 × 10⁻⁶. 15 The dislocation strengthening effect is 283.01 MPa.

[0113] Image Pro Plus software was used to statistically analyze the microstructure morphology of metallographic images. The area method was used to determine the ratio of primary and secondary α phases. The bounding rectangle method (using the aspect ratio of the smallest bounding rectangle instead of the aspect ratio of layers at complex overlap locations) was used to determine the aspect ratio of each primary and secondary phase layer. An area-weighted algorithm was then used to obtain the average aspect ratio. More than 200 phase data points were analyzed each time. After data processing, a modified Orowan formula was used to calculate the dislocation strengthening effect, calculating primary and secondary α strengthening separately. The primary α strengthening coefficient was set to 10, and the secondary α strengthening coefficient was set to 1000.

[0114]

[0115] In the formula, M is Taylor factor, G is shear modulus (GPa), b is Burgers vector, A is lamellar aspect ratio, δ is lamellar width (m), f is phase ratio, r0 is dislocation loop radius (m), and v is Poisson's ratio.

[0116] Statistical analysis showed that the proportion of primary α cells was 52.11%, with a width of 3.3775 × 10⁻⁶. -6 m, length-to-width ratio 5.3387; secondary α ratio 7.96%, width 9.0×10 -8 m, with an aspect ratio of 3.459. The calculated primary α enhancement effect is 40.0611 MPa, and the secondary α enhancement effect is 211.5817 MPa.

[0117] The strength of the alloy matrix is ​​taken as 180 MPa for pure titanium.

[0118] Adding the calculated solid solution strengthening, grain boundary strengthening, dislocation strengthening, primary α strengthening, secondary α strengthening, and matrix strength, we obtain the predicted yield strength of 971.53 MPa in this embodiment.

[0119] A tensile specimen was taken at the same location, and the yield strength was measured to be 988 MPa.

[0120] The calculated strength in this embodiment has an error of -1.67% compared to the actual strength, proving that the calculation method and results in this embodiment are accurate and reliable.

[0121] Example 3:

[0122] Titanium alloys with the following chemical composition were prepared by weight percentage:

[0123] Al: 5.3%, Mo: 3%, Cr: 2%, V: 2%, Sn: 1.5%, Zr: 1.5%, Fe: ≤0.1%, O: ≤0.1%, balance Ti.

[0124] This alloy requires electrode pressing, ingot melting, ingot blanking, and forging processes. The hot deformation process parameters for forging are 15°C above the phase transformation point and 35% hot deformation. The subsequent heat treatment parameters are 880°C / 2h / AC + 650°C / 4h / AC.

[0125] Samples were taken 1 cm below the surface of the forging to prepare metallographic specimens, XRD specimens, elastic modulus specimens, and tensile specimens, and the microstructure was obtained as follows: Figure 7 XRD data such as Figure 8 The elastic modulus data are shown in Table 4.

[0126] Table 4. Young's modulus, shear modulus, and Poisson's ratio of three parallel samples in Example 3.

[0127]

[0128] Based on the preset elemental composition, the alloying elements calculated as weight percentages are converted into atomic percentages, and the solid solution strengthening effect is calculated using the dislocation-solute interaction equation:

[0129]

[0130] In the formula, x i B is the concentration of solute i (at.%). i Let be the strengthening coefficient of solute i (MPa·at). -2 / 3 M is the Taylor factor, μ is the solute shear modulus (GPa), and λ is the solute shear modulus. i Let R be the mismatch coefficient of component i, and R be a parameter based on the Seitz radius of the solute atom. Solute enhancement coefficient B i See Table 1.

[0131] The calculated solid solution strengthening effect is 224.8693 MPa.

[0132] The area of ​​β grains in the low-magnification microstructure was statistically analyzed and converted into a circle using the equal area method to obtain the diameter of the equivalent circle. The grain boundary strengthening effect was calculated using the Hall-Petch formula.

[0133]

[0134] In the formula, k is a constant related to the matrix material; for titanium alloys, the constant k = 750 MPa·μm. 1 / 2 d represents the β grain size.

[0135] The calculated equivalent circle diameter is 414.88 μm, and the grain boundary strengthening effect is 36.82138 MPa.

[0136] The raw XRD data were denoised and flattened, and the corresponding peak values ​​were calibrated. Microstrain was calculated using multi-peak fitting with Jade's built-in half-peak method. Data such as the elastic modulus were obtained through specimen testing, with the average of at least three parallel specimens used as the final result. The dislocation strengthening effect was calculated using the Bailey-Hirsch and Williamson-Hall formulas.

[0137]

[0138] In the formula, α is the dislocation interaction constant, M is the Taylor factor, G is the shear modulus (GPa), b is the Burgers vector, and ρ is the dislocation density (1 / m). 2 E is the elastic modulus (GPa), v is Poisson's ratio, and ε is microstrain.

[0139] The calculated microstrain is 0.00505, and the dislocation density is 3.06 × 10⁻⁶. 15 The dislocation strengthening effect is 309.6917 MPa.

[0140] Image Pro Plus software was used to statistically analyze the microstructure morphology of metallographic images. The area method was used to determine the ratio of primary and secondary α phases. The bounding rectangle method (using the aspect ratio of the smallest bounding rectangle instead of the aspect ratio of layers at complex overlap locations) was used to determine the aspect ratio of each primary and secondary phase layer. An area-weighted algorithm was then used to obtain the average aspect ratio. More than 200 phase data points were analyzed each time. After data processing, a modified Orowan formula was used to calculate the dislocation strengthening effect, calculating primary and secondary α strengthening separately. The primary α strengthening coefficient was set to 10, and the secondary α strengthening coefficient was set to 1000.

[0141]

[0142] In the formula, M is Taylor factor, G is shear modulus (GPa), b is Burgers vector, A is lamellar aspect ratio, δ is lamellar width (m), f is phase ratio, r0 is dislocation loop radius (m), and v is Poisson's ratio.

[0143] Statistical analysis showed that the proportion of primary α cells was 60.771%, with a width of 3.16 × 10⁻⁶. -6 m, length-to-width ratio 4.461; secondary α ratio 7.7285%, width 1.42×10 -7 m, with an aspect ratio of 4.609. The calculated primary α enhancement effect is 19.04219 MPa, and the secondary α enhancement effect is 163.1378 MPa.

[0144] The strength of the alloy matrix is ​​taken as 180 MPa for pure titanium.

[0145] The calculated solid solution strengthening effect, grain boundary strengthening effect, dislocation strengthening effect, primary α strengthening effect, secondary α strengthening effect, and matrix strength are added together to obtain the predicted yield strength of 933.56227 MPa in this embodiment.

[0146] A tensile specimen was taken at the same location, and the yield strength was measured to be 945 MPa.

[0147] The calculated strength in this embodiment has an error of -1.21% compared to the actual strength, proving that the calculation method and results in this embodiment are accurate and reliable.

Claims

1. A yield strength calculation method based on mesh organization titanium alloy organization appearance, its characterized in that, The method comprises the following steps: Step 1: calculate the solid solution strengthening effect according to the element composition of the titanium alloy; Step 2: calculate the grain boundary strengthening effect according to the average grain size of the original beta grains; Step 3: calculate the dislocation strengthening effect according to the dislocation density of the alloy; Step 4: calculate the alpha phase strengthening effect according to the proportion, size and aspect ratio of the basket-shaped alpha phase; In step 4, the alpha phase strengthening effect is calculated by using the improved Orowan formula: In the formula, M is the Taylor factor, G is the shear modulus, b is the burgers vector, A is the lamellar aspect ratio, δ is the lamellar width, f is the phase proportion, r0 is the dislocation ring radius, and v is the Poisson's ratio; Step 5: obtain the alloy matrix strength according to the critical decomposition shear stress of pure titanium; Step 6: add the calculation results of steps 1-5 to obtain the yield strength of the alloy.

2. The method for calculating yield strength based on basketweave microstructure of titanium alloy microstructure morphology according to claim 1, characterized in that, In step 1, the dislocation-solute interaction equation is used to calculate the solid solution strengthening effect: where x i is the concentration of solute i, at.%, B i is the strengthening coefficient of solute i, M is the Taylor factor, μ is the shear modulus of solute, λ i is the misfit coefficient of solute i, R is a parameter based on the Seitz radius of solute atom.

3. The method for calculating yield strength based on basket weave microstructure of titanium alloy microstructure topography according to claim 1, characterized in that, In step 2, the Hall-Petch formula is used to calculate the grain boundary strengthening effect: In the formula, k is a constant related to the base material, and the constant k = 750 MPa μm for a titanium alloy 1 / 2 , and d is the β grain size.

4. The method for calculating yield strength based on basketweave microstructure of titanium alloy microstructure topography according to claim 1, characterized in that, In step 3, the Bailey-Hirsch formula and the Williamson-Hall formula are used to calculate the dislocation strengthening effect: In the formula, α is the dislocation interaction constant, M is the Taylor factor, G is the shear modulus, b is the burgers vector, ρ is the dislocation density, E is the elastic modulus, v is the Poisson's ratio, and ε is the micro-strain.

5. The method for calculating yield strength based on basketweave microstructure of titanium alloy microstructure topography according to claim 1, characterized in that, In step 4, the Image Pro Plus software is used to measure the phase morphology data.

6. The method for calculating yield strength based on basketweave microstructure of titanium alloy microstructure morphology according to claim 5, characterized in that, In step 4, each phase morphology data needs to be at least 200 effective phases.

7. The method for calculating yield strength based on basketweave microstructure of titanium alloy microstructure topography according to claim 1, characterized in that, In step 4, the circumscribed rectangle method is used to measure the aspect ratio of the alpha phase, and the circumscribed rectangle measurement method is different under different interlacing conditions: (a) circumscribed rectangle of single lamellar alpha phase without interlacing, and (b) circumscribed rectangle of simple interlaced lamellar alpha phase.

8. The method for calculating yield strength based on basketweave microstructure of titanium alloy microstructure topography according to claim 1, characterized in that, In step 4, the area weighting method is used to calculate the aspect ratio.

9. The method for calculating yield strength based on basketweave microstructure of titanium alloy microstructure topography according to claim 1, characterized in that, In step 5, the alloy matrix strength is taken as 180 MPa of pure titanium.

Images