A method for predicting alloy creep life with multi-scale coupling

Abstract

The application provides a method for predicting alloy creep life in a multi-scale coupling manner, comprising the following steps: S1, constructing crystal structures of pure elements, Ti-based binary alloys and Ti80 alloys; S2, obtaining lattice constants of the crystal structures; S3, obtaining basic physical properties of the ground states by using a VASP calculation software package; S4, predicting the creep behaviors of the Ti80 alloy under different temperatures and different loads by using a CALPHAD method; S5, constructing a finite element polycrystal numerical model based on the real crystal phase structure of the Ti80 alloy; and S6, simulating the creep service behaviors of the Ti80 alloy under different temperatures and different loads by using a finite element calculation software based on the polycrystal finite element numerical model. The application builds a multi-scale coupling alloy high-temperature / high-pressure creep behavior simulation method based on automatic parameter transmission, and solves the problems of long alloy creep experiment period, high time cost and high economic cost.

Description

Technical Field

[0001] This invention relates to the field of high-temperature / high-pressure creep service technology for alloy materials, and in particular to a method for predicting the creep life of alloys using multi-scale coupling. Background Technology

[0002] Creep in metallic materials is generally divided into three stages: instantaneous creep, steady-state creep, and accelerated creep. Creep typically occurs under high-temperature service conditions, and its influencing factors include time, stress, temperature, microstructure, and structure. In the steady-state creep stage, the creep rate tends to stabilize. Over time, the initial creep rate gradually decreases to a stable value. This stable creep state persists for a long time and accounts for a large portion of the entire creep process.

[0003] Creep experiments are lengthy and costly in terms of both time and money, and the results are not universally applicable. Therefore, it is necessary to study a creep life prediction model.

[0004] Common creep life prediction models are mainly empirical models, including Norton power law model, time parameter method, theta projection method, Ω model and Wilshire model, etc. They are all based on fitting parameters based on experimental results. Generally speaking, the more parameters fitted, the higher the accuracy.

[0005] Most parameters in empirical models do not have physical meaning, and the model results are quite sensitive to parameters. Their reliability will decrease when extrapolating to predict creep life under long-term service conditions. They have poor universality among different materials. They are merely a characterization of existing experimental data and are difficult to predict creep behavior under different materials, temperatures, and loads. Summary of the Invention

[0006] In view of this, the present invention aims to propose a multi-scale coupled method for predicting the creep life of alloys, specifically involving the high-temperature / high-pressure creep service behavior of Ti80 alloy. It establishes a multi-scale coupled simulation method for high-temperature / high-pressure creep behavior of alloys based on automatic parameter transfer, thereby solving the problems of long experimental cycles and high time and economic costs in alloy creep testing.

[0007] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0008] A method for predicting the creep life of an alloy using multi-scale coupling includes the following steps:

[0009] S1: Construct the crystal structure of pure elements, the crystal structure of Ti-based binary alloys, and the crystal structure of Ti80 alloy from known databases or software packages;

[0010] S2: Perform structural relaxation on the initial crystal structure to obtain its stable lattice constant;

[0011] S3: Based on the stable lattice constant, the VASP calculation software is used to obtain its basic physical properties in the ground state, including elastic properties, stacking fault energy, and diffusion coefficient;

[0012] S4: Using the CALPHAD method, the interaction parameters between alloying elements were fitted to obtain the stacking fault energy and diffusion coefficient of Ti80 alloy. The relative creep rate model was used in combination with the creep behavior of pure Ti under different temperatures and loads to predict the creep behavior of Ti80 alloy under different temperatures and loads.

[0013] S5: Based on the actual crystal phase structure of Ti80 alloy, a finite element polycrystalline numerical model is constructed using the Voronoi algorithm;

[0014] S6: Based on the polycrystalline finite element numerical model, finite element calculation software is used to mesh the model, set the temperature field, stress field and boundary conditions, and simulate the creep service behavior of Ti80 alloy under different temperatures and loads.

[0015] Furthermore, in step S1, pure Ti has a hexagonal close-packed (HCP) structure in its ground state. The crystal structure of pure Ti is constructed based on the Materials Project, OQMD, SprInger Materials, ICSD, and NIST databases. A 5×4×4 supercell is expanded on the basis of α-Ti. Then, the near-α type Ti80 alloy crystal structure is constructed using the mcsqs module in ATAT software based on the special quasi-random SQS method.

[0016] Furthermore, in step S2, the initial crystal structure is optimized based on the VASP software package, including the following steps:

[0017] S21: First, set the parameters "ISIF=A1, IBRION=B1" to optimize the initial structure so that the energy and force of the crystal structure reach the convergence standard;

[0018] S22: Based on the optimized crystal structure, change the scaling factor and step size, and set the parameters "ISIF=A2, IBRION=B2" again to optimize the crystal structure again so that the energy and force of the crystal structure reach the convergence standard;

[0019] S23: Based on the crystal structure under different scaling factors, set the parameters "IBRION=C, NSW=D, ISMEAR=E" to make the energy and force of the crystal structure reach the convergence standard;

[0020] S24: Based on the energy-volume of each crystal structure under different scaling factors, the energy-volume solid state equation of state described in formula (1) is used to calculate the lattice constant, total energy of the ground state, and bulk modulus of each crystal structure.

[0021]

[0022] Where A1, B1, A2, B2, C, D, and E are preset empirical parameters, V is the volume, and E(V) is the energy of the unit cell under different volumes.

[0023] Furthermore, step S3 includes the following steps:

[0024] S31: Based on the crystal structure obtained in step S2, the elastic properties, including elastic constants, elastic modulus, and Poisson's ratio, are calculated using the stress-strain method.

[0025] S32: Calculate stacking fault energy using the slab model;

[0026] S33: The diffusion coefficient is obtained based on the Arrhenius diffusion model, and the diffusion coefficient is calculated according to formula (12);

[0027]

[0028] Where Q is the diffusion activation energy, k B is Boltzmann's constant, and T is temperature.

[0029] Furthermore, step S31 includes the following steps:

[0030] Step 311: The second-order tensor of the elastic coefficient is obtained from the generalized Hooke's law shown in formula (2). Small strains are applied in different directions, and the stress tensor after applying small deformation is obtained by optimizing the atomic positions. Then, the elastic constants are obtained according to the stress-strain relationship.

[0031] σ ij =C ij ε kl (2)

[0032] Where σ ij and ε kl These are the stress tensor and strain tensor, respectively, C ij The elastic constants are C, where the hexagonal structure has a total of 5 independent elastic constants, namely C 11 C 33 C44 C 66 C 12 C 13 ;

[0033] Step 312: Based on the calculated elastic constants, the polycrystalline elastic modulus is calculated using the Voigt-Reuss-Hill (VRH) approximation algorithm according to the formulas shown in (3)-(8):

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] Where B is the bulk modulus and G is the shear modulus;

[0041] Step 313: Calculate Young's modulus E and Poisson's ratio using empirical models according to formulas (9)-(10);

[0042]

[0043]

[0044] Where E is Young's modulus and ν is shear modulus.

[0045] Furthermore, step S32 includes the following steps:

[0046] S321: Calculate the generalized stacking fault energy according to formula (11). The generalized stacking fault energy is defined as the energy difference per unit area between a stacking fault supercell (u≠0) and a perfect unit cell (u=0). The stacking fault vector u represents the distance that the upper half of the unit cell moves relative to the lower half when it slips. This vector starts from 0.0b and moves to 1.0b with a step size of 0.1b. b is the Burgers vector when slipping.

[0047]

[0048] Where E(u) is the total energy of the supercell containing the stacking fault vector u, E(0) is the energy of the perfect lattice, A represents the stacking fault area, and γ SFE (u) represents a generalized stacking fault containing the stacking fault vector u;

[0049] S322: A vacuum layer is added above each model. During calculation, the atoms in the upper layer move relative to the atoms in the lower layer along the slip direction.

[0050] Furthermore, step S33 includes the following steps:

[0051] S331: The diffusion of alloying elements in the HCP structure considers two different diffusion directions, namely the diffusion coefficient D parallel to the c-axis direction calculated according to formula (13). || And the diffusion coefficient D perpendicular to the c-axis is calculated according to formula (14). ⊥ ;

[0052]

[0053]

[0054] Where C || and C ⊥ These are the diffusion precession factors parallel to and perpendicular to the c-axis, respectively, where c is the concentration of the alloying element, and f is the diffusion precession factor. Bz f Ax f Bx w is the jump correlation factor. A w B These are the jump frequencies in directions A and B, respectively.

[0055] Furthermore, in step S4, the stacking fault energy and diffusion coefficient of the multi-component alloy are calculated using the CALPHAD method according to Formula 15:

[0056] φ= 0 φ+Δφ (15)

[0057] in, It is a linear mixture of stacking fault energies in a pure elemental HCP structure; To account for the excess portion of stacking fault energy due to the interaction between various alloying elements.

[0058] Furthermore, step S4 includes the following steps:

[0059] Step 41: The linear mixture component in the CALPHAD model is simulated and calculated according to Equation 16;

[0060] 0 φ=∑ i x i 0 φ i (16)

[0061] Step 42: The excess portion in the CALPHAD model is simulated using Equation 17;

[0062]

[0063] Step 43: Based on the calculation results of the CALPHAD method, the creep rate of Ti80 alloy relative to Ti alloy is obtained using the relative creep rate model, and simulation calculation is performed using Equation 18:

[0064]

[0065] Where τratio is the relative creep rate of Ti80 alloy relative to Ti alloy, ε Ti80合金 ε represents the creep rate of the Ti80 alloy. Ti D represents the relative creep rate of the Ti alloy. eff γ is the diffusion coefficient. SFE Let G be the stacking fault energy, E be the shear modulus, E be the Young's modulus, and b be the Burgers vector.

[0066] Step 44: Based on the relative creep rate of Ti80 alloy, and combined with the creep rate of Ti alloy under different temperatures and loads, extrapolate the creep rate of Ti80 alloy under the same service conditions.

[0067] Furthermore, step S5 includes the following steps:

[0068] S51: A small program for generating Voronoi polycrystals using the Voronoi function language provided by the Scipy library in Python;

[0069] S52: Use the script interface of the finite element software to transfer the py file of the program in step S51 to the finite element simulation software, and directly generate Voronoi polycrystalline geometric models in batches in the finite element software.

[0070] Step S6 includes the following steps:

[0071] S61: Based on the polycrystalline model constructed in step 5, perform mesh generation on it;

[0072] S62: Based on the polycrystalline model constructed in step 5, set the temperature field, stress field, and boundary conditions;

[0073] S63: The creep service behavior of M alloy under different temperatures and loads is simulated using finite element simulation software ABAQUA or COMSOL.

[0074] Compared with existing technologies, the multi-scale coupling method for predicting alloy creep life described in this invention has the following advantages:

[0075] The multi-scale coupled method for predicting the creep life of alloys described in this invention starts from first-principles calculations at the atomic scale, based on the computational phase diagram (CALPHAD) model, combined with the basic theoretical model at the microscale and the polycrystalline model at the mesoscale, and adopts an automatic parameter transfer method. The front-end calculation results are used as inputs for multi-physics field (temperature, load) finite element analysis, and finally the creep life prediction model under different temperatures and loads is obtained. This makes the method for predicting the creep life of Ti80 alloy simple, efficient and accurate, overcomes the shortcomings of the traditional "trial and error method", and saves resources and time. Attached Figure Description

[0076] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0077] Figure 1 This is a logic diagram of the multi-scale coupling method for predicting alloy creep life according to an embodiment of the present invention;

[0078] Figure 2 This is a schematic diagram of the crystal structure of α-Ti in an embodiment of the present invention;

[0079] Figure 3 This is a schematic diagram of the crystal structure of the Ti80 alloy in an embodiment of the present invention;

[0080] Figure 4 This is a schematic diagram of the state equation fitting curves for Ti, Al, Nb, Zr, and Mo in an embodiment of the present invention.

[0081] Figure 5 This is a schematic diagram of base surface sliding in an embodiment of the present invention;

[0082] Figure 6 This is a schematic diagram of a cylindrical sliding structure in an embodiment of the present invention;

[0083] Figure 7 This is a schematic diagram of the first-stage conical surface sliding in an embodiment of the present invention;

[0084] Figure 8 This is a schematic diagram of the sliding of the secondary conical surface in an embodiment of the present invention;

[0085] Figure 9 This is a schematic diagram of the stacking fault energy curve of the pure element hcp structure in an embodiment of the present invention;

[0086] Figure 10 Ti in the embodiments of the present invention 47 A schematic diagram of the stacking fault energy curve of X;

[0087] Figure 11 This is a schematic diagram of the diffusion coefficient of pure Ti in an embodiment of the present invention;

[0088] Figure 12 This is a schematic diagram of the diffusion coefficient of the Ti alloy in this embodiment;

[0089] Figure 13 This is a schematic diagram of the mutual parameter curves of the stacking fault energy of Ti alloy in an embodiment of the present invention;

[0090] Figure 14 This is an example of generating a Voronoi polycrystalline geometric model in an embodiment of the present invention;

[0091] Figure 15 The above are creep curves of Ti80 alloy under different temperatures and loads in embodiments of the present invention.

[0092] Figure 16 This is a block diagram of the method for predicting the creep life of Ti80 alloy using multi-scale coupling, as described in an embodiment of the present invention. Detailed Implementation

[0093] To make the technical means and objectives and effects of the present invention easier to understand, the embodiments of the present invention will be described in detail below with reference to specific illustrations.

[0094] It should be noted that all directional and positional terms used in this invention, such as "up," "down," "left," "right," "front," "back," "vertical," "horizontal," "inner," "outer," "top," "lower," "lateral," "longitudinal," and "center," are only used to explain the relative positional relationships and connections between components in a specific state (as shown in the accompanying drawings). They are merely for the convenience of describing the invention and do not require the invention to be constructed and operated in a specific orientation; therefore, they should not be construed as limitations on the invention. Furthermore, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated.

[0095] In the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0096] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0097] like Figures 1-16 As shown, this invention proposes a method for predicting the creep life of alloys using multi-scale coupling, comprising the following steps:

[0098] S1: Construct the crystal structures of pure elements, Ti-based binary alloys, and Ti80 alloys from known databases or software packages; wherein, the crystal structures of pure elements are the corresponding pure element crystal structures of the elements contained in Ti80 alloy, including the crystal results of pure Ti, pure Al, pure Nb, pure Zr, and pure Mo; and the crystal structures of Ti-based binary alloys are the crystal structures of binary alloys composed of Ti-based elements combined with the elements contained in Ti80 alloy.

[0099] S2: Perform high-precision structural relaxation on the initial crystal structure to obtain its stable lattice constant;

[0100] S3: Based on the stable lattice constant, the VASP calculation software is used to obtain its basic physical properties in the ground state, including elastic properties, stacking fault energy, and diffusion coefficient;

[0101] S4: Using the CALPHAD method, the interaction parameters between alloying elements were fitted to obtain the stacking fault energy and diffusion coefficient of Ti80 alloy. The relative creep rate model was used in combination with the creep behavior of pure Ti under different temperatures and loads to predict the creep behavior of Ti80 alloy under different temperatures and loads.

[0102] S5: Based on the real crystal phase structure of Ti80 alloy, the Voronoi algorithm is used to link the macroscopic mechanical behavior and microstructure of crystal materials. The creep behavior of crystal materials is described by combining the physical mechanisms of crystal dislocation slip, twinning and phase transformation, and a finite element polycrystalline model is constructed.

[0103] S6: Based on the polycrystalline finite element numerical model, finite element calculation software is used to mesh the model, set the temperature field, stress field and boundary conditions, and simulate the creep service behavior of Ti80 alloy under different temperatures and loads.

[0104] The multi-scale coupling method for predicting the creep life of alloys described in this invention first obtains the pure elemental crystal structure of the corresponding element in Ti80 alloy, the crystal structure of Ti-based binary alloys, and the crystal structure of Ti80 alloy from known databases or software packages. The crystal structures of pure Ti and Ti80 alloys are optimized to obtain stable lattice constants. Then, the basic physical properties of the ground state are calculated using a computational software package. The stacking fault energy and diffusion coefficient of Ti80 alloy are calculated using the CALPHAD method. Combined with a relative creep rate model, the creep behavior of Ti80 alloy under different temperatures and loads is predicted. A basic theoretical model is established at the microscale. Based on the actual grain and orientation distribution of Ti80 alloy, a polycrystalline model is constructed at the mesoscale using the Voronoi algorithm. Finite element simulation software is then used to simulate and analyze the constructed polycrystalline model and creep rate model under different temperatures and loads, obtaining a creep life prediction model for Ti80 alloy under different temperatures and loads.

[0105] The multi-scale coupled method for predicting the creep life of alloys described in this invention starts from first-principles calculations at the atomic scale, based on the computational phase diagram (CALPHAD) model, combined with the basic theoretical model at the microscale and the polycrystalline model at the mesoscale, and adopts an automatic parameter transfer method. The front-end calculation results are used as inputs for multi-physics field (temperature, load) finite element analysis, and finally the creep life prediction model under different temperatures and loads is obtained. This makes the method for predicting the creep life of Ti80 alloy simple, efficient and accurate, overcomes the shortcomings of the traditional "trial and error method", and saves resources and time.

[0106] As a preferred example of the present invention, in step S1, pure Ti has a hexagonal close-packed (HCP) structure in its ground state, i.e., α-Ti, with space group P63 / MMC(194). The crystal structure of pure Ti is constructed based on the MaterialsProject, OQMD, SprIngerMaterials, ICSD, and NIST databases, as follows: Figure 2 As shown, a single cell contains 2 atoms; secondly, a 5×4×4 supercell (160 atoms) is built on the basis of α-Ti. Then, using the mcsqs module in ATAT software, based on the quasi-random approximation (special quasi-random SQS) method, the crystal structure of the near-α type Ti80 alloy is constructed, and its crystal structure is shown in the figure. Figure 3As shown, it contains 17 Al atoms, 2 Nb atoms, 2 Zr atoms, 1 Mo atom and 138 Ti atoms (atomic ratio: 86.3 at% Ti, 10.6 at% Al, 1.3 at% Nb, 1.3 at% Zr, 0.6 at% Mo).

[0107] As a preferred example of the present invention, in step S2, the initial crystal structure is optimized based on the VASP software package, including the following steps:

[0108] S21: First, set the parameters "ISIF=A1, IBRION=B1" to optimize the initial structure so that the energy and force of the crystal structure reach the convergence standard;

[0109] S22: Based on the optimized crystal structure, change the scaling factor and step size, and set the parameters "ISIF=A2, IBRION=B2" again to optimize the crystal structure again so that the energy and force of the crystal structure reach the convergence standard;

[0110] S23: Based on the crystal structure under different scaling factors, set the parameters "IBRION=C, NSW=D, ISMEAR=E" to make the energy and force of the crystal structure reach the convergence standard;

[0111] S24: Based on the energy-volume of each crystal structure under different scaling factors, the energy-volume solid state equation of state described in formula (1) is used to calculate the lattice constant, total energy of the ground state, and bulk modulus of each crystal structure.

[0112]

[0113] Where A1, B1, A2, B2, C, D, and E are preset empirical parameters, V is the volume, and E(V) is the energy of the unit cell under different volumes.

[0114] As a preferred configuration, A1 = 3, B1 = 2, A2 = 4, B2 = 2, C = -1, D = 0, E = -5, and the energy convergence criterion is 10. - 6 eV, the convergence criterion for force is In step S22, the scaling factor is changed from 0.97 to 1.03, with a step size of 0.01.

[0115] Based on the optimization method in step 2, the fitting curve of the pure element crystal is as follows: Figure 4 As shown in Table 1, the lattice constants of the pure elements are shown in Table 2, and the lattice constants of the Ti80 alloy are shown in Table 3.

[0116]

[0117] Table 1. Fitting results of the structural state equation of pure elemental HCP

[0118]

[0119] Table 2. Lattice constants of HCP structures of pure elements

[0120]

[0121] Table 3. Lattice constants of Ti and Ti80 alloys

[0122] As a preferred example of the present invention, step S3 includes the following steps:

[0123] S31: Based on the crystal structure obtained in step S2, the elastic properties, including elastic constants, elastic modulus, and Poisson's ratio, are calculated using the stress-strain method.

[0124] Specifically, step S31 includes the following steps:

[0125] Step 311: The second-order tensor of the elastic coefficient is obtained from the generalized Hooke's law shown in formula (2). Small strains are applied in different directions, and the stress tensor after applying small deformation is obtained by optimizing the atomic positions. Then, the elastic constants are obtained according to the stress-strain relationship.

[0126] σ ij =C ij ε kl (2)

[0127] Where σ ij and ε kl These are the stress tensor and strain tensor, respectively, C ij The elastic constants are influenced by the symmetry of the crystal structure; the higher the symmetry, the fewer the independent elastic constants. The hexagonal structure has a total of 5 independent elastic constants, namely C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C20, C12, C2 ...2, C20, C12, C 11 C 33 C 44 C 66 C 12 C 13 ;

[0128] Step 312: Based on the calculated elastic constants, the polycrystalline elastic modulus is obtained through the Voigt-Reuss-Hill (VRH) approximation algorithm, including bulk modulus B, shear modulus G, and Young's modulus E. The bulk modulus B and shear modulus G are calculated according to the formulas shown in (3)-(8):

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] Step 313: Calculate Young's modulus and Poisson's ratio using an empirical model, as shown in formulas (9)-(10);

[0136]

[0137]

[0138] The calculation results are shown in Table 4:

[0139]

[0140] Table 4. Elastic properties of Ti80 alloy

[0141] S32: Stacking fault energy was calculated using the Slab model; in this application, both Ti and Ti80 alloys have a face-centered cubic structure, and their slip systems can be divided into... Dislocation slip and<a+c> Dislocation slip, where<a+c> Dislocation slip is the only slip system that can coordinate c-axis strain. Dislocation slip can be divided into basal slip {0001}<11-20>( Figure 5 As shown), cylindrical sliding system {10-10}<11-20> ( Figure 6 (as shown) and first-order conical surface slip {10-11}<11-20> ( Figure 7 (as shown),<a+c> Dislocation slip is second-order conical slip {11-22}<11-23>( Figure 8 (As shown).

[0142] Specifically, step S32 includes the following steps:

[0143] S321: Calculate the generalized stacking fault energy according to formula (11). The generalized stacking fault energy is defined as the energy difference per unit area between a stacking fault supercell (u≠0) and a perfect unit cell (u=0). The stacking fault vector u represents the distance that the upper half of the unit cell moves relative to the lower half when it slips. This vector starts from 0.0b and moves to 1.0b with a step size of 0.1b. b is the Burgers vector when slipping.

[0144]

[0145] Where E(u) is the total energy of the supercell containing the stacking fault vector u, E(0) is the energy of the perfect lattice, A represents the stacking fault area, and γ SFE (u) represents a generalized stacking fault containing the stacking fault vector u;

[0146] S322: A vacuum layer is added above each model. During calculation, the atoms in the upper layer move relative to the atoms in the lower layer along the slip direction.

[0147] This setting is to eliminate the effects caused by periodic boundary conditions.

[0148] The calculation results of its layered energy are summarized in Table 5:

[0149] Ti 317 317 0 0 Al -133 247 -60.625 -2971.91 Nb -204 247 -59.146 -2899.4 Zr 194 308 -6.438 -315.574 Mo 276 282 -34.146 -1673.87

[0150] Table 5. Pure elements and Ti 47 Stacking fault energy of X

[0151] S33: The diffusion coefficient is obtained based on the Arrhenius diffusion model, and the diffusion coefficient is calculated according to formula (12);

[0152]

[0153] Where Q is the diffusion activation energy, k B is Boltzmann's constant, and T is temperature.

[0154] Specifically, step S33 includes the following steps:

[0155] S331: The diffusion of alloying elements in the HCP structure considers two different diffusion directions: the direction parallel to the c-axis, as shown in Formula 13, and the direction perpendicular to the c-axis, as shown in Formula 14.

[0156]

[0157]

[0158] Where C || and C ⊥ These are the diffusion precession factors parallel to and perpendicular to the c-axis, respectively, where c is the concentration of the alloying element, and f is the diffusion precession factor. Bz f Ax f Bx w is the jump correlation factor. A w B The jump frequencies in directions A and B are respectively, and the diffusion coefficients of pure Ti and Ti alloys are as follows: Figures 11-12 As shown.

[0159] As a preferred example of the present invention, in step S4, the stacking fault energy and diffusion coefficient of the multi-element alloy are calculated according to Formula 15 using the CALPHAD method.

[0160] φ= 0 φ+Δφ (15)

[0161] in It is a linear mixture of stacking fault energies in a pure elemental HCP structure; To account for the excess portion of stacking fault energy due to the interaction between various alloying elements.

[0162] Specifically, step S4 includes the following steps:

[0163] Step 41: The linear mixture component in the CALPHAD model is simulated and calculated according to Equation 16;

[0164] 0 φ=∑ i x i 0 φ i (16)

[0165] Step 42: The excess portion in the CALPHAD model is simulated using Equation 17;

[0166]

[0167] Figure 13 The interaction parameter is the stacking fault energy of the Ti alloy.

[0168] Step 43: Based on the above calculation results, the creep rate of Ti80 alloy relative to Ti alloy is obtained using the relative creep rate model, and simulation calculation is performed using Formula 18:

[0169]

[0170] Where, τ ratio ε represents the relative creep rate of Ti80 alloy relative to Ti alloy. Ti80合金 ε represents the creep rate of the Ti80 alloy. Ti Let be the relative creep rate of the Ti alloy, where ε Ti D is the reference creep rate for Ti80 alloy. eff γ is the diffusion coefficient. SFE Let G be the stacking fault energy, E be the shear modulus, E be the Young's modulus, and b be the Burgers vector.

[0171] Step 44: Based on the relative creep rate of Ti80 alloy, extrapolate the creep rate of Ti80 alloy under the same service conditions by using the creep rate of Ti alloy under different temperatures and loads.

[0172] As a preferred example of the present invention, step S5 includes the following steps:

[0173] S51: A small program for generating Voronoi polycrystals using the Voronoi function language provided by the Scipy library in Python;

[0174] S52: Use the script interface of the finite element software to transfer the .py file of this program to the finite element simulation software, and directly generate Voronoi polycrystalline geometric models in batches within the finite element software, such as... Figure 14 As shown.

[0175] As a preferred example of the present invention, step S6 includes the following steps:

[0176] S61: Based on the polycrystalline model constructed in step 5, perform mesh generation on it;

[0177] S62: Based on the polycrystalline model constructed in step 5, set the temperature field, stress field, and boundary conditions;

[0178] S63: Using finite element simulation software ABAQUA or COMSOL, the creep service behavior of Ti80 alloy under different temperatures and loads was simulated, such as... Figure 15 As shown.

[0179] The above-described embodiments can overcome the shortcomings of the traditional "trial and error method" and save resources and time. This specific embodiment is an illustration of the method of the present invention in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any parameter changes or calculation simplifications made based on the principle of the technical solution of the present invention, as long as they meet the purpose of the invention, are within the protection scope of the present invention.

Claims

1. A method for predicting the creep life of an alloy using multi-scale coupling, characterized in that, Includes the following steps: S1: Construct the crystal structure of pure elements, the crystal structure of Ti-based binary alloys, and the crystal structure of Ti80 alloy from known databases or software packages; S2: Perform structural relaxation on the initial crystal structure to obtain its stable lattice constant; S3: Based on the stable lattice constant, the VASP calculation software is used to obtain its basic physical properties in the ground state, including elastic properties, stacking fault energy, and diffusion coefficient; S4: Using the CALPHAD method, the interaction parameters between alloying elements were fitted to obtain the stacking fault energy and diffusion coefficient of Ti80 alloy. The relative creep rate model was used in combination with the creep behavior of pure Ti under different temperatures and loads to predict the creep behavior of Ti80 alloy under different temperatures and loads. In step S4, the stacking fault energy and diffusion coefficient of the multi-component alloy are calculated using the CALPHAD method according to Formula 15: (15) in, 0 φ The linear mixing of stacking fault energies in a pure elemental HCP structure; Δ φ To account for the excess portion of stacking fault energy due to the interactions between various alloying elements; Step S4 also includes the following steps: Step 41: The linear mixture component in the CALPHAD model is simulated and calculated according to Equation 16; (16) Step 42: The excess portion in the CALPHAD model is simulated using Equation 17; (17) Step 43: Based on the calculation results of the CALPHAD method, the creep rate of Ti80 alloy relative to Ti alloy is obtained using the relative creep rate model, and simulation calculation is performed using Equation 18: (18) Where τratio is the relative creep rate of Ti80 alloy relative to Ti alloy. ε Ti80合金 The creep rate of Ti80 alloy, ε Ti denoted as the relative creep rate of the Ti alloy. D eff The diffusion coefficient is... γ SFE For stacking fault energy, G Shear modulus E For Young's modulus, b It is the Burgers vector; Step 44: Based on the relative creep rate of Ti80 alloy, and combined with the creep rate of Ti alloy under different temperatures and loads, extrapolate the creep rate of Ti80 alloy under the same service conditions. S5: Based on the actual crystal phase structure of Ti80 alloy, a finite element polycrystalline numerical model is constructed using the Voronoi algorithm; S6: Based on the polycrystalline finite element numerical model, finite element calculation software is used to mesh the model, set the temperature field, stress field and boundary conditions, and simulate the creep service behavior of Ti80 alloy under different temperatures and loads.

2. The method for predicting alloy creep life using multi-scale coupling according to claim 1, characterized in that, In step S1, pure Ti has a hexagonal close-packed structure in the ground state. The crystal structure of pure Ti is constructed based on the Materials Project, OQMD, SprInger Materials, ICSD, and NIST databases. α Based on Ti, a 5×4×4 supercell was expanded, and then the near-α type Ti80 alloy crystal structure was constructed using the mcsqs module in ATAT software based on the quasi-random approximation method.

3. The method for predicting alloy creep life using multi-scale coupling according to claim 2, characterized in that, In step S2, the initial crystal structure is optimized based on the VASP software package, including the following steps: S21: First, set the parameters "ISIF=A1, IBRION=B1" to optimize the initial structure so that the energy and force of the crystal structure reach the convergence criterion; S22: Based on the optimized crystal structure, change the scaling factor and step size, and set the parameters "ISIF=A2, IBRION=B2" again to optimize the crystal structure again so that the energy and force of the crystal structure reach the convergence standard; S23: Based on the crystal structure under different scaling factors, set the parameters "IBRION=C, NSW=D, ISMEAR=E" to make the energy and force of the crystal structure reach the convergence standard; S24: Based on the energy-volume of each crystal structure under different scaling factors, the energy-volume solid state equation of state described in formula (1) is used to calculate the lattice constant, total energy of the ground state, and bulk modulus of each crystal structure. (1) Where A1, B1, A2, B2, C, D, and E are preset empirical parameters, V is the volume, and E(V) is the energy of the unit cell under different volumes.

4. The method for predicting alloy creep life using multi-scale coupling according to claim 1, 2, or 3, characterized in that, Step S3 includes the following steps: S31: Based on the crystal structure obtained in step S2, the elastic properties, including elastic constants, elastic modulus, and Poisson's ratio, are calculated using the stress-strain method. S32: Calculate stacking fault energy using the slab model; S33: The diffusion coefficient is obtained based on the Arrhenius diffusion model, and the diffusion coefficient is calculated according to formula (12); (12) in ，Q For diffusion activation energy, k B Boltzmann's constant, T For temperature.

5. The method for predicting alloy creep life using multi-scale coupling according to claim 4, characterized in that, Step S31 includes the following steps: Step 311: The second-order tensor of the elastic coefficient is obtained from the generalized Hooke's law shown in formula (2). Small strains are applied in different directions, and the stress tensor after applying small deformation is obtained by optimizing the atomic positions. Then, the elastic constants are obtained according to the stress-strain relationship. (2) in σ ij and ε kl These are the stress tensor and the strain tensor, respectively. C ij These are the elastic constants, and the hexagonal structure has a total of 5 independent elastic constants, namely... C 11 , C 33 , C 44 , C 66 , C 12 , C 13 ; Step 312: Based on the calculated elastic constants, the polycrystalline elastic modulus is calculated using the Voigt-Reuss-Hill approximation algorithm according to the formulas shown in (3)-(8): (3) (4) (5) (6) (7) (8) Where B is the bulk modulus and G is the shear modulus; Step 313: Calculate Young's modulus using an empirical model based on formulas (9) and (10). E Compared to Poisson; (9) (10) Where E is Young's modulus and ν is shear modulus.

6. The method for predicting alloy creep life using multi-scale coupling according to claim 4, characterized in that, Step S32 includes the following steps: S321: Calculate the generalized stacking fault energy according to formula (11). The generalized stacking fault energy is defined as the energy difference per unit area between the supercell containing stacking faults and the perfect unit cell, where the stacking fault vector u represents the distance moved by the upper half of the unit cell relative to the lower half when it slips. This vector starts from 0.

0. b Start with 0.1 b As the step size, move to 1.

0. b , b This is the Burgers vector during slip; (11) in, E(u) For vectors containing stacking faults u The supercell can always, E(0) For the energy of a perfect crystal lattice, A Represents the area of ​​stacking faults. γ SFE (u) For vectors containing stacking faults u Generalized stacking faults; S322: A vacuum layer is added above each model. During calculation, the atoms in the upper layer move relative to the atoms in the lower layer along the slip direction.

7. The method for predicting alloy creep life using multi-scale coupling according to claim 4, characterized in that, Step S33 includes the following steps: S331: The diffusion of alloying elements in the HCP structure considers two different diffusion directions, namely the diffusion coefficient parallel to the c-axis calculated according to formula (13). D || And the diffusion coefficient perpendicular to the c-axis is calculated according to formula (14). D ⊥ ; (13) (14) in C || and C ⊥ Parallel to c axis and perpendicular to c The diffusion pre-factor of the axis, c The concentration of alloying elements. f Bz , f Ax , f Bx For jump correlation factor, w A , w B These are the jump frequencies in directions A and B, respectively.

8. The method for predicting alloy creep life using multi-scale coupling according to claim 1, characterized in that, Step S5 includes the following steps: S51: A small program for generating Voronoi polycrystals using the Voronoi function language provided by the Scipy library in Python; S52: Use the script interface of the finite element software to transfer the py file of the program in step S51 to the finite element simulation software, and directly generate Voronoi polycrystalline geometric models in batches in the finite element software. Step S6 includes the following steps: S61: Based on the polycrystalline model constructed in step 5, perform mesh generation on it; S62: Based on the polycrystalline model constructed in step 5, set the temperature field, stress field, and boundary conditions; S63: The creep service behavior of M alloy under different temperatures and loads is simulated using finite element simulation software ABAQUA or COMSOL.

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