A calculation method for elastic modulus of multi-component and multi-phase alloys and a composition design method

Abstract

The present invention discloses a method for calculating the elastic modulus of a multi-component multiphase alloy, comprising the following steps: 1) constructing a special quasi-random structure of a solid solution in an alloy using a Monte Carlo model; 2) calculating the variation of the thermal expansion coefficient of each component phase of the alloy with temperature using a quasi-harmonic approximation method, and obtaining the lattice constant of each component phase at different temperatures; 3) calculating the variation of the phase fraction of each component phase in the alloy with temperature using a CALPHAD method; 4) calculating the elastic constants of each component phase at different temperatures using first principles, obtaining the elastic constants of the multi-component multiphase alloy at a finite temperature based on a multi-component multiphase alloy elastic modulus calculation model, and obtaining the elastic modulus of the multi-component multiphase alloy through numerical processing. The present invention also discloses a method for designing the composition of a multi-component multiphase alloy, wherein, given an alloy system, the multi-component multiphase alloy elastic modulus calculation model is used to obtain the relationship between the variation of the alloy elastic modulus with temperature and composition, and to screen out an alloy composition that meets the design requirements of the alloy elastic modulus.

Description

Technical Field

[0001] The present invention relates to the technical field of alloy material calculation and design, and in particular to a method for calculating the elastic modulus of a multi-component and multi-phase alloy and a method for designing its composition. Background Art

[0002] The mechanical properties of alloy materials primarily refer to their macroscopic properties, such as elastic properties (elastic modulus, shear modulus, Poisson's ratio, etc.), plastic properties (yield strength, elongation, etc.), and hardness. They serve as the primary basis for material selection in the design of various engineering structures. A range of internal and external factors, including the material's chemical composition, crystal lattice, grain size, external forces (static, dynamic, impact, etc.), temperature, and processing methods, all influence the mechanical properties of alloy materials.

[0003] Elastic modulus is the most important macroscopic property among the mechanical properties of alloy materials, and usually refers to the resistance of an object or substance to elastic deformation. Experimentally, the elastic modulus is defined as the slope of the stress-strain curve of an object in the elastic deformation region. The harder the material, the higher the elastic modulus. In addition, the deformation amount generated by the force on the object in different directions is combined into a matrix according to different degrees of freedom, which is the elastic constant. The elastic constant can be used to obtain not only the elastic modulus of the material, but also its plastic properties, elongation and other related mechanical indicators. Therefore, conducting research on the elastic modulus of alloys is of great significance to the development of alloy materials with excellent mechanical properties.

[0004] Currently, the calculation of elastic modulus of multi-component and multi-phase alloys mainly includes finite element simulation, geometric method and empirical formula method.

[0005] (1) The rationality of model construction and the density of mesh division in the finite element simulation method have a great influence on the actual results. In addition, there are many factors that affect the elastic modulus of the alloy, such as solid solubility and temperature, which cannot be taken into account one by one in the finite element simulation.

[0006] In addition, the finite element simulation method is affected by the alloy composition and alloy phase composition, and the same method or model cannot be transplanted on a large scale. These are the limitations of finite element simulation.

[0007] (2) The geometric method is to simply superimpose the elastic moduli of different phases in the alloy after calculation, that is, when two phase alloy materials are connected in series: E c =E a V a +E b V b ; When two-phase alloys are connected in parallel: Among them E a , E b , E c are the alloy phases a, b and the elastic modulus of the alloy, Va , V b are the volume fractions of alloy phases a and b, respectively, and V a +V b =1.

[0008] When the geometric method is applied to two-phase alloys, although the numerical results of the elastic modulus are relatively close to the experimentally measured results, previous studies have shown that when dealing with alloys with three or more phases, the calculated results deviate greatly from the experimentally measured results. In addition, the phases in actual alloy materials are not simply in parallel or series. The orientations of the grains are different and they are in a random and disordered state, which cannot be simplified by parallel or series connection. In addition, the empirical formula method requires a large number of experiments to establish an empirical calculation formula for the elastic modulus of a specific alloy system through regression equations. Although this method has a certain degree of calculation accuracy, it requires a large number of experiments, and the obtained empirical formula is only valid for a specific alloy system and cannot be applied to other alloy systems.

[0009] In summary, neither the finite element method, the geometric method nor the empirical formula method can effectively solve the problem of calculating the elastic modulus of multi-component and multi-phase alloys.

[0010] Traditionally, when designing materials, the main method used is trial and error to obtain alloy materials that meet the mechanical property requirements. That is, casting alloys are prepared by smelting, and then related subsequent processing processes are used to obtain alloy materials that meet the design requirements. However, the trial and error method has a long cycle and is subject to a series of influencing factors such as the environment and process in the material preparation project. This greatly affects the efficiency of new material design and increases the R&D cost of alloy materials.

[0011] First-principles calculations require only crystal structure information as input, without requiring any other experimental, empirical, or semi-empirical parameters, and are highly portable. However, the following challenges remain when using first-principles methods to calculate the elastic modulus of alloys for alloy composition design:

[0012] (1) Calculations based on first principles are usually performed at 0K without considering the effect of temperature. However, alloys are usually used at a finite temperature in practice. Therefore, considering the effect of temperature on the elastic modulus is of great significance for material research and development.

[0013] (2) Elastic modulus calculations based on first principles usually use primitive cells or supercells as raw data, only considering the most primitive structural factors and ignoring the solid solubility problem in actual alloys. Therefore, the introduction of solid solubility issues in first principles calculations is crucial for alloy composition design;

[0014] (3) At present, the first-principles calculation uses the single-phase crystal structure as the original data, and the elastic modulus obtained is also the calculation result of the single phase. However, the actual alloy is usually a multi-phase alloy composed of multiple alloying elements. Therefore, it is urgent to develop a calculation method for the elastic modulus of multi-component and multi-phase alloys based on the first-principles calculation of the elastic modulus of single-phase alloys.

[0015] Based on the first principles and phase diagram calculation method, the above problems can be solved and the composition design of high modulus multi-component and multi-phase alloys can be guided. In actual industrial production, it can greatly reduce the composition design cost of new alloy materials, improve the R&D efficiency of enterprises, and has broad application prospects. Summary of the Invention

[0016] The technical problem to be solved by the present invention is: the present invention provides a method for calculating the elastic modulus of a multi-component and multi-phase alloy and a method for designing the alloy composition, which can effectively improve the efficiency of alloy material design and reduce production costs.

[0017] In order to solve the above technical problems, the technical solution proposed by the present invention is:

[0018] A method for calculating the elastic modulus of a multi-component multi-phase alloy, comprising the following steps:

[0019] Step a, constructing a special quasi-random structure of the solid solution in the alloy using the Monte Carlo model;

[0020] Step b, using a quasi-harmonic approximation method to calculate the relationship between the thermal expansion coefficient of each component phase of the alloy and the temperature, and obtain the lattice constant of each component phase at different temperatures;

[0021] Step c, calculating the relationship between the phase fraction of each component phase in the alloy and the temperature using the CALPHAD method;

[0022] Step d: Construct a calculation model for the elastic modulus of multi-component and multi-phase alloys:

[0023]

[0024] where φ α is the phase fraction, is the elastic constant of the constituent phase, C ij is the elastic constant of the multiphase alloy material;

[0025] Calculate the elastic constants of each phase at different temperatures using first principles The elastic constants of each component phase and phase fraction φ α Substituted into the elastic modulus calculation model of multi-component multiphase alloy, the elastic constant C of the multi-component multiphase alloy at finite temperature is obtained ij ;

[0026] Step e, the elastic constant C of the multiphase alloy material obtained in step d ij Numerical processing is performed to obtain the elastic modulus of the alloy.

[0027] Preferably, in step a, the solubility of the solid solution in the alloy constituent phase is less than or equal to the solubility in the actual alloy phase.

[0028] Preferably, in step b, the crystal structure of each component phase is first optimized with high precision, and then calculated using the quasi-harmonic approximation method.

[0029] Preferably, in step d, the step of constructing a calculation model for the elastic modulus of a multi-component multi-phase alloy is:

[0030] (1) Obtaining the phase fractions of each component phase at different temperatures according to step c;

[0031] (2) Obtaining the inverse matrix of the elastic constants of each constituent phase according to step b;

[0032] (3) The phase fraction of each component phase is summed with the product of the inverse matrix of the elastic constant at the corresponding temperature, and then the matrix is ​​inversely transformed to obtain the elastic modulus calculation model of the multi-component multi-phase alloy.

[0033] The present invention also provides a multi-component multi-phase alloy composition design method, which designs the alloy composition based on the above-mentioned elastic modulus calculation method, comprising the following steps:

[0034] Step 1) selecting an alloy system that can meet the elastic modulus design requirements through alloying methods;

[0035] Step 2) Given an alloy system, a multi-component and multi-phase alloy elastic modulus calculation model is used to obtain the relationship between the alloy elastic modulus and temperature and composition, and to select an alloy composition that meets the alloy elastic modulus design requirements.

[0036] The calculation method of the elastic modulus of a multi-component multi-phase alloy and the composition design method provided by the present invention have the following advantages over the prior art:

[0037] The method for calculating the elastic modulus of a multi-component, multi-phase alloy and the method for designing its composition of the present invention are based on first principles and quasi-harmonic approximation, coupled with a phase diagram calculation method. The elastic modulus of the multi-component, multi-phase alloy can be obtained solely through calculation and used for composition design. The effects of solid solubility and temperature on the elastic modulus of the alloy material are introduced, thereby improving the calculation accuracy. The problems of traditional experimental methods and trial-and-error methods in designing high-modulus alloys, such as long cycles and high production costs, and harsh environmental requirements during the alloy preparation process, are overcome. The method can effectively improve the efficiency of alloy material design, reduce production costs, and widely guide the design of alloy compositions related to the mechanical properties of materials in industrial production. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flowchart for calculating the elastic modulus of multi-component and multi-phase alloys and a comparison chart between the calculated results and the experimental results.

[0039] Figure 2(a) is a diagram of the crystal structure of pure Mg in a 4×4×4 supercell.

[0040] FIG2( b ) is a crystal structure diagram of a 384-atom Mg-9.375 at. % Al solid solution.

[0041] Figure 2(c) is Mg 17 Al 12 Crystal structure diagram.

[0042] Figure 2(d) is a diagram of the crystal structure of Mg2Si.

[0043] Figure 3(a) shows the thermal expansion coefficient of pure Mg as a function of temperature, and the inset shows the nuclear MH free energy as a function of volume.

[0044] Figure 3(b) shows the change of unit cell volume of pure Mg with temperature.

[0045] Figure 3(c) shows the change of elastic modulus of pure Mg with temperature.

[0046] Figure 4(a) shows the thermal expansion coefficient of the Mg-9.375at.%Al solid solution as a function of temperature, and the inset shows the core Hertz free energy as a function of volume.

[0047] FIG4( b ) is a graph showing the change in unit cell volume of Mg-9.375 at. % Al solid solution with temperature.

[0048] FIG4( c ) is a graph showing the change in unit cell volume of Mg-9.375 at. % Al solid solution with temperature.

[0049] Figure 5(a) is Mg 17 Al 12 The thermal expansion coefficient of the nucleus varies with temperature, and the inset shows the nuclear MH free energy as a function of volume.

[0050] Figure 5(b) is Mg 17 Al 12 The plot of the unit cell volume changing with temperature.

[0051] Figure 5(c) is Mg 17 Al 12 Variation of elastic modulus with temperature.

[0052] Figure 6(a) shows the thermal expansion coefficient of Mg2Si as a function of temperature, and the inset shows the nuclear M-H free energy as a function of volume.

[0053] Figure 6(b) shows the change of the unit cell volume of Mg2Si with temperature.

[0054] Figure 6(c) shows the change of elastic modulus of Mg2Si with temperature.

[0055] Figure 7 This is a graph showing the change in the fraction of each component phase of the Mg87.81Al8.27Si3.92 (at.%) alloy with temperature calculated using the CALPHAD method.

[0056] Figure 8 This is a comparison chart of the calculated and experimental results of the elastic modulus of Mg87.81Al8.27Si3.92 (at.%) alloy.

[0057] Figure 9 This is the correspondence diagram between the calculated elastic modulus of the 623.15KMg-Al-Si system and the alloy composition. DETAILED DESCRIPTION

[0058] The following is a detailed description of the specific embodiments of the present invention. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0059] Figures 1 to 8 An embodiment of the method for calculating the elastic modulus of a multi-component multi-phase alloy of the present invention is shown, which specifically includes the following steps:

[0060] Step a, using Monte Carlo model to construct the solid solubility (S s ) phase with a special quasi-random structure (SQS).

[0061] The special quasi-random structure is achieved by adjusting the arrangement of some atoms in the supercell and making the atomic arrangement within a certain distance range as close as possible to the actual crystal through the correlation function, thereby simulating the random process of atomic substitution in the solid solution by constructing a supercell.

[0062] The solid solubility is less than or equal to the solid solubility in the actual alloy phase, and the closer it is to the solid solubility in the actual alloy, the higher the accuracy.

[0063] In step b, the crystal structure of each component phase is first optimized with high precision. This involves performing structural relaxation on the crystal structure after normal geometric optimization, adjusting the convergence precision of energy and force to avoid imaginary frequencies. The temperature dependence of the thermal expansion coefficient of each alloy component phase is calculated using the quasi-harmonic approximation to obtain the lattice constants of each component phase at different temperatures.

[0064] Introducing the influence of temperature on the elastic modulus of alloy materials improves the calculation accuracy and helps to obtain the relationship between the elastic modulus of alloy materials and temperature, guiding the design of material composition so that its elastic modulus can meet the service requirements of different temperatures.

[0065] Step c, calculate the phase fraction (φ α ) changes with temperature (T).

[0066] The thermodynamic database is obtained by thermodynamically optimizing the alloy phase diagram, thereby obtaining the phase fraction of each component phase in the alloy.

[0067] Step d: Obtain the phase fractions of each component phase at different temperatures according to step c, and obtain the inverse matrix of the elastic constants of each component phase according to step b; sum the products of the phase fractions of each component phase and the inverse matrix of the elastic constants at the corresponding temperature, and then perform an inverse transformation of the matrix; and obtain a calculation model for the elastic modulus of a multi-component multiphase alloy.

[0068] Calculation model of elastic modulus of multi-component and multi-phase alloys:

[0069]

[0070] where φ α is the phase fraction, is the elastic constant of the constituent phase, C ij is the elastic constant of the multiphase alloy material, and the elastic constants of each component phase at different temperatures are calculated using the first principle. The elastic constants of each component phase and phase fraction φ α Substituted into the elastic modulus calculation model of multi-component multiphase alloy, the elastic constant C of the multi-component multiphase alloy at finite temperature is obtained ij .

[0071] Step e, the elastic constant C of the multiphase alloy material obtained in step d ij The elastic modulus of the alloy can be obtained by numerical processing.

[0072] Elastic constant C ij There are several ways to perform numerical processing:

[0073] Assume B is the bulk modulus, G is the shear modulus, E is the Young's modulus, v is the Poisson's ratio, and B V is the Voigt bulk modulus, B R is the Reuss modulus, G V is the Voigt shear modulus, G R is the Reuss shear modulus, and has the following relationship:

[0074] B=1 / 2(BV +B R ), G=1 / 2(G V +G R ), E=9BG / (3B+G), v=(3B-2G) / [2(3B+G)]

[0075] (1) When C ij When the cubic crystal criterion is met,

[0076] B V =B R =1 / 3(C 11 +2C 12 )

[0077] G V =(C 11 -C 12 +3C 44 ) / 5,

[0078] G R =(5(C 11 -C 11 )C 44 ) / [4C 44 +3(C 11 -C 12 )]

[0079] (2) When C ij When the hexagonal crystal criterion is met,

[0080] B V =1 / 9[2(C 11 +C 12 )+4C 13 +C 33 ]

[0081] B R =((C 11 +C 12 )C 33 -2C 13 2 ) / (C 11 +C 12 +2C 33 -4C 13 )

[0082] G V =1 / 30(C 11 +C 12 +2C 33 -4C 13 +12C 44 +12C 66 )

[0083] G R=5 / 2[(C 11 +C 12 )C 33 -2C 13 2 ) 2 C 44 C 66 / (3B V C 44 C 66 +(C 11 +C 12 )C 33 -2C 13 2 ) 2 (C 44 +C 66 )]

[0084] (3) When C ij When the orthorhombic crystal criterion is met,

[0085] B V =1 / 9[C 11 +C 22 +C 33 +2(C 12 +C 13 +C 23 )]

[0086] B R =Δ[C 11 (C 22 +C 33 -2C 23 )+C 22 (C 33 -2C 13 )-2C 33 C 12 +C 12 (2C 23 -C 12 )+C 13 (2C 12 -C 13 )+C 23 (2C 13 -C 23 )] -1

[0087] G V =1 / 15[C 11 +C 22 +C 33 +3(C 44 +C 55 +C 66 )-(C 12 +C 13 +C 23 )]

[0088]

[0089] Δ=C 13 (C 12 C 23 -C 13 C 22 )+C 23 (C 12 C 13 -C 23 C 11 )+C 33 (C 11 C 22 -C 12 2 )

[0090] (4) When C ij When the tetragonal crystal criterion is met,

[0091] B V =1 / 9[2(C 11 +C 22 )+C 33 +4C 13 )]

[0092] B R =C 2 / M

[0093] G V =1 / 30(M+3C 11 -3C 12 +12C 44 +6C 66 )

[0094] G R =15[18B V / C 2 +6 / (C 11 -C 12 )+6 / C 44 +3 / C 66 ] -1

[0095] M=C 11 +C 12 +2C 33 -4C 13

[0096] C 2 =(C 11 +C 12 )C 33 -2C 13 2

[0097] (5) When C ij When the monoclinic crystal criterion is met,

[0098] B V =1 / 9[C 11 +C 22 +C 33 +2(C 12 +C 13 +C 23 )]

[0099]

[0100] G V =1 / 15[C 11 +C 22 +C 33 +3(C 44 +C 55 +C 66 )-(C 12 +C 13 +C 23 )]

[0101]

[0102] a=C 33 C 55 -C 33 2

[0103] b=C 23 C 55 -C 25 C 35

[0104] c=C 13 C 35 -C 15 C 33

[0105] d=C 13 C 55 -C 15 C 35

[0106] e=C 13 C 25 -C 15 C 23

[0107] f=C 11 (C 22 C 55 -C 25 2 )-C 12 (C 12 C55 -C 15 C 25 )+C 15 (C 12 C 25 -C 15 C 22 )+C 25 (C 23 C 35 -C 25 C 33 )g=C 11 C 22 C 33 -C 11 C 23 2 -C 22 C 13 2 -C 33 C 12 2 +2C 12 C 13 C 23

[0108] Ω=2[C 15 C 25 (C 33 C 12 -C 13 C 23 )+C 15 C 35 (C 22 C 13 -C 12 C 23 )+C 25 C 35 (C 11 C 23 -C 12 C 13 )]-[C 15 2 (C 22 C 33 -C 23 2 )+C 25 2 (C 11 C 33 -C 13 2 )+C 35 2 (C 11 C 22 -C 12 2 )]+gC 55

[0109] The present invention also provides a multi-component multi-phase alloy composition design method, which is performed according to the elastic modulus calculation method described above, comprising the following steps:

[0110] Step 1) Filtering out structural phases with high elastic modulus by calculating the elastic modulus of the structural phases, and determining an alloy system that can achieve the elastic modulus design requirement through an alloying method based on the high modulus structural phases;

[0111] Step 2) Use first principles and quasi-harmonic approximation methods to calculate the relationship between the elastic modulus of the alloy constituent phases (including the solid solution phase) and temperature, and use the multi-component multiphase alloy elastic modulus calculation model to obtain the relationship between the alloy elastic modulus and temperature and composition, and determine the alloy composition and temperature that meet the alloy elastic modulus design requirements.

[0112] Taking Mg-Al-Si alloy as an example, a composition range of Mg alloy with an elastic modulus higher than 60 GPa at a temperature of 623.15 K is designed. The calculation method of the elastic modulus and the composition design method of the multi-component multi-phase alloy of the present invention are described.

[0113] 1. Experimental samples

[0114] 1) Using a tray balance, 52.7194 g of Mg particles with a purity of 99.99% (based on 2% melting loss), 2.4186 g of Al particles, and 6.3975 g of Si particles were weighed. They were melted in a vacuum induction melting furnace and poured into a mold with a diameter of 30 mm and a height of 100 mm. After cooling, the mold was sealed with a quartz glass tube and homogenized at 673 K for 30 days. Then, the mold was cold-water quenched. The alloy composition was determined by EPMA to be Mg87.81Al8.27Si3.92 (at.%).

[0115] 2) After the sample was processed into a size of 10×20×60 mm, the experimental value of its elastic modulus changing with temperature was tested using ultrasonic excitation method under argon atmosphere.

[0116] 2. Calculation of elastic modulus

[0117] Step a, through the first principle calculation, it is known that the elastic modulus of Mg2Si at 0K is 104GPa, which is much larger than the design requirement of 60GPa, indicating that the Mg-Al-Si alloy that meets the design requirements can be obtained by adjusting the content of Mg2Si phase in the alloy. From the alloy phase diagram, it can be seen that at room temperature, the Mg87.81Al8.27Si3.92 (at.%) alloy consists of Mg-Al solid solution + Mg2Si + Mg 17 Al 12It consists of three phases, which transform into a Mg-Al solid solution + Mg2Si two-phase region at 660K as the temperature increases. Al has a high solid solubility in the Mg matrix, reaching a maximum of 11.85 at.%, which decreases significantly with decreasing temperature, reaching 9.89 at.% Al at 673K ​​and approximately 2.0 at.% Al at room temperature. Based on the SQS solid solution structural phase design principle, a 4×4×4 supercell was expanded based on the pure Mg crystal structure. Using a special quasi-random structural model, 36 Mg atoms were replaced with Al atoms, resulting in a Mg-Al solid solution phase with a solid solubility of 9.375 at.%, as shown in Figure 2(a).

[0118] Step b, construct pure Mg, Mg without solid solubility 17 Al 12 The crystal structure models of the Mg2Si phase are shown in Figures 2(b), 2(c) and 2(d).

[0119] Step c: Calculate the relationship between the thermal expansion coefficient of each component phase and the temperature (T).

[0120] The quasi-harmonic approximation was used to calculate the relative abundance of pure Mg, Mg-9.375at.%Al solid solution phase, Mg 17 Al 12 The relationship between the thermodynamic properties and elastic modulus of the Mg2Si phase and the temperature is shown in Figures 3, 4, 5, and 6. As can be seen from the figure, as the temperature increases, the lattice expansion of each component phase occurs, and the unit cell volume increases with the increase of temperature. 17 Al 12 phase is more significant; in addition, with the increase of temperature, the elastic modulus gradually decreases, especially for Mg-9.375at.%Al solid solution and Mg 17 Al 12 Comparing the relationship between the elastic modulus of pure Mg and Mg-9.375at.%Al solid solution phase and temperature, we can see that the solid solution atoms have a good strengthening effect at low temperatures, but at the same time, the change of the solid solution phase with temperature is more significant. At the same time, in the calculation process, we can obtain the elastic constants of each phase at different temperatures.

[0121] The convergence test determined that pure Mg, Mg-9.375at.%Al solid solution, Mg 17 Al 12The cutoff energies of Mg2Si and Mg2Si were 420 eV, 440 eV, 400 eV, and 520 eV, respectively. The crystal structure was optimized using the generalized gradient approximation functional (GGA). The interaction potential between electrons and ions was simulated using ultrasoft pseudopotentials. The K point of the first Brillouin zone was determined using the Monkhorst-Pack method, and the structure was optimized using the Brodyden-Fletcher-Goldfarb-Shanno (BFGS) minimization method. The convergence criterion for geometry optimization was: the energy of the self-consistent iteration was 1.0 × 10 -6 eV / atom; the convergence criterion for the interatomic interaction force is The energy convergence criterion for phonon general optimization is 1.0×10 -8 eV / atom, and the finite displacement method is used to calculate the phonon spectrum.

[0122] Step d, calculate the phase fraction (φ) of each component of Mg87.81Al8.27Si3.92 (at.%) alloy by CALPHAD phase diagram calculation method. α ) changes with temperature, such as Figure 7 As shown. At low temperature, the alloy consists of Mg-Al solid solution, Mg 17 Al 12 and Mg2Si three-phase composition, with the increase of temperature, the Mg-Al solid solution fraction gradually increases, while Mg2Si and Mg 17 Al 12 The phase fraction gradually decreases and transforms into a two-phase region consisting of Mg-Al solid solution and Mg2Si at 660K.

[0123] Step e: Substitute the calculation results of steps c and d into the elastic modulus calculation model of multi-component and multi-phase alloys:

[0124]

[0125] Get as Figure 8 The elastic modulus of Mg87.81Al8.27Si3.92 (at.%) alloy changes with temperature without considering solid solution (pentagram line) and considering solid solution (triangle line).

[0126] Figure 8 As shown, the experimental values ​​of the elastic modulus at low temperatures (300-450K) (represented by circles) agree with the calculated values ​​(represented by stars) without considering solid solubility. At high temperatures (600-700K), the experimental values ​​(represented by circles) agree with the calculated values ​​(represented by triangles) considering a solid solubility of 9.375 at. % Al. This is because the alloy has a lower solid solubility at low temperatures and a higher solid solubility at high temperatures. Comparing the calculated and experimental values ​​demonstrates the accuracy of the present method for calculating the elastic modulus of multi-component, multi-phase alloys.

[0127] 3. Alloy composition design

[0128] According to the calculation steps of the elastic modulus calculation method of multi-component multiphase alloy, the elastic constants of each component phase (Mg), (Al), (Si), Mg2Si, βMgAl, εMgAl and γMgAl of the Mg-Al-Si alloy system at 623.15K are calculated and obtained as follows: Figure 9 The corresponding diagram of the elastic modulus and alloy composition of the 623.15KMg-Al-Si alloy shown in the figure. It can be seen from the figure that the elastic modulus of the Mg-Al-Si alloy decreases with the increase of Mg, with a minimum of 36.502Gpa, and increases with the increase of Si, with a maximum of 147.191Gpa. The alloy composition design requires that the elastic modulus of the 623.15K alloy is greater than 60Gpa, so a plane parallel to the bottom surface is made at 60Gpa. The composition where the plane and the curved surface intersect is the limit composition that meets the design requirements, and considering that the Mg alloy composition should be based on (Mg), combined with the phase composition of the Mg-Al-Si alloy phase diagram at the 623.15K isothermal section, the alloy composition is determined to be Mg. x Al y Si 1-x-y (where 0.67≤x≤0.87, 0<y≤0.87-x) can meet the composition design requirement that the elastic modulus of 623.15K alloy is greater than 60GPa.

[0129] The alloy composition design method of the present invention illustrates the change in the elastic modulus of an alloy with temperature within a certain composition range, and can clearly obtain a one-to-one correspondence between the elastic modulus of the alloy, the alloy composition, and the temperature. By giving the elastic modulus requirements required for composition design, it is possible to screen out alloy compositions that meet the requirements and efficiently complete the alloy composition design.

[0130] The above examples are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, they are not intended to limit the present invention. Therefore, any simple modifications, equivalent variations, and modifications to the above examples that do not depart from the technical solution of the present invention and are based on the technical essence of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for calculating the elastic modulus of a multi-component multi-phase alloy, characterized in that: The calculation method of the elastic modulus comprises the following steps: Step a, constructing a special quasi-random structure of the solid solution in the alloy using the Monte Carlo model; Step b, using a quasi-harmonic approximation method to calculate the relationship between the thermal expansion coefficient of each component phase of the alloy and the temperature, and obtain the lattice constant of each component phase at different temperatures; Step c, calculating the relationship between the phase fraction of each component phase in the alloy and the temperature using the CALPHAD method; Step d: Construct a calculation model for the elastic modulus of multi-component and multi-phase alloys: where φ α is the phase fraction, is the elastic constant of the constituent phase, C ij is the elastic constant of the multi-component multiphase alloy; Calculate the elastic constants of each phase at different temperatures using first principles The elastic constants of each component phase and phase fraction φ α Substituted into the elastic modulus calculation model of multi-component multiphase alloy, the elastic constant C of the multi-component multiphase alloy at finite temperature is obtained ij ; Step e, the elastic constant C of the multiphase alloy material obtained in step d ij Numerical processing is performed to obtain the elastic modulus of the alloy.

2. The method for calculating the elastic modulus of a multi-component multi-phase alloy according to claim 1, wherein: In the step a, the solubility of the solid solution in the alloy constituent phase is less than or equal to the solubility in the actual alloy phase.

3. The method for calculating the elastic modulus of a multi-component multi-phase alloy according to claim 1, wherein: In the step b, the crystal structure of each component phase is first optimized with high precision, and then calculated using the quasi-harmonic approximation method.

4. The method for calculating the elastic modulus of a multi-component multi-phase alloy according to claim 1, wherein: In the step d, the steps of constructing a multi-element multi-phase alloy elastic modulus calculation model are: (1) Obtaining the phase fractions of each component phase at different temperatures according to step c; (2) Obtaining the inverse matrix of the elastic constants of each constituent phase according to step b; (3) The phase fraction of each component phase is summed with the product of the inverse matrix of the elastic constant at the corresponding temperature, and then the matrix is ​​inversely transformed to obtain the elastic modulus calculation model of the multi-component multi-phase alloy.

5. A multi-component multi-phase alloy composition design method, characterized in that: The design of alloy composition based on the calculation method of elastic modulus according to any one of claims 1 to 4 comprises the following steps: Step 1) selecting an alloy system that can meet the elastic modulus design requirements through alloying methods; Step 2) Given an alloy system, a multi-component and multi-phase alloy elastic modulus calculation model is used to obtain the relationship between the alloy elastic modulus and temperature and composition, and to select an alloy composition that meets the alloy elastic modulus design requirements.

Images