A phase field model of complex phase structure transformation based on dislocation theory

Abstract

The application is a phase field model of complex phase structure transformation based on the theory of stacking fault, comprising the following steps: establishing a sublattice free energy model of complex phase structure according to the thermodynamic parameters of the alloy, and thermodynamically describing the alloy system; establishing a stress-strain model of phase transformation according to the stacking fault theory and the phase structure transformation in the alloy, and solving the elastic strain energy of the alloy system; establishing a phase field evolution equation related to the composition and order parameter; setting appropriate initial parameters, solving the phase field equation to obtain the evolution results of the composition field and the order parameter field of the alloy with time and space, and drawing visual images; and analyzing the microstructure evolution diagram of each precipitated phase of the alloy with time. The application provides a phase field model of complex phase structure transformation based on the theory of stacking fault, and the method can predict the process of phase transformation or decomposition of the alloy strengthening phase at high temperature for a long time.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of material microstructure control, and particularly to a phase field model of complex phase structure transformation based on a dislocation theory. BACKGROUND

[0002] High-temperature alloy is an alloy system for service above 600℃, which has excellent high-temperature performance such as oxidation resistance, high-temperature strength and fatigue resistance, and is widely used in aerospace, gas turbine wheel and chemical industry. In high-temperature alloy, many complex phases often exist at the same time, which can be directly observed from the alloy phase diagram. There are a large number of three-phase coexistence zones and the like in the alloy, and these phases have different complex structures and different effects on the high-temperature performance of the alloy. For example, in a cobalt-based high-temperature alloy, after aging at 900℃ for a long time, the precipitated phases in the alloy include γ' phase, χ phase and β phase, and μ phase also exists at 1000℃. Among them, only the γ' phase is a strengthening phase, which has a strengthening effect on the high-temperature performance of the alloy, and other precipitated phases will cause the performance of the cobalt-based high-temperature alloy to deteriorate in a high-temperature service environment, thereby affecting the service life and safety.

[0003] Domestic and foreign experts have conducted a large number of studies on the long-time aging stable phase of high-temperature alloy at high temperature. For example, Zhu L L, Wei C D, Qi H Y, Jiang L, Jin Z P, Zhao J C. Experimental investigation of phase equilibria in the Co-rich part of the Co-Al-X(X=W, Mo, Nb, Ni, Ta) ternary systems using diffusion multiples[J]. Journal of Alloys and Compounds, 2017, 691: 110-118. This document uses experimental methods to prepare diffusion couples of Co single element, W single element and CoAl alloy, and studies the equilibrium phase composition of Co-Al-W ternary alloy at 900℃. It is found that the face-centered cubic structure γ' phase is not a stable phase, and the close-packed hexagonal structure χ phase and body-centered cubic structure β phase can stably exist.

[0004] It is worth noting that in nickel-based, cobalt-based and high-entropy high-temperature alloy alloys, the best performance can only be exhibited when the matrix phase and the strengthening phase coexist, but when actually put into use, long-term aging under high-temperature service environment will cause the strengthening phase to be excessively coarse, unstable decomposition or phase transition to produce complex structure precipitated phase. However, in experimental research, it is difficult to obtain intuitive and continuous process when observing the phase transition of the strengthening phase of the alloy at high temperature, and therefore it is difficult to understand the nature of the phase transition process, such as the phase transition driving force, the migration direction of the alloying element, the phase transition rate and the like. Therefore, it is very advantageous to establish a phase field model of complex phase structure transition based on the dislocation theory to study the unstable phase transition process of the strengthening phase of the high-temperature alloy. At the same time, the existing simulation methods do not consider the thermodynamic model of the complex phase structure coupled with the sublattice model and the elastic energy model of the complex structure transition based on the dislocation, and therefore it is very necessary to establish a phase field model of complex phase structure transition based on the dislocation theory to study the unstable phase transition process of the strengthening phase of the high-temperature alloy. SUMMARY

[0005] The technical problem solved by the present application is to provide a phase field model of complex phase structure transition based on the dislocation theory.

[0006] The technical solution for achieving the object of the present application is as follows:

[0007] A phase field model of complex phase structure transition based on the dislocation theory comprises the following steps:

[0008] Step 1: Establishing sublattice models of fcc face-centered cubic and hcp close-packed hexagonal structures according to the thermodynamic parameters of the alloy, and thermodynamically describing the alloy system;

[0009] Step 2: Establishing a stress-strain model of structural phase transition according to the dislocation theory and the phase structure transition of the alloy, and solving the elastic strain energy of the alloy system;

[0010] Step 3: Establishing a phase field dynamics equation related to the composition and order parameter in combination with the system free energy of the alloy;

[0011] Step 4: Setting appropriate physical parameters of the alloy and input parameters of the simulation system, solving the dynamics equation, drawing the microstructure morphology diagram and the composition evolution diagram according to the solving data, and analyzing the microstructure evolution characteristics and the dynamics evolution law of the alloy multiple precipitated phases.

[0012] Compared with the prior art, the present application has the following significant advantages:

[0013] The method quantitatively describes the chemical free energy of the alloy by combining the phase field method and the sublattice model, and establishes a stress-strain model of structural phase transition according to the dislocation theory and the phase structure transition of the alloy to describe the elastic energy of the alloy, which can not only describe the system free energy of the ternary high-temperature alloy, but also describe the system free energy of the multi-phase high-temperature alloy, and provides a specific method for high-throughput phase field simulation of the alloy, and can more truly simulate the actual situation of the alloy. The kinetic evolution equation of the composition and order parameter of the high-temperature alloy is established, and the phase field model of the complex phase structure transition based on the dislocation theory is obtained. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 is a schematic diagram of the crystallography of the γ' phase of fcc structure and the χ phase of hcp structure on the (001) plane.

[0015] Figure 2 is a microstructure diagram of Co-8.25Al-10W (at.%) alloy, the grid size is 256Δx * ×256Δy * , the aging temperature is 1173K, wherein (a) the aging time is 1.25×10 3 , (b) the aging time is 1.45×10 3 , (c) the aging time is 3×10 3 , and (d) the aging time is 1.3×10 4 .

[0016] Figure 3 is the change of the area fraction of the γ' phase and the χ phase with the aging time of the Co-8.25Al-10W at.% alloy aged at 1173K.

[0017] Figure 4 is a process flow diagram of the present application. DETAILED DESCRIPTION

[0018] The present application will be further described below in conjunction with the drawings

[0019] A phase field model of complex phase structure transition based on dislocation theory. Comprising the following steps:

[0020] Step one: according to the thermodynamic parameters of the alloy, the sublattice model of fcc face-centered cubic and hcp close-packed hexagonal structure is established, and the thermodynamic description of the alloy system is carried out;

[0021] Step two: according to the dislocation theory and the phase structure transition of the alloy, a stress-strain model of structural phase transition is established to solve the elastic strain energy of the alloy system;

[0022] Step three: combine the system free energy of the alloy to establish the phase field dynamics equation related to the composition and order parameter;​

[0023] Step 4: Set appropriate alloy physical parameters and simulation system input parameters, solve the kinetic equations, draw microstructure diagrams and composition evolution diagrams based on the solution data, and analyze the microstructure evolution characteristics and kinetic evolution laws of various precipitates in the alloy.

[0024] The invention will be further described in detail below with reference to examples:

[0025] Take Co-Al-W alloy as an example.

[0026] In step one, sublattice models of the fcc face-centered cubic and hcp close-packed hexagonal structures are established based on the thermodynamic parameters of the alloy, and their thermodynamic descriptions are performed. ch =f(c i η) represents the chemical free energy density of the alloy, and its specific expression is as follows:

[0027]

[0028] c i Let be the concentration of the element, η be the order parameter used to characterize structural changes, and ω be the system free energy loss that prevents different phases from occupying the same spatial position. The placeholder fraction represents the probability of a component i being placed in the sublattice s.

[0029] The thermodynamic model of the χ phase is (Co,W)3(Al,Co,W). Al can only occupy position 2 in lattice, and its probability of occupying position 1 is... The occupancy probability of element W is 0, while the occupancy probability of element W is obtained by coupling the order parameter and concentration. Right now:

[0030]

[0031]

[0032] The thermodynamic model of the γ' phase is (Al,Co,W)3(Al,Co,W). The occupancy probabilities of Al and W elements are obtained by coupling order parameters and concentrations. Al occupies the face-centered position, i.e., lattice 1, while Co occupies the vertex position, i.e., lattice 2.

[0033]

[0034]

[0035] In step two, based on stacking fault theory and phase transformation of the alloy, a stress-strain model for structural phase transformation is established. Figure 1 It is between the FCC structure and the HCP structure. The stress-free strains between the γ / χ phases are respectively:

[0036]

[0037] q represents each element of the alloy. The elastic energy density expression of the alloy system is:

[0038]

[0039] wherein is the intrinsic strain, is the lattice dilatation coefficient.

[0040] In step three, the system free energy includes the chemical free energy f ch , the elastic energy f el and the gradient energy f grad , the gradient energy density expression is:

[0041] wherein β γ′γ , β χγ′ and β χγ are the structure-related gradient energy coefficients, k Al , k Co and k W are the composition-related gradient energy coefficients, and the gradient energy coefficients are functions of the interfacial energy.

[0042] In step three, the kinetic equations of the composition and order parameter evolution are:

[0043]

[0044]

[0045]

[0046]

[0047] M ij is the kinetic coefficient related to the element diffusion (i, j = Al, Co, W), which is related to the composition and the atomic mobility M i ; V m is the molar volume of the alloy. L m is the kinetic coefficient related to the structure evolution, which is used to adjust the precipitation rate of the diffusion-controlled precipitates. t is the simulation time, is the Hamiltonian operator, and the evolution equations are finally solved by the semi-implicit Fourier spectral method.

[0048] Step four, the initial composition is set to be Co-8.25Al-10W (at. %) alloy, and the calculation grid size is 256Δx* x 256 Ay * Figure 2 is a diagram of microstructure evolution of Co-8.25Al-10W (at.%) alloy at 1173 K, according to calculated values.

[0049] Figure 2 Figure 4 is a microstructure diagram of Co-8.25Al-10W (at.%) alloy at 1173 K, wherein (a) the aging time is 1.25 x 10 3 (b) the aging time is 1.45 x 10 3 (c) the aging time is 3 x 10 3 (d) the aging time is 1.3 x 10 4 It can be found from the figure that only γ' phase will appear in the alloy in the early stage of aging, but with the extension of aging time, the cubic and ordered γ' phase will be decomposed into the strip-shaped χ phase.

[0050] Figure 3 Figure 5 is a diagram of the area fraction of γ' phase and χ phase of Co-8.25Al-10W at.% alloy at 1173 K with the change of aging time. It can be seen from the figure that in the early stage of aging, the area fraction of γ' phase rises rapidly, reaches the maximum value and then begins to decline until the equilibrium. The change of the area fraction of χ phase is different, which is 0 in the early stage of aging, and increases to the equilibrium value with the extension of aging time. It shows that χ phase is precipitated after γ' phase, and the precipitation and growth of χ phase will make γ' phase dissolve and decompose. This can be used as a theoretical reference for design and application, and the microstructure design is optimized.

Claims

1. A phase field model of complex phase structure transformation based on the theory of stacking faults, characterized in that, The method comprises the following steps: Step one: establish sublattice model of fcc and hcp structure according to thermodynamic parameters of the alloy, and make thermodynamic description of the alloy system; Step two: establish stress-strain model of structure phase transition according to dislocation theory and phase structure transition of the alloy, and solve elastic strain energy of the alloy system; Step three: establish phase field kinetic equation related to composition and order parameter in combination with free energy of the alloy system; Step four: set appropriate physical parameters of the alloy and input parameters of the simulation system, solve the kinetic equation, draw organization morphology diagram and composition evolution diagram according to the solving data, and analyze to obtain organization evolution characteristics and kinetic evolution law of multiple precipitated phases of the alloy; In step one, the sublattice model of complex phase structure is established according to the thermodynamic parameters of the alloy, and the thermodynamic description is carried out, f ch = f(c i ,η) is the chemical free energy density of the alloy, which contains the specific expression of the sublattice chemical free energy of the multi-phase as follows: c i is the concentration of the element, η is an order parameter used to characterize the structural change, and ω is the free energy cost of preventing different phases from occupying the same space, is the occupation fraction, which represents the probability of occupation of the element i in the sublattice s.

2. The phase field model of complex phase structure transformation based on the theory of stacking faults according to claim 1, characterized in that, In step two, the stress-strain model is established according to the dislocation theory and the phase structure transition of the alloy, and the elastic energy of the alloy system is solved, and the stress-free strain when the phase transition from n phase to m phase occurs is written as: wherein is the size length of the m-phase unit cell in the x-axis direction on the simulated crystal face under the stress-free state, q represents each element of the alloy; the elastic energy density expression of the alloy system is: wherein is the intrinsic strain, is the lattice dilatation coefficient.

3. The phase field model of complex phase structure transformation based on the theory of stacking faults according to claim 1, characterized in that, The system free energy F = ∫ V [f ch +f grad +f el ]dV, including chemical free energy f ch , elastic energy f el and gradient energy f grad , the gradient energy density expression is: where β mn is a structure-dependent gradient energy coefficient, k i is a composition-dependent gradient energy coefficient, which is a function of the interfacial energy.

4. The phase field model of complex phase structure transformation based on the theory of stacking faults according to claim 1, characterized in that, In step three, the kinetic equation of the composition and the order parameter evolution is: M ij is the kinetic coefficient related to the element diffusion, which is related to the composition and the atomic mobility M i ; V m is the molar volume of the alloy; L m is the kinetic coefficient characterizing the structural evolution, which is used to adjust the precipitation rate of the precipitate controlled by diffusion; t is the simulation time, ▽ is the Hamiltonian operator, and the evolution equation is finally solved by the semi-implicit Fourier-spectral method.

Images