CN113327654B - Phase field simulation method for predicting nano alpha twin crystal precipitation and microstructure evolution in titanium alloy under local stress state - Google Patents
Phase field simulation method for predicting nano alpha twin crystal precipitation and microstructure evolution in titanium alloy under local stress state Download PDFInfo
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Abstract
The invention relates to the field of metallurgical casting, in particular to a phase field simulation method for predicting nano alpha twin crystal precipitation and microstructure evolution in a titanium alloy under a local stress state, which comprises the following steps: s1, obtaining information such as Gibbs free energy density, interface energy and phase change strain tensors of different alpha variants of two phases in a beta-alpha solid phase change process of the titanium alloy; s2, establishing a phase field dynamics model, and solving a phase field control equation to obtain an order parameter result value; s3, changing the orientation and the size of the stress load in the phase transition process under a certain supercooling degree to obtain the morphology information of different microstructures; and S4, carrying out visual processing on corresponding microstructure evolution results under different input conditions, and clarifying the influence rule of the local stress state on the nano alpha twin crystal nucleation and evolution process. The method can reproduce the beta-alpha transformation process in the titanium alloy, and provides a visual prediction method for the microstructure form and the evolution process of the microstructure form under the action of thermal-force coupling.
Description
Technical Field
The invention relates to the field of metallurgical casting, in particular to a phase field simulation method for predicting nano alpha twin crystal precipitation and microstructure evolution in a titanium alloy under a local stress state.
Background
Titanium alloy is used as a traditional engineering alloy, has the advantages of low density, high strength, high temperature resistance, corrosion resistance and the like, and is widely applied to the fields of aerospace, navigation, medical treatment and the like. The diverse microstructure of titanium alloys is mainly derived from the thermo-mechanical processing process of deformation and phase transformation coupling. The beta-alpha transformation is the key of the formation of a titanium alloy microstructure under the high-temperature deformation condition, the formation of the microstructure is often influenced by external force and residual stress after thermal processing, the separation of an alpha phase change body is selectively acted, and a plurality of typical alpha twin crystal variants, triangular cone type variant clusters and the like can be formed, so that the formation of an alpha transformation texture is caused. The strong texture even constitutes a "macro" occurrence, significantly reducing the fatigue and creep properties of the alloy. However, depending on experimental methods alone, complex local stress states are difficult to characterize. In order to assist in the design and performance optimization of the alloy, the typical microstructure morphology of the titanium alloy under the thermal-force coupling is predicted through computer simulation, the formation mechanism of the titanium alloy is revealed, and the influence rule of the local stress state on the nano alpha twin crystal nucleation and evolution process is clarified. The method has important guiding significance for further improving the service performance of the titanium alloy.
Disclosure of Invention
First, the technical problem to be solved
The invention provides a phase field simulation method for predicting nano alpha twin crystal precipitation and microstructure evolution in a titanium alloy under a local stress state, in order to design and optimize the microstructure and texture of the titanium alloy. The method can reproduce the beta- & gtalpha solid state transformation process, and provides an effective prediction method for regulating and controlling nano alpha twin crystal nucleation and precipitation and microstructure evolution rules by means of an external stress load.
(II) technical scheme
In order to achieve the above purpose, the main technical scheme adopted by the invention is as follows:
a phase field simulation method for predicting nano alpha twin crystal precipitation and microstructure evolution in a titanium alloy under a local stress state comprises the following steps:
s1, obtaining local free energy density of each phase in the solid state transition of beta-alpha according to the target heat treatment temperature of the titanium alloy, the Gibbs free energy curve of beta and alpha phases and balance components in the two-phase balance; introducing interface energy into the total chemical free energy term through the gradient term; calculating an alpha variant phase change strain tensor under a Cartesian coordinate system, and obtaining phase change strain tensors of the rest eleven alpha variants through space rotation symmetry operation;
s2, establishing a phase field dynamics model and determining a plurality of input parameters according to Gibbs free energy density of each phase and alpha variant phase change strain tensor information of the titanium alloy in the beta-alpha solid phase change obtained in the step S1, and calculating two phase field order parameter result values through a phase field control equation;
s3, keeping the target heat treatment temperature unchanged, changing different external stress loads, and calculating to obtain microstructure morphology information of nano alpha twin crystal nucleation and evolution;
and S4, carrying out visual processing on the microstructure and component evolution results in the step S3, and obtaining an influence rule of the stress state on nano alpha twin crystal nucleation and evolution.
The step S1 comprises the following steps of:
the expression of the chemical free energy density of beta and alpha phases in the titanium alloy is as follows:
wherein the method comprises the steps ofAs an interpolation function, a free energy curve for connecting beta and alpha phases;and->The equilibrium molar free energy (unit is J/mol) of alpha and beta phases is closely related to the system temperature T (unit is K) and the alloying element c (unit is at.%), and fitting approximation is carried out by Landau polynomials; phi (phi) p Or phi q (p, q=1, & ltDEG & gt, 12) represents 12 alpha phase variants; />Characterization of the energy barrier between different alpha variants, < ->Characterization of the energy barrier between beta and 12 alpha variants, omega 1 And omega 2 Is energy barrier height (unit J/mol);
in the phase field model, the interfacial energy is an additional free energy related to structural or concentration non-uniformity at the interface; the interface energy is introduced into the chemical free energy term by adding a gradient term, and the gradient term expression is as follows:
k c and k is equal to φ The gradient energy coefficient tensor is characterized in that the front and back terms respectively represent the chemical free energy change and the additional chemical free energy generated by the non-uniform structure;representing the composition gradient in m -1 ；/>Representing the gradient of a structural field variable, the unit is m -1 ；
Phase change strain of variant 1The expression is as follows:
the phase change strain tensor of the remaining eleven alpha variants is obtained by spatially rotationally symmetric operation.
According to the phase field simulation method for predicting nano alpha twin crystal precipitation and microstructure evolution in the titanium alloy under the local stress state, a rotationally symmetrical operation matrix corresponding to a variant 2 phase change strain tensor is as follows:
phase change strain of modification 2The expression is as follows:
wherein R is T A transposed matrix of R; the remaining alpha variants and so on.
The step S2 comprises the following steps of:
the total free energy of the system is expressed as the functional of the field variable, and comprises local chemical free energy, gradient energy, elastic strain energy and interaction energy items under an external force field, namely:
wherein the meaning and units of each symbol are: f represents the total free energy (unit: J/mol), G m Is the molar free energy (unit: J/mol), k c And k is equal to φ Gradient term coefficients (unit: J.m) for component and structural field variables 2 /mol)，E el Represents elastic strain energy (unit: J/mol),is the interaction energy (unit: J/mol) between external stress and variants;
the evolution of the concentration field over time is governed by a diffusion equation, commonly referred to as the Cahn-hillard equation:
m is diffusion mobility, characterizes solute diffusion rate in mol.m 2 The larger the value of/sJ, the faster the diffusion, a variable that is dependent on the temperature parameter;
the evolution of a long program parametric field over time is described by a relaxation equation, commonly referred to as the time dependent Ginzburg-Landau (TDGL) equation or Allen-Cahn equation:
L φ is a dynamic coefficient representing the relaxation of a structure, and has the unit of m 3 The larger the value of J/s, the faster the structural relaxation; random noise term ζ c (r, t) and ζ p And (r, t) respectively representing fluctuation of the concentration order parameter and the structural order parameter, and simulating the nucleation process of alpha phase in the system.
The step S3 comprises the following steps of:
the elastic strain energy expression is:
wherein n is a unit inverted lattice vector, C ijkl The elastic constant tensor of the system is characterized,is the macroscopic average strain of the system (in%) and V is the system volume (in m) 3 )；
B pq (n) is the interaction potential of two bodies, the unit is J/mol, and the expression is:
the phase change stress corresponding to the variant p is expressed in GPa, and the expression is as follows:
wherein the method comprises the steps ofPhase change strain which is the p-th variant;
Ω jk (n) is the Green's function tensor in GPa -1 The method comprises the following steps:
{φ p (r)} g is thatIs expressed as:
under strain control boundary conditions, the elastic interaction between the applied stress and each variant can be expressed as:
taking into account the additional contribution of the alpha phase precipitation to the phase change driving force under the condition of the additional stress load, the additional contribution is estimated as elastic interaction energy between the additional uniform strain and each alpha phase change strain tensor;c is the average strain under applied stress ijkl And->Consistent with its physical meaning in the elastic strain energy term.
The design idea of the invention is as follows: considering the limitation of characterization test in experimental research, the advantages of a material calculation simulation method are fully exerted, the elastic interaction energy between the external stress and alpha variants is calculated by adopting a mesoscale phase field dynamics method, and the formation and evolution mechanism of the local stress state in the titanium alloy on the nano alpha twin crystal clusters is clarified. The effective prediction method lays a theoretical and method foundation for regulating and controlling the nano alpha twin crystal precipitation and microstructure evolution process by using the external stress load.
(III) beneficial effects
The invention has the advantages and beneficial effects that:
1. the titanium alloy is used as a common light high-strength structural material, the experimental cost for optimizing the thermal-force processing technology is high, and in the solid phase transformation process, the interfacial energy, the elastic strain energy and the elastic interaction energy between external stress and variants are difficult to characterize through experiments, and the development rule of typical microstructure morphology and texture under thermal-force coupling is greatly limited. According to the invention, a numerical simulation method is utilized to research the influence rule of different external stress loads on nano alpha twin crystal precipitation and microstructure evolution in the titanium alloy at a certain temperature, so that the limitations of experimental research can be effectively avoided.
2. The invention can introduce key influencing factors such as interfacial energy, elastic strain energy, interaction energy between local stress and variants and the like into numerical simulation, can truly reproduce the structure morphology of beta-alpha solid phase transition in the titanium alloy under thermal-force coupling, relatively accurately simulate the evolution process of microstructure, and provide reliable information for improving and optimizing the mechanical properties of the titanium alloy. The phase field method is used as a numerical simulation method, and can quantitatively study the influence of interfacial energy of a phase interface, anisotropy, elastic strain energy, stress load, interaction among variants and other key factors on the shape growth of the microstructure.
Drawings
FIG. 1 is a flowchart showing the creation of a numerical model program in the present invention.
FIG. 2 is a graph showing free energy of Ti-3Mo alloy in accordance with one embodiment of the present invention; in the figure, the abscissa represents the Mo element component content, and the ordinate represents the gibbs free energy value.
FIG. 3 is a graph showing the effect of different applied sizes on the microstructure morphology of the Ti-3Mo alloy in an embodiment of the invention; wherein, (a) is a microstructure evolution diagram under the condition that the external stress is 10MPa, (b) is a microstructure evolution diagram under the condition that the external stress is 20MPa, and (c) is a microstructure evolution diagram under the condition that the external stress is 30 MPa.
FIGS. 4 (a) -4 (c) are graphs showing the effect of different applied sizes on the volume fraction of different variants precipitated in the Ti-3Mo alloy according to one embodiment of the invention; wherein, fig. 4 (a) is the volume fraction of the different variants under the applied stress of 10MPa, fig. 4 (b) is the volume fraction of the different variants under the applied stress of 20MPa, and fig. 4 (c) is the volume fraction of the different variants under the applied stress of 30 MPa. In the figure, the abscissa represents the alpha variant species, and the ordinate represents the volume fraction value.
FIGS. 5 (a) -5 (c) are graphs showing the effect of different applied sizes on the microstructure of Ti-3Mo alloy in accordance with one embodiment of the present invention. Wherein, FIG. 5 (a) is a microstructure polar diagram under an applied stress of 10MPa, FIG. 5 (b) is a microstructure polar diagram under an applied stress of 20MPa, and FIG. 5 (c) is a microstructure polar diagram under an applied stress of 30 MPa.
FIG. 6 is a flow chart of a simulation method for predicting nano alpha twin precipitation and microstructure evolution in a titanium alloy under an applied stress.
Detailed Description
As shown in fig. 6, the simulation method for predicting nano alpha twin precipitation and microstructure evolution in the titanium alloy under the applied stress comprises the following steps: firstly, thermodynamic data of a titanium alloy system and alpha variant phase change strain parameters are collected; then, establishing a phase field dynamics model; next, inputting various physical parameters, boundary conditions, interface energy, external stress load and other conditions into the model; solving a phase field control equation by using a Fortran language programming program; and visualizing the output structure and component field variables, counting the volume fractions of different types of alpha variants, and calculating the texture strength of the tissue under different stress conditions.
The present invention will be described in detail below with reference to specific embodiments for better explaining the present invention.
Examples take the Ti-3Mo (at.%) alloy as an example:
(1) Thermodynamic and phase change strain tensor calculation
Firstly, according to the phase transition temperature of Ti-3Mo alloy, obtaining Gibbs free energy curve of alpha and beta two phases at target temperature by thermodynamic calculation, adopting Landau polynomial to fit it, at the same time according to free energy curve and coupling phase field structure field variable phi p A solution type expression is fitted to describe the local free energy densities of alpha and beta phases of the Ti-3Mo alloy system.
The solution formula is as follows:
wherein the method comprises the steps ofAs an interpolation function, a free energy curve is used to connect the β and α phases.And->The equilibrium molar free energy (in J/mol) of the alpha and beta phases, respectively, is closely related to the system temperature T (in K) and the alloying element c (in at.%), and is approximated by fitting a Landau polynomial. Phi (phi) p Or phi q (p, q=1, & ltDEG & gt, 12) represents 12 alpha phase variants. />Characterization of the energy barrier between different alpha variants, < ->Characterization of the energy barrier between beta and 12 alpha variants, omega 1 And omega 2 The unit is J/mol for the energy barrier height. Differences between energy barriers due to differences in orientation between different alpha variants are ignored here.
In the phase field model, the interfacial energy is an additional free energy related to structural or concentration non-uniformity at the interface. The interface energy is introduced into the chemical free energy term by adding a gradient term, and the gradient term expression is as follows:
k c and k is equal to φ The gradient energy coefficient tensor is characterized in that the front and back terms respectively represent the chemical free energy change and the additional chemical free energy generated by the non-uniform structure;representing the composition gradient in m -1 ；/>Representing the gradient of a field variable in m -1 . The contributions of both the structural field and the concentration field variable gradient terms are considered here.
In calculating the phase change strain tensor of the alpha variant, a specific coordinate system is established, namely x [101 ]]-y[1-2-1]-z[11-1]Based on the difference of lattice constants of alpha and beta phases on the three orientation axes, the phase change strain tensor of variant 1 is obtained, namely
The phase change strain tensors of the remaining eleven alpha variants can be obtained through spatially rotationally symmetric operation; taking the example of obtaining the phase change strain tensor of variant 2, the corresponding rotationally symmetric operation matrix is:
variants therefore2 phase change strainCan be expressed as:
wherein R is T A transposed matrix of R; the remaining alpha variants and so on.
The total free energy of the system is expressed as the functional of a field variable, and comprises energy items such as local chemical free energy, gradient energy, elastic strain energy, interaction energy under an external force field and the like, namely:
wherein the meaning and units of each symbol are: f represents the total free energy (unit: J/mol), G m Is the molar free energy (unit: J/mol), k c And k is equal to φ Gradient term coefficients (unit: J.m) for component and structural field variables 2 /mol)，E el Represents elastic strain energy (unit: J/mol),is the interaction energy (unit: J/mol) between external stress and variants.
(2) Establishment of phase field control equation
The evolution of the concentration field over time is governed by a diffusion equation, commonly referred to as the Cahn-hillard equation:
m is diffusion mobility, characterizes solute diffusion rate in mol.m 2 /sJ. The larger the value, the faster the diffusion, and is a variable depending on parameters such as temperature.
The evolution of a long program parametric field over time is described by a relaxation equation, commonly referred to as the time dependent Ginzburg-Landau (TDGL) equation or Allen-Cahn equation:
L φ is a dynamic coefficient representing the relaxation of a structure, and has the unit of m 3 The larger the value of J/s, the faster the structural relaxation. Random noise term ζ c (r, t) and ζ p And (r, t) respectively representing fluctuation of the concentration order parameter and the structural order parameter, and simulating the nucleation process of alpha phase in the system.
(3) Calculation of elastic Strain energy, external stress and interaction energy between variants
The microstructure evolution of an alloy typically involves a lattice rearrangement that results in a lattice mismatch between coexisting phases. If adjacent interphase interfaces are coherent or semi-coherent, an elastic strain field is created in the vicinity of the interface. The elastic strain energy is dependent on the volume and morphology of the coexisting phases and is distributed among the coexisting phases. The elastic strain energy expression is:
wherein n is a unit inverted lattice vector, C ijkl The elastic constant tensor (unit: GPa) of the system is characterized,is the macroscopic average strain (unit:%) of the system and V is the system volume (unit: m) 3 )。
B pq (n) is the interaction potential of two bodies, the unit is J/mol, and the expression is:
is variant p pairThe unit of the corresponding phase change stress is GPa, and the expression is:
wherein the method comprises the steps ofPhase change strain which is the p-th variant.
Ω jk (n) is the Green's function tensor in GPa -1 The method comprises the following steps:
{φ p (r)} g is thatIs expressed as:
under strain control boundary conditions, the elastic interaction between the applied stress and each variant can be expressed as:
taking into account the additional contribution of the applied stress load to the phase change driving force of alpha phase precipitation, the elastic interaction energy between the applied uniform strain and each alpha phase change strain tensor can be measured. Considering that the phase change strain tensor of each variant is different, the elastic interaction energy with each variant is different when stress is applied, and the difference affects the nucleation and growth of a certain alpha phase change body.C is the average strain under applied stress ijkl And (3) withThe physical meaning is the same as that of the elastic strain energy.
(4) Result output
The method mainly solves a control equation of a structural field and a concentration field based on a semi-implicit Fourier spectrum method according to a phase field model and calculation parameters thereof. According to the embodiment of the invention, a program describing the microstructure and texture evolution process of the Ti-3Mo alloy under different externally applied stress loads at a certain temperature is written by adopting Fortran language, and then the program is converted into a more visual image form by utilizing visual software according to the sequence parameter evolution result output by the program, so that the aim of visualizing the solid-state phase change process in the Ti-3Mo alloy is fulfilled.
As shown in fig. 1, the specific flow of the numerical model program establishment is as follows: firstly, collecting single-phase Gibbs free energy data under a titanium alloy system, calculating elastic strain energy and interaction energy between stress and variants, and fitting the total chemical free energy of the system; then, a phase field dynamics model is established, various physical parameters, boundary conditions, interface energy, strain energy, interaction energy and other conditions are input into the model, and a phase field control equation, namely a Cahn-Hilliard equation and an Allen-Cahn equation, is solved by means of a semi-implicit Fourier spectrum method; and carrying out iterative solution on the output structure and the component field variables.
A specific example is provided below. Aiming at Ti-3Mo alloy, the solid state transformation from beta to alpha occurs at the target heat treatment temperature T=500K, and the main physical parameters are as follows:
physical property parameter value and unit
| Physical property parameters | Numerical value and unit |
| Mo element component c | 0.03(at.％) |
| Gradient term coefficient k φ ,k c | 10.0,10.0(Jm 2 /mol) |
| Energy barrier coefficient omega 1 ,ω 2 | 1.0,0.5(J/mol) |
| System temperature T | 500(K) |
| Interface energy gamma α/β | 100(J/m 2 ) |
| Applied stress sigma app | 0.01,0.02,0.03(GPa) |
| Free energy normalization parameter G 0 | 4.0×10 3 (J/mol) |
| Lattice point spacing l 0 | 0.5(nm) |
| Phase field dynamics coefficient L | 3.0(m 3 /J/s) |
| Space and time step dx, dt | 0.5,0.001 |
| N x ×N y ×N z (grids) | 64×64×64(grids) |
The specific implementation manner of this embodiment is as follows:
(1) Based on a thermodynamic database, gibbs free energy parameter information of each phase at a certain phase transition temperature is obtained, wherein the free energy curve of the Ti-Mo alloy is shown in figure 2. Information such as alpha/beta interfacial energy, phase lattice constant and elastic constant tensor in Ti-3Mo alloy is collected, and as can be seen from fig. 2, when the content of Mo is 3at.% at the temperature of T=500K, the free energy of beta phase is higher than the free energy of alpha phase, so that the beta-alpha solid state transformation process can occur.
(2) According to the phase field equation, the parameters are brought into a phase field model for the Ti-3Mo alloy system, and two phase field control equations, namely an Allen-Cahn equation and a Cahn-Hilliard equation, are solved.
(3) Programming the model and equation established by using Fortran language, bringing initial values and periodic boundary conditions into the model and equation, running a program, obtaining a corresponding result and performing visualization processing. At the target heat treatment temperature T=500K, the influence results of the stress load of 10,30 and 50MPa applied along the line [11-1] on the nano alpha twin crystal nucleation and growth, microstructure morphology and texture evolution process in the Ti-3Mo alloy are examined and shown in the figures 3, 4 and 5.
As can be seen from FIGS. 3 (a) - (c), the variation species in the system gradually changed from random (unstressed) precipitation to mainly variants 3,5,7 at applied stresses of 10,20 and 30MPa, respectively. This is because the energy values corresponding to the three variants are the lowest in consideration of the interaction energy of the applied stress with the various variants.
As can be seen from fig. 4 (a) - (c), the volume fractions of the variants gradually precipitated variants 3,5,7 as the main variants at an applied stress of 10,20 and 30MPa, respectively. Corresponding to the microstructure of fig. 3.
As can be seen from fig. 5 (a) - (c), the maximum values of the texture intensities of fig. 5 (b) and (c) slightly decrease, but the areas of strong textures of fig. 5 (b) and (c) are increased compared to fig. 5 (a), at the applied stresses of 10,20 and 30MPa, respectively. Illustrating the progressive enhancement of the selection of variants 3,5,7 by the applied stress.
The comparison shows that as the applied stress load increases, the volume fraction of the alpha phase change bodies 3,5,7 increases, and other alpha phase change bodies are found to be inhibited from nucleation and growth; in addition, these three variants may form a triangular pyramid type variant cluster, with {10-11} twin crystals formed between any two variants. Such triangular pyramid type variant clusters dominate the microstructure as the applied stress increases. The alpha/beta relationship still remains the same at the nanoscale, indicating that the applied stress load along <111> is the main cause of inducing such nano twins.
The titanium alloy is used as a common light high-strength structural material, the experimental cost for optimizing the thermal-force processing technology is high, and in the solid phase transformation process, the interfacial energy, the elastic strain energy and the elastic interaction energy between external stress and variants are difficult to characterize through experiments, and the development rule of typical microstructure morphology and texture under thermal-force coupling is greatly limited. According to the invention, a numerical simulation method is utilized to research the influence rule of different external stress loads on nano alpha twin crystal precipitation and microstructure evolution in the titanium alloy at a certain temperature, so that the limitations of experimental research can be effectively avoided.
The invention can introduce key influencing factors such as interfacial energy, elastic strain energy, interaction energy between local stress and variants and the like into numerical simulation, can truly reproduce the structure morphology of beta-alpha solid phase transition in the titanium alloy under thermal-force coupling, relatively accurately simulate the evolution process of microstructure, and provide reliable information for improving and optimizing the mechanical properties of the titanium alloy. The phase field method is used as a numerical simulation method, and can quantitatively study the influence of interfacial energy of a phase interface, anisotropy, elastic strain energy, stress load, interaction among variants and other key factors on the shape growth of the microstructure.
The embodiment results show that the method can reproduce the beta- & gtalpha transformation process in the titanium alloy, provides a visual prediction method for the microstructure form and the evolution process of the titanium alloy under the action of thermal-force coupling, and provides theoretical guidance for regulating and controlling nano alpha twin crystal nucleation and growth and further optimizing the microstructure of the titanium alloy by utilizing the variant selection action.
It should be understood that the above description of the specific embodiments of the present invention is only for illustrating the technical route and features of the present invention, and is for enabling those skilled in the art to understand the present invention and implement it accordingly, but the present invention is not limited to the above-described specific embodiments. All changes or modifications that come within the scope of the appended claims are intended to be embraced therein.
Claims (2)
1. A phase field simulation method for predicting nano alpha twin crystal precipitation and microstructure evolution in a titanium alloy under a local stress state is characterized by comprising the following steps:
s1, obtaining local free energy density of each phase in the solid state transition of beta-alpha according to the target heat treatment temperature of the titanium alloy, the Gibbs free energy curve of beta and alpha phases and balance components in the two-phase balance; introducing interface energy into the total chemical free energy term through the gradient term; calculating an alpha variant phase change strain tensor under a Cartesian coordinate system, and obtaining phase change strain tensors of the rest eleven alpha variants through space rotation symmetry operation;
s2, establishing a phase field dynamics model and determining a plurality of input parameters according to Gibbs free energy density of each phase and alpha variant phase change strain tensor information of the titanium alloy in the beta-alpha solid phase change obtained in the step S1, and calculating two phase field order parameter result values through a phase field control equation;
s3, keeping the target heat treatment temperature unchanged, changing different external stress loads, and calculating to obtain microstructure morphology information of nano alpha twin crystal nucleation and evolution;
s4, carrying out visual treatment on the microstructure and component evolution result in the S3 to obtain an influence rule of a stress state on nano alpha twin crystal nucleation and evolution;
the step S1 includes the following:
the expression of the chemical free energy density of beta and alpha phases in the titanium alloy is as follows:
wherein the method comprises the steps ofAs an interpolation function, a free energy curve for connecting beta and alpha phases; />And (3) withThe equilibrium molar free energy of alpha and beta phases is J/mol, the equilibrium molar free energy is closely related to the system temperature T and the alloying element c, the unit of the system temperature T is K, the unit of the alloying element c is at%, and fitting approximation is performed through Landau polynomials; ɸ p Or ɸ q (p, q=1, & ltDEG & gt, 12) represents 12 alpha phase variants; />The energy barrier between the different alpha variants is characterized,characterization of the energy barrier between beta and 12 alpha variants, omega 1 And omega 2 The unit J/mol is the energy barrier height;
in the phase field model, the interfacial energy is an additional free energy related to structural or concentration non-uniformity at the interface; the interface energy is introduced into the chemical free energy term by adding a gradient term, and the gradient term expression is as follows:
k c and k is equal to ɸ The gradient energy coefficient tensor is characterized in that the front and back terms respectively represent the chemical free energy change and the additional chemical free energy generated by the non-uniform structure; and c represents a component gradient in m -1 ；▽ɸ p Representing the gradient of a structural field variable, the unit is m -1 ；
Phase change strain of variant 1The expression is as follows:
obtaining phase change strain tensors of the remaining eleven alpha variants through spatial rotation symmetry operation;
the step S2 includes the following:
the total free energy of the system is expressed as the functional of the field variable, and comprises local chemical free energy, gradient energy, elastic strain energy and interaction energy items under an external force field, namely:
wherein the meaning and units of each symbol are: f represents the total free energy, unit: j/mol, G m The molar free energy, unit: j/mol, k c And k is equal to ɸ The gradient term coefficients for the component and structural field variables, unit: j.m 2 /mol，E el Represents elastic strain energy, unit: j/mol of the catalyst is selected,units of interaction energy between external stress and variants: j/mol;
the evolution of the concentration field over time is governed by a diffusion equation, commonly referred to as the Cahn-hillard equation:
m is diffusion mobility, characterizes solute diffusion rate in mol.m 2 The larger the value of/sJ, the faster the diffusion, a variable that is dependent on the temperature parameter;
the evolution of a long program parametric field over time is described by a relaxation equation, commonly referred to as the time dependent Ginzburg-Landau (TDGL) equation or Allen-Cahn equation:
L ɸ is a dynamic coefficient representing the relaxation of a structure, and has the unit of m 3 The larger the value of J/s, the faster the structural relaxation; random noise term ζ c (r, t) and ζ p (r, t) respectively representing fluctuation of concentration order parameters and structural order parameters, and simulating a nucleation process of alpha phase in the system;
the step S3 includes the following:
the elastic strain energy expression is:
wherein n is a unit inverted lattice vector, C ijkl The elastic constant tensor of the system is characterized,is the macroscopic average strain of the system, the unit is V is the system volume, and the unit is m 3 ；
B pq (n) is the interaction potential of two bodies, the unit is J/mol, and the expression is:
the phase change stress corresponding to the variant p is expressed in GPa, and the expression is as follows:
wherein the method comprises the steps ofPhase change strain which is the p-th variant;
Ω jk (n) is the Green function tensor in GPa- 1 The method comprises the following steps:
{ɸ p (r)} g is thatIs expressed as:
under strain control boundary conditions, the elastic interaction between the applied stress and each variant can be expressed as:
taking into account the additional contribution of the alpha phase precipitation to the phase change driving force under the condition of the additional stress load, the additional contribution is estimated as elastic interaction energy between the additional uniform strain and each alpha phase change strain tensor;c is the average strain under applied stress ijkl And->Consistent with its physical meaning in the elastic strain energy term.
2. The phase field simulation method for predicting nano alpha twin precipitation and microstructure evolution in a titanium alloy in a local stress state as claimed in claim 1, wherein a rotationally symmetric operation matrix corresponding to a variant 2 phase change strain tensor is:
phase change strain of modification 2The expression is as follows:
wherein R is T A transposed matrix of R; the remaining alpha variants and so on.
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