CN-121999947-A - Crystal phase field simulation method for complex concentration alloy grain boundary evolution under high temperature environment

CN121999947ACN 121999947 ACN121999947 ACN 121999947ACN-121999947-A

Abstract

The invention discloses a crystal phase field simulation method for complex concentration alloy grain boundary evolution under a high-temperature environment, and belongs to the field of material calculation and microstructure simulation. The method comprises the steps of establishing a Helmholtz free energy functional coupling an atomic density field and a concentration field, establishing an evolution equation set based on Cahn-Hilliard dynamic equations, carrying out high-efficiency numerical solution by adopting a semi-implicit Fourier spectrum method, and setting different temperature conditions and carrying out dynamic simulation on an initial polycrystalline tissue. The method can describe the interaction of the grain boundary structure, elastic energy and chemical field automatically, and realize the dynamic processes of grain boundary migration, coarsening and structure evolution at high temperature from atomic scale uncovering. In particular, the simulation results can reproduce migration of grain boundaries at 0.6Tm temperature, destabilization of grain boundary structure at 0.8Tm temperature, and pre-melting and solid-liquid coexistence phenomena occurring at the triple-fork grain boundaries near the melting point Tm. The invention provides an effective theoretical simulation tool for predicting the microstructure stability and evolution mechanism of the complex concentration alloy under the high-temperature extreme condition.

Inventors

LI JIA
FANG QIHONG
Yi Xiaoai
CHEN YANG
FENG HUI

Assignees

湖南大学

Dates

Publication Date: 20260508
Application Date: 20260316

Claims (5)

1. A crystal phase field simulation method for complex concentration alloy grain boundary evolution under a high-temperature environment relates to a combination of classical density functional theory and thermodynamic theory, uses a spatially continuous atomic density field to describe a microstructure, and can couple grain boundaries, dislocation, elastic energy and the like of a material, and is characterized in that: Establishing a Helmholtz free energy equation related to the complex concentration alloy, and introducing a periodic atomic density equation of the complex concentration alloy into the Helmholtz free energy equation for calculation; Establishing a kinetic equation of Helmholtz free energy, wherein the kinetic equation of the Helmholtz free energy is in accordance with a Cahn-Hillard kinetic equation; The dynamic equation of the complex concentration alloy is solved through a semi-implicit Fourier spectrum method, and discretization treatment is carried out on the atomic density field dynamic equation and the concentration field dynamic equation to obtain an atomic density evolution dynamic equation and a concentration field evolution dynamic equation at the next moment; Step (4) according to the properties of the complex concentration alloy, carrying in initial condition parameters of the complex concentration alloy, setting the number of initial crystal grains, and setting different temperatures to obtain the evolution conditions of grain boundaries with different temperatures; And (5) comparing and analyzing the change conditions of the simulated complex concentration alloy grain boundaries with different temperatures in the step (4) to obtain the evolution condition of the complex concentration alloy grain boundaries in a high-temperature environment.
2. The method for simulating the grain boundary evolution of a complex concentration alloy in a crystal phase field in a high-temperature environment according to claim 1, wherein in the step (1), two periodic atomic density equations related to the complex concentration alloy are introduced into a free energy equation, and the method specifically comprises the following steps: The free energy equation of the crystal phase field of the complex concentration alloy is derived from the free energy equation of the crystal phase field of the pure substance, except that the free energy equation of the crystal phase field of the complex concentration alloy comprises two order parameters of a density field and a concentration field, and the dimensionless free energy equation is as follows: (1) where F is the total free energy of the beam, Is the boltzmann constant, T is the temperature, n is the atomic density function, contains element a and element B, And Is a fitting parameter that is used to determine the fitting parameters, Is a mixed entropy coefficient which is used to generate a high-frequency signal, Is the mixed entropy of the light and the light, Is a function of the effective association and, Is the energy coefficient of the gradient and, Is a concentration gradient term; the calculation equation of the mixed entropy is related to the concentration, and the equation is that (2) Wherein c is the concentration at which the concentration is, Is the reference concentration; the effective correlation function of complex concentration alloys is defined as: (3) Wherein the method comprises the steps of (4) (5) Wherein the method comprises the steps of And Is a correlation function of elements a and B, which are defined in fourier space by a set of reciprocal spatial peaks.
3. The free energy function of the complex concentration alloy according to claims 1 and 2 requires solving the density field and the concentration field respectively, according to Cahn-Hillard power equation, which are as follows: (6) (7) Wherein the method comprises the steps of And Is a dimensionless mobility parameter that is a function of the non-dimensional mobility, Is a laplace operator.
4. The dynamic equations of the density field and the concentration field according to claim 3, which are obtained by numerically solving by using a semi-implicit fourier spectrum method, wherein the atomic density evolution dynamic equation and the concentration field evolution dynamic equation at the next moment are specifically as follows: (8) (9) Wherein the method comprises the steps of And The fourier transform at the time of density field and density t respectively, And The fourier transforms of the density field and the concentration field at time t +1 respectively, Is the step of the time that is required, Is the transformation of the laplace operator in fourier space.
5. The method of setting parameters according to step (4) of claim 1, wherein effective simulation parameters, polynomial fitting parameters, are determined And 1.4 And 1, respectively, mixed entropy coefficient 0.005 Gradient coefficient of energy 1.

Description

Crystal phase field simulation method for complex concentration alloy grain boundary evolution under high temperature environment Technical Field The invention belongs to the field of material computing science and microstructure simulation, and particularly relates to a numerical simulation method based on a crystal phase field model, which is used for researching dynamic evolution behavior of a crystal boundary in a complex concentration alloy system under a high-temperature condition. And establishing evolution conditions of grain boundaries at different temperatures, and realizing analysis of complex concentration alloy grain boundaries in high-temperature environments. The method provides an effective theoretical calculation tool for revealing the stability and evolution rule of the microstructure of the alloy in an extreme environment. Background The long-term service stability of polycrystalline materials in high-temperature extreme environments such as aerospace propulsion systems, advanced nuclear energy equipment and high-end chemical reactors is fundamentally dependent on the evolution behavior of the internal microstructure. Among these, grain boundaries, i.e. the two-dimensional interface regions separating grains of different crystallographic orientations, play a crucial role. It not only serves as a fast diffusion channel for atoms, but also serves as an active site for solute element segregation, second phase precipitation, dislocation accumulation and annihilation. Under thermal activation, grain boundaries migrate, slip, and even interact with other defects, which directly control the high temperature creep resistance, fatigue life, environmental corrosion rate, and tendency of coarsening of the material. Therefore, the evolution mechanism of the grain boundary under the condition of precisely revealing and predicting the high temperature is a basic stone for developing a new generation of high-performance alloy, optimizing the heat treatment process and evaluating the service life of the alloy, and has great scientific and engineering significance. Direct observation of atomic scale high temperature dynamic processes relying on traditional experimental means presents a significant challenge. First, there is a difficult reconciliation between the observation scale and the kinetic rate. The core processes of grain boundary migration, atomic diffusion, etc. occur on nano-micrometer spatial scales and millisecond-second or even longer time scales. Although techniques such as in situ high temperature Transmission Electron Microscopy (TEM) provide extremely high spatial resolution, their field of view is extremely limited, it is difficult to capture statistically significant collective behavior in polycrystalline materials, and high energy electron beams are extremely prone to induce additional irradiation damage at high temperatures, even changing the intrinsic evolution path of the material. Second, accurate reproduction and single variable control of complex physicochemical environments is extremely difficult. In actual service, high temperatures are often coupled with mechanical stresses and complex chemical environments. The multi-field coupling environment is completely reproduced in experiments, and the contribution of a single thermodynamic driving force is precisely decoupled, so that the multi-field coupling environment is hardly realized. In addition, experimental methods typically provide "start" and "end" states of the evolution process, or a few discrete "snapshots", for continuous evolution of the dynamic process, it is difficult to obtain complete data. In view of the above-mentioned bottlenecks of experimental research, computational materials methods, in particular mesoscale simulation based on physical fields, have become an indispensable research tool. Among the simulation methods, the phase field method is widely used because of the complexity of tracking a sharp interface, and the morphological evolution of a microstructure is naturally described by introducing a continuous sequence parameter field and solving a dynamics equation of the continuous sequence parameter field. However, when focusing on the specific and key problem of grain boundary evolution in a high-temperature complex concentration alloy system, the existing mainstream phase field model has remarkable limitation in the integrity and precision of physical description, and the traditional phase field method cannot describe the core structure and energy of crystal defects such as grain boundaries, dislocation and the like in a self-consistent manner. In summary, the current state of the art is that the experimental observation means has inherent difficulties in capturing details of grain boundary evolution at high temperature, dynamic and atomic scales, in terms of space-time resolution and environmental control, while the mainstream calculation model has short plates for accurately describing the physical nat