CN114970106B - Method and system for predicting radiation hardening based on microstructure - Google Patents

Abstract

The invention discloses a method and a system for predicting radiation hardening based on a microstructure, which comprises the following steps: obtaining the chemical free energy density of the nuclear power alloy material according to the Avogardlo constant, the atom molar volume, the defect atom concentration, the defect forming energy, the Boltzmann constant and the absolute temperature of the nuclear power alloy material; acquiring the elastic free energy density of the nuclear power alloy material based on the crystal plasticity of the nuclear power alloy material; constructing a thermodynamic system model for representing the evolution of the irradiation defects of the nuclear power alloy material according to the chemical free energy density and the elastic free energy density; based on a thermodynamic system model, constructing a phase field kinetic model by acquiring the chemical mobility of irradiation point defects, the generation rate of the point defects under irradiation conditions and the concentration of defect atoms of a nuclear power alloy material; the invention introduces microscopic defects in the process of considering irradiation and considers the hardening of the defects in the stretching process, thereby improving the prediction precision of irradiation hardening and the engineering application value of calculation simulation.

Description

A method and system for predicting radiation hardening based on microstructure

technical field

The invention relates to the technical field of performance prediction of nuclear power materials under irradiation conditions, in particular to a method and system for prediction of radiation hardening based on microstructure.

Background technique

From 2020 to 2050, my country plans to develop fast neutron breeder reactors, and one of the key points of project development is the issue of nuclear materials. Due to the generation of a large number of point defects and their interaction with atoms during service, the main elements of the material segregate at grain boundaries and dislocations, resulting in radiation-induced precipitation, dislocation rings, voids and other radiation defects. These defects can hinder dislocation movement, causing radiation hardening, and at the same time reducing the ductility of the material leading to material deterioration. Therefore, understanding the relationship between irradiation defects and changes in material properties is crucial for the long-life use and lifetime prediction of nuclear power materials.

Due to the radioactivity of neutron radiation and the difficulty of neutron experiments, the current research on the radiation effect of nuclear power materials mostly uses heavy ion radiation to simulate the effect of neutron radiation. However, due to the small damage of the irradiated layer (<1 μm) and the small size of the sample, it poses a challenge to the mechanical property experiment of heavy ion irradiated materials. At present, nano-indentation is widely used, but this technology can only be used to detect the change of hardness before and after irradiation and extrapolate the change of yield strength of the material. The calculated value is often different from the measured value of the microstructure, and it is difficult to establish Stress-strain response relationship of irradiated materials. Another testing technique is the microcolumn tension/compression test, which can better reflect the radiation hardening effect, but the equipment is difficult to obtain and the cost is high. Furthermore, some scholars proposed to use various simulation methods to predict the radiation stress-strain response and study the interaction of defects. Radiation hardening is closely related to irradiation microstructure. Phase field simulation, as a microscopic simulation method, has attracted extensive attention from scholars at home and abroad due to its unique advantages at the microstructure level. Phase field method can be used to simulate defects and performance changes. Collaborative research to improve the prediction accuracy of material radiation hardening and obtain the stress-strain response relationship is a new direction for the prediction of radiation performance and life evolution of nuclear power materials.

Contents of the invention

In order to solve the above problems, the object of the present invention is to provide a method and system for predicting radiation hardening based on microstructure, based on phase field simulation and crystal plasticity theory, comprehensively considering radiation microscopic defects, and improving the prediction accuracy and engineering performance of radiation hardening. applicability.

In order to achieve the above technical purpose, this application provides a method for predicting radiation hardening based on microstructure, including the following steps:

According to the Avogadro constant, atomic molar volume, defect atom concentration, defect formation energy, Boltzmann constant, and absolute temperature of the nuclear power alloy material, the chemical free energy density of the nuclear power alloy material is obtained;

Based on the crystal plasticity of nuclear power alloy materials, obtain the elastic free energy density of nuclear power alloy materials;

According to the chemical free energy density and elastic free energy density, construct a thermodynamic system model for characterizing the evolution of radiation defects in nuclear power alloy materials;

Based on the thermodynamic system model, the phase field dynamics model is constructed by obtaining the chemical mobility of point defects of nuclear power alloy materials, the generation rate of point defects under irradiation conditions, and the concentration of defect atoms. Among them, the phase field dynamics model is used For radiation hardening prediction of nuclear power alloy materials.

Preferably, in the process of obtaining the elastic free energy density, the elastic free energy density is obtained by collecting elastic constants and elastic strain tensors of nuclear power alloy materials.

Preferably, during the process of collecting the elastic strain tensor, the external strain, non-uniform strain and intrinsic strain of the nuclear power alloy material are collected to generate the elastic strain tensor.

Preferably, in the process of collecting the intrinsic strain, by obtaining the volume expansion coefficient related to the defect, the defect equilibrium concentration at a certain temperature, the plastic strain tensor, and the concentration of defect atoms, according to the coupled crystal plasticity theory, the intrinsic strain is obtained .

Preferably, in the process of obtaining the plastic strain tensor, by obtaining the slip coefficient amount, the plastic shear rate of the slip system, the initial plastic shear rate, the strain sensitivity index, the Schimid tensor factor, the shear stress, the critical shear The shear stress generates the plastic strain tensor. When the shear stress of the system is greater than the critical shear stress, slip occurs, and the Schimid tensor factor is obtained by obtaining the slip direction and the normal direction of the slip system.

Preferably, in the process of obtaining the critical shear stress, based on radiation hardening and strain hardening, by obtaining the critical shear stress when the nuclear power alloy material is not irradiated, the increase of the critical shear stress after being irradiated function, as well as the strength factor related to the defect type, the shear modulus of the material, the Burgers vector, the hardening constant, the initial hardening coefficient, the hardening exponent, the saturated critical shear stress, the density of the defect, the size of the defect, and construct the hardening equation, And according to the differential method, the critical shear stress is obtained.

Preferably, in the process of constructing the hardening equation, based on the phase field variable, the initial hardening coefficient and the saturation critical shear stress are obtained by considering the first hardening parameter of the austenite matrix, the second hardening parameter of the dislocation loop and the concentration of defect atoms .

Preferably, in the process of constructing the phase field dynamics model, a relationship expression model between the stress-strain field and the plastic strain is constructed; wherein, the strain field is obtained by fast Fourier transform, and the stress field is obtained according to the generalized Hooke's law , according to the theory of crystal plasticity, to obtain the plastic strain.

Preferably, in the process of predicting the radiation hardening of the nuclear power alloy material, the free energy variation is obtained according to the variation of the chemical free energy to the composition and the variation of the elastic energy to the composition;

Based on the phase field dynamics model, according to the semi-implicit Fourier spectrum method, by obtaining the free energy variation and the relational expression model, the chemical free energy density, plastic strain and elastic free energy density for the next iteration are respectively obtained until Iterate to the set applied tensile strain value, and after the data is quantitatively processed, the radiation hardening prediction of the nuclear power alloy material is carried out.

The invention also discloses a microstructure-based radiation hardening prediction system, including:

The chemical free energy density generation module is used to obtain the chemical freedom of nuclear power alloy materials according to the Avogadro constant, atomic molar volume, defect atom concentration, defect formation energy, Boltzmann constant, and absolute temperature of nuclear power alloy materials Energy density;

The elastic free energy density generation module is used to obtain the elastic free energy density of nuclear power alloy materials based on the crystal plasticity of nuclear power alloy materials;

The thermodynamic system module is used to construct a thermodynamic system model for characterizing the evolution of radiation defects in nuclear power alloy materials according to the chemical free energy density and elastic free energy density;

The radiation hardening prediction module is used to construct a phase field dynamics model based on a thermodynamic system model by obtaining the chemical mobility of point defects in nuclear power alloy materials, the generation rate of point defects under irradiation conditions, and the concentration of defect atoms. Among them, the phase field dynamics model is used to predict the radiation hardening of nuclear power alloy materials.

The invention discloses the following technical effects:

The present invention uses phase field simulation to study the relationship between radiation hardening and defects, and obtains stress-strain curves, which can make up for the shortcomings of experimental research to a limited extent;

The present invention introduces microscopic defects in the process of considering irradiation, considers the hardening of defects in the stretching process, and improves the prediction accuracy of radiation hardening and the engineering application value of calculation simulation;

The prediction method mentioned in the present invention is simple, and the required parameters are obtained by conventional TEM characterization and tensile experiments.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the embodiments. Obviously, the accompanying drawings in the following description are only some of the present invention. Embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without paying creative labor.

Fig. 1 is a schematic flowchart of phase field simulation for predicting radiation hardening according to the present invention.

Fig. 2 is a comparison of dislocation loop distribution experiments and simulations of 316 austenitic stainless steel irradiated at room temperature at room temperature according to the present invention.

Fig. 3 is a comparison between experiment and simulation of stress-strain curves of 316 austenitic stainless steel at room temperature and 550°C according to the present invention.

Fig. 4 is the prediction of the stress-strain curve of the radiation hardening of 316 austenitic stainless steel according to the present invention.

Fig. 5 is a comparison between the radiation hardening predicted by the phase field of the 316 austenitic stainless steel according to the present invention and the experiment.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only It is a part of the embodiments of this application, not all of them. The components of the embodiments of the application generally described and illustrated in the figures herein may be arranged and designed in a variety of different configurations. Accordingly, the following detailed description of the embodiments of the application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of the application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative efforts belong to the scope of protection of the present application.

As shown in Figures 1-5, the present invention provides a method for predicting radiation hardening based on microstructure, comprising the following steps:

According to the Avogadro constant, atomic molar volume, defect atom concentration, defect formation energy, Boltzmann constant, and absolute temperature of the nuclear power alloy material, the chemical free energy density of the nuclear power alloy material is obtained;

Based on the crystal plasticity of nuclear power alloy materials, obtain the elastic free energy density of nuclear power alloy materials;

According to the chemical free energy density and elastic free energy density, construct a thermodynamic system model for characterizing the evolution of radiation defects in nuclear power alloy materials;

Based on the thermodynamic system model, the phase field dynamics model is constructed by obtaining the chemical mobility of point defects of nuclear power alloy materials, the generation rate of point defects under irradiation conditions, and the concentration of defect atoms. Among them, the phase field dynamics model is used For radiation hardening prediction of nuclear power alloy materials.

Further preferably, in the process of obtaining the elastic free energy density, the present invention obtains the elastic free energy density by collecting the elastic constant and elastic strain tensor of the nuclear power alloy material.

Further preferably, in the process of collecting the elastic strain tensor, the present invention generates the elastic strain tensor by collecting external strain, non-uniform strain, and intrinsic strain of the nuclear power alloy material.

Further preferably, in the process of collecting the intrinsic strain, the present invention obtains the volume expansion coefficient related to the defect, the defect equilibrium concentration at a certain temperature, the plastic strain tensor, and the concentration of defect atoms. According to the coupled crystal plasticity theory, Get the eigenstrain.

Further preferably, in the process of obtaining the plastic strain tensor, the present invention obtains the slip coefficient amount, the plastic shear rate of the slip system, the initial plastic shear rate, the strain sensitivity index, the Schmid tensor factor, the shear stress , the critical shear stress to generate the plastic strain tensor, wherein, when the system shear stress is greater than the critical shear stress, slip occurs, and the Schimid tensor factor is obtained by obtaining the slip direction and the normal direction of the slip system.

Further preferably, in the process of obtaining the critical shear stress, the present invention is based on radiation hardening and strain hardening, by obtaining the critical shear stress when the nuclear power alloy material is not irradiated, and the critical shear stress caused after being irradiated. Increasing function of stress, and strength factor related to defect type, shear modulus of material, Burgers vector, hardening constant, initial hardening coefficient, hardening exponent, saturation critical shear stress, density of defects, size of defects, build Hardening equation, and according to the difference method, the critical shear stress is obtained.

Further preferably, in the process of constructing the hardening equation, based on the phase field variable, considering the first hardening parameter of the austenite matrix, the second hardening parameter of the dislocation loop and the concentration of defect atoms in the present invention, the initial hardening coefficient and saturated critical shear stress.

Further preferably, in the process of constructing the phase field dynamics model in the present invention, the present invention also constructs a relationship expression model based on the stress-strain field and plastic strain; wherein, the strain field is obtained by fast Fourier transform, according to The generalized Hooke's law obtains the stress field, and according to the crystal creeping theory, obtains the plastic strain.

Further preferably, in the process of predicting the radiation hardening of nuclear power alloy materials, the present invention obtains the free energy variation according to the variation of chemical free energy to composition and the variation of elastic energy to composition;

Based on the phase field dynamics model, according to the semi-implicit Fourier spectrum method, by obtaining the free energy variation and the relational expression model, the chemical free energy density, plastic strain and elastic free energy density for the next iteration are respectively obtained until the iteration To the set applied tensile strain value, after quantitative processing of the data, the radiation hardening prediction of the nuclear power alloy material is carried out.

The invention also discloses a microstructure-based radiation hardening prediction system, including:

The chemical free energy density generation module is used to obtain the chemical freedom of nuclear power alloy materials according to the Avogadro constant, atomic molar volume, defect atom concentration, defect formation energy, Boltzmann constant, and absolute temperature of nuclear power alloy materials Energy density;

The elastic free energy density generation module is used to obtain the elastic free energy density of nuclear power alloy materials based on the crystal plasticity of nuclear power alloy materials;

The thermodynamic system module is used to construct a thermodynamic system model for characterizing the evolution of radiation defects in nuclear power alloy materials according to the chemical free energy density and elastic free energy density;

The radiation hardening prediction module is used to construct a phase field dynamics model based on a thermodynamic system model by obtaining the chemical mobility of point defects in nuclear power alloy materials, the generation rate of point defects under irradiation conditions, and the concentration of defect atoms. Among them, the phase field dynamics model is used to predict the radiation hardening of nuclear power alloy materials.

Embodiment 1: The embodiment uses a microstructure-based radiation hardening prediction method provided by the present invention, taking 316 austenitic stainless steel as an example, including the following steps:

Fig. 1 is a schematic flowchart of a prediction method based on microstructure radiation hardening provided by the embodiment of this specification.

Step 102: Establish a 316 austenitic stainless steel irradiation thermodynamic system model to obtain thermodynamic parameters

The system thermodynamics is specifically expressed as a function of field variables:

Among them, F is the total free energy of the system (unit is J), which is composed of chemical free energy F _ch (unit is J) and elastic free energy F _el (unit is J). f _ch is the chemical free energy density (in J/m ³ ), f _el is the elastic free energy density (in J/m ³ ), and dV is the unit volume of the system (in m ³ ).

The expression for the chemical free energy density is:

Among them, N is Avogadro's constant (unit is mol-1), Ω is atomic molar volume (unit is m ³ /mol), c _i is defect atom concentration (unit is at.%), E _i is defect The formation energy of (in J), k _B is Boltzmann's constant (in J/K), and T is the absolute temperature (in K).

Determine E _i based on first-principle calculations or literature reference values. The value of E _i must be determined so that the simulated defect microstructure is similar to the experiment, and the rest of the constants are constant values.

Step 104: Consider crystal plasticity, establish the elastic free energy expression of 316 austenitic stainless steel, obtain parameters,

The expression for establishing the elastic free energy density based on crystal plasticity is:

为弹性应变张量。Among them, C _ijkl is the elastic constant,

is the elastic strain tensor.

为外应变，ε_ij为非均匀应变，

为体系总的本征应变，其表达式为，

is the external strain, ε _ij is the non-uniform strain,

is the total eigenstrain of the system, and its expression is,

为某一温度下的缺陷平衡浓度(单位为at.％)，δ_ij为Kronecker常数，

为塑性应变张量，通过在相场模拟中耦合晶体塑性理论计算而得。where _ε0 is the volume expansion coefficient associated with defects,

is the defect equilibrium concentration (in at.%) at a certain temperature, _δij is the Kronecker constant,

is the plastic strain tensor, calculated by coupling the theory of crystal plasticity in the phase field simulation.

由

计算而得，室温下

C_ijkl由第一性原理计算或文献得到。Value ε ₀ =0.001;

Depend on

Calculated at room temperature

C _ijkl is obtained from first-principles calculations or literature.

Step 106: Establish crystal plasticity model and obtain parameters

The expression of the plastic strain tensor is:

为滑移系α的塑性剪切率(单位为s-1)，

为初始塑性剪切率(单位为s-1)，n为应变敏感指数，

为Schimid张量因子，I_α为滑移方向，n_α为滑移系的法向，τ^α＝σ:m_α为剪切应力，σ为应力张量，

为临界剪切应力。当系统剪切应力大于临界剪切应力时，发生滑移。Among them, N is the total slip coefficient of the system,

is the plastic shear rate of the slip system α (unit is s-1),

is the initial plastic shear rate (unit is s-1), n is the strain sensitivity index,

is the Schimid tensor factor, I _α is the slip direction, n _α is the normal direction of the slip system, τ ^α = σ:m _α is the shear stress, σ is the stress tensor,

is the critical shear stress. Slip occurs when the system shear stress is greater than the critical shear stress.

的初始值τ₀由计算而得，τ₀＝Sσ_y，其中σ_y为材料的屈服强度，由实验而得，S为Schmid因子，取0.41。The value of n is 20 according to the crystal plastic finite element; the calculation of m ^α depends on the slip system of different materials, for 316 austenitic stainless steel it is {111}<110> slip system;

The initial value τ ₀ of is obtained by calculation, τ ₀ =Sσ _y , where σ _y is the yield strength of the material, obtained by experiment, and S is the Schmid factor, which is 0.41.

Step 108: Determine the radiation hardening and strain hardening, and obtain the hardening value of the critical shear stress:

The specific expression considering radiation hardening and strain hardening is,

为未辐照材料的临界剪切应力，

为辐照引起的临界剪切应力的增加，α为与缺陷类型相关的强度因子，μ为材料的剪切模量，b为伯氏矢量，q^αβ为硬化常数，

为初始硬化系数(单位为MPa)，m为硬化指数，τ_s为饱和临界剪切应力(MPa)，N为缺陷的密度，d为缺陷的尺寸，dt为模拟时间步长，

为β滑移系的塑性剪切率。in,

is the critical shear stress of the unirradiated material,

is the increase of the critical shear stress caused by irradiation, α is the intensity factor related to the defect type, μ is the shear modulus of the material, b is the Burgers vector, q ^αβ is the hardening constant,

is the initial hardening coefficient (in MPa), m is the hardening exponent, τ _s is the saturation critical shear stress (MPa), N is the defect density, d is the defect size, dt is the simulation time step,

is the plastic shear rate of the β-slip system.

The hardening parameters of the dislocation loops should be different from those of the austenite matrix. Based on the combination of the composition field and crystal plasticity of the phase field simulation, the hardening parameters of the overall system are expressed as follows,

为奥氏体基体的硬化参数，

为位错环的硬化参数。

和

被认为与奥氏体集体参数成比例，

其中k为常数。in,

is the hardening parameter of the austenitic matrix,

is the hardening parameter of the dislocation loop.

and

is considered to be proportional to the austenite collective parameter,

where k is a constant.

N and d, determined by TEM of the irradiated sample, are 4.27×1022m-3 and 5.7nm, respectively. The irradiation defect in this embodiment is a dislocation loop, and α is the strengthening factor of the dislocation loop, which can be obtained from relevant literature. It is taken as 0.4, and the calculated τ ^ir is 121.9 MPa.

和τ_s为拟合值，采用与τ₀成比例的方式，

τ_s/τ₀，分别根据室温和550℃的实验的应力应变曲线拟合得到。m采用文献值和拟合相结合的方式。Considering the hardening process of the same slip system, the value of q ^αβ is 1;

and τ _s are fitted values, which are proportional to τ ₀ ,

τ _s /τ ₀ are obtained by fitting the stress-strain curves of experiments at room temperature and 550°C, respectively. m uses a combination of literature values and fitting.

The hardening parameters for dislocation loops should be differentiated from those for the austenitic matrix. According to the formula,

Among them, α _L represents the strengthening factor of the irradiated dislocation loop and α _ρ forest dislocation respectively, α _L usually takes 0.3-0.45, and α _ρ usually takes 0.2. In this embodiment, k is 2 for the dislocation loop in the crystal plasticity model.

Using the difference method to solve the hardening equation,

The calculated critical shear stress is a necessary parameter for calculating the plastic strain in step 106 .

Step 110: Solve the stress equation

The stress-strain field and plastic strain are obtained by solving the following relationship,

考虑模拟初始时的塑性应变为0。in,

Consider the plastic strain at the beginning of the simulation to be 0.

The solution of the stress-strain field adopts the method of fast Fourier transform,

ε_kl(r)为傅里叶逆变换求解的应变场，由广义胡克定律可以求得应力场。Among them, Ω _ik (n) is the Green's function, n _j , n _l are the unit vectors in Fourier space, and _ci (g) is the Fourier transform of the components. Initial value of plastic strain

ε _kl (r) is the strain field obtained by inverse Fourier transform, and the stress field can be obtained by generalized Hooke's law.

Then the plastic strain can be obtained according to the crystal plasticity formula in step 106 .

Step 112: Establish the defect evolution phase field equation and solve it

The details of the phase field dynamics model are as follows:

根据步骤110应力应变场求解方法求解出的应变场与塑性应变场，根据步骤104弹性能对成分的变分可以具体表达为，Among them, M _i is the chemical mobility of point defects under irradiation, and g _i is the generation rate of point defects under irradiation conditions. The variation of free energy with respect to composition is related to chemical free energy and elastic energy, respectively, δF/δc _i =δ(F _ch +F _el )/δc _i . The variation of chemical free energy to composition can be obtained by the formula in step 102,

According to the strain field and plastic strain field solved by the stress-strain field solution method in step 110, the variation of the elastic energy to the composition according to step 104 can be specifically expressed as,

M _i = c _i D _i /k _B /T, where D _i is the diffusion coefficient of point defects;

Substitute the obtained free energy variation into the phase field dynamics equation, and use the semi-implicit Fourier spectrum method to solve the phase field dynamics equation. The obtained component field is iterated into the chemical free energy in step 102 and the stress-strain field is solved in step 110, and the plastic strain and free energy variation in the next iterative step can be obtained until the set value of the applied tensile strain is iterated. The data can be quantitatively processed by software such as MATLAB to predict the radiation hardening. Table 1 provides the main physical parameters of the specific examples. In the above technical scheme, the applicable service temperature of the radiation hardening prediction method is 25°C-600°C , the applicable strain range of the radiation hardening prediction method is 0-0.05.

Table 1

Fig. 2 is the experimental and simulated comparison of the microstructure of 316 austenitic stainless steel irradiated at room temperature by 1dpa using a method for predicting radiation hardening based on microstructure proposed by the present invention. The irradiation defects are mainly dislocation loops, which is different from the actual experiment. Compared with the better consistency, the characteristics of uneven distribution of heavy ion irradiation defects are better simulated, indicating that the method proposed by the present invention can be used to predict the microstructure of materials irradiated.

Fig. 3 is a comparison between experiments and simulations of the stress-strain response of unirradiated 316 austenitic stainless steel using a microstructure-based radiation hardening prediction method proposed by the present invention. It can be found that the room temperature and high temperature stress-strain responses simulated based on the present invention correspond well to experiments and literature. The method proposed by the invention can be used to obtain the stress-strain response of materials.

(M取3.06)计算得到的屈服强度值为673MPa，由纳米压痕测试得到的实际屈服强度为865MPa，可以发现，本发明不仅可以得到离子辐照后材料的应力应变响应，同时可以提高辐照硬化的预测精度。Fig. 4 is a stress-strain curve after radiation hardening obtained by using a microstructure-based radiation hardening prediction method proposed by the present invention for 316 austenitic stainless steel irradiated at room temperature at 1 dpa. The yield strength after irradiation obtained from this stress-strain curve was 813 MPa. According to the TEM tissue map, the defect density and size are obtained from the discrete hardening model (DBH model)

(M takes 3.06) the calculated yield strength value is 673MPa, and the actual yield strength obtained by the nanoindentation test is 865MPa. It can be found that the present invention not only can obtain the stress-strain response of the material after ion irradiation, but also can improve the irradiation Hardened prediction accuracy.

Fig. 5 is a comparison of the prediction and experimental value of the yield strength change of 316 austenitic stainless steel after irradiation by a radiation hardening prediction method based on microstructure provided by the present invention, and it is compared with the traditional discrete strengthening model (DBH model) at the same time The predicted yield strength change was compared with the prediction accuracy. According to the above several groups of experiments, the irradiation microscopic defects are mainly irradiation dislocation loops. It can be found that the phase field model can predict the irradiation hardening well, and has a high prediction accuracy. At the same time, compared with the uncertainty of the value of α in the traditional discrete hardening model (DBH model), α in the phase field model takes a uniform value of 0.4, which improves the unity and certainty of the prediction results.

The results of the examples show that the invention predicts the radiation hardening effect of the material and obtains the stress-strain response relationship, providing a new prediction method for the radiation hardening of the material. This can be used as a theoretical reference for the design of nuclear power structural materials and life prediction under irradiation conditions, which improves the engineering applicability of phase field theory.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each procedure and/or block in the flowchart and/or block diagram, and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

In the description of the present invention, it should be understood that the terms "first" and "second" are used for description purposes only, and cannot be interpreted as indicating or implying relative importance or implicitly indicating the quantity of indicated technical features. Thus, a feature defined as "first" and "second" may explicitly or implicitly include one or more of these features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these modifications and variations.

Claims (8)

1. A microstructure-based irradiation hardening prediction method is characterized by comprising the following steps:

acquiring the chemical free energy density of the nuclear power alloy material according to the Avogardlo constant, the atom molar volume, the defect atom concentration, the defect formation energy, the Boltzmann constant and the absolute temperature of the nuclear power alloy material;

acquiring the elastic free energy density of the nuclear power alloy material based on the crystal plasticity of the nuclear power alloy material;

constructing a thermodynamic system model for representing the evolution of the irradiation defects of the nuclear power alloy material according to the chemical free energy density and the elastic free energy density;

based on the thermodynamic system model, constructing a phase field kinetic model by obtaining the chemical mobility of irradiation point defects, the generation rate of the point defects under irradiation conditions and the concentration of defect atoms of the nuclear power alloy material; obtaining free energy variation according to variation of chemical free energy to components and variation of elastic energy to components; substituting the free energy component into the phase field dynamic model, solving the phase field dynamic model by adopting a semi-implicit Fourier spectrum method, obtaining chemical free energy density, plastic strain and elastic free energy density for next iteration on the basis of the component field obtained by solving and a relation expression model of a stress strain field and plastic strain until the iteration reaches the set additional tensile strain value, and performing radiation hardening prediction on the nuclear power alloy material through MATLAB.

2. The method of claim 1, wherein the step of predicting radiation hardening based on the microstructure comprises:

in the process of obtaining the elastic free energy density, the elastic free energy density is obtained by collecting the elastic constant and the elastic strain tensor of the nuclear power alloy material.

3. The method for predicting radiation hardening based on microstructure according to claim 2, wherein:

and in the process of collecting the elastic strain tensor, collecting the external strain, the non-uniform strain and the intrinsic strain of the nuclear power alloy material to generate the elastic strain tensor.

4. The method of claim 3, wherein the step of predicting radiation hardening based on the microstructure comprises:

in the process of collecting intrinsic strain, acquiring a volume expansion coefficient related to a defect, a defect equilibrium concentration at a certain temperature, a plastic strain tensor and a defect atom concentration, and acquiring a plastic strain tensor used in the intrinsic strain calculation process based on a coupled crystal plasticity theory in phase field simulation.

5. The method of claim 4, wherein the step of predicting radiation hardening based on the microstructure comprises:

in the process of obtaining the plastic strain tensor, the plastic strain tensor is generated by obtaining the number of slip systems, the plastic shear rate of the slip systems, the initial plastic shear rate, the strain sensitivity index, the Schimid tensor factor, the shear stress and the critical shear stress, wherein when the system shear stress is larger than the critical shear stress, slip occurs, and the Schimid tensor factor is obtained by obtaining the slip direction and the normal direction of the slip systems.

6. The method of claim 5, wherein the step of predicting radiation hardening based on the microstructure comprises:

in the process of obtaining the critical shear stress, based on irradiation hardening and strain hardening, a hardening equation is constructed by obtaining the critical shear stress of the nuclear power alloy material when the nuclear power alloy material is not irradiated, an increasing function of the critical shear stress caused after the nuclear power alloy material is irradiated, and an intensity factor related to the defect type, a shear modulus of the material, a Berth vector, a hardening constant, an initial hardening coefficient, a hardening index, a saturated critical shear stress, the density of the defect, and the size of the defect, and the critical shear stress is obtained according to a difference method.

7. The method of claim 6, wherein the step of predicting radiation hardening based on the microstructure comprises:

in the process of constructing a phase field dynamics model, constructing a relation expression model of a stress strain field and plastic strain; the method comprises the steps of obtaining a strain field in a fast Fourier transform mode, obtaining a stress field according to a generalized Hooke law, and obtaining the plastic strain according to the plastic strain tensor.

8. A system for predicting radiation hardening based on a microstructure, comprising:

the chemical free energy density generation module is used for acquiring the chemical free energy density of the nuclear power alloy material according to the Avogardo constant, the atom molar volume, the defect atom concentration, the defect forming energy, the Boltzmann constant and the absolute temperature of the nuclear power alloy material;

the elastic free energy density generating module is used for acquiring the elastic free energy density of the nuclear power alloy material based on the crystal plasticity of the nuclear power alloy material;

the thermodynamic system module is used for constructing a thermodynamic system model for representing the evolution of the irradiation defects of the nuclear power alloy material according to the chemical free energy density and the elastic free energy density;

the irradiation hardening prediction module is used for constructing a phase field dynamics model by acquiring the chemical mobility of irradiation point defects, the generation rate of the point defects under the irradiation condition and the defect atom concentration of the nuclear power alloy material based on the thermodynamic system model; obtaining free energy variation according to variation of chemical free energy to components and variation of elastic energy to components; substituting the free energy component into the phase field dynamic model, solving the phase field dynamic model by adopting a semi-implicit Fourier spectrum method, obtaining chemical free energy density, plastic strain and elastic free energy density for next iteration on the basis of the component field obtained by solving and a relation expression model of a stress strain field and plastic strain until the iteration reaches the set additional tensile strain value, and performing radiation hardening prediction on the nuclear power alloy material through MATLAB.

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