Creep mechanics native modeling method based on multi-physical mechanism

Abstract

The invention relates to a multi-physical mechanism-based creep mechanics native modeling method, which comprises the following steps of: in a creep process, solving a kinetic equation according to initial microstructure information to obtain a total creep rate of a system; in a very small time interval, a differential equation set related to dislocation density evolution is further solved, so that the movable dislocation density and the immovable dislocation density at the current creep rate are obtained, and the movable dislocation density and the immovable dislocation density serve as input parameters of the next deformation process; and continuously updating the creep information by repeating the steps until the deformation reaches the Griffis fracture condition, and finally outputting a complete creep curve. The method solves the problem that a current modeling method for evaluating the creep behavior generally comprises a large number of empirical parameters and needs to depend on experimental data for fitting, and the universality of the modeling method is limited.

Description

Technical Field

[0001] The present invention belongs to the technical field of computational mechanics, and relates to a constitutive modeling method of creep mechanics based on multi-physical mechanisms, which is applied to the study of creep damage and life prediction behavior of structural materials and the design and optimization of new creep-resistant metal materials. Background Art

[0002] Predicting the creep rupture life of structural materials is a key issue in the identification and design of new materials. Over the past century, researchers have invested a lot of energy in creep mechanisms, creep life prediction, and improving creep resistance through material design, which is of great significance to structural safety in industrial fields such as aerospace, power generation, and nuclear energy. However, quantitative descriptions of microstructural parameters such as plastic slip and creep holes are usually difficult to obtain through conventional external experiments or in situ experiments. The complex and time-consuming experimental process may affect the accuracy of the experimental results, especially in high temperature environments. In order to quantitatively predict the creep mechanical response of metal materials at high temperatures, explore the relationship between microstructure and mechanical properties, and establish a computational model that can be used for numerical analysis, it has become a scientific problem that needs to be solved urgently.

[0003] Currently, constitutive modeling methods used to evaluate creep behavior can be roughly divided into two categories: phenomenological-based models and physics-based models. Phenomenological models rely on creep experimental data and use empirical relationships for extrapolation. These early theories and formulas have important value in engineering applications. However, due to the difficulty in simultaneously obtaining the evolution law of the microstructure under different temperatures and loading conditions, such models show limitations under stress and temperature conditions beyond the calibration range. In order to overcome these limitations, some physics-based models introduce the effects of microdeformation and damage mechanisms, which can quantify the creep damage of materials and predict long-term life to a certain extent. However, such models still have theoretical deficiencies, such as incomplete descriptions of grain boundary sliding and void evolution, and failure to fully explore potential competing mechanisms. In addition, these models usually contain a large number of empirical parameters and need to rely on experimental data for fitting, which limits their universality.

[0004] To address the above challenges, we proposed a constitutive modeling method for creep mechanics based on multi-physics mechanisms. This method is based on a unified thermodynamic framework and incorporates the coordinated evolution of point defects, dislocations, grain boundaries, and voids into the computational model. By constructing kinetic equations, quantitative and non-empirical predictions of the creep behavior of metal materials under high temperature conditions are achieved. This method not only deepens the understanding of the microscopic creep mechanism, but also provides valuable insights for designing materials with specific microstructures to enhance their creep resistance. Summary of the invention

[0005] In view of this, the present invention provides a constitutive modeling method of creep mechanics based on multi-physical mechanisms in order to solve the problem that the current constitutive modeling method for evaluating creep behavior usually contains a large number of empirical parameters and needs to rely on experimental data for fitting, which limits its universality.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A constitutive modeling method of creep mechanics based on multi-physics mechanism comprises the following steps:

[0008] S1. Based on the initial microstructure information, the kinetic equation is solved to obtain the total creep rate of the system;

[0009] The creep behavior is controlled by the coupled dynamics of various microstructures and defects, including zero-dimensional point defects, one-dimensional dislocations, two-dimensional grain boundaries, and three-dimensional voids. In a unified thermodynamic framework, multiple thermally activated mechanisms, including intragranular and grain boundary vacancy diffusion, dislocation slip and climb, grain boundary sliding, and void evolution, are considered; based on these mechanisms, the total creep rate is expressed as:

[0010]

[0011] in, They are the accumulated plastic strains of vacancy diffusion, dislocation movement, grain boundary sliding, and void evolution;

[0012] S2, solving the differential equations related to the evolution of dislocation density, obtaining the movable dislocation density and the immovable dislocation density at the current creep rate, and using them as input parameters for the next deformation process;

[0013] During the creep deformation process, dislocations will multiply, store and annihilate, which not only changes the density of dislocations, but also affects their types and spatial distribution, thus significantly affecting the creep behavior of the material; the evolution rate of different types of dislocation density over time is expressed by the mathematical formula:

[0014]

[0015] Among them, m d represents the number of active dislocation density evolution mechanisms, ρ j represents the dislocation density corresponding to the i-th dislocation density evolution mechanism;

[0016] S3, repeating steps S1 and S2, continuously updating creep information until the deformation reaches the Griffith fracture condition, and outputting a complete creep curve.

[0017] Furthermore, in the calculation of the vacancy diffusion creep rate in step S1, the construction of the kinetic equation is specifically as follows:

[0018] The plastic deformation caused by diffusion creep is entirely due to the migration of materials during the diffusion process. The driving force comes from the difference in the chemical potential of point defects when the grain boundary is subjected to tensile or compressive stress. In this process, the grain boundary is regarded as a perfect source or sink of vacancies. Therefore, when vacancies diffuse inside the grain or along the grain boundary, the creep rate is expressed as:

[0019]

[0020] In the formula, c eq is the vacancy equilibrium concentration, σ n is the applied normal stress, Ω a is the atomic volume, k B is the Boltzmann constant, T is the temperature, d is the grain size, δ gb is the grain boundary layer thickness, D bulk and D gb are the bulk diffusion coefficient and the grain boundary diffusion coefficient, respectively.

[0021] Furthermore, in the calculation of the dislocation movement creep rate in step S1, the construction of the dislocation sliding and climbing mechanical equations is specifically as follows:

[0022] Viscoplasticity is usually defined as time-dependent plastic deformation beyond the elastic state, which is closely related to the viscous motion of dislocations. In this case, creep strain is gradually accumulated due to the motion of dislocations. The creep rate contributed by dislocation motion is expressed by the Orowan equation:

[0023]

[0024] In the formula, are shear strain rate and plastic strain rate, M is Taylor factor, ρ m is the mobile dislocation density, b is the Burgers vector, is the average dislocation velocity, which depends on the average obstacle spacing and the time it takes for a dislocation to move between obstacles, the latter of which includes the waiting time in front of the obstacle (Δt w ) and the time to move between obstacles (Δt tr ):

[0025]

[0026] The presence of various types of obstacles leads to a reduction in the mean free path. The average spacing of obstacles is expressed as the geometric mean of the spacing of individual obstacles:

[0027]

[0028] Among them, n d is the number of obstacle types, wi is the proportion of different obstacle types, is the obstacle distance;

[0029] Usually dislocations overcome obstacles through thermally activated slip or climb-assisted slip processes. These two mechanisms are coupled and can occur simultaneously. The total waiting time is calculated by visualizing the bypass process as a parallel circuit. The average waiting time of dislocations is expressed as:

[0030]

[0031] Among them, Δt slip ,Δt climb denote the theoretical waiting times for thermally activated sliding and climbing, respectively;

[0032] The process of dislocation sliding over an obstacle is essentially a force-heat coupling activation process. The waiting time of dislocation sliding is described by the Kocks-type activation enthalpy law:

[0033]

[0034] Among them, v D is the Debye frequency, n d is the number of obstacle types, ΔE i (τ i ) is the activation energy;

[0035] Based on the dislocation theory and thermal activation model, the behavior of dislocations crossing obstacles with the assistance of external force and heat is unified as the process of dislocation detachment point pinning; according to the properties of the material, the lattice friction, solid solution atoms, forest dislocations, grain boundaries, and precipitation particles inside the material are considered to hinder the dislocation slip, so as to evaluate the waiting time for dislocation slip; therefore, the force-activation energy relationship corresponding to different obstacles is as follows:

[0036]

[0037] ΔE dis (τ dis )=E dis (ζ cr ,τ dis )-E dis (ζ eq ,τ dis ) (10)

[0038]

[0039] Depending on the type of precipitating particles, dislocations will experience two different behaviors when encountering precipitating particles: cutting-through mechanism and bypassing mechanism. The corresponding activation energy relationships are:

[0040]

[0041] In the formula, ΔE fr ,ΔE ss ,ΔE dis ,ΔE gb ,ΔE dis , They represent the activation energies corresponding to lattice friction, solution atoms, dislocations, grain boundaries, and precipitated particles, respectively, and τ fr ,τ ss ,τ dis ,τ gb ,τ dis ,τ prec They represent the external shear stress corresponding to lattice friction, solution atoms, dislocations, grain boundaries, and precipitated particles, respectively. fr0 and ΔE fr They represent the energy per unit length of the dislocation line and the increase in energy after the dislocation line changes from the initial state to the line tension state, is the total energy barrier related to the interaction energy and line energy, is the average dislocation binding energy generated by the interaction between solute atoms and dislocations, Γ is the dislocation line tension, and w c is the coarsening amplitude of the dislocation segment, ζ cr and eq are the critical dislocation configuration and the equilibrium dislocation configuration, L * is the length of the dislocation segment involved in the local activation event, L gb is the average spacing between the grain boundary pinning points, h is the height of the kink pair, A1 = cos 2 β+sin 2 β / (1-v) and A2 = [(1+v)cos 2 β+(1-2v)sin 2 β] / (1-v) is the intrinsic parameter of the dislocation, β is the angle between the dislocation line and the Burgers vector, is the critical width of the kink pair, r core is the dislocation core radius;

[0042] Dislocation climb caused by vacancy diffusion is another important creep / plasticity mechanism besides dislocation slip. At high temperature and low strain rate, edge dislocations occur through the climb mechanism, which is driven by vacancy diffusion on the dislocation line. Dislocation climb is a typical thermally activated process with an activation energy (ΔE climb ) is obtained by the following formula:

[0043] ΔE climb (τ climb )=E vf +E mb +E jog -τ climb Ωa (13)

[0044] Among them, E vf and E mb represent the vacancy formation energy and vacancy migration energy, E jog is the step formation energy, Ω a is the atomic volume, and accordingly, the average climb velocity of the dislocation is:

[0045]

[0046] Where n c is the number of neighboring atoms, v0 = 2(b / d SF ) 2 v D is the vibration frequency, d SF is the stacking fault width;

[0047] In this method, the waiting time for climb is determined by the ratio of the average climb velocity of edge dislocations to the average climb distance before bypassing the obstacle; therefore, the average climb waiting time of edge dislocations is expressed as:

[0048]

[0049] In the formula, R e is the edge dislocation ratio, l climb is the average climbing distance to bypass obstacles;

[0050] The running time depends on the movement distance and running speed of the dislocation. Since the running time of the dislocation is obviously less than the waiting time, it is assumed that the running speed of the dislocation is the shear wave speed, that is, Based on this, the running time is expressed as:

[0051]

[0052] in, is the average obstacle spacing, G is the shear modulus, and ρ is the material density.

[0053] Furthermore, in the calculation of the grain boundary sliding creep rate in step S1, the construction of the kinetic equation is specifically as follows:

[0054] If the grain boundary slip is caused by the climb slip of dislocations, the grain boundary slip rate is determined by the climb rate, since climb is usually a slow process. In this case, the climb frequency (v c ) is expressed as:

[0055]

[0056] Where P jog is the probability of finding a step on a dislocation, S dis the diffusion activation entropy, E d is the diffusion activation energy, τ x is the stress required for climbing along the interface; assuming that dislocations are uniformly distributed along the grain boundary and their spacing is determined by the edge dislocation stress field, the dislocation climb rate along the grain boundary is:

[0057]

[0058] Among them, N gb-d is the number of grain boundary dislocations per unit length, τ gb-d is the applied shear stress;

[0059] If the dislocation moves in the region adjacent to the grain boundary, then Eq. (17) is simplified by the bulk diffusion coefficient, and the shear strain rate during the climb-slip process is, The climb rate is controlled, but the strain is generated by slip, which is expressed as:

[0060]

[0061] Among them, M gb is the number of grain boundaries per unit volume, A gb is the area swept by the dislocation along the grain boundary; since the dislocation enters the boundary area from the slip zones on both sides of the grain boundary,

[0062]

[0063] Substituting formula (20) into (19), for τ x Ω a <<k B T,τ=τ x =σ / 2, Conditions, the following form:

[0064]

[0065] Furthermore, in the calculation of the creep rate of the pore evolution in step S1, the construction of the kinetic equation is specifically as follows:

[0066] After creep enters the third stage, the creep rate gradually accelerates, eventually leading to fracture. Under high stress conditions, when the plastic deformation rate is very fast, the form of creep fracture is usually similar to ductile fracture at room temperature. Creep damage is mainly manifested in the nucleation, growth and aggregation of holes in high stress concentration areas, especially at grain boundaries, which eventually lead to fracture. With the nucleation of spherical crown holes at grain boundaries, the total energy of the system will change. The free energy change caused by hole nucleation is divided into three parts: first, the increase in surface energy caused by the new hole surface; second, the disappearance of the original grain boundary area leads to a decrease in interfacial energy; third, the release of elastic strain energy caused by the formation of holes; therefore, the activation energy of hole nucleation is expressed as:

[0067] ΔE voids-neclei =-σ n V voids +A voids γ voids -A gb γ gb (twenty two)

[0068] Among them, V voids is the pore volume, A voids and A gb are the surface areas corresponding to the pores and grain boundaries, γ voids and γ gb are the hole surface energy and grain boundary energy respectively; for the spherical cap hole shape, the surface energy tension balance equation is:

[0069]

[0070] in, is the hole tip angle; voids , A voids , A gb Substituting the calculation formula into formula (21), we get:

[0071]

[0072] Let ΔE voids-neclei / dr=0, the critical core radius of the pores that can exist stably without sintering is obtained, r c :

[0073]

[0074] r c Substituting into formula (24), the critical nucleation work of the hole is obtained as:

[0075]

[0076] in, is the shape factor of the hole;

[0077] The nucleation rate is defined as the number of void cores formed on the unit volume of the grain boundary; a void of critical radius can be stable if it gains a vacancy, and the steady state will disappear (the size automatically decreases) if it loses a vacancy; therefore, the nucleation rate depends on the number of nuclei with a radius on the unit volume of the grain boundary and the number of vacancies transferred to the void core per unit time; accordingly, the total nucleation rate in the steady state is:

[0078]

[0079] Where n0 = l voids -3is the number of potential nucleation sites, l voids is the half-hole spacing, ΔE vac-gb is the activation energy for vacancy diffusion along grain boundaries;

[0080] The basis of the pore diffusion growth model is that the pores gradually grow by absorbing vacancies. The diffusion of vacancies usually migrates through the pore surface and then transports along the grain boundary. During the creep process, due to the existence of stress gradient, the pore growth rate is closely related to the diffusion rate of vacancies. Therefore, the pore growth rate is expressed as:

[0081]

[0082] Among them, a voids is the hole radius, δ gb is the grain boundary width;

[0083] Since the dynamics of the nucleation and growth of voids are similar to the phase transition process, a kinetic model similar to the phase transition is used to describe it; Johnson-Mehl is used to describe the evolution of voids, especially in the nucleation and growth of voids; for spherical new voids, according to formulas (27) and (28), the volume fraction of the evolving voids is expressed as:

[0084]

[0085] Where t is time. According to Gurson's formula, the hole growth is controlled by the hydrostatic part of plastic strain, and the damage is expressed by the change of hole volume fraction as follows:

[0086]

[0087] In the formula, f voids is the pore volume fraction, is the total plastic strain rate calculated by the plastic velocity gradient; considering that the damage evolves with holes, the plastic strain rate contributed by the hole evolution is:

[0088]

[0089] Pore ​​aggregation occurs in many modes, each with several variants, depending on microstructural factors, loading conditions and plastic flow characteristics; among them, the aggregation of spherical pores often leads to elongated deformation and directional effects:

[0090]

[0091] In the formula, is the critical porosity for pore aggregation, is the aggregation factor, and are the saturated porosity and the failed porosity, respectively.

[0092] Furthermore, the dislocation multiplication mechanism in the dislocation evolution mechanism of step S2 includes Frank-Read dislocation source, grain boundary nucleation, double cross slip to form dislocation ring and edge dislocation dipole multiplication mechanism; Combining the above mechanisms, the expression of dislocation density multiplication rate is:

[0093]

[0094] In the formula, ρ m is the mobile dislocation density, L F-R is the initial dislocation length of the Frank-Read dislocation source, E F-R and E bc-s are the activation energies corresponding to the Frank-Read dislocation source and the double cross slip multiplication mechanism, n F-R is the number of propagated dislocation loops, τ gb is the shear stress corresponding to grain boundary nucleation, L bc-s is the length of the double cross slip dislocation segment, d SF is the stacking fault width, h and h cr are the separation distance and critical distance between two parallel slip planes, respectively.

[0095] Furthermore, considering the interaction between dislocations, network nodes and grain boundaries, the dislocation storage mechanism in the dislocation evolution mechanism of step S2 includes dislocation network node storage and grain boundary storage; accordingly, the dislocation density storage rate is:

[0096]

[0097] In the formula, K hkl is the mean free path coefficient, ρ im is the immobile dislocation density, D gb is the grain boundary diffusion rate.

[0098] Furthermore, the dislocation annihilation mechanism in the dislocation evolution mechanism of step S2 includes four dislocation annihilation mechanisms: screw dislocation single cross slip, screw dislocation spontaneous annihilation, edge dislocation climb and edge dislocation spontaneous annihilation. The dislocation density annihilation rate is described by the following formula:

[0099]

[0100] Among them, E sc-s represents the activation energy of single cross slip, ψ represents the angle between the main slip plane and the cross slip plane, n represents the number of active slip systems, τ0 represents the critical decomposed shear stress, τ fr represents the lattice friction stress, τ sro represents the shear stress of the disordered interface, S is the Schmidt factor ratio, τ a is the external shear stress, τ i represents the internal shear stress, Eclimb is the climb activation energy, E vf is the vacancy formation energy.

[0101] Furthermore, in order to more comprehensively describe the complex spatiotemporal evolution of dislocations, the eight other dislocation evolution mechanisms considered in step S2 reflect the evolution characteristics of dislocations in different spatial positions (inside the dislocation cell and on the dislocation cell wall), different motion states (movable and immovable), and different dislocation types (screw type and edge type); specifically, they include: movable screw dislocations inside dislocation cells Fixed screw dislocation inside the dislocation cell Movable edge dislocation inside a dislocation cell Immobile edge dislocation inside a dislocation cell Mobile screw dislocations in dislocation cell walls Immobile screw dislocation in dislocation cell wall Mobile edge dislocations in dislocation cell walls and immovable edge dislocations in dislocation cell walls

[0102] The evolution rate equations of these eight dislocations are summarized as follows:

[0103]

[0104] In order to solve the evolution equations of different types of dislocations, the dislocation density conservation principle must be satisfied; specifically, the evolution rate of the total dislocation density should be equal to the sum of the evolution rates of movable dislocations and immobile dislocations; based on this principle, the evolution equation of the total dislocation density is expressed as:

[0105]

[0106] Where f represents the volume fraction of the dislocation cell wall.

[0107] Furthermore, the Griffith fracture criterion in step S3 is:

[0108] For a crack of a given size, there is a critical stress σ c :When σ≤σ c When σ>σ c When the crack expands, the crack rapidly expands and causes fracture; when the crack expands, the change of system energy comes from two aspects: on the one hand, due to elastic strain energy, The release reduces the energy of the system, while the creation of new surfaces increases the energy.

[0109] U2=4a voids γ voids ; Assume that the crack length corresponding to the maximum value of the total energy change of the system is 2a voids , then when When , the increase in crack length will cause the system energy to increase, so the crack cannot expand automatically; When , the crack extension reduces the total energy of the system, and the crack can spontaneously expand unstably. Let:

[0110]

[0111] The critical stress for unstable crack growth is obtained by solving:

[0112]

[0113] The beneficial effects of the present invention are:

[0114] 1. The present invention discloses a constitutive modeling method of creep mechanics based on multi-physical mechanisms, including two important components: the creep mechanism kinetic equation and the dislocation density evolution equation. In the creep process, the kinetic equation is first solved based on the initial microstructure information to obtain the total creep rate of the system. In a very small time interval, we further solve the set of differential equations related to the evolution of dislocation density to obtain the movable dislocation density and immovable dislocation density at the current creep rate, and use them as input parameters for the next deformation process. By repeating the above steps, the creep information is continuously updated until the deformation reaches the Griffith fracture condition, and finally a complete creep curve is output. This solves the problem that the current constitutive modeling method used to evaluate creep behavior needs to rely on experimental data for fitting, which limits its universality. It can be applied to the study of creep damage and life prediction behavior of structural materials and the design and optimization of new creep-resistant metal materials.

[0115] 2. Based on dislocation theory and thermal activation model, the present invention proposes a constitutive modeling method of creep mechanics based on multi-physical mechanisms, which realizes the quantitative and non-empirical prediction of the high-temperature creep response of metal materials. The calculation parameters used in the model have clear physical meanings, which solves the drawbacks of traditional models that rely on creep experimental data fitting, significantly reduces experimental costs and time, and improves prediction efficiency and reliability. Compared with traditional methods, the present invention can not only accurately describe the evolution of point defects and dislocations in the first and second stages of creep, but also breaks through the limitations of previous studies on the analysis of physical mechanisms in the late stage of creep, and deeply captures the potential physical mechanisms of grain boundary sliding and hole evolution. By revealing the complex coupling between vacancies, dislocations, grain boundaries and holes, the invention successfully realizes the smooth transition from the second stage of creep to the third stage of accelerated deformation, and provides theoretical support for understanding creep fracture behavior. In addition, the invention can also make high-precision predictions of the creep life of different materials, providing important technical support for the selection, performance optimization and life evaluation of materials in high-temperature environments, and showing a wide range of engineering application potential and academic value.

[0116] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0117] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0118] Figure 1 It is a flow chart of the constitutive modeling method of creep mechanics based on multi-physics mechanism of the present invention;

[0119] Figure 2 Schematic diagram of the relationship between different creep mechanisms of the present invention. DETAILED DESCRIPTION

[0120] The following describes the embodiments of the present invention through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0121] like Figure 1 A constitutive modeling method of creep mechanics based on multi-physics mechanism is shown, comprising the following steps:

[0122] S1. Based on the initial microstructure information, the kinetic equation is solved to obtain the total creep rate of the system;

[0123] Creep behavior is controlled by the coupled dynamics of various microstructures and defects, including zero-dimensional point defects, one-dimensional dislocations, two-dimensional grain boundaries, and three-dimensional voids. Therefore, in a unified thermodynamic framework, we consider multiple thermally activated mechanisms such as intragranular and grain boundary vacancy diffusion, dislocation slip and climb, grain boundary sliding, and void evolution. Based on these mechanisms, the overall creep rate can be expressed as:

[0124]

[0125] in, They are the accumulated plastic strains of vacancy diffusion, dislocation movement, grain boundary sliding and hole evolution. 1) Vacancy diffusion kinetic equation:

[0126] The plastic deformation caused by diffusion creep is entirely due to the migration of materials during the diffusion process. The driving force comes from the difference in the chemical potential of point defects when the grain boundaries are subjected to tensile or compressive stress. In this process, the grain boundaries are regarded as perfect sources or sinks of vacancies. Therefore, when vacancies diffuse inside the grains or along the grain boundaries, the creep rate can be expressed as:

[0127]

[0128] In the formula, c eq is the vacancy equilibrium concentration, σ n is the applied normal stress, Ω a is the atomic volume, k B is the Boltzmann constant, T is the temperature, d is the grain size, δ gb is the grain boundary layer thickness, D bulk and D gb are the bulk diffusion coefficient and the grain boundary diffusion coefficient, respectively.

[0129] 2) Mechanical equations of dislocation slip and climb:

[0130] Viscoplasticity is usually defined as time-dependent plastic deformation beyond the elastic state, which is closely related to the viscous motion of dislocations. In this case, creep strain is gradually accumulated due to the motion of dislocations. The creep rate contributed by dislocation motion can be expressed by the Orowan equation:

[0131]

[0132] In the formula, are shear strain rate and plastic strain rate, M is Taylor factor, ρ m is the mobile dislocation density, b is the Burgers vector, is the average dislocation velocity, which depends on the average obstacle spacing and the time it takes for the dislocation to move between obstacles. The latter includes the waiting time in front of the obstacle (Δt w ) and the time to move between obstacles (Δt tr ):

[0133]

[0134] The presence of various types of obstacles leads to a reduction in the mean free path. Here we choose to express the average distance between obstacles as the geometric mean of the distances between individual obstacles:

[0135]

[0136] Among them, n d is the number of obstacle types, w i is the proportion of different obstacle types, is the obstacle distance.

[0137] In general, dislocations can overcome obstacles by either thermally activated slip or climb-assisted slip processes. These two mechanisms are coupled and can occur simultaneously. Therefore, the total waiting time can be calculated by visualizing the bypass process as a parallel circuit, and the average waiting time of the dislocation is expressed as:

[0138]

[0139] Among them, Δt slip ,Δt climb represent the theoretical waiting times for thermally activated sliding and climbing, respectively.

[0140] The process of dislocation sliding over an obstacle is essentially a process of force-heat coupling activation. The waiting time for dislocation sliding can be described by the Kocks-type activation enthalpy law:

[0141]

[0142] Among them, v D is the Debye frequency, n d is the number of obstacle types, ΔE i (τ i ) is the activation energy.

[0143] Based on dislocation theory and thermal activation model, the behavior of dislocations crossing obstacles with the assistance of external force and heat can be unified as the process of dislocation detachment point pinning. According to the properties of the material, we can consider the hindering effect of factors such as lattice friction, solid solution atoms, forest dislocations, grain boundaries, and precipitated particles inside the material on dislocation slip, so as to evaluate the waiting time for dislocation slip. Therefore, the force-activation energy relationship corresponding to different obstacles is as follows:

[0144]

[0145] ΔE dis (τ dis )=E dis (ζ cr ,τ dis )-E dis (ζ eq ,τ dis ) (10)

[0146]

[0147] It is worth noting that, depending on the type of precipitating particles, dislocations will experience two different behaviors when encountering precipitating particles: cutting-through mechanism and bypassing mechanism. The corresponding activation energy relationships are:

[0148]

[0149] Where ΔE fr ,ΔE ss ,ΔE dis ,ΔE gb ,ΔE dis , They represent the activation energies corresponding to lattice friction, solution atoms, dislocations, grain boundaries, and precipitated particles, respectively, and τ fr ,τ ss ,τ dis ,τ gb ,τ dis ,τ prec They represent the external shear stress corresponding to lattice friction, solution atoms, dislocations, grain boundaries, and precipitated particles, respectively. fr0 and ΔE fr They represent the energy per unit length of the dislocation line and the increase in energy after the dislocation line changes from the initial state to the line tension state, is the total energy barrier related to the interaction energy and line energy, is the average dislocation binding energy generated by the interaction between solute atoms and dislocations, Γ is the dislocation line tension, and w c is the coarsening amplitude of the dislocation segment, ζ cr and eq are the critical dislocation configuration and the equilibrium dislocation configuration, L * is the length of the dislocation segment involved in the local activation event, L gb is the average spacing between the grain boundary pinning points, h is the height of the kink pair, A1 = cos 2 β+sin 2 β / (1-v) and A2 = [(1+v)cos 2 β+(1-2v)sin 2 β] / (1-v) is the intrinsic parameter of the dislocation, β is the angle between the dislocation line and the Burgers vector, is the critical width of the kink pair, r core is the radius of the dislocation core.

[0150] Dislocation climb caused by vacancy diffusion is another important creep / plasticity mechanism besides dislocation slip. At high temperature and low strain rate, edge dislocations can occur via a climb mechanism, which is driven by vacancy diffusion along the dislocation line. Dislocation climb is a typical thermally activated process, and its activation energy (ΔE climb ) can be obtained by the following formula:

[0151] ΔE climb (τ climb )=E vf +E mb +E jog -τ climb Ωa (13)

[0152] Among them, E vf and E mb represent the vacancy formation energy and vacancy migration energy, E jog is the step formation energy, Ω a is the atomic volume. Correspondingly, the average climb velocity of the dislocation is:

[0153]

[0154] Where n c is the number of neighboring atoms, v0 = 2(b / d SF ) 2 v D is the vibration frequency, d SF is the stacking fault width.

[0155] In this method, the waiting time for climb can be determined by the ratio of the average climb velocity of edge dislocations to the average climb distance before bypassing the obstacle. Therefore, the average climb waiting time of edge dislocations can be expressed as:

[0156]

[0157] In the formula, R e is the edge dislocation ratio, l climb is the average climbing distance to bypass an obstacle.

[0158] The running time depends on the movement distance and running speed of the dislocation. Since the running time of the dislocation is significantly less than the waiting time, it is reasonable to assume that the running speed of the dislocation is the shear wave speed, that is, Based on this, the running time is expressed as:

[0159]

[0160] in, is the average obstacle spacing, G is the shear modulus, and ρ is the material density.

[0161] 3) Grain boundary sliding mechanical equation:

[0162] If the grain boundary slip is caused by the climb slip of dislocations, then the grain boundary slip rate is determined by the climb rate, since climb is generally a slow process. In this case, the climb frequency (v c ) can be expressed as:

[0163]

[0164] Where P jog is the probability of finding a step on a dislocation, S d is the diffusion activation entropy, Ed is the diffusion activation energy, τ x is the stress required for climbing along the interface. Assuming that dislocations are uniformly distributed along the grain boundary and their spacing is determined by the edge dislocation stress field, the dislocation climb rate along the grain boundary is:

[0165]

[0166] Among them, N gb-d is the number of grain boundary dislocations per unit length, τ gb-d is the external shear stress.

[0167] If the dislocation moves in the region adjacent to the grain boundary, then Eq. (17) can be simplified using the bulk diffusion coefficient. The shear strain rate during the climb-slip process is The climb rate is controlled, but the strain is generated by slip, which is expressed as:

[0168]

[0169] Among them, M gb is the number of grain boundaries per unit volume, A gb is the area swept by the dislocation along the grain boundary. Since the dislocation enters the boundary area from the slip zones on both sides of the grain boundary,

[0170]

[0171] Substituting formula (20) into (19), for τ x Ω a <<k B T,τ=τ x =σ / 2, Conditions, we can get the following form:

[0172]

[0173] 4) Pore evolution dynamics equation:

[0174] After creep enters the third stage, the creep rate gradually accelerates, eventually leading to fracture. Under high stress conditions, when the plastic deformation rate is very fast, the form of creep fracture is usually similar to ductile fracture at room temperature. Creep damage is mainly manifested in the nucleation, growth and aggregation of voids in areas of high stress concentration, especially at grain boundaries, which eventually lead to fracture. As spherical cap-shaped voids nucleate at grain boundaries, the total energy of the system will change. The free energy change caused by void nucleation can be divided into three parts: first, the increase in surface energy caused by the surface of the new void; second, the disappearance of the original grain boundary area leads to a decrease in interfacial energy; and third, the release of elastic strain energy caused by the formation of voids. Therefore, the activation energy of void nucleation can be expressed as:

[0175] ΔE voids-neclei=-σ n V voids +A voids γ voids -A gb γ gb (twenty two)

[0176] Among them, V voids is the pore volume, A voids and A gb are the surface areas corresponding to the pores and grain boundaries, γ voids and γ gb are the hole surface energy and grain boundary energy respectively. For the spherical cap hole shape, the surface energy tension balance equation can be written as:

[0177]

[0178] in, is the hole tip angle. voids , A voids , A gb Substituting the calculation formula into formula (21), we get:

[0179]

[0180] Let ΔE voids-neclei / dr=0, the critical core radius of the pores that can exist stably without sintering is obtained, r c :

[0181]

[0182] r c Substituting into formula (24), the critical nucleation work of the hole is obtained as:

[0183]

[0184] in, is the shape factor of the hole.

[0185] The nucleation rate is defined as the number of void cores formed on the unit volume of the grain boundary. A void of critical radius can be stable if it gains a vacancy, and it will disappear (automatically reduce in size) if it loses a vacancy. Therefore, the nucleation rate depends on the number of nuclei with a radius on the unit volume of the grain boundary and the number of vacancies transferred to the void core per unit time. Accordingly, the total nucleation rate in the steady state is:

[0186]

[0187] Where n0 = l voids -3 is the number of potential nucleation sites, l voids is the half-hole spacing, ΔEvac-gb is the activation energy for vacancy diffusion along grain boundaries.

[0188] The basis of the pore diffusion growth model is that the pores gradually grow by absorbing vacancies. The diffusion of vacancies usually migrates through the pore surface and then transports along the grain boundaries. During creep, due to the existence of stress gradients, the pore growth rate is closely related to the diffusion rate of vacancies. Therefore, the pore growth rate is expressed as:

[0189]

[0190] Among them, a voids is the hole radius, δ gb is the grain boundary width.

[0191] Since the dynamics of the nucleation and growth of voids are similar to the phase transition process, a kinetic model similar to the phase transition can be used to describe them. Johnson-Mehl can be used to describe the evolution of voids, especially in the nucleation and growth of voids. For spherical new voids, according to formulas (27) and (28), the volume fraction of the evolving voids can be expressed as:

[0192]

[0193] Where t is time. According to Gurson's formula, the pore growth is controlled by the hydrostatic part of plastic strain, and the damage is expressed by the change of pore volume fraction as:

[0194]

[0195] In the formula, f voids is the pore volume fraction, is the total plastic strain rate calculated by the plastic velocity gradient. Considering that the damage is a hole evolution, we get the plastic strain rate contributed by the hole evolution as:

[0196]

[0197] Pore ​​aggregation occurs in many modes, each with several variants, depending on microstructural factors, loading conditions and plastic flow characteristics. Among them, the aggregation of spherical pores often leads to elongated deformation and directional effects:

[0198]

[0199] In the formula, is the critical porosity for pore aggregation, is the aggregation factor, and are the saturated porosity and the failed porosity, respectively.

[0200] 5) Griffith fracture criterion:

[0201] Griffith believed that the huge difference between theoretical strength and actual strength was due to the presence of microcracks in the material. For a crack of a given size, there is a critical stress σ c :When σ≤σ c When σ>σ c When the crack expands, the change in system energy comes from two aspects: on the one hand, due to elastic strain energy, The release reduces the energy of the system, while the creation of new surfaces increases the energy, U2 = 4a voids γ voids Assume that the crack length corresponding to the maximum value of the total energy change of the system is 2a voids , then: when When , the increase in crack length will cause the system energy to increase, so the crack cannot expand automatically; When , the crack expansion reduces the total energy of the system, and the crack can spontaneously expand unstably. Order:

[0202]

[0203] The critical stress for unstable crack growth is obtained by solving:

[0204]

[0205] S2, solving the differential equations related to the evolution of dislocation density, obtaining the movable dislocation density and the immovable dislocation density at the current creep rate, and using them as input parameters for the next deformation process;

[0206] In current thermal creep models, the evolution of dislocation density plays a crucial role. The change in strain rate of the material is closely related to the dislocation density. During creep deformation, dislocations multiply, store, and annihilate, which not only changes the density of dislocations, but also affects their type and spatial distribution, thus significantly affecting the creep behavior of the material. The evolution rate of different types of dislocation density over time can be expressed mathematically as:

[0207]

[0208] Among them, m d represents the number of active dislocation density evolution mechanisms, ρ j represents the dislocation density corresponding to the i-th dislocation density evolution mechanism. Dislocation multiplication mechanisms include several typical forms, such as Frank-Read dislocation source, grain boundary nucleation, double cross slip to form dislocation loops, and edge dislocation dipole multiplication mechanism. Combining the above mechanisms, the dislocation density multiplication rate can be summarized as follows:

[0209]

[0210] In the formula, ρ m is the mobile dislocation density, L F-R is the initial dislocation length of the Frank-Read dislocation source, E F-R and E bc-s are the activation energies corresponding to the Frank-Read dislocation source and the double cross slip multiplication mechanism, n F-R is the number of propagated dislocation loops, τ gb is the shear stress corresponding to grain boundary nucleation, L bc-s is the length of the double cross slip dislocation segment, d SF is the stacking fault width, h and h cr are the separation distance and critical distance between two parallel slip planes, respectively.

[0211] Considering the interaction between dislocations, network nodes and grain boundaries, the dislocation storage mechanism includes dislocation network node storage and grain boundary storage. Accordingly, the dislocation density storage rate can be written as:

[0212]

[0213] In the formula, K hkl is the mean free path coefficient, ρ im is the immobile dislocation density, D gb is the grain boundary diffusion rate.

[0214] Dislocation annihilation mechanisms include four typical dislocation annihilation mechanisms: screw dislocation single cross slip, screw dislocation spontaneous annihilation, edge dislocation climb and edge dislocation spontaneous annihilation. Correspondingly, the dislocation density annihilation rate can be described by the following formula:

[0215]

[0216] Among them, E sc-s represents the activation energy of single cross slip, ψ represents the angle between the main slip plane and the cross slip plane, n represents the number of active slip systems, τ0 represents the critical decomposed shear stress, τ fr represents the lattice friction stress, τ sro represents the shear stress of the disordered interface, S is the Schmidt factor ratio, τ a is the external shear stress, τ i represents the internal shear stress, E climb represents the climb activation energy, E vf is the vacancy formation energy.

[0217] In order to more comprehensively describe the complex spatiotemporal evolution of dislocations, this method considers eight types of dislocation evolution rates. The classification of these categories reflects the evolution characteristics of dislocations in different spatial locations (inside the dislocation cell and on the dislocation cell wall), different motion states (movable and immovable), and different dislocation types (screw type and edge type). Specifically, they include: movable screw dislocations inside dislocation cells; Fixed screw dislocation inside the dislocation cell Movable edge dislocation inside a dislocation cell Immobile edge dislocation inside a dislocation cell Mobile screw dislocations in dislocation cell walls Immobile screw dislocation in dislocation cell wall Mobile edge dislocations in dislocation cell walls and immovable edge dislocations in dislocation cell walls The evolution rate equations of these eight dislocations are summarized as follows:

[0218]

[0219] In order to solve the evolution equations of different types of dislocations, the dislocation density conservation principle must be satisfied. Specifically, the evolution rate of the total dislocation density should be equal to the sum of the evolution rates of movable dislocations and immovable dislocations. Based on this principle, the evolution equation of the total dislocation density can be expressed as:

[0220]

[0221] Where f represents the volume fraction of the dislocation cell wall.

[0222] S3, repeating steps S1 and S2, continuously updating creep information until the deformation reaches the Griffith fracture condition, and outputting a complete creep curve.

[0223] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A constitutive modeling method of creep mechanics based on multi-physics mechanism, characterized in that: The following steps are involved: S1. Based on the initial microstructure information, the kinetic equation is solved to obtain the total creep rate of the system; The creep behavior is controlled by the coupled dynamics of various microstructures and defects, including zero-dimensional point defects, one-dimensional dislocations, two-dimensional grain boundaries, and three-dimensional voids. In a unified thermodynamic framework, multiple thermally activated mechanisms, including intragranular and grain boundary vacancy diffusion, dislocation slip and climb, grain boundary sliding, and void evolution, are considered. Based on these mechanisms, the overall creep rate is expressed as: in, They are the accumulated plastic strains of vacancy diffusion, dislocation movement, grain boundary sliding, and void evolution; S2, solving the differential equations related to the evolution of dislocation density, obtaining the movable dislocation density and the immovable dislocation density at the current creep rate, and using them as input parameters for the next deformation process; During the creep deformation process, dislocations will multiply, store and annihilate, which not only changes the density of dislocations, but also affects their types and spatial distribution, thus significantly affecting the creep behavior of the material; the evolution rate of different types of dislocation density over time is expressed by the mathematical formula: Among them, m d represents the number of active dislocation density evolution mechanisms, ρ j represents the dislocation density corresponding to the i-th dislocation density evolution mechanism; S3, repeating steps S1 and S2, continuously updating creep information until the deformation reaches the Griffith fracture condition, and outputting a complete creep curve.

2. The constitutive modeling method of creep mechanics based on multi-physics mechanism as claimed in claim 1, characterized in that: In the calculation of the vacancy diffusion creep rate in step S1, the construction of the kinetic equation is specifically as follows: The plastic deformation caused by diffusion creep is entirely due to the migration of materials during the diffusion process. The driving force comes from the difference in the chemical potential of point defects when the grain boundary is subjected to tensile or compressive stress. In this process, the grain boundary is regarded as a perfect source or sink of vacancies. Therefore, when vacancies diffuse inside the grain or along the grain boundary, the creep rate is expressed as: In the formula, c eq is the vacancy equilibrium concentration, σ n is the applied normal stress, Ω a is the atomic volume, k B is the Boltzmann constant, T is the temperature, d is the grain size, δ gb is the grain boundary layer thickness, D bulk and D gb are the bulk diffusion coefficient and the grain boundary diffusion coefficient, respectively.

3. The constitutive modeling method of creep mechanics based on multi-physics mechanism as claimed in claim 2, characterized in that: Furthermore, in the calculation of the dislocation movement creep rate in step S1, the construction of the dislocation sliding and climbing mechanical equations is specifically as follows: Viscoplasticity is usually defined as time-dependent plastic deformation beyond the elastic state, which is closely related to the viscous motion of dislocations. In this case, creep strain is gradually accumulated due to the motion of dislocations. The creep rate contributed by dislocation motion is expressed by the Orowan equation: In the formula, are shear strain rate and plastic strain rate, M is Taylor factor, ρ m is the mobile dislocation density, b is the Burgers vector, is the average dislocation velocity, which depends on the average obstacle spacing and the time it takes for a dislocation to move between obstacles, the latter of which includes the waiting time in front of the obstacle (Δt w ) and the time to move between obstacles (Δt tr ): The presence of various types of obstacles leads to a reduction in the mean free path. The average spacing of obstacles is expressed as the geometric mean of the spacing of individual obstacles: Among them, n d is the number of obstacle types, w i is the proportion of different obstacle types, is the obstacle distance; Usually dislocations overcome obstacles through thermally activated slip or climb-assisted slip processes. These two mechanisms are coupled and can occur simultaneously. The total waiting time is calculated by visualizing the bypass process as a parallel circuit. The average waiting time of dislocations is expressed as: Among them, Δt slip ,Δt climb denote the theoretical waiting times for thermally activated sliding and climbing, respectively; The process of dislocation sliding over an obstacle is essentially a force-heat coupling activation process. The waiting time of dislocation sliding is described by the Kocks-type activation enthalpy law: Among them, v D is the Debye frequency, n d is the number of obstacle types, ΔE i (τ i ) is the activation energy; Based on the dislocation theory and thermal activation model, the behavior of dislocations crossing obstacles with the assistance of external force and heat is unified as the process of dislocation detachment point pinning; according to the properties of the material, the lattice friction, solid solution atoms, forest dislocations, grain boundaries, and precipitation particles inside the material are considered to hinder the dislocation slip, so as to evaluate the waiting time for dislocation slip; therefore, the force-activation energy relationship corresponding to different obstacles is as follows: Depending on the type of precipitating particles, dislocations will experience two different behaviors when encountering precipitating particles: cutting-through mechanism and bypassing mechanism. The corresponding activation energy relationships are: In the formula, ΔE fr ,ΔE ss ,ΔE dis ,ΔE gb ,ΔE dis , They represent the activation energies corresponding to lattice friction, solution atoms, dislocations, grain boundaries, and precipitated particles, respectively, and τ fr ,τ ss ,τ dis ,τ gb ,τ dis ,τ prec They represent the external shear stress corresponding to lattice friction, solution atoms, dislocations, grain boundaries, and precipitated particles, respectively. fr0 and ΔE fr They represent the energy per unit length of the dislocation line and the increase in energy after the dislocation line changes from the initial state to the line tension state, is the total energy barrier related to the interaction energy and line energy, is the average dislocation binding energy generated by the interaction between solute atoms and dislocations, Γ is the dislocation line tension, and w c is the coarsening amplitude of the dislocation segment, ζ cr and eq are the critical dislocation configuration and the equilibrium dislocation configuration, L * is the length of the dislocation segment involved in the local activation event, L gb is the average spacing between the grain boundary pinning points, h is the height of the kink pair, A1 = cos 2 β+sin 2 β / (1-v) and A2 = [(1+v)cos 2 β+(1-2v)sin 2 β] / (1-v) is the intrinsic parameter of the dislocation, β is the angle between the dislocation line and the Burgers vector, is the critical width of the kink pair, r core is the dislocation core radius; Dislocation climb caused by vacancy diffusion is another important creep / plasticity mechanism besides dislocation slip. At high temperature and low strain rate, edge dislocations occur through the climb mechanism, which is driven by vacancy diffusion on the dislocation line. Dislocation climb is a typical thermally activated process with an activation energy (ΔE climb ) is obtained by the following formula: D.E. climb (t climb )=E vf +E mb +E jog -t climb Oh a (13) Among them, E vf and E mb represent the vacancy formation energy and vacancy migration energy, E jog is the step formation energy, Ω a is the atomic volume, and accordingly, the average climb velocity of the dislocation is: Where n c is the number of neighboring atoms, v0 = 2(b / d SF ) 2 v D is the vibration frequency, d SF is the stacking fault width; In this method, the waiting time for climb is determined by the ratio of the average climb velocity of edge dislocations to the average climb distance before bypassing the obstacle; therefore, the average climb waiting time of edge dislocations is expressed as: In the formula, R e is the edge dislocation ratio, l climb is the average climbing distance to bypass obstacles; The running time depends on the movement distance and running speed of the dislocation. Since the running time of the dislocation is obviously less than the waiting time, it is assumed that the running speed of the dislocation is the shear wave speed, that is, Based on this, the running time is expressed as: in, is the average obstacle spacing, G is the shear modulus, and ρ is the material density.

4. The constitutive modeling method of creep mechanics based on multi-physics mechanism as claimed in claim 3, characterized in that: In the calculation of the grain boundary sliding creep rate in step S1, the construction of its kinetic equation is specifically as follows: If the grain boundary slip is caused by the climb slip of dislocations, the grain boundary slip rate is determined by the climb rate, since climb is usually a slow process. In this case, the climb frequency (v c ) is expressed as: Where P jog is the probability of finding a step on a dislocation, S d is the diffusion activation entropy, E d is the diffusion activation energy, τ x is the stress required for climbing along the interface; assuming that dislocations are uniformly distributed along the grain boundary and their spacing is determined by the edge dislocation stress field, the dislocation climb rate along the grain boundary is: Among them, N gb-d is the number of grain boundary dislocations per unit length, τ gb-d is the applied shear stress; If the dislocation moves in the region adjacent to the grain boundary, then Eq. (17) is simplified by the bulk diffusion coefficient, and the shear strain rate during the climb-slip process is, The climb rate is controlled, but the strain is generated by slip, which is expressed as: Among them, M gb is the number of grain boundaries per unit volume, A gb is the area swept by the dislocation along the grain boundary; since the dislocation enters the boundary area from the slip zones on both sides of the grain boundary, Substituting formula (20) into (19), for τ x Ω a <<k B T,τ=τ x =σ / 2, Conditions, the following form:

5. The constitutive modeling method of creep mechanics based on multi-physics mechanism as claimed in claim 4, characterized in that: In the calculation of the creep rate of the pore evolution in step S1, the construction of the kinetic equation is specifically as follows: After creep enters the third stage, the creep rate gradually accelerates, eventually leading to fracture. Under high stress conditions, when the plastic deformation rate is very fast, the form of creep fracture is usually similar to ductile fracture at room temperature. Creep damage is mainly manifested in the nucleation, growth and aggregation of holes in high stress concentration areas, especially at grain boundaries, which eventually lead to fracture. With the nucleation of spherical crown holes at grain boundaries, the total energy of the system will change. The free energy change caused by hole nucleation is divided into three parts: first, the increase in surface energy caused by the new hole surface; second, the disappearance of the original grain boundary area leads to a decrease in interfacial energy; third, the release of elastic strain energy caused by the formation of holes; therefore, the activation energy of hole nucleation is expressed as: D.E. voids-neclei =-s n V voids +A voids c voids -A gb c gb (22) Among them, V voids is the pore volume, A voids and A gb are the surface areas corresponding to the pores and grain boundaries, γ voids and γ gb are the hole surface energy and grain boundary energy respectively; for the spherical cap hole shape, the surface energy tension balance equation is: in, is the hole tip angle; voids , A voids , A gb Substituting the calculation formula into formula (21), we get: Let ΔE voids-neclei / dr=0, the critical core radius of the pores that can exist stably without sintering is obtained, r c : r c Substituting into formula (24), the critical nucleation work of the hole is obtained as: in, is the shape factor of the hole; The nucleation rate is defined as the number of void cores formed on the unit volume of the grain boundary; a void of critical radius can be stable if it gains a vacancy, and the steady state will disappear (the size automatically decreases) if it loses a vacancy; therefore, the nucleation rate depends on the number of nuclei with a radius on the unit volume of the grain boundary and the number of vacancies transferred to the void core per unit time; accordingly, the total nucleation rate in the steady state is: Where n0 = l voids -3 is the number of potential nucleation sites, l voids is the half-hole spacing, ΔE vac-gb is the activation energy for vacancy diffusion along grain boundaries; The basis of the pore diffusion growth model is that the pores gradually grow by absorbing vacancies. The diffusion of vacancies usually migrates through the pore surface and then transports along the grain boundary. During the creep process, due to the existence of stress gradient, the pore growth rate is closely related to the diffusion rate of vacancies. Therefore, the pore growth rate is expressed as: Among them, a voids is the hole radius, δ gb is the grain boundary width; Since the dynamics of the nucleation and growth of voids are similar to the phase transition process, a kinetic model similar to the phase transition is used to describe it; Johnson-Mehl is used to describe the evolution of voids, especially in the nucleation and growth of voids; for spherical new voids, according to formulas (27) and (28), the volume fraction of the evolving voids is expressed as: Where t is time. According to Gurson's formula, the hole growth is controlled by the hydrostatic part of plastic strain, and the damage is expressed by the change of hole volume fraction as follows: In the formula, f voids is the pore volume fraction, is the total plastic strain rate calculated by the plastic velocity gradient; considering that the damage evolves with holes, the plastic strain rate contributed by the hole evolution is: Pore ​​aggregation occurs in many modes, each with several variants, depending on microstructural factors, loading conditions and plastic flow characteristics; among them, the aggregation of spherical pores often leads to elongated deformation and directional effects: In the formula, is the critical porosity for pore aggregation, is the aggregation factor, and are the saturated porosity and the failed porosity, respectively.

6. The constitutive modeling method of creep mechanics based on multi-physics mechanism as claimed in claim 1, characterized in that: The dislocation multiplication mechanism in the dislocation evolution mechanism of step S2 includes Frank-Read dislocation source, grain boundary nucleation, double cross slip to form dislocation ring and edge dislocation dipole multiplication mechanism. Combining the above mechanisms, the expression of dislocation density multiplication rate is: In the formula, ρ m is the mobile dislocation density, L F-R is the initial dislocation length of the Frank-Read dislocation source, E F-R and E bc-s are the activation energies corresponding to the Frank-Read dislocation source and the double cross slip multiplication mechanism, n F-R is the number of propagated dislocation loops, τ gb is the shear stress corresponding to grain boundary nucleation, L bc-s is the length of the double cross slip dislocation segment, d SF is the stacking fault width, h and h cr are the separation distance and critical distance between two parallel slip planes, respectively.

7. The constitutive modeling method of creep mechanics based on multi-physics mechanism as claimed in claim 6, characterized in that: Considering the interaction between dislocations, network nodes and grain boundaries, the dislocation storage mechanism in the dislocation evolution mechanism of step S2 includes dislocation network node storage and grain boundary storage; accordingly, the dislocation density storage rate is: In the formula, K hkl is the mean free path coefficient, ρ im is the immobile dislocation density, D gb is the grain boundary diffusion rate.

8. The constitutive modeling method of creep mechanics based on multi-physics mechanism as claimed in claim 7, characterized in that: Furthermore, the dislocation annihilation mechanism in the dislocation evolution mechanism of step S2 includes four dislocation annihilation mechanisms: screw dislocation single cross slip, screw dislocation spontaneous annihilation, edge dislocation climb and edge dislocation spontaneous annihilation. The dislocation density annihilation rate is described by the following formula: Among them, E sc-s represents the activation energy of single cross slip, ψ represents the angle between the main slip plane and the cross slip plane, n represents the number of active slip systems, τ0 represents the critical decomposed shear stress, τ fr represents the lattice friction stress, τ sro represents the shear stress of the disordered interface, S is the Schmidt factor ratio, τ a is the external shear stress, τ i represents the internal shear stress, E climb is the climb activation energy, E vf is the vacancy formation energy.

9. The constitutive modeling method of creep mechanics based on multi-physics mechanism as claimed in claim 8, characterized in that: In order to more comprehensively describe the complex spatiotemporal evolution of dislocations, the eight other dislocation evolution mechanisms considered in step S2 reflect the evolution characteristics of dislocations in different spatial positions (inside the dislocation cell and on the dislocation cell wall), different motion states (movable and immovable), and different dislocation types (screw type and edge type); specifically, they include: movable screw dislocations inside dislocation cells; Fixed screw dislocation inside the dislocation cell Movable edge dislocation inside a dislocation cell Immobile edge dislocation inside a dislocation cell Mobile screw dislocations in dislocation cell walls Immobile screw dislocation in dislocation cell wall Mobile edge dislocations in dislocation cell walls and immovable edge dislocations in dislocation cell walls The evolution rate equations of these eight dislocations are summarized as follows: In order to solve the evolution equations of different types of dislocations, the dislocation density conservation principle must be satisfied; specifically, the evolution rate of the total dislocation density should be equal to the sum of the evolution rates of movable dislocations and immobile dislocations; based on this principle, the evolution equation of the total dislocation density is expressed as: Where f represents the volume fraction of the dislocation cell wall.

10. The constitutive modeling method of creep mechanics based on multi-physics mechanism as claimed in claim 1, characterized in that: The Griffith fracture criterion in step S3 is: For a crack of a given size, there is a critical stress σ c :When σ≤σ c When σ>σ c When the crack expands, the crack rapidly expands and causes fracture; when the crack expands, the change of system energy comes from two aspects: on the one hand, due to elastic strain energy, The release reduces the energy of the system, while the creation of new surfaces increases the energy, U2 = 4a voids γ voids ; Assume that the crack length corresponding to the maximum value of the total energy change of the system is 2a voids , then when When , the increase in crack length will cause the system energy to increase, so the crack cannot expand automatically; When , the crack extension reduces the total energy of the system, and the crack can spontaneously expand unstably. Let: The critical stress for unstable crack growth is obtained by solving:

Images