A Creep Mechanics Constitutive Modeling Method Based on Multiple Physical Mechanisms

Abstract

The present invention relates to a method for constructing a creep mechanics model based on multiple physical mechanisms. During the creep process, first, according to the initial microstructural information, the kinetic equation is solved to obtain the total creep rate of the system; within an extremely small time interval, we further solve the differential equations related to the evolution of dislocation density, so as to obtain the mobile dislocation density and immobile 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; to solve the problem that the current constitutive modeling methods used to evaluate creep behavior usually contain a large number of empirical parameters and rely on experimental data for fitting, which limits their universality.

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, in order to solve the problem that the current constitutive modeling method for evaluating creep behavior usually includes a large number of empirical parameters and relies on experimental data for fitting, which limits its universality, the present invention provides a constitutive modeling method for creep mechanics based on multiple physical mechanisms.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A constitutive modeling method for creep mechanics based on multiple physical mechanisms, comprising the following steps:

[0008] S1. According to the initial microstructure information, solve the kinetic equation to obtain the total creep rate of the system;

[0009] 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 pores. Under a unified thermodynamic framework, various thermally activated mechanisms such as vacancy diffusion within grains and along grain boundaries, dislocation slip and climb, grain boundary sliding, and pore evolution are considered. Based on these mechanisms, the total creep rate is expressed as:

[0010]

[0011] Wherein, are the accumulated plastic strains due to vacancy diffusion, dislocation motion, grain boundary sliding, and pore evolution, respectively;

[0012] S2. Solve the differential equations related to the evolution of dislocation density to obtain the mobile dislocation density and immobile dislocation density at the current creep rate, and use them as input parameters for the next deformation process;

[0013] During the creep deformation process, dislocations will proliferate, be stored, and annihilate, which not only changes the dislocation density but also affects its type and spatial distribution, thus significantly affecting the creep behavior of the material. The evolution rates of different types of dislocation densities over time are expressed by mathematical formulas as:

[0014]

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

[0016] S3. Repeat steps S1 and S2, continuously update the creep information until the deformation reaches the Griffith fracture condition, and output the complete creep curve.

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

[0018] Plastic deformation caused by diffusional creep stems entirely from the migration of matter during diffusion, and its driving force comes from the difference in the chemical potential of point defects at the grain boundaries under tensile or compressive stress. During this process, the grain boundaries are regarded as perfect sources or sinks of vacancies. Therefore, when vacancies diffuse within the grains or along the grain boundaries, the creep rate is expressed as:

[0019]

[0020] In the formula, c eq is the equilibrium vacancy 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 creep rate of dislocation motion in step S1, the construction of the dislocation slip and climb kinetics 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, the creep strain gradually accumulates due to the motion of dislocations, and the creep rate contributed by the dislocation motion is expressed by the Orowan equation as:

[0023]

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

[0025]

[0026] The presence of multiple types of obstacles leads to a reduction in the mean free path, and the average spacing of the obstacles is expressed as the geometric mean of the individual obstacle spacings:

[0027]

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

[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] where Δt slip , Δt climb represent the theoretical waiting times for thermally activated slip and climb, respectively;

[0032] The process of dislocation slip over obstacles is essentially a force-thermal coupled activation process. The waiting time of dislocation slip is described by the Kocks-type activation enthalpy law as:

[0033]

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

[0035] Based on dislocation theory and the thermal activation model, the behavior of dislocations overcoming obstacles with the assistance of external force and heat is unified as the process of dislocation detachment from point pinning. Considering the properties of the material, factors such as lattice friction, solute atoms, forest dislocations, grain boundaries, and precipitate particles inside the material that impede dislocation slip are taken into account to evaluate the waiting time of dislocation slip. Therefore, the force-activation energy relationships corresponding to different obstacles are as follows:

[0036]

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

[0038]

[0039] According to the type of precipitate particles, dislocations will experience two different behaviors, the cutting mechanism and the bypass mechanism, when encountering precipitate particles. The corresponding activation energy relationships for the two are:

[0040]

[0041] In the formula, ΔE fr , ΔE ss , ΔE dis , ΔE gb , ΔE dis , respectively represent the activation energies corresponding to lattice friction, solute atoms, dislocations, grain boundaries, and precipitate particles, τ fr , τ ss , τ dis , τ gb , τ dis , τ prec respectively represent the applied shear stresses corresponding to lattice friction, solute atoms, dislocations, grain boundaries, and precipitate particles, E fr0 and ΔE fr respectively 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 the line energy. is the average dislocation binding energy generated by the interaction between solute atoms and dislocations, Γ is the dislocation line tension, w c is the coarsening amplitude of the dislocation segment, ζ cr and ζ eq respectively represent the critical dislocation configuration and the equilibrium dislocation configuration, L * is the length of the dislocation segment participating in the local activation event, L gb is the average spacing between grain boundary pinning points, h is the height corresponding to 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) are the intrinsic parameters 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 in addition to dislocation slip; at high temperatures and low strain rates, 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, and its 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 respectively represent the vacancy formation energy and the vacancy migration energy, E jog is the jog formation energy, Ω a is the atomic volume. Correspondingly, the average climb velocity of the dislocation is:

[0045]

[0046] In the formula, n c is the number of nearest neighbor 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 time waiting for climb is determined by the ratio of the average climb velocity of the edge dislocation to the average climb distance before bypassing the obstacle; therefore, the average climb waiting time of the edge dislocation is expressed as:

[0048]

[0049] In the formula, R e is the proportion of edge dislocations, l climb is the average climb distance for bypassing the obstacle;

[0050] 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 assumed that the running speed of the dislocation is the transverse wave speed, that is Accordingly, the running time is expressed as:

[0051]

[0052] Among them, 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 its kinetic equation is specifically as follows:

[0054] If the grain boundary sliding is caused by the climb and slip of dislocations, the grain boundary sliding 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] In the formula, P jog is the probability of finding a jog on the dislocation, S dis the diffusion activation entropy, E d is the diffusion activation energy, τ x is the stress required for climb along the interface; assuming that dislocations are uniformly distributed along the grain boundary and their spacing is determined by the stress field of edge dislocations, the dislocation climb rate along the grain boundary is:

[0057]

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

[0059] If the dislocations move within the region of adjacent grain boundaries, Equation (17) is simplified using the bulk diffusion coefficient, and the shear strain rate during the climb-slip process, controlled by the climb rate, but the strain is generated by slip, is expressed as:

[0060]

[0061] where M gb is the number of grain boundaries per unit volume, A gb is the area swept by the dislocations along the grain boundary; since the dislocations enter the boundary region from the slip zones on both sides of the grain boundary, then

[0062]

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

[0064]

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

[0066] After creep enters the third stage, the creep rate gradually increases and finally leads 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, and creep damage is mainly manifested as the nucleation, growth and coalescence of pores in high stress concentration regions, especially at grain boundaries, which ultimately trigger fracture; as spherical cap-shaped pores nucleate at grain boundaries, the total energy of the system will change, and the free energy change caused by pore nucleation is divided into three parts: one is the increase in surface energy caused by the new pore surface; the second is the decrease in interface energy due to the disappearance of the original grain boundary area; the third is the release of elastic strain energy caused by the formation of pores; therefore, the activation energy of pore nucleation is expressed as:

[0067] ΔE voids-neclei = -σ n V voids + A voids γ voids - A gb γ gb (22)

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

[0069]

[0070] wherein, is the cavity tip angle; substituting the calculation formulas for V voids , A voids , A gb into formula (21), we get:

[0071]

[0072] Let ΔE voids-neclei / dr = 0, and the critical core radius at which the pores can stably exist without sintering, r c :

[0073]

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

[0075]

[0076] wherein, is the shape factor of the pores;

[0077] The nucleation rate is defined as the number of pore cores formed on the grain boundaries per unit volume per unit time; a pore with the critical radius can become stable by obtaining a vacancy, and will disappear (its size will automatically decrease) when losing a vacancy; therefore, the nucleation rate depends on the number of nuclei with a radius of in the grain boundaries per unit volume, and the number of vacancies transferred to the pore cores per unit time; correspondingly, the total nucleation rate at steady state is:

[0078]

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

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

[0081]

[0082] where a voids is the pore radius, δ gb is the grain boundary width;

[0083] Since the kinetics of the pore nucleation and growth processes are similar to those of the phase transformation process, a phase transformation kinetics model is used to describe it. Johnson-Mehl is used to describe the pore evolution process, especially in pore nucleation and growth. For spherical new pores, according to equations (27) and (28), the volume fraction of pore evolution is expressed as:

[0084]

[0085] where t is the time. According to the Gurson formula, the pore growth is controlled by the hydrostatic part of the plastic strain, and the damage is expressed by the change in the pore volume fraction as:

[0086]

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

[0088]

[0089] Pore coalescence occurs in multiple modes, and each mode has several variants, which depend on the microstructure factors, loading conditions, and plastic flow characteristics; among them, the coalescence of spherical pores often leads to slender deformation and direction effects:

[0090]

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

[0092] Furthermore, in the dislocation multiplication mechanism of the dislocation evolution mechanism in step S2, it includes Frank-Read dislocation sources, grain boundary nucleation, formation of dislocation loops by double cross-slip, and the multiplication mechanism of edge dislocation dipoles; combining the above mechanisms, the expression for the 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 respectively, n F-R is the number of proliferated 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 the critical distance between two parallel slip planes respectively.

[0095] Furthermore, considering the interaction between dislocations and 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; correspondingly, 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 diffusivity.

[0098] Furthermore, the dislocation annihilation mechanism in the dislocation evolution mechanism of step S2 includes four dislocation annihilation mechanisms: single cross-slip of screw dislocations, spontaneous annihilation of screw dislocations, climb of edge dislocations, and spontaneous annihilation of edge dislocations. 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 primary slip plane and the cross-slip plane, n represents the number of active slip systems, τ0 represents the critical resolved shear stress, τ fr represents the lattice friction stress, τ sro represents the shear stress at the disordered interface time, S is the Schmidt factor ratio, τ a is the external shear stress, τ i represents the internal shear stress, Eclimb represents the climb activation energy, E vf is the vacancy formation energy.

[0101] Furthermore, to more comprehensively describe the complex spatio-temporal evolution of dislocations, the classification of the other eight dislocation evolution mechanisms considered in step S2 reflects the evolution characteristics of dislocations at different spatial positions (inside dislocation cells and dislocation cell walls), different motion states (mobile and immobile), and different dislocation types (screw and edge); specifically including: mobile screw dislocations inside dislocation cells immobile screw dislocations inside dislocation cells mobile edge dislocations inside dislocation cells immobile edge dislocations inside dislocation cells mobile screw dislocations in dislocation cell walls immobile screw dislocations in dislocation cell walls mobile edge dislocations in dislocation cell walls and immobile edge dislocations in dislocation cell walls

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

[0103]

[0104] To solve the evolution equations of different types of dislocations, the principle of dislocation density conservation must be satisfied; specifically, the evolution rate of the total dislocation density should be equal to the sum of the evolution rates of mobile 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 the crack will not expand; when σ > σ c the crack will rapidly expand and lead to fracture; when the crack expands, the change in the system energy comes from two aspects: on the one hand, due to the elastic strain energy, the release reduces the system energy, and on the other hand, the generation of new surfaces increases the energy,

[0109] U2 = 4a voids γ voids ; assuming that the crack length corresponding to the maximum value of the total system energy change is 2a voids , then when When the crack length increases, the system energy rises, so the crack cannot expand automatically; while when When, the crack propagation reduces the total energy of the system, and the crack can spontaneously and unstably propagate. Let:

[0110]

[0111] Solving gives the critical stress for unstable crack propagation as:

[0112]

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

[0114] 1. A creep mechanics constitutive modeling method based on multiple physical mechanisms disclosed by the present invention includes two important components: a creep mechanism kinetic equation and a dislocation density evolution equation. During creep, first, according to the initial microstructure information, the kinetic equation is solved to obtain the total creep rate of the system. In an extremely small time interval, we further solve the differential equations related to dislocation density evolution to obtain the mobile dislocation density and immobile dislocation density at the current creep rate, and use them as input parameters for the next deformation process. By repeating the above steps and continuously updating the creep information until the deformation reaches the Griffith fracture condition, a complete creep curve is finally output. It solves the problem that the current constitutive modeling method for evaluating creep behavior needs to rely on experimental data for fitting, which limits its universality, and can be applied to the research on 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 creep mechanics constitutive modeling method based on multiple physical mechanisms, realizing 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, solving the drawbacks of traditional models relying on creep experimental data fitting, significantly reducing the experimental cost and time, and improving the prediction efficiency and reliability. Compared with traditional methods, the present invention can not only accurately describe the point defect and dislocation evolution processes in the first and second stages of creep, but also breaks through the limitations of previous studies in the physical mechanism analysis of the later stage of creep, deeply capturing the potential physical mechanisms of grain boundary sliding and pore evolution. By revealing the complex coupling effects among vacancies, dislocations, grain boundaries and pores, the invention successfully realizes the smooth transition from the second stage to the third stage of accelerated deformation in creep, and provides a theoretical support for understanding creep fracture behavior. In addition, the invention can also accurately predict the creep life of different materials, providing important technical support for material selection, performance optimization and life assessment under high-temperature environments, and showing broad engineering application potential and academic value.

[0116] Other advantages, objects and features of the present invention will be set forth in part in the following description, and in part will be obvious to those skilled in the art upon examination of the following, or may be learned by practice of the present invention. The objects and other advantages of the present invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out hereinafter. Description of the Drawings

[0117] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings, where:

[0118] Figure 1 is a flowchart of the creep mechanics constitutive modeling method based on multiple physical mechanisms of the present invention;

[0119] Figure 2 is a schematic diagram of the relationship between different creep mechanisms of the present invention. Detailed Embodiments

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

[0121] As Figure 1 shown, a creep mechanics constitutive modeling method based on multiple physical mechanisms includes the following steps:

[0122] S1. According to the initial microstructure information, solve the kinetic equation 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 pores. Therefore, within a unified thermodynamic framework, we consider various thermally activated mechanisms such as intragranular and grain boundary vacancy diffusion, dislocation slip and climb, grain boundary sliding, and pore evolution. Based on these mechanisms, the total creep rate can be expressed as:

[0124]

[0125] where are the plastic strains accumulated by vacancy diffusion, dislocation motion, grain boundary sliding, and pore evolution, respectively. Among them, 1) The kinetic equation of vacancy diffusion:

[0126] Plastic deformation caused by diffusion creep stems entirely from the migration of matter during the diffusion process. Its driving force comes from the difference in the chemical potential of point defects at grain boundaries under tensile or compressive stress. During this process, the grain boundary is regarded as a perfect source or sink of vacancies. Therefore, when vacancies diffuse within the grains or along the grain boundaries, the creep rate can be expressed as:

[0127]

[0128] where c eq is the equilibrium concentration of vacancies, 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) Kinetic equations for 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, the creep strain gradually accumulates due to the movement of dislocations. The creep rate contributed by dislocation movement can be expressed by the Orowan equation as:

[0131]

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

[0133]

[0134] The presence of multiple types of obstacles leads to a reduction in the mean free path. Here, the average spacing of obstacles is chosen to be expressed as the geometric mean of the individual obstacle spacings:

[0135]

[0136] where n d is the number of obstacle types, w i is the proportion of different obstacle types, is the obstacle spacing.

[0137] Generally, dislocations can overcome obstacles through 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 dislocations is expressed as:

[0138]

[0139] where Δt slip , Δt climb represent the theoretical waiting times for thermally activated slip and climb, respectively.

[0140] The process of dislocation slip over an obstacle is essentially a force-thermal coupled activation process. The waiting time of dislocation slip can be described by the Kocks-type activation enthalpy law as:

[0141]

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

[0143] Based on dislocation theory and the thermal activation model, the behavior of dislocations overcoming obstacles with the assistance of external force and heat can be unified as the process of dislocation detachment from point pinning. According to the properties of the material, we can consider the hindering effects of lattice friction, solute atoms, forest dislocations, grain boundaries, and precipitate particles inside the material on dislocation slip, so as to evaluate the waiting time of dislocation slip. Therefore, the force-activation energy relationships corresponding to different obstacles are as follows:

[0144]

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

[0146]

[0147] It should be noted that according to the type of precipitate particles, dislocations will experience two different behaviors, the cutting mechanism and the bypass mechanism, when encountering precipitate particles. The corresponding activation energy relationships for the two are:

[0148]

[0149] In the formula, ΔE fr , ΔE ss , ΔE dis , ΔE gb , ΔE dis , respectively represent the activation energies corresponding to lattice friction, solute atoms, dislocations, grain boundaries, and precipitate particles, τ fr , τ ss , τ dis , τ gb , τ dis , τ prec respectively represent the applied shear stresses corresponding to lattice friction, solute atoms, dislocations, grain boundaries, and precipitate particles, E fr0 and ΔE fr respectively 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 the line energy, is the average dislocation binding energy generated by the interaction between solute atoms and dislocations, Γ is the dislocation line tension, w c is the coarsening amplitude of the dislocation segment, ζ cr and ζ eq respectively represent the critical dislocation configuration and the equilibrium dislocation configuration, L * is the length of the dislocation segment participating in the local activation event, L gb is the average spacing between grain boundary pinning points, h is the height corresponding to 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) are the intrinsic parameters 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 in addition to dislocation slip. At high temperatures and low strain rates, edge dislocations can occur through the climb mechanism, which is driven by vacancy diffusion on the dislocation line. Dislocation climb is a typical thermally activated process, and its activation energy (ΔE climb ) can be obtained from 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 the vacancy migration energy respectively, E jog is the jog formation energy, and Ω a is the atomic volume. Accordingly, the average climb velocity of the dislocation is:

[0153]

[0154] In the formula, n c is the number of nearest neighbor atoms, v0 = 2(b / d SF ) 2 v D is the vibration frequency, and 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 the edge dislocation to the average climb distance before bypassing the obstacle. Therefore, the average waiting time for the edge dislocation to climb can be expressed as:

[0156]

[0157] In the formula, R e is the proportion of the edge dislocation, and l climb is the average climb distance for bypassing the 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 transverse wave speed, that is Accordingly, the running time is expressed as:

[0159]

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

[0161] 3) Grain boundary sliding kinetic equation:

[0162] If the grain boundary sliding is caused by the climb-sliding of dislocations, the grain boundary sliding rate is determined by the climb rate because the climb is usually a slower process. In this case, the climb frequency (v c ) can be expressed as:

[0163]

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

[0165]

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

[0167] If the dislocations move within the region of adjacent grain boundaries, Equation (17) can be simplified using the bulk diffusion coefficient. The shear strain rate during the climb - slip process, controlled by the climb rate, but the strain is produced by slip, is expressed as:

[0168]

[0169] where M gb is the number of grain boundaries per unit volume, A gb is the area swept by the dislocations along the grain boundary. Since the dislocations enter the boundary region from the slip zones on both sides of the grain boundary, then

[0170]

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

[0172]

[0173] 4) Hole evolution kinetic equation:

[0174] After creep enters the third stage, the creep rate gradually increases and finally leads 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 as the nucleation, growth, and coalescence of holes in high - stress concentration regions, especially at grain boundaries, which ultimately trigger fracture. As spherical - cap - shaped holes nucleate at grain boundaries, the total energy of the system changes. The change in free energy caused by hole nucleation can be divided into three parts: one is the increase in surface energy caused by the new hole surface; the second is the decrease in interface energy due to the disappearance of the original grain boundary area; the third is the release of elastic strain energy caused by the formation of holes. Therefore, the activation energy for hole nucleation can be expressed as:

[0175] ΔE voids-neclei= -σ n V voids + A voids γ voids - A gb γ gb (22)

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

[0177]

[0178] where is the cavity tip angle. Substituting the calculation formulas for V voids , A voids , A gb into formula (21), we get:

[0179]

[0180] Let ΔE voids-neclei / dr = 0, and we obtain the critical core radius r c at which the pores can stably exist without sintering:

[0181]

[0182] Substituting r c into formula (24), we get the critical nucleation work of the pores as:

[0183]

[0184] where is the shape factor of the pores.

[0185] The nucleation rate is defined as the number of pore cores formed on the grain boundaries per unit volume per unit time. A pore with the critical radius can become stable by obtaining one vacancy and will disappear (its size will automatically decrease) by losing one vacancy. Therefore, the nucleation rate depends on the number of nuclei with a radius of in the grain boundaries per unit volume and the number of vacancies transferred to the pore cores per unit time. Accordingly, the total nucleation rate at steady state is:

[0186]

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

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

[0189]

[0190] where a voids is the pore radius, and δ gb is the grain boundary width.

[0191] Since the kinetics of pore nucleation and growth processes are similar to those of phase transformation processes, a phase transformation kinetics model can be used to describe them. Johnson-Mehl can be used to describe the pore evolution process, especially in pore nucleation and growth. For spherical new pores, according to equations (27) and (28), the volume fraction of pore evolution can be expressed as:

[0192]

[0193] where t is time. According to the Gurson formula, pore growth is controlled by the hydrostatic part of plastic strain, and damage is represented by the change in pore volume fraction as:

[0194]

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

[0196]

[0197] Pore coalescence occurs in multiple modes, each with several variants, which depends on microstructural factors, loading conditions, and plastic flow characteristics. Among them, the coalescence of spherical pores often leads to elongation deformation and direction effects:

[0198]

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

[0200] 5) Griffith fracture criterion:

[0201] Griffith believed that the huge difference between the theoretical strength and the 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 , the crack will not expand; when σ > σ c , the crack will expand rapidly and lead to fracture. When the crack expands, the change in the system energy comes from two aspects: on the one hand, due to the elastic strain energy, the release reduces the system energy, and on the other hand, the generation of a new surface increases the energy, U2 = 4a voids γ voids . Assuming that the crack length corresponding to the maximum value of the total energy change of the system is 2a voids , then: when , the increase in the crack length will cause the system energy to increase, so the crack cannot expand automatically; while when , the crack expansion reduces the total energy of the system, and the crack can spontaneously and unstably expand. Let:

[0202]

[0203] Solving, the critical stress for the unstable crack expansion is obtained as:

[0204]

[0205] S2. Solve the differential equations related to the evolution of the dislocation density to obtain the mobile dislocation density and the immobile dislocation density at the current creep rate, and use them as the input parameters for the next deformation process;

[0206] In the current thermal creep model, the evolution of the dislocation density plays a crucial role. The change in the strain rate of the material is closely related to the dislocation density. During the creep deformation process, dislocations will proliferate, be stored, and annihilate, which not only changes the dislocation density but also affects its type and spatial distribution, thus significantly affecting the creep behavior of the material. The evolution rates of different types of dislocation densities over time can be expressed by mathematical formulas as:

[0207]

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

[0209]

[0210] In the formula, ρ m is the density of mobile dislocations, 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 respectively, n F-R is the number of multiplied 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 the critical distance between two parallel slip planes respectively.

[0211] Considering the interaction between dislocations and 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 density of immobile dislocations, D gb is the grain boundary diffusivity.

[0214] The dislocation annihilation mechanism includes four typical dislocation annihilation mechanisms: single cross-slip of screw dislocations, spontaneous annihilation of screw dislocations, climb of edge dislocations, and spontaneous annihilation of edge dislocations. Accordingly, 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 primary slip plane and the cross-slip plane, n represents the number of active slip systems, τ0 represents the critical resolved shear stress, τ fr represents the lattice friction stress, τ sro represents the shear stress at the disordered interface time, 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] To more comprehensively describe the complex spatio-temporal evolution of dislocations, this method considers eight dislocation evolution rates. The classification of these categories reflects the evolution characteristics of dislocations at different spatial positions (inside dislocation cells and dislocation cell walls), different motion states (mobile and immobile), and different dislocation types (screw and edge). Specifically, it includes: mobile screw dislocations inside dislocation cells Immobile screw dislocations inside dislocation cells Mobile edge dislocations inside dislocation cells Immobile edge dislocations inside dislocation cells Mobile screw dislocations in dislocation cell walls Immobile screw dislocations in dislocation cell walls Mobile edge dislocations in dislocation cell walls And immobile edge dislocations in dislocation cell walls The evolution rate equations for these eight dislocations are summarized as follows:

[0218]

[0219] To solve the evolution equations of different types of dislocations, the principle of dislocation density conservation must be satisfied. Specifically, the evolution rate of the total dislocation density should be equal to the sum of the evolution rates of mobile and immobile 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 dislocation cell walls.

[0222] S3. Repeat steps S1 and S2, continuously update the creep information until the deformation reaches the Griffith fracture condition, and output the complete creep curve.

[0223] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not restrictive. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A creep mechanics constitutive modeling method based on multiple physical mechanisms, characterized in that, It includes the following steps: S1. Solve the kinetic equation according to the initial microstructure information to obtain the total creep rate of the system; 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 pores. Under a unified thermodynamic framework, various thermally activated mechanisms such as intragranular and grain boundary vacancy diffusion, dislocation slip and climb, grain boundary sliding, and pore evolution are considered; Based on these mechanisms, the total creep rate is expressed as: (1) Among them, are the plastic strains accumulated by vacancy diffusion, dislocation movement, grain boundary sliding, and pore evolution, respectively; S2. Solve the differential equations related to the evolution of dislocation density to obtain the mobile dislocation density and immobile dislocation density at the current creep rate, and use them as input parameters for the next deformation process; During the creep deformation process, dislocations will proliferate, store, and annihilate, which not only changes the dislocation density but also affects their type and spatial distribution, thus significantly affecting the creep behavior of the material; The evolution rates of different types of dislocation densities over time are expressed by mathematical formulas as: (35) Among them, represents the number of active dislocation density evolution mechanisms, represents the -th dislocation density corresponding to the dislocation density evolution mechanism; S3. Repeat steps S1 and S2, continuously update the creep information until the deformation reaches the Griffith fracture condition, and output the complete creep curve; In the calculation of the vacancy diffusion creep rate in step S1, the construction of its kinetic equation is specifically as follows: The plastic deformation caused by diffusion creep completely stems from the migration of matter during the diffusion process, and its driving force comes from the difference in the chemical potential of point defects when the grain boundary is subjected to tensile or compressive stress. During 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: (2) In the formula, is the vacancy equilibrium concentration, is the applied normal stress, is the atomic volume, is the Boltzmann constant, is the temperature, is the grain size, is the grain boundary layer thickness, and are the bulk diffusion coefficient and the grain boundary diffusion coefficient, respectively.

2. The multi-physics mechanism-based creep mechanics-based constitutive modeling method according to claim 1, characterized in that In the calculation of the dislocation motion creep rate in step S1, the construction of its dislocation slip and climb kinetic equations is specifically as follows: Viscoplasticity is defined as time-dependent plastic deformation beyond the elastic state, which is closely related to the viscous motion of dislocations. In this case, the creep strain gradually accumulates due to the motion of dislocations, and the creep rate contributed by dislocation motion is expressed by the Orowan equation as: (3) In the formula, are the shear strain rate and the plastic strain rate respectively, is the Taylor factor, is the mobile dislocation density, is the Burgers vector, is the average dislocation movement velocity, which depends on the average obstacle spacing and the time for the dislocation to move between obstacles, and the latter time for the dislocation to move between obstacles includes the waiting time in front of the obstacle and the time for moving between obstacles : (4) 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 individual obstacle spacings: (5) Among them, is the number of obstacle types, is the proportion of different obstacle types, is the obstacle spacing; Dislocations overcome obstacles through thermally activated slip or climb-assisted slip processes, and these two mechanisms are coupled and can occur simultaneously; The total waiting time is calculated by visualizing the bypass process as a parallel circuit, and the average waiting time of dislocations is expressed as: (6) Among them, respectively represent the theoretical waiting times for thermally activated slip and climb; The process of dislocation slip over obstacles is essentially a force-thermal coupled activation process, and the waiting time of dislocation slip is described by the Kocks-type activation enthalpy law as: (7) Among them, is the Debye frequency, is the number of obstacle types, is the activation energy; Based on dislocation theory and the thermal activation model, the behavior of dislocations overcoming obstacles with the assistance of external forces and heat is unified as the process of dislocations breaking away from point pinning; According to the properties of the material, factors such as lattice friction, solute atoms, forest dislocations, grain boundaries, and precipitate particles inside the material that hinder dislocation slip are considered to evaluate the waiting time of dislocation slip; Therefore, the force-activation energy relationships corresponding to different obstacles are as follows: (8) (9) (10) (11) According to the type of precipitate particles, dislocations will experience two different behaviors, the cutting mechanism and the bypass mechanism, when encountering precipitate particles, and the corresponding activation energy relationships for the two are: (12) In the formula, respectively represent the activation energies corresponding to lattice friction, solute atoms, dislocations, grain boundaries, and precipitate particles, respectively represent the applied shear stresses corresponding to lattice friction, solute atoms, dislocations, grain boundaries, and precipitate particles, and respectively 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 the line energy, is the average binding energy of the dislocation generated by the interaction between the solute atom and the dislocation, is the dislocation line tension, is the coarsening amplitude of the dislocation segment, and are the critical dislocation configuration and the equilibrium dislocation configuration respectively, is the length of the dislocation segment participating in the local activation event, is the average spacing between the grain boundary pinning points, is the height corresponding to the kink pair, and are the intrinsic parameters of the dislocation, is the angle between the dislocation line and the Burgers vector, is the critical width of the kink pair, is the dislocation core radius; Dislocation climb caused by vacancy diffusion is another important creep / plasticity mechanism in addition to dislocation slip; at high temperatures and low strain rates, edge dislocations occur through the climb mechanism, which is driven by vacancy diffusion along the dislocation line; dislocation climb is a typical thermally activated process, and its activation energy is obtained by the following formula: (13) Among them, and represent the vacancy formation energy and the vacancy migration energy respectively, is the jog formation energy, is the atomic volume. Correspondingly, the average climb velocity of the dislocation is: (14) In the formula, is the number of nearest neighbor atoms, is the vibration frequency, 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 obstacles; therefore, the average waiting time for climb of edge dislocations is expressed as: (15) In the formula, is the proportion of edge dislocations, is the average climb distance around obstacles; The running time depends on the moving distance and running speed of dislocations. Since the running time of dislocations is significantly less than the waiting time, it is assumed that the running speed of dislocations is the shear wave speed, that is , and based on this, the running time is expressed as: (16) Among them, is the average obstacle spacing, is the shear modulus, is the material density.

3. The creep mechanics-based constitutive modeling method based on multiple physical mechanisms according to claim 2, characterized in that In the calculation of the creep rate of grain boundary slip in step S1, the construction of its kinetic equation is specifically as follows: If grain boundary sliding is caused by dislocation climb-slip, the grain boundary sliding rate is determined by the climb rate because climb is a slower process. In this case, the climb frequency is expressed as: (17) wherein, is the probability of finding jogs on the dislocation, is the entropy of activation for diffusion, is the activation energy for diffusion, is the stress required for climb along the interface; assuming that dislocations are uniformly distributed along the grain boundary and their spacing is determined by the stress field of edge dislocations, the dislocation climb rate along the grain boundary is: (18) Among them, is the number of grain boundary dislocations per unit length, is the applied shear stress; If the dislocation moves within the region of adjacent grain boundaries, Equation (17) simplifies with the bulk diffusion coefficient, and the shear strain rate during the climb-slip process, is controlled by the climb rate, but the strain is generated by slip and is expressed as: (19) Among them, is the number of grain boundaries per unit volume, is the area swept by the dislocation along the grain boundary; since the dislocation enters the boundary region from the slip regions on both sides of the grain boundary, then (20) Substitute formula (20) into (19). For , , conditions, we get the following form: (21)。 4. The multi-physics mechanism-based creep mechanics-based constitutive modeling method according to claim 3, characterized in that, In the calculation of the creep rate of pore evolution in step S1, the construction of its kinetic equation is specifically as follows: After creep enters the third stage, the creep rate gradually increases and finally leads to fracture; under high stress conditions, when the plastic deformation rate is very fast, the form of creep fracture is similar to ductile fracture at room temperature, and creep damage is manifested as the nucleation, growth and coalescence of pores in high stress concentration regions, especially at grain boundaries, which ultimately trigger fracture; as spherical cap-shaped pores nucleate at grain boundaries, the total energy of the system will change, and the free energy change caused by pore nucleation is divided into three parts: one is the increase in surface energy caused by the new pore surface; the second is the decrease in interface energy due to the disappearance of the original grain boundary area; the third is the release of elastic strain energy caused by the formation of pores; therefore, the activation energy of pore nucleation is expressed as: (22) Among them, is the pore volume, and are the surface areas corresponding to pores and grain boundaries respectively, and are the surface energy of pores and the grain boundary energy respectively; for the spherical cap-shaped pore shape, the surface energy tension balance equation is: (23) Among them, is the cavity tip angle; substituting the calculation formula for into formula (21), we get: (24) Let , the critical core radius at which the pores can stably exist without sintering is obtained, : (25) Substitute into Equation (24), and the critical nucleation work of the pores is obtained as follows: (26) Among them, is the shape factor of the hole; The nucleation rate is defined as the number of pore nuclei formed on the grain boundary per unit volume per unit time; a pore with a critical radius can become stable by obtaining a vacancy, and the steady state will disappear and the size will automatically decrease if it loses a vacancy; therefore, the nucleation rate depends on the number of nuclei with a radius of in the grain boundary per unit volume and the number of vacancies transferred to the pore nuclei per unit time; correspondingly, the total nucleation rate at steady state is: (27) In the formula, is the number of potential nucleation sites, is the half-spacing of the pores, is the activation energy for vacancy diffusion along the grain boundary; The basis of the pore diffusion growth model is that pores gradually increase by absorbing vacancies, and the diffusion of vacancies migrates through the pore surface and is then transported along the grain boundary. During creep, due to the existence of a stress gradient, the growth rate of pores is closely related to the diffusion rate of vacancies. Therefore, the pore growth rate is expressed as: (28) Among them, is the pore radius, is the grain boundary width; Since the kinetics of the pore nucleation and growth process is similar to the phase transformation process, a phase transformation kinetics model is used to describe it; Johnson-Mehl is used to describe the pore evolution process, especially in pore nucleation and growth; for spherical new pores, according to formulas (27) and (28), the volume fraction of pore evolution is expressed as: (29) Among them, is the time. According to the Gurson formula, the growth of voids is controlled by the hydrostatic part of plastic strain, and the damage is expressed by the change in the void volume fraction as follows: (30) wherein, is the pore volume fraction, is the total plastic strain rate calculated through the plastic velocity gradient; considering that damage is caused by pore evolution, the plastic strain rate contributed by pore evolution is as follows: (31) Pore coalescence occurs in multiple modes, and each mode has several variants, which depend on microstructural factors, loading conditions and plastic flow characteristics; among them, the coalescence of spherical pores often leads to elongated deformation and direction effects: (32) In the formula, is the critical porosity for pore coalescence, is the coalescence factor, and are the saturated porosity and the failure porosity, respectively.

5. The creep mechanics-based constitutive modeling method based on multiple physical mechanisms according to claim 1, characterized in that In the dislocation evolution mechanism of step S2, the dislocation multiplication mechanism includes Frank-Read dislocation sources, grain boundary nucleation, double cross-slip to form dislocation loops and edge dislocation dipole multiplication mechanism forms; combining the above mechanisms, the expression of the dislocation density multiplication rate is: (36) In the formula, is the mobile dislocation density, is the initial dislocation length of the Frank-Read dislocation source, and are the activation energies corresponding to the Frank-Read dislocation source and the double cross-slip multiplication mechanism respectively, is the number of multiplied dislocation loops, is the shear stress corresponding to grain boundary nucleation, is the length of the double cross-slip dislocation segment, is the stacking fault width, and are the separation distance and the critical distance between two parallel slip planes respectively.

6. The method for constructing a creep mechanics model based on multiple physical mechanisms according to claim 5, characterized in that, Considering the interaction between dislocations and 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; correspondingly, the dislocation density storage rate is: (37) In the formula, is the mean free path coefficient, is the density of immobile dislocations, is the grain boundary diffusivity.

7. The method for building a creep mechanics model based on multiple physical mechanisms according to claim 6, wherein In the dislocation evolution mechanism of step S2, the dislocation annihilation mechanism includes four dislocation annihilation mechanisms: single cross-slip of screw dislocations, spontaneous annihilation of screw dislocations, climb of edge dislocations and spontaneous annihilation of edge dislocations. The dislocation density annihilation rate is described by the following formula: (38) Among them, represents the activation energy of single cross-slip, represents the angle between the primary slip plane and the cross-slip plane, represents the number of active slip systems, represents the critical resolved shear stress, represents the lattice friction stress, represents the shear stress of the disordered interface time, is the Schmidt factor ratio, is the external shear stress, represents the internal shear stress, represents the activation energy of climb, is the vacancy formation energy.

8. The modeling method of creep mechanics based on multiple physical mechanisms according to claim 7, characterized in that To more comprehensively describe the complex spatio-temporal evolution of dislocations, the classification of the other eight dislocation evolution mechanisms considered in step S2 reflects the evolution characteristics of dislocations at different spatial positions, different motion states, and different dislocation types; specifically including: mobile screw dislocations inside dislocation cells , immobile screw dislocations inside dislocation cells , mobile edge dislocations inside dislocation cells , immobile edge dislocations inside dislocation cells , mobile screw dislocations in dislocation cell walls , immobile screw dislocations in dislocation cell walls , mobile edge dislocations in dislocation cell walls , and immobile edge dislocations in dislocation cell walls ; The evolution rate equations of these eight dislocations are summarized as follows: (39) In order to solve the evolution equations of different types of dislocations, the principle of dislocation density conservation must be satisfied; specifically, the evolution rate of the total dislocation density should be equal to the sum of the evolution rates of mobile and immobile dislocations; based on this principle, the evolution equation of the total dislocation density is expressed as: (40) Among them, represents the volume fraction of the dislocation cell wall.

9. The multi-physics mechanism-based creep mechanics-based constitutive modeling method according to claim 1, characterized in that The Griffith fracture criterion in step S3 is: For a crack of a given size, there exists a critical stress : When , the crack will not expand; when , the crack will expand rapidly and lead to fracture; when the crack expands, the change in the system energy comes from two aspects: on the one hand, due to the elastic strain energy , the release of which reduces the system energy, and on the other hand, the generation of a new surface increases the energy ; assuming that the crack length corresponding to the maximum value of the total system energy change is , then when , the increase in the crack length will cause the system energy to increase, so the crack cannot expand automatically; while when , the expansion of the crack reduces the total system energy, and the crack can spontaneously and unstably expand. Let: (33) The critical stress for the unstable crack propagation obtained by solving is: (34) 。

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