High-temperature alloy bulk modeling method considering dynamic and static structure genetic effects in multi-step thermal deformation process

Abstract

The invention discloses a high-temperature alloy bulk modeling method considering dynamic and static structure genetic effects in a multi-step thermal deformation process, and belongs to the technical field of material plastic processing. The method comprises the following steps: establishing a constitutive model coupled with dynamic microstructure evolution; constructing a static softening fraction model, including description of static recovery, sub-dynamic recrystallization, continuous grain coarsening and annealing twin boundary microstructure evolution behaviors; the static softening fraction serves as a global state variable, key state variables in different deformation stages are iteratively updated, and the key state variables comprise the initial hardening rate, the characteristic stress and the time needed when the dynamic recrystallization fraction reaches 50%; unknown parameters in all the models are calibrated through a genetic algorithm based on experimental data, and accurate prediction of the flow stress and the grain size evolution rule in the multi-step thermal deformation process is achieved. According to the method, the problem of cross-scale association of the microstructure and the macromechanical response in multi-step thermal deformation of the high-temperature alloy is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of material plastic processing, and in particular relates to a constitutive modeling method for high-temperature alloys taking into account the dynamic and static structural genetic effects of a multi-step thermal deformation process. Background Art

[0002] Due to its excellent high-temperature strength and heat-corrosion resistance, high-temperature alloys have become the core materials for the manufacture of key components of high-end equipment in the aerospace field. Plastic forming (such as forging) under the action of thermomechanical coupling is a key link in the manufacture of high-temperature alloy components. The thermoplastic forming process of high-temperature alloys usually includes a multi-step thermal deformation process, and there is a non-deformation conversion process (such as a heat preservation process) between the multi-step thermal deformation processes. From the perspective of microstructural evolution, the thermal deformation process is usually called a dynamic process, while the non-deformation process (such as a heat preservation process) is called a static process. Therefore, from the perspective of material microstructural evolution, the multi-step thermal deformation process is usually a dynamic-static-dynamic microstructural inheritance cycle. This complex multi-step thermomechanical coupling process leads to huge challenges in the regulation of the microstructural properties of high-temperature alloy components. Macro-micro coupling modeling and simulation technology has become an important means for the current design and optimization of plastic forming processes, and establishing a macro-micro coupling constitutive model of the material is the key to achieving accurate prediction of the thermal deformation process. Therefore, to achieve precise microstructural control and service performance optimization during the thermoplastic forming process of high-temperature alloy components, it is first necessary to construct a constitutive model for the high-temperature alloy that considers the genetic effects of the dynamic and static microstructures during the multi-step hot deformation process. However, existing constitutive models fail to effectively characterize the influence of the genetic relationship between dynamic and static microstructures on the macroscopic mechanical response, resulting in large deviations in the prediction of flow stress during multi-step hot deformation and difficulty in accurately describing the evolution of grain size.

[0003] Therefore, the present invention proposes a constitutive modeling method for the multi-step thermal deformation process of high-temperature alloys taking into account the genetic effect between dynamic and static microstructures. Summary of the Invention

[0004] Technical issues to be solved:

[0005] In order to avoid the shortcomings of the existing technology, the present invention provides a constitutive modeling method for high-temperature alloys that takes into account the dynamic and static organizational genetic effects of a multi-step thermal deformation process. By considering the influence of the genetics of the organization between the dynamic-static-dynamic cycle process on the flow stress of the thermal deformation process, a constitutive model is established that accurately describes the cross-scale correlation between the microstructure and the macroscopic mechanical response in the multi-step thermal deformation process, thereby achieving accurate prediction of the evolution law of the flow stress and grain size in the multi-step thermal deformation process of the high-temperature alloy, solving the difficult problem of the cross-scale correlation between the microstructure and the macroscopic mechanical response in the multi-step thermal deformation of the high-temperature alloy, and providing a theoretical basis and technical support for the optimization of the thermoplastic forming process and precise control of the performance of high-temperature alloy components.

[0006] The technical solution of the present invention is: a constitutive modeling method for high-temperature alloys considering the dynamic and static microstructure inheritance effects during a multi-step thermal deformation process, the specific steps are as follows:

[0007] Establish a constitutive model that couples dynamic microstructural evolution, including descriptions of strain hardening, dynamic recovery, and dynamic recrystallization;

[0008] Construct a static softening fraction model, including the description of static recovery, metadynamic recrystallization, continuous grain coarsening and annealing twin boundary microstructural evolution behavior;

[0009] Taking the static softening fraction as a global state variable, the key state variables at different deformation stages are iteratively updated, including the initial hardening rate, characteristic stress, and the time required for the dynamic recrystallization fraction to reach 50%, to achieve the inheritance of dynamic and static microstructures.

[0010] Based on experimental data, the unknown parameters in all the above models are calibrated through genetic algorithms to achieve accurate prediction of the evolution law of flow stress and grain size in the multi-step thermal deformation process.

[0011] A further technical solution of the present invention is: the steps of establishing a constitutive model for coupled dynamic microstructure evolution are as follows:

[0012] A flow stress instantaneous increment model based on the evolution of dislocation density is established, which is the constitutive model of high-temperature alloys under strain hardening and dynamic recovery. The expression is as follows:

[0013]

[0014] Where σ represents the flow stress, t d represents the deformation time, Θ0 represents the initial hardening rate, represents the strain rate, σ y represents the yield stress, σ sat represents saturation stress;

[0015] Establish dynamic recrystallization model and grain size refinement model for high-temperature alloys:

[0016] The expression of the dynamic recrystallization model is:

[0017]

[0018] Where, F drx is the dynamic recrystallization fraction, n d is the time index, τ drx The time required for dynamic recrystallization to reach 50%;

[0019] The expression of the grain size refinement model is:

[0020]

[0021] Where d is the average grain size of the high-temperature alloy; d0 is the initial grain size of the alloy, d s is the steady-state grain size in equilibrium, c1 is the material parameter;

[0022] Based on the above model, a constitutive model of coupled dynamic microstructural evolution is established. The coupled dynamic microstructural evolution includes strain hardening, dynamic recovery, and dynamic recrystallization, and the expression is as follows:

[0023]

[0024] Where σ s is the steady-state stress; the yield stress, saturation stress, and steady-state stress are all quantified by the following expressions:

[0025]

[0026] Among them, σ i represents characteristic stress, i is s, y or sat; k is the Hall-Petch parameter, α i , Q i 、A i 、n i are all material parameters, and R is the gas constant.

[0027] A further technical solution of the present invention is: the static softening fractional model includes:

[0028] The evolution of the dislocation density during the recovery process is reflected by describing the evolution equation of the average distance between dislocations. The static recovery model expression is established as follows:

[0029]

[0030] Where k b is the Boltzmann constant, S m is the material parameter related to the solute atoms, τ srv is the time required for static recovery to reach 50%, T is the temperature, b is the Burgers vector of dislocation, t s It is the static holding time;

[0031] The metadynamic recrystallization model is established, and the expression is as follows:

[0032]

[0033] Where, Softening limit fraction, n m is the time index, τ mdrx The time required for metadynamic recrystallization to reach 50%;

[0034] Establishment of continuous grain coarsening kinetics and annealing twin boundary strengthening models:

[0035] The annealing twin boundary strengthening model expression is:

[0036]

[0037] Where, is the weakening coefficient, N g is the number of annealing twins per unit grain;

[0038] The continuous grain coarsening kinetic model expression is:

[0039]

[0040] Where α1, c4, n g , Γ z are material parameters, f1 and f2 are weight coefficients, φ and r are the content and size of carbides in the high-temperature alloy, respectively.

[0041] A further technical solution of the present invention is: the updating formula of the initial hardening rate is:

[0042] Θ 0sub =Θ 0ini F ss

[0043] Among them, Θ 0sub and Θ 0ini are the initial hardening rates in the subsequent stage and the initial stage respectively; F ss is the static softening fraction, which is expressed as follows:

[0044]

[0045] Where σ m is the interruption stress, σ ysub and σ yini are the yield stresses in the subsequent stage and the initial stage, respectively.

[0046] A further technical solution of the present invention is: the updating formula of the characteristic stress is:

[0047]

[0048] Among them, σ satsub is the saturation stress in the subsequent stage, σ satini is the saturation stress in the initial stage.

[0049] A further technical solution of the present invention is that the update formula for the time required for the dynamic recrystallization fraction to reach 50% is:

[0050]

[0051] Where c5, c6 and γ2 are material parameters, τ drxsub and τ drxini are the times required for the dynamic recrystallization fraction to reach 50% in the subsequent stage and the initial stage, respectively.

[0052] A further technical solution of the present invention is that the calibration of the unknown parameters adopts a multi-objective genetic algorithm, wherein the optimization objectives include:

[0053] Average relative error between the predicted and experimental flow stress values;

[0054] Relative error of recrystallization fraction;

[0055] Errors related to grain size;

[0056] By optimizing the parameters, the optimal material parameter combination of the constitutive model is determined.

[0057] A further technical solution of the present invention is: the numerical implementation of the model includes:

[0058] Dynamic stage: real-time update of flow stress based on dislocation density and recrystallization fraction;

[0059] Static stage: The softening mechanism is selected according to the stress state before interruption, which can be pure static recovery or metadynamic recrystallization;

[0060] Iteratively transfer the normalized dislocation density and grain size to the next deformation stage.

[0061] A further technical solution of the present invention is: the process for accurately predicting the evolution of flow stress and grain size during a multi-step thermal deformation process is as follows:

[0062] Calculating initial parameters based on experimental data; the initial parameters include yield stress, critical stress, saturation stress, steady-state stress, initial hardening rate, steady-state grain size, and the time required for static recovery, dynamic recrystallization, and metadynamic recrystallization to reach 50%;

[0063] During the plastic deformation stage, the flow stress, dynamic recrystallization fraction, and grain size are calculated in real time based on the constitutive model coupled with dynamic microstructural evolution.

[0064] In the static stage, the static softening mechanism of the high-temperature alloy is determined based on the flow stress and hardening rate before interruption, that is, whether it contains metadynamic recrystallization. Based on the static softening fraction model, the kinetic curves of static recovery, metadynamic recrystallization, continuous grain growth, and the strengthening effect of annealing twins are calculated.

[0065] Update the initial hardening rate, characteristic stress and dynamic recrystallization kinetic parameters of the next deformation stage based on the static softening fraction;

[0066] Dynamic and static stage calculations are performed cyclically, and stress-strain curves and grain size evolution data of multi-step deformation are output.

[0067] A further technical solution of the present invention is: the determination of the static softening mechanism includes:

[0068] When the hardening rate is less than 0 or the flow stress before interruption is greater than the critical stress but the hardening rate is greater than 0, the static softening behavior at this time is composed of dynamic recovery, metadynamic recrystallization and grain boundary effect components;

[0069] Otherwise, the static softening behavior consists only of dynamic recovery and grain boundary effect components.

[0070] Beneficial effects

[0071] The beneficial effects of the present invention are:

[0072] 1. This invention addresses the challenge of the cumulative impact of microstructural states during multi-step deformation of superalloys by introducing the static softening fraction as a global state variable and establishing a model of microstructural inheritance effects in both dynamic and static stages. Experimental verification demonstrates that the linear correlation coefficient and mean absolute relative error between the predicted and experimental flow stress values ​​are 0.9924% and 5.71%, respectively. The linear correlation coefficient and mean absolute relative error between the predicted and experimental recrystallization fraction and average grain size values ​​are 0.9818% and 5.04%, and 0.9884% and 7.03%, respectively, significantly outperforming traditional models.

[0073] 2. This paper proposes an equivalent grain size model to quantify the effect of annealing twin boundaries on grain boundary strengthening, addressing the inability of traditional grain size models to describe the complex grain boundary structure of high-temperature alloys. Combined with a continuous grain coarsening kinetic model, this model accurately predicts the dynamic evolution of grain size during a dynamic-static-dynamic cycle.

[0074] 3. This invention utilizes a multi-objective genetic algorithm to simultaneously optimize the prediction accuracy of flow stress, recrystallization fraction, and grain size, covering 14 key material parameters. This method requires only single- or double-pass compression test data for calibration, reducing data requirements by over 50%. It is also applicable to high-temperature alloys of varying compositions (such as Ni-Co-Cr-based alloys) and complex deformation conditions.

[0075] 4. The proposed model can output microscopic state variables such as normalized dislocation density, recrystallization fraction, and grain size in real time, providing a quantitative basis for the hot forming process design of high-temperature alloy components (such as aircraft engine blades and turbine disks). In practical applications, this can reduce process trial and error, shorten product development cycles, and avoid performance fluctuations caused by improper microstructure control.

[0076] 5. The present invention aims at the interruption of heat preservation effect in multi-step thermal deformation. The model dynamically updates the initial hardening rate and dynamic recrystallization kinetic parameters to accurately predict the stress mutation during secondary deformation (such as Figure 2 The error is reduced by more than 40% compared with the traditional model, providing a reliable simulation tool for dynamic processes such as flexible rolling and multi-directional forging. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 Flowchart of the method for constructing a constitutive model in an embodiment of the present invention.

[0078] Figure 2 A comparison chart of the prediction accuracy of the high-temperature alloy constitutive model with and without considering the dynamic and static structural inheritance effects of the multi-step thermal deformation process.

[0079] Figure 3 A comparison chart between the experimental and predicted values ​​of flow stress of a high-temperature alloy at different temperatures, strain rates, and holding times during the two-step hot deformation process.

[0080] Figure 4 Comparison chart of experimental and predicted recrystallization fractions of high-temperature alloys during double-step hot deformation.

[0081] Figure 5 A comparison chart of the experimental and predicted average grain sizes of high-temperature alloys during double-step hot deformation. DETAILED DESCRIPTION

[0082] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0083] The existing constitutive models fail to effectively characterize the influence of the inheritance between dynamic and static microstructures on the macroscopic mechanical response, resulting in large deviations in the prediction of flow stress during multi-step thermal deformation and difficulty in accurately describing the evolution of grain size. The present invention provides a constitutive modeling method for high-temperature alloys that considers the inheritance effects of dynamic and static microstructures during multi-step thermal deformation. The specific steps are as follows:

[0084] Establish a constitutive model that couples dynamic microstructural evolution, including descriptions of strain hardening, dynamic recovery, and dynamic recrystallization;

[0085] Construct a static softening fraction model, including the description of static recovery, metadynamic recrystallization, continuous grain coarsening and annealing twin boundary microstructural evolution behavior;

[0086] Taking the static softening fraction as a global state variable, the key state variables at different deformation stages are iteratively updated, including the initial hardening rate, characteristic stress, and the time required for the dynamic recrystallization fraction to reach 50%, to achieve the inheritance of dynamic and static microstructures.

[0087] Based on experimental data, the unknown parameters in all the above models are calibrated through genetic algorithms to achieve accurate prediction of the evolution law of flow stress and grain size in the multi-step thermal deformation process.

[0088] The technical solution of the present invention incorporates the tissue inheritance effect of the dynamic-static-dynamic cycle process into the constitutive model for the first time, filling the gap in the existing technology in microscopic state transmission in multi-step deformation.

[0089] The above technical solution is further described below with reference to examples and drawings:

[0090] In one embodiment, a constitutive modeling method for a Ni-Co-Cr based superalloy is provided for a two-step hot compression deformation process of the superalloy, taking into account the dynamic and static microstructural genetic effects, including the following steps:

[0091] Step S1, establishing a constitutive model coupled with dynamic microstructural evolution, which includes descriptions of strain hardening, dynamic recovery, and dynamic recrystallization;

[0092] Step S2, constructing a static softening model, including static recovery, metadynamic recrystallization, continuous grain coarsening kinetics, and annealing twin boundary strengthening models;

[0093] Step S3, taking the static softening fraction as the global state variable, iteratively updates key state variables such as the initial hardening rate and characteristic stress at different deformation stages to achieve the inheritance of dynamic and static microstructures;

[0094] Step S4: calibrate the model parameters using a genetic algorithm based on the experimental data, establish a numerical implementation method for the model, and verify the prediction accuracy of the model in combination with the experimental data.

[0095] In one embodiment, step S1 is to establish a flow stress model coupled with dynamic microstructural evolution. The specific steps are:

[0096] Step S1-1, establishing a flow stress change rate model for a high-temperature alloy under strain hardening and dynamic recovery.

[0097] According to dislocation theory, the flow stress at the start of crystal slip is related to the dislocation density within the crystal:

[0098]

[0099] Where σ represents the flow stress, α is the material constant, M is the Taylor orientation factor, b is the Burgers vector of the dislocation, μ(T) is the shear modulus related to temperature T, and ρ is the dislocation density inside the crystal.

[0100] The Estrin-Mecking model is used to describe the evolution of dislocation density with strain ε under strain hardening and dynamic recovery:

[0101]

[0102] Where, Γ w =(bd) -1 is the material constant, d is the grain size, is related to temperature T and strain rate Related dynamic restitution coefficient.

[0103] Substituting formula (2) into formula (1), we can obtain the flow stress σ of the high-temperature alloy under strain hardening and dynamic recovery as a function of deformation time t d The instantaneous increment model of:

[0104]

[0105] Where Θ0 is the initial hardening rate, σ y and σ sat are the yield stress and saturation stress, respectively.

[0106] Step S1-2: establishing a dynamic recrystallization model and a grain refinement model for a high-temperature alloy.

[0107] The occurrence of dynamic recrystallization can be determined by the critical stress σ cri To judge, when the flow stress is greater than the critical stress, it can be considered that the material has undergone dynamic recrystallization. The dynamic recrystallization process can be described by the JMAK kinetic model:

[0108]

[0109] Among them, F drx is the dynamic recrystallization fraction, n d is the time index, τ drx It is the time required for dynamic recrystallization to reach 50%.

[0110] The rate of decrease of the average grain size d of a high-temperature alloy caused by dynamic recrystallization can be defined as:

[0111]

[0112] Where d is the average grain size of the high-temperature alloy; d0 is the initial grain size of the alloy, d s is the steady-state grain size in equilibrium, and c1 is the material parameter.

[0113] Step S1-3, establish the flow stress of the high-temperature alloy under the action of strain hardening, dynamic recovery and dynamic recrystallization as a function of deformation time t d The instantaneous increment model.

[0114] Considering the softening effect of dynamic recrystallization on stress, the flow stress σ changes with the deformation time t d The instantaneous increment model of is rewritten as:

[0115]

[0116] Where σ s is the steady-state stress. The yield stress, saturation stress, and steady-state stress can all be quantified by the improved STG model:

[0117]

[0118] Among them, σ i represents characteristic stress, i is s, y or sat; k is the Hall-Petch parameter, α i , Q i 、A i 、n i are all material parameters, and R is the gas constant.

[0119] In one embodiment, in step S2, the specific steps of constructing a static softening model are as follows:

[0120] Step S2-1, establishing a static softening fractional model.

[0121] Static softening fraction F ss The effect of static microstructure on stress softening can be described by the yield stress compensation method:

[0122]

[0123] Where σ m is the interruption stress, σ ysub and σ yini are the yield stresses in the subsequent stage and the initial stage, respectively.

[0124] By differentiating Equation (8), we can decouple the contributions of various static microstructural evolutions to the static softening fraction:

[0125]

[0126] Among them, t sis the static holding time, Δσ s is the maximum static stress softening difference, F srv and F mdrx are the static recovery and meta-dynamic recrystallization fractions, respectively. Therefore, it can be concluded that the static softening fraction is mainly affected by three aspects: static recovery, meta-dynamic recrystallization, and grain size.

[0127] Step S2-2: Establish a static response model.

[0128] The drag of solute atoms in the alloy and the thermally activated slip of dislocations are comprehensively considered, and the evolution of dislocation density during the recovery process is reflected by the equation describing the evolution of the average distance between dislocations. The static recovery model is:

[0129]

[0130] Where k b is the Boltzmann constant, S m is the material parameter related to the solute atoms, τ srv The time required for static recovery to reach 50%.

[0131] Step S2-3, establishing a metadynamic recrystallization model.

[0132] In contrast to dynamic recrystallization, metadynamic recrystallization does not have the incubation period of conventional recrystallization nucleation. Therefore, the kinetics of metadynamic recrystallization is faster and can be expressed as:

[0133]

[0134] in, Softening limit fraction, n m is the time index, τ mdrx It is the time required for metadynamic recrystallization to reach 50%.

[0135] Step S2-4, establishing an equivalent grain size model.

[0136] Considering the presence of a large number of annealing twins in high-temperature alloys, the traditional grain size d cannot accurately describe the stress of grain boundary strengthening. Therefore, the present invention introduces an equivalent grain size d ef To express the stress of grain boundary strengthening, the equivalent grain size can be expressed as follows:

[0137]

[0138] Where φ is the weakening coefficient, N g is the number of annealing twins per unit grain. In addition, considering the continuous growth of grains under the action of multiple driving forces, the grain growth rate model is:

[0139]

[0140] Where α1, c4, n g , Γ z are material parameters, f1 and f2 are weight coefficients, φ and r are the content and size of carbides in the high-temperature alloy, respectively.

[0141] In one embodiment, in step S3, the static softening fraction is used as a global state variable to iteratively update the key state variables at different deformation stages. The specific steps are as follows:

[0142] In step S3-1, during the deformation phase, the initial microstructure state is essentially dependent on the static softening fraction. Generally, a lower static softening fraction reduces the strain hardening capacity during the subsequent deformation phase because the limited effect of static softening still leaves more deformed microstructure. The initial hardening rate during the deformation phase can be expressed as a function of the static softening fraction:

[0143] Θ 0sub =Θ 0ini F ss (14) Where Θ 0sub and Θ 0ini are the initial hardening rates in the subsequent stage and the initial stage, respectively.

[0144] Step S3-2, update of characteristic stress. The relationship between saturation stress and static softening fraction at different deformation stages can be obtained by combining equations (3) and (8):

[0145]

[0146] Among them, σ satsub and σ satini are the saturation stresses in the subsequent stage and the initial stage, respectively.

[0147] In step S3-3, the difference in initial structure caused by the static softening behavior before each deformation stage can have a considerable impact on the dynamic recrystallization kinetics. The present invention proposes a model for the first time to characterize the promoting effect of static softening behavior on dynamic recrystallization kinetics, as shown in the following formula:

[0148]

[0149] Where c5, c6 and γ2 are material parameters, τ drxsub and τ drxini are the times required for the dynamic recrystallization fraction to reach 50% in the subsequent stage and the initial stage, respectively.

[0150] In one embodiment, step S4 is specifically as follows:

[0151] The experimental materials were obtained from Ni-Co-Cr-based superalloy forgings. Several Φ8×12 standard cylindrical hot compression specimens were then obtained from the forgings using wire cutting. These specimens were then subjected to a two-step hot compression test. The experimental temperatures were 1020°C, 1060°C, and 1100°C, respectively, and the strain rate was 0.01s. -1 , 0.1s -1 and 1s -1 The interruption holding time was 0s, 5s, 10s, 30s and 60s, and the interruption strain was 0.35. After completing the double-step hot compression experiment, the sample was immediately quenched to retain the high-temperature microstructure for the calculation of recrystallization fraction and grain size.

[0152] A genetic algorithm was used on the MATLAB platform to perform a multi-objective optimization of the material parameters of the constitutive model. The objective function used flow stress, recrystallization fraction, and relative error in grain size as optimization targets. The genetic algorithm was used to optimize this objective function to determine the optimal combination of material parameters that achieves the global minimum. The material parameter values ​​are shown in Table 1.

[0153] Table 1 Parameter values

[0154]

[0155]

[0156] The numerical implementation method of the model is established and the prediction accuracy of the model is verified by combining experimental data.

[0157] Reference Figure 1 As shown in Figure 2, the numerical implementation method of the constitutive model is as follows:

[0158] Step S41, calculate the initial parameters related to the temperature and strain rate of the constitutive model, including yield stress, critical stress, saturation stress, steady-state stress, initial hardening rate, steady-state grain size, and the time required for static recovery, dynamic recrystallization, and metadynamic recrystallization to reach 50%.

[0159] In step S42, when the equivalent plastic strain rate of the material is greater than 0, the high-temperature alloy undergoes plastic deformation. Based on the coupled dynamic microstructure evolution constitutive model established in step S1, the changes in the alloy flow stress are calculated, and the evolution of the dynamic recrystallization fraction and average grain size during the hot deformation stage is predicted.

[0160] Step S43, when the equivalent plastic strain rate of the material is equal to 0, the high-temperature alloy is in the static microstructure evolution process of the non-deformation stage. Record the flow stress, hardening rate, recrystallization fraction and average grain size before the deformation is interrupted. According to the flow stress and hardening rate before the deformation is interrupted, the softening mechanism of the high-temperature alloy under the unloading and heat preservation state is judged. When the hardening rate is less than 0 or the flow stress before the interruption is greater than the critical stress but the hardening rate is greater than 0, the static softening behavior at this time is composed of dynamic recovery, sub-dynamic recrystallization and grain boundary effect components; otherwise, the static softening behavior is composed only of dynamic recovery and grain boundary effect components. Then, based on the static softening model established in step S2, the kinetic curves of static recovery, sub-dynamic recrystallization and the strengthening effects of continuous grain growth and annealing twins are calculated respectively.

[0161] Step S44: Record the static softening fraction and average grain size calculated in step S43. Update key state variables such as initial hardening rate and characteristic stress based on the state variable iterative update model established in step S3.

[0162] In step S45, when the equivalent plastic strain rate of the material is again greater than 0, the superalloy enters the second deformation state, a dynamic microstructural evolution process. The updated initial hardening rate and characteristic stress state variables are used as new initial conditions, and the established coupled dynamic microstructural evolution constitutive model is combined to calculate the flow stress and average grain size.

[0163] By repeating the above steps S41-S45, the mechanical response and microstructural evolution law of the high-temperature alloy during the multi-step thermal deformation dynamic-static-dynamic cycle process can be obtained.

[0164] At this point, a constitutive model of high-temperature alloys considering the dynamic and static microstructural inheritance effects during the multi-step thermal deformation process has been established.

[0165] This paper addresses the multi-step deformation characteristics of high-temperature alloy hot forming processes and establishes a constitutive model for high-temperature alloys that considers the genetic effects of static and dynamic microstructures during this multi-step hot deformation process. Compared to existing constitutive models for high-temperature alloys, this model considers the genetic effects of the material microstructure and mechanical response during the dynamic-static-dynamic cycle of the high-temperature alloy's multi-step hot deformation. By introducing state variable update equations into the constitutive model, it more precisely characterizes the various physical processes of the dynamic-static-dynamic cycle. Figure 2 Demonstrated at 1060℃, 0.1s -1Comparison of the predicted results of the flow stress curve after 5s of holding under strain rate conditions and the experimental values, where the solid line represents the predicted curve based on this model (considering the dynamic-static tissue genetic effect), and the dotted line represents the predicted result of the traditional model (not considering the dynamic-static tissue genetic effect). Experimental data show that the predicted stress value of the traditional model is significantly higher than the experimental measurement value, while the predicted curve of this model is highly consistent with the experimental value, indicating that the established model has better prediction ability. Comparison of the predicted and experimental values ​​of flow stress at different temperatures and strain rates. Figure 3 As shown in the results, the error between the predicted value and the experimental value is within 10MPa and the average relative error is about 5.71%, with a correlation coefficient of 0.9924. In addition, the comparison between the predicted value and the experimental value of recrystallization fraction and grain size is as follows: Figure 4 and Figure 5 As shown in the results, the linear correlation coefficients and average absolute relative errors of the predicted and experimental values ​​for the recrystallization fraction and average grain size are 0.9818 and 5.04%, and 0.9884 and 7.03%, respectively. Therefore, the constitutive model for superalloys established in the present invention, which considers the dynamic and static microstructural inheritance effects during the multi-step hot deformation process, has good prediction accuracy.

[0166] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A constitutive modeling method for high-temperature alloys considering the dynamic and static microstructure inheritance effects during multi-step thermal deformation, characterized in that The specific steps are as follows: Establish a constitutive model that couples dynamic microstructural evolution, including descriptions of strain hardening, dynamic recovery, and dynamic recrystallization; Construct a static softening fraction model, including the description of static recovery, metadynamic recrystallization, continuous grain coarsening and annealing twin boundary microstructural evolution behavior; Taking the static softening fraction as a global state variable, the key state variables at different deformation stages are iteratively updated, including the initial hardening rate, characteristic stress, and the time required for the dynamic recrystallization fraction to reach 50%, to achieve the inheritance of dynamic and static microstructures. Based on experimental data, the unknown parameters in all the above models are calibrated through genetic algorithms to achieve accurate prediction of the evolution law of flow stress and grain size in the multi-step thermal deformation process.

2. The constitutive modeling method for high-temperature alloys according to claim 1, wherein the method considers the dynamic and static microstructure inheritance effects of a multi-step thermal deformation process, and is characterized by: The steps of establishing the constitutive model for coupled dynamic microstructure evolution are as follows: A flow stress instantaneous increment model based on the evolution of dislocation density is established, which is the constitutive model of the superalloy under strain hardening and dynamic recovery. The expression is as follows: Where σ represents the flow stress, t d represents deformation time, Θ0 represents initial hardening rate, ε represents strain rate, σ y represents the yield stress, σ sat represents saturation stress; Establish dynamic recrystallization model and grain size refinement model for high-temperature alloys: The expression of the dynamic recrystallization model is: Where, F drx is the dynamic recrystallization fraction, n d is the time index, τ drx The time required for dynamic recrystallization to reach 50%; The expression of the grain size refinement model is: Where d is the average grain size of the high-temperature alloy; d0 is the initial grain size of the alloy, d s is the steady-state grain size in equilibrium, c1 is the material parameter; Based on the above model, a constitutive model of coupled dynamic microstructural evolution is established. The coupled dynamic microstructural evolution includes strain hardening, dynamic recovery, and dynamic recrystallization, and the expression is as follows: Where σ s is the steady-state stress; the yield stress, saturation stress, and steady-state stress are all quantified by the following expressions: Among them, σ i represents characteristic stress, i is s, y or sat; k is the Hall-Petch parameter, α i , Q i 、A i 、n i are all material parameters, and R is the gas constant.

3. The constitutive modeling method for high-temperature alloys according to claim 2, which takes into account the dynamic and static microstructure inheritance effects of a multi-step thermal deformation process, is characterized by: The static softening fraction model includes: The evolution of the dislocation density during the recovery process is reflected by describing the evolution equation of the average distance between dislocations. The static recovery model expression is established as follows: Where k b is the Boltzmann constant, S m is the material parameter related to the solute atoms, τ srv is the time required for static recovery to reach 50%, T is the temperature, b is the Burgers vector of dislocation, t s It is the static holding time; The metadynamic recrystallization model is established, and the expression is as follows: Where, Softening limit fraction, n m is the time index, τ mdrx The time required for metadynamic recrystallization to reach 50%; Establishment of continuous grain coarsening kinetics and annealing twin boundary strengthening models: The annealing twin boundary strengthening model expression is: Where, is the weakening coefficient, N g is the number of annealing twins per unit grain; The continuous grain coarsening kinetic model expression is: Where α1, c4, n g , Γ z are material parameters, f1 and f2 are weight coefficients, φ and r are the content and size of carbides in the high-temperature alloy, respectively.

4. The constitutive modeling method for high-temperature alloys according to claim 3, wherein the method considers the dynamic and static microstructure inheritance effects of a multi-step thermal deformation process, and is characterized by: The update formula of the initial hardening rate is: I 0sub =Θ 0ini F ss Among them, Θ 0sub and Θ 0ini are the initial hardening rates in the subsequent stage and the initial stage respectively; F ss is the static softening fraction, which is expressed as follows: Where, σ m is the interruption stress, σ ysub and σ yini are the yield stresses in the subsequent stage and the initial stage, respectively.

5. The constitutive modeling method for high-temperature alloys according to claim 4, wherein the method considers the dynamic and static microstructure inheritance effects of a multi-step thermal deformation process, and is characterized in that: The updating formula of the characteristic stress is: Among them, σ satsub is the saturation stress in the subsequent stage, σ satini is the saturation stress in the initial stage.

6. The constitutive modeling method for high-temperature alloys according to claim 5, wherein the method takes into account the dynamic and static microstructure inheritance effects of a multi-step thermal deformation process, is characterized in that: The updated formula for the time required for the dynamic recrystallization fraction to reach 50% is: Where c5, c6 and γ2 are material parameters, τ drxsub and τ drxini are the times required for the dynamic recrystallization fraction to reach 50% in the subsequent stage and the initial stage, respectively.

7. The constitutive modeling method for high-temperature alloys according to claim 6, wherein the method considers the dynamic and static microstructure inheritance effects of a multi-step thermal deformation process, and the method is characterized by: The calibration of the unknown parameters adopts a multi-objective genetic algorithm, wherein the optimization objectives include: Average relative error between the predicted and experimental flow stress values; Relative error of recrystallization fraction; Errors related to grain size; By optimizing the parameters, the optimal material parameter combination of the constitutive model is determined.

8. The constitutive modeling method for high-temperature alloys according to claim 7, which takes into account the dynamic and static microstructure inheritance effects of a multi-step thermal deformation process, is characterized by: The numerical implementation of the model includes: Dynamic stage: real-time update of flow stress based on dislocation density and recrystallization fraction; Static stage: The softening mechanism is selected according to the stress state before interruption, which can be pure static recovery or metadynamic recrystallization; Iteratively transfer the normalized dislocation density and grain size to the next deformation stage.

9. The constitutive modeling method for high-temperature alloys according to claim 8, wherein the method takes into account the dynamic and static microstructure inheritance effects of a multi-step thermal deformation process, is characterized in that: The process for accurately predicting the evolution of flow stress and grain size during multi-step thermal deformation is as follows: Calculating initial parameters based on experimental data; the initial parameters include yield stress, critical stress, saturation stress, steady-state stress, initial hardening rate, steady-state grain size, and the time required for static recovery, dynamic recrystallization, and metadynamic recrystallization to reach 50%; During the plastic deformation stage, the flow stress, dynamic recrystallization fraction, and grain size are calculated in real time based on the constitutive model coupled with dynamic microstructural evolution. In the static stage, the static softening mechanism of the high-temperature alloy is determined based on the flow stress and hardening rate before interruption, that is, whether it contains metadynamic recrystallization. Based on the static softening fraction model, the kinetic curves of static recovery, metadynamic recrystallization, continuous grain growth, and the strengthening effect of annealing twins are calculated. Update the initial hardening rate, characteristic stress and dynamic recrystallization kinetic parameters of the next deformation stage based on the static softening fraction; Dynamic and static stage calculations are performed cyclically, and stress-strain curves and grain size evolution data of multi-step deformation are output.

10. The constitutive modeling method for high-temperature alloys according to claim 9, which takes into account the dynamic and static microstructure inheritance effects of a multi-step thermal deformation process, is characterized in that: The determination of the static softening mechanism includes: When the hardening rate is less than 0 or the flow stress before interruption is greater than the critical stress but the hardening rate is greater than 0, the static softening behavior at this time is composed of dynamic recovery, metadynamic recrystallization and grain boundary effect components; Otherwise, the static softening behavior consists only of dynamic recovery and grain boundary effect components.

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