Method for establishing constitutive model of GH4742 alloy

Abstract

The invention provides a GH4742 alloy constitutive model building method, and relates to the field of hot working, in particular to the field of aircraft part hot working, and the method comprises the steps that a plurality of deformation temperature points and a plurality of strain rate points are obtained; according to the multiple deformation temperature points and the multiple strain rate points, an isothermal constant strain rate compression experiment is conducted on the GH4742 alloy bar, and experiment data are obtained; according to the experimental data, a constitutive model of the GH4742 alloy is established; the constitutive model comprises an Arrhenius model and / or a machine learning model. The method is suitable for the building process of the constitutive model of the GH4742 alloy, and is used for solving the problem of lack of research on the constitutive model of the GH4742 alloy at present.

Description

Technical Field

[0001] The present application relates to the field of thermal processing, specifically to the field of thermal processing of aircraft parts, and in particular to a method for establishing a constitutive model of a GH4742 alloy. Background Art

[0002] Nickel-based high-temperature alloys have high high-temperature strength, good oxidation resistance and corrosion resistance, and have excellent fatigue performance, fracture toughness and other comprehensive properties. They have good organizational stability at operating temperature and are key materials for manufacturing parts working under high temperatures such as gas turbines and engines.

[0003] GH4742 alloy is a precipitation-strengthened nickel-based high-temperature alloy with high creep strength in the range of 500-800°C and good comprehensive properties. It is widely used in high-temperature load-bearing parts such as turbine disks, compressor disks, load-bearing rings and fasteners working under high stress, especially high-performance aircraft engines.

[0004] At present, the research on GH4742 alloy mainly focuses on heat treatment process, composition segregation, antioxidant behavior and mechanical properties, but lacks research on the constitutive (relationship) model of GH4742 alloy. Summary of the invention

[0005] The present application provides a method for establishing a constitutive model of a GH4742 alloy, so as to solve the problem of the current lack of research on the constitutive (relationship) model of the GH4742 alloy.

[0006] In the first aspect, the present application provides a method for establishing a constitutive model of a GH4742 alloy, the method comprising: obtaining multiple deformation temperature points and multiple strain rate points; performing an isothermal constant strain rate compression test on a GH4742 alloy bar according to the multiple deformation temperature points and the multiple strain rate points to obtain experimental data; establishing a constitutive model of the GH4742 alloy according to the experimental data; the constitutive model comprises an Arrhenius model and / or a machine learning model. The method is applicable to the process of establishing a constitutive model of the GH4742 alloy, and is used to solve the problem of the current lack of research on the constitutive model of the GH4742 alloy.

[0007] Optionally, the experimental data includes deformation temperature, strain rate, and flow stress.

[0008] Optionally, when the constitutive model is an Arrhenius model, the constitutive model of the GH4742 alloy is established according to the experimental data, including: constructing according to the experimental data Curve and Curve; σ represents flow stress; represents the strain rate; α represents the first material parameter; according to Curve and The slope of the curve is used to determine the first material parameter; based on the first material parameter, a curve and ln[sinh(ασ)]-1 / T curve; T represents the deformation temperature; according to The second material parameter is determined according to the slope of the curve; the deformation activation energy of the GH4742 alloy is determined according to the slope of the ln[sinh(ασ)]-1 / T curve; the third material parameter is determined according to the first material parameter, the second material parameter, the deformation activation energy, the deformation temperature, the strain rate, and the Z parameter model; wherein the Z parameter model is expressed as the following formula:

[0009]

[0010] Wherein, Z represents the Z parameter; R represents the gas constant; T represents the deformation temperature; Q represents the deformation activation energy; α represents the first material parameter; n represents the second material parameter; A3 represents the third material parameter; represents the strain rate;

[0011] An Arrhenius model is determined according to the deformation activation energy, the first material parameter, the second material parameter, the third material parameter, and the Arrhenius equation.

[0012] Alternatively, the Arrhenius model is expressed as the following formula:

[0013]

[0014] Among them, σ represents flow stress; Q represents deformation activation energy; R represents gas constant; T represents deformation temperature.

[0015] Alternatively, the Arrhenius model is expressed as the following formula:

[0016]

[0017] Here, ε represents the strain.

[0018] Optionally, the machine learning model includes a support vector machine (SVM) model or an error back propagation neural network (BP) model.

[0019] Optionally, when the constitutive model is an SVM model, a constitutive model of the GH4742 alloy is established according to experimental data, including: determining a first training sample set according to the experimental data; the first training sample set includes multiple first training samples, each first training sample includes a set of deformation temperature, strain rate, and strain, each first training sample corresponds to a first label, and the first label is flow stress; based on the first training sample set, the initial SVM model is trained to obtain the constitutive model.

[0020] Optionally, when the constitutive model is a BP model, a constitutive model of the GH4742 alloy is established according to experimental data, including: determining a second training sample set according to the experimental data; the second training sample set includes multiple second training samples, each second training sample includes a set of deformation temperature, strain rate, and strain, each second training sample corresponds to a second label, and the second label is flow stress; training the BP neural network based on the second training sample set to obtain the constitutive model.

[0021] Optionally, the plurality of deformation temperature points include: 950°C, 985°C, 1020°C, 1055°C, 1090°C, 1125°C, and 1160°C.

[0022] Optionally, multiple strain rate points include: 0.001s -1 、0.01s -1 , 0.1s -1 , and 1s -1 .

[0023] The present application conducts an isothermal constant strain rate compression test on a GH4742 alloy bar to obtain experimental data, and establishes a constitutive model of the GH4742 alloy based on the experimental data, thereby providing a method for establishing a constitutive model of the GH4742 alloy. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0025] Figure 1 A schematic diagram of the original structure of the GH4742 alloy provided in the embodiment of the present application;

[0026] Figure 2 The flow stress curve of the GH4742 alloy at different deformation temperatures provided in the embodiments of the present application;

[0027] Figure 3 The material parameter fitting relationship curve provided in the embodiment of the present application;

[0028] Figure 4 lnZ-ln[sinh(ασ)] curve at peak stress provided in the embodiment of the present application;

[0029] Figure 5 A schematic diagram showing the correlation between the predicted value of flow stress of the Arrhenius constitutive relationship model for peak stress of GH4742 alloy provided in the embodiment of the present application and the experimental value;

[0030] Figure 6 A polynomial fitting relationship curve between material constants and strain provided in the embodiment of the present application;

[0031] Figure 7 A schematic diagram of the correlation between the predicted value of flow stress and the experimental value of the strain-compensated Arrhenius equation constitutive relationship model for GH4742 alloy provided in the embodiment of the present application;

[0032] Figure 8 A schematic diagram of the correlation between the predicted value of flow stress of the SVM model provided in the embodiment of the present application and the experimental value;

[0033] Fig. 9 A schematic diagram of the correlation between the predicted value of flow stress of the GWO-BP model and the experimental value provided in the embodiment of the present application;

[0034] Fig.10 A schematic diagram of constitutive model error comparison provided in an embodiment of the present application;

[0035] Fig.11 A schematic flow chart of the method for establishing a constitutive model for GH4742 alloy provided in an embodiment of the present application. DETAILED DESCRIPTION

[0036] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0037] It should be noted that, in the embodiments of the present application, words such as "exemplarily" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplarily" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplarily" or "for example" is intended to present related concepts in a specific way.

[0038] In order to facilitate the clear description of the technical solutions of the embodiments of the present application, in the embodiments of the present application, words such as "first" and "second" are used to distinguish between identical items or similar items with basically the same functions and effects. Those skilled in the art can understand that words such as "first" and "second" do not limit the quantity and execution order.

[0039] Nickel-based high-temperature alloys have high high-temperature strength, good oxidation resistance and corrosion resistance, and have excellent fatigue performance, fracture toughness and other comprehensive properties. They have good organizational stability at operating temperature and are key materials for manufacturing parts working under high temperatures such as gas turbines and engines.

[0040] GH4742 alloy is a precipitation-strengthened nickel-based high-temperature alloy with high creep strength in the range of 500-800°C and good comprehensive properties. It is widely used in high-temperature load-bearing parts such as turbine disks, compressor disks, load-bearing rings and fasteners working under high stress, especially high-performance aircraft engines.

[0041] At present, the research on GH4742 alloy mainly focuses on heat treatment process, composition segregation, antioxidant behavior and mechanical properties, but lacks research on the constitutive (relationship) model of GH4742 alloy.

[0042] In order to study the hot working process system of the constitutive model of GH4742 alloy, experiments and analyses can be carried out on GH4742 alloy, mainly including the following parts:

[0043] 1. Experimental materials and methods.

[0044] The experimental material is GH4742 alloy bar, and its specific composition can be shown in the following Table 1:

[0045] Table 1: Chemical composition of GH4742 alloy (mass fraction, %)

[0046] C Cr Mo Co Al Ti Nb Ni 0.04-0.08 13.0-15.0 4.5-5.5 9.0-11.0 2.4-2.8 2.4-2.8 2.4-2.8 margin

[0047] As shown in Table 1, the composition (mass fraction, %) of the GH4742 alloy rod is: C 0.04-0.08, Cr 13.0-15.0, Mo 4.5-5.5, Co 9.0-11.0, Al 2.4-2.8, Ti 2.4-2.8, Nb 2.4-2.8, Ni balance.

[0048] For example, Figure 1 The original structure diagram of the GH4742 alloy provided in the embodiment of the present application is shown in FIG. Figure 1 As shown, the original structure of the experimental material is relatively uniform, with an average grain size of about 120μm; there is also a certain amount of granular second phase near the grain boundary.

[0049] Isothermal constant strain rate compression test was carried out on Gleeble-3500 hot working simulation test machine, the sample size was 8 (mm) in diameter and 12 mm in height. The compression deformation temperatures were: 950℃, 985℃, 1020℃, 1055℃, 1090℃, 1125℃ and 1160℃; the strain rates were: 0.001s -1 , 0.01s -1 , 0.1s -1 and 1s -1 ; The height reduction rate is 60%, and the corresponding true strain is about 0.92. In order to reduce the influence of end face friction, tantalum sheets are attached to both ends of the sample. The sample is heated to the deformation temperature at a heating rate of 10℃ / s and kept warm for 300s, then compressed and deformed, and cooled to room temperature after compression. The entire heating, compression and cooling process are carried out in a vacuum environment. The true stress and true strain data under different experimental parameters are obtained through the dedicated data acquisition software configured by the hot working simulation test machine. The deformed sample is cut along the axis, the cut surface is ground and polished, and finally the metallographic structure is observed using an XJP-9A optical microscope.

[0050] 2. High temperature flow stress behavior.

[0051] For example, Figure 2 The flow stress curves of the GH4742 alloy at different deformation temperatures provided in the embodiments of the present application are shown in FIG. Figure 2 As shown in (a), the strain rate is 0.01s -1 Flow stress curve at . Figure 2 As shown in (b), the strain rate is 1s -1 Flow stress curve at . Figure 2 (a) and Figure 2 The curves shown in (b) are, from top to bottom, the flow stress curves of GH4742 alloy at 950°C, 985°C, 1020°C, 1055°C, 1090°C, 1125°C and 1160°C. The flow stress variation characteristics at a strain rate of 0.001s-1 are similar to those at 0.01s-1; the flow stress variation characteristics at a strain rate of 0.1s-1 are similar to those at 1s-1.

[0052] from Figure 2It can be seen that in the initial stage of deformation, the flow stress increases sharply with the increase of true strain. The main reason is that when the true strain is small, the work hardening effect caused by dislocation proliferation, entanglement and accumulation is dominant. With the continuous increase of true strain, due to the cross-slip, climb and annihilation of dislocations, dynamic recovery or dynamic recrystallization occurs, thereby reducing the work hardening rate and slowing down the rising trend of flow stress. When the true strain is about 0.15, the flow stress reaches a peak value; then, with the further increase of true strain, the flow stress begins to slowly decrease because the dynamic softening effect exceeds the work hardening effect. Under different process parameters, the dynamic softening degree shown in the flow stress-strain curve is different. When the deformation temperature is low and the strain rate is high, the dynamic softening effect is more obvious.

[0053] from Figure 2 It can also be seen that the flow stress of GH4742 alloy increases with decreasing deformation temperature and increasing strain rate, indicating that the alloy is a negative deformation temperature and positive strain rate sensitive material. The main reason is that with decreasing deformation temperature, atomic kinetic energy decreases, dislocation movement activity decreases, the number of active slip systems decreases, and the grain boundary migration rate is inhibited, thus increasing the flow stress. With increasing strain rate, dislocation proliferation accelerates, and high-density dislocation entanglement intensifies; at the same time, due to the short deformation time, dynamic recovery, dynamic recrystallization and other mechanisms are not fully carried out, so the work hardening is more obvious, resulting in increased flow stress. From the perspective of reducing deformation resistance, GH4742 alloy should try to choose to be hot formed at higher deformation temperature and lower strain rate conditions.

[0054] 3. Constitutive (relationship) model based on Arrhenius equation.

[0055] 3.1 Form of the Arrhenius model.

[0056] In order to explore the relationship between strain rate, deformation temperature and stress during thermal deformation of materials, the Arrhenius equation is proposed. The Arrhenius equation has the following different forms:

[0057]

[0058] According to the form of flow stress in the Arrhenius equation, formula (1) and formula (2) are called exponential equation and power function equation respectively, which are applicable to high stress level (ασ>1.2) and low stress level (ασ<0.8) respectively; formula (3) is a hyperbolic sine equation, which is applicable to all stress levels. σ represents flow stress, represents strain rate, Q represents deformation activation energy (J / mol), R represents gas constant (J / (mol·K)), and T represents deformation temperature (K). β, n1, n, A1, A2, A3 and α are constants, α=β / n1. For the purpose of distinction, α can be called the first material parameter, n can be called the second material parameter, and A3 can be called the third material parameter.

[0059] Taking the natural logarithm of both sides of formula (1)-formula (3), we can get:

[0060]

[0061] 3.2. Peak flow stress constitutive relationship model based on Arrhenius equation.

[0062] 3.2.1. The constitutive relationship model of the Arrhenius equation for peak flow stress is established.

[0063] For example, Figure 3 The material parameter fitting relationship curve provided in the embodiment of the present application is shown in FIG. Figure 3 As shown in (a) of Curves, such as Figure 3 As shown in (b) of Curves, such as Figure 3 As shown in (c) in Curves, such as Figure 3 As shown in (d) in the figure, it is the ln[sinh(ασ)]-1 / T curve. Figure 3 The curves in (a), (b) and (c) are, from left to right, the relationship curve at 950°C, the relationship curve at 985°C, the relationship curve at 1020°C, the relationship curve at 1055°C, the relationship curve at 1090°C, the relationship curve at 1125°C, and the relationship curve at 1160°C. Figure 3 The curves in (d) are from top to bottom (strain rate is) 1s -1 The relationship curve under 0.1s -1 The relationship curve below, 0.01s -1 The relationship curve below, and 0.001s -1 The relationship curve below.

[0064] According to the above formula (4) and formula (5), the above Figure 3 As shown in (a) The curve and the above Figure 3 As shown in (b) The curve can be obtained by linear fitting at different deformation temperatures. The slope of the curve can be obtained, and the β and n1 values ​​can be obtained. Further, according to α=β / n1, the α values ​​corresponding to the curves at different deformation temperatures can be calculated, and then the average value is calculated to obtain α, which is about 0.00468.

[0065] Substitute the α value into the above formula (6) and construct Figure 3 As shown in (c) The curve and Figure 3 The ln[sinh(ασ)]-1 / T curve shown in (d) in FIG. The slope of the curve is n. Find the n values ​​corresponding to the curves at different deformation temperatures, and then calculate the average value to get n, which is about 4.12530. The slope of the ln[sinh(ασ)]―1 / T curve is At different strain rates The average value of the value is about 25.43341, and further calculation shows that the deformation activation energy Q of GH4742 alloy at peak stress is about 872.30859 KJ / mol.

[0066] In order to quantitatively describe the combined effect of deformation temperature and strain rate on flow stress, it can be represented by the following Z parameter model:

[0067]

[0068] In formula (7), Z represents the Z parameter.

[0069] Combining formula (7) with formula (3) yields:

[0070]

[0071] Taking the logarithm of both sides of the equation (8) yields:

[0072] lnZ=lnA3+nln[sinh(ασ)] Formula (9)

[0073] Deformation activation energy Q, deformation temperature T and strain rate Substituting into the above formula (7), we can obtain the Z value and lnZ value under different process parameters, and further draw the lnZ-ln[sinh(ασ)] curve under peak stress.

[0074] For example, Figure 4 The lnZ-ln[sinh(ασ)] curve at peak stress provided by the embodiment of the present application. Figure 4 It can be obtained that lnA3 at peak stress is about 73.36115, and the corresponding A3 value is about 7.25008×10 31 .

[0075] Substituting the first material parameter α, the second material parameter n and the third material parameter A3 at the peak stress calculated above into the above formula (6), the following Arrhenius model of the peak stress of GH4742 alloy can be obtained:

[0076]

[0077] 3.2.2 Analysis of prediction accuracy of the Arrhenius equation constitutive relationship model for peak flow stress.

[0078] The deformation temperature T and strain rate set in the hot compression experiment Substituting the deformation activation energy Q value into the above formula (10), the flow stress value predicted by the model can be obtained.

[0079] For example, Figure 5 This is a schematic diagram of the correlation between the predicted value of the flow stress of the Arrhenius constitutive relationship model of the peak stress of the GH4742 alloy provided in the embodiment of the present application and the experimental value. Figure 5 As shown, with the experimental flow stress value as the horizontal axis and the calculated value of the model shown by the above formula (10) as the vertical axis, an error scatter plot can be obtained. Figure 5 It can be seen that the data points are basically distributed within the error band of ±15%, which shows that the model shown in the above formula (10) has a high prediction accuracy.

[0080] In order to further investigate the predictive ability of the established Arrhenius equation peak flow stress constitutive relationship model, standard statistical parameters R (correlation coefficient) and AARE (average absolute relative error) were used for quantitative evaluation. The calculation formulas of R and AARE are as follows:

[0081]

[0082] In formula (11) and formula (12), E i represents the experimentally measured flow stress data, P i It represents the predicted data obtained by using the model shown in the above formula (10). Represents the average value of experimentally measured flow stress data. i Represents the average value of the predicted data. N represents the amount of data.

[0083] Substituting the predicted value of flow stress calculated by formula (10) and the experimental value into formula (11) and formula (12) respectively, it can be calculated that the correlation coefficient of the Arrhenius equation peak stress constitutive model of GH4742 alloy (the model shown in the above formula 10) is R = 0.993, and the average absolute relative error is AARE = ​​8.986%, which also shows that the established peak stress constitutive relationship formula (10) has a high prediction accuracy.

[0084] 3.3 Strain compensation constitutive relationship model based on Arrhenius equation.

[0085] Since the Arrhenius equation peak stress constitutive relation model ignores the effect of strain, in order to enable the model to fully predict the flow stress during the entire deformation process, the Arrhenius equation needs to be strain compensated.

[0086] 3.3.1 Establishment of the constitutive relationship model of the strain-compensated Arrhenius equation.

[0087] Taking the flow stress of GH4742 alloy under different deformation conditions as the constitutive modeling data, according to the above material constant solution process, the values ​​of α, n, Q, and lnA3 under different strains of 0.1 to 0.9 (interval of 0.05, a total of 18 strains) can be calculated.

[0088] For example, the material parameters may be specifically shown in Table 2 below:

[0089] Table 2: Material parameters at different strains

[0090] ε α n Q <![CDATA[lnA3]]> 0.05 0.00547 4.86564 1030.49109 87.20322 0.10 0.00508 4.18786 936.01153 78.86669 0.15 0.00507 3.95222 893.95009 75.10634 0.20 0.00511 3.78968 856.52456 71.79261 0.25 0.00517 3.70633 830.95018 69.54942 0.30 0.00527 3.64476 813.73184 68.06367 0.35 0.00540 3.57202 786.08167 65.62836 0.40 0.00550 3.58998 773.89156 64.61218 0.45 0.00562 3.61791 756.35402 63.10147 0.50 0.00577 3.67149 738.31782 61.54148 0.55 0.00592 3.69700 723.30159 60.25390 0.60 0.00607 3.77649 717.95417 59.82258 0.65 0.00620 3.87383 717.75637 59.83997 0.70 0.00633 3.94282 722.33998 60.26856 0.75 0.00643 4.01740 723.28536 60.35895 0.80 0.00650 4.09529 723.63987 60.40173 0.85 0.00656 4.17488 723.37727 60.37891 0.90 0.00664 4.24367 733.51048 61.29849

[0091] Considering the influence of strain on flow stress, polynomial fitting can be performed on the material parameters under different strains. The fitting results show that the fitting accuracy of the 6th, 7th and 8th order polynomials is not much different and all are high. To simplify the fitting model, the 6th order polynomial fitting is selected. The mathematical model between the material parameters and strain obtained by the polynomial fitting is shown in the following formula (13):

[0092]

[0093] For example, Figure 6 The polynomial fitting relationship curve between the material constant and the strain provided in the embodiment of the present application is shown in FIG. Figure 6 As shown in (a) in FIG. , it is the fitting relationship curve between the first material parameter α and the strain ε. Figure 6 As shown in (b), it is the fitting relationship curve between the second material parameter n and the strain ε. Figure 6 As shown in (c) in the figure, it is the fitting relationship curve between deformation activation energy Q and strain ε. Figure 6As shown in (d), it is the fitting relationship curve of the third material parameter A3 related parameter lnA3 and the strain ε.

[0094] Substituting the above formula (13) into the above formula (6), the Arrhenius equation constitutive relationship model (Arrhenius model) of GH4742 alloy under the entire strain can be obtained as follows:

[0095]

[0096] 3.3.2 Analysis of prediction accuracy of strain compensated Arrhenius equation constitutive relationship model.

[0097] For example, Figure 7 This is a schematic diagram of the correlation between the predicted value of flow stress and the experimental value of the strain compensation Arrhenius equation constitutive relationship model of GH4742 alloy provided in the embodiment of the present application. Figure 7 As shown, most of the data points are within the ±15% error band.

[0098] Substituting the predicted flow stress values ​​and the experimental values ​​into formula (11), the calculated correlation coefficient R is 0.991; substituting into formula (12), the calculated average absolute relative error AARE is 9.813%. This shows that the established strain compensation Arrhenius equation constitutive relationship model has good prediction ability and can be used to characterize the flow stress behavior of GH4742 alloy.

[0099] 4. Constitutive relationship model based on machine learning.

[0100] 4.1. Support vector machine model.

[0101] 4.1.1 Basic principles of support vector machines.

[0102] Support Vector Machine (SVM) has good generalization ability and shows unique advantages in solving small sample, nonlinear and high-dimensional pattern recognition problems. In the process of establishing the constitutive relationship model based on SVM, given the first training sample set D = {(x l ,y l ), (x2, y2), …, (x i ,y i )}, based on the first training sample set, find a partitioning hyperplane in the sample space to separate samples of different categories. i ∈Rn is the input variable (which can also be understood as a training sample), y i∈R is the output variable (which can also be understood as a label). Using a nonlinear function, the input vector can be mapped from the original feature space to a high-dimensional Hilbert space, thereby converting the nonlinear problem into a linearly separable problem and obtaining the optimal regression function. According to the principle of structural risk minimization, the objective function and constraints are set as follows:

[0103]

[0104] In formula (15), J(ω,b,e) is the objective function ; ω is the spatial weight coefficient; γ is the penalty coefficient of the loss function, and γ ≥ 0; b is the deviation; e is the training error; e i is the training error of the ith training sample.

[0105] The objective function optimization in formula (15) is transformed into solving the dual space:

[0106]

[0107] In formula (16), a is the Lagrange multiplier. i is the Lagrange multiplier.

[0108] According to the Lagrangian function, ω, b, e are obtained i and a i The partial derivative of is:

[0109]

[0110] According to formula (17), the linear equation can be obtained:

[0111]

[0112] In formula (18), y=[y1,y2,…,y i ] T , I is the unit matrix, a=[a1,a2,…,a i ] T ;

[0113] The kernel function is used to calculate the similarity or inner product between input vectors. This application selects a radial basis kernel function with stronger generalization ability, which is expressed as the following formula (19):

[0114]

[0115] In formula (19), δ represents the kernel function width.

[0116] 4.1.2. Establishment and verification of support vector machine constitutive relationship model.

[0117] (1) Establishment of constitutive relationship model of support vector machine.

[0118] According to the above basic principles of SVM, the constitutive relationship model of GH4742 alloy based on SVM can be summarized as follows:

[0119]

[0120] In formula (20), n represents the total number of training samples. i represents a training sample. j represents the central variable. ||x i ,x j || represents x i and x j The Euclidean distance between .

[0121] The compression deformation temperature, strain rate and strain (true strain) of GH4742 alloy were used as input variables xi, and the flow stress σ was used as the output variable to establish the SVM model. 504 sets of flow stress data were input into the established SVM model, 75% of which were randomly selected for model training, and the remaining 25% of the data were used for model testing.

[0122] (2) Verification of the constitutive relationship model of support vector machine.

[0123] For example, Figure 8 Schematic diagram of the correlation between the predicted value of flow stress of the SVM model and the experimental value provided in the embodiment of the present application. Figure 8 As shown in (a) in the figure, it is the correlation between the predicted value and the experimental value when the SVM model is trained using the training samples. Figure 8 (b) shows the correlation between the predicted value and the experimental value when the SVM model is tested or verified using the test sample (or verification sample). Figure 8 It can be seen that the vast majority of data points are distributed within the ±15% error band.

[0124] Substituting the flow stress prediction value and experimental value of the training sample SVM model into formula (11), the calculated correlation coefficient R is 0.999; substituting the flow stress prediction value and experimental value of the training sample SVM model into formula (12), the calculated average absolute relative error AARE is 4.493%. Similarly, the correlation coefficient R of the test sample SVM model can be calculated to be 0.997, and the average absolute relative error AARE is 5.626%. This shows that the established SVM constitutive relationship model has good prediction ability and can be used to characterize the flow stress behavior of GH4742 alloy.

[0125] 4.2. GWO-BP network model.

[0126] 4.2.1. Basic principles of GWO-BP network.

[0127] At present, the BP model used for predicting the flow behavior during metal hot deformation is usually three layers (input layer, hidden layer and output layer), and the initial weights and thresholds of the neural network will have a great impact on the prediction accuracy of the model. Therefore, based on the Back Propagation Neural Network Model (BP) model, the present application introduces the Grey Wolf Optimizer (GWO) algorithm to optimize the initial weights and thresholds of the BP model. The basic principle is to optimize the weights and thresholds of the BP neural network through the GWO algorithm, and then assign the optimal weights and thresholds to the BP neural network to complete the prediction, so as to improve the prediction accuracy of the model.

[0128] The core of the GWO algorithm is to optimize parameters by simulating the hunting process of gray wolves, such as searching, encircling and attacking prey. The algorithm divides gray wolves into optimal gray wolves, suboptimal gray wolves, third-optimal gray wolves and remaining gray wolves. The behavior of each level of gray wolves must strictly obey the leadership of the previous level, so as to optimize the group. When designing GWO, in order to mathematically model the social hierarchy of wolves, the optimal solution is regarded as α, the suboptimal and third-optimal solutions are regarded as β and δ respectively; the remaining candidate solutions are assumed to be ω. Encircling prey, hunting and attacking prey are the three main processes of GWO, as described below

[0129] Step 1: Encirclement. When searching for prey, the gray wolf will gradually approach and encircle the prey. The mathematical model is as follows:

[0130]

[0131] In formula (21) and formula (22), t is the number of iterations. is the motion vector. and is the coefficient vector. is the prey position vector. is the position vector of the gray wolf. and Calculated by the following formula:

[0132]

[0133] In formula (23) and formula (24), and Represents a random number in the range [0,1]; is the distance convergence factor, and its variation range decreases linearly from 2 to 0. Its value can be obtained by the following formula:

[0134]

[0135] In formula (25), t max Indicates the maximum number of iterations.

[0136] Step 2: Hunting. During the hunting process, the second-best gray wolf β and the third-best gray wolf δ update their positions under the leadership of the best gray wolf α. The mathematical model is as follows:

[0137]

[0138] In formula (25), Represents the updated position of the gray wolf individual (i.e., the optimal solution vector). as well as It can be calculated by the following formula:

[0139]

[0140] In formula (26), Represents the current position vector of wolf a. Represents the current position vector of β wolf. Represents the current position vector of δwolf. as well as represent dynamic coefficients, which determine the intensity and direction of the gray wolf's movement toward its prey. as well as It can be obtained by the following formula:

[0141]

[0142] In formula (28), Represents the position vector of wolf a relative to other wolves. Represents the position vector of wolf β relative to other wolves. Represents the position vector of δ wolf relative to other wolves. as well as represents a random vector.

[0143] Step 3: Attack. The last step of attacking the gray wolf is to capture the target, that is, to obtain the optimal solution. The optimal solution is mainly achieved by reducing To obtain the value of When the value of takes any value in the interval [-2k,2k] and |A|<1, the gray wolf will attack its prey.

[0144] 4.2.2 Establishment and verification of GWO-BP network constitutive relationship model.

[0145] The GH4742 alloy was compressed and the compression deformation temperature T, strain rate and strain (true strain) of the GH4742 alloy were used as input variables, and the flow stress was used as the output variable to establish the GWO-BP model. 504 sets of flow stress data were input into the established model, and 75% of the data were randomly selected for model training, and the remaining 25% of the data were used for model testing. The BP model parameters were set as follows: the network structure was a three-layer structure of input layer-hidden layer-output layer; the activation functions of the hidden layer and the output layer were tansig and purelin respectively, and the training algorithm was trainlm; the maximum number of iterations was 1000; the learning rate was 0.1; and the target error was 1×10-5. GWO was used to optimize the initial weights and thresholds of each neural node of the BP model. The number of wolf packs was set to 10 and the maximum number of iterations was 100. The fitness value of the wolf pack was calculated, the optimal wolf position was compared and updated, and finally the initial weights and thresholds optimized by GWO were output. The BP network was trained with the initial weights and thresholds optimized by GWO. After the training, the test set data was substituted into the trained model to predict the flow stress, and the prediction performance was evaluated.

[0146] (2) Verification of the GWO-BP network constitutive relationship model.

[0147] For example, Fig. 9 This is a schematic diagram of the correlation between the predicted value of the flow stress of the GWO-BP model and the experimental value provided in the embodiment of the present application. Fig. 9 As shown in (a) in the figure, it is the correlation between the predicted value and the experimental value when the GWO-BP model is trained using the training samples. Fig. 9 (b) shows the correlation between the predicted value and the experimental value when the GWO-BP model is tested or verified using the test sample (or verification sample). Fig. 9 It can be seen that the vast majority of data points are distributed within the ±15% error band.

[0148] The correlation coefficient R of the training sample GWO-BP network model calculated according to the above formula (11) is 0.997, and the average absolute relative error AARE of the training sample GWO-BP network model calculated according to formula (12) is 5.194%; the correlation coefficient R of the test sample GWO-BP network model is 0.997, and the average absolute relative error AARE is 5.471%. This shows that the established GWO-BP constitutive relationship model has good predictive ability and can be used to characterize the flow stress behavior of GH4742 alloy.

[0149] 5. Comparison of errors of different constitutive models.

[0150] In summary, it can be seen that the AARE of the strain compensation Arrhenius constitutive relationship model is 9.813%, the AARE of the test sample SVM model and the test sample GWO-BP model are 5.626% and 5.471% respectively. The three different models have high prediction accuracy, and their AAREs are all less than 10%; among them, the prediction accuracy of the SVM and GWO-BP models is higher. To further compare the prediction accuracy of different constitutive relationship models, the relative error RE of the three models can be calculated according to the following formula i :

[0151]

[0152] For example, Fig.10 This is a schematic diagram of the constitutive model error comparison provided in the embodiment of the present application. Fig.10 As shown in (a) in the figure, it is the relative error of the strain-compensated Arrhenius model. Fig.10 (b) in the figure shows the relative error of the SVM model. Fig.10 (c) in the figure shows the relative error of the GWO-BP model.

[0153] Fig.10 The numbers listed above the rectangular bars in the figure represent the percentage of the number of predicted samples within a specific relative error range to the total number of predicted samples. The relative error ranges of the strain-compensated Arrhenius model, SVM model, and GWO-BP model are -44.920~23.176%, -21.443~14.685%, and -19.827~19.861%, respectively, indicating that the relative error range of the predicted values ​​of the strain-compensated Arrhenius model is the largest, while the relative error ranges of the predicted values ​​of the SVM and GWO-BP models are smaller.

[0154] from Fig.10 It can also be seen that the number of predicted samples with a relative error of ±15% of the strain compensated Arrhenius model prediction value accounts for about 80.556% of the total number of samples, while the proportion of the test sample SVM model prediction value with a relative error within ±15% reaches 92.969%, and the proportion within ±10% also reaches 81.746%; the prediction accuracy of the test sample GWO-BP model is higher, with a relative error within ±15% accounting for as high as 93.750%; the proportion within ±10% also reaches 84.127%.

[0155] Based on the understanding of the above embodiments, the present application embodiment provides a method for establishing a constitutive model of a GH4742 alloy. Fig.11 The following is a flow chart of the method for establishing the constitutive model of the GH4742 alloy provided in the embodiment of the present application. Fig.11 As shown, the method includes the following steps:

[0156] S101, obtaining multiple deformation temperature points and multiple strain rate points.

[0157] Optionally, the plurality of deformation temperature points include: 950°C, 985°C, 1020°C, 1055°C, 1090°C, 1125°C, and 1160°C.

[0158] Optionally, multiple strain rate points include: 0.001s -1 、0.01s -1 , 0.1s -1 , and 1s -1 .

[0159] S102. According to multiple deformation temperature points and multiple strain rate points, an isothermal constant strain rate compression test is performed on the GH4742 alloy bar to obtain experimental data.

[0160] The experimental data may include deformation temperature, strain rate, and flow stress.

[0161] S103. Based on the experimental data, a constitutive model of GH4742 alloy is established.

[0162] Among them, the constitutive model includes an Arrhenius model and / or a machine learning model.

[0163] Optionally, the machine learning model can be a SVM model or a BP model.

[0164] In a possible implementation, when the constitutive model is an Arrhenius model, the above S103 may specifically include the following steps:

[0165] Step 1a: Based on the experimental data, construct Curve and curve.

[0166] Where, σ represents the flow stress; represents the strain rate; α represents the first material parameter.

[0167] Step 2a: According to Curve and The slope of the curve determines the first material parameter.

[0168] Step 3a: construct according to the first material parameter curve and ln[sinh(ασ)]-1 / T curve.

[0169] in, curve, curve, The curve and ln[sinh(ασ)]-1 / T curve can be specifically referred to above Figure 3 As shown, no further description is given here.

[0170] Step 3a: According to The slope of the curve determines the second material parameter.

[0171] Step 4a: Determine the deformation activation energy of the GH4742 alloy according to the slope of the ln[sinh(ασ)]-1 / T curve.

[0172] Step 5a: Determine the third material parameter according to the first material parameter, the second material parameter, the deformation activation energy, the deformation temperature, the strain rate, and the Z parameter model.

[0173] The Z parameter model can be specifically referred to as shown in the above formula (7), which will not be described in detail.

[0174] Step 6a: Determine the Arrhenius model according to the deformation activation energy, the first material parameter, the second material parameter, the third material parameter, and the Arrhenius equation.

[0175] For steps 1a to 6a, please refer to the above 3.2.1 for details, which will not be repeated here.

[0176] In another possible implementation, the constitutive model may also be the Arrhenius model shown in the above formula (13) and formula (14). For details, please refer to the above 3.3.1, which will not be repeated here.

[0177] In another possible implementation, when the constitutive model is an SVM model, the above S103 may specifically include the following steps:

[0178] Step 1b: Determine the first training sample set based on experimental data.

[0179] The first training sample set includes multiple first training samples, each of which includes a set of deformation temperature, strain rate, and strain, and each of the first training samples corresponds to a first label, which is flow stress.

[0180] Step 2b: training the initial SVM model based on the first training sample set to obtain a constitutive model.

[0181] For example, as described above, the first training sample set may include multiple first training samples. Specifically, one or more first training samples may be input into the initial SVM model each time to obtain the predicted value output by the initial SVM model, and the loss function (loss) is calculated based on the predicted value and the first label. The parameters in the SVM model are optimized according to the loss function until the initial SVM model converges to obtain the SVM model (constitutive model).

[0182] Optionally, the conditions for the initial SVM model to converge may include: the number of times the first training sample is input into the initial SVM model reaches a number threshold, and / or the error between the prediction value output by the initial SVM model and the first label is less than an error threshold.

[0183] The number threshold can be set to, for example, 500 times, 1000 times, or 2000 times. The embodiment of the present application does not limit the specific value of the number threshold. The error threshold can be set to, for example, 5%, 10%, or 15%. The embodiment of the present application does not limit the specific value of the error threshold.

[0184] In another possible implementation, when the constitutive model is a BP model, the above S103 may specifically include the following steps:

[0185] Step 1c: Determine the second training sample set based on the experimental data.

[0186] The second training sample set includes multiple second training samples, each second training sample includes a set of deformation temperature, strain rate, and strain, each second training sample corresponds to a second label, and the second label is flow stress.

[0187] Step 2c: training the BP neural network based on the second training sample set to obtain a constitutive model.

[0188] The details of step 2c may refer to the above step 2b, which will not be repeated here.

[0189] Based on the understanding of the above embodiments, this application is based on the isothermal constant strain rate compression experiment of GH4742 high temperature alloy under the conditions of deformation temperature 950~1160℃, strain rate 0.001~1s-1, and height reduction rate 60%, and the flow behavior of the alloy is learned; the alloy peak stress Arrhenius, strain compensation Arrhenius, SVM and GWO-BP constitutive relationship models are constructed respectively, and the model accuracy is compared and analyzed. The main conclusions are as follows:

[0190] (1) The flow stress curve of GH4742 alloy shows obvious softening phenomenon at low deformation temperature and high strain rate; with the increase of deformation temperature and the decrease of strain rate, the flow stress curve gradually shows steady-state flow characteristics.

[0191] (2) The peak stress and strain compensation Arrhenius equation constitutive relationship models of GH4742 alloy were constructed respectively. The correlation coefficient R of the peak stress Arrhenius constitutive relationship model is 0.993, and the average absolute relative error AARE is 8.986%; the correlation coefficient R of the strain compensation Arrhenius constitutive relationship model is 0.991, and the average absolute relative error AARE is 9.813%.

[0192] (3) The SVM and GWO-BP network machine learning constitutive relationship models of GH4742 alloy were constructed respectively. Among them, the correlation coefficient R of the training sample SVM model is 0.999, and the average absolute relative error AARE is 4.493%; the correlation coefficient R of the test sample SVM model is 0.997, and the average absolute relative error AARE is 5.626%. The correlation coefficient R of the training sample GWO-BP model is 0.997, and the average absolute relative error AARE is 5.194%; the correlation coefficient R of the test sample GWO-BP model is 0.997, and the average absolute relative error AARE is 5.471%.

[0193] Although the present application has been described in conjunction with specific features and embodiments thereof, it is obvious that various modifications and combinations may be made thereto without departing from the spirit and scope of the present application. Accordingly, this specification and the drawings are merely exemplary illustrations of the present application as defined by the appended claims, and are deemed to have covered any and all modifications, variations, combinations or equivalents within the scope of the present application. Obviously, those skilled in the art may make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

[0194] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for establishing a constitutive model of GH4742 alloy, characterized in that: The method comprises: Obtain multiple deformation temperature points and multiple strain rate points; According to the multiple deformation temperature points and the multiple strain rate points, an isothermal constant strain rate compression test is performed on the GH4742 alloy bar to obtain experimental data; According to the experimental data, a constitutive model of GH4742 alloy is established; the constitutive model includes an Arrhenius model and / or a machine learning model.

2. The method according to claim 1, characterized in that The experimental data include deformation temperature, strain rate, and flow stress.

3. The method according to claim 2, characterized in that In the case where the constitutive model is an Arrhenius model, the constitutive model of the GH4742 alloy is established according to the experimental data, including: According to the experimental data, construct Curve and Curve; σ represents flow stress; represents the strain rate; α represents the first material parameter; According to the Curve and The slope of the curve determines the first material parameter; According to the first material parameters, construct curve and ln[sinh(ασ)]-1 / T curve; T represents the deformation temperature; according to The slope of the curve determines the second material parameter; Determine the deformation activation energy of the GH4742 alloy according to the slope of the ln[sinh(ασ)]-1 / T curve; Determining a third material parameter according to the first material parameter, the second material parameter, the deformation activation energy, the deformation temperature, the strain rate, and the Z parameter model; Among them, the Z parameter model is expressed as the following formula: Wherein, Z represents the Z parameter; R represents the gas constant; T represents the deformation temperature; Q represents the deformation activation energy; α represents the first material parameter; n represents the second material parameter; A3 represents the third material parameter; represents the strain rate; The Arrhenius model is determined according to the deformation activation energy, the first material parameter, the second material parameter, the third material parameter, and the Arrhenius equation.

4. The method according to claim 3, characterized in that The Arrhenius model is expressed as the following formula: Among them, σ represents flow stress; Q represents deformation activation energy; R represents gas constant; T represents deformation temperature.

5. The method according to claim 3, characterized in that: The Arrhenius model is expressed as the following formula: Here, ε represents the strain.

6. The method according to claim 2, characterized in that The machine learning model includes a support vector machine (SVM) model or an error back propagation neural network (BP) model.

7. The method according to claim 6, characterized in that In the case where the constitutive model is a SVM model, the constitutive model of the GH4742 alloy is established according to the experimental data, including: Determine a first training sample set according to the experimental data; the first training sample set includes a plurality of first training samples, each of the first training samples includes a set of deformation temperature, strain rate, and strain, each first training sample corresponds to a first label, and the first label is flow stress; The initial SVM model is trained based on the first training sample set to obtain the constitutive model.

8. The method according to claim 6, characterized in that In the case where the constitutive model is a BP model, the constitutive model of the GH4742 alloy is established according to the experimental data, including: Determine a second training sample set according to the experimental data; the second training sample set includes a plurality of second training samples, each second training sample includes a set of deformation temperature, strain rate, and strain, each second training sample corresponds to a second label, and the second label is flow stress; The BP neural network is trained based on the second training sample set to obtain the constitutive model.

9. The method according to any one of claims 1 to 8, characterized in that: The plurality of deformation temperature points include: 950°C, 985°C, 1020°C, 1055°C, 1090°C, 1125°C, and 1160°C.

10. The method according to any one of claims 1 to 8, characterized in that: The multiple strain rate points include: 0.001s -1 、0.01s -1 , 0.1s -1 , and 1s -1 .

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