A method for correcting the hot compression stress-strain curve by numerical simulation

Abstract

The present invention discloses a method for correcting the thermal compression stress-strain curve by using numerical simulation, which can solve the problem that it is difficult to accurately calculate the stress-strain curve of materials due to the temperature gradient and friction existing in the specimen in the traditional method. First, the load-displacement data and the specimen temperature gradient during the thermal compression process are obtained through experiments, then the strain distribution of the specimen is calculated by using numerical simulation, and then the axial stress of each point on the middle section is calculated according to the elastoplastic deformation theory, and the theoretical load of the middle section is obtained by integration. This theoretical load should be equal to the load obtained from the experiment, and thus the corrected stress-strain curve can be calculated. The method provided by the present invention takes into account the temperature gradient during thermal compression deformation, and corrects the stress-strain curve by using a method combining experiments, numerical simulation and theoretical calculation, and the calculation result is more accurate.

Description

Technical Field

[0001] The invention relates to the field of hot compression performance testing of metal materials, in particular to a method for correcting a hot compression stress-strain curve by using numerical simulation. Background Art

[0002] In the hot forging process of metal materials, the use of numerical simulation to analyze the thermal deformation behavior of materials is an important means to optimize process parameters and mold size. In order to obtain more accurate simulation results, it is necessary to accurately describe the high-temperature deformation behavior of the material and give an accurate stress-strain curve. Usually, a Gleeble thermal simulation tester is used to perform hot compression experiments to obtain the stress-strain curve of the material at different temperatures and strain rates. However, during the hot compression experiment, due to the friction at both ends of the sample, the sample undergoes uneven deformation, forming a drum shape, that is, a shape with a large diameter in the middle section and a small diameter at both ends. If the uneven deformation of the sample is ignored and the material stress-strain curve is directly calculated, the stress result will be too large and the obtained stress-strain curve will be inaccurate.

[0003] In order to correct the influence of uneven deformation of the specimen on the stress-strain calculation, the friction correction method is usually used. The bulging factor and friction factor are calculated by calculating the difference between the maximum radius of the middle section and the radius of the upper and lower end surfaces after the specimen is deformed, and then the stress-strain curve is corrected.

[0004] However, this method only considers the effect of friction on deformation. In the actual hot compression test, there is still a certain temperature gradient on the sample, and the temperature has a great influence on the deformation of the material under high temperature conditions. Due to the low temperature and high strength at both ends of the sample, the deformation at both ends of the sample is further limited, making the drum shape of the sample more obvious after compression. Therefore, the traditional friction correction method can no longer obtain an accurate stress-strain relationship.

[0005] The use of numerical simulation technology to analyze hot compression experiments is a commonly used method in this field. In the simulation, the sample usually needs to be meshed. The intersection between the grid lines is called a node, and the smallest area surrounded by the grid lines is called a unit. The force on the hot compression test specimen is simple. The load is applied along the length direction of the specimen, that is, the axial direction, and the middle section is its symmetry plane. Before the compression deformation, the node of a certain grid section with the same radial coordinate as the node and the node on the adjacent grid section is the corresponding node of the node. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that the existing methods cannot accurately calculate the stress-strain curve due to the friction and temperature gradient in the thermal compression process, and to propose a method for correcting the thermal compression stress-strain curve using numerical simulation.

[0007] The technical solution of the present invention is:

[0008] A method for correcting the hot compression stress-strain curve by numerical simulation is provided. First, experimental data such as load-displacement and specimen temperature gradient during the hot compression process are obtained through hot compression experiments and data processing. Then, the load-displacement data and the specimen temperature gradient are substituted into a numerical simulation software for hot compression numerical simulation to calculate the strain and strain rate distributions of the simulated specimen, establish a true equivalent stress function for hot compression, and calculate the true equivalent stress using the simulated strain and strain rate data. According to the elastoplastic deformation theory, the axial stress of each node on the middle cross-section is calculated, and the theoretical load on the middle cross-section is obtained by integration. This theoretical load is consistent with the load during the hot compression process obtained from the experiment, thereby solving the true equivalent stress function for hot compression and realizing the correction of the hot compression stress-strain curve.

[0009] A method for correcting the hot compression stress-strain curve by numerical simulation is provided, and the method is carried out according to the following steps:

[0010] Step 1: Prepare a cylindrical specimen for hot compression of metal. The length of the specimen is L0, and the radius of the specimen is R0; weld a plurality of thermocouples on the specimen and conduct a hot compression experiment. The heating temperature of the specimen is T; the plurality of thermocouples are longitudinally arranged on the specimen cylinder surface and are equally spaced between the middle part and the end part of the specimen;

[0011] The hot compression experiment is usually carried out on a Gleeble thermal simulation testing machine. At this time, there is a temperature gradient on the specimen, the temperature at the center of the specimen is the highest, and the temperatures at both ends of the specimen are lower due to heat transfer. During the conventional hot compression experiment, this temperature gradient is often ignored, and only one thermocouple is welded at the center of the specimen, assuming that the temperature on the specimen is uniform, which will lead to inaccurate stress and strain calculations in the subsequent calculations. Adopting the technical solution of the present invention, welding a plurality of thermocouples on the specimen to measure the temperatures at different positions of the specimen can accurately obtain the temperature distribution on the specimen and provide accurate boundary conditions for subsequent calculations. In particular, the hot compression experiment can also be carried out on a high-temperature compression testing machine heated by a resistance furnace. At this time, it can be considered that the temperature of the heating furnace is a uniform temperature field, and the specimen temperature is equal to the temperature of the heating furnace. At this time, the temperature distribution on the specimen is uniform and the temperature gradient is zero. This is a special case in the implementation process of the present invention, and only the problem that the specimen becomes drum-shaped due to end face friction, resulting in inaccurate calculation of the stress-strain curve, needs to be corrected.

[0012] Step 2: Extract the hot compression experimental data, including the compression amount S at each moment varying with the compression time, the load amount F corresponding to each compression amount S, and the temperatures of each thermocouple corresponding to each compression amount S;

[0013] And calculate the corresponding initial equivalent strain and initial equivalent stress

[0014] Interpolate the compression amounts S at equal intervals to obtain K compression amounts S K and further obtain the load amounts F corresponding to the respective compression amounts S K ; K,Exp ;

[0015] Obtain the middle cross-sectional radius R of the specimen after the hot compression experiment Exp ;

[0016] Fit the temperatures of each thermocouple at each compression amount S, and calculate the end-face temperature T of the specimen at each compression amount S S ;

[0017] By processing the data obtained from the experiment, the initial equivalent strain and initial equivalent stress of the material are obtained. This solution method does not consider the non-uniform deformation of the specimen, and the obtained equivalent strain and equivalent stress are average values, which are not accurate and need to be further corrected.

[0018] During the hot compression deformation process, due to the heat conduction effect, there is a temperature gradient on the specimen, and as the hot compression progresses, the length of the specimen shortens, resulting in a change in the temperature gradient on the specimen. By adopting the technical solution of the present invention, the real-time temperature of the specimen end-face at different compression amounts can be obtained and used as a boundary condition for subsequent calculations to ensure the accuracy of the calculations.

[0019] Step Three: Numerically simulate the hot compression experiment in Step One through a numerical simulation software, where the simulation parameters are: the initial equivalent strain obtained in Step Two initial equivalent stress specimen end-face temperature T S , the middle cross-sectional temperature of the specimen is the heating temperature T in Step One. Preset K output states in the numerical simulation, set the grid side length of the simulated specimen as a, and the friction coefficient as μ. Use the friction coefficient μ as the control variable of the simulation. By adjusting the value of the friction coefficient μ multiple times, the maximum radius R of the specimen after the numerical simulation Sim is equal to the middle cross-sectional radius R measured and obtained in Step Two Exp ;

[0020] By adopting the technical solution of the present invention, the non-uniformity of the specimen temperature during the experiment is considered, and the obtained specimen end-face temperatures corresponding to different compression amounts are used as boundary conditions for numerical simulation, making the numerical simulation more in line with the actual situation, and the calculated specimen strain and strain rate results are more accurate.

[0021] Step Four: After the numerical simulation is completed, the numerical simulation software gives the node data of each node of the middle grid cross-section of the simulated specimen in K output states. The node data includes the equivalent strain ε0 and axial strain ε under the corresponding output statez 、Equivalent strain rate Axial strain rate component Radial strain rate component Circumferential strain rate component and the radial coordinate value r;

[0022] Meanwhile, the node data of each node of the adjacent grid sections in K output states of the simulated specimen are given by the numerical simulation software. The node data includes the equivalent strain ε1, equivalent strain rate and shear strain rate components The adjacent grid sections are the upper or lower grid sections of the middle grid section in the corresponding output state;

[0023] Due to the temperature gradient on the specimen and the action of specimen end face friction, the specimen deformation is uneven, forming a drum shape. Therefore, on the middle section of the specimen, the strain and strain rate in the central region are larger, and the strain and strain rate in the edge region are smaller; adopting the technical solution of the present invention, the strain and strain rate data of each node of the middle grid section of the numerical simulation specimen are extracted, and the range formed by the obtained strain and strain rate is greater than the average equivalent strain and equivalent strain rate. Therefore, the stress-strain curve calculated can be effectively extrapolated.

[0024] Step Five: Set the true equivalent stress function of hot compression as:

[0025]

[0026] where the equivalent strain is ε, and the equivalent strain rate m is an integer greater than or equal to 3; A ij is an unknown coefficient, and both i and j are integers greater than or equal to 0 and less than or equal to m;

[0027] Substitute the equivalent strain and equivalent strain rate of each node of the middle grid section and adjacent grid sections in K output states into the true equivalent stress function, and calculate the true equivalent stress σ0 of each node of the corresponding middle grid section and the true equivalent stress σ1 of each node of the adjacent grid sections; among them, σ0 and σ1 are algebraic expressions containing the unknown coefficient A ij ;

[0028] When a metallic material deforms at high temperature, the magnitude of its stress is affected by the strain rate, temperature, and magnitude of strain. When deforming under a fixed temperature condition, the magnitude of stress is only related to the strain rate and magnitude of strain, that is, the true equivalent stress-strain relationship of the material is a binary function of strain and strain rate. By adopting the technical solution of the present invention, a polynomial function is used to describe the deformation behavior of the material, and the function form is simple and convenient for calculation. To make the function description more accurate, the value range of parameter m is m≥3, and the larger the value of m, the higher the accuracy of the function.

[0029] Step Six: Solve the axial stress σ of each node on the intermediate grid section under K output states according to the incremental theory of elastoplastic deformation, the equilibrium differential equation, and the boundary conditions z , and the solution formula is:

[0030]

[0031] where, σ r is the radial stress, σ θ is the circumferential stress, σ′ z , σ′ r , σ′ θ are the stress deviators in the corresponding three directions respectively, and the mean stress σ m =(σ z +σ r +σ θ ) / 3; τ zr is the shear stress acting on the adjacent grid sections and along the radial direction; dh is the axial distance between each node on the intermediate grid section and the corresponding node on the adjacent grid section, and the solution formula contains an unknown coefficient A ij ;

[0032] By adopting the technical solution of the present invention, the axial stress is calculated using the strain and strain rate data of the intermediate section. Although the overall specimen undergoes non-uniform deformation, since the intermediate grid section is a symmetry plane, therefore, the direction of the strain principal axis remains unchanged when each node on the intermediate grid section deforms, and the axial stress σ of each node on the intermediate grid section can be obtained by applying the incremental theory for calculation z ;

[0033] Step Seven: Double-integrate the axial stress σ described in Step Six along the circumferential and radial directions to obtain the theoretically calculated axial load F of the intermediate grid section under each output state z : K,Sim :

[0034] F K,Sim =∫∫σ z drdθ;

[0035] Adopting the technical solution of the present invention, the axial load on the intermediate grid section is obtained. Since the intermediate grid section is the symmetry plane of the specimen and its temperature always remains constant at the experimental temperature T, the corrected stress-strain curve is more accurate;

[0036] Step eight: Through the formula: F K,Sim = ∫∫σ z drdθ = F K,Exp , solve to obtain the value of A ij , and then substitute the value of A ij into the true equivalent stress function ;

[0037] Step nine: When the equivalent strain and equivalent strain rate are given, the corrected stress-strain curve can be obtained.

[0038] Another method for correcting the hot compression stress-strain curve by numerical simulation is provided, which is characterized in that the method is carried out according to the following steps:

[0039] Step one: Prepare a metal hot compression cylindrical specimen with a specimen length of L0 and a specimen radius of R0; weld a plurality of thermocouples on the specimen and conduct a hot compression experiment with the heating temperature of the specimen being T; the plurality of thermocouples are longitudinally arranged on the specimen cylinder surface and are equally spaced between the middle part and the end part of the specimen;

[0040] Step two: Extract the hot compression experiment data, including the compression amount S at each moment varying with the compression time, the load amount F corresponding to each compression amount S, and the temperature of each thermocouple corresponding to each compression amount S;

[0041] And calculate and obtain the corresponding: initial equivalent strain and initial equivalent stress

[0042] Interpolate at equal intervals for each compression amount S to obtain K compression amounts S K , and further obtain the load amount F K corresponding to each compression amount S K,Exp ;

[0043] Obtain the radius R Exp of the middle section of the specimen after the hot compression experiment;

[0044] Fit the temperatures of each thermocouple at each compression amount S to calculate the end face temperature T S of the specimen at each compression amount S;

[0045] Step three: Numerically simulate the hot compression experiment in step one through a numerical simulation software, where the simulation parameters are: the initial equivalent strain obtained in step twoInitial equivalent stress Temperature T of the specimen end face S , the temperature of the middle cross-section of the specimen is the heating temperature T in Step 1. In the numerical simulation, K output states are preset, the side length of the simulated specimen grid is set to a, and the friction coefficient is μ. The friction coefficient μ is used as the control variable of the simulation. By adjusting the value of the friction coefficient μ multiple times, the maximum radius R of the specimen after numerical simulation Sim is equal to the middle cross-section radius R measured in Step 2 Exp ;

[0046] Step 4: After the numerical simulation is completed, the node data of each node of the middle grid cross-section of the simulated specimen under K output states are given by the numerical simulation software. The node data includes the equivalent strain ε0, axial strain ε z , equivalent strain rate axial strain rate component radial strain rate component circumferential strain rate component and radial coordinate value r;

[0047] At the same time, the node data of each node of the adjacent grid cross-section of the simulated specimen under K output states are given by the numerical simulation software. The node data includes the equivalent strain ε1, equivalent strain rate and shear strain rate component The adjacent grid cross-section is the upper or lower grid cross-section of the middle grid cross-section under the corresponding output state;

[0048] Step 5: Set the true equivalent stress function of hot compression as:

[0049]

[0050] where, equivalent strain ε, equivalent strain rate m is an integer greater than or equal to 3; A ij is an unknown coefficient, and both i and j are integers greater than or equal to 0 and less than or equal to m;

[0051] Substitute the equivalent strain and equivalent strain rate of each node of the middle grid cross-section and the adjacent grid cross-section under K output states into the true equivalent stress function, and calculate the true equivalent stress σ0 of each node of the corresponding middle grid cross-section and the true equivalent stress σ1 of each node of the adjacent grid cross-section; among them, σ0 and σ1 are algebraic expressions containing the unknown coefficient A ij ;

[0052] The difference from the previous method is that, to calculate the stress magnitude under different conditions of the material, the value range of strain is usually 0 ≤ ε ≤ 1, and the value range of strain rate is usually By adopting this embodiment, after normalizing the exponents of each term of the stress function, it can be ensured that the value will not be too small, so the coefficient A ij can be reduced, and the calculation error of

[0053] Step 6: According to the incremental theory of elastoplastic deformation, the equilibrium differential equation, and the boundary conditions, solve the axial stress σ of each node of the intermediate grid section under K output states z , and the solution formula is:

[0054]

[0055] where σ r is the radial stress, σ θ is the circumferential stress, σ′ z , σ′ r , σ′ θ are the stress deviators corresponding to three directions respectively, the mean stress σ m =(σ z +σ r +σ θ ) / 3; τ zr is the shear stress acting on the adjacent grid section and along the radial direction; dh is the axial distance between each node of the intermediate grid section and the corresponding node of the adjacent grid section, and the solution formula contains the unknown coefficient A ij ;

[0056] Step 7: Integrate the axial stress σ z obtained in Step 6 doubly along the circumferential and radial directions to obtain the axial load F K,Sim calculated theoretically for each output state of the intermediate grid section:

[0057] F K,Sim =∫∫σ z drdθ;

[0058] Step 8: Through the formula F K,Sim =∫∫σ z drdθ = F K,Exp , solve to obtain the value of A ij , and then substitute the value of A ij into the true equivalent stress function ;

[0059] Step 9: When the equivalent strain and the equivalent strain rate are given, a corrected stress-strain curve can be obtained.

[0060] It should be noted that the expression of the true equivalent stress function of the present invention includes, but is not limited to, the above two function forms, and other forms of true equivalent stress functions can also be constructed, as long as the function can describe the true stress-strain relationship of the material and is easy to solve the unknown coefficients.

[0061] For the above two methods, there are further limitations:

[0062] In step six, the equilibrium differential equation is used to calculate the radial stress σ r as follows:

[0063] (1) Solve the rate of change of the radial stress at each node of the intermediate grid section:

[0064]

[0065] (2) Solve the radial stress at each node of the intermediate grid section:

[0066]

[0067] where N is the total number of nodes in the radial direction of the specimen, and N = R0 / a + 1; σ r (n) is the radial stress at the nth node; is the rate of change of the radial stress at the nth node; dr(n) is the distance between the nth node and the (n + 1)th node;

[0068] For the above two methods, there are further limitations:

[0069] In step seven, the axial load F theoretically calculated for the intermediate grid section under each output state K,Sim is calculated specifically as follows: (1) Sum σ z along different circumferential elements: where F K (n) is the load after integrating the axial stress of the nth element in the circumferential direction, r(n) is the radial coordinate of the nth node, dr(n) is the distance between the nth node and the (n + 1)th node; σ z(n) is the axial stress of the nth node;

[0070] (2) Sum σ z along different radial elements:

[0071] The present invention provides a process for solving differential equations by the Euler method using the trapezoidal formula. Those skilled in the art can, through simple changes, use other methods to solve differential equations to obtain the radial stress σ r .

[0072] The advantages of the present invention are: (1) A method for correcting the hot compression stress-strain curve using numerical simulation in the present invention obtains the true temperature gradient on the specimen during the material deformation process through experiments and substitutes it into the numerical simulation calculation. The boundary conditions are more in line with the actual situation, simulating the real deformation process, and the calculated results are more accurate.

[0073] (2) The method for correcting the hot compression stress-strain curve using numerical simulation according to the present invention extracts the data of the nodes on the middle cross-section of the numerically simulated specimen. During the experiment and simulation, the temperature of the middle cross-section remains at a constant temperature value, and the middle cross-section is a symmetric plane with the stress principal axis direction unchanged. Therefore, the calculated stress results are more accurate.

[0074] (3) The method for correcting the hot compression stress-strain curve using numerical simulation according to the present invention extracts the deformation data of each node on the middle cross-section of the numerical simulation. Due to the uneven deformation of the specimen, the strain and strain rate are large at the center and small at the edge. The range formed by the strain and strain rate is greater than the average equivalent strain and average strain rate, and the obtained stress-strain curve can be effectively extrapolated. Description of the Drawings

[0075] Figure 1 is a schematic diagram of the solution process for the corrected stress-strain curve of the present invention;

[0076] Figure 2 is a schematic diagram of the thermocouple welding of the hot compression specimen of the present invention;

[0077] Figure 3 is a schematic diagram of the strain distribution and microelement selection in the hot compression numerical simulation of the present invention;

[0078] Figure 4 is a schematic diagram of the force analysis of the microelement on the middle cross-section of the hot compression specimen of the present invention;

[0079] Figure 5 is a schematic diagram of the node numbering of the present invention;

[0080] Figure 6 is a schematic diagram of the node numbering and element numbering of the present invention;

[0081] Figure 7 is the hot compression load-displacement curve of the titanium alloy in Example 1 of the present invention;

[0082] Figure 8A is the temperature change curve at different positions of the hot compression specimen of the titanium alloy in Example 1 of the present invention;

[0083] Figure 8B is the temperature change law of the end face of the hot compression specimen of the titanium alloy in Example 1 of the present invention;

[0084] Figure 9 is the comparison of the stress-strain curves of the titanium alloy before and after correction in Example 1 of the present invention.

[0085] Figure 10 is the hot compression load-displacement curve of the superalloy in Example 2 of the present invention;

[0086] Figure 11A Temperature change curves at different positions of the hot compression specimen of the superalloy in Example 2 of the present invention;

[0087] Figure 11B Temperature change law of the end face of the hot compression specimen of the superalloy in Example 2 of the present invention;

[0088] Figure 12 Comparison of stress-strain curves of the superalloy in Example 2 of the present invention before and after correction. Detailed implementation manners

[0089] The disclosed examples will be described more fully with reference to the accompanying drawings, in which some (but not all) of the disclosed examples are shown. In fact, many different examples can be described and these examples should not be construed as limited to the examples set forth herein. Rather, these examples are described so that this disclosure will be thorough and complete and will fully convey the scope of this disclosure to those skilled in the art.

[0090] Example 1, in combination with Figures 7 to 9 is described as follows. This example is carried out according to the following steps:

[0091] In Step 1, the metal hot compression cylindrical specimen is made of titanium alloy material, the length L0 of the specimen is 15 mm, the radius R0 of the specimen is 5 mm, three thermocouples are welded on the specimen, the heating temperature T of the specimen is 750 °C, and the spacing between the four thermocouples is 2.5 mm;

[0092] In Step 2, the load-displacement data obtained from the hot compression experiment are as Figure 7 shown. Equal interval interpolation is performed on each compression amount S to obtain 150 compression amounts S K , and their corresponding load amounts F K,Exp ;

[0093] The temperatures of the three thermocouples corresponding to each compression amount S are as Figure 8A shown. By data fitting, the temperature T of the end face of the specimen corresponding to the displacement of S is obtained as S as Figure 8B shown;

[0094] The relationship between the initial equivalent stress and the initial equivalent strain is calculated and obtained as Figure 9 shown;

[0095] The radius R of the middle cross-section of the specimen after hot compression is measured and obtained as Exp 7.32 mm;

[0096] In Step 3, the side length of the specimen grid for the numerical simulation is 0.2 mm;

[0097] In step five, the true equivalent stress function is where the parameter m takes the value of 8, that is:

[0098]

[0099] In step nine, the strain value range of 0 to 1 is substituted, and the strain rate value of 0.001 s -1 is substituted, and the corrected stress-strain curve is obtained as Figure 9 shown.

[0100] Example 2, in combination with Figures 10 to 12 description, this example is carried out according to the following steps:

[0101] In step one, the metal hot compression cylindrical specimen is a superalloy material, the specimen length L0 is 12 mm, the specimen radius R0 is 4 mm, four thermocouples are welded on the specimen, the heating temperature T of the specimen is 1070 °C, and the spacing between the four thermocouples is 1.5 mm;

[0102] In step two, the load-displacement data obtained from the hot compression experiment is as Figure 10 shown. Equal-interval interpolation is performed on each compression amount S to obtain 200 compression amounts S K , and the corresponding load amount F K,Exp ;

[0103] The temperatures of the four thermocouples corresponding to each compression amount S are as Figure 11A shown. The temperature T of the specimen end face corresponding to the displacement of S is obtained by data fitting S as Figure 11B shown;

[0104] The relationship between the initial equivalent stress and the initial equivalent strain is as Figure 12 shown;

[0105] The middle cross-section radius R of the specimen after hot compression is measured and obtained Exp to be 6.15 mm;

[0106] In step three, the side length of the specimen grid for the numerical simulation is 0.125 mm;

[0107] In step five, the true equivalent stress function is where the parameter m takes the value of 10, that is:

[0108]

[0109] In step nine, the strain value range of 0 to 1 is substituted, and the strain rate value of 0.01 s-1 , the corrected stress-strain curve is as Figure 12 shown.

[0110] Descriptions of different advantageous arrangements have been presented for purposes of illustration and description, but the description is not intended to be exclusive or limited to examples of the disclosed forms. Many modifications and variations will be apparent to those of ordinary skill in the art. Additionally, different advantageous examples may describe different advantages compared to other advantageous examples. The selected example or examples are chosen and described in order to best illustrate the principles of the examples, the practical application, and to enable those of ordinary skill in the art to understand the disclosure of various examples that have various modifications suitable for the particular use contemplated.

Claims

1. A method for correcting the hot compression stress-strain curve by numerical simulation, characterized in that: First, obtain the experimental data of load-displacement and specimen temperature gradient during hot compression through hot compression experiments and process the data. Then, substitute the load-displacement data and specimen temperature gradient into a numerical simulation software for hot compression numerical simulation to calculate the strain and strain rate distributions of the simulated specimen, establish a true equivalent stress function for hot compression, and calculate the true equivalent stress using the simulated strain and strain rate data. Calculate the axial stress of each node on the middle cross-section according to the elastic-plastic deformation theory, and integrate to obtain the theoretical load on the middle cross-section. This theoretical load is consistent with the load during the hot compression process obtained from the experiment, thereby solving the true equivalent stress function for hot compression and realizing the correction of the hot compression stress-strain curve The establishment of the true equivalent stress function for hot compression and the calculation of the true equivalent stress using the simulated strain and strain rate data are carried out as follows: Among them, the equivalent strain is ε, and the equivalent strain rate is m is an integer greater than or equal to 3; Aij are unknown coefficients, and both i and j are integers greater than or equal to 0 and less than or equal to m; Substitute the equivalent strain and equivalent strain rate of each node on the middle grid cross-section and the adjacent grid cross-sections under K output states into the true equivalent stress function to calculate the true equivalent stress σ0 of each node on the corresponding middle grid cross-section and the true equivalent stress σ1 of each node on the adjacent grid cross-sections; where, σ0 and σ1 are algebraic expressions containing unknown coefficients Aij 2. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 1, characterized in that: The hot compression experiment is carried out as follows: Prepare a metal hot compression cylindrical specimen with a specimen length of L0 and a specimen radius of R0; weld multiple thermocouples on the specimen and conduct a hot compression experiment with the heating temperature of the specimen being T; the multiple thermocouples are longitudinally arranged on the specimen cylinder surface and are equally spaced between the middle and the ends of the specimen 3. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 2, characterized in that: The data obtained from the hot compression experiment and the data processing are carried out as follows: Extract the hot compression experiment data, which includes the compression amount S at each moment varying with the compression time, the load amount F corresponding to each compression amount S, and the temperature of each thermocouple corresponding to each compression amount S Calculate the obtained initial equivalent strain corresponding to each compression amount S and the initial equivalent stress Interpolate the compression amounts S at equal intervals to obtain K compression amounts S K , and further obtain the load amounts F K corresponding to each compression amount S K,Exp ; Obtain the intermediate cross-sectional radius R of the specimen after the hot compression experiment Exp ; Fit the temperatures of each thermocouple at each compression amount S, and calculate the specimen end face temperature T at each compression amount S S .

4. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 3, characterized in that: The hot compression numerical simulation is carried out as follows: Numerically simulate the hot compression experiment using numerical simulation software, where the simulation parameters are: the obtained initial equivalent strain Initial equivalent stress Specimen end face temperature T S , the temperature of the middle cross-section of the specimen is the heating temperature T. Preset K output states in the numerical simulation. Set the grid side length of the simulated specimen to a and the friction coefficient to μ. Take the friction coefficient μ as the control variable of the simulation. By adjusting the value of the friction coefficient μ multiple times, the maximum radius R of the specimen after numerical simulation Sim is equal to the radius R of the middle cross-section Exp .

5. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 4, characterized in that: The strain and strain rate data of the simulated specimen are obtained as follows: The node data of each node on the middle grid section under K output states of the simulated specimen are given by the numerical simulation software. The node data include the equivalent strain ε0, the axial strain ε z , the equivalent strain rate , the axial strain rate component , the radial strain rate component , the circumferential strain rate component and the radial coordinate value r; Meanwhile, the node data of each node on the adjacent grid cross-sections in K output states of the simulated specimen are given by the numerical simulation software. The node data include the equivalent strain ε1 and the equivalent strain rate as well as the shear strain rate components The adjacent grid cross-sections are the upper or lower grid cross-sections of the middle grid cross-section in the corresponding output state.

6. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 1, characterized in that: The calculation of the axial stress of each node on the middle cross-section is carried out as follows: Solve for the axial stress σ of each node in the intermediate grid section under K output states according to the incremental theory of elastoplastic deformation, the equilibrium differential equation, and the boundary conditions z , and the solution formula is: Among them, σ r is the radial stress, σ θ is the circumferential stress, σ z ′, σ r ′, σ θ ′ are the stress deviators corresponding to three directions respectively, and the mean stress σ m =(σ z +σ r +σ θ ) / 3; τ zr is the shear stress acting on the adjacent grid sections and along the radial direction; dh is the axial distance between the nodes of the intermediate grid section and the corresponding nodes of the adjacent grid section, and the solution formula contains unknown coefficients Aij.

7. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 6, characterized in that: The equilibrium differential equation calculates the radial stress σ r in the following manner: (1) Solve the radial stress change rate of each node on the middle grid cross-section (2) Solve the radial stress of each node on the middle grid cross-section Where N is the total number of nodes in the radial direction of the specimen, and N = R0 / a + 1; σ r(n) is the radial stress at the nth node; is the rate of change of the radial stress at the nth node; dr(n) is the distance between the nth node and the (n + 1)th node.

8. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 7, wherein: The integration to obtain the theoretical load on the middle cross-section is carried out as follows: Integrate the axial stress σ z doubly along the circumferential and radial directions to obtain the axial load F K,Sim calculated theoretically for the intermediate grid section in each output state: F K,Sim = ∫∫σ z drdθ。 9. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 8, wherein: The theoretical load F of the integral acquisition intermediate section K,Sim is carried out as follows: (1) Sum σ z for different cells along the circumferential direction: Among them, F K (n) is the load after integrating the axial stress of the nth unit in the circumferential direction, r(n) is the radial coordinate of the nth node, and dr(n) is the distance between the nth node and the (n + 1)th node; σ z (n) is the axial stress of the nth node; (2) Sum F under each output state K (n) Sum different units along the radial direction:

10. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 9, wherein: The solution of the true equivalent stress function for hot compression and the realization of the correction of the hot compression stress-strain curve are carried out as follows: Through the formula: F K,Sim = ∫∫σ z drdθ = F K,Exp , the value of A ij is obtained by solving. Then substitute the value of A ij into the true equivalent stress function . When the equivalent strain and the equivalent strain rate are given, the corrected stress-strain curve can be obtained.

11. A method for correcting the hot compression stress-strain curve by numerical simulation, wherein: The method is carried out according to the following steps: Step 1: Prepare a metal hot compression cylindrical specimen with a specimen length of L0 and a specimen radius of R0; weld multiple thermocouples on the specimen and conduct a hot compression experiment with the heating temperature of the specimen being T; the multiple thermocouples are longitudinally arranged on the specimen cylinder surface and are equally spaced between the middle and the ends of the specimen Step 2: Extract the hot compression experiment data, which includes the compression amount S at each moment varying with the compression time, the load amount F corresponding to each compression amount S, and the temperature of each thermocouple corresponding to each compression amount S and calculate the corresponding initial equivalent strain for each amount of compression S and the initial equivalent stress Interpolate the compression amounts S at equal intervals to obtain K compression amounts S K and further obtain the load amounts F K corresponding to the compression amounts S K,Exp ; Obtain the intermediate cross-section radius R of the specimen after the hot compression experiment Exp ; Perform a linear fit on the temperatures of each thermocouple at each compression amount S, and calculate the specimen end face temperature T at each compression amount S S ; Step 3: Numerically simulate the hot compression experiment in Step 1 using numerical simulation software, where the simulation parameters are: the initial equivalent strain obtained in Step 2 Initial equivalent stress Specimen end face temperature T S , the specimen middle cross-section temperature is the heating temperature T in Step 1. Preset K output states in the numerical simulation, set the grid side length of the simulated specimen to a, and the friction coefficient to μ. Take the friction coefficient μ as the control variable of the simulation. By adjusting the value of the friction coefficient μ multiple times, the maximum radius R of the specimen after numerical simulation Sim is equal to the middle cross-section radius R measured and obtained in Step 2 Exp ; Step 4: After the numerical simulation is completed, the numerical simulation software gives the nodal data of each node on the middle grid section under K output states of the simulated specimen. The nodal data includes the equivalent strain ε0, axial strain ε z , equivalent strain rate axial strain rate component radial strain rate component circumferential strain rate component and the radial coordinate value r; Meanwhile, node data of each node on the adjacent grid cross-section under K output states of the simulated specimen is given by the numerical simulation software, and the node data includes the equivalent strain ε1 and the equivalent strain rate as well as the shear strain rate component The adjacent grid cross-section is the upper or lower grid cross-section of the middle grid cross-section under the corresponding output state; Step 5: Set the true equivalent stress function for hot compression as: Among them, the equivalent strain is ε, and the equivalent strain rate m is an integer greater than or equal to 3; A ij is an unknown coefficient, and both i and j are integers greater than or equal to 0 and less than or equal to m; Substitute the equivalent strains and equivalent strain rates of each node on the middle grid cross-section and adjacent grid cross-sections under K output states into the true equivalent stress function, and calculate the true equivalent stress σ0 of each node on the corresponding middle grid cross-section and the true equivalent stress σ1 of each node on the adjacent grid cross-sections; where σ0 and σ1 are algebraic expressions containing the unknown coefficient A ij ; Step 6: Solve for the axial stress σ of each node on the intermediate grid section under K output states according to the incremental theory of elastoplastic deformation, the equilibrium differential equation, and the boundary conditions z , and the solution formula is: Among them, σ r is the radial stress, σ θ is the circumferential stress, σ z ′, σ r ′, σ θ ′ are the stress deviators corresponding to three directions respectively, and the mean stress σ m =(σ z +σ r +σ θ ) / 3; τ zr is the shear stress acting on the adjacent grid sections and along the radial direction; dh is the axial distance between the nodes of the middle grid section and the corresponding nodes of the adjacent grid sections, and the solution formula contains the unknown coefficient A ij ; Step 7: Integrate the axial stress σ described in Step 6 z doubly along the circumferential and radial directions to obtain the axial load F calculated theoretically for the intermediate grid section in each output state K,Sim : F K,Sim = ∫∫σ z drdθ Step 8: Through the formula: F K,Sim = ∫∫σ z drdθ = F K,Exp , solve to obtain the value of A ij , and then substitute the value of A ij into the true equivalent stress function ; Step Nine: When the equivalent strain and equivalent strain rate are given, a corrected stress-strain curve can be obtained.

12. A method for correcting the hot compression stress-strain curve by numerical simulation, characterized in that: The method is carried out according to the following steps: Step One: Prepare a metal hot-compression cylindrical specimen with a specimen length of L0 and a specimen radius of R0; weld a plurality of thermocouples on the specimen and conduct a hot-compression experiment with the heating temperature of the specimen being T; the plurality of thermocouples are longitudinally arranged on the cylindrical surface of the specimen and are equally spaced between the middle and the end of the specimen; Step Two: Extract the hot-compression experiment data, including the compression amount S at each moment varying with the compression time, the load amount F corresponding to each compression amount S, and the temperature of each thermocouple corresponding to each compression amount S; and calculate to obtain the corresponding initial equivalent strain for each compression amount S and the initial equivalent stress Interpolate the compression amounts S at equal intervals to obtain K compression amounts S K , and further obtain the load amounts F K corresponding to each compression amount S K,Exp ; Obtain the middle cross-section radius R of the specimen after the hot compression experiment Exp ; Fit the temperatures of each thermocouple at each compression amount S, and calculate the specimen end face temperature T at each compression amount S S ; Step 3: Numerically simulate the hot compression experiment in Step 1 using numerical simulation software, where the simulation parameters are: the initial equivalent strain obtained in Step 2 Initial equivalent stress Specimen end face temperature T S , the specimen middle cross-section temperature is the heating temperature T in Step 1. Preset K output states in the numerical simulation, set the grid side length of the simulated specimen as a, and the friction coefficient as μ. Take the friction coefficient μ as the control variable of the simulation. By adjusting the value of the friction coefficient μ multiple times, make the maximum radius R of the specimen after numerical simulation Sim equal to the middle cross-section radius R measured and obtained in Step 2 Exp ; Step Four: After the numerical simulation is completed, the numerical simulation software gives the nodal data of each node on the middle grid section under K output states of the simulated specimen. The nodal data includes the equivalent strain ε0, axial strain ε z , equivalent strain rate axial strain rate component radial strain rate component circumferential strain rate component and the radial coordinate value r; Meanwhile, node data of each node of adjacent grid sections under K output states of the simulated specimen are given by the numerical simulation software. The node data includes the equivalent strain ε1 and the equivalent strain rate as well as the shear strain rate components The adjacent grid sections are the upper or lower grid sections of the middle grid section under the corresponding output state; Step Five: Set the hot-compression true equivalent stress function as: Among them, the equivalent strain ε and the equivalent strain rate m is an integer greater than or equal to 3; A ij is an unknown coefficient, and both i and j are integers greater than or equal to 0 and less than or equal to m; Substitute the equivalent strains and equivalent strain rates of each node in the middle grid section and adjacent grid sections under K output states into the true equivalent stress function, and calculate the true equivalent stress σ0 of each node in the corresponding middle grid section and the true equivalent stress σ1 of each node in the adjacent grid section; where σ0 and σ1 are algebraic expressions containing the unknown coefficient A ij ; Step 6: Solve for the axial stress σ of each node on the intermediate grid section under K output states according to the incremental theory of elastoplastic deformation, the equilibrium differential equation, and the boundary conditions z , and the solution formula is: Among them, σ r is the radial stress, σ θ is the circumferential stress, σ z ′, σ r ′, σ θ ′ are the stress deviators corresponding to three directions respectively, and the mean stress σ m = (σ z + σ r + σ θ ) / 3; τ zr is the shear stress acting on the adjacent grid sections and along the radial direction; dh is the axial distance between the nodes of the middle grid section and the corresponding nodes of the adjacent grid sections, and the solution formula contains the unknown coefficient A ij ; Step 7: Integrate the axial stress σ described in Step 6 z doubly along the circumferential and radial directions to obtain the axial load F calculated theoretically for the intermediate grid section under each output state K,Sim : F K,Sim = ∫∫σ z drdθ; Step Eight: Through the formula F K,Sim = ∫∫σ z drdθ = F K,Exp , solve to obtain the value of A ij , and then substitute the value of A ij into the true equivalent stress function ; Step Nine: When the equivalent strain and equivalent strain rate are given, a corrected stress-strain curve can be obtained.

13. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 11 or 12, characterized in that: In Step 6, the radial stress σ is calculated using the equilibrium differential equation r as follows: (1) Solve the radial stress change rate of each node of the middle grid section: (2) Solve the radial stress of each node of the middle grid section: where N is the total number of nodes in the radial direction of the specimen, and N = R0 / a + 1; σ r (n) is the radial stress at the nth node; is the rate of change of the radial stress at the nth node; dr(n) is the distance between the nth node and the (n + 1)th node.

14. The method for correcting the hot compression stress-strain curve by numerical simulation according to claim 11 or 12, characterized in that: In Step 7, the axial load F K,Sim calculated theoretically for the intermediate grid cross-section under each output state is as follows: (1) Sum σ z over different elements in the circumferential direction: Among them, F K (n) is the load after integrating the axial stress of the nth unit in the circumferential direction, r(n) is the radial coordinate of the nth node, and dr(n) is the distance between the nth node and the (n + 1)th node; σ z (n) is the axial stress of the nth node; (2) Sum F K (n) over different elements in the radial direction:

Images