CN115017697A - Method for correcting thermal compression stress-strain curve by using numerical simulation - Google Patents
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Abstract
The invention discloses a method for correcting a thermal compression stress-strain curve by using numerical simulation, which can solve the problem that the stress-strain curve of a material is difficult to accurately calculate due to temperature gradient and friction of a sample in the traditional method. Firstly, load displacement data and a sample temperature gradient in a thermal compression process are obtained through an experiment, then, the strain distribution of the sample is calculated through numerical simulation, the axial stress of each point of a middle section is calculated according to an elastic-plastic deformation theory, the theoretical load of the middle section is obtained through integration, the theoretical load is equal to the load obtained through the experiment, and therefore a corrected stress-strain curve can be obtained through calculation. The method provided by the invention considers the temperature gradient during thermal compression deformation, and corrects the stress-strain curve by combining experiments, numerical simulation and theoretical calculation, so that the calculation result is more accurate.
Description
Technical Field
The invention relates to the field of testing of hot compression performance of metal materials, in particular to a method for correcting a hot compression stress-strain curve by using numerical simulation.
Background
In the process of hot forging and forming of the metal material, the deformation behavior of the material in hot working is analyzed by numerical simulation, and the method is an important means for optimizing process parameters and the size of a die. In order to obtain more accurate simulation results, the high-temperature deformation behavior of the material needs to be accurately described, and an accurate stress-strain curve is given. Thermal compression experiments are usually performed using a Gleeble thermal simulation tester to obtain stress-strain curves of materials at different temperatures and strain rates. However, during the thermal compression experiment, the sample is unevenly deformed due to friction at both ends of the sample, and is formed into a drum shape, i.e., a shape with a large diameter at the middle section and a small diameter at both end faces. If the uneven deformation of the sample is neglected, and the stress-strain curve of the material is directly calculated, the stress result is larger, and the obtained stress-strain curve is inaccurate.
In order to correct the influence of such uneven deformation of the sample on the calculation of the stress strain, a friction correction method is generally used. And calculating a bulging factor and a friction factor by calculating the difference between the maximum radius of the middle section and the radii of the upper end surface and the lower end surface after the sample is deformed, and then correcting the stress-strain curve.
However, this method only considers the influence of friction on deformation, and in the actual thermal compression experiment process, a certain temperature gradient still exists on the sample, and the temperature has a great influence on the deformation of the material under the high temperature condition. Because the temperature at the two ends of the sample is lower, the strength is higher, the deformation of the two ends of the sample is further limited, and the drum shape of the compressed sample is more obvious. Therefore, the conventional friction correction method cannot obtain an accurate stress-strain relationship.
The analysis of the thermal compression experiment by using a numerical simulation technique is a method generally adopted in the field, in the simulation, a sample is generally required to be subjected to grid division, intersection points among grid lines are called nodes, and a minimum area surrounded by the grid lines is called a unit. The sample of the hot compression experiment is simply stressed, the load is loaded along the length direction of the sample, namely the axial direction, and the middle section is a symmetrical plane of the sample. Before compression deformation, the node of a certain grid section has the same radial coordinate with the node, and the node on the adjacent grid section is the corresponding node of the node.
Disclosure of Invention
The purpose of the invention is: in order to solve the problem that the stress-strain curve cannot be accurately calculated by the conventional method due to friction and temperature gradient in the thermal compression process, a method for correcting the thermal compression stress-strain curve by using numerical simulation is provided.
The technical scheme of the invention is as follows:
the method comprises the steps of firstly obtaining experimental data such as load displacement and sample temperature gradient in the thermal compression process through a thermal compression experiment and processing the data, then substituting the load displacement data and the sample temperature gradient into a numerical simulation software to carry out thermal compression numerical simulation, calculating and obtaining strain and strain rate distribution of a simulation sample, establishing a thermal compression real equivalent stress function, calculating real equivalent stress by using the simulated strain and strain rate data, calculating axial stress of each node of a middle section according to an elastoplastic deformation theory, integrating to obtain a middle section theoretical load, and enabling the theoretical load to be consistent with the thermal compression process load obtained through the experiment, so that the thermal compression real equivalent stress function is solved, and the thermal compression stress-strain curve is corrected.
Providing a method for correcting a thermal compression stress-strain curve by using numerical simulation, wherein the method is carried out according to the following steps:
the method comprises the following steps: preparing a metal thermocompression columnar sample with a length L 0 Radius of specimen is R 0 (ii) a Welding a plurality of thermocouples on the sample, and carrying out a hot compression experiment, wherein the heating temperature of the sample is T; the thermocouples are longitudinally arranged on the cylindrical surface of the sample and are arranged between the middle part of the sample and the end part of the sample at equal intervals;
thermal compression experiments are generally carried out on a Gleeble thermal simulation tester, in which a temperature gradient exists on a sample, the center temperature of the sample is the highest, and the temperatures at the two ends of the sample are lower due to the heat transfer effect. During conventional thermal compression experiments, such temperature gradients are often ignored, only one thermocouple is welded at the center of the specimen, and the temperature on the specimen is considered uniform, which leads to inaccurate stress-strain calculations. By adopting the technical scheme of the invention, a plurality of thermocouples are welded on the sample to measure the temperature of the sample at different positions, so that the temperature distribution on the sample can be accurately obtained, and accurate boundary conditions are provided for subsequent calculation. In particular, the thermal compression test may be performed in a high temperature compression tester using resistance furnace heating, where the furnace temperature is considered to be a uniform temperature field and the sample temperature is equal to the furnace temperature. At the moment, the temperature of the sample is uniformly distributed, the temperature gradient is zero, which is a special case in the implementation process of the invention, and the problem of inaccurate calculation of the stress-strain curve is caused only by correcting the sample to be drum-shaped caused by end face friction.
Step two: extracting thermal compression experimental data, wherein the data comprises compression quantity S at each moment along with the change of compression time, load quantity F corresponding to each compression quantity S and temperature of each thermocouple corresponding to each compression quantity S;
and calculating to obtain the following corresponding compression quantity S: initial equivalent strain
And initial equivalent stress
Performing equal interval interpolation on each compression quantity S to obtain K compression quantities S K And further obtaining each compression amount S K Corresponding load F K,Exp ；
Obtaining the middle section radius R of the sample after the thermal compression experiment is finished Exp ；
Fitting the thermocouple temperatures under the compression quantities S, and calculating to obtain the end surface temperature T of the sample under the compression quantities S S ；
The initial equivalent strain and the initial equivalent stress of the material are obtained by processing the data obtained by the experiment, the solving method does not consider the uneven deformation of the sample, and the obtained equivalent strain and equivalent stress are average values which are inaccurate and need to be further corrected.
In the thermal compression deformation process, due to the heat conduction effect, a temperature gradient exists on the sample, and the length of the sample is shortened along with the progress of thermal compression, so that the temperature gradient on the sample is changed.
Step three: carrying out numerical simulation on the thermal compression experiment in the first step through numerical simulation software, wherein simulation parameters are as follows: the initial equivalent strain obtained in step two
Initial equivalent stress
End face temperature T of sample S Setting the middle section temperature of the sample as the heating temperature T in the first step, presetting K output states in numerical simulation, setting the side length of a simulation sample grid as a and the friction coefficient as mu, taking the friction coefficient mu as a control variable of the simulation, and adjusting the value of the friction coefficient mu for multiple times to enable the maximum radius R of the numerically-simulated sample to be equal to the maximum radius R of the numerically-simulated sample Sim Equal to the radius R of the intermediate section obtained by the measurement in step two Exp ；
By adopting the technical scheme of the invention, the nonuniformity of the sample temperature in the experimental process is considered, and the obtained end face temperatures of the samples corresponding to different compression amounts are taken as boundary conditions to be substituted into the numerical simulation, so that the numerical simulation is more in line with the actual situation, and the strain and strain rate results of the samples obtained by calculation are more accurate.
Step four: after the numerical simulation is finished, the numerical simulation software gives node data of each node of the middle grid section under K output states of the simulation sample,the nodal data includes equivalent strain epsilon at corresponding output states 0 Axial strain epsilon z Equivalent strain rate
Axial strain rate component
Radial strain rate component
Component of hoop strain rate
And a radial coordinate value r;
meanwhile, the numerical simulation software provides node data of each node of the adjacent grid section under the K output states of the simulation sample, and the node data comprises equivalent strain epsilon under the corresponding output state 1 Equivalent strain rate
And a shear strain rate component
The adjacent grid section is an upper layer or a lower layer grid section corresponding to the middle grid section in the output state;
due to the temperature gradient on the sample and the friction effect of the end face of the sample, the sample is deformed unevenly and forms a drum shape, so that the strain and the strain rate of a central area are high, and the strain rate of a marginal area are low on the middle section of the sample; by adopting the technical scheme of the invention, the strain and strain rate data of each node of the middle grid section of the numerical simulation sample are extracted, and the range formed by the obtained strain and strain rate is larger than the average equivalent strain and equivalent strain rate, so that the stress-strain curve obtained by calculation can be effectively extrapolated.
Step five: setting the thermal compression true equivalent stress function as:
wherein the equivalent strain ε, the equivalent strain rate
m is an integer of 3 or more; a. the ij Is an unknown coefficient, i and j are integers which are more than or equal to zero and less than or equal to m;
substituting the equivalent strain and the equivalent strain rate of each node of the middle grid section and the adjacent grid sections into the real equivalent stress function in K output states to calculate the real equivalent stress sigma of each node of the corresponding middle grid section 0 And the true equivalent stress sigma of each node of the adjacent grid section 1 (ii) a Wherein σ 0 And σ 1 Is composed of unknown coefficients A ij An algebraic expression of (a);
when a metal material is deformed at a high temperature, the stress magnitude is influenced by the strain rate, the temperature and the strain magnitude. When the material is deformed under the fixed temperature condition, the stress magnitude is only related to the strain rate and the strain magnitude, namely the real equivalent stress-strain relation of the material is a binary function of the strain and the strain rate. By adopting the technical scheme of the invention, the deformation behavior of the material is described by utilizing a polynomial function, and the function form is simple and convenient to calculate. In order to make the function description more accurate, the value range of the parameter m is that m is more than or equal to 3, and the larger the value of m is, the higher the accuracy of the function is.
Step six: solving the axial stress sigma of each node of the middle grid section under K output states according to the increment theory of elastic-plastic deformation, a balanced differential equation and boundary conditions z The solving formula is:
wherein σ r For radial stress, σ θ Is hoop stress, σ' z 、σ′ r 、σ′ θ Are respectively corresponding toStress offset in three directions, mean stress σ m ＝(σ z +σ r +σ θ )/3；τ zr Shear stress in the radial direction for acting on the cross section of the adjacent grid; dh is the axial distance between each node of the section of the middle grid and the corresponding node of the section of the adjacent grid, and the solution formula contains an unknown coefficient A ij ；
By adopting the technical scheme of the invention, the axial stress is calculated by utilizing the strain and strain rate data of the middle section, and although the whole sample is unevenly deformed, the middle grid section is a symmetrical plane, so that the strain main shaft direction is always unchanged when each node on the middle grid section is deformed, and the axial stress sigma of each node on the middle grid section can be obtained by applying incremental theory calculation z ；
Step seven: subjecting the axial stress sigma of step six to z Performing double integration along the annular direction and the radial direction to obtain the axial load F theoretically calculated by the middle grid section in each output state K,Sim ：
F K,Sim ＝∫∫σ z drdθ；
By adopting the technical scheme of the invention, the axial load on the middle grid section is obtained, and because the middle grid section is a symmetrical plane of the sample, the temperature of the middle grid section is always kept unchanged at the experimental temperature T, the corrected stress-strain curve is more accurate;
step eight: by the formula: f K,Sim ＝∫∫σ z drdθ＝F K,Exp Solving to obtain A ij Value of A, then ij Value substitution into the true equivalent stress function
Performing the following steps;
step nine: when the equivalent strain and the equivalent strain rate are given, a corrected stress-strain curve can be obtained.
Another method for correcting the thermal compression stress-strain curve by using numerical simulation is provided, which is characterized in that: the method is carried out according to the following steps:
the method comprises the following steps: preparation of Metal Hot compression column testSample, length of sample L 0 Radius of specimen is R 0 (ii) a Welding a plurality of thermocouples on the sample, and carrying out a hot compression experiment, wherein the heating temperature of the sample is T; the thermocouples are longitudinally arranged on the cylindrical surface of the sample and are arranged between the middle part of the sample and the end part of the sample at equal intervals;
step two: extracting thermal compression experimental data, wherein the data comprises compression quantity S at each moment along with the change of compression time, load quantity F corresponding to each compression quantity S and temperature of each thermocouple corresponding to each compression quantity S;
and calculating to obtain the following corresponding compression quantity S: initial equivalent strain
And initial equivalent stress
Performing equal interval interpolation on each compression quantity S to obtain K compression quantities S K And further obtaining each compression amount S K Corresponding load F K,Exp ；
Obtaining the middle section radius R of the sample after the thermal compression experiment is finished Exp ；
Fitting the thermocouple temperatures under the compression quantities S, and calculating to obtain the end surface temperature T of the sample under the compression quantities S S ；
Step three: carrying out numerical simulation on the thermal compression experiment in the first step through numerical simulation software, wherein simulation parameters are as follows: the initial equivalent strain obtained in step two
Initial equivalent stress
End face temperature T of sample S Setting the middle section temperature of the sample as the heating temperature T in the first step, presetting K output states in numerical simulation, setting the side length of a simulation sample grid as a, setting the friction coefficient as mu, and taking the friction coefficient mu as the simulatedControlling the variable to enable the maximum radius R of the sample after numerical simulation by adjusting the value of the friction coefficient mu for multiple times Sim Equal to the radius R of the intermediate section obtained by the measurement in step two Exp ；
Step four: after the numerical simulation is finished, the numerical simulation software gives node data of each node of the middle grid section under K output states of the simulation sample, and the node data comprises equivalent strain epsilon under the corresponding output state 0 Axial strain epsilon z Equivalent strain rate
Axial strain rate component
Radial strain rate component
Component of hoop strain rate
And a radial coordinate value r;
meanwhile, the numerical simulation software provides node data of each node of the adjacent grid section under the K output states of the simulation sample, and the node data comprises equivalent strain epsilon under the corresponding output state 1 Equivalent strain rate
And shear strain rate component
The adjacent grid section is an upper layer or a lower layer grid section corresponding to the middle grid section in the output state;
step five: setting the thermal compression true equivalent stress function as:
wherein the equivalent strain ε, the equivalent strain rate
m is an integer of 3 or more; a. the ij Is an unknown coefficient, i and j are integers which are more than or equal to zero and less than or equal to m;
substituting the equivalent strain and the equivalent strain rate of each node of the middle grid section and the adjacent grid sections into the real equivalent stress function in K output states to calculate the real equivalent stress sigma of each node of the corresponding middle grid section 0 And the true equivalent stress sigma of each node of the adjacent grid section 1 (ii) a Wherein σ 0 And σ 1 Is composed of unknown coefficients A ij An algebraic expression of (a);
the difference from the above method is that in order to calculate the stress of the material under different conditions, the value range of the strain is usually 0 ≦ epsilon ≦ 1, and the value range of the strain rate is usually 0 ≦ epsilon ≦ 1
By adopting the embodiment, after the indexes of the stress function are normalized, the normalization processing can be ensured
Is not too small, so that the coefficient A can be reduced ij The calculation error of (2).
Step six: solving the axial stress sigma of each node of the middle grid section under K output states according to the increment theory of elastic-plastic deformation, a balanced differential equation and boundary conditions z The solving formula is:
wherein σ r For radial stress, σ θ Is hoop stress, σ' z 、σ′ r 、σ′ θ The stress offsets corresponding to three directions, the average stress sigma m ＝(σ z +σ r +σ θ )/3；τ zr Shear stress in the radial direction for acting on the cross section of the adjacent grid; dh is the axial distance between each node of the section of the middle grid and the corresponding node of the section of the adjacent grid, and the solution formula contains an unknown coefficient A ij ；
Step seven: subjecting the axial stress sigma of step six to z Performing double integration along the annular direction and the radial direction to obtain the axial load F theoretically calculated by the middle grid section in each output state K,Sim ：
F K,Sim ＝∫∫σ z drdθ；
Step eight: by the formula F K,Sim ＝∫∫σ z drdθ＝F K,Exp Solving to obtain A ij Value of A, then ij Value substitution into the true equivalent stress function
Performing the following steps;
step nine: when the equivalent strain and the equivalent strain rate are given, a corrected stress-strain curve can be obtained.
It should be noted that, the real equivalent stress function expression of the present invention includes, but is not limited to, the above two function forms, and other forms of real equivalent stress functions can be constructed, only the function is required to describe the real stress-strain relationship of the material, and the unknown coefficient is easy to solve.
For both of the above methods, there are further limitations:
in the sixth step, the radial stress sigma is calculated by balancing a differential equation r The following were used:
(1) solving the radial stress change rate of each node of the section of the middle grid:
(2) solving the radial stress of each node of the section of the middle grid:
wherein N is the total number of nodes in the radial direction of the sample, and N is R 0 /a+1；σ r (n) is the radial stress at the nth node;
is the radial stress rate of change at the nth node; dr (n) is the distance between the nth node and the (n + 1) th node;
for both of the above methods, there are further limitations:
step seven, the axial load F theoretically calculated by the section of the middle grid under each output state K,Sim The specific calculation method is as follows: (1) will sigma z Summing different cells along the ring:
wherein, F K (n) is the load of the nth unit after axial stress is integrated in the annular 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; sigma z(n) Axial stress at the nth node;
(2) will σ z Summing along different units in the radial direction:
the invention provides a process for solving a differential equation by adopting an Eulerian method of a trapezoidal formula, and a person skilled in the art can obtain radial stress sigma by simply changing and solving the differential equation by adopting other methods r 。
The invention has the advantages that: (1) according to the method for correcting the thermal compression stress-strain curve by using numerical simulation, the real temperature gradient on the sample in the material deformation process is obtained through experiments and substituted into numerical simulation calculation, the boundary condition is more consistent with the actual condition, the real deformation process is simulated, and the calculated result is more accurate.
(2) According to the method for correcting the thermal compression stress-strain curve by using numerical simulation, data of a node of the middle section of a numerical simulation sample are extracted, the temperature of the middle section is kept at a constant temperature value in the experiment and simulation processes, the middle section is a symmetrical plane, and the direction of a stress main shaft of the middle section does not change, so that the stress result obtained by calculation is more accurate.
(3) According to the method for correcting the thermal compression stress-strain curve by using numerical simulation, deformation data of each node of a numerical simulation middle section are extracted, and the stress-strain curve obtained can be effectively extrapolated due to the fact that a sample is not uniformly deformed, the strain and strain rate at the center is high, the strain and strain rate at the edge is low, the range formed by the strain and strain rate is larger than the average equivalent strain and the average strain rate.
Drawings
FIG. 1 is a schematic diagram of a process for solving a modified stress-strain curve according to the present invention;
FIG. 2 is a schematic view of a thermo-electric welding of a thermo-compressed coupon according to the present invention;
FIG. 3 is a schematic diagram of the distribution of thermal compression numerical simulation strain and the selection of micro-elements according to the present invention;
FIG. 4 is a schematic view of the force analysis of the micro element of the middle section of the thermal compression test sample according to the present invention;
FIG. 5 is a node numbering diagram according to the present invention;
FIG. 6 is a schematic diagram of node numbering and unit numbering according to the present invention;
FIG. 7 is a thermal compression load displacement curve of a titanium alloy in accordance with example 1 of the present invention;
FIG. 8A is a temperature profile of a titanium alloy hot-compressed sample at different positions according to example 1 of the present invention;
FIG. 8B is a graph showing the temperature change of the end face of the titanium alloy thermocompression bonded sample in accordance with example 1 of the present invention;
FIG. 9 is a comparison of stress-strain curves of the titanium alloy of example 1 before and after the correction.
FIG. 10 is a graph of the hot compression load displacement of the superalloy of example 2 of the present invention;
FIG. 11A is a graph showing the temperature change at different positions of a hot-compressed sample of a superalloy of example 2 according to the present invention;
FIG. 11B is a graph showing the temperature variation of the end face of the hot-pressed superalloy specimens in example 2 of the present invention;
FIG. 12 is a comparison of the stress-strain curves of the superalloy of example 2 of the present invention before and after correction.
Detailed Description
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. Indeed, many different examples may be described and 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 the disclosure to those skilled in the art.
Example 1, described with reference to fig. 7 to 9, this example was carried out as follows:
in the first step, the metal thermal compression columnar sample is a titanium alloy material, and the length L of the sample 0 Is 15mm, and the radius R of the sample 0 The temperature of the sample is 5mm, three thermocouples are welded on the sample, the heating temperature T of the sample is 750 ℃, and the arrangement distance of the four thermocouples is 2.5 mm;
in the second step, as shown in fig. 7, the load displacement data obtained by the thermal compression experiment is interpolated at equal intervals to obtain 150 compressed quantities S K And its corresponding load capacity F K,Exp ；
The temperatures of the three thermocouples corresponding to each compression amount S are shown in FIG. 8A, and the corresponding sample end surface temperature T when the displacement is S is obtained by data fitting S As shown in FIG. 8B;
calculating to obtain the initial equivalent stress
And initial equivalent strain
The relationship of (a) is shown in FIG. 9;
measuring the intermediate section radius R of the sample after acquisition of the thermal compression Exp 7.32 mm;
in the third step, the side length of the numerical simulation sample grid is 0.2 mm;
in the fifth step, the real equivalent stress function is
Wherein the value of the parameter m is 8, namely:
in the ninth step, the range of the substituted strain value is 0-1, and the value of the substituted strain rate is 0.001s -1 The corrected stress-strain curve is shown in fig. 9.
Example 2, described with reference to fig. 10 to 12, this example was carried out as follows:
in the first step, the metal thermal compression columnar sample is made of a high-temperature alloy material, and the length L of the sample 0 12mm, specimen radius R 0 The temperature is 4mm, four thermocouples are welded on the sample, the heating temperature T of the sample is 1070 ℃, and the arrangement distance of the four thermocouples is 1.5 mm;
in the second step, as shown in fig. 10, the load displacement data obtained by the thermal compression experiment is interpolated at equal intervals for each compression amount S to obtain 200 compression amounts S K And its corresponding load capacity F K,Exp ；
The temperatures of the four thermocouples corresponding to each compression amount S are shown in fig. 11A, and the sample end surface temperature T corresponding to the displacement S is obtained by data fitting S As shown in FIG. 11B;
calculating to obtain the initial equivalent stress
And initial equivalent strain
The relationship of (a) is shown in FIG. 12;
measuring the intermediate section of the sample after obtaining the thermal compressionRadius R Exp 6.15 mm;
in the third step, the side length of the numerical simulation sample grid is 0.125 mm;
in step five, the real equivalent stress function is
Wherein the value of the parameter m is 10, namely:
in the ninth step, the range of the substituted strain value is 0-1, and the value of the substituted strain rate is 0.01s -1 The corrected stress-strain curve is shown in fig. 12.
The description of the different advantageous arrangements has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the examples in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art. Additionally, the different advantageous examples may describe different advantages as compared to other advantageous examples. The example or examples selected are chosen and described in order to best explain the principles of the examples, the practical application, and to enable others of ordinary skill in the art to understand the disclosure for various examples with various modifications as are suited to the particular use contemplated.
Claims (16)
1. A method for correcting a thermal compression stress-strain curve by using numerical simulation is characterized by comprising the following steps of: firstly, experimental data such as load displacement, sample temperature gradient and the like in a thermal compression process are obtained through a thermal compression experiment and are subjected to data processing, then the load displacement data and the sample temperature gradient are substituted into a numerical simulation software to carry out thermal compression numerical simulation, strain and strain rate distribution of a simulation sample are obtained through calculation, a thermal compression real equivalent stress function is established, real equivalent stress is calculated by using the simulated strain and strain rate data, axial stress of each node of a middle section is calculated according to an elastoplastic deformation theory, a middle section theoretical load is obtained through integration, the theoretical load is consistent with the thermal compression process load obtained through the experiment, the thermal compression real equivalent stress function is solved, and correction of a thermal compression stress-strain curve is achieved.
2. The method for correcting the thermal compression stress-strain curve using numerical simulation as claimed in claim 1, wherein:
the thermal compression experiment was performed as follows:
preparing a metal thermocompression columnar sample with a length L 0 Radius of specimen is R 0 (ii) a Welding a plurality of thermocouples on the sample, and carrying out a hot compression experiment, wherein the heating temperature of the sample is T; the thermocouples are longitudinally arranged on the cylindrical surface of the sample and are arranged between the middle part of the sample and the end part of the sample at equal intervals.
3. The method for correcting the thermal compression stress-strain curve using numerical simulation as claimed in claim 2, wherein:
the data obtained by the thermal compression experiment and the data processing are carried out as follows:
extracting thermal compression experimental data, wherein the data comprises compression quantity S at each moment along with the change of compression time, load quantity F corresponding to each compression quantity S and temperature of each thermocouple corresponding to each compression quantity S;
calculating to obtain the following corresponding compression quantity S: initial equivalent strain
And initial equivalent stress
Performing equal interval interpolation on each compression quantity S to obtain K compression quantities S K And further obtaining each compression amount S K Corresponding load F K,Exp ；
Obtaining the middle section radius R of the sample after the thermal compression experiment is finished Exp ；
Fitting the thermocouple temperatures under the compression quantities S, and calculating to obtain the end surface temperature T of the sample under the compression quantities S S 。
4. The method for correcting the thermal compression stress-strain curve using numerical simulation as claimed in claim 3, wherein:
the thermal compression numerical simulation is carried out as follows:
carrying out numerical simulation on the thermal compression experiment through numerical simulation software, wherein simulation parameters are as follows: the initial equivalent strain obtained
Initial equivalent stress
End face temperature T of sample S Setting the middle section temperature of the sample as the heating temperature T, presetting K output states in numerical simulation, setting the side length of a simulation sample grid as a and the friction coefficient as mu, using the friction coefficient mu as a control variable of the simulation, and adjusting the value of the friction coefficient mu for multiple times to ensure that the maximum radius R of the numerically-simulated sample is R Sim Equal to the intermediate section radius R obtained by the measurement Exp 。
5. The method for correcting the thermal compression stress-strain curve by using numerical simulation as claimed in claim 4, wherein:
the strain and strain rate data of the obtained simulation sample are as follows:
the node data of each node of the middle grid section under K output states of the simulation sample is given by numerical simulation software, and the node data comprises equivalent strain epsilon under the corresponding output state 0 Axial strain epsilon z Equivalent strain rate
Axial strain rate component
Radial strain rate component
Component of hoop strain rate
And a radial coordinate value r;
meanwhile, the numerical simulation software gives out the node data of each node of the adjacent grid section under the K output states of the simulation sample, and the node data comprises the equivalent strain epsilon under the corresponding output state 1 Equivalent strain rate
And shear strain rate component
The adjacent grid section is an upper layer or a lower layer grid section corresponding to the middle grid section in the output state.
6. The method for correcting the thermal compression stress-strain curve by using numerical simulation as claimed in claim 5, wherein:
the establishing of the thermal compression real equivalent stress function and the calculation of the real equivalent stress by using the simulated strain and strain rate data are carried out according to the following modes:
wherein the equivalent strain ε, the equivalent strain rate
m is an integer of 3 or more; aij is an unknown coefficient, i and j are integers which are more than or equal to zero and less than or equal to m;
substituting the equivalent strain and the equivalent strain rate of each node of the middle grid section and the adjacent grid sections into the real equivalent stress function in K output states to calculate the real equivalent stress sigma of each node of the corresponding middle grid section 0 And the true equivalent stress sigma of each node of the adjacent grid section 1 (ii) a Wherein σ 0 And σ 1 Is an algebraic expression containing the unknown coefficients Aij.
7. The method for correcting the thermal compression stress-strain curve by using numerical simulation as claimed in claim 5, wherein:
the establishing of the thermal compression real equivalent stress function and the calculation of the real equivalent stress by using the simulated strain and strain rate data are carried out according to the following modes:
wherein the equivalent strain ε, the equivalent strain rate
m is an integer of 3 or more; a. the ij Is an unknown coefficient, i and j are integers which are more than or equal to zero and less than or equal to m;
substituting the equivalent strain and the equivalent strain rate of each node of the middle grid section and the adjacent grid sections into the real equivalent stress function under K output states, and calculating the real equivalent stress sigma of each node of the corresponding middle grid section 0 And the true equivalent stress sigma of each node of the adjacent grid section 1 (ii) a Wherein σ 0 And σ 1 Is composed of unknown coefficients A ij Is used as the algebraic expression of (1).
8. The method for correcting the thermal compression stress-strain curve by using numerical simulation according to claim 6 or 7, wherein:
the axial stress of each node of the middle section is calculated as follows:
solving the axial stress sigma of each node of the middle grid section under K output states according to the increment theory of elastic-plastic deformation, a balanced differential equation and boundary conditions z The solving formula is:
wherein σ r For radial stress, σ θ Is hoop stress, σ' z 、σ′ r 、σ′ θ The stress offsets corresponding to three directions, the average stress sigma m ＝(σ z +σ r +σ θ )/3；τ zr Shear stress in the radial direction for acting on the cross section of the adjacent grid; dh is the axial distance between each node of the section of the middle mesh and the corresponding node of the section of the adjacent mesh, and the solution formula contains an unknown coefficient Aij.
9. The method for correcting the thermal compression stress-strain curve using numerical simulation as claimed in claim 8, wherein:
the equilibrium differential equation calculates the radial stress σ r The method is carried out as follows:
(1) solving the radial stress change rate of each node of the section of the middle grid:
(2) solving the radial stress of each node of the section of the middle grid:
wherein N is the total number of nodes in the radial direction of the sample, and N is R 0 /a+1；σ r (n) is the radial stress at the nth node;
is the radial stress rate of change at the nth node; dr (n) is the distance between the nth node and the (n + 1) th node.
10. The method for correcting the thermal compression stress-strain curve using numerical simulation as claimed in claim 9, wherein:
the integration to obtain the middle section theoretical load is carried out as follows:
applying the axial stress σ z Performing double integration along the annular direction and the radial direction to obtain the axial load F theoretically calculated by the middle grid section in each output state K,Sim ：
F K,Sim ＝∫∫σ z drdθ。
11. The method for correcting the thermal compression stress-strain curve using numerical simulation as claimed in claim 10, wherein:
the integration obtains the middle section theoretical load F K,Sim The method is carried out as follows:
(1) will be at each output state z Summing different cells along the ring:
wherein, F K (n) is the load of the nth unit after axial stress is integrated in the annular 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; sigma z (n) is the axial stress of the nth node;
(2) will be in each output state F K (n) summing along different radial units:
12. the method for correcting the thermal compression stress-strain curve using numerical simulation as claimed in claim 11, wherein:
the method for solving the thermal compression real equivalent stress function to realize the correction of the thermal compression stress-strain curve is carried out as follows:
by the formula: f K,Sim ＝∫∫σ z drdθ＝F K,Exp Solving to obtain A ij Value of A, then ij Value substitution into the true equivalent stress function
When the equivalent strain and the equivalent strain rate are given, a corrected stress-strain curve can be obtained.
13. A method for correcting a thermal compression stress-strain curve by using numerical simulation is characterized by comprising the following steps of: the method is carried out according to the following steps:
the method comprises the following steps: preparing a metal thermocompression columnar sample with a length L 0 Radius of specimen is R 0 (ii) a Welding a plurality of thermocouples on the sample, and carrying out a hot compression experiment, wherein the heating temperature of the sample is T; the thermocouples are longitudinally arranged on the cylindrical surface of the sample and are arranged between the middle part of the sample and the end part of the sample at equal intervals;
step two: extracting thermal compression experimental data, wherein the data comprises compression quantity S at each moment along with the change of compression time, load quantity F corresponding to each compression quantity S and temperature of each thermocouple corresponding to each compression quantity S;
and calculating to obtain the following corresponding compression quantity S: initial equivalent strain
And initial equivalent stress
Performing equal interval interpolation on each compression quantity S to obtain K compression quantities S K And further obtaining each compression amount S K Corresponding load F K,Exp ；
Obtaining the middle section radius R of the sample after the thermal compression experiment is finished Exp ；
Carrying out linear fitting on the temperature of each thermocouple under each compression S, and calculating to obtain the end surface temperature T of the sample under each compression S S ；
Step three: carrying out numerical simulation on the thermal compression experiment in the first step through numerical simulation software, wherein simulation parameters are as follows: the initial equivalent strain obtained in step two
Initial equivalent stress
End face temperature T of sample S Setting the middle section temperature of the sample as the heating temperature T in the first step, presetting K output states in numerical simulation, setting the side length of a simulation sample grid as a and the friction coefficient as mu, using the friction coefficient mu as a control variable of the simulation, and integrating the value of the friction coefficient mu for multiple times to enable the maximum radius R of the numerically-simulated sample to be equal to the maximum radius R of the numerically-simulated sample Sim Equal to the radius R of the intermediate section obtained by the measurement in step two Exp ；
Step four:
after the numerical simulation is finished, the numerical simulation software gives node data of each node of the middle grid section under K output states of the simulation sample, and the node data comprises equivalent strain epsilon under the corresponding output state 0 Axial strain epsilon z Equivalent strain rate
Axial strain rate component
Radial strain rate component
Component of hoop strain rate
And a radial coordinate value r;
meanwhile, the numerical simulation software provides node data of each node of the adjacent grid section under the K output states of the simulation sample, and the node data comprises equivalent strain epsilon under the corresponding output state 1 Equivalent strain rate
And a shear strain rate component
The adjacent grid sections are upper layer or lower layer grid sections corresponding to the middle grid section in the output state;
step five: setting the thermal compression true equivalent stress function as:
wherein the equivalent strain ε, the equivalent strain rate
m is an integer of 3 or more; a. the ij Is an unknown coefficient, i and j are integers which are more than or equal to zero and less than or equal to m;
substituting the equivalent strain and the equivalent strain rate of each node of the middle grid section and the adjacent grid sections into the real equivalent stress function under K output states, and calculating the real equivalent stress sigma of each node of the corresponding middle grid section 0 And the true equivalent stress sigma of each node of the adjacent grid section 1 (ii) a Wherein σ 0 And σ 1 Is composed of unknown coefficients A ij An algebraic expression of (a);
step six: according to the increment theory of elastic-plastic deformation, equilibrium differential equationEquation and boundary condition solution of axial stress sigma of each node of intermediate grid section under K output states z The solving formula is:
wherein σ r For radial stress, σ θ Is hoop stress, σ' z 、σ′ r 、σ′ θ The stress offsets corresponding to three directions, the average stress sigma m ＝(σ z +σ r +σ θ )/3；τ zr Shear stress in the radial direction for acting on the adjacent grid section; dh is the axial distance between each node of the section of the middle grid and the corresponding node of the section of the adjacent grid, and the solution formula contains an unknown coefficient A ij ；
Step seven: subjecting the axial stress sigma of step six to z Performing double integration along the annular direction and the radial direction to obtain the axial load F theoretically calculated by the middle grid section in each output state K,Sim ：
F K,Sim ＝∫∫σ z drdθ
Step eight: by the formula: f K,Sim ＝∫∫σ z drdθ＝F K,Exp Solving to obtain A ij Value of A, then ij Value substitution into the true equivalent stress function
Performing the following steps;
step nine: when the equivalent strain and the equivalent strain rate are given, a corrected stress-strain curve can be obtained.
14. A method for correcting a thermal compression stress-strain curve by using numerical simulation is characterized by comprising the following steps of: the method is carried out according to the following steps:
the method comprises the following steps: preparing a metal thermocompression columnar sample with a length L 0 Radius of specimen is R 0 (ii) a Welding a plurality of thermocouples to the sampleCarrying out a thermal compression experiment, wherein the heating temperature of the sample is T; the thermocouples are longitudinally arranged on the cylindrical surface of the sample and are arranged between the middle part of the sample and the end part of the sample at equal intervals;
step two: extracting thermal compression experimental data, wherein the data comprises compression quantity S at each moment along with the change of compression time, load quantity F corresponding to each compression quantity S and temperature of each thermocouple corresponding to each compression quantity S;
and calculating to obtain the following corresponding compression quantity S: initial equivalent strain
And initial equivalent stress
Performing equal interval interpolation on each compression quantity S to obtain K compression quantities S K And further obtaining each compression amount S K Corresponding load F K,Exp ；
Obtaining the middle section radius R of the sample after the thermal compression experiment is finished Exp ；
Fitting the thermocouple temperatures under the compression quantities S, and calculating to obtain the end surface temperature T of the sample under the compression quantities S S ；
Step three: carrying out numerical simulation on the thermal compression experiment in the first step through numerical simulation software, wherein simulation parameters are as follows: the initial equivalent strain obtained in step two
Initial equivalent stress
End face temperature T of sample S Setting the middle section temperature of the sample as the heating temperature T in the first step, presetting K output states in numerical simulation, setting the side length of a simulation sample grid as a and the friction coefficient as mu, using the friction coefficient mu as a control variable of the simulation, and adjusting the value of the friction coefficient mu for multiple times to enable the numerical modelMaximum radius R of the sample after simulation Sim Equal to the radius R of the intermediate section obtained by the measurement in step two Exp ；
Step four:
after the numerical simulation is finished, the numerical simulation software gives node data of each node of the middle grid section under K output states of the simulation sample, and the node data comprises equivalent strain epsilon under the corresponding output state 0 Axial strain epsilon z Equivalent strain rate
Axial strain rate component
Radial strain rate component
Component of hoop strain rate
And a radial coordinate value r;
meanwhile, the numerical simulation software provides node data of each node of the adjacent grid section under the K output states of the simulation sample, and the node data comprises equivalent strain epsilon under the corresponding output state 1 Equivalent strain rate
And a shear strain rate component
The adjacent grid section is an upper layer or a lower layer grid section corresponding to the middle grid section in the output state;
step five: setting the thermal compression true equivalent stress function as:
wherein the equivalent strain ε, the equivalent strain rate
m is an integer of 3 or more; a. the ij Is an unknown coefficient, i and j are integers which are more than or equal to zero and less than or equal to m;
substituting the equivalent strain and the equivalent strain rate of each node of the middle grid section and the adjacent grid sections into the real equivalent stress function under K output states, and calculating the real equivalent stress sigma of each node of the corresponding middle grid section 0 And the true equivalent stress sigma of each node of the adjacent grid section 1 (ii) a Wherein σ 0 And σ 1 Is composed of unknown coefficients A ij An algebraic expression of (a);
step six: solving the axial stress sigma of each node of the middle grid section under K output states according to the increment theory of elastic-plastic deformation, a balance differential equation and boundary conditions z The solving formula is:
wherein σ r For radial stress, σ θ Is hoop stress, σ' z 、σ′ r 、σ′ θ The stress offsets corresponding to three directions, the average stress sigma m ＝(σ z +σ r +σ θ )/3；τ zr Shear stress in the radial direction for acting on the adjacent grid section; dh is the axial distance between each node of the section of the middle grid and the corresponding node of the section of the adjacent grid, and the solution formula contains an unknown coefficient A ij ；
Step seven: subjecting the axial stress sigma of step six to z Performing double integration along the annular direction and the radial direction to obtain the axial load F theoretically calculated by the middle grid section in each output state K,Sim ：
F K,Sim ＝∫∫σ z drdθ；
Step eight: by the formula F K,Sim ＝∫∫σ z drdθ＝F K,Exp Solving to obtain A ij Value of A, then ij Value substitution into the true equivalent stress function
The preparation method comprises the following steps of (1) performing;
step nine: when the equivalent strain and the equivalent strain rate are given, a corrected stress-strain curve can be obtained.
15. A method for correcting thermal compression stress-strain curve using numerical simulation according to claim 13 or 14, wherein: in the sixth step, the radial stress sigma is calculated by the equilibrium differential equation r The following were used:
(1) solving the radial stress change rate of each node of the section of the middle grid:
(2) solving the radial stress of each node of the section of the middle grid:
wherein N is the total number of nodes in the radial direction of the sample, and N is R 0 /a+1；σ r (n) is the radial stress at the nth node;
is the radial stress rate of change at the nth node; dr (n) is the distance between the nth node and the (n + 1) th node.
16. A method for correcting thermal compression stress-strain curve using numerical simulation according to claim 13 or 14, wherein: step seven, the axis of the theoretical calculation of the section of the middle grid under each output stateTo a load F K,Sim The specific calculation method is as follows:
(1) will sigma z Summing different cells along the ring:
wherein, F K (n) is the load of the nth unit after axial stress is integrated in the annular 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; sigma z (n) is the axial stress of the nth node;
(2) f is to be K (n) summing along different radial units:
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