CN117786871A - Thermoforming limit diagram prediction method introducing temperature change history - Google Patents
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Abstract
The invention discloses a thermoforming limit diagram prediction method introducing temperature change history, which relates to the technical field of metal plate thermoforming processing and has the technical key points that: in the hot stamping process, the cold punch is in contact with the hot plate, the plate material and air are subjected to radiation heat dissipation for the hot plate and the high-temperature plate material, so that the temperature of the high-temperature plate material is reduced, the temperature distribution of the plate material is uneven in the hot forming process, the hot forming limit prediction of metal is inaccurate, the temperature change history has important influence on the plate material forming process, the influence of the plate material temperature change process on the hot forming limit diagram is better analyzed, the forming performance of the material, the failure problem in the prediction stamping process and the like are evaluated, and the method for combining the stress-strain relation, the yield criterion, the instability theory and the like of the material with a temperature change model is provided.
Description
Technical Field
The invention relates to the technical field of metal sheet thermoforming processing, in particular to a thermoforming limit diagram prediction method introducing temperature change history.
Background
The rapid development of the automobile industry greatly improves the travel efficiency of people and promotes the social development, but simultaneously brings a plurality of safety problems and environmental problems. The light-weight design is realized on the basis of ensuring safety, the problems of automobile fuel consumption and tail gas emission can be effectively reduced, and the automobile is a necessary trend of automobile development in the future. Optimizing the structural design of an automobile, using novel materials and corresponding advanced manufacturing techniques are main methods for realizing light-weight design, and in order to improve the shock resistance and the anti-collision performance of the automobile, the materials selected for structural components of the automobile are inevitably changed towards the direction of light weight and high strength, and high-strength steel, ultrahigh-strength steel, aluminum and magnesium alloy materials are gradually replacing the traditional steel for automobile bodies, and have become an important way for meeting the requirements of weight reduction, emission reduction and safety improvement of automobiles. The ultra-high strength steel plate has poor plastic formability at room temperature, large required stamping force, large rebound quantity after stamping forming and poor dimensional and shape precision of parts, so that the conventional cold stamping forming process is difficult to solve the difficult problem of the high strength steel plate in automobile body manufacturing, and the hot stamping forming process is generally adopted to deform the high strength steel plate to obtain qualified parts.
Hot stamping is a high temperature deformation process of sheet metal, and the final forming quality of the sheet metal will be affected by a number of process factors. In addition to the edge pressing force which needs to be considered in the traditional cold stamping, the influence of factors such as high-temperature friction, stamping speed, initial forming temperature and the like needs to be additionally considered, on the other hand, at high temperature, the mechanical properties of the metal material show obvious strain rate and temperature correlation, so how to accurately predict the formability of the plate at high temperature is a problem which needs to be solved in the application of the hot stamping technology. The forming limit is an important performance index and process parameter in the field of sheet forming, reflecting the maximum degree of deformation that a sheet can achieve before plastic destabilization. The most common and intuitive method used at present is a Forming Limit Diagram (FLD), wherein the FLD is a strip-shaped area formed by local instability limit real strains epsilon 1 and epsilon 2 of a plate under different strain paths, comprehensively reflects the forming limit of the plate under the action of unidirectional tensile stress, bidirectional tensile stress, plane strain and intermediate state, and the forming limit diagram is the simplest and intuitive method for judging and evaluating the forming capability of the plate, and is also a common criterion for judging failure in punching numerical simulation.
The FLD determined by standard experiments is influenced by nonlinearity of a strain path, friction conditions, strain gradients and the like, so that obtaining accurate FLD is a difficult task, while theoretical calculation of FLD can eliminate the influence of the factors, however, the current theory of FLD is limited to isothermal conditions, the deformation process of metal in the actual process is difficult to accurately predict, the conventional related experimental device and method are mainly used for optimizing and improving an M-K method or researching and obtaining isothermal forming limit of a metal plate, and the influence of temperature change history on FLD is not deeply researched, such as the Chinese patent with application number 202110741658.8 is mainly used for improving the M-K theory, so that the calculation efficiency of the FLD theory is improved; another example is the chinese patent application No. 201410076406.8, which discloses a metal sheet hot forming limit experimental apparatus and a testing method, which can prevent heat transfer between a sheet and a punch during an experiment by heating the sheet and the punch in a sealed box, so as to reduce the experimental error, however, forming a steel sheet with variable strength is a non-isothermal process, in an actual hot stamping process, a die is usually at room temperature, so that a high-temperature sheet contacts with the die to generate a severe heat exchange, and thus, the hot stamping forming is a process of continuously changing temperature, while the forming limit obtained by the existing method is obtained at a certain constant temperature, and the differential temperature forming limit of the metal sheet cannot be obtained. In the research of the influence of temperature on FLD, as disclosed in patent (application number is CN 201210192708.2), a simulation prediction method of the transient forming limit of the ultra-high strength steel is disclosed, the transient forming limit of the ultra-high strength steel is predicted by adopting M-K theory, however, the prediction method has no universality, the prediction precision is extremely dependent on the selection of constitutive equation, yield criterion and the like, and the specific experimental result is lacking for verification.
Therefore, although the traditional method for predicting the forming limit diagram can solve the problem of evaluating the forming performance in the hot forming process of part of metal plates, the prediction of the FLD in the metal hot forming process cannot be effectively solved.
Disclosure of Invention
The invention aims to solve the problems and provide a thermal forming limit diagram prediction method introducing temperature change history, which combines stress-strain relation, yield criterion, instability theory and the like of materials with a temperature change model, can simulate the temperature change process in the actual hot stamping process, is used for obtaining a thermal forming curve of a plate in a non-isothermal process, and is used for reasonably designing the thermal forming process to improve the forming quality of a thermal forming part.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
the invention provides a thermoforming limit diagram prediction method introducing temperature change history, which comprises the following steps:
s1, determining a constitutive model of a material, wherein the constitutive model comprises a stress-strain relation, a yield criterion, a hardening rule and mechanical performance parameters of the material at different temperatures;
s2, in the hot stamping process, according to heat transfer generated by the plate, such as contact heat transfer between the plate and a mold and convection between the plate and air, radiating heat to the high-temperature plate and radiating heat to the high-temperature plate, and constructing a change relation of the temperature of the plate along with time and space in the hot forming process by utilizing a thermal equation to form a temperature change model of the plate;
s3, analyzing the relation among variables of stamping speed, die size, male die stroke and plate deformation, and constructing a system theoretical calculation model;
s4, under a specific stress state, combining the constitutive model, the temperature change model, the theoretical calculation model and the instability model, and establishing a thermoforming limit model under a variable temperature condition to predict thermoforming limit; the method comprises the following steps:
s4.1, giving a theoretical calculation model of each item of data initial value of the system according to actual conditions, for example, the stroke of the male die and the strain rate value of the plate are 0, and the initial value of the temperature of the plate is T 0 Giving the punch speed and the die size;
s4.2, calculating mechanical property parameters and stress-strain relation of the material in the material constitutive model at the current temperature according to the temperature T of the plate;
s4.3, in unit time, along with the deformation of the moving plate of the male die, the displacement, the speed and the size of the die of the male die are brought into a theoretical calculation model to obtain a value of a main strain rate in the thermoforming process, and the main strain increment in unit time is further determined;
s4.4, inputting the parameters obtained in the step S4.2 and the step S4.3 into a destabilization model together, calculating data of stress components and secondary strain increment under the current main strain increment, judging whether the material is destabilized according to a destabilization criterion, outputting the strain and temperature if the material is destabilized, entering the step S5 to update the stress state, and continuing the steps S4.5 and S4.6 if the material is not destabilized;
s4.5, inputting the obtained stress component and the data of contact thermal resistance, punch temperature and die size into a temperature change model to output a heat flux coefficient, and further calculating the temperature of the plate material after unit time;
s4.6, updating the temperature of the plate in the step S4.2 by using the temperature value calculated in the step S4.5, and continuing to calculate;
and S5, setting the next stress state, repeating the process in the step S4 until the stress state is 1, outputting strain data under different strain paths and drawing an FLC curve under the condition that the stress state is from 0 to 1.
Further, the heat transfer generated by the sheet in step S2 includes contact heat transfer between the sheet and the mold, convection heat supply between the sheet and air, and radiation heat dissipation of the high-temperature sheet itself.
Further, the constitutive model in step S1 includes defining stress-strain relationships, yield criteria, and hardening models for the material at different temperatures.
Further, the temperature change model in step S2 is formed according to thermal contact conduction, convection and heat radiation, and constructed using newton' S heat equation.
Further, the thermoforming limit model in step S4 is temperature and strain data when the critical state is reached under different strain paths under the non-isothermal condition of the introduced heat transfer simulation, and then a thermoforming limit curve is drawn.
Compared with the prior art, the beneficial effect of this scheme:
the invention provides a prediction method for a thermal forming limit diagram introducing temperature change history, which is a method for combining a stress-strain relation, a yield criterion, a instability theory and the like of a material with a temperature change model, wherein the temperature change history is introduced when the thermal forming limit of a metal plate is predicted, and influences the prediction of the thermal forming limit, and the thermal forming limit obtained by the conventional method is different from the thermal forming limit which is mostly at a certain constant temperature; or the limit strain curves at different temperatures are interpolated to obtain the stress curve, so that the stress curve can better fit the actual situation and has actual engineering application value.
Drawings
FIG. 1 is a schematic illustration of an Nakazima experiment in an embodiment of the invention;
FIG. 2 is a graph of predicted temperature and test temperature for a temperature change model in an embodiment of the invention;
FIG. 3 is a model of an M-K trench in an embodiment of the invention;
FIG. 4 is a flow chart of FLD prediction in an embodiment of the invention;
FIG. 5 is a comparison of FLD predictions and experimental results in an example of the present invention.
Detailed Description
In order that those skilled in the art will better understand the present invention, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings, wherein it is to be understood that the illustrated embodiments are merely exemplary of some, but not all, of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other. The present invention will be described in detail with reference to examples.
Examples:
according to the scheme provided by the embodiment of the invention, as described in the above summary of the invention, a thermoforming limit diagram prediction method introducing temperature change history is provided, comprising the following steps:
step 1, determining a constitutive model of a material, wherein the constitutive model comprises a stress-strain relation, a yield criterion, a hardening rule and mechanical performance parameters of the material at different temperatures;
step 2, in the hot stamping process, according to heat transfer generated by the plate, such as contact heat transfer between the plate and a mold, convection between the plate and air, heat is given to the high-temperature plate and the high-temperature plate radiates heat, and a change relation of the temperature of the plate along with time and space in the hot forming process is constructed by utilizing a thermal equation, so as to form a temperature change model of the plate;
step 3, analyzing the relation among variables of stamping speed, die size, male die stroke and plate deformation, and constructing a system theoretical calculation model;
and 4, under a specific stress state, combining the constitutive model, the temperature change model, the theoretical calculation model and the instability model, and establishing a thermoforming limit model under a variable temperature condition to predict the thermoforming limit. The method comprises the following steps:
step 4.1, endowing each item of theoretical calculation model of the system according to actual conditionsInitial values of data, e.g. punch travel and sheet strain values of 0, sheet temperature initial value of T 0 Giving the punch speed and the die size;
step 4.2, calculating mechanical property parameters and stress-strain relation of the material in the material constitutive model at the current temperature according to the temperature T of the plate;
step 4.3, in unit time, along with the deformation of the moving plate of the male die, the displacement, the speed and the size of the die of the male die are brought into a theoretical calculation model to obtain a value of a main strain rate in the thermoforming process, and the main strain increment in unit time is further determined;
step 4.4, inputting the parameters obtained in the step 4.2 and the step 4.3 into a destabilization model together, calculating data such as stress components, secondary strain increments and the like under the current main strain increment, judging whether the material is destabilized according to a destabilization criterion, outputting the strain magnitude and the temperature magnitude and entering a step 5 to update the stress state if the material is destabilized, and continuing the steps 4.5 and 4.6 if the material is not destabilized;
step 4.5, inputting the obtained stress component into a temperature change model in combination with data such as contact thermal resistance, punch temperature, die size and the like to output a heat flux coefficient, and further calculating the temperature of the plate after unit time;
and 4.6, updating the temperature of the plate in the step 4.2 by using the temperature value calculated in the step 4.5, and continuing to calculate.
And 5, setting the next stress state, repeating the process in the step 4 until the stress state is 1, and outputting the strain data under different strain paths and drawing the FLC curve under the condition that the stress state is from 0 to 1.
The following is a specific implementation of the embodiment of the present invention:
the invention relates to a method for introducing temperature change history when predicting a metal thermoforming limit curve, which can combine different constitutive equations, instability theory, yield criteria and the like.
(1) Constitutive model for determining high-strength steel
The constitutive model of the high-strength steel comprises a stress-strain relation, a yield criterion, a hardening rule and the like, the temperature of the hot forming process of the high-strength steel is 600-800 ℃, the constitutive equation of the high-strength steel also changes along with the change of the temperature, and according to the past experience, under the action of considering the hardening rule, the constitutive equation of the high-strength steel can be expressed as the following formula:
the parameters n, m and n1 respectively represent a hardening index, a strain rate sensitivity coefficient and a softening compensation coefficient, can reflect the mechanical properties of the material, and only depend on the characteristics of the material and the temperature of the plate material, and serve as the performance parameters of the material to represent the mechanical properties at the current temperature. The relationship with temperature is as follows:
n(T)＝0.065(T/100)-0.217
n 1 (T)＝0.67(T/100) 2 -9.21(T/100)+29.628
m(T)＝0.226-0.011(T/100)
K(T)＝1287.7-51(T/100)；
the yield criterion used for high strength steel is Hill48 anisotropic yield criterion, the anisotropy axes are denoted 1, 2 and 3, and the equations are shown below:
where F, G, H and N are functions of the anisotropy coefficient r. The parameter F is equal to G and can be expressed as 1/(1-r). H and N are equal to r/(1-r) and (1-2 r)/(1-r), respectively, wherein r is the thickness anisotropy coefficient, and the ratio of the transverse strain to the thickness strain of the plate in the unidirectional tensile test is calculated.
(2) Considering heat transfer generated by a plate in the hot stamping process, constructing a change relation of the temperature of the plate with time and space in the hot forming process by utilizing a thermal equation, and forming a temperature change model of the plate;
taking the Nakazima experimental procedure as an example, which is essentially a hemispherical rigid punch bulging experiment, an experimental diagram is shown in fig. 1. A model of the temperature change during thermoforming was constructed on the basis of this experiment.
The heat radiation and thermal contact conduction which are smaller in value are ignored, and the heat radiation and thermal contact conduction respectively occur on the upper surface and the lower surface of the plate, so that the change relation of the temperature of the plate along with time and space in the thermoforming process is constructed by utilizing a thermal equation, and a temperature change model of the plate is formed.
The heat transfer formula for a sheet can be expressed as:
θ∈(0,α)
t∈(0,d/v)；
wherein T represents the Kelvin temperature of the plate, h θ Represents the heat flux at point (D, θ). The parameters ρ, λ and c represent the sheet density, thermal conductivity and specific heat capacity, respectively.
Since the damage of the sheet material in the thermoforming process mainly occurs in the pole region, to simplify the temperature change model, the center part (D, 0) of the sheet material is selected for research, and the above formula can be simplified as follows:
t∈(0,d/v)；
wherein the parameters ρ, λ and c represent the sheet density, thermal conductivity and specific heat capacity, respectively, and δ represents the plate thickness, the above amounts being the determination amounts, the key being the determination of the heat flux hθ at (D, θ), based on which the change of temperature with time can be quantitatively described.
The heat flux hθ can be expressed as a heat radiation coefficient h θ-Uppe r and heat conductivity h θ-Punch And (3) summing.
h θ ＝h θ-Upper +h θ-Punch ；
The calculation formula of the two emissivity coefficients is as follows:
X θ -t op +X θ-die ＝1；
wherein TCR is contact thermal resistance, is defined as a function of positive stress in the thickness direction, sigma 1, sigma 2, sigma 3 are stress components, kappa is Stefan-Boltzmann constant, and xi represents emissivity coefficient of the metal plate. X represents the radiation visual angle coefficient, and the subscripts respectively represent the top surface and the inner surface, so that the temperature change of the plate can be calculated by determining various parameters and stress components of the plate, and the construction of a plate temperature change model is completed.
As shown in fig. 2, which is a comparison of the final temperature reached by the Nakazima experiment under different strain paths with the actual temperature of the experiment simulated by using a temperature variation model.
Analysis shows that the final temperatures reached by different strain paths are different, the final temperatures in the plane strain, the uniaxial stress and the balanced biaxial stress states are 787 ℃, 781 ℃ and 770 ℃, and the final temperatures are matched with experimental data, so that the reliability of a temperature change model is reflected, and the reason for analyzing the existence of errors is as follows:
1) The temperature change in the central region of the plate is estimated by equation. However, the necked down grid in the experiment was not precisely centered in the plate due to friction and uneven temperature distribution.
2) Sheet strain rate during Nakazima experiments is dependent on the press speed. When necking occurs during stretching, the necking grid prediction process takes longer.
(3) Through theoretical analysis, the relation among various parameters in Nakazima experiments, such as stamping speed, die size, male die stroke, plate deformation and other variables is analyzed, and a system theoretical calculation model is constructed;
the parameters in fig. 1 are as follows:
d＝φtanα-D secα+D
l＝2(φsecα-D tanα+Dα)
where d represents punch displacement, l represents sheet length, v represents punch speed, ε 1 represents the main strain rate.
(4) And combining the constitutive model, the temperature change model, the theoretical calculation model and the instability model to establish a hot forming limit model of the variable-temperature high-strength steel. In this embodiment, the destabilizing model is an M-K destabilizing model.
And 4.1, endowing a system theoretical calculation model with various data initial values according to actual conditions, endowing a male die stroke, a plate strain value and a main strain increment of 0, and enabling the initial temperature of the plate to be about 820 ℃. The punch speed was given as 10mm/s for stretching the hot sheet, and the die size was given as appropriate, providing D as 50mm and Φ as 51mm.
Step 4.2, calculating mechanical property parameters and stress-strain relation of the material in the material constitutive model at the current temperature according to the temperature T of the plate;
step 4.3, in unit time, along with the deformation of the moving plate of the male die, the displacement, the speed and the size of the die of the male die are brought into a theoretical calculation model to obtain a value of a main strain rate in the thermoforming process, and the main strain increment in unit time is further determined;
and 4.4, inputting the parameters obtained in the step 4.2 and the step 4.3 into an M-K instability model together, and obtaining stress strain data under the current condition. A schematic of the M-K destabilization model is shown in fig. 3.
Existence of M-K instability model and principal axisThe narrow band of corner defects, which has a uniform area a and a defect area b, can predict the fatigue life of the plate at a certain temperature to obtain a forming limit curve.
For the homogeneous zone a and the defect zone b, there are three assumptions, namely geometrical defects, force balance and deformation coordination, the relationship is as follows:
f 0 ＝δ 0 b /δ 0 a
with the increase of stress, plastic strain is generated in the uniform region and the defect region, the plastic strain increment in the defect region is larger than that in the uniform region, when the ratio of the plastic strain increment reaches a critical value, the material is considered to reach a concentrated unstability state, and the critical strain values under different strain paths are plotted on a maximum-minimum strain graph by using a curve, so that a steady-state thermoforming curve can be obtained.
Calculating the stress component, the secondary strain increment and other data under the current main strain increment, judging whether the material is unstable or not according to the instability criterion, outputting the strain and temperature if the material is unstable, entering the step 5 to update the stress state, and continuing the step 4.5 if the material is not unstable;
step 4.5, inputting the obtained stress component into a temperature change model by combining the data such as contact thermal resistance, punch temperature, die size and the like to output a heat flux coefficient, and further calculating the temperature of the plate material after unit time;
the temperature of the changed plate is input into the constitutive model, the mechanical property and stress-strain relation of the plate at the current temperature are calculated, the mechanical property and stress-strain relation and the changed main strain increment are input into the M-K destabilization model together, the temperature of the plate in the next state is obtained, the above processes are repeated until the plate destabilization is judged in the destabilization model, and the temperature and strain data at the moment are output. The above process may be explained by the FLD prediction flowchart as shown in fig. 4.
(5) Setting the next stress state, repeating the process in the step 4 until the stress state is 1, and under the condition that the stress state is from 0 to 1, drawing the obtained strain data in an FLD graph, wherein the maximum and minimum main strains of the uniform region in the M-K instability model are points on a forming limit curve under the corresponding strain path, different strain paths are realized by changing stress ratios, the final state marks under the different strain paths are that the plastic strain increment of two regions in the M-K instability model reaches a critical value, drawing the critical strain values under the different strain paths in the maximum and minimum main strain diagram to be a steady-state thermoforming limit curve, the time for reaching the critical state corresponding to the different strain paths is different, and the final temperature is also different, and the final temperature corresponding to the different paths should be marked on the forming limit curve.
Comparing the data at the constant temperature of 750 ℃ and 775 ℃ and the data at 800 ℃ with experimental data, as shown in fig. 5, the fact that the sheet temperature data change in the stretching process cannot be fit with the experimental data is found, the abnormal phenomenon that the limit strain of the experimental data 772 ℃ is larger than the limit strain at the constant temperature of 775 ℃ appears, the model data invented by the patent are mapped in the graph, the final temperature of the predicted result and the corresponding limit strain conform to the test data for the experimental strain path, the forming limit of the sheet can be influenced by the temperature history change in the theoretical interpretation, and the influence of the temperature change history in the sheet thermoforming process is well explained.
The above specific embodiments are provided for illustrative purposes only and are not intended to limit the invention, and modifications, no inventive contribution, will be made to the embodiments by those skilled in the art after having read the present specification, as long as they are within the scope of the patent statutes.
Claims (5)
1. A thermoforming limit diagram prediction method introducing temperature change history is characterized in that: the method comprises the following steps:
s1, determining a constitutive model of a material, wherein the constitutive model comprises a stress-strain relation, a yield criterion, a hardening rule and mechanical performance parameters of the material at different temperatures;
s2, in the hot stamping process, according to heat transfer generated by the plate, such as contact heat transfer between the plate and a mold and convection between the plate and air, radiating heat to the high-temperature plate and radiating heat to the high-temperature plate, and constructing a change relation of the temperature of the plate along with time and space in the hot forming process by utilizing a thermal equation to form a temperature change model of the plate;
s3, analyzing the relation among variables of stamping speed, die size, male die stroke and plate deformation, and constructing a system theoretical calculation model;
s4, under a specific stress state, combining the constitutive model, the temperature change model, the theoretical calculation model and the instability model, and establishing a thermoforming limit model under a variable temperature condition to predict thermoforming limit; the method comprises the following steps:
s4.1, giving a theoretical calculation model of each item of data initial value, such as a punch stroke value and a plate strain rate value of 0, a plate temperature initial value of T0, and giving punch speed and die size according to actual conditions;
s4.2, calculating mechanical property parameters and stress-strain relation of the material in the material constitutive model at the current temperature according to the temperature T of the plate;
s4.3, in unit time, along with the deformation of the moving plate of the male die, the displacement, the speed and the size of the die of the male die are brought into a theoretical calculation model to obtain a value of a main strain rate in the thermoforming process, and the main strain increment in unit time is further determined;
s4.4, inputting the parameters obtained in the step S4.2 and the step S4.3 into a destabilization model together, calculating data of stress components and secondary strain increment under the current main strain increment, judging whether the material is destabilized according to a destabilization criterion, outputting the strain and temperature if the material is destabilized, entering the step S5 to update the stress state, and continuing the steps S4.5 and S4.6 if the material is not destabilized;
s4.5, inputting the obtained stress component and the data of contact thermal resistance, punch temperature and die size into a temperature change model to output a heat flux coefficient, and further calculating the temperature of the plate material after unit time;
s4.6, updating the temperature of the plate in the step S4.2 by using the temperature value calculated in the step S4.5, and continuing to calculate;
and S5, setting the next stress state, repeating the process in the step S4 until the stress state is 1, outputting strain data under different strain paths and drawing an FLC curve under the condition that the stress state is from 0 to 1.
2. A method of predicting a thermoforming limit map incorporating a temperature change history as claimed in claim 1, wherein: the heat transfer generated by the plate in the step S2 comprises contact heat transfer between the plate and the mold, convection heat supply between the plate and air and radiation heat dissipation of the high-temperature plate.
3. A method of predicting a thermoforming limit map incorporating a temperature change history as claimed in claim 1, wherein: the constitutive model in step S1 includes defining stress-strain relationships, yield criteria and hardening models for the material at different temperatures.
4. A method of predicting a thermoforming limit map incorporating a temperature change history as claimed in claim 1, wherein: the temperature change model in step S2 is formed according to thermal contact conduction, convection and heat radiation, and constructed using newton' S heat equation.
5. A method of predicting a thermoforming limit map incorporating a temperature change history as claimed in claim 1, wherein: the thermoforming limit model in step S4 is temperature and strain data when the different strain paths reach the critical state under the non-isothermal condition of the introduced heat transfer simulation, and then a thermoforming limit curve is drawn.
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