CN117783475A - Method for predicting rheological stress in thermal deformation process of Ti80 titanium alloy - Google Patents
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Abstract
The invention relates to a method for predicting rheological stress in a Ti80 titanium alloy thermal deformation process, belongs to the technical field of titanium alloy thermal processing stress analysis, and is used for providing guidance and assistance for actual production of titanium alloy. A method of predicting rheological stress during thermal deformation of a Ti80 titanium alloy, comprising: selecting a sample and preparing a thermal compression sample; performing a thermal compression experiment; drawing stress-strain curves of the test sample at different deformation temperatures and different strain rates, and obtaining change curves of peak stress at different deformation temperatures and different strain rates according to the stress-strain curves; and simulating the change rule of peak stress by using an Arrhenius model with hyperbolic sine shape, and establishing an constitutive equation for predicting rheological stress in the thermal deformation process of the Ti80 titanium alloy. The method realizes the construction of the rheological stress model in the thermal deformation behavior of the Ti80 titanium alloy material, has a guiding effect on the optimization of process parameters, and can provide guidance and help for actual production.
Description
Technical Field
The invention relates to the technical field of titanium alloy hot working stress analysis, in particular to a method for predicting rheological stress in a Ti80 titanium alloy hot deformation process.
Background
Stress-strain curves under different heat deformation parameters show different forms and can reflect different deformation characteristics of the alloy. Therefore, in the actual production process, the research on the thermal deformation flow stress of the titanium alloy has a guiding effect on the optimization of process parameters, and the influence factors of the rheological stress are various, such as deformation temperature, strain quantity, strain rate and original tissue morphology of the material. The constitutive model of the material can reflect the relation between the rheological stress and technological parameters such as deformation temperature, strain rate and the like. A reliable titanium alloy thermal deformation constitutive equation can provide help for optimizing titanium alloy thermal deformation parameters, and meanwhile simulation and prediction of a titanium alloy plastic deformation process can be carried out.
In the thermal deformation process of the titanium alloy, along with the evolution process of a complex microstructure, besides the common dynamic recovery, dynamic recrystallization, grain growth and other processes in the metal crystal, the phase transformation process, alpha phase spheroidization and the like can also occur, so that different structure states can be obtained, and the comprehensive performance of the material is affected. The complex deformation behavior also presents difficulties in the selection of process parameters during the actual hot working process. Therefore, the evolution rule of the thermal deformation structure of the titanium alloy needs to be mastered, and guidance and assistance are provided for actual production.
Disclosure of Invention
In view of the above analysis, embodiments of the present invention aim to provide a method for predicting rheological stress during thermal deformation of Ti80 titanium alloys, which is used to provide guidance and assistance for actual production of titanium alloys.
The aim of the invention is mainly realized by the following technical scheme:
a method for predicting rheological stress in a Ti80 titanium alloy hot deformation process, comprising the steps of:
s1, selecting a thermal compression sample, and manufacturing: selecting a Ti80 plate to be predicted as a sample, and processing the sample into a cylindrical thermal compression sample with the diameter of phi 10 multiplied by 15mm by using linear cutting equipment and a numerical control lathe;
s2, thermal compression experiment: performing a thermal simulation compression experiment on the thermal compression sample by using a Gleeble-3800 thermal simulation testing machine, and setting deformation temperature, strain rate and deformation amount to obtain rheological pressures at different deformation temperatures and different strain rates;
s3: drawing stress-strain curves of the test sample at different deformation temperatures and different strain rates, and obtaining change curves of peak stress at different deformation temperatures and different strain rates according to the stress-strain curves;
s4: and simulating the change rule of peak stress by using an Arrhenius model with hyperbolic sine shape, and establishing an constitutive equation for predicting rheological stress in the thermal deformation process of the Ti80 titanium alloy.
Further, in step S2, the deformation temperature is 820-940 ℃, and the strain rate is 0.01S -1 ～50s -1 The deformation is 60% -70%.
Further, in step S2, the thermal simulation compression experiment is: heating the thermal compression sample to the deformation temperature at a heating speed of 8-12 ℃/s, preserving heat for 3-5min, then carrying out thermal compression experiment at the strain speed, and cooling with water.
Further, step S4 includes building an Arrhenius model of hyperbolic sine type, an Arrhenius model of power function form and an Arrhenius model of exponential form, and then taking logarithms of the Arrhenius model of power function form and the Arrhenius model of exponential form on two sides respectively to obtain a power function logarithm form of the Arrhenius model and an exponent logarithm form of the Arrhenius model:
wherein, the formula (1) is an Arrhenius model with hyperbolic sine shape;
the formula (2) is a power function form of an Arrhenius model;
the formula (3) is an exponential form of the Arrhenius model;
the formula (4) is a logarithmic form of a power function of an Arrhenius model;
the formula (5) is the exponential of the Arrhenius model in logarithmic form;
n 1 ，n 2 is a work hardening index; alpha, beta and A are thermal deformation material constants; r is the universal gas constant (8.314J/(mol.K)),at strain rate, T is deformation temperature, sigma p And Q is thermal deformation activation energy.
Further, step S4 further includes obtaining corresponding strain rate, deformation temperature and peak stress according to the change curves of peak stress at different deformation temperatures and different strain rates in step S3, and performing linear fitting by taking a logarithmic form according to the power function of the Arrhenius model to obtain a linear regression curve slope, i.e., n at different deformation temperatures and different strain rates 1 ；
Performing linear fitting on a scatter diagram in a logarithmic form according to the index of the Arrhenius model, wherein the slope of the obtained linear regression curve is the beta value under different deformation temperatures and different strain rates;
according to alpha = beta/n 1 And calculating to obtain an alpha value.
Further, step S4 further includes taking the logarithm of two sides of the hyperbolic sine-type Arrhenius model, obtaining a logarithmic form of the hyperbolic sine-type Arrhenius model, substituting the α value into the logarithmic form of the hyperbolic sine-type Arrhenius model, and makingPerforming linear fitting on the scatter diagram, wherein the slope of the linear regression curve is n2:
wherein the Arrhenius model with the formula (6) being hyperbolic sine is in logarithmic form.
Further, step S4 further includes taking the logarithmic form of the hyperbolic sine-type Arrhenius model to obtain a hyperbolic sine-type Arrhenius model polynomial, and performing ln [ sinh (ασ p )]-performing linear fitting on a 1000/T scatter diagram, substituting a linear regression curve slope into an Arrhenius model transfer polynomial of hyperbolic sine type, and obtaining thermal deformation activation energy Q under different deformation temperatures and different strain rates:
wherein, formula (7) is an Arrhenius model polynomial of hyperbolic sine type.
Further, step S4 further includes introducing a Zener-hollkon parameter, and substituting the Zener-hollkon parameter into the hyperbolic sinusoidal Arrhenius model polynomial to obtain a relation between the peak stress and the Z parameter of the Ti80 titanium alloy:
lnZ＝lnA+n 2 ln[sinh(ασ p )] (9)
wherein formula (8) is a Zener-holomon parameter;
equation (9) is a relation between the peak stress of Ti80 titanium alloy and Z parameter.
Further, step S4 further includes obtaining corresponding strain rate, deformation temperature and peak stress according to the change curves of the peak stress at different deformation temperatures and different strain rates in step S3, performing linear fitting according to a scatter diagram made according to the relation between the peak stress and the Z parameter of the Ti80 titanium alloy, and obtaining a value a by calculating the longitudinal intercept of the obtained linear regression curve as lnA.
Further, step S4 also includes calculating n as calculated by any one of claims 1-9 1 、n 2 And substituting the alpha, beta and A values into the hyperbolic sine Arrhenius model to obtain an constitutive equation of rheological stress in the thermal deformation process of the Ti80 titanium alloy.
Compared with the prior art, the invention has at least one of the following beneficial effects:
1. according to the invention, rheological stress in the thermal deformation process of the Ti80 titanium alloy is researched by a thermal simulation experiment mode; the method can help to optimize the thermal deformation parameters of the titanium alloy by establishing the constitutive model of the material, and can simulate and predict the plastic deformation process of the titanium alloy. The invention realizes the construction of the rheological stress model in the thermal deformation behavior of the Ti80 titanium alloy material, is important for grasping the evolution rule of the thermal deformation structure of the titanium alloy, has a guiding function for optimizing the technological parameters, and can provide guidance and assistance for actual production.
2. The method can flexibly select the deformation temperature and the strain rate according to actual conditions, so that the simulation of all working condition conditions in the Ti80 production process can be realized, and the method has universality; meanwhile, the method is not limited to Ti80 titanium alloy, and can be applied to other titanium alloys so as to predict rheological stress behavior in the thermal deformation process of the titanium alloy.
In the invention, the technical schemes can be mutually combined to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to refer to like parts throughout the several views.
FIG. 1 is a graph showing the peak stress at different deformation temperatures and different strain rates for an example;
FIG. 2 is a comparison of predicted values and experimental measurements of rheological stress at different deformation temperatures and different strain rates for the examples.
Detailed Description
Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form a part hereof, and together with the description serve to explain the principles of the invention, and are not intended to limit the scope of the invention.
The invention provides a method for predicting rheological stress in a Ti80 titanium alloy thermal deformation process, which comprises the following steps:
s1, selecting a thermal compression sample, and manufacturing: selecting a Ti80 plate to be predicted as a sample, and processing the sample into a cylindrical thermal compression sample with the diameter of phi 10 multiplied by 15mm by using linear cutting equipment and a numerical control lathe;
s2, thermal compression experiment: performing a thermal simulation compression experiment on the thermal compression sample by using a Gleeble-3800 thermal simulation testing machine, and setting deformation temperature, strain rate and deformation amount to obtain rheological pressures at different deformation temperatures and different strain rates;
s3: drawing stress-strain curves of the test sample at different deformation temperatures and different strain rates, and obtaining change curves of peak stress at different deformation temperatures and different strain rates according to the stress-strain curves;
s4: and simulating the change rule of peak stress by using an Arrhenius model with hyperbolic sine shape, and establishing an constitutive equation for predicting rheological stress in the thermal deformation process of the Ti80 titanium alloy.
Specifically, in step S2, the deformation temperature is 820-940 ℃, and the strain rate is 0.01S -1 ～50s -1 The deformation is 60% -70%. In the experimental process, the sample is heated to the experimental deformation temperature at a heating speed of 8-12 ℃/s, and the temperature is kept for 3-5min to ensure that the internal temperature of the sample is uniformly distributed, so that the internal tissue of the sample is uniform; then, thermal compression experiments were performed at different strain rates, and water cooled to fix the high temperature deformed tissue.
Specifically, in step S4, a hyperbolic sinusoidal Arrhenius model is used to simulate the change rule of peak stress, and an constitutive equation for predicting rheological stress in the thermal deformation process of the Ti80 titanium alloy is established, which comprises the following steps:
the hyperbolic sine type Arrhenius model is expressed by a formula (1), and the formula (2) and the formula (3) are expressed by an Arrhenius model in a power function form and an exponential form:
wherein n is 1 ，n 2 Is a work hardening index; alpha, beta and A are thermal deformation material constants; r is the universal gas constant (8.314J/(mol.K)),at strain rate, T is deformation temperature, sigma p And Q is thermal deformation activation energy.
Taking the logarithm of the two sides of the formula (2) and the formula (3) to obtain the formula (4) and the formula (5):
obtaining corresponding strain rate, deformation temperature and peak stress according to the change curves of the peak stress at different deformation temperatures and different strain rates in the step S3, performing linear fitting according to the scatter diagram of the formula (4) and the formula (5), and obtaining the slope of the linear regression curve, namely n at different deformation temperatures and different strain rates 1 And beta value.
According to alpha = beta/n 1 And calculating to obtain an alpha value.
Taking the logarithm of the two sides of the formula (1) to obtain a formula (6):
substituting the alpha value obtained by calculation into formula (6) to makePerforming linear fitting on the scatter diagram, wherein the slope of the linear regression curve is n 2 。
Obtaining a formula (7) by shifting the formula (6), and performing ln [ sinh (alpha sigma) p )]-performing linear fitting on the 1000/T scatter diagram, obtaining the slope of a linear regression curve, substituting the slope into the curve (7), and obtaining the thermal deformation activation energy Q under different deformation temperatures and different strain rates.
To describe the combined effect of different deformation temperatures and different strain rates on the flow stress of Ti80 titanium alloys, a Zener-hollloon parameter was introduced to verify the accuracy of the heat distortion equation:
substituting formula (8) into formula (7) to obtain formula (9) can represent the relation between the peak stress of Ti80 titanium alloy and Z parameter:
lnZ＝lnA+n 2 ln[sinh(ασ p )] (9)
and (3) obtaining corresponding strain rate, deformation temperature and peak stress according to the change curves of the peak stress at different deformation temperatures and different strain rates in the step (S3), performing linear fitting by making a scatter diagram according to the formula (9), obtaining a linear regression curve with a longitudinal intercept of lnA, and obtaining an A value through calculation.
N obtained by the above calculation 1 、n 2 Substituting the alpha, beta and A values into the formula (1) to obtain an constitutive equation of the rheological stress in the thermal deformation process of the Ti80 titanium alloy. The predicted values of the corresponding peak stress under different deformation temperatures and strain rates can be obtained by substituting the different deformation temperatures and strain rates into the equation, and can be used for predicting the rheological stress in the thermal deformation process of the Ti80 titanium alloy.
The method can flexibly select the deformation temperature and the strain rate according to actual conditions, so that the simulation of all working condition conditions in the Ti80 production process can be realized, and the method has universality; meanwhile, the method is not limited to Ti80 titanium alloy, and can be applied to other titanium alloys so as to predict rheological stress behavior in the thermal deformation process of the titanium alloy.
Examples
In the embodiment, ti80 titanium alloy plates produced by a certain factory are selected, and the specific components are as follows: 6.2% of Al, 2.9% of Nb, 0.85% of Mo, 2.3% of Zr, 0.051% of O, not more than 0.01% of C, not more than 0.01% of H, not more than 0.01% of N, and the balance of Ti and unavoidable impurities.
The method provided by the invention is used for predicting the rheological stress in the thermal deformation process of the Ti80 titanium alloy plate, and comprises the following steps:
s1, selecting a thermal compression sample, and manufacturing: selecting the Ti80 plate as a sample, and processing the sample into a cylindrical thermal compression sample with the diameter of phi 10 multiplied by 15mm by using linear cutting equipment and a numerical control lathe;
s2, thermal compression experiment: performing a thermal simulation compression experiment on the thermal compression sample by using a Gleeble-3800 thermal simulation testing machine, and setting deformation temperature, strain rate and deformation amount to obtain rheological pressures at different deformation temperatures and different strain rates;
wherein the deformation temperature is 820 ℃, 850 ℃, 880 ℃, 910 ℃ and 940 ℃; strain rate of 0.01s -1 、0.1s -1 、1s -1 、10s -1 The deformation is 60%;
in the experimental process, the sample is heated to the experimental deformation temperature at the heating speed of 10 ℃/s, and the temperature is kept for 3min to ensure that the internal temperature of the sample is uniformly distributed, so that the internal tissue of the sample is uniform; then, a thermal compression experiment is carried out at a set strain rate, and water cooling is carried out to fix the high-temperature deformed tissue.
S3: drawing stress-strain curves of the test sample at different deformation temperatures and different strain rates, and obtaining change curves of peak stress at different deformation temperatures and different strain rates according to the stress-strain curves, as shown in figure 1;
s4: simulating a change rule of peak stress by using an Arrhenius model with hyperbolic sine shape, and establishing an constitutive equation for predicting rheological stress in the thermal deformation process of the Ti80 titanium alloy, wherein the constitutive equation comprises the following steps:
the hyperbolic sine type Arrhenius model is expressed by a formula (1), and the formula (2) and the formula (3) are expressed by an Arrhenius model in a power function form and an exponential form:
wherein n is 1 ，n 2 Is a work hardening index; alpha, beta and A are thermal deformation material constants; r is the universal gas constant (8.314J/(mol.K)),at strain rate, T is deformation temperature, sigma p And Q is thermal deformation activation energy.
Taking the logarithm of the two sides of the formula (2) and the formula (3) to obtain the formula (4) and the formula (5):
obtaining corresponding strain rate, deformation temperature and peak stress according to the change curves of the peak stress at different deformation temperatures and different strain rates in the step S3, performing linear fitting according to the scatter diagram of the formula (4) and the formula (5), and obtaining the slope of the linear regression curve, namely n at different deformation temperatures and different strain rates 1 And beta value, n is measured 1 ＝6.598、β＝0.0561。
According to alpha = beta/n 1 The alpha value is calculated, alpha value=0.0085.
Taking the logarithm of the two sides of the formula (1) to obtain a formula (6):
substituting the alpha value obtained by calculation into formula (6) to makePerforming linear fitting on the scatter diagram, wherein the slope of the linear regression curve is n 2 N is measured 2 ＝4.79。
Obtaining a formula (7) by shifting the formula (6), and performing ln [ sinh (alpha sigma) p )]-1000/T scatter diagram is subjected to linear fitting, linear regression curve slope is obtained and then substituted into the formula (7), thermal deformation activation energy Q under different deformation temperatures and different strain rates is obtained, and average value is obtainedQ＝454.275kJ/mol。
The Zener-Hollomon parameter was introduced to verify the accuracy of the heat distortion equation:
substituting formula (8) into formula (7) to obtain formula (9) can represent the relation between the peak stress of Ti80 titanium alloy and Z parameter:
lnZ＝lnA+n 2 ln[sinh(ασ p )] (9)
obtaining corresponding strain rate, deformation temperature and peak stress according to the change curves of the peak stress at different deformation temperatures and different strain rates in the step S3, performing linear fitting according to a scatter diagram of formula (9), obtaining a linear regression curve with a longitudinal intercept of lnA, and obtaining an A value by calculation, wherein the A value is=2.12x10 19 。
N obtained by the above calculation 1 、n 2 Substituting alpha, beta and A values into the formula (1) to obtain the Ti80 titanium alloy with the strain rate of 0.01s at the temperature of 820-940 DEG C -1 ～10s -1 Constitutive equation of rheological stress; the deformation temperature and the strain rate are substituted into the equation to obtain the predicted values of the rheological stress under different deformation temperatures and strain rates, and the fitting relation between the predicted values and the actual measured values is good as shown in figure 2.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.
Claims (10)
1. A method for predicting rheological stress during thermal deformation of a Ti80 titanium alloy, comprising the steps of:
s1, selecting a thermal compression sample, and manufacturing: selecting a Ti80 plate to be predicted as a sample, and processing the sample into a cylindrical thermal compression sample with the diameter of phi 10 multiplied by 15mm by using linear cutting equipment and a numerical control lathe;
s2, thermal compression experiment: performing a thermal simulation compression experiment on the thermal compression sample by using a Gleeble-3800 thermal simulation testing machine, and setting deformation temperature, strain rate and deformation amount to obtain rheological pressures at different deformation temperatures and different strain rates;
s3: drawing stress-strain curves of the test sample at different deformation temperatures and different strain rates, and obtaining change curves of peak stress at different deformation temperatures and different strain rates according to the stress-strain curves;
s4: and simulating the change rule of peak stress by using an Arrhenius model with hyperbolic sine shape, and establishing an constitutive equation for predicting rheological stress in the thermal deformation process of the Ti80 titanium alloy.
2. The method for predicting the rheological stress during thermal deformation of a Ti80 titanium alloy according to claim 1, wherein in the step S2, the deformation temperature is 820-940 ℃ and the strain rate is 0.01S -1 ～50s -1 The deformation is 60% -70%.
3. The method for predicting rheological stress during thermal deformation of Ti80 titanium alloy according to claim 2, wherein in step S2, the thermal simulation compression test is: heating the thermal compression sample to the deformation temperature at a heating speed of 8-12 ℃/s, preserving heat for 3-5min, then carrying out thermal compression experiment at the strain speed, and cooling with water.
4. The method for predicting rheological stress in thermal deformation of Ti80 titanium alloy according to claim 1, wherein step S4 comprises establishing an Arrhenius model, an Arrhenius model in power function form and an Arrhenius model in exponential form, and then taking logarithms of the Arrhenius model in power function form and the Arrhenius model in exponential form on two sides respectively to obtain a power function logarithm form of the Arrhenius model and an exponent logarithm form of the Arrhenius model:
wherein, the formula (1) is an Arrhenius model with hyperbolic sine shape;
the formula (2) is a power function form of an Arrhenius model;
the formula (3) is an exponential form of the Arrhenius model;
the formula (4) is a logarithmic form of a power function of an Arrhenius model;
the formula (5) is the exponential of the Arrhenius model in logarithmic form;
n 1 ，n 2 is a work hardening index; alpha, beta and A are thermal deformation material constants; r is the universal gas constant (8.314J/(mol.K)),at strain rate, T is deformation temperature, sigma p And Q is thermal deformation activation energy.
5. The method for predicting the rheological stress during thermal deformation of a Ti80 titanium alloy according to claim 4, whereinStep S4 further comprises obtaining corresponding strain rate, deformation temperature and peak stress according to the change curves of peak stress at different deformation temperatures and different strain rates in step S3, and performing linear fitting by taking a logarithmic form according to the power function of the Arrhenius model to obtain a linear regression curve slope, namely n at different deformation temperatures and different strain rates 1 ；
Performing linear fitting on a scatter diagram in a logarithmic form according to the index of the Arrhenius model, wherein the slope of the obtained linear regression curve is the beta value under different deformation temperatures and different strain rates;
according to alpha = beta/n 1 And calculating to obtain an alpha value.
6. The method for predicting rheological stress during thermal deformation of Ti80 titanium alloy according to claim 5, wherein step S4 further comprises taking the logarithm of two sides of a hyperbolic sinusoidal Arrhenius model to obtain a hyperbolic sinusoidal Arrhenius model, substituting the alpha value into the hyperbolic sinusoidal Arrhenius model to obtain a logarithm, and makingPerforming linear fitting on the scatter diagram, wherein the slope of the linear regression curve is n 2 ：
Wherein the Arrhenius model with the formula (6) being hyperbolic sine is in logarithmic form.
7. The method of predicting rheological stress during thermal deformation of Ti80 titanium alloy according to claim 6, wherein step S4 further comprises taking the hyperbolic sinusoidal Arrhenius model as a logarithmic form term to obtain a hyperbolic sinusoidal Arrhenius model term, and taking ln [ sinh (ασ p )]-1000/T scatter plot for linear fitting, substituting slope of linear regression curve into Arrhenius of hyperbolic sine typeModel polynomial equation, calculate thermal deformation activation energy Q under different deformation temperatures and different strain rates:
wherein, formula (7) is an Arrhenius model polynomial of hyperbolic sine type.
8. The method of predicting the rheological stress during thermal deformation of a Ti80 titanium alloy of claim 7, wherein step S4 further comprises introducing a Zener-holllon parameter, substituting the Zener-holllon parameter into the hyperbolic sinusoidal Arrhenius model polynomial to obtain a relationship between the peak stress and the Z parameter of the Ti80 titanium alloy:
lnZ＝lnA+n 2 ln[sinh(ασ p )] (9)
wherein formula (8) is a Zener-holomon parameter;
equation (9) is a relation between the peak stress of Ti80 titanium alloy and Z parameter.
9. The method for predicting rheological stress during thermal deformation of Ti80 titanium alloy according to claim 8, wherein step S4 further comprises obtaining corresponding strain rate, deformation temperature and peak stress according to the change curves of peak stress at different deformation temperatures and different strain rates in step S3, performing linear fitting according to a scatter diagram of the relation between the peak stress and the Z parameter of the Ti80 titanium alloy, and obtaining a value a by calculating with a longitudinal intercept of lnA.
10. The method for predicting the rheological stress during thermal deformation of a Ti80 titanium alloy according to claim 9, wherein step S4 further comprises calculating n according to any one of claims 1 to 9 1 、n 2 And substituting the alpha, beta and A values into the hyperbolic sine Arrhenius model to obtain an constitutive equation of rheological stress in the thermal deformation process of the Ti80 titanium alloy.
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