CN107305174B - Numerical representation method and system for material stress-strain constitutive relation - Google Patents

Numerical representation method and system for material stress-strain constitutive relation Download PDF

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CN107305174B
CN107305174B CN201710162538.6A CN201710162538A CN107305174B CN 107305174 B CN107305174 B CN 107305174B CN 201710162538 A CN201710162538 A CN 201710162538A CN 107305174 B CN107305174 B CN 107305174B
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CN107305174A (en
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寿比南
陈朝晖
朱国栋
尹立军
钱才富
魏安鹏
李光海
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Cscbpv Beijing Technology Service Center Co ltd
China Special Equipment Inspection and Research Institute
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    • G01—MEASURING; TESTING
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    • G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • G—PHYSICS
    • G01—MEASURING; TESTING
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    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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Abstract

The invention relates to the field of materials, and provides a numerical characterization method of a material stress-strain constitutive relation, which comprises the following steps of setting test parameters, wherein the test parameters comprise sample temperature; performing a tensile test on the material according to the test parameters to obtain tensile test data of the material, wherein the tensile test data comprises stress data and strain data; establishing a stress-strain curve according to the stress data and the strain data; selecting a corresponding stress-strain numerical model according to the attribute of the material, fitting a stress-strain curve of the material, and solving parameters in the stress-strain numerical model, wherein the error between a result obtained by the numerical characterization method and an actual value is small, so that the numerical characterization method is more practical; a system for implementing the numerical characterization method and a method for solving the stress-strain relationship of the material are also provided.

Description

Numerical representation method and system for material stress-strain constitutive relation
Technical Field
The invention relates to the field of material performance characterization methods, in particular to a numerical characterization method and a numerical characterization system for a material stress-strain constitutive relation and a method for solving the material stress-strain relation.
Background
The method can more clearly and specifically obtain the physical properties of the material in various aspects for accurate measurement and calculation of the physical property value of the material, provides clear and accurate guidance and reference for the practical application of the material, and particularly requires that products manufactured by the corresponding material can meet the safety requirements of product application in the technical field with harsh requirements on the product application of the material, and has high reliability and stability if the requirements meet the special requirements of high temperature, high pressure, flammability, explosiveness and the like. For example, pressure vessels in industrial applications are often used to store hazardous media, and safe operation is of paramount importance. In the product design using materials, safety and economy need to be considered, most of the existing pressure container materials mainly consider the performance of an elastic stage below the yield point of the materials, and after the materials pass through the yield stage in the stretching process, the resistance to deformation is enhanced, so that the stress required for the materials to continue to deform is increased, and therefore, the design of the pressure container needs to be carried out by utilizing the numerical result of the elastic-plastic performance of the materials. In the existing numerical method for material performance of the American ASME standard, due to the difference between material classification and performance, the deviation between the measured result and the performance of the actual material in China is often large, and the refined requirement of design cannot be met, so that a method and a means capable of accurately representing the physical performance of the material in China need to be found to meet the development requirements of material application and product design. For other countries, it is also necessary to establish a numerical method of material properties from the actual physical properties of the materials used in the actual country.
Disclosure of Invention
The invention aims to solve the problems in the prior art, provides a numerical characterization method of the material stress-strain constitutive relation, which is reliable in basis, more consistent in constitutive relation, more accurate in mathematical expression, smaller in error and more in accordance with design safety and economy, provides a system for implementing the material stress-strain constitutive relation characterization method, which is reliable and in accordance with material characteristic requirements, and also provides a method for obtaining the material stress-strain relation so as to overcome the technical defects that the material performance characterization method is large in error and the curve is not consistent with the constitutive relation of the material. The stress data strain number of the material is simulated by a numerical model through actually measuring the stress data strain number of the material, so that the solved stress strain constitutive relation is ensured to be more consistent with the real mechanical property of the material, and a reliable basis is provided for the design of mechanical containers such as pressure containers and the like.
In order to solve the above problems of the prior art, a first aspect of the present invention provides a method for numerically characterizing a material stress-strain constitutive relation, including the following steps:
a) setting test parameters, wherein the test parameters comprise sample temperature;
b) performing a tensile test on the material according to the test parameters to obtain tensile test data of the material, wherein the tensile test data comprises stress data and strain data;
c) establishing a stress-strain curve according to the stress data and the strain data;
d) and selecting a corresponding stress-strain numerical model according to the attribute of the material, fitting a stress-strain curve of the material, and solving parameters in the stress-strain numerical model.
In a second aspect of the present invention, a system for implementing a numerical characterization method of a material stress-strain constitutive relation is provided, which includes a loading device for applying a load to a material sample, a force measuring device for measuring a force applied to a material to be measured, a strain rate measuring device for measuring a strain rate, a heating device for heating the material, a temperature measuring device for measuring a temperature of the material, and a calculating device for processing the stress data and the strain data to obtain a parameter in a stress-strain numerical model.
In a third aspect of the present invention, a method for obtaining a stress-strain relationship of a material is provided, including inputting a temperature parameter and a material parameter to a stress-strain relationship obtaining module, where the stress-strain relationship obtaining module obtains, according to the temperature parameter, a stress-strain relationship corresponding to the temperature and the material from a stress-strain numerical model in the numerical characterization method of a material stress-strain constitutive relationship provided in the first aspect of the present invention corresponding to the material parameter.
The method and the system measure the actual tensile mechanical property of the material, simulate the actually measured stress-strain curve by using the numerical model, ensure the conformity of the trend of the numerical model and the error amount, ensure that the established numerical model is more in line with the mechanical property of the material, and provide reliable basis for the design of pressure containers and mechanical parts; the method is suitable for materials in different countries after physical property parameters are actually measured.
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Further objects, features and advantages of the present invention will become apparent from the following description of embodiments of the invention, with reference to the accompanying drawings, in which:
FIG. 1 is a schematic flow chart diagram illustrating a numerical characterization method for stress-strain constitutive relations according to an embodiment of the present invention;
FIG. 2 is a flow chart illustrating a method for numerical characterization of stress-strain constitutive relations according to an embodiment of the present invention;
FIG. 3 is a flow chart illustrating a method for numerical characterization of stress-strain constitutive relation according to an embodiment of the present invention;
FIG. 4 is a flow chart illustrating a method for numerical characterization of stress-strain constitutive relation according to an embodiment of the present invention;
FIG. 5 is a flow chart illustrating a method for numerical characterization of stress-strain constitutive relation according to an embodiment of the present invention
FIG. 6 is a schematic diagram of a material sample structure in an embodiment of a method for numerical characterization of stress-strain constitutive relation according to the present invention;
FIG. 7 is a drawing model diagram illustrating a numerical method for stress-strain constitutive relation characterization according to an embodiment of the present invention;
FIG. 8 is a graph illustrating the fitting of the elastic modulus of austenitic stainless steel S31608 in one embodiment of the stress-strain constitutive relation numerical characterization method of the present invention;
FIG. 9 is a graph illustrating the fitting results of a 100 ℃ tensile curve in one embodiment of the numerical characterization method for stress-strain constitutive relation according to the present invention;
FIG. 10 is a diagram illustrating model parameter fitting results in one embodiment of a stress-strain constitutive relation numerical characterization method of the present invention;
FIG. 11 is a diagram illustrating model parameter fitting results in one embodiment of a stress-strain constitutive relation numerical characterization method of the present invention;
FIG. 12 is a diagram illustrating model parameter fitting results in one embodiment of a stress-strain constitutive relation numerical characterization method of the present invention;
FIG. 13 is a diagram illustrating a fitting result of a stress-strain curve according to an embodiment of the numerical characterization method for stress-strain constitutive relation of the present invention;
FIG. 14 is a graph illustrating the results of elastic modulus fitting in one embodiment of a stress-strain constitutive relation numerical characterization method of the present invention;
FIG. 15 is a graphical representation of the yield strength fit results in one embodiment of a stress-strain constitutive relation numerical characterization method of the present invention;
FIG. 16 is a diagram illustrating model parameter fitting results in one embodiment of a stress-strain constitutive relation numerical characterization method of the present invention;
FIG. 17 is a diagram illustrating model parameter fitting results in one embodiment of a stress-strain constitutive relation numerical characterization method of the present invention;
FIG. 18 is a graph illustrating a fitting result of a stress-strain curve according to an embodiment of the numerical characterization method for stress-strain constitutive relation of the present invention;
FIG. 19 is a structural diagram of a numerical characterization system for the constitutive relation of stress and strain of materials according to the present invention.
Detailed Description
The numeralization of the material tensile curve refers to the mathematical fitting of the stress-strain relationship of the material by adopting a functional relational expression method. Tests show that most of pressure container materials have remarkable strain strengthening characteristics in the stretching process, and the strain strengthening performance of the materials can be fully utilized by performing elastic-plastic analysis on the structure during the analysis and design of the pressure container, so that the pressure bearing capacity of the pressure container can be more reasonably evaluated. However, since there is no standard for the corresponding data, the elastic-plastic analysis method of materials has been rarely used for a long time. The lack of basic data in the standard limits the development of the analysis design level of the pressure vessel to a certain extent. The invention provides a stress-strain constitutive relation model suitable for a material on the basis of a pressure container material tensile test, and completes the numerical representation of a material tensile curve, thereby solving the material stress-strain constitutive relation.
As shown in FIG. 1, the method for characterizing the constitutive relation of stress and strain of a material according to the present invention comprises determining stress and strain data by a tensile test based on the characteristics of the material, establishing a curve, selecting a corresponding model to fit the curve, and determining model parameters to determine an exact formula expression of a numerical model, specifically comprising,
s101, setting test parameters, wherein the test parameters comprise the temperature of the sample.
S102, performing a tensile test on the material according to the test parameters to obtain tensile test data of the material, wherein the tensile test data comprises stress data and strain data.
S103, establishing a stress-strain curve according to the stress data and the strain data.
S104, according to the attributes of the material, selecting a corresponding stress-strain numerical model, fitting a stress-strain curve of the material, and solving parameters in the stress-strain numerical model, so that the actual mechanical tensile stress-strain curve of the material is measured at a set temperature, the numerical model is adopted for simulation, the parameters in the model are solved, the parameters of the numerical model are complete, and the model can be used for better representing the mechanical property of the material at the set temperature, so that a reliable mechanical design standard is provided in the future design of pressure containers or mechanical parts. The numerical characterization method of the material stress-strain constitutive relation provided by the invention comprises a measuring and calculating step, and can be understood as a measuring and calculating method.
Example one
According to the method, materials with different attributes are measured, a numerical model is adopted to simulate the materials, parameters in the model are solved, and the mechanical property of the measured materials is obtained.
According to the classification of the metal material into the material with the obvious yield stage and the material without the obvious yield stage, selecting a corresponding numerical model, when the material is the material with the obvious yield stage, and the corresponding stress-strain numerical model is,
Figure GDA0001293948620000051
in the formula TsThe minimum temperature of the disappearance of the yield platform of the tensile curve is shown, a and b are parameters in the stress-strain numerical model, and the mechanical property of the material with the obvious yield stage can be shown by solving the parameters a and bAnd (5) figuring out.
When the material is a material without obvious yield strength, the corresponding stress-strain numerical model is,
Figure GDA0001293948620000052
in the formula, a, b and d are parameters in the stress-strain numerical model, and the different models are designed according to the classification method of materials in China, so that the corresponding models are more in line with the actual situation.
It should be noted that, the parameters a, b, d in the stress-strain numerical model just represent one variable, and a common multiple in the parameters may also be extracted, for example, b is replaced by 0.001 × b, and then the stress-strain numerical model becomes:
Figure GDA0001293948620000053
and
Figure GDA0001293948620000054
this may be the case for other parameters.
In order to measure and calculate the numerical model parameters corresponding to the mechanical properties of the material at different temperatures, as shown in fig. 2, the numerical characterization method of the present invention further includes, S105, setting different temperatures, and repeating steps S102, S103, and S104 to obtain the stress-strain curves and the parameters in the stress-strain numerical model of the material at different temperatures.
In order to characterize the mechanical properties of the material at continuous temperature and establish the stress-strain constitutive relation of the material at continuous temperature, the numerical characterization method of the invention further comprises S106, establishing a parameter temperature curve according to the parameters in the stress-strain numerical model obtained at different temperatures, fitting a parameter temperature model according to the parameter temperature curve,
when there are a plurality of parameters in the stress-strain numerical model, in order to ensure the reliability of the parameter calculation in the numerical characterization method, thereby ensuring that the error of the fitting result is smaller, and adopting a method of sequentially solving parameters, as shown in figure 3, the numerical characterization method further comprises the steps of S107 selecting one of the parameters in the stress-strain numerical model, S108 establishing a parameter temperature curve, fitting a parameter temperature model, substituting the different temperatures into the parameter temperature model, finding fitting parameters, substituting the fitting parameters into a stress-strain numerical model of the material, fitting the stress-strain curve by using the stress-strain numerical model of the material with the fitted parameters substituted, and solving the rest parameters in the stress-strain numerical model of the material; s109 selects one of the other parameters in the stress-strain digitized model, and performs step S108 until all the parameters in the stress-strain digitized model are found, so that the found parameters make the results of the digitized model and the measured stress-strain curve more consistent, and the error is smaller.
The stress-strain numerical model comprises an elastic modulus parameter, and in order to establish the elastic modulus value at continuous temperature, the elastic modulus parameter provided in the conventional method is the corresponding value at discrete temperature, so that the numerical characterization method is more widely applied, an elastic modulus temperature relation graph needs to be established according to the discrete elastic modulus parameter, an elastic modulus temperature curve is fitted according to the elastic modulus temperature relation graph, and the curve parameter is solved.
Considering the deformation of the section of the material in the test, the stress data and the strain data of the test are processed, so that the stress-strain relationship is more consistent with the actual situation, and the step S103 of the invention comprises the following steps oftt＝σ(1+et) Processing said stress data into true stress data, where σttRepresenting the true stress at time t in a tensile test, sigma representing the stress data measured in said tensile test,etdata representing the measured strain at time t in a tensile test; according to the formulat＝ln(1+e) Processing said strain data into true strain data, whereintThe true strain is represented by the presence of,erepresenting engineering strain; and (3) carrying out the following treatment on the true stress of the material in a yield stage and/or a strain strengthening stage: sigmas＝σt·K(T)In the formula K(T)The normalized coefficient is represented by a normalized coefficient,
Figure GDA0001293948620000061
in the formula sigmaRp0.2(standard)Denotes the standard yield stress, σ, of the materialRp0.2(test)The yield stress of the material is converted into the real stress in a tensile test, and the stress is processed into a value below the standard, so that the safety is ensured.
The test parameters of the invention also include the sample requirement, the strain rate, the frequency of data acquisition and the strain range, and the step S102 also includes selecting the diameter of the material for the test of the tensile test; marking the material number of the sample on the sample; marking the samples at intervals; the diameter of the sample before the tensile test was measured a plurality of times to find an average value, and the cross-sectional area of the sample was calculated.
In the step S102 of the invention, uniform stretching is adopted in the stretching test, when the strain range is 0-7.5%, the strain rate is used for controlling the test rate, and the strain rate of the stretching test is measured by using an extensometer; when the strain range is larger than 7.5%, the test speed is controlled by the displacement speed of the cross beam according to the strain range
Figure GDA0001293948620000071
To determine in the formula
Figure GDA0001293948620000072
To the stretching rate, LeIs the beam displacement, veIs the displacement rate.
In order to make the numerical characterization method of the present invention widely applicable, the test temperature range in the embodiment of the present invention is 20 ℃ to 700 ℃.
In order to make the test result more representative, the diameter of the sample is 8mm to 15mm, for example, the diameter of the sample is selected to be phi 10 mm.
In the case of the tensile test, the step of marking the test sample at intervals according to the embodiment of the present invention includes: setting the original gauge length L of the sample050mm, one at every 10mm on the sample using a scriberMarking, wherein the gauge length precision of the scriber is less than or equal to +/-1 percent (L)0)。
In order to enable the stress-strain constitutive relation obtained in the embodiment of the present invention to be applied to various temperature occasions, the tensile test in the embodiment of the present invention includes normal temperature tensile and high temperature tensile. For example, in the case of normal temperature stretching, the temperature of the stretching test in the step S102 is 10 ℃ to 35 ℃, and the stretching rate is
Figure GDA0001293948620000075
In the high temperature stretching, the temperature of the stretching test in the step S102 is set to be more than 100 ℃, the sample is heated to a preset temperature, the sample is kept at the preset temperature for at least 10 minutes, and the stretching rate is
Figure GDA0001293948620000073
In an embodiment of the present invention, said step S103 further comprises a step of determining a standard stress value Rp of said material at said temperature0.2By the following formula,
Figure GDA0001293948620000074
intersection point (, Rp) is obtained0.2) And when the stress-strain curve is established, enabling the distance between the stress-strain curve and the intersection point to be within a threshold range. This ensures that the stress-strain curve can be brought closer to the intersection point (, Rp)0.2) Fully takes the standard stress value Rp into consideration0.2The effect on the curve. Similarly, after the intersection point is obtained, when the stress-strain curve is established, the coordinate of the intersection point is added to the stress data and the strain data in the step S102, the stress-strain curve is established according to the stress data, the strain data and the data of the intersection point, and a fitting weight value is applied to the stress data, the strain data and the data of the intersection point, wherein the fitting weight value corresponding to the data of the intersection point is greater than the fitting weight value corresponding to the stress data and the strain data. Thus, the curve is closer to the intersection point. Important innovation of the intersection pointAnd is thus embodied.
For the material with the obvious yield stage, after the parameters of the stress-strain model at a certain temperature are obtained, different temperatures are set, the steps S102, S103 and S104 are repeated to obtain the stress-strain curve of the material at different temperatures and the parameters a and b in the stress-strain numerical model, fitting is carried out according to the corresponding parameters a and b at different temperatures to obtain the parameter temperature model corresponding to the parameter a, and the parameter temperature model corresponding to the parameter b is obtained. In this way, continuous parameters under a stress-strain model at continuous temperature can be obtained, so that the method in the embodiment of the invention can be widely applied, and the result has universality.
The method comprises the steps of obtaining a parameter temperature model corresponding to a parameter a, obtaining new values of the parameter a at different temperatures according to the parameter temperature model corresponding to the parameter a, substituting the new values of the parameter a into a stress-strain numerical model, fitting a stress-strain curve of the material according to stress data and strain data obtained at different temperatures, obtaining a parameter b in the stress-strain numerical model at different temperatures, and obtaining a parameter temperature model corresponding to the parameter b.
In the process of sequentially solving the parameters of the model, in order to reduce the influence of the error of the fitting result of a certain parameter on the stress-strain model, the error of the temperature fitting result of the parameter needs to be judged, and when the error is smaller than a threshold value, the next parameter is fitted2Making a decision if the coefficient R is determined2And when the temperature of the material is less than the threshold value, solving new values of the parameter a at different temperatures according to the parameter temperature model corresponding to the parameter a, substituting the new values of the parameter a into the stress-strain numerical model, fitting a stress-strain curve of the material according to the stress data and the strain data acquired at different temperatures, solving a parameter b in the stress-strain numerical model at different temperatures, and acquiring the parameter temperature model corresponding to the parameter b.
Similarly, the step of obtaining stress-strain model parameters at continuous temperature for a material with an obvious yield stage further includes setting different temperatures, repeating steps S102, S103, and S104 to obtain stress-strain curves of the material and parameters a, b, and d in the stress-strain numerical model at different temperatures, fitting according to corresponding parameters a, b, and d at different temperatures to obtain a parameter temperature model corresponding to parameter a, obtain a parameter temperature model corresponding to parameter b, and obtain a parameter temperature model corresponding to parameter b. Similarly, the parameters may be sequentially obtained, and specifically, after obtaining the parameter temperature model corresponding to the parameter a, new values of the parameter a at different temperatures are obtained according to the parameter temperature model corresponding to the parameter a, the new values of the parameter a are substituted into the stress-strain numerical model, the stress-strain curve of the material is fitted according to the stress data and the strain data obtained at different temperatures, the parameter b in the stress-strain numerical model at different temperatures is obtained, and the parameter temperature model of the parameter b is obtained; solving new values of the parameter b at different temperatures according to a parameter temperature model corresponding to the parameter b, substituting the new value of the parameter a and the new value of the parameter b into a stress-strain numerical model, fitting a stress-strain curve of the material according to stress data and strain data acquired at different temperatures, solving a parameter d in the stress-strain numerical model at different temperatures, and acquiring a parameter temperature model of the parameter d. Similarly, in order to reduce the error of the parameter temperature model, the method specifically includes, after obtaining the parameter temperature model corresponding to the parameter a, determining a determination coefficient R2 of a fitting result of the parameter a, if the determination coefficient R2 is smaller than a threshold, obtaining new values of the parameter a at different temperatures according to the parameter temperature model corresponding to the parameter a, substituting the new values of the parameter a into the stress-strain numerical model, fitting a stress-strain curve of the material according to stress data and strain data obtained at different temperatures, obtaining a parameter b in the stress-strain numerical model at different temperatures, and obtaining a parameter temperature model of the parameter b; judging a judgment coefficient R2 of a fitting result of the parameter b, if the judgment coefficient R2 is smaller than a threshold value, solving new values of the parameter b at different temperatures according to a parameter temperature model corresponding to the parameter b, substituting the new values of the parameter a and the parameter b into a stress-strain numerical model, fitting a stress-strain curve of the material according to stress data and strain data obtained at different temperatures, solving a parameter d in the stress-strain numerical model at different temperatures, and obtaining a parameter temperature model of the parameter d.
In the stress-strain constitutive relation numerical representation method of the embodiment of the present invention, there are a plurality of parameters in the stress-strain numerical model, as shown in fig. 4, the numerical representation method further includes, S110, selecting one of the parameters in the stress-strain numerical model, S111, establishing a parameter temperature curve, fitting a parameter temperature model, substituting the different temperatures into the parameter temperature model, solving a fitting parameter, and determining a determination coefficient R of a fitting result of the selected parameter2Making a decision if the coefficient R is determined2When the stress-strain curve is smaller than the threshold value, substituting the fitting parameters into the stress-strain numerical model of the material, fitting the stress-strain curve by using the stress-strain numerical model of the material with the substituted fitting parameters, and solving the rest parameters in the stress-strain numerical model of the material; s112, selecting one of the other parameters in the stress-strain numerical model, and performing step S111 until all the parameters in the stress-strain numerical model are obtained.
In the embodiment of the invention, a polynomial is adopted for fitting in the fitting process of the parameter temperature model in the stress-strain constitutive relation numerical representation method, for example, the step of fitting the parameter temperature model comprises the step of fitting by adopting a cubic polynomial; for example, a quadratic polynomial or a cubic polynomial is used to fit the elastic modulus value, and for a sample made of austenitic stainless steel, a quadratic polynomial is used to fit an elastic modulus temperature curve to obtain an elastic modulus temperature curve model,
Ey(T)＝1.806×10-4T2-0.618T +1958, fitting a cubic polynomial to a sample of the material being a low carbon steel material, the elastic modulus temperature curve model being,
Ey(T)＝-5.144×10-7T3+1.821×10-4T2-0.07197T+2025。
in the method for numerically characterizing the stress-strain constitutive relation in the embodiment of the invention, for a material with an obvious yield stage, a parameter temperature model corresponding to the parameter a is,
a(T)＝-4.803×10-3tanh[0.02293(T-425)]+0.004803；
the parametric temperature model corresponding to the parameter b is,
Figure GDA0001293948620000101
in the method for numerically characterizing the stress-strain constitutive relation in the embodiment of the invention, for a material without an obvious yield stage, the parameter temperature model corresponding to the parameter a is,
a(T)＝-9.899×10-8T3+8.767×10-5T2-0.002013T+2.79；
the parametric temperature model corresponding to the parameter b is,
b(T)＝7.926×10-8T3-7.425×10-5T2+0.01949T+2.787；
the parameter temperature model corresponding to the parameter d is,
d(T)＝-1.376×10-6T3+1.653×10-3T2-0.7244T+321.6。
the stress-strain constitutive relation numerical characterization method in the embodiment of the invention can simulate the stress-strain constitutive relation of the material more truly, further fit results at different temperatures, establish temperature curves of parameters in the constitutive relation, thus obtaining parameters at continuous temperatures, substitute the parameters at continuous temperatures into the model, thus obtaining the stress-strain constitutive relation at continuous temperatures, can meet the requirements of different temperatures, has wide temperature coverage range and wide application, and provides good basis for processing design.
Example two
As shown in fig. 1, the method for numerically characterizing the material stress-strain constitutive relation in the embodiment of the present invention includes, S101, setting test parameters, where the test parameters include a sample temperature.
S102, performing a tensile test on the material according to the test parameters to obtain tensile test data of the material, wherein the tensile test data comprises stress data and strain data.
S103, establishing a stress-strain curve according to the stress data and the strain data.
S104, selecting a corresponding stress-strain numerical model according to the attribute of the material, fitting a stress-strain curve of the material, and solving parameters in the stress-strain numerical model. The numerical characterization method in the embodiment of the invention is close to reality, takes the stress-strain data of the tensile test as the fitting basis, adopts the numerical model corresponding to the material property to carry out fitting, obtains parameters, has high reliability of the obtained result, and can meet the requirement of actual production design.
The step S101 of setting test parameters further includes setting a sample requirement of the material sample, setting a strain rate, setting a frequency of data financial resources, setting a strain range, and setting a stretching rate, where the sample used in the present invention may be a cylindrical sample, the diameter may be 8mm to 15mm, or 10mm, different stretching rates are set according to different temperatures, and stretching at normal temperature is performed at an ambient temperature ranging from 10 ℃ to 35 ℃. The strain range is 0-7.5%. Within this range, the tensile specimen strain is measured using an extensometer and the tensile rate of the test is controlled by the strain rate of the specimen. A drawing rate of
Figure GDA0001293948620000115
The strain range is greater than 7.5%. In this range, the stretching rate of the specimen was controlled by the beam displacement amount without using an extensometer.A drawing rate of
Figure GDA0001293948620000116
Displacement rate of the beam according to the formula
Figure GDA0001293948620000117
And (4) calculating. Selecting a test scheme and parameters, clamping a sample, and adjusting the positions of the upper and lower cross beams according to the length of the sample in step S102, clamping the sample, and keeping the sample centered. And (4) carrying out load, displacement and deformation value zero clearing in an appropriate link according to a clamping mode and the self characteristics of the testing machine, entering a testing state, and sequentially loading until the test sample is broken. And (5) disassembling the test sample, and measuring data required by the test.
The high-temperature stretching is carried out within a specific temperature range, and meets the requirement that the error is within +/-0.004 theta (theta is a specified temperature) or +/-2 ℃ and the maximum value is taken. Step S102 includes gradually heating the sample to a predetermined test temperature. The temperature of the sample measured by the thermocouple may not exceed the upper deviation of the temperature error when the sample is heated. When the temperature of the sample measured by the thermocouple reaches the specified temperature of the test, the temperature needs to be kept for at least 10 minutes, so that the accuracy of the measurement result is ensured. And after the heat preservation is finished, the extensometer is zeroed. In the first stage, the strain range is 0-7.5%. Within this range, the tensile specimen strain is measured using an extensometer and the tensile rate of the test is controlled by the strain rate of the specimen. A drawing rate of
Figure GDA0001293948620000111
Displacement rate of the beam according to the formula
Figure GDA0001293948620000112
And (4) calculating. The strain range is greater than 7.5%. Within this range, the extensometer may not be used and the drawing rate is
Figure GDA0001293948620000113
Displacement rate of the beam according to the formula
Figure GDA0001293948620000114
And (4) calculating. And starting the machine in sequence to enter an online state, selecting a test scheme and parameters, installing a clamping block, adjusting the positions of an upper beam and a lower beam according to the length of the sample, installing and clamping the sample, and ensuring the sample to be centered. And moving the sample to a heating furnace, heating to a specified temperature, ensuring that the sample is in a low stress state in the heating process, and preserving the temperature for at least 10min after the temperature reaches the required temperature. And resetting the force value and the displacement value, adjusting the extensometer to be zero, entering a test state, and loading until the sample is broken. And disassembling the test sample, and collecting test data required by the measurement test by a control system of the tensile testing machine. The step S102 includes recording the stress data and the strain data, adjusting the experimental data according to a trimming rule, and performing the trimming according to a digital trimming rule of "four-round six-in five-double" when the experimental data is trimmed. When in appointment making: a) the strength performance is reduced to about 1 Mpa; b) the elongation after fracture is trimmed to about 0.5%; c) the reduction of area is trimmed to 1%.
In step S103, a stress-strain curve is established according to the stress data and the strain data, a corresponding curve can be established directly through the strain data and the stress data, the stress data and the strain data can also be processed, the influence of the change of the cross-sectional area of the material in the tensile test process on the test result is fully considered, and the stress-strain curve is established according to a formula σtt＝σ(1+et) Processing said stress data into true stress data, where σttRepresenting the true stress at time t in a tensile test, sigma representing the stress data measured in said tensile test,etdata representing the measured strain at time t in a tensile test; according to the formulat＝ln(1+e) Processing said strain data into true strain data, whereintThe true strain is represented by the presence of,erepresenting engineering strain; and (3) carrying out the following treatment on the true stress of the material in a yield stage and/or a strain strengthening stage: sigmas＝σt·K(T)In the formula K(T)The normalized coefficient is represented by a normalized coefficient,
Figure GDA0001293948620000121
in the formula sigmaRp0.2(standard)Denotes the standard yield stress, σ, of the materialRp0.2(test)Represents the yield stress sigma of the material in a tensile test0.2By the following formula,. sigmaRp0.2(test)＝σ0.2(1+et) True stress converted; on the other hand, the requirement that the measured curve need not deviate significantly from the standard value can also be taken into account, for example, by following the standard stress value rp0.2 of the material at said temperature, by means of the following formula,
Figure GDA0001293948620000122
intersection point (, Rp) is obtained0.2) When the stress-strain curve is established, enabling the distance between the stress-strain curve and the intersection point to be within a threshold range; or according to the standard stress value Rp of said material at said temperature0.2By the following formula,
Figure GDA0001293948620000123
intersection point (, Rp) is obtained0.2) When the stress-strain curve is established, the coordinates of the intersection point are added to the stress data and the strain data in step S102, the stress-strain curve is established according to the stress data, the strain data and the data of the intersection point, and a fitting weight value is applied to the stress data, the strain data and the data of the intersection point, for example, the strain data, the stress data and the data of the intersection point may be multiplied by the fitting weight value, the fitting weight value multiplied by the data of the intersection point is greater than other fitting weight values, if the fitting weight value multiplied by the intersection point is 2, the other fitting weight values are 1, so that the fitting weight value corresponding to the data of the intersection point is greater than the fitting weight value corresponding to the stress data and the strain data.
In the step S104, the step of selecting the corresponding stress-strain numerical model according to the property of the material includes, when the material is a material with an obvious yield stage, selecting the stress-strain numerical model as,
Figure GDA0001293948620000131
in the formula TsRepresenting the lowest temperature of the disappearance of the yield platform of the tensile curve, and a and b are parameters in the stress-strain numerical model; when the material is a material that does not have a significant yield strength, the stress-strain numerical model is selected to be,
Figure GDA0001293948620000132
wherein a, b and d are parameters in the stress-strain numerical model. The requirement to separate the material into a material with a distinct yield phase and a material without a distinct yield phase is met.
As shown in fig. 2, the numerical characterization method in the embodiment of the present invention further includes setting different temperatures in S105, and repeating steps S102, S103, and S104 to obtain the stress-strain curve of the material and the parameters in the stress-strain numerical model at different temperatures. Parameters in the numerical model at different temperatures are obtained through tests at different temperatures, so that the stress strain numerical model obtained by the numerical characterization method in the embodiment of the invention is applied to various temperature occasions.
As shown in fig. 1 and fig. 2, the numerical characterization method in the embodiment of the present invention further includes, S106, establishing a parameter temperature curve according to parameters in the stress-strain numerical model obtained at different temperatures, and fitting the parameter temperature model according to the parameter temperature curve, so as to obtain parameters of the stress-strain numerical model at continuous temperatures. Alternatively, as shown in fig. 3, the numerical characterization method in the embodiment of the present invention further includes, S107, selecting one of the parameters in the stress-strain numerical model; s108, establishing a parameter temperature curve, fitting a parameter temperature model, substituting different temperatures into the parameter temperature model, solving fitting values of the selected parameters at different temperatures, substituting the fitting values into a stress-strain numerical model of the material, fitting the stress-strain curve by using the stress-strain numerical model of the material with the substituted fitting values, and solving the rest parameters in the stress-strain numerical model of the material at different temperatures; s109 quantifying the model from the stress-strainAnd selecting one of the rest parameters, and repeating the step S108 until all the parameters in the stress-strain numerical model are solved, so that the parameters are solved in sequence, and the fitting result can be ensured to be consistent with the stress-strain curve obtained by the tensile test. Alternatively, as shown in fig. 4, the numerical characterization method in the embodiment of the present invention further includes, S110, selecting one of the parameters in the stress-strain numerical model; s111, establishing a parameter temperature curve, fitting a parameter temperature model, substituting different temperatures into the parameter temperature model, solving fitting parameters, and determining a coefficient R of a fitting result of the selected parameters2Making a decision if the coefficient R is determined2When the stress-strain curve is smaller than the threshold value, substituting the fitting parameters into the stress-strain numerical model of the material, fitting the stress-strain curve by using the stress-strain numerical model of the material with the substituted fitting parameters, and solving the rest parameters in the stress-strain numerical model of the material; s112, selecting one of the other parameters in the stress-strain numerical model, and implementing the step S111 until all the parameters in the stress-strain numerical model are solved, so that the rationality of the result is ensured in the process of sequentially solving the parameters, and finally the error between the fitting curve and the tensile test curve is ensured to meet the requirement.
In the numerical characterization method in the embodiment of the present invention, the stress-strain numerical model in step S104 includes an elastic modulus parameter, step S104 further includes establishing an elastic modulus temperature relationship diagram according to the elastic modulus value at the discrete temperature, fitting an elastic modulus temperature curve according to the elastic modulus temperature relationship diagram, and solving the curve parameter, wherein the fitting process may employ a quadratic polynomial for fitting or a cubic polynomial for fitting, for example, the material is austenitic stainless steel, the quadratic polynomial is employed for fitting, the elastic modulus temperature curve model is,
Ey(T)＝1.806×10-4T2-0.618T+1958。
for example, when the material is a low-carbon steel material, the elastic modulus temperature curve model is,
Ey(T)＝-5.144×10-7T3+1.821×10-4T2-0.07197T+2025。
the numerical characterization method of the material stress-strain constitutive relation selects the corresponding fitting model according to the material characteristics, performs fitting after obtaining the stress-strain curve of the tensile test, calculates the parameters in the fitting model, further performs the test at different temperatures, obtains the parameter temperature model, calculates the parameters at continuous temperatures, has wide application range and high reliability, and is more consistent with the material intrinsic characteristics.
EXAMPLE III
As shown in fig. 5, an embodiment of the method for characterizing the constitutive relation of stress and strain of a material according to the present invention employs a tensile test to obtain test data of the material, specifically includes, S201, according to a material formulation test method, setting a sample requirement of a material sample, setting a strain rate, setting a frequency of data financial resources, setting a strain range, setting a tensile rate, and setting a test temperature, as shown in fig. 6, a sample with a diameter of 10mm is selected as a sample employed in the embodiment of the present invention, the sample is divided into a room-temperature tensile state and a high-temperature tensile state during the tensile state, the tensile rate is set in two cases, when the sample is stretched at room temperature, the tensile temperature is 10-35 ℃, the tensile temperature can also be set to 23 ℃ ± 5 ℃, and the tensile rate can also be set at 20 ℃, and the tensile rate is the
Figure GDA0001293948620000151
When the strain range is between 0% and 7.5%, the strain of the tensile sample is measured by adopting the extensometer, the tensile rate of the test is controlled by the strain rate of the sample, when the strain range is more than 7.5%, the tensile rate of the sample is controlled by adopting the beam displacement, the relation between the beam displacement and the time is recorded to obtain the beam displacement rate, and the beam displacement rate v is obtainedeAnd rate of stretching
Figure GDA0001293948620000152
The relationship between is
Figure GDA0001293948620000153
In order to conveniently record the displacement of the cross beam, a mark can be made on the sample, a plurality of marks can be made at intervals and fixed length, and the displacement of the cross beam is easy to measure; the temperature at high temperature may be set higher than the temperature at room temperature stretching, for example, 50 to 750 ℃, or 50, 100, 150, 200, 250, 300, 350, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 725, 750 ℃, and the high temperature stretching test temperature may be selected for the temperature points of different materials, and the stretching rate may be set
Figure GDA0001293948620000154
Similarly, when the strain range is less than 7.5% and more than 7.5%, the stretching rate is controlled by adopting a strategy of stretching at normal temperature, and when stretching at high temperature, the sample needs to be heated in order to ensure the temperature of the sample, the temperature of the sample is measured, and the sample is ensured to be maintained at the required temperature for at least ten minutes, so that the measurement result is ensured to be reliable and effective, and the temperature of the sample can be measured by a thermocouple. S202, performing a tensile test, wherein the tensile test adopts equipment which is a tensile testing machine, can load the sample, can measure the tensile rate of the sample at the same time, and records the stress data and the strain data of the sample.
S203, changing the temperature of the tensile test and the corresponding set tensile rate, carrying out a plurality of samples, and replacing a new sample after each tensile test because the internal structure of the sample can be irreversibly changed after each tensile test is finished, and carrying out the test by using a plurality of samples so as to obtain the stress data and the strain data of the material at different temperatures; on the other hand, different materials are transformed to be subjected to tensile tests at different temperatures, so that stress data and strain data of the different materials at different temperatures are finally obtained.
S204, a stress-strain curve is made according to the relation between the stress data and the strain data.
S205 classifies the material subjected to the tensile test as a material having a significant yield stage or a material not having a significant yield stage according to whether the stress-strain curve has a significant yield stage, for example, during the tensile test, the low alloy steel Q345R is found to be a material having a significant yield stage, and the austenitic stainless steel S31608 is found to be a material not having a significant yield stage.
S206, according to whether the test material belongs to the material with the obvious yield stage or not, different numerical models are selected to process the stress-strain curve obtained by the tensile test of the test material, and the numerical expression can be selected and is fitted by fitting software such as Matlab to the stress-strain curve to obtain the parameter value in the numerical model. An alternative model for a material with a distinct yield phase is,
Figure GDA0001293948620000161
c＝-10tanh(T-Ts) +10.55, wherein TsRepresenting the lowest temperature of the disappearance of the yield platform of the tensile curve, and a and b are parameters in the stress-strain numerical model; and for materials that do not have a significant yield stage, the model selected is,
Figure GDA0001293948620000162
in the formula, a, b and d are parameters in the stress-strain numerical model, and values of the parameters in the model at different temperatures are obtained after fitting, so that the stress-strain constitutive relation of the material is obtained, namely the determined numerical model. In order to be closer to the real characteristics of the material, the numerical characterization method provided by the embodiment of the invention also processes the stress-strain curve before fitting the stress-strain curve, and processes the stress-strain curve according to a formula sigmatt＝σ(1+et) Processing said stress data into true stress data, where σttRepresenting the true stress at time t in a tensile test, sigma representing the stress data measured in said tensile test,etdata representing the measured strain at time t in a tensile test; according to the formulat＝ln(1+e) Processing said strain data into true strain data, whereintThe true strain is represented by the presence of,erepresenting engineering strain; and (3) carrying out the following treatment on the true stress of the material in a yield stage and/or a strain strengthening stage: sigmas＝σt·K(T)In the formula K(T)The normalized coefficient is represented by a normalized coefficient,
Figure GDA0001293948620000163
in the formula sigmaRp0.2(standard)Denotes the standard yield stress, σ, of the materialRp0.2(test)Represents the yield stress sigma of the material in a tensile test0.2By the following formula,. sigmaRp0.2(test)＝σ0.2(1+et) True stress converted; on the other hand, according to the standard stress value Rp of said material at said temperature0.2By the following formula,
Figure GDA0001293948620000171
intersection point (, Rp) is obtained0.2) When the stress-strain curve is established, adding the coordinates of the intersection point into the stress data and the strain data, establishing the stress-strain curve according to the stress data, the strain data and the data of the intersection point, and applying a fitting weight value to the stress data, the strain data and the data of the intersection point, wherein the fitting weight value of the fitting weight value corresponding to the data of the intersection point is greater than the fitting weight value of the fitting weight value corresponding to the stress data and the strain data; on the other hand, because the material is subjected to tensile tests at different temperatures, the elastic modulus in the stress-strain numerical model can be also taken according to different temperatures, and the existing elastic modulus value EyThe method only gives a value at a specific temperature, the temperature adopted in the method is mostly different from the specific temperature, and in order to select the value of the elastic modulus more truly, the relation of the elastic modulus and the temperature is fitted, so that the error of the fitted curve meets the requirement of a threshold value, and fitting can be carried out by adopting a cubic polynomial or a quadratic polynomial. The existing standard value is mostly the value under the specific temperature, thus reducing the error brought by selecting the temperature different from the specific temperature for testing.
In order to meet the requirement of continuous temperature, the numerical value characterization method in the embodiment of the invention also fits the parameters obtained at different temperatures to obtain the parameter temperature relationship, so that the corresponding model parameters can be obtained by selecting any temperature within the temperature range, the accuracy of the model is greatly improved, various requirements can be met, and the method particularly meets the use environment of the model needing high precision.
S207, after obtaining model parameters, even obtaining parameters of a model of parameter temperature of the model parameters, verifying whether a numerical formula in the model is accurate or not so as to re-confirm the parameters, in practice, obtaining the parameters in sequence, then establishing a parameter temperature curve, substituting parameter values corresponding to the temperature in a tensile test in the temperature curve established once into a stress-strain numerical model, substituting collected stress data and strain data into fitting software, establishing a fitting model, establishing a fitting stress-strain curve, comparing the fitting stress-strain curve with the stress-strain curve obtained by the tensile test, judging errors of the two curves, judging repeatability through visual observation, or judging a judgment coefficient R2Whether the error meets the threshold requirement or not is judged, if not, the stress-strain curve is fitted by using the numerical model with the substituted partial parameters, the rest parameters are solved, similarly, the parameters in the numerical model can be acquired one by one through repeated error judgment, and finally, the error between the fitting curve established after the acquired numerical model is substituted into the parameters and the curve established by the tensile test is ensured to be smaller than the threshold value.
S208, the established numerical model is verified in the actual engineering, relevant actual parameters are extracted according to the engineering application, and if the relevant actual parameters are different from theoretical values, the model can be optimized according to the actual values.
S209, establishing a standard method, obtaining a numerical representation method of constitutive relation of the material with obvious yield point and material with unobvious yield point by the method, and applying the numerical representation method to the relevant standards of the pressure container.
Example four
As shown in fig. 6, which is a schematic structural diagram of the material sample adopted in this embodiment of the present invention, a sample with a diameter of phi 10mm is selected in the test, the sample is a standard sample recommended by the standard, and the tolerance of the sample meets the relevant requirements in the standard (GB/T4338-2006) of the metal material high-temperature tensile test method.
The test sample is processed according to the pattern shown in fig. 6, steel seal marks are made at two ends in the processing process, and the marking contents comprise: material brand, sample number, steel mill number; and (3) rechecking the processed sample, wherein the rechecking contents comprise: the shape, the size, the roughness, the allowable deviation and the like, the sample which does not meet the requirements cannot be used for the test, and burrs carried on the surface of the sample need to be removed; checking the number of the sample and filling the original record.
In order to avoid the influence of sharp defects on the surface of the sample on the test result, the original gauge length mark adopts a marking mode. Marking the original scale distance L of the sample by using a marking instrument to mark the scale distance with the corresponding length on the sample0The marking is carried out every 10mm when the thickness is 50mm, and the gauge length precision of a scriber is less than or equal to +/-1 percent (L0).
Measuring the original diameter of the sample by a vernier caliper with the precision of not less than 0.02mm0. During measurement, the measurement is carried out at the two ends and the middle part of the length direction of the sample by using a mode of vertical measurement averaging, the cross section area of the tensile sample is calculated, and an original record is filled.
The test scheme of the test is distinguished according to normal temperature stretching and high temperature stretching, and the whole stretching process in the test adopts a test method of uniform stretching. The room temperature stretching of this test was carried out at an ambient temperature in the range of 10 ℃ to 35 ℃. In the first stage, the strain range is 0-7.5%. Within this range, the tensile specimen strain is measured using an extensometer and the tensile rate of the test is controlled by the strain rate of the specimen. A drawing rate of
Figure GDA0001293948620000183
In the second stage, the strain range is greater than 7.5%. In this range, the stretching rate of the specimen was controlled by the beam displacement amount without using an extensometer. A drawing rate of
Figure GDA0001293948620000181
Displacement rate of the beam according to the formula
Figure GDA0001293948620000182
And (4) calculating.
And starting the machine in sequence to enter a test state, selecting a test scheme and parameters, clamping a sample, adjusting the positions of the upper and lower cross beams according to the length of the sample, clamping the sample, and keeping the sample centered. And (4) carrying out load, displacement and deformation value zero clearing in an appropriate link according to a clamping mode and the self characteristics of the testing machine, entering a testing state, and sequentially loading until the test sample is broken. And (5) disassembling the test sample, and measuring data required by the test.
The high-temperature stretching is carried out within a specific temperature range, and meets the requirement that the error is within +/-0.004 theta (theta is a specified temperature) or +/-2 ℃ and the maximum value is taken. The sample was gradually heated to the test specification temperature. The temperature of the sample measured by the thermocouple may not exceed the upper deviation of the temperature error when the sample is heated. When the temperature of the sample measured by the thermocouple reaches the test specification temperature, the temperature needs to be maintained for at least 10 minutes. And after the heat preservation is finished, the extensometer is zeroed. In the first stage, the strain range is 0-7.5%. Within this range, the tensile specimen strain is measured using an extensometer and the tensile rate of the test is controlled by the strain rate of the specimen. A drawing rate of
Figure GDA0001293948620000191
Displacement rate of the beam according to the formula
Figure GDA0001293948620000192
And (4) calculating.
In the second stage, the strain range is greater than 7.5%. Within this range, the extensometer may not be used and the drawing rate is
Figure GDA0001293948620000193
Displacement rate of the beam according to the formula
Figure GDA0001293948620000194
And (4) calculating. And starting the machine in sequence to enter an online state, selecting a test scheme and parameters, installing a clamping block, adjusting the positions of an upper beam and a lower beam according to the length of the sample, installing and clamping the sample, and ensuring the sample to be centered. Transferring the sample to a sample holderAnd heating the sample to a specified temperature in a heating furnace, ensuring that the sample is in a low stress state in the heating process, and preserving the temperature for at least 10min after the temperature reaches the required temperature. And resetting the force value and the displacement value, adjusting the extensometer to be zero, entering a test state, and loading until the sample is broken. Disassembling the sample, measuring the data required by the test
Test data are collected by a control system of the tensile testing machine. And when the test data are reduced, the digital reduction rule of 'four-round six-in five-double' is executed. When in appointment making:
a) the strength performance is reduced to about 1 Mpa;
b) the elongation after fracture is trimmed to about 0.5%;
c) the reduction of area is trimmed to 1%.
The data collected are processed, and a model of the elongation of the rod-shaped material is shown in FIG. 7, which model has an original cross-sectional area A0Original length of L0At a certain time t during the stretching of the model, the instantaneous cross-sectional area of the model is A, and the instantaneous length is L. Meanwhile, the model is assumed to keep the shape of a cylinder all the time during the stretching process, and the volume is kept unchanged. Then from the above assumptions, the equation can be written:
Figure GDA0001293948620000195
A·L＝A0·L0thereby obtaining
Figure GDA0001293948620000196
I.e. deducing sigmatt＝σ(1+et) And the method is a conversion formula between engineering stress and real stress.
Because the length of the material is also changed continuously in the stretching process, the engineering strain is the same as the engineering stress, and the real mechanical property of the material cannot be reflected, the engineering strain of the material should be converted into the real strain before the stretching curve is subjected to numerical processing. The true strain of a material should be expressed as the integral of the instantaneous increase in strain of the material, i.e.t＝∫dtIt is expanded at t0The integral from the time to the time t can be obtained
Figure GDA0001293948620000201
Is a conversion formula between engineering strain and real strain. And substituting the measured engineering stress data into corresponding conversion formulas to convert the engineering stress data into real strain and real stress.
The real stress and strain values of the sample can reflect the actual stress-strain relation of the material in the stretching process, but the difference of the mechanical property and the chemical composition of the samples processed and manufactured by different manufacturers is considered, and meanwhile, the national standard value is slightly lower than the actual mechanical property of the material during the preparation, so if the real stress and strain of the material used for the stretching curve are fitted, the properties of the materials produced by different manufacturers cannot be unified, the fitting result is higher than the national standard value, and the fitting result cannot be applied to elastoplasticity analysis design. In consideration of the factors, a mathematical method is used to unify the performance of the pressure vessel materials produced by different manufacturers to the national standard level so as to reduce the error caused by the performance difference of the sample, and meanwhile, the fitting result is in orbit with the national standard value in terms of numerical value, so that the reliability of the fitting result is increased.
When the real stress value of the sample is converted into the standard stress value, the elastic modulus of the sample is determined by the properties of the material, and the elastic modulus of the material is not conservatively processed in the process of preparing the national standard, so that when the real stress of the sample is standardized, the curve of the elastic stage is not processed, and only the curve of the yield stage and the strain strengthening stage is processed to be reduced to the standard value. The actual stress of the yield stage and the strain strengthening stage is reduced to a standard value by a processing method such as a formula sigmas＝σt·K(T)The parameter K (T) is introduced as the normalization factor of the material, where the subscript T denotes the temperature and K (T) is defined by
Figure GDA0001293948620000202
The standard value of the material Rp0.2 is directly obtained by inquiring GB150-2011, and the material Rp0.2The test value of (2) is disclosed by the value of Rp0.2 in the test result output from the testing machineFormula sigmatt＝σ(1+et) Is obtained after the calculation of (1).
The true strain does not have a reduction process in the standard, and therefore does not need to be reduced to the standard value. And integrating the stress standard values of the yield stage and the strain strengthening stage obtained by calculation and the real stress value of the elastic stage to obtain complete material tensile standard stress value data, and corresponding the data to the material real strain data to obtain a standard value stress-strain relation curve of the material in the tensile process.
The classification of pressure vessel materials is various, the fitting requirements of different materials are often difficult to meet by using the same fitting model, and the fitting accuracy can be better improved by providing different fitting models for materials with different properties. The embodiment of the invention takes the existence of an obvious yield platform as a dividing condition, divides the materials in China into two types, respectively puts forward numerical models for tensile curves of the two types of materials, independently performs numerical representation on each grade of material, and fits the standard real stress-strain relation of the material into a continuous function related to temperature in an allowable temperature range, wherein the specific fitting method is as follows.
The embodiment of the invention provides a numerical model capable of accurately fitting the tensile curve of the material without the obvious yield stage through the summary analysis of the tensile test results of the materials such as austenitic stainless steel and the like, and the expression is as follows:
Figure GDA0001293948620000211
the established numerical model of the tensile curve of the non-yielding material is used for describing the tensile curve of the material at any specified temperature, wherein the first item on the right side of the equal sign is used for representing the elastic stage of the material, the second item is used for representing the strain strengthening stage, and the three fitting parameters of a, b and d are determined by the fitting result of the material curve at the specific temperature.
The numerical method provided by the embodiment of the invention is used for fitting the material tensile curve, and the test number needs to be firstly matchedFurther processing is carried out. Taking into account the Rp of the material0.2The value is an important mechanical property parameter of the material, and Rp is obtained by reversely deducing a numerical result of a material tensile curve0.2The values should be consistent with the standard values, so that the fitting process needs to be performed on Rp0.2This feature point is specially treated. Before the fitting begins, the Rp of the material at each test temperature point needs to be looked up in GB150-20110.2The standard value is obtained by inverting the coordinate (Rp) of the intersection point of the 0.2 percent engineering deviation line and the material stretching curve from the formula (4-2)0.2) And supplementing the stress and strain values of the coordinates of the intersection points corresponding to the temperatures into a material standard stress and strain value data table to serve as fitting reference data, wherein under an ideal condition, the numerical result of the material tensile curve should pass through the intersection points.
Figure GDA0001293948620000212
In the formula (4-1), the numerical method proposed in the embodiment of the present invention uses the elastic modulus as a material mechanical property parameter at the time of fitting. Because the elastic modulus value of the material in the national standard is normalized in a table form, the standard value of the elastic modulus is a discrete function related to the temperature, and the numerical process of the embodiment of the invention requires that all parameters are continuous in an allowable temperature range, therefore, the elastic modulus standard value of the material at each test temperature point needs to be searched in GB150-2011, a proper function model is searched to fit the elastic modulus of the material, the function model is described as a continuous function related to the temperature, and the fitting result is substituted into the formula (4-1) to complete the supplement of the elastic modulus standard value in the allowable temperature range of the material.
And after the preparation work is finished, importing basic data required by fitting. And opening curve fitting software, introducing a real stress and strain standard value table of the material to be fitted into the software, and inputting a formula (4-1) tensile curve numerical model. In performing the data table import, Rp calculated by equation (4-2) is used to ensure the final result of the curve fitting0.2Characteristic points, need to be on Rp0.2Adding extra to the feature pointsFitting the weight values to Rp0.2The feature points appear more important than other data points in the fitting process, and the specific weight distribution depends on the density degree of the test data.
And after the data import work is finished, the numerical representation work of the curve is started to be finished. And (3) preliminarily fitting the standard stress and strain values of the material at each temperature point by using a formula (4-1), and solving the numerical values of the fitting parameters a, b and d at different temperatures by using a, b and d as undetermined parameters in the fitting process. When the numerical result of the preliminary fitting is used, fitting parameters a, b and c at a certain temperature are substituted into a formula (4-1), and a continuous real stress-strain relation curve of the material at the temperature can be obtained.
The fitted curve obtained through the above work already has the function of describing the stress-strain relationship of the material at various temperatures, but from the perspective of engineering application, the method of using tabulated listing for all fitted parameters is not convenient for the use of the numerical result in practical engineering. Meanwhile, due to the limitation of the number of the test temperature points, the obtained preliminary fitting result is not continuous within the allowable temperature range, so that other methods are needed to further describe the fitting parameters in the model. In the test, the trend change of the tensile curve of the material is only related to the property and the temperature of the material, so that the temperature is selected as the variable X, the values of the fitting parameters a, b and d are fitted, and all the fitting parameters are uniformly expressed as a function of the temperature. The function of representing the fitting parameters as the temperature has the advantages that after the grade of the material is determined, the real stress-strain relationship of the material is only determined by the temperature, when the numerical result of the tensile curve of the material is used, only the use temperature and the grade type are needed to be input, the real stress-strain relationship curve of the material at the temperature can be automatically generated by a numerical model, and a complicated parameter substituting process is not needed.
When the parameters a, b and d are fitted, it should be noted that in the process of numerical representation of the material tensile curve, the parameters are buckled with each other, and the change of any parameter value can cause the change of the fitted curve, so that a large error is generated between the fitted result and the actual mechanical property of the material. Therefore, in order to minimize fitting errors caused by continuous characterization of parameters, when fitting parameters are continuously fitted, the three parameters are fitted one by one, after one parameter fitting is completed, the parameters which are not fitted need to be recalculated, and then the latest calculation result is fitted. The fitting of the three parameters has no requirement on the sequence, but from the viewpoint of fitting accuracy, the fitting should be started from the parameter with a more complex numerical value.
An embodiment of the invention first fits the parameter a. And (3) taking the numerical value of the parameter a at each temperature as a vertical coordinate, drawing a curve by taking the corresponding temperature as a horizontal coordinate, observing the line type of the drawn curve, and selecting a function type which is closest to the line type of the curve for fitting. And obtaining a fitting relation of the a value and the temperature. Substituting the functional relation of the value a and the temperature into the formula (4-1) to obtain a formula (4-3):
Figure GDA0001293948620000231
after the fitting formula of the value a is obtained, the numerical values of the parameter b and the parameter d need to be recalculated, the standard stress and strain relation of the material at each temperature point is fitted again by using the formula (4-3), the numerical values of the fitting parameters b and d at different temperatures are obtained, the fitting is sequentially carried out on the b and the d, and the b value and the d value are respectively fitted into a function of the temperature. The embodiment of the invention first fits the fitting parameter b: drawing a curve by taking the value b as a vertical coordinate and the temperature as a horizontal coordinate, observing the change trend of the value b along with the temperature, selecting a function type closest to the change trend of the value b to fit the value b to obtain a fitting relational expression of the value b relative to the temperature, and substituting the fitting result into a formula (4-3) to obtain a formula (4-4):
Figure GDA0001293948620000232
the parameters a and b in the formula (4-1) are both expressed as a function of temperature in the formula (4-4), and if the value d is also expressed as a function of temperature, the whole material tensile curve numerical model can be expressed as a function of temperature. The fitting method of the d value is similar to that of the a and the b, and the standard real stress-strain relation obtained by the tensile test is re-fitted by using a formula (4-4), so that the numerical value of the fitting parameter d corresponding to each test temperature is obtained. Fitting the d value in the fitting result as a function of temperature: and (3) observing the change trend of the d value along with the temperature by taking the temperature as an abscissa and the d value as an ordinate, selecting a function model closest to the change trend, fitting the function relation of the d value and the temperature to obtain a fitting relation of the d value with respect to the temperature, and substituting the relation into the formula (4-4) to obtain a formula (4-5).
Figure GDA0001293948620000233
The equations (4-5) are the complete material tensile curve numerical results. After the fitting is finished, error analysis is carried out on the formula (4-5), and if the error is within an allowable range, the fitting work is finished; if the error is too large, the test data needs to be fitted again.
In the numerical results shown in equation (4-5), the fitting parameters are all functions of temperature, and the true stress-strain relationship of the material is only related to temperature. When the numerical result is applied, the real stress-strain relation of the material at the temperature can be obtained by inputting any temperature value in the allowable temperature range into the formula (4-5). The fitting mode is convenient to understand in engineering application, can ensure that the stress-strain relation of a specific material at a specific temperature is unique, and is suitable for being applied to the analysis design standard of a pressure container to standardize the material performance.
For materials with a distinct yield stage, such as: mild steel, etc., the examples of the present invention established a fitting model as shown in equation (4-6) which differs from the no yield stage material model in that:
a yield stage fitting coefficient c is added, which is used to correct the length of the yield plateau in the material numeralization curve.
Incorporating Rp of the material0.2A performance parameter for stress corresponding to yield plateau in a numerical result of the materialThe value is corrected.
The model can better fit the tensile curves of the material in the elastic stage, the yield stage and the strain strengthening stage, and can complete the description of the trend of the yield platform changing along with the temperature when the numerical representation is carried out on the material yield stage.
Figure GDA0001293948620000241
c＝-10tanh(T-Ts)+10.05 (4-6)
When the material with obvious yield stage is fitted, the elastic modulus and Rp of the material corresponding to each test temperature point are firstly searched in a pressure container standard (GB150-2011) according to the test condition0.2The standard value of the stress and strain value is calculated by a formula (4-2), the intersection point coordinate of the 0.2% engineering deviation line and the material test value curve is reversely deduced, and the stress and strain value of the intersection point coordinate at each temperature point is supplemented into a material standard real stress and strain value data table to be used as fitting reference data.
Introducing standard real stress and strain value data tables into curve fitting software, and inputting elastic modulus and Rp of the material0.2The standard value of (2). Observe the elastic modulus, Rp of the material0.2According to the variation trend of the temperature, fitting the elastic modulus and Rp0.2 by using a function model which is closest to the curve trend, and fitting the elastic modulus and the Rp0.2Expressed as a continuous function with respect to temperature. And (3) substituting the fitting result of the material performance parameter into a formula (4-6), fitting the standard real stress-strain relation of the material at each temperature point by using a numerical model of the formula (4-6), and solving the numerical values of the fitting parameters a and b corresponding to each test temperature point to obtain an initial fitting curve of the material tensile curve at each temperature.
And making a functional relation curve of a fitting parameter a value and temperature in a coordinate system, observing the change trend of the a value along with the temperature, fitting the functional relation of the a value and the temperature by using a function model closest to the trend of the a value, and representing the a value as a continuous function related to the temperature. Substituting the fitting result into the formula (4-6) to obtain the formula (4-7):
Figure GDA0001293948620000251
after the fitting of the a value is completed, the fitting result of the b value at each temperature needs to be calculated again. And (3) refitting the standard real stress-strain relation of the material at each test temperature point by using a numerical model shown in a formula (4-7), solving the numerical value of a fitting parameter b corresponding to each test temperature point, drawing a functional relation curve of the b value and the temperature in a coordinate system, observing the change trend of the b value along with the temperature, fitting the functional relation of the b value along with the change of the temperature by using a functional model which is closest to the trend of the b value, and expressing the b value as a continuous function related to the temperature. Substituting the fitting result into the formula (4-7) to obtain the formula (4-8):
Figure GDA0001293948620000252
analyzing the error between the fitting result and the test value in the formula (4-8), and finishing the fitting work if the error is within an allowable range; if the error is larger, the test data needs to be fitted again. All the fitting parameters and performance parameters in the formula (4-8) are functions of temperature, and the model accurately describes curve changes of an elastic stage, a yield stage and a strain strengthening stage of a material tensile curve. When the numerical result is used, the working condition temperature is input, and the real stress-strain relation of the material at the temperature can be obtained.
The numerical method provided by the embodiment of the invention summarizes the relation between the temperature and the tensile curve, and provides a method for expressing the tensile curve of a certain material as a function of the temperature. Meanwhile, the fitting result of the model is suitable for any temperature within the allowable temperature range of the material, so that the fitting result of the tensile curve is not limited to a plurality of fixed temperature points any more, curve fitting is carried out within a continuous temperature range, and the flexibility of the fitting result in engineering application is ensured.
Because different materials show larger difference on the tensile curve, a uniform model is difficult to summarize on the premise of ensuring the accurate fitting result of each grade of material. Compared with other tensile curve fitting methods, the method provided by the embodiment of the invention is more flexible in the fitting process, variables in the model are obtained by fitting actual curves, the maximum consistency with the test result is kept on the numerical value, different fitting models are used for different materials, different fitting parameters are selected according to the difference of the line types of the tensile curves of the materials at different temperatures, the test results of the different materials can be more accurately fitted, the accuracy of the fitting curve of each material at each temperature point is ensured, and the condition that the fitting accuracy is sacrificed to ensure the uniformity of the model of the fitting result is avoided.
For a material with a yield stage, the yield platform plays a very important role in the stress-strain relationship of the material, and if the yield stage of the material is neglected, the accuracy of the fitting result is influenced. The numerical method of the embodiment of the invention realizes numerical representation of the tensile curve of the low-carbon steel material in the yield stage. In the fitting result, the yield strength of the material and the length of the yield platform change along with the temperature, when the material is at a higher temperature, the yield platform in the numerical result disappears, and the fitting result is consistent with the characteristics of a high-temperature tensile curve of the material. Compared with other fitting models, the numerical method provided by the embodiment of the invention has higher precision in fitting the material yield stage, and ensures the accuracy of the numerical result of the tensile curve in engineering application.
Considering from the perspective of computer application, as a data base for elastic-plastic analysis of a material, a numerical result of a material tensile curve is directly used by CAE software, and therefore whether a curve fitting result is convenient for a computer to use or not is an important index for judging the rationality of a fitting model. The speed of the computer is high when mathematical operation is carried out, the speed is low when selection is carried out, if the model uses the piecewise function, although the accuracy of model fitting can be increased to a certain extent, the piecewise function can greatly increase the time consumed by computer operation from the viewpoint of data processing of the computer, and is not beneficial to the application of the fitting model in engineering. The model uses all continuous functions in the fitting process, and the method has the advantages of reducing a large number of machines consumed by a computer in processing the selection statement, increasing the running speed of the computer in processing data and saving time cost.
EXAMPLE five
In this embodiment, S31608 is taken as an example to describe the fitting process and the fitting result of the numerical method provided in the embodiment of the present invention to the stainless steel material, and perform error analysis.
All functions in the numerical model provided by the invention are continuous and high-order conductible functions in a definition domain, and standard values of the elastic modulus given in the pressure container standard (GB150-2011) are discrete, so curve fitting needs to be carried out on the standard values in the national standard at first, and the discrete standard values are described into a continuous function form which can be used by the model. The standard value of the modulus of elasticity was fitted using a quadratic polynomial, and the fitting results are shown in equations (4-9).
Ey(T)＝1.806×10-4T2-0.618T+1958 (4-9)
The fitting curve is shown in fig. 8 and is the fitting result of the elastic modulus of the austenitic stainless steel S31608, wherein the black points are the standard values of the elastic modulus in GB150-2011, and the solid line is the fitting result. In the image, the fitting curve can basically ensure that the standard value, the fitting value and the judgment coefficient R of the standard value pass through2The coefficient is 0.9981, the fitting error is in a reasonable range, and the fitting result is ideal.
Using equation (4-2) for material Rp0.2The corresponding stress and strain theoretical values are calculated, and the calculation results are shown in table 1:
rp of Table 1S316080.2Theoretical value of stress and strain
Temperature/. degree.C Strain of stress/MPa
20 0.305128 205
100 0.292593 175
150 0.286559 161
200 0.281421 149
250 0.277654 139
300 0.274857 131
350 0.273256 126
400 0.272781 123
450 0.273333 121
500 0.274375 119
550 0.275 117
And (4) filling the calculation result into a material standard real stress-strain value table to serve as important reference data during fitting. Add a "weight" field to the data table where Rp0.2The corresponding stress and strain values are weighted more than other values, and the specific weight proportion depends on the density degree of data. And importing the data table into curve fitting software to finish the preparation work of curve numerical representation.
Embodiments of the present invention fit curves using the curve fitting tool box of MATLAB. And (4) opening a cftool box after importing the data table to be fitted into MATLAB software. Clicking a Data button, selecting a group of test Data to be fitted, and selecting curve fitting weight while fitting by taking stress as an abscissa and strain as an ordinate because the numerical model takes the stress as an independent variable. After data are imported into a cftool box, a Fitting button is clicked to fit a curve, an option of a custom Fitting formula is selected during Fitting, a numerical model shown in a formula (4-1) is input into a column of the Fitting formula, a Fitting button is clicked to complete preliminary Fitting of the curve, and as shown in fig. 9 (taking a 100 ℃ tensile curve Fitting result as an example), for a preliminary Fitting result of the cftool box on S31608 at 100 ℃, relevant characteristics of the tensile curve can be accurately fitted through the preliminary Fitting, and optimal solutions of Fitting parameters a, b and d at specific temperatures are solved. After completing the preliminary fitting for all test temperatures of S31608, values of fitting parameters a, b, d at each temperature were recorded, as shown in Table 2
TABLE 2S31608 tensile curve preliminary fitting results
Temperature/. degree.C a b D
20 2.535 3.099 309.2
100 1.217 4.463 258.7
150 1.53 4.218 247.4
200 1.621 4.182 233.4
250 1.685 4.278 222.5
300 1.976 4.081 214.9
350 2.222 4.024 211.6
400 2.457 3.813 208.7
450 2.396 3.857 205.5
500 2.205 3.808 199.5
550 1.83 4.222 194.8
The relationship between the fitting parameters and the temperature in table 2 is represented in the form of a discrete function, and does not meet the requirement that the fitting parameters are continuous within the allowable temperature range, so that the fitting parameters need to be subjected to function fitting, and the fitting parameters are described as continuous functions with respect to the temperature. However, if the three functions are fitted at the same time, errors of fitting results are superposed, and a large error occurs in the fitting result of the final tensile curve, so that the three functions need to be fitted in sequence. After each time the fitting of one parameter is completed, the values of the other parameters need to be recalculated, and then the fitting work of the next parameter is performed. The embodiment of the invention selects to fit the fitting parameter a at first, selects a cubic polynomial to fit, and the fitting result is shown as a formula (4-10):
a(T)＝-9.899×10-8T3+8.767×10-5T2-0.002013T+2.79 (4-10)
as shown in fig. 10, the determination coefficient R2 of the fitting result of the value a is 0.9048, the fitting result is not ideal, and it can be seen from the fitting curve that the fitting curve is greatly different from the calculated value, and the fitting value is greatly different from the calculated value of the value a at three temperature points of 100 ℃, 150 ℃ and 200 ℃, so that the influence of the fitting error of the value a on the fitting result of the stretching curve needs to be corrected by recalculating the value b and the value d. Using the function model of formula (4-3), the test values at each temperature were re-fitted, and the b and d values in the fitting results were recorded, as shown in table 3:
TABLE 3S31608 tensile Curve second fitting results
Figure GDA0001293948620000281
Figure GDA0001293948620000291
Similarly, the b value and the d value obtained by quadratic fitting need to be fitted one by one, fitting parameters b and d are described as continuous functions related to temperature, a cubic polynomial is selected to fit the b value, and the fitting result is shown in formula (4-11):
b(T)＝7.926×10-8T3-7.425×10-5T2+0.01949T+2.787 (4-11)
as shown in fig. 11, the fitting curve has a b-value determination coefficient R2 of 0.9743, and the fitting result is ideal. It should be noted, however, that slight errors in any of the parameters during the curve fitting process may cause the final result of the curve fitting to be inconsistent with the actual performance of the material, and therefore, the value of d still needs to be recalculated before fitting the fitting parameter d. Using the functional model of equation (4-4), the test values at each temperature were fitted for the third time, and the d value in the fitting results was recorded, as shown in table 4:
TABLE 4S31608 third time fitting of tensile curves
Table.4-3The third fitting result of the stress-strain curve of S31608
Temperature/. degree.C D
20 307.4
100 265
150 245.3
200 232
250 222.3
300 214.9
350 212.1
400 207.7
450 205
500 201.8
550 193.5
The fitting process is also required for the d value obtained by the third fitting, as in the case of the a and b values. A cubic polynomial is chosen to fit the value of d, describing d as a continuous function with respect to temperature. It should be noted that the d value is the last parameter to be fitted in the numerical model, the fitting error cannot be corrected by fitting other parameters, and the fitting error of the d value directly affects the final error of the fitting result of the whole curve, so that fitting of the d value is strict, and if the error of the fitting result is large, fitting should be performed again. The result of the d value is shown in equations (4-12):
d(T)＝-1.376×10-6T3+1.653×10-3T2-0.7244T+321.6 (4-12)
as shown in fig. 12, the decision coefficient R2 for the d value is 0.9996, and the correlation between the fitting result and the calculated value of the parameter d is very high, and the fitting result is satisfactory. By summarizing the above fitting results, a numerical model of the tensile curve of the austenitic stainless steel material S31608 can be obtained, and the final fitting results are shown in the formula (4-13):
Figure GDA0001293948620000301
Ey(T)＝1.806×10-4T2-0.618T+1958
a(T)＝-9.899×10-8T3+8.767×10-5T2-0.002013T+2.79
b(T)＝7.926×10-8T3-7.425×10-5T2+0.01949T+2.787
d(T)＝-1.376×10-6T3+1.653×10-3T2-0.7244T+321.6 (4-13)
the fitting result obtained finally is shown in fig. 13, and as can be seen from the figure, the fitting degree of fit between the fitting curve and the measured curve is high. S31608, where the long dotted line is the fitting result of the numerical method (numerical characterization method) used in the embodiment of the present invention, the short dotted line is the fitting result of the MPC model, and the solid line is the standard stress, strain value of the test result. By error analysis, the determination coefficient R between the tensile curve and the test value is obtained by the numerical method of the embodiment of the invention2The fitting error can be accepted, and the fitting result is satisfactory. The fitting results of the two models were compared: from the stress perspective, when the strain is the same, the stress value calculated by the numerical method of the embodiment of the invention is closer to the test value than the MPC model, and the fitting error is smaller; from the perspective of strain, the numerical method used in the embodiment of the present invention is more accurate in determining the strain value during tensile strength, and the MPC model has a situation that the tensile strength determination is too early.
EXAMPLE six
In this embodiment, Q345R is taken as an example to describe the fitting process and the fitting result of the numerical method provided by the embodiment of the present invention to the low carbon steel material, and to perform error analysis.
The formula (4-6) refers to two material performance parameters of elastic modulus and Rp0.2, and before the two parameters are used for fitting, standard values of the two parameters need to be fitted, and discrete function values are fitted into a usable continuous function form. The standard value of the modulus of elasticity of Q345R was fitted using a cubic polynomial, and the fitting results are shown in equations (4-14):
Ey(T)＝-5.144×10-7T3+1.821×10-4T2-0.07197T+2025 (4-14)
fig. 14 shows the fitting result of the low-carbon steel Q345R with an elastic modulus of 0.9995, a very small fitting error and an ideal fitting result. Rp of Q345R using cubic polynomial0.2Fitting the standard values, wherein the fitting result is shown in an equation (4-15):
σRp0.2(T)＝1.468×10-6T3-8.237×10-4T2-0.2833T+350.9 (4-15)
the fitted curve is shown in fig. 15:
fig. 15 shows the result of the rp0.2 fitting of Q345R, the decision coefficient is 0.9995, the error of the fitting result is within an acceptable range, and the fitting result can be used in the next fitting work. Calculation of Q345R at Rp from equation (4-2)0.2The theoretical values of stress and strain at the points are shown in table 5:
table 5 Rp of Q345R0.2Theoretical value of stress and strain
Temperature/. degree.C Strain/% stress/MPa
20 0.171642 345
100 0.159898 315
150 0.152062 295
200 0.143979 275
250 0.132979 250
300 0.125683 230
350 0.120787 215
400 0.117647 200
450 0.11875 190
Importing the calculation result into a test data table, adding a 'weight' field in the test data table, and setting weights for all test data, wherein Rp0.2The corresponding stress and strain values are weighted more than other test values, and the specific proportion depends on the density degree of data.
Fitting the test data using fitting software, such as the cftool kit of MATLAB, using equation (4-6) as the fitting model, to complete the preliminary fitting of the tensile curve, with the fitting results shown in table 6:
TABLE 6Q345R tensile curve preliminary fitting results
Table.6The preliminary fitting result of the stress-strain curve of Q345R
Temperature/. degree.C a value b value
20 0.01 12.1
100 0.008 14.05
150 0.0058 14.07
200 0.0085 14.39
250 0.00925 12.93875
300 0.0121 11.488
350 0.0106 12.36825
400 0.00741 16.538
450 0.00236 24.95575
Fitting the fitting parameters a and b one by one, and after one parameter is fitted, recalculating the other parameter, wherein the fitting parameter a is fitted firstly. In order to reduce the influence of fitting fluctuation of the value a on the yield plateau, the embodiment of the present invention selects a tanh function model to fit the parameter a, and the fitting result is shown in the formula (4-16):
a(T)＝-4.803×10-3tanh[0.02293(T-425)]+0.004803 (4-16)
the fitted curve is shown in fig. 16:
it can be seen that the fitting result of the parameter a is not ideal due to the influence of factors such as the change of the yielding platform, and if the b values in tables 4 to 7 are continuously used, a large error occurs in the fitting result, so that the b value needs to be recalculated by using the formula (4 to 7), and the recalculated b value needs to be fitted, and the calculation result is shown in table 7: TABLE 7Q345R tensile Curve second fitting results
Temperature/. degree.C a value (calculated by formula 4-16) b value
20 0.0096 12.1
100 0.0096 13.66
150 0.0096 13.09
200 0.0096 12.41
250 0.0096 11.71
300 0.0096 11.52
350 0.0094 12.32
400 0.00741 15.46
450 0.00236 22.8
Fitting the value b, wherein the value b is the last parameter to be fitted, so that the fitting of the value b is strict, a Gaussian function is selected to fit the parameter b, and the fitting result is shown in a formula (4-17):
Figure GDA0001293948620000331
the fitted curve is shown in fig. 17:
the determination coefficient of the b-value fitting result is 0.9955, and the fitting result is ideal. Summarizing the above fitting results of Q345R tensile curve numerical parameters, a Q345R tensile curve numerical model can be obtained, and the final fitting results are shown in the formula (4-18):
Figure GDA0001293948620000332
c＝-10tanh(T-320)+10.05
Ey(T)＝-5.144×10-7T3+1.821×10-4T2-0.07197T+2025
σRp0.2(T)＝1.468×10-6T3-8.237×10-4T2-0.2833T+350.9
a(T)＝-4.803×10-3tanh[0.02293(T-425)]+0.004803
Figure GDA0001293948620000333
fig. 18 is a graph comparing the actual measurement curve and the fitting result in the present example, and it is clear from the graph that the result matching degree is high. The yield platform is a remarkable characteristic of the low-carbon steel material, and if the stress-strain relationship of the low-carbon steel material is required to be accurately described, the description of the yield platform is essential, and the numerical method used in the embodiment of the invention fits the stress-strain relationships of the Q345R in the elastic stage, the yield stage and the strain strengthening stage at different temperatures to a certain extent, and completes the description of the characteristic that the Q345R has the yield stage within 300 ℃ and does not have the yield stage after 300 ℃. The embodiment of the invention controls the judgment coefficient of the numerical result of the Q345R to be more than 0.98, and has higher fitting precision of the tensile curve, within a reasonable range of error and ideal fitting result for the numerical result of the pressure container material with obvious yield stage. Compared with an MPC model (model in ASME), the fitting result of the embodiment of the invention is more stable, the fitting error and the test value are always kept in a smaller difference, and the change trend of the fitting result is basically consistent with the test result. Therefore, it can be summarized that the material property numeralization method used in the embodiment of the present invention can more accurately fit a material yield stage curve when fitting the tensile curve of Q345R, and meanwhile, the fit error is smaller than that of the MPC model, and the fit result is more accurate.
EXAMPLE seven
As shown in fig. 19, the present invention further provides a system 300 for characterizing material stress-strain constitutive relation, which implements the method for characterizing material stress-strain constitutive relation, including a loading device 301 for applying a load to a material sample, a force measuring device 302 for measuring a force applied to the material to be measured, a strain rate measuring device 303 for measuring a strain rate, a heating device 304 for heating the material, a temperature measuring device 305 for measuring a temperature of the material, and a calculating device 306 for processing the stress data and the strain data to obtain parameters in a stress-strain numerical model.
The loading device 301 in the embodiment of the present invention employs a tensile testing machine, and a computer is used to perform digital control on the testing machine. For the calibration of the force measuring system of the tensile testing machine, according to the Chinese standard: the testing of the static uniaxial testing machine is carried out according to the relevant specifications in the calibration (GB/T16825.1) of the first part of the tensile force and/or the force measuring system of the compression testing machine, and the calibration accuracy of the force measuring system is 1 grade. Data acquisition and processing working reference standards for tensile testing: in the first part of the metal material tensile test, the requirements of annex A in a room temperature test method (GB/T228.1-2010) are carried out, the tensile force applied to the material is measured by adopting the tensile testing machine in the embodiment of the invention, and the force measuring device 302 is the tensile testing machine.
The strain rate measuring device 303 adopted by the invention is an extensometer, the extensometer used in the test conforms to relevant regulations in the calibration standard (GB/T12160) of the extensometer for the Chinese standard single-axis test, and the accuracy grade is 1 grade.
The heating device 304 in this embodiment of the present invention is a high temperature furnace, and the high temperature furnace used in this test is used to heat the sample subjected to the high temperature tensile test.
The temperature measurement device 305 in the embodiments of the present invention is a thermocouple, and the thermocouple used meets the level 2 temperature measurement requirements specified in the working precious metal thermocouple certification code standard (JJG 141). The lowest resolution of the temperature measuring device 305 is 1 deg.c, and the error is within ± 0.004 θ ℃ (θ is the prescribed temperature) or ± 2 deg.c, taking the maximum value.
The numerical characterization system of the material stress-strain constitutive relation utilizes tensile experiment data, selects a numerical model corresponding to a material to simulate a tensile stress-strain curve, calculates parameters in the model, and then obtains a complete numerical model for characterizing the material stress-strain constitutive relation, so that the numerical characterization system of the material stress-strain constitutive relation is more in line with the real characteristics of the material, and provides a reliable basis for the design of a pressure container.
EXAMPLE seven
According to the measured and calculated material numerical model, the invention also provides a method for solving the stress-strain relationship of the material, which comprises the steps of inputting a temperature parameter and a material parameter to a stress-strain relationship solving module, wherein the stress-strain relationship solving module is used for solving the stress-strain relationship corresponding to the temperature and the material from the stress-strain numerical model corresponding to the material parameter according to the temperature parameter, so that the consumption of repeated calculation is reduced, and the efficiency of obtaining a material performance parameter curve is increased. The material parameters comprise the grade and the type of the material. The stress-strain relationship obtaining module may be a software program code executed on computer hardware, and specifically, stress-strain model data corresponding to the material parameter and the temperature parameter is stored, and the expression form of the stress-strain model data may be a graph curve or a data point sequence.
The numerical value characterization method is real and reliable, and provides a good theoretical basis for design. The method and the system in the embodiment of the invention have reliable test basis, more consistent constitutive relation, more accurate mathematical expression and less error, better meet the requirements of design safety and economy, overcome the technical defects of large error of a material performance characterization method and inconsistent curve and constitutive relation of materials, and simultaneously provide the characteristic of the materials at discrete temperature aiming at the conventional standard. The stress data strain number of the actually measured material is simulated by adopting a numerical model, the solved stress-strain constitutive relation is ensured to be more consistent with the real mechanical property of the material, a reliable basis is provided for the design of mechanical containers such as pressure containers and the like, and the method and the system can be applied to the material property parameter after the material property parameter is actually measured aiming at the material property condition of different countries.

Claims (33)

1. A numerical characterization method of material stress-strain constitutive relation comprises,
a) setting test parameters, wherein the test parameters comprise a sample temperature T;
b) performing a tensile test on the material according to the test parameters to obtain tensile test data of the material, wherein the tensile test data comprises stress data and strain data;
c) establishing a stress-strain curve according to the stress data and the strain data;
d) selecting a corresponding stress-strain numerical model according to the attribute of the material, fitting a stress-strain curve of the material, and solving parameters in the stress-strain numerical model; wherein the content of the first and second substances,
said step d) comprises, when said material is a material with a distinct yield phase, selecting said stress-strain numerical model as,
Figure FDA0002742330750000011
in the formula TsThe lowest temperature of the tensile curve yield platform disappearance is shown, a and b are parameters in the stress-strain numerical model,trepresenting true strain, σtRepresenting true stress, EyDenotes the modulus of elasticity, σ, of the materialRp0.2Representing the true standard yield stress.
2. The method for numerical characterization of the stress-strain constitutive relation of a material according to claim 1, wherein the step d) further comprises, when the material is a material without significant yield strength, selecting the stress-strain numerical model as,
Figure FDA0002742330750000012
wherein a, b and d are parameters in the stress-strain numerical model,trepresenting true strain, σtRepresenting true stress, EyRepresenting the modulus of elasticity of the material.
3. The method for numerical characterization of the stress-strain constitutive relation of a material according to any one of claims 1 to 2, further comprising setting different temperatures, and repeating the steps b), c) and d) to obtain the stress-strain curve of the material at different temperatures and parameters in the stress-strain numerical model.
4. The method for numerical characterization of material stress-strain constitutive relation according to claim 3, further comprising step e) establishing a parametric temperature curve according to parameters in the stress-strain numerical model obtained at different temperatures, and fitting a parametric temperature model according to the parametric temperature curve.
5. The method of numerical characterization of material stress-strain constitutive relation according to claim 3, the stress-strain numerical model has a plurality of parameters, the numerical characterization method further comprises the steps of selecting one parameter from the parameters in the stress-strain numerical model, implementing the step f) to establish a parameter temperature curve, fitting a parameter temperature model, substituting the different temperatures into the parameter temperature model, finding fitted values of the selected parameter at different temperatures, substituting the fitted values into a stress-strain numerical model of the material, fitting the stress-strain curve by using the stress-strain numerical model of the material with the fitted value substituted, and solving the rest parameters in the stress-strain numerical model of the material at different temperatures; and f) selecting one of the other parameters in the stress-strain numerical model, and implementing the step f) until all the parameters in the stress-strain numerical model are solved.
6. The method for numerical characterization of material stress-strain constitutive relation according to any one of claims 1 to 2, wherein the stress-strain numerical model includes elastic modulus parameters, an elastic modulus temperature relation graph is established according to the elastic modulus values at discrete temperatures, and an elastic modulus temperature curve is fitted according to the elastic modulus temperature relation graph to obtain curve parameters.
7. A method for numerical characterization of the material stress-strain constitutive relation according to any one of claims 1 to 2, characterized in that said step c) comprises, according to the formula σtt＝σ(1+et) Processing said stress data into true stress data, where σttRepresenting the true stress at time t in a tensile test, sigma representing the stress data measured in said tensile test,etdata representing the measured strain at time t in a tensile test; according to the formulat＝ln(1+e) Processing said strain data into true strain data, whereintTo representThe true strain is the true strain of the strain,erepresenting engineering strain; and (3) carrying out the following treatment on the true stress of the material in a yield stage and/or a strain strengthening stage: sigmas＝σt·K(T)In the formula σsValue representing the true stress normalization, K(T)The normalized coefficient is represented by a normalized coefficient,
Figure FDA0002742330750000021
in the formula sigmaRp0.2(standard)Denotes the standard yield stress, σ, of the materialRp0.2(test)Represents the yield stress sigma of the material in a tensile test0.2By the following formula,. sigmaRp0.2(test)＝σ0.2(1+et) The true stress converted.
8. The method for numerical characterization of the material stress-strain constitutive relation according to any one of claims 1 to 2, wherein the test parameters further include a sample requirement, a strain rate, a data acquisition frequency and a strain range, and the step b) further includes selecting a diameter of the sample when the material is subjected to a tensile test; marking the material number of the sample on the sample; marking the samples at intervals; the diameter of the sample before the tensile test was measured a plurality of times to find an average value, and the cross-sectional area of the sample was calculated.
9. The method for numerical characterization of the material stress-strain constitutive relation according to any one of claims 1 to 2, wherein the tensile test in the step b) adopts constant-speed tensile, when the strain range is 0 to 7.5%, the strain rate is used for controlling the test rate, and a extensometer is used for measuring the strain rate of the tensile test; when the strain range is larger than 7.5%, the test speed is controlled by the displacement speed of the cross beam according to the strain range
Figure FDA0002742330750000031
To determine in the formula
Figure FDA0002742330750000032
To the stretching rate, LeIs the beam displacement, veIs the beam displacement rate.
10. The method for numerical characterization of the material stress-strain constitutive relation according to any one of claims 1 to 2, wherein the sample temperature is in a range of 20 ℃ to 700 ℃.
11. The method for numerical characterization of the material stress-strain constitutive relation according to claim 8, wherein the diameter of the specimen is 10 mm.
12. A method for numerical characterization of the material stress strain constitutive relation according to claim 8 wherein the step of marking at intervals of the specimen comprises: setting the original gauge length L of the sample0Marking the sample by a scriber every 10mm at 50mm, wherein the distance precision of the scriber is +/-1%. L0Within the range.
13. The method for numerical characterization of the material stress-strain constitutive relation according to claim 9, wherein the temperature of the tensile test in the step b) is 10 ℃ to 35 ℃, and the tensile rate is set to be
Figure FDA0002742330750000033
14. The method for numerically characterizing the stress-strain constitutive relation of a material according to claim 9, wherein the temperature of the tensile test in the step b) is 100 ℃ or higher, the sample is heated to a predetermined temperature, the sample is kept at the predetermined temperature for at least 10 minutes, and the tensile rate is set to be
Figure FDA0002742330750000034
15. As claimed inSolving the numerical characterization method of the material stress-strain constitutive relation of any one of 1 to 2, wherein the step c) further comprises obtaining a material stress-strain constitutive relation by the following formula according to a standard stress value Rp0.2 of the material at the temperature,
Figure FDA0002742330750000035
an intersection point (Rp0.2) is obtained, where the strain variable, σ, is expressedrp0.2And representing standard yield stress variable, and enabling the distance between the stress-strain curve and the intersection point to be within a threshold value range when the stress-strain curve is established.
16. The method for numerical characterization of the material stress-strain constitutive relation according to any one of claims 1 to 2, wherein the step c) further comprises obtaining the material stress-strain constitutive relation according to the following formula according to a standard stress value Rp0.2 of the material at the temperature of the sample,
Figure FDA0002742330750000041
an intersection point (Rp0.2) is obtained, where the strain variable, σ, is expressedrp0.2Representing a standard yield stress variable, adding the coordinates of the intersection point into the stress data and the strain data in the step b) when the stress-strain curve is established, establishing the stress-strain curve according to the stress data, the strain data and the data of the intersection point, and multiplying the stress data, the strain data and the data of the intersection point by a fitting weight value, wherein the fitting weight value corresponding to the data of the intersection point is larger than the fitting weight value corresponding to the stress data and the strain data.
17. The method for numerical characterization of the material stress-strain constitutive relation according to claim 1, further comprising setting different temperatures, repeating steps b), c) and d) to obtain the stress-strain curve of the material and parameters a and b in the stress-strain numerical model at different temperatures, fitting according to the corresponding parameters a and b at different temperatures to obtain a parameter temperature model corresponding to the parameter a, and obtaining a parameter temperature model corresponding to the parameter b.
18. The method for numerical characterization of the stress-strain constitutive relation of a material according to claim 17, further comprising, after obtaining the parameter temperature model corresponding to parameter a, obtaining new values of parameter a at different temperatures according to the parameter temperature model corresponding to parameter a, substituting the new values of parameter a into the stress-strain numerical model, fitting a stress-strain curve of the material according to the stress data and strain data obtained at different temperatures, obtaining parameter b in the stress-strain numerical model at different temperatures, and obtaining the parameter temperature model corresponding to parameter b.
19. The method for numerical characterization of material stress-strain constitutive relation according to claim 17, further comprising obtaining a parameter temperature model corresponding to parameter a, and then determining a determination coefficient R of the fitting result of parameter a2Making a decision if the coefficient R is determined2And when the temperature of the material is less than the threshold value, solving new values of the parameter a at different temperatures according to the parameter temperature model corresponding to the parameter a, substituting the new values of the parameter a into the stress-strain numerical model, fitting a stress-strain curve of the material according to the stress data and the strain data acquired at different temperatures, solving a parameter b in the stress-strain numerical model at different temperatures, and acquiring the parameter temperature model corresponding to the parameter b.
20. The method for numerical characterization of the material stress-strain constitutive relation according to claim 2, further comprising setting different temperatures, repeating steps b), c) and d) to obtain parameters a, b and d in the stress-strain curve and the stress-strain numerical model of the material at different temperatures, fitting according to the corresponding parameters a, b and d at different temperatures to obtain a parameter temperature model corresponding to the parameter a, obtain a parameter temperature model corresponding to the parameter b, and obtain a parameter temperature model corresponding to the parameter d.
21. The method for numerical characterization of the stress-strain constitutive relation of a material according to claim 20, further comprising, after obtaining the parameter temperature model corresponding to parameter a, obtaining new values of parameter a at different temperatures according to the parameter temperature model corresponding to parameter a, substituting the new values of parameter a into the stress-strain numerical model, fitting the stress-strain curve of the material according to the stress data and strain data obtained at different temperatures, obtaining parameter b in the stress-strain numerical model at different temperatures, and obtaining the parameter temperature model of parameter b; solving new values of the parameter b at different temperatures according to a parameter temperature model corresponding to the parameter b, substituting the new value of the parameter a and the new value of the parameter b into a stress-strain numerical model, fitting a stress-strain curve of the material according to stress data and strain data acquired at different temperatures, solving a parameter d in the stress-strain numerical model at different temperatures, and acquiring a parameter temperature model of the parameter d.
22. The method for numerical characterization of material stress-strain constitutive relation according to claim 20, further comprising obtaining a parameter temperature model corresponding to parameter a, and then determining a determination coefficient R of the fitting result of parameter a2Making a decision if the coefficient R is determined2When the temperature of the material is less than the threshold value, solving new values of the parameter a at different temperatures according to the parameter temperature model corresponding to the parameter a, substituting the new values of the parameter a into the stress-strain numerical model, fitting a stress-strain curve of the material according to stress data and strain data obtained at different temperatures, solving a parameter b in the stress-strain numerical model at different temperatures, and obtaining a parameter temperature model of the parameter b; determination coefficient R of fitting result to parameter b2Making a decision if the coefficient R is determined2When the temperature of the material is less than the threshold value, solving new values of the parameter b at different temperatures according to a parameter temperature model corresponding to the parameter b, substituting the new value of the parameter a and the new value of the parameter b into a stress-strain numerical model, fitting a stress-strain curve of the material according to stress data and strain data acquired at different temperatures, and solving different parametersAnd obtaining a parameter temperature model of the parameter d according to the parameter d in the stress-strain numerical model under the temperature.
23. A method according to claim 3, wherein the stress-strain constitutive relation of the material has a plurality of parameters, the method further comprises selecting one of the parameters in the stress-strain numerical model, performing step h) to establish a parametric temperature curve, fitting a parametric temperature model, substituting the different temperatures into the parametric temperature model to obtain a fitting parameter, and determining the determination coefficient R of the fitting result of the selected parameter2Making a decision if the coefficient R is determined2When the stress-strain curve is smaller than the threshold value, substituting the fitting parameters into the stress-strain numerical model of the material, fitting the stress-strain curve by using the stress-strain numerical model of the material with the substituted fitting parameters, and solving the rest parameters in the stress-strain numerical model of the material; and c) selecting one of the other parameters in the stress-strain numerical model, and implementing the step h) until all the parameters in the stress-strain numerical model are solved.
24. A method for numerical characterization of a material stress-strain constitutive relation according to any one of claims 4, 5, 17 to 23 wherein the step of fitting a parametric temperature model includes fitting using a cubic polynomial.
25. The method for numerical characterization of material stress-strain constitutive relation according to claim 6, further comprising fitting the elastic modulus value using a quadratic polynomial or a cubic polynomial.
26. The method for numerical characterization of the material stress-strain constitutive relation according to claim 25, wherein the material is austenitic stainless steel, the elastic modulus temperature curve model is,
Ey(T)＝1.806×10-4T2-0.618T +1958, in which Ey(T)The values of the modulus of elasticity with the temperature T of the sample are shown.
27. The method according to claim 25, wherein the material is a low carbon steel material, the temperature curve model of the elastic modulus is,
Ey(T)＝-5.144×10-7T3+1.821×10-4T2-0.07197T +2025, wherein Ey(T)The values of the modulus of elasticity with the temperature T of the sample are shown.
28. A method for numerical characterization of the material stress-strain constitutive relation according to claim 1 or 17 or 18 or 19, wherein when the material is a material with a significant yield stage, the parameter a corresponds to a parametric temperature model of,
a(T)＝-4.803×10-3tanh[0.02293(T-425)]+0.004803, wherein a(T)Represents the value of the parameter a as a function of the sample temperature T;
the parametric temperature model corresponding to the parameter b is,
Figure FDA0002742330750000061
in the formula b(T)The value of the parameter b is shown as a function of the sample temperature T.
29. A method for numerical characterization of the material stress-strain constitutive relation according to claim 2 or 20 or 21 or 22, wherein when the material is a material without significant yield phase, the parametric temperature model corresponding to the parameter a is,
a(T)＝-9.899×10-8T3+8.767×10-5T2-0.002013T +2.79, wherein a(T)Represents the value of the parameter a as a function of the sample temperature T;
the parametric temperature model corresponding to the parameter b is,
b(T)＝7.926×10-8T3-7.425×10-5T2+0.01949T +2.787 wherein b(T)Represents the value of the parameter b as a function of the temperature T of the sample;
the parameter temperature model corresponding to the parameter d is,
d(T)＝-1.376×10-6T3+1.653×10-3T2-0.7244T +321.6, wherein d(T)The value of the parameter d is shown as a function of the sample temperature T.
30. A numerical characterization system for material stress-strain constitutive relation, which implements the numerical characterization method for material stress-strain constitutive relation as defined in any one of claims 1 to 29, and comprises a loading device for applying a load to a material sample, a force measuring device for measuring the force applied to a material to be measured, a strain rate measuring device for measuring the strain rate, a heating device for heating the material, a temperature measuring device for measuring the temperature of the material, and a calculating device for processing the stress data and the strain data to obtain parameters in a stress-strain numerical model.
31. A numerical characterization system of a material stress-strain constitutive relation according to claim 30 wherein the loading device comprises a tensile testing machine and the force measuring device comprises the tensile testing machine; the strain rate measuring device comprises an extensometer; the heating device comprises a high-temperature furnace; the temperature measuring device includes a thermocouple.
32. A method for obtaining a stress-strain relationship of a material, comprising inputting a temperature parameter and a material parameter to a stress-strain relationship obtaining module, wherein the stress-strain relationship obtaining module obtains the stress-strain relationship corresponding to the temperature and the material from a stress-strain numerical model in the numerical characterization method of the material stress-strain constitutive relationship according to any one of claims 1 to 29 corresponding to the material parameter according to the temperature parameter.
33. The method for obtaining stress-strain relationship of material as claimed in claim 32, wherein the material parameters include grade and kind of material.
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