Corrected J-C model-based stainless steel high-temperature mechanical property extrapolation method
By correcting the classic J-C model, introducing fit constants to improve the temperature softening term, and constructing a high-temperature mechanical performance extrapolation model, the problems of insufficient accuracy and high cost of high-temperature mechanical performance measurement in the existing technology are solved, and the extrapolation prediction of the mechanical performance of the material at any temperature is realized, which improves the prediction accuracy and applicability.
Patent Information
- Application Number
- CN202510192562.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-21
- Publication Date
- 2025-06-10
AI Technical Summary
The prior art has problems such as insufficient accuracy, difficulty in measuring ultra-high temperature mechanical properties, and high cost of high temperature tensile experiments when describing the high temperature mechanical behavior of different metals or alloys. The maximum operating temperature of most indentation instruments is low, making it impossible to analyze the mechanical properties of materials under higher temperature conditions.
By correcting the classic J-C model, using several sets of stress-strain data of the material at different temperatures, fitting constants are introduced to improve the temperature softening term, and a high-temperature mechanical performance extrapolation model based on the corrected J-C model is constructed to realize extrapolation prediction of the constitutive relationship of the material at any temperature.
It significantly improves the model's extrapolation prediction ability of high-temperature mechanical behavior, improves prediction accuracy, and is suitable for extrapolation of high-temperature mechanical properties of more types of materials. It has strong versatility and practical value, and can provide theoretical support for material design and structural reliability evaluation under high temperature conditions.
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Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of extrapolation research on mechanical properties of materials, and specifically relates to a method for extrapolating high-temperature mechanical properties of stainless steel based on a modified Johnson-Cook (J-C) model. Background Art
[0002] The mechanical constitutive relationship of materials is a mathematical model that describes the stress-strain relationship of materials, which is of great significance for studying the mechanical properties of materials and is also the basis for carrying out load-bearing and failure analysis of engineering structures. With the increasingly harsh service environment of materials, the high-temperature and high-strain-rate conditions that materials need to withstand are becoming increasingly complex, and the stress of materials is closely related to factors such as strain, temperature, and strain rate. Therefore, establishing an accurate and reliable constitutive model for each material and deeply studying its high-temperature mechanical properties have become the focus of current work.
[0003] Currently, in order to deeply understand the high-temperature mechanical behavior of materials, stress-strain data of materials under different temperature conditions are mainly obtained through mechanical property test experiments, and then the mechanical behavior of materials is described using existing constitutive models. However, this method has problems such as insufficient accuracy in describing the constitutive relationships of different metals or alloys, difficulty in measuring ultra-high-temperature mechanical properties, and high costs for high-temperature tensile experiments. Currently, commercial high-temperature micro-nano indentation instruments have been developed by Hysitron in the United States, MTS, and Micromaterials in the United Kingdom, and have been widely used in related fields. However, the maximum operating temperature (600°C - 700°C) of most indentation instruments is relatively low, and it is impossible to analyze the mechanical properties of materials under higher temperature conditions. Although tensile experiments can conduct mechanical property tests above 1000°C, since each tensile experiment requires consuming a material sample, it will cost a huge amount to conduct mechanical property tests one by one for each temperature condition. By modifying existing constitutive models, the above problems can be better solved, and the extrapolation prediction of the mechanical properties of materials at any temperature can be achieved. Summary of the Invention
[0004] The purpose of the present invention is to provide a method for extrapolating high-temperature mechanical properties of stainless steel based on a modified J-C model. By using several groups of stress-strain data of materials at different temperatures, the classical J-C constitutive model is modified to achieve the extrapolation prediction of the constitutive relationship of this material at any temperature. This method provides a new solution for predicting the stress-strain curve of metals or alloys with temperature changes, and provides a theoretical basis and technical means for studying the method of extrapolating high-temperature mechanical properties of materials.
[0005] The technical solution adopted by the present invention is as follows: A method for extrapolating high-temperature mechanical properties of stainless steel based on a modified J-C model, and the specific operation steps are as follows:
[0006] Step 1: Obtain the stress-strain curves of the metal or alloy under different temperature conditions in the high-temperature tensile experiment at the same strain rate;
[0007] Step 2: Select a reference temperature, perform polynomial fitting on the stress-strain curve at the reference temperature, and determine the relevant parameters in the high-temperature mechanical property extrapolation model;
[0008] Step 3: According to the stress-strain curves at non-reference temperatures in the high-temperature tensile experiment, fit and solve the parameters in the temperature term again;
[0009] Step 4: Combine the results of the two fittings to construct a high-temperature mechanical property extrapolation model for the metal or alloy at this strain rate based on the modified Johnson-Cook constitutive relation.
[0010] The features of the present invention also lie in that,
[0011] The high-temperature mechanical property extrapolation model described in Step 1 is specifically:
[0012] σ = (A 1 + B 1 ε + …… + B i ε n )[1 - (DT * ) m , where: A 1 , B 1 , ……, B i , n are fitting parameters, D is a constant, and m is the temperature softening coefficient.
[0013] The different temperatures in Step 1 include 20°C, 100°C, 200°C, 300°C, 400°C, 500°C, 600°C.
[0014] The principle for selecting the reference temperature in Step 2 is: the temperature corresponding to the highest stress-strain curve;
[0015] At the reference temperature, [1 - (DT * ) m is 1, and the stress-strain curve at the reference temperature obtained from the high-temperature tensile experiment is fitted polynomially n times with σ = A 1 + B 1 ε + …… + B i ε n , and the values of A 1 , B 1 , ……, B i in the high-temperature mechanical property extrapolation model are determined according to the fitting results.Coefficient; When selecting the degree of the polynomial, it is necessary to balance the accuracy of data fitting and the complexity of the model, and avoid overfitting. A higher-degree polynomial can better describe the detailed changes in the data, but it may also lead to overfitting, while a lower-degree polynomial may not be able to fully describe the basic trend of the data.
[0016] Furthermore, the fitting parameter n takes values from 1 to 6.
[0017] Solving the temperature softening coefficient m and the constant D in the temperature coefficient of the high-temperature mechanical property extrapolation model specifically includes the following steps:
[0018] Making a formal modification to the high-temperature mechanical property extrapolation model and transforming it into From this, lnT is obtained * and show a linear relationship, and m is the slope, and m and D together form the intercept; according to the stress-strain curve at non-reference temperatures in the high-temperature tensile experiment, obtain versus lnT * relationship, respectively fit and solve the values of m and D for each strain, and calculate the average values respectively to obtain the values of the parameters m and D in the temperature coefficient of the high-temperature mechanical property extrapolation model.
[0019] The strain rate in Step 1 is 100 s -1 .
[0020] The high-temperature mechanical property extrapolation model described in Step 1 is established based on the classical J-C model, and the form of the classical J-C model is as follows:
[0021]
[0022] where: σ is the stress; ε is the strain; A is the yield stress; B is the strain hardening coefficient; n 1 is the strain hardening exponent; C is the strain rate hardening coefficient; is the strain rate; is the reference strain rate, taking 100 s -1 ; T is the temperature; T ref is the reference temperature, taking 20 °C; T melt is the melting temperature, taking 1500 °C; m is the temperature softening coefficient.
[0023] The beneficial effects of the present invention are:
[0024] The high-temperature mechanical property extrapolation method of the present invention based on the modified J-C model improves the temperature softening term in the classical J-C model by introducing a fitting constant, enabling the modified model to more accurately reflect the characteristics of the stress-strain relationship of the material changing with temperature, and significantly improving the extrapolation prediction ability of the model for high-temperature mechanical behavior. The prominent beneficial effects of this invention patent include:
[0025] 1. High precision. By introducing a fitting coefficient into the temperature term, the prediction accuracy of the model for the mechanical behavior under high-temperature environments is improved.
[0026] 2. Wide applicability. The modified Johnson-Cook (J-C) model can be applied to the extrapolation prediction of the high-temperature mechanical properties of more types of materials, and has strong generality and practical value.
[0027] 3. Strong engineering practicability. In engineering practical applications, the modified model can provide theoretical support and technical guidance for material design, performance optimization, and structural reliability assessment under high-temperature conditions, thereby accelerating the development and application process of new high-temperature materials. Description of the Drawings
[0028] Figure 1 It is a stress-strain data graph of 304 stainless steel alloy obtained by experiments under different temperature conditions in Example 6 of this application;
[0029] Figure 2 It is a result graph of polynomial fitting of the stress-strain curve of 304 stainless steel alloy at room temperature in Example 6 of this application;
[0030] Figure 3 It is the relationship graph of lnx 1 and ln(1 - y) obtained from the stress-strain curves of 304 stainless steel alloy at 100°C, 200°C, 300°C, 400°C, 500°C, and 600°C in Example 6 of this application;
[0031] Figure 4 It is a comparison graph of the stress-strain curve data obtained by experiments under different temperature conditions and the stress-strain curve data obtained under more temperature conditions in Example 6 of this application; Detailed Implementation Modes
[0032] The present invention will be described in detail below with reference to the drawings and specific embodiments.
[0033] Example 1
[0034] The extrapolation method for the high-temperature mechanical properties of stainless steel based on the modified J-C model of the present invention is specifically operated as follows:
[0035] Step 1: Under the same strain rate, obtain the stress-strain curves of metals or alloys under different temperature conditions in high-temperature tensile experiments;
[0036] Step 2: Select a reference temperature, and perform polynomial fitting on the stress-strain curve at the reference temperature to determine the relevant parameters in the high-temperature mechanical property extrapolation model;
[0037] Step 3: According to the stress-strain curve at non-reference temperatures in the high-temperature tensile experiment, fit and solve the parameters in the temperature term again;
[0038] Step 4: Combine the results of the two fittings to construct an extrapolation model for the high-temperature mechanical properties of the metal or alloy at this strain rate based on the modified Johnson-Cook constitutive relation.
[0039] Example 2
[0040] Step 1: At the same strain rate, obtain the stress-strain curves of the metal or alloy under different temperature conditions in the high-temperature tensile experiment;
[0041] The high-temperature mechanical property extrapolation model described in Step 1 is established based on the classical Johnson-Cook model, and the form of the classical Johnson-Cook model is as follows:
[0042]
[0043] Where: σ is the stress; ε is the strain; A is the yield stress; B is the strain hardening coefficient; n 1 is the strain hardening exponent; C is the strain rate hardening coefficient; is the strain rate; is the reference strain rate, taking 100 s -1 ; T is the temperature; T ref is the reference temperature, taking 20 °C; T melt is the melting temperature, taking 1500 °C; m is the temperature softening coefficient;
[0044] The specific form of the high-temperature mechanical property extrapolation model in Step 1 is:
[0045] σ = A 1 + B 1 ε + …… + B i ε n ) [1 - (DT * ) m , where: A 1 , B 1 , ……, B i , n are fitting parameters, n takes 1 to 6; D is a constant, and m is the temperature softening coefficient.
[0046] Step 2: Select a reference temperature and perform polynomial fitting on the stress-strain curve at the reference temperature to determine the relevant parameters in the high-temperature mechanical property extrapolation model;
[0047] Step 3: According to the stress-strain curve at non-reference temperatures in the high-temperature tensile experiment, fit and solve the parameters in the temperature term again;
[0048] Step 4: Combine the results of the two fittings to construct an extrapolation model for the high-temperature mechanical properties of the metal or alloy at this strain rate based on the modified Johnson-Cook constitutive relation.
[0049] Example 3
[0050] Based on Example 2,
[0051] The different temperatures described in Step 1 include 20°C, 100°C, 200°C, 300°C, 400°C, 500°C, and 600°C.
[0052] The principle for selecting the reference temperature in Step 2 is: the temperature corresponding to the highest stress-strain curve;
[0053] At the reference temperature, [1 - (DT * ) m is 1, and for the stress-strain curve at the reference temperature obtained from the high-temperature tensile experiment, use σ = A 1 + B 1 ε + …… + B i ε n to perform an nth-degree polynomial fitting, and determine the coefficients A 1 , B 1 , ……, B i in the high-temperature mechanical property extrapolation model according to the fitting results.
[0054] Example 4
[0055] Based on Example 3,
[0056] Solve for the temperature softening coefficient m and the constant D in the temperature coefficient of the high-temperature mechanical property extrapolation model, which specifically includes the following steps:
[0057] Modify the form of the high-temperature mechanical property extrapolation model and transform it into From this, it can be obtained that lnT * and are linearly related, and m is the slope, and m and D together form the intercept; according to the stress-strain curves at non-reference temperatures in the high-temperature tensile experiment, obtain the relationship between and lnT * at each strain, respectively fit and solve the values of m and D at each strain, and find the average values respectively to obtain the values of the parameters m and D in the temperature coefficient of the high-temperature mechanical property extrapolation model.
[0058] Example 5
[0059] The extrapolation method for the high-temperature mechanical properties of stainless steel based on the modified Johnson-Cook model of the present invention specifically operates as follows:
[0060] Step 1: At the same strain rate, obtain the stress-strain curves of the metal or alloy under different temperature conditions in the high-temperature tensile experiment;
[0061] Step 2: Select a reference temperature, and perform polynomial fitting on the stress-strain curve at the reference temperature to determine the relevant parameters in the high-temperature mechanical property extrapolation model;
[0062] Step 3: According to the stress-strain curves at non-reference temperatures in the high-temperature tensile experiment, perform fitting and solution on the parameters in the temperature term again;
[0063] Step 4: Combine the results of the two fittings to construct a high-temperature mechanical property extrapolation model for the metal or alloy at this strain rate based on the modified Johnson-Cook constitutive relation.
[0064] Example 6
[0065] This example provides a high-temperature mechanical property extrapolation method based on the modified Johnson-Cook model, which can be used for extrapolating the high-temperature mechanical properties of materials and accurately describing and predicting the variation relationship of the stress-strain curve of the metal or alloy with temperature.
[0066] This example uses the stress data of 304 stainless steel alloy at different strains and temperatures under a strain rate of 100s -1 obtained from experiments in other scholars' papers. Figure 1 Fig.
[0067]
[0068] is the stress-strain curves of 304 stainless steel alloy at 20°C, 100°C, 200°C, 300°C, 400°C, 500°C, and 600°C. The reference temperature is selected as 20°C. The classical Johnson-Cook model is as follows: 1 where: σ is the stress; ε is the strain; A is the yield stress; B is the strain hardening coefficient; n is the strain hardening exponent; C is the strain rate hardening coefficient; is the strain rate; -1 is the reference strain rate, taken as 100s ref ; T is the temperature; T melt is the reference temperature, taken as 20°C; T melt is the melting temperature, taken as 1500°C; m is the temperature softening coefficient.
[0069] This example aims to accurately describe and extrapolate the variation relationship of the material stress-strain curve with temperature at a strain rate of 100s -1 , that is . Then the second logarithmic term in the classical Johnson-Cook model is equal to 0, and the form of the modified high-temperature mechanical property extrapolation Johnson-Cook model is as follows:
[0070] σ = (A 1 + B 1 ε + …… + B i ε n )(1 - (DT * )) m
[0071] Where: A 1 , B 1 , ……, B i , and n are fitting parameters; D is a constant.
[0072] The room temperature of the experimental conditions is 20 degrees, and T ref is also 20 °C, that is, T * = 0, then the value of the temperature term is 1, and the modified J-C model can be simplified to
[0073] σ = A 1 + B 1 ε + …… + B i ε n
[0074] Based on the stress-strain curve data obtained from the experiment at the reference temperature of 20 °C, as shown in the stress-strain curve of the 20 °C experiment in Figure 1 , select an appropriate polynomial degree and perform polynomial fitting on this curve using the above formula; a higher-degree polynomial can describe the detailed changes in the data but may also lead to overfitting, while a lower-degree polynomial may not be able to fully describe the basic trend of the data.
[0075] By performing polynomial fitting on the stress-strain curve of the 20 °C experiment in Figure 1 , the values of A 1 , B 1 , and B i are obtained. Figure 2 is the result graph of polynomial fitting for the stress-strain curve of 304 stainless steel alloy at room temperature. In this embodiment, the fourth-degree polynomial can accurately describe the stress-strain relationship and will not show overfitting at the same time. Therefore, the fourth-degree polynomial is selected to perform polynomial fitting on the stress-strain curve at room temperature, and the result of the fourth-degree polynomial obtained by fitting is
[0076] σ = 419.59 + 938.85ε + 12519.77ε 2 - 42348.48ε 3 + 37606.06ε 4 .
[0077] Simplify the modified J-C model to:
[0078]
[0079] Using the stress-strain data of 304 stainless steel alloy obtained from experiments at 100°C, 200°C, 300°C, 400°C, 500°C, and 600°C, as Figure 1 shown in the experimental stress-strain curves at non-reference temperatures, the relationship diagram of lnT * versus at each strain is obtained. As Figure 3 shown, based on the linear relationship presented between and lnT * at each strain, the values of m and D are fitted and solved. Figure 3 The slope of the slant line corresponding to each strain value in
[0080] (two are drawn as examples for ε = 0.1 and ε = 0.5) is the value of m, and the intercept value of each slant line is mlnD. The average of the m values and D values calculated from each slant line gives m = 0.68 and D = 0.99.
[0081] σ=(419.59 + 938.85ε + 12519.77ε 2 - 42348.48ε 3 + 37606.06ε 4 )
[0082]
[0083] Figure 4 The stress-strain curves under different temperature conditions obtained from experiments, the stress-strain curves under different temperature conditions obtained using the extrapolation model of high-temperature mechanical properties, and the stress-strain curves under the conditions of 700°C, 800°C, 900°C, 1000°C, and 1100°C extrapolated using the extrapolation model of high-temperature mechanical properties are shown. It can be seen that the stress-strain curves obtained using the extrapolation model of high-temperature mechanical properties are in good agreement with the experimental data, indicating that the extrapolation model of high-temperature mechanical properties of 304 stainless steel alloy derived has good accuracy.
[0084] According to the above steps, it is possible to extrapolate and predict the mechanical properties of a material under any high-temperature condition through the stress-strain relationship data of the material under a finite set of temperature conditions.
[0085] The above are only some implementation schemes of the present invention. For those skilled in the art, without departing from the principle of the present invention, several improvements and refinements made to the present invention should also be regarded as the protection scope of the present invention.
Claims
1. A method for extrapolating high temperature mechanical properties of stainless steel based on the modified JC model, characterized in that: The specific steps are as follows: Step 1: Under the same strain rate, obtain the stress-strain curve of the metal or alloy under different temperature conditions in the high temperature tensile test; Step 2: Select a reference temperature and perform polynomial fitting on the stress-strain curve at the reference temperature to determine the relevant parameters in the high-temperature mechanical properties extrapolation model; Step 3: According to the stress-strain curve at the non-reference temperature in the high-temperature tensile test, the parameters in the temperature term are fitted and solved again; Step 4: Combining the two fitting results, construct an extrapolation model of the high-temperature mechanical properties of the metal or alloy at the strain rate based on the modified JC constitutive relation.
2. The method for extrapolating high temperature mechanical properties of stainless steel based on the modified JC model according to claim 1, characterized in that: The high temperature mechanical properties extrapolation model described in step 1 is specifically: σ=(A1+B1ε+……+B i ε n )[1-(DT * ) m ], where: A1, B1, ..., B i , n is the fitting parameter, D is a constant, and m is the temperature softening coefficient.
3. The method for extrapolating high temperature mechanical properties of stainless steel based on the modified JC model according to claim 1, characterized in that: The different temperatures in step 1 include 20°C, 100°C, 200°C, 300°C, 400°C, 500°C, and 600°C.
4. The method for extrapolating high temperature mechanical properties of stainless steel based on the modified JC model according to claim 1, characterized in that: The reference temperature selection principle in step 2 is: the temperature corresponding to the highest curve in the stress-strain curve; At the reference temperature, [1-(DT * ) m ] is 1, and the stress-strain curve at the reference temperature obtained by the high temperature tensile test is expressed by σ=A1+B1ε+……+B i ε n Perform n-order polynomial fitting, and determine A1, B1, ..., B in the high temperature mechanical properties extrapolation model based on the fitting results. i coefficient.
5. The method for extrapolating high temperature mechanical properties of stainless steel based on the modified JC model according to claim 3, characterized in that: The fitting parameter n is 1-6.
6. The method for extrapolating high temperature mechanical properties of stainless steel based on the modified JC model according to claim 4, characterized in that: The temperature softening coefficient m and constant D in the temperature coefficient of the high temperature mechanical properties extrapolation model are solved, which specifically includes the following steps: The high temperature mechanical properties extrapolation model is formally modified and transformed into It follows that lnT * and It is a linear relationship, with m being the slope, and m and D together forming the intercept; According to the stress-strain curve at non-reference temperature in the high temperature tensile test, the With lnT * The relationship between m and D is obtained by fitting and solving the values of m and D at each strain, and the average values are calculated to obtain the values of parameters m and D in the temperature coefficient of the high-temperature mechanical properties extrapolation model.
7. The method for extrapolating high temperature mechanical properties of stainless steel based on the modified JC model according to claim 3, characterized in that: The strain rate in step 1 is 100s -1 .
8. The method for extrapolating high temperature mechanical properties of stainless steel based on the modified JC model according to claim 1, characterized in that: The high temperature mechanical properties extrapolation model described in step 1 is established based on the classic JC model, and the classic JC model is as follows: Where: σ is stress; ε is strain; A is yield stress; B is strain hardening coefficient; n1 is strain hardening exponent; C is strain rate hardening coefficient; is the strain rate; As the reference strain rate, take 100s -1 ; T is temperature; T ref is the reference temperature, take 20℃; T melt is the melting temperature, which is 1500℃; m is the temperature softening coefficient.