A method for predicting the high-temperature elastic modulus of supermartensitic stainless steel
By conducting high-temperature compression experiments and data fitting on super martensitic stainless steel samples, an elastic modulus prediction model considering temperature and strain rate was established, which solved the problem of inaccurate simulation results in the existing technology and achieved rapid and accurate elastic modulus prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ANGANG STEEL CO LTD
- Filing Date
- 2026-05-06
- Publication Date
- 2026-07-31
AI Technical Summary
Existing technologies cannot efficiently and accurately obtain dynamic elastic modulus that matches real thermomechanical processing conditions (i.e., simultaneously including temperature, strain, and strain rate changes), resulting in inaccurate simulation results during the hot working of supermartensitic stainless steel.
High-temperature compression tests were conducted on super martensitic stainless steel samples at different temperatures and strain rates using a thermodynamic simulation testing machine. Data were collected and stress-strain curves were plotted. An initial elastic modulus prediction model with deformation temperature and strain rate as variables was established through linear regression and nonlinear fitting, including dynamic intercept and slope, and a complete elastic modulus prediction model was constructed.
The model can quickly establish an elastic modulus prediction model, significantly shorten the testing cycle, accurately reflect the change law of elastic modulus of materials during hot working, and improve the reliability of simulation results and process optimization capabilities.
Smart Images
Figure CN122490797A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of stainless steel hot working technology, specifically to a method for predicting the high-temperature elastic modulus of super martensitic stainless steel. Background Technology
[0002] The elastic modulus is one of the most fundamental mechanical property parameters of a material. It defines the linear relationship between stress and strain during elastic deformation and is a measure of a material's resistance to elastic deformation. In all numerical simulations of materials processing and structural design, the elastic modulus is an indispensable core input parameter. The accuracy of its value directly determines the reliability of the simulation results, thus affecting process optimization, quality control, equipment design, and lifecycle prediction.
[0003] Super martensitic stainless steel achieves an excellent balance of strength, toughness, corrosion resistance, and weldability through ultra-low carbon, high nickel-molybdenum alloy design and precise heat treatment. However, it is precisely this complex multiphase microstructure and multi-mechanism synergistic strengthening characteristics that pose a significant challenge to the accurate prediction of its mechanical properties, especially its elastic modulus.
[0004] Currently, methods for obtaining the high-temperature elastic modulus of materials mainly include room-temperature extrapolation or empirical formula methods, static testing methods, and dynamic testing methods. Room-temperature extrapolation or empirical formula methods often employ simple linear or piecewise linear formulas, expressing the elastic modulus as a single function of temperature, for example: E(T) = a - bT. This method completely ignores the effects of strain and strain rate. In actual hot working processes (such as rolling and forging), materials simultaneously undergo intense plastic deformation and microstructure evolution, which alter the material's stiffness in real time. Therefore, parameters such as temperature and strain rate have a significant impact on the material's elastic modulus. Numerous experiments have shown that the elastic modulus does not change linearly with temperature, especially near the phase transition point or in the high-temperature range, where its decreasing trend is more complex. This ultimately leads to significant deviations between the results obtained using this method and actual values. Static testing methods include high-temperature tensile, bending, or vibratory spring methods. The elastic modulus is calculated by applying a static load to the sample at an isothermal temperature. However, at high temperatures, the creep effect of materials is significant. During static loading, creep and elastic deformation occur simultaneously and are difficult to separate clearly, leading to an underestimation or distortion of the measured "elastic" modulus value. Furthermore, each temperature point requires a separate sample and a lengthy holding and testing process, resulting in high costs and time consumption, and making it difficult to obtain dense data covering the entire process window. Dynamic testing methods measure the material's properties in a near-equilibrium state without macroscopic plastic deformation. This differs significantly from actual hot working processes and shares similar limitations with static testing methods.
[0005] In summary, existing technologies share a common drawback: they cannot efficiently and accurately obtain dynamic elastic modulus that matches actual thermomechanical processing conditions (i.e., simultaneously including changes in temperature, strain, and strain rate). Therefore, there is an urgent need for a method that can closely integrate with actual high-temperature deformation processes and rapidly and efficiently establish accurate elastic modulus prediction models. Summary of the Invention
[0006] To address the problem of efficiently and accurately obtaining the dynamic elastic modulus that matches actual thermomechanical processing conditions in existing technologies, this invention provides a method for predicting the high-temperature elastic modulus of supermartensitic stainless steel, specifically including the following steps:
[0007] A set of super martensitic stainless steel samples were subjected to high-temperature compression tests under different temperatures and strain rates using a thermodynamic simulation testing machine. The experimental stress values, experimental strain values, experimental time and experimental temperature data were collected, and multiple sets of stress-strain curves were plotted. Calculate the slope of the linear segment on each set of stress-strain curves, and define the slope of the linear segment on the stress-strain curves as the elastic modulus at the corresponding deformation temperature and strain rate. An initial elastic modulus prediction model is established with deformation temperature and strain rate as variables. The initial elastic modulus prediction model includes dynamic intercept and dynamic slope. A reference elastic modulus and a reference temperature are set. With deformation temperature as the independent variable and elastic modulus as the dependent variable, linear regression analysis is performed for each strain rate to obtain the dynamic intercept and dynamic slope at different strain rates. The dynamic intercept includes a logarithmic strain rate function and a quadratic strain rate function, and the dynamic slope includes a quadratic strain rate function. The logarithmic strain rate function and the quadratic strain rate function include undetermined constants. Using strain rate as the independent variable, nonlinear fitting is performed on the logarithmic strain rate function and the quadratic strain rate function respectively to determine the undetermined constants in the logarithmic strain rate function and the quadratic strain rate function. The determined dynamic intercept and dynamic slope are then substituted into the initial elastic modulus prediction model to obtain the complete elastic modulus prediction model.
[0008] Furthermore, the group of supermartensitic stainless steel samples were taken from the same billet and had the same size specifications.
[0009] Furthermore, the deformation temperature range is 950℃~1150℃, and the strain rate range is 0.01s. - ¹~1s - ¹.
[0010] Furthermore, the steps for calculating the elastic modulus at the corresponding deformation temperature and strain rate include: In the initial stage of deformation, the stress-strain curve is locally magnified to identify the linear segment of the stress-strain curve; Perform linear regression analysis on the linear segment; Calculate the slope of the linear segment on each set of stress-strain curves, and define the slope as the elastic modulus at the corresponding deformation temperature and strain rate.
[0011] Furthermore, the initial elastic modulus prediction model is established, and the expression of the initial elastic modulus prediction model is:
[0012] in, For elastic modulus, The deformation temperature, For strain rate, For dynamic intercept, This represents the dynamic slope.
[0013] Furthermore, a reference elastic modulus is set. and reference temperature The dynamic intercept The expression is:
[0014] The dynamic slope The expression is:
[0015] in, The logarithmic strain rate function It is a quadratic strain rate function.
[0016] Furthermore, the logarithmic strain rate function The expression is:
[0017] The second strain rate function The expression is:
[0018] in , , , , and is an undetermined constant.
[0019] Furthermore, the step of determining the undetermined constant includes: With deformation temperature For independent variables, elastic modulus Assuming the function value, linear regression analysis is performed for each strain rate to obtain the dynamic intercept at different strain rates. and dynamic slope ; With strain rate Independent variable, dynamic slope For the function value, the second strain rate function Perform nonlinear fitting and calculate the undetermined constants. , and The determined second-order strain rate function is obtained. ; Dynamic intercept The expression, dynamic slope Combining the expression with the logarithmic strain rate function, we obtain the formula:
[0020] Introducing intermediate variables Let the intermediate variable Then, by strain rate Independent variable, intermediate variable The function value is the logarithmic strain rate function. Perform nonlinear fitting and calculate the undetermined constants. , and The determined logarithmic strain rate function is obtained. .
[0021] Compared with the prior art, the present invention has the following beneficial effects: This invention requires only a small number of high-temperature compression experiments to quickly establish an elastic modulus prediction model, significantly shortening the testing cycle. At the same time, it fully considers the comprehensive influence of temperature, strain, and strain rate on the elastic modulus, accurately reflecting the dynamic mechanical properties of materials under real thermomechanical processing conditions. The elastic modulus prediction model established by this invention is constructed based on actual high-temperature deformation process data and can truly reflect the change law of elastic modulus of materials during hot processing. Attached Figure Description
[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0023] Figure 1 This is a flowchart of a method for predicting the high-temperature elastic modulus of super martensitic stainless steel according to the present invention.
[0024] Figure 2 This is a schematic diagram of a typical stress-strain curve of the super martensitic stainless steel in this invention.
[0025] Figure 3 This is a partial enlarged view of a typical stress-strain curve of the super martensitic stainless steel in this invention. Detailed Implementation
[0026] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.
[0027] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.
[0028] like Figure 1 As shown, this invention discloses a method for predicting the high-temperature elastic modulus of super martensitic stainless steel, which mainly includes the following steps: S1. A set of super martensitic stainless steel samples were subjected to high-temperature compression tests under different temperatures and strain rates using a thermal simulation testing machine. The experimental stress values, experimental strain values, experimental time and experimental temperature data were collected, and multiple sets of stress-strain curves were plotted.
[0029] In a preferred embodiment of this application, the group of supermartensitic stainless steel samples are taken from the same billet and have the same size specifications.
[0030] In a preferred embodiment of this application, the deformation temperature range is 950℃~1150℃, and the strain rate range is 0.01s. - ¹~1s - ¹.
[0031] S2. Calculate the slope of the linear segment on each set of stress-strain curves, and define the slope of the linear segment on the stress-strain curves as the elastic modulus at the corresponding deformation temperature and strain rate.
[0032] S21. In the initial stage of deformation, the stress-strain curve is locally magnified to find the linear segment of the stress-strain curve.
[0033] S22. Perform linear regression analysis on the linear segment.
[0034] S23. Calculate the slope of the linear segment on each set of stress-strain curves, and define the slope as the elastic modulus at the corresponding deformation temperature and strain rate.
[0035] S3. Establish an initial elastic modulus prediction model with deformation temperature and strain rate as variables. The initial elastic modulus prediction model includes dynamic intercept and dynamic slope.
[0036] In a preferred embodiment of this application, the initial elastic modulus prediction model is established, and the expression of the initial elastic modulus prediction model is as follows:
[0037] in, For elastic modulus, The deformation temperature, For strain rate, For dynamic intercept, This represents the dynamic slope.
[0038] S4. Set the reference elastic modulus and reference temperature, and use the deformation temperature as the independent variable and the elastic modulus as the dependent variable. Perform linear regression analysis for each strain rate to obtain the dynamic intercept and dynamic slope at different strain rates. The dynamic intercept includes the logarithmic strain rate function and the quadratic strain rate function, and the dynamic slope includes the quadratic strain rate function. The logarithmic strain rate function and the quadratic strain rate function include undetermined constants.
[0039] As a preferred embodiment of this application, a reference elastic modulus is set. and reference temperature The dynamic intercept The expression is:
[0040] The dynamic slope The expression is:
[0041] in, The logarithmic strain rate function It is a quadratic strain rate function.
[0042] The logarithmic strain rate function The expression is:
[0043] The second strain rate function The expression is:
[0044] in , , , , and is an undetermined constant.
[0045] S5. Using strain rate as the independent variable, perform nonlinear fitting on the logarithmic strain rate function and the quadratic strain rate function respectively to determine the undetermined constants in the logarithmic strain rate function and the quadratic strain rate function. Substitute the determined dynamic intercept and dynamic slope into the initial elastic modulus prediction model to obtain the complete elastic modulus prediction model.
[0046] S51, based on deformation temperature For independent variables, elastic modulus Assuming the function value, linear regression analysis is performed for each strain rate to obtain the dynamic intercept at different strain rates. and dynamic slope .
[0047] S52, with strain rate Independent variable, dynamic slope For the function value, the second strain rate function Perform nonlinear fitting and calculate the undetermined constants. , and The determined second-order strain rate function is obtained. .
[0048] S53, Dynamic intercept The expression, dynamic slope Combining the expression with the logarithmic strain rate function, we obtain the formula: .
[0049] S54. Introducing intermediate variables Let the intermediate variable Then, by strain rate Independent variable, intermediate variable The function value is the logarithmic strain rate function. Perform nonlinear fitting and calculate the undetermined constants. , and The determined logarithmic strain rate function is obtained. .
[0050] S55, Determine the dynamic intercept and dynamic slope Substituting the initial elastic modulus prediction model, we obtain the complete elastic modulus prediction model.
[0051] Example S1. Super martensitic stainless steel was melted in a medium-frequency induction heating furnace and cast into ingots. These ingots were then machined into cylindrical specimens with a diameter of 8 mm and a height of 15 mm. A total of 20 specimens were processed, forming one group. These specimens were heated using a thermodynamic simulation testing machine to 1200℃ and held for 5 minutes. They were then cooled to different deformation temperatures of 950℃, 1050℃, and 1150℃. The specimens were then compressed at these deformation temperatures at compression rates of 0.01 s⁻¹. -1 0.1s -1 1s -1 During the experiment, parameters such as stress, strain, time, and temperature were collected. Corresponding stress-strain curves were obtained from the stress and strain data, such as... Figure 2 The figure shown is a typical stress-strain curve of super martensitic stainless steel.
[0052] S2. Analyze the stress-strain curve obtained from S1. In the initial stage of deformation, such as... Figure 3 The stress-strain curve is magnified locally. A linear segment of the stress-strain curve is identified, and linear regression analysis is performed on this segment to obtain its slope. The slopes of the straight lines corresponding to different deformation temperatures and strain rates are then determined. This slope represents the elastic modulus of the material, denoted as . ,in The deformation temperature, The strain rate is given, and the results are listed in Table 1 below.
[0053] Table 1 Elastic modulus at different deformation temperatures and strain rates
[0054] S3. Establish the initial elastic modulus prediction model, the expression of which is:
[0055] in, For elastic modulus, The deformation temperature, For strain rate, For dynamic intercept, This represents the dynamic slope.
[0056] S4. Set the reference elastic modulus and reference temperature The dynamic intercept The expression is:
[0057] The dynamic slope The expression is:
[0058] in, The logarithmic strain rate function It is a quadratic strain rate function.
[0059] The logarithmic strain rate function The expression is:
[0060] The second strain rate function The expression is:
[0061] in , , , , and is an undetermined constant.
[0062] In this embodiment, a reference elastic modulus is selected. =3447.4MPa, reference temperature =1000℃.
[0063] S5, mix S2 with temperature corresponding Temperature The independent variable is the elastic modulus. The strain rate is selected as a function value, with a value of 0.01 s⁻¹. -1 0.1s -1 1s -1 Linear regression analysis was performed, and the results were obtained respectively. and The values are listed in Table 2 below.
[0064] Table 2 Regression Analysis and The result
[0065] Please refer to Table 2 above. Value and The values and corresponding strain rates are used as the basic data, with strain rate as the independent variable. For the function value, the second strain rate function Perform nonlinear fitting to determine the undetermined constants. , , Thus, the secondary strain rate function is determined. for:
[0066] Dynamic intercept The expression, dynamic slope Combining the expression with the logarithmic strain rate function, we obtain the formula:
[0067] With strain rate as the independent variable, The values are function values, and the calculation results are shown in Table 3 below.
[0068] Table 3 Strain rate and numerical values
[0069] Logarithmic strain rate function Perform nonlinear fitting to determine the undetermined constants. , , Thus, the logarithmic strain rate function is determined. for:
[0070] The determined logarithmic strain rate function and a defined second strain rate function Substituting into the initial elastic modulus prediction model, we obtain the complete elastic modulus prediction model as follows:
[0071] Given a set of deformation temperatures and strain rates, the elastic modulus of the material under these conditions can be calculated using the established complete elastic modulus prediction model.
[0072] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for predicting the high-temperature elastic modulus of supermartensitic stainless steel, characterized in that, Includes the following steps: A set of super martensitic stainless steel samples were subjected to high-temperature compression tests under different temperatures and strain rates using a thermodynamic simulation testing machine. The experimental stress values, experimental strain values, experimental time and experimental temperature data were collected, and multiple sets of stress-strain curves were plotted. Calculate the slope of the linear segment on each set of stress-strain curves, and define the slope of the linear segment on the stress-strain curves as the elastic modulus at the corresponding deformation temperature and strain rate. An initial elastic modulus prediction model is established with deformation temperature and strain rate as variables. The initial elastic modulus prediction model includes dynamic intercept and dynamic slope. A reference elastic modulus and a reference temperature are set. With deformation temperature as the independent variable and elastic modulus as the dependent variable, linear regression analysis is performed for each strain rate to obtain the dynamic intercept and dynamic slope at different strain rates. The dynamic intercept includes a logarithmic strain rate function and a quadratic strain rate function, and the dynamic slope includes a quadratic strain rate function. The logarithmic strain rate function and the quadratic strain rate function include undetermined constants. Using strain rate as the independent variable, nonlinear fitting is performed on the logarithmic strain rate function and the quadratic strain rate function respectively to determine the undetermined constants in the logarithmic strain rate function and the quadratic strain rate function. The determined dynamic intercept and dynamic slope are then substituted into the initial elastic modulus prediction model to obtain the complete elastic modulus prediction model.
2. The method for predicting the high-temperature elastic modulus of super martensitic stainless steel according to claim 1, characterized in that, The group of supermartensitic stainless steel samples were taken from the same billet and had the same size specifications.
3. The method for predicting the high-temperature elastic modulus of super martensitic stainless steel according to claim 1, characterized in that, The deformation temperature range is 950℃~1150℃, and the strain rate range is 0.01s. - ¹~1s - ¹.
4. The method for predicting the high-temperature elastic modulus of super martensitic stainless steel according to claim 1, characterized in that, The steps for calculating the elastic modulus at the corresponding deformation temperature and strain rate include: In the initial stage of deformation, the stress-strain curve is locally magnified to identify the linear segment of the stress-strain curve; Perform linear regression analysis on the linear segment; Calculate the slope of the linear segment on each set of stress-strain curves, and define the slope as the elastic modulus at the corresponding deformation temperature and strain rate.
5. The method for predicting the high-temperature elastic modulus of super martensitic stainless steel according to claim 1, characterized in that, The initial elastic modulus prediction model is established, and the expression of the initial elastic modulus prediction model is as follows: in, For elastic modulus, The deformation temperature. For strain rate, For dynamic intercept, This represents the dynamic slope.
6. The method for predicting the high-temperature elastic modulus of super martensitic stainless steel according to claim 5, characterized in that, Set the reference elastic modulus and reference temperature The dynamic intercept The expression is: The dynamic slope The expression is: in, The logarithmic strain rate function It is a quadratic strain rate function.
7. The method for predicting the high-temperature elastic modulus of super martensitic stainless steel according to claim 6, characterized in that, The logarithmic strain rate function The expression is: The second strain rate function The expression is: in , , , , and is an undetermined constant.
8. The method for predicting the high-temperature elastic modulus of super martensitic stainless steel according to claim 7, characterized in that, The steps for determining the undetermined constants include: With deformation temperature For independent variables, elastic modulus Assuming the function value, linear regression analysis is performed for each strain rate to obtain the dynamic intercept at different strain rates. and dynamic slope ; With strain rate Independent variable, dynamic slope For the function value, the second strain rate function Perform nonlinear fitting and calculate the undetermined constants. , and The determined second-order strain rate function is obtained. ; Dynamic intercept The expression, dynamic slope Combining the expression with the logarithmic strain rate function, we obtain the formula: Introducing intermediate variables Let the intermediate variable Then, by strain rate Independent variable, intermediate variable The function value is the logarithmic strain rate function. Perform nonlinear fitting and calculate the undetermined constants. , and The determined logarithmic strain rate function is obtained. .