A method of analysing stress strain curves

Abstract

This invention relates to the field of steel experimental curve analysis, specifically to a method for analyzing stress-strain curves, comprising the following steps: conducting a compression deformation simulation experiment using a thermodynamic simulation testing machine and collecting experimental data; plotting a first stress-strain curve and performing high-order polynomial fitting to determine the segmentation points of the first stress-strain curve; dividing the first stress-strain curve based on the segmentation points, removing portions of the segmented curve that meet the rejection criteria, and plotting a second stress-strain curve; fitting the second stress-strain curve, recording the second fitting coefficient and comparing it with a fitting coefficient threshold, and repeating the rejection and refitting strategy until a stress-strain curve with satisfactory accuracy is obtained. This invention significantly improves the smoothness of the stress-strain curve and the accuracy of feature point recognition by using segmented fitting and dynamic threshold rejection of interfering data, providing a reliable basis for the analysis of the thermal deformation behavior of metallic materials. It has the advantages of simple operation, strong adaptability, and high engineering application value.

Description

Technical Field

[0001] This invention relates to the field of steel experimental curve analysis, and more specifically to a method for analyzing stress-strain curves. Background Technology

[0002] In thermoplastic processing, the flow stress of a metal directly reflects its deformation resistance in a high-temperature, flexible state, serving as a core basis for determining process parameters such as rolling and forging. Simultaneously, the changing characteristics of flow stress also imply information about the evolution of the material's internal microstructure, particularly the occurrence and development of dynamic recrystallization. This process not only affects the mechanical response during deformation but also plays a decisive role in the grain size, microstructure uniformity, and overall mechanical properties of the final product. Therefore, achieving accurate measurement of the flow stress in metallic materials is of great significance for process optimization and microstructure control.

[0003] Currently, the mainstream method for obtaining the flow stress of metallic materials is to conduct isothermal constant strain rate compression or tension tests on samples using a thermodynamic simulation testing machine, collecting stress and its corresponding strain data in real time, and then plotting a complete stress-strain curve. Based on this curve, researchers can analyze the critical conditions for dynamic recrystallization, extract characteristic parameters such as peak stress and steady-state stress, or construct deformation resistance constitutive models suitable for numerical simulation. However, due to limitations in experimental testing conditions, the actual obtained stress-strain curves often fail to achieve the ideal smooth shape. On the one hand, extensometers or load sensors are susceptible to electromagnetic interference, environmental vibration, or their own resolution limitations during signal acquisition, leading to high-frequency noise mixed into the measurement data. On the other hand, insufficient PID control accuracy of the temperature control system or unstable thermocouple contact may cause small fluctuations in the sample temperature, resulting in periodic or random fluctuations in the flow stress. The combined effect of these factors causes the stress-strain curve to exhibit varying degrees of fluctuation and distortion. When the fluctuations are significant, key characteristic information such as the starting point of dynamic recrystallization and peak stress can easily be obscured or confused, making subsequent mechanism analysis, parameter extraction, and constitutive modeling difficult.

[0004] Patent CN112784443B, entitled "Strain Curve Simulation Method," discloses a method for simulating stress-strain curves to obtain simulated stress-strain curves of an object under test sandwiched between a mass block and a testing platform. This method obtains the first acceleration curve of the mass block and the second acceleration curve of the testing platform, extracts the effective portion of the acceleration curves within a specific time period, and uses integral calculations based on the effective curves to obtain the strain and stress curves of the object under test. Finally, it calculates the simulated stress-strain curve using an exponential equation, which is then used to connect to the measured stress-strain curve. This patent focuses on simulating curves with a high strain range using acceleration data to compensate for the lack of measured data when the strain is large, providing more complete data support for computer-aided engineering software. However, the simulated curves generated by this method are based on a specific physical model and mathematical extrapolation, and their accuracy is highly dependent on the accuracy of the initial acceleration data and the applicability of the selected exponential equation. When measured data itself contains noise due to factors such as electromagnetic interference, vibration, or temperature fluctuations, the displacement, stress, and even the final simulation curve calculated based on this data will also introduce errors. The curve shape may still be affected by fluctuations in the original data. This still presents uncertainties for characteristic stress analysis that requires precise identification of curve abrupt change points (such as the critical point of dynamic recrystallization). Its mathematical mechanism focuses on curve extension based on physical processes, rather than smoothing existing fluctuating data or accurately identifying feature points.

[0005] Therefore, there is an urgent need to develop a more effective method for analyzing stress-strain curves, which can overcome the shortcomings of existing methods and accurately determine the characteristic stress from the stress-strain curves. Summary of the Invention

[0006] To address the problems of inaccurate feature point identification and large curve fluctuations caused by noise interference in existing stress-strain curves, this invention provides a method for analyzing stress-strain curves, specifically including the following steps:

[0007] S1. Conduct compression deformation simulation experiments based on a thermal simulation testing machine and collect experimental data, including sample temperature data, experimental stress data, and experimental strain data.

[0008] Furthermore, in the compression deformation simulation experiment, a suitable sampling frequency is set. Satisfying the formula:

[0009] in, Indicates the deformation rate. This represents an undetermined constant with a value range of 200-500.

[0010] S2. Based on the experimental stress data and experimental strain data, plot and output the first stress-strain curve, fit the first stress-strain curve with a higher-order polynomial and output the fitted curve, differentiate the fitted curve, plot the relationship curve between the fitted curve and the derivative of the fitted curve, and determine the dividing point of the first stress-strain curve.

[0011] S21. Establish the equation of the fitted curve based on the fitted curve:

[0012] in Indicates stress, Indicates strain.

[0013] S22. Apply the fitted curve equation to the strain... Differentiate: .

[0014] S23. Plot the relationship curve between the fitted curve and the derivative of the fitted curve. Based on the inflection point of the relationship curve, determine the critical point corresponding to the critical stress. Based on the first stress-strain curve, determine the peak point corresponding to the peak stress. If there is a recrystallization steady-state stage, determine the starting point of dynamic recrystallization entering the steady-state stage.

[0015] S24. The dividing points of the first stress-strain curve include the critical point corresponding to the critical stress, the peak point corresponding to the peak stress, and the starting point of the dynamic recrystallization and entry into the steady state stage.

[0016] S3. Based on the segmentation point, the first stress-strain curve is segmented, and a higher-order polynomial is used to fit each segment of the segmented curve. The first fitting coefficient and the fitted stress value of each segment are recorded. The fitting difference between the fitted stress value and the experimental stress data is calculated. The absolute value of the fitting difference is compared with the first stress threshold. The parts of the segmented curve that meet the elimination conditions are eliminated and the second stress-strain curve is plotted.

[0017] S31. Calculate the fitted stress value for each segment of the piecewise curve. .

[0018] S32. Calculate the fitted stress value. and the experimental stress data The fitting difference is calculated by comparing the absolute value of the fitting difference with a first stress threshold. Compare them.

[0019] S33. The formula for the rejection condition is as follows:

[0020] Remove the portions of the piecewise curve that meet the removal criteria and plot the second stress-strain curve.

[0021] S4. Fit the second stress-strain curve using a higher-order polynomial, record the second fitting coefficient and compare it with the fitting coefficient threshold. If the second fitting coefficient exceeds the fitting coefficient threshold, the accuracy of the second stress-strain curve meets the standard. If the fitting coefficient does not exceed the fitting coefficient threshold, repeat the elimination and refitting strategy until a stress-strain curve with the required accuracy is obtained.

[0022] S41. Calculate the refit stress value for each segment of the piecewise curve. .

[0023] S42. Calculate the refitted stress value. and the experimental stress data The refit difference is then compared with the absolute value of the refit difference to a second stress threshold.

[0024] S43. Eliminate the piecewise curves that meet the elimination criteria, and repeat the elimination and refitting strategy until a stress-strain curve with satisfactory accuracy is obtained.

[0025] S44. The formula for further elimination conditions is:

[0026] in, Indicates the second stress threshold. This indicates the number of iterations for the elimination and refitting strategy.

[0027] Furthermore, the fitting coefficient threshold is 0.99.

[0028] Compared with the prior art, the present invention has the following beneficial effects: This invention provides a method for analyzing stress-strain curves. By introducing a data elimination mechanism based on feature point segmented fitting and dynamic threshold adjustment, it can effectively identify and remove abnormal data caused by factors such as electromagnetic interference and temperature fluctuations during the experiment, significantly improving the smoothness and accuracy of the stress-strain curves. While ensuring the overall goodness of fit of the curves, the method of this invention can more accurately determine key characteristic parameters such as critical stress, peak stress, and the steady-state initiation point of dynamic recrystallization, providing a reliable basis for the analysis of the thermal deformation behavior of metallic materials. Furthermore, this method is simple to operate, highly adaptable, and can be widely applied to the processing of data from various thermodynamic simulation experiments, possessing significant engineering application value. Attached Figure Description

[0029] 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.

[0030] Figure 1 This is a flowchart of a stress-strain curve analysis method according to the present invention.

[0031] Figure 2 This is a schematic diagram of a typical stress-strain curve in Embodiment 1 of the present invention.

[0032] Figure 3 This is a schematic diagram of the relationship between the derivative of stress with respect to strain and stress in Embodiment 1 of the present invention.

[0033] Figure 4 This is the stress-strain curve finally obtained in Embodiment 1 of the present invention. Detailed Implementation

[0034] 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.

[0035] 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.

[0036] like Figure 1 As shown, this invention discloses a method for analyzing stress-strain curves, which mainly includes the following steps: S1. Conduct compression deformation simulation experiments based on a thermal simulation testing machine and collect experimental data, including sample temperature data, experimental stress data, and experimental strain data.

[0037] In a preferred embodiment of this application, a suitable sampling frequency is set in the compression deformation simulation experiment. Satisfying the formula:

[0038] in, Indicates the deformation rate. This represents an undetermined constant with a value range of 200-500.

[0039] S2. Based on the experimental stress data and experimental strain data, plot and output the first stress-strain curve, fit the first stress-strain curve with a higher-order polynomial and output the fitted curve, differentiate the fitted curve, plot the relationship curve between the fitted curve and the derivative of the fitted curve, and determine the dividing point of the first stress-strain curve.

[0040] S21. Establish the equation of the fitted curve based on the fitted curve:

[0041] in Indicates stress, Indicates strain.

[0042] S22. Apply the fitted curve equation to the strain... Differentiate: .

[0043] S23. Plot the relationship curve between the fitted curve and the derivative of the fitted curve. Based on the inflection point of the relationship curve, determine the critical point corresponding to the critical stress. Based on the first stress-strain curve, determine the peak point corresponding to the peak stress. If there is a recrystallization steady-state stage, determine the starting point of dynamic recrystallization entering the steady-state stage.

[0044] S24. The dividing points of the first stress-strain curve include the critical point corresponding to the critical stress, the peak point corresponding to the peak stress, and the starting point of the dynamic recrystallization and entry into the steady state stage.

[0045] S3. Based on the segmentation point, the first stress-strain curve is segmented, and a higher-order polynomial is used to fit each segment of the segmented curve. The first fitting coefficient and the fitted stress value of each segment are recorded. The fitting difference between the fitted stress value and the experimental stress data is calculated. The absolute value of the fitting difference is compared with the first stress threshold. The parts of the segmented curve that meet the elimination conditions are eliminated and the second stress-strain curve is plotted.

[0046] S31. Calculate the fitted stress value for each segment of the piecewise curve. .

[0047] S32. Calculate the fitted stress value. and the experimental stress data The fitting difference is calculated by comparing the absolute value of the fitting difference with a first stress threshold. Compare them.

[0048] S33. The formula for the rejection condition is as follows:

[0049] Remove the portions of the piecewise curve that meet the removal criteria and plot the second stress-strain curve.

[0050] S4. Fit the second stress-strain curve using a higher-order polynomial, record the second fitting coefficient and compare it with the fitting coefficient threshold. If the second fitting coefficient exceeds the fitting coefficient threshold, the accuracy of the second stress-strain curve meets the standard. If the fitting coefficient does not exceed the fitting coefficient threshold, repeat the elimination and refitting strategy until a stress-strain curve with the required accuracy is obtained.

[0051] S41. Calculate the refit stress value for each segment of the piecewise curve. .

[0052] S42. Calculate the refitted stress value. and the experimental stress data The refit difference is then compared with the absolute value of the refit difference to a second stress threshold.

[0053] S43. Eliminate the piecewise curves that meet the elimination criteria, and repeat the elimination and refitting strategy until a stress-strain curve with satisfactory accuracy is obtained.

[0054] S44. The formula for further elimination conditions is:

[0055] in, Indicates the second stress threshold. This indicates the number of iterations for the elimination and refitting strategy.

[0056] In a preferred embodiment of this application, the fitting coefficient threshold is 0.99.

[0057] Example 1 S1. The specimen is heated to 1200℃ on a thermal simulation testing machine, and then cooled to 1100℃. A compression deformation simulation experiment is carried out at this temperature, with a strain rate of 1s. -1 The deformation was 50%. During the experiment, sample temperature, stress, and strain parameters were collected, and the deformation rate was determined accordingly. The value is set to 500, which sets the sampling frequency during the experiment. =500Hz.

[0058] S2. Based on the stress and strain data obtained in step 1, plot the corresponding stress-strain curves, i.e., stress-strain curves. With strain The relationship curve between them, such as Figure 2 As shown. The Origin data processing software was used to process... Figure 2 The stress-strain curve in the image is fitted using a seventh-order polynomial. The equation corresponding to the fitted curve is:

[0059] The coefficients of the equation corresponding to the fitted curve are shown in Table 1 below: Table 1. Coefficients of the equation corresponding to the fitted curve in Example 1

[0060] The above fitted curve equation is for Differentiating, we get:

[0061] The coefficients corresponding to the derivatives of the fitted curve equations are shown in Table 2 below: Table 2. Coefficients corresponding to the derivative of the fitted curve equation in Example 1

[0062] draw - Relationship curve, such as Figure 3 As shown. Find the inflection point of the curve and determine the critical point corresponding to the critical stress. The coordinates of this point are (0.18, 113.8). Then, determine the peak point corresponding to the peak stress from the drawn stress-strain curve. The corresponding coordinates are (0.42, 127). The coordinates of the starting point of dynamic recrystallization steady state are (0.67, 126.6).

[0063] S3. Based on the critical point, peak point, and starting point of dynamic recrystallization leading to steady state determined in S2, the stress-strain curve plotted from the experimental data obtained in S1 is divided into four segments. Then, a seventh-order polynomial is used to fit each segment of the curve, with fitting coefficients of 0.993, 0.999, 0.999, and 0.996, respectively. Under the same strain conditions, the stress value is calculated using the higher-order polynomial obtained after fitting. Compared with experimental values Make a difference, select After the pressure reaches 1 MPa, data points that meet the rejection criteria will be removed.

[0064] After the stress-strain data collected in S4 and S1 were processed by S3, data points meeting the rejection criteria were removed. The remaining data were used as the basis for redrawing the stress-strain curve, which was then fitted using a seventh-order polynomial. The fitting coefficient R was recorded as 0.999. The resulting stress-strain curve met the accuracy requirements for subsequent analysis.

[0065] Example 2 S1. The specimen is heated to 1200℃ on a thermal simulation testing machine, then cooled to 950℃. A compression deformation simulation experiment is performed at this temperature, with a strain rate of 0.5 s⁻¹. -1 The deformation was 50%. During the experiment, sample temperature, stress, and strain parameters were collected, and the deformation rate was determined accordingly. The value is set to 400, which sets the sampling frequency during the experiment. =200Hz.

[0066] S2. Based on the stress and strain data obtained in step 1, plot the corresponding stress-strain curves, i.e., stress-strain curves. With strain The relationship curve between them. The stress-strain curve was fitted using Origin data processing software. A ninth-order polynomial was used to fit the curve, and the equation corresponding to the fitted curve is:

[0067] The coefficients of the equation corresponding to the fitted curve are shown in Table 3 below: Table 3. Coefficients of the equation corresponding to the fitted curve in Example 2

[0068] The above fitted curve equation is for Differentiating, we get:

[0069] The coefficients corresponding to the derivative of the fitted curve equation are shown in the table below: Table 4. Coefficients corresponding to the derivative of the fitted curve equation in Example 2

[0070] draw - Find the inflection point of the curve and determine the critical point corresponding to the critical stress. The coordinates of this point are (0.26, 140.8). Then, determine the peak point corresponding to the peak stress from the drawn stress-strain curve. The corresponding coordinates are (0.55, 147.7).

[0071] S3. Based on the critical point and peak point determined in S2, the stress-strain curve plotted from the experimental data obtained in S1 is divided into three segments. Then, a ninth-order polynomial is used to fit each segment of the curve, with fitting coefficients of 0.983, 0.989, 0.991, and 0.986, respectively. Under the same strain condition, the stress value is calculated using the higher-order polynomial obtained after fitting. Compared with experimental values Make a difference, select After the pressure reaches 1 MPa, data points that meet the rejection criteria will be removed.

[0072] After the stress-strain data collected in S4 and S1 are processed by S3, data points meeting the rejection criteria are removed. The remaining data are used as the basis for redrawing the stress-strain curve, and a ninth-order polynomial is used to fit it. The resulting fitting coefficient R is recorded as 0.986. The obtained fitting coefficient R is no greater than 0.99. Then, a selected threshold is set... Halved =0.5MPa, meaning data was further removed according to the elimination criteria. After this second data removal, the remaining data were used as the base data, and a ninth-order polynomial was used for fitting. The final fitting coefficient was R=0.998. The obtained stress-strain curve meets the accuracy requirements for subsequent analysis.

[0073] 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 analyzing stress-strain curves, characterized in that, Includes the following steps: Compression deformation simulation experiments were conducted using a thermal simulation testing machine, and experimental data were collected. The experimental data included sample temperature data, experimental stress data, and experimental strain data. Based on the experimental stress data and experimental strain data, a first stress-strain curve is plotted and output. A higher-order polynomial is used to fit the first stress-strain curve and the fitted curve is output. The derivative of the fitted curve is calculated, and the relationship curve between the fitted curve and the derivative of the fitted curve is plotted to determine the dividing point of the first stress-strain curve. The first stress-strain curve is segmented based on the segmentation point. A higher-order polynomial is used to fit each segment of the fitted curve after segmentation. The first fitting coefficient and the fitted stress value of each segment are recorded. The fitting difference between the fitted stress value and the experimental stress data is calculated. The absolute value of the fitting difference is compared with the first stress threshold. The parts of the segmented curve that meet the elimination conditions are eliminated and the second stress-strain curve is plotted. The second stress-strain curve is fitted using a higher-order polynomial. The second fitting coefficient is recorded and compared with the fitting coefficient threshold. If the second fitting coefficient exceeds the fitting coefficient threshold, the accuracy of the second stress-strain curve is up to standard. If the fitting coefficient does not exceed the fitting coefficient threshold, the strategy of elimination and refitting is repeated until a stress-strain curve with up to standard accuracy is obtained.

2. The method for analyzing stress-strain curves according to claim 1, characterized in that, In the compression deformation simulation experiment, a suitable sampling frequency was set. Satisfying the formula: in, Indicates the deformation rate. This represents an undetermined constant with a value range of 200-500.

3. The method for analyzing stress-strain curves according to claim 1, characterized in that, The steps for determining the segmentation points of the first stress-strain curve include: Based on the fitted curve, establish the equation for the fitted curve: in Indicates stress, Indicates strain; The fitted curve equation is applied to the strain Differentiate: Plot the relationship between the fitted curve and the derivative of the fitted curve. Determine the critical point corresponding to the critical stress based on the inflection point of the relationship curve. Determine the peak point corresponding to the peak stress based on the first stress-strain curve. If there is a recrystallization steady state stage, determine the starting point of dynamic recrystallization entering the steady state stage. The dividing points of the first stress-strain curve include the critical point corresponding to the critical stress, the peak point corresponding to the peak stress, and the starting point of the dynamic recrystallization and entry into the steady state stage.

4. The method for analyzing stress-strain curves according to claim 1, characterized in that, The steps for plotting the second stress-strain curve include: Calculate the fitted stress value for each segment of the piecewise curve. ; Calculate the fitted stress value and the experimental stress data The fitting difference is calculated by comparing the absolute value of the fitting difference with a first stress threshold. Compare; The formula for the rejection criteria is as follows: Remove the portions of the piecewise curve that meet the removal criteria and plot the second stress-strain curve.

5. The method for analyzing stress-strain curves according to claim 1, characterized in that, The steps of the re-elimination and refitting strategy include: Calculate the refit stress value for each segment of the piecewise curve. ; Calculate the refitted stress value and the experimental stress data The refit difference is then compared with the absolute value of the refit difference to a second stress threshold. Segmented curves that meet the further elimination criteria are eliminated, and the elimination and refitting strategy is repeated until a stress-strain curve with satisfactory accuracy is obtained.

6. The method for analyzing stress-strain curves according to claim 5, characterized in that, The formula for further elimination is: in, Indicates the second stress threshold. This indicates the number of iterations for the elimination and refitting strategy.

7. The method for analyzing stress-strain curves according to claim 1, characterized in that, The fitting coefficient threshold is 0.99.

Images