Work hardening index acquisition method
By fitting the lgσture-lgεture curve of martensitic aged stainless steel using the ZC model, the problem of insufficient fitting accuracy of existing models under nonlinear characteristics is solved, and a higher accuracy in obtaining the work hardening index is achieved.
Patent Information
- Application Number
- CN202511047559.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-29
- Publication Date
- 2025-11-11
AI Technical Summary
Existing Hollomon and Modified Ludwik models cannot accurately fit the lgσture-lgεture curves of martensitic aging stainless steel and other metallic materials, resulting in large errors in the work hardening index n, especially under nonlinear characteristics, the fitting results do not conform to reality.
The ZC model was used to fit the lgσture-lgεture curve of martensitic aging stainless steel. The stress-strain data were converted by the formulas σture=(1+ε)·σ and εture=ln(1+ε), and the work hardening index n was obtained by nonlinear fitting using Origin software.
It improves the accuracy of obtaining the work hardening index of nonlinear characteristic materials such as martensitic aging stainless steel, making the fitting results closer to the actual range, with a fitting accuracy of 0.999, which is better than the existing model.
Smart Images
Figure CN120927428A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of uniaxial static tensile mechanical property testing of metallic materials, specifically relating to a method for obtaining the work hardening index. Background Technology
[0002] The work hardening index n reflects the ability of a metallic material to resist uniform plastic deformation. Its value is between 0 and 1. It is a performance index that characterizes the strain hardening behavior of metallic materials and is of great significance for evaluating the plastic forming ability of materials and predicting the plastic deformation behavior of materials under complex stress states.
[0003] Currently, the work hardening index n of materials is mainly obtained using uniaxial static tensile testing. Firstly, the lgσ during the uniform plastic deformation stage of the material is measured through uniaxial static tensile testing. ture -lgε ture The curve represents the true stress σ of the material. ture With the true strain ε of the material ture The curve between the logarithms of the two is then used to fit the work hardening index using a relevant model. Commonly used fitting models include the Hollomon model and the Modified Ludwik model.
[0004] The Hollomon model is the most widely used, but it can only fit data with linear characteristics. Its mathematical expression is: lgσ ture =lgK+n·lgε ture K is the hardening coefficient.
[0005] The Modified Ludwik model can be used to fit data with nonlinear characteristics, and its expression is: lgσ ture =lgK+(n1+n2·lgε) ture )·lgε ture .
[0006] For example, in some metallic materials such as martensitic aging stainless steel, lgσ during the uniform plastic deformation stage ture -lgε ture The curve exhibits obvious nonlinear characteristics. For this type of metallic material, linear fitting using the Hollomon model cannot accurately reflect the true work hardening situation of the material, and the obtained work hardening index n has a large error; while the Modified Ludwik model will produce two values, n1 and n2, both of which are less than 0, which is inconsistent with the objective fact that the work hardening index n is generally accepted to be between 0 and 1. Summary of the Invention
[0007] To address the shortcomings of existing technologies, this invention provides a method for obtaining the work hardening index, used to solve the problem of lgσ. ture-lgε ture The problem of obtaining the work hardening index of metallic materials with nonlinear data characteristics.
[0008] The present invention achieves the above-mentioned technical objectives through the following technical means.
[0009] A method for obtaining the work hardening index, using the following ZC model for the lgσ of the material. ture -lgε ture The curve is fitted to obtain the work hardening index n:
[0010]
[0011] In the formula, exp(·) represents the exponential function with base e, lg(·) represents the logarithmic function with base 10, n is the work hardening exponent, K is the hardening coefficient, a and b are constant coefficients, and σ ture For the true stress of the material, ε ture For the true strain of the material.
[0012] Furthermore, the constant coefficients a < 0 and b = -0.2.
[0013] Furthermore, the lgσ of the material was obtained by uniaxial static tensile testing. ture -lgε ture curve.
[0014] Furthermore, stress-strain data are recorded during the tensile test until the specimen fractures tensilely, and the yield strength and tensile strength data are recorded therein.
[0015] The stress σ and strain ε measured in the range from yield strength to tensile strength can be converted into true stress σ using the following formula. ture and true strain ε ture :
[0016] σ ture = (1+ε)·σ
[0017] ε ture =ln(1+ε)
[0018] Based on σ ture and ε ture Plot lgσ ture -lgε ture curve.
[0019] Furthermore, the tensile specimen is a cylindrical proportional specimen, and a tensile force is applied along the axial direction of the cylindrical proportional specimen.
[0020] Furthermore, the tensile strain rate ranges from 0.00025 to 0.0025 / s.
[0021] Furthermore, lgσ was performed using Origin software. ture -lgε ture Curve plotting and fitting.
[0022] Furthermore, regarding lgσ ture -lgε ture The curve represents a non-linear material.
[0023] Furthermore, the work hardening index n is used to obtain the work hardening index n of martensitic aging stainless steel.
[0024] The beneficial effects of this invention are as follows:
[0025] This invention provides a method for obtaining the work hardening index, which can be used for martensitic aging stainless steel and other materials with a work hardening index of lgσ. ture -lgε ture For metallic materials with nonlinear data characteristics, the work hardening index is obtained. The proposed ZC model has higher fitting accuracy than existing models, and the obtained work hardening index is within the fluctuation range of the actual work hardening index of the material. Attached Figure Description
[0026] Figure 1 This is a schematic diagram of curve fitting for the ZC model of this invention;
[0027] Figure 2 The curve fitting graph is shown for the samples with aging times of 1 to 8 hours in the test examples.
[0028] Figure 3 The curve fitting graphs are for the samples with aging times of 12 to 100 hours in the test examples;
[0029] Figure 4 The variation of the work hardening index values for samples aged for 1 and 2.5 hours in the test examples;
[0030] Figure 5 The variation of the work hardening index values for samples with aging times ranging from 4 to 100 hours in the test examples;
[0031] Figure 6 This is a comparison of the fitting results of the present invention with those of two other methods. Detailed Implementation
[0032] The embodiments of the present invention are described in detail below. Examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, but should not be construed as limiting the present invention.
[0033] I. Technical Solution
[0034] The work hardening index of martensitic aging stainless steel is obtained according to the following steps:
[0035] Step 1: Collect the true stress σ of martensitic aging stainless steel through a uniaxial static tensile test. ture With the true strain ε of the material ture The data was used to plot the lgσ during the uniform plastic deformation stage of the material. ture -lgε ture Curve. Wherein:
[0036] The specimens were subjected to tensile testing at room temperature using a tensile testing machine. The specimens were cylindrical proportional specimens. Tensile force was applied along the axial direction of the cylindrical proportional specimens. The tensile strain rate ranged from 0.00025 to 0.0025 / s.
[0037] Record stress-strain data during the tensile process until the specimen fractures, and record the yield strength and tensile strength data.
[0038] The stress σ and strain ε measured in the range from yield strength to tensile strength can be converted into true stress σ using the following formula. ture and true strain ε ture :
[0039] σ ture = (1+ε)·σ
[0040] ε ture =ln(1+ε)
[0041] Then, the true stress σ was calculated separately. ture and true strain ε ture Performing logarithmic operations yields lgσ ture and lgε ture Based on lgσ ture and lgε ture The data was used to plot lgσ using the data analysis software Origin. ture -lgε ture curve.
[0042] Step 2, apply the following ZC model to lgσ ture -lgε ture The work hardening index n of martensitic aging stainless steel is obtained by fitting the curve.
[0043] Reference Figure 1 As shown, the mathematical expression of the ZC model above is:
[0044]
[0045] In the formula, exp(·) represents an exponential function with the natural constant e as the base, lg(·) represents a logarithmic function with the base 10, n is the work hardening exponent, K is the hardening coefficient, and a and b are constant coefficients to be determined by fitting. In this embodiment, a<0 and b=-0.2;
[0046] In this embodiment, Origin software is used to perform nonlinear fitting on the curve.
[0047] II. Test
[0048] Multiple cylindrical scale specimens of martensitic aging stainless steel were prepared and aged for 1, 2.5, 4, 8, 12, 22, 35, 50, 75, and 100 hours, respectively. Uniaxial static tensile tests were then conducted to obtain the lgσ value of the material during the uniform plastic deformation stage. ture -lgε ture Curve data.
[0049] like Figure 2 and Figure 3 The figure shows the curve fitting graphs for each group of samples mentioned above. The graphs show the lgσ of the martensitic aging stainless steel. ture -lgε ture The curve exhibits obvious nonlinear characteristics. The fitting accuracy R of the Hollomon model is... 2 The fitting accuracy R0 of the Modified Ludwik model ranges from 0.91211 to 0.94924. 2 The fitting accuracy ranges from 0.99422 to 0.99816. Among the two existing methods, the Modified Ludwik model has higher fitting accuracy, but deviations occur in both the initial and final stages of fitting. In comparison, the ZC model proposed in this invention has a higher fitting accuracy R0. 2 The accuracy ranges from 0.99903 to 0.99969, which is higher than the fitting accuracy of the Hollomon and Modified Ludwik models.
[0050] For several groups of samples with aging times ranging from 1 to 100 hours, the fitting results obtained from the three models are shown in Table 1 below. Among them, although the Modified Ludwik model has a higher fitting accuracy, the fitting results n1 and n2 are both negative, which is inconsistent with the case where the work hardening index is greater than 0.
[0051] Table 1: Comparison of Fitting Results for the Three Models
[0052]
[0053] d(lgσ ture ) / d(lgε tureThis can reflect the change in the work hardening index from yield strength to tensile strength. The region with a relatively stable value change represents the stage of uniform plastic deformation of the material. The d(lgσ) of each group of samples... ture ) / d(lgε ture The curve showing the change with strain is as follows: Figure 4 and Figure 5 As shown in the figure, the work hardening index shows a gradual decreasing trend, with a relatively stable area appearing near the tensile strength (within the yellow box in the figure).
[0054] Combining the fitting results data in Table 1 and Figure 4 and Figure 5 d(lgσ) ture ) / d(lgε ture The data was summarized to obtain Figure 6 The scatter plots of the fitting results are shown below. Figure (a) shows the distribution of the work hardening index obtained from the three models; Figure (b) shows the distribution of lgK obtained from the three models; and Figure (c) shows the work hardening index obtained using this invention and the relationship between d(lgσ) and each group. ture ) / d(lgε ture The relative situation between ).
[0055] The Hollomon model fitting results significantly exceed... Figure 4 and Figure 5 Within the medium-stability region (by d(lgσ) ture ) / d(lgε ture The range of fluctuations in the work hardening index, as reflected by this. Conversely, Figure 6 (c) The fitting results of the present invention shown are all within the above-mentioned range, and the fitting accuracy is greater than 0.999. Therefore, it is verified that the present invention has advantages in both the reliability and accuracy of the fitting results.
[0056] This invention is not limited to the above-described embodiments. Any obvious improvements, substitutions, or modifications that can be made by those skilled in the art without departing from the essence of this invention are within the scope of protection of this invention.
Claims
1. A method for obtaining the work hardening index, characterized in that: The following ZC model is used for the lgσ of the material. ture -lgε ture The curve is fitted to obtain the work hardening index n: In the formula, exp(·) represents the exponential function with base e, lg(·) represents the logarithmic function with base 10, n is the work hardening exponent, K is the hardening coefficient, a and b are constant coefficients, and σ ture For the true stress of the material, ε ture For the true strain of the material.
2. The method for obtaining the work hardening index according to claim 1, characterized in that: The constant coefficients a < 0 and b = -0.
2.
3. The method for obtaining the work hardening index according to claim 1, characterized in that: The lgσ of the material was obtained by uniaxial static tensile testing. ture -lgε ture curve.
4. The method for obtaining the work hardening index according to claim 3, characterized in that: During the tensile test, stress-strain data are recorded until the specimen fractures tensilely, and the yield strength and tensile strength data are recorded. The stress σ and strain ε measured in the range from yield strength to tensile strength can be converted into true stress σ using the following formula. ture and true strain ε ture : s ture =(1+ε)·σ e ture =ln(1+ε) Based on σ ture and ε ture Plot lgσ ture -lgε ture curve.
5. The method for obtaining the work hardening index according to claim 3, characterized in that: The tensile specimen is a cylindrical proportional specimen, and a tensile force is applied along the axial direction of the cylindrical proportional specimen.
6. The method for obtaining the work hardening index according to claim 5, characterized in that: The tensile strain rate ranges from 0.00025 to 0.0025 / s.
7. The method for obtaining the work hardening index according to claim 3, characterized in that: Using Origin software to perform lgσ ture -lgε ture Curve plotting and fitting.
8. The method for obtaining the work hardening index according to claim 1, characterized in that: For lgσ ture -lgε ture The curve represents a non-linear material.
9. The method for obtaining the work hardening index according to claim 8, characterized in that: Used to obtain the work hardening index n of martensitic aging stainless steel.
10. The method for obtaining the work hardening index according to claim 3, characterized in that: The uniaxial static tensile test was conducted at room temperature.