Fitting method of johnson-cook constitutive model for drawing of ptw7ir1 alloy ultrafine wire
By decoupling the Johnson-Cook constitutive model and combining the Hollom rule and the JIA rule, the constitutive model parameters of low strain rate ultrafine wires in PtW7Ir1 alloy were fitted, which solved the problem of large deviation in simulation results in the existing technology and realized high-precision simulation of the drawing process and prediction of fracture defects.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- KUNMING UNIV OF SCI & TECH
- Filing Date
- 2026-03-12
- Publication Date
- 2026-06-26
AI Technical Summary
The lack of Johnson-Cook constitutive model parameters for drawing low strain rate ultrafine wires from PtW7Ir1 alloy in the existing technology leads to a large deviation between the simulation results and the actual processing conditions. It is difficult to accurately predict the drawing force, stress concentration location and fracture trend, and cannot effectively guide the optimization of the production process.
By decoupling the Johnson-Cook constitutive model, extracting each coefficient independently, and combining the Hollom rule and the JIA rule, tensile tests covering the actual low strain rate and temperature range were designed to fit constitutive model parameters suitable for PtW7Ir1 alloy, including yield strength, strain hardening modulus, hardening index, strain rate strengthening coefficient, and thermal softening index.
It accurately describes the mechanical response of materials during multi-pass drawing processes, improves simulation accuracy, effectively predicts fracture defects, and guides the optimization of actual production processes.
Smart Images
Figure CN122287197A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of numerical simulation technology for metal material processing, specifically to a fitting method for the Johnson-Cook constitutive model used in drawing ultrafine PtW7Ir1 alloy wires. Background Technology
[0002] As the core power unit of aviation equipment, aero-engines require their turbine blades and other hot-end components to operate under harsh conditions of high temperature, high pressure, and corrosive exhaust gases for extended periods. Among these, PtW7Ir1 alloy, with its excellent high-temperature mechanical properties, good oxidation resistance, and stable resistance temperature characteristics, has become a key material for manufacturing the sensitive grid wires of high-temperature resistance strain gauges. With the continuous improvement of the thrust-to-weight ratio of aero-engines, the service environment of hot-end components is becoming increasingly severe, placing higher demands on the dimensional accuracy, mechanical properties, and reliability of PtW7Ir1 alloy wires.
[0003] PtW7Ir1 alloy possesses high strength, high melting point, and low plasticity. During the drawing process to ultrafine wires, it exhibits significant work hardening and high deformation resistance, making it highly susceptible to defects such as fracture and cracking, resulting in low yield and high processing costs. Finite element numerical simulation technology has become an effective means of analyzing the mechanism of metal plastic forming, predicting forming defects, and optimizing process parameters. To obtain high-precision simulation results, it is essential to rely on a constitutive model that accurately describes the dynamic mechanical behavior of the material. The Johnson-Cook (JC) constitutive model, due to its simplicity and ability to simultaneously reflect strain hardening, strain rate strengthening, and temperature softening effects, is widely used in the numerical simulation of metal plastic forming.
[0004] Current research on the constitutive relations of platinum-based alloys is limited, particularly regarding constitutive parameters for low-strain-rate ultrafine filament drawing of PtW7Ir1 alloy, which are largely lacking. This leads to the use of general parameters or parameters analogous to those of other alloys in drawing process simulations, resulting in significant discrepancies between simulation results and actual processing conditions. Consequently, it is difficult to accurately predict drawing force, stress concentration locations, and fracture trends, hindering effective guidance for optimizing actual production processes. Therefore, it is necessary to construct an accurate Johnson-Cook constitutive model for low-strain-rate ultrafine filament drawing of PtW7Ir1 alloy to fill the gap in constitutive data for this material, providing a reliable basis for improving the accuracy of ultrafine filament drawing simulations, analyzing drawing mechanisms, and predicting fracture defects. Summary of the Invention
[0005] To address the aforementioned technical problems, this invention provides a fitting method for the Johnson-Cook constitutive model used in drawing ultrafine PtW7Ir1 alloy wires.
[0006] To achieve the above technology, the specific solution is as follows: S1. Decouple the standard form of the Johnson-Cook constitutive model and extract the coefficients of each term independently to obtain the constitutive model parameters to be solved. S2. Under a preset environment, a room temperature quasi-static uniaxial tensile test was conducted on the standard PtW7Ir1 alloy processed specimen to obtain its engineering stress-strain curve and convert it into true stress-strain. S3. Determine the yield strength A and elastic modulus of PtW7Ir1 alloy based on S2; S4. Calculate the actual stress after necking using the Hollom rule and the JIA rule. Obtain the strain hardening modulus B and the hardening index n from the actual stress before and after necking. S5. Obtain the yield stress data of the material based on tensile tests and calculate the strain rate hardening coefficient using the least squares method. and heat softening index ; The constitutive model parameters, including yield strength A, strain hardening modulus B, hardening exponent n, strain rate strengthening coefficient C, and thermal softening exponent m, were obtained by fitting using the least squares method, thus completing the fitting of the constitutive model.
[0007] Specifically, in S1, three items are extracted independently, and each item is represented as follows: Considering only the strain hardening term: ; Consider strain hardening and strain rate strengthening terms: ; Considering strain hardening and temperature softening terms: ; in, Equivalent flow stress; Yield strength; It is the strain hardening modulus; Equivalent plastic strain; The hardening index; The strain rate strengthening coefficient; This is the current equivalent plastic strain rate; Reference strain rate; The current temperature; For reference temperature; This refers to the melting point temperature of the material. Normalized temperature; This is the thermal softening index.
[0008] Specifically, in S2, the preset environmental condition is: reference strain rate. =0.0021s -1 And reference temperature =298K, at which room temperature quasi-static uniaxial tensile test was conducted.
[0009] Specifically, in S2, the conversion formula includes: In the formula, Represents actual stress; Represents actual response; This is the equivalent plastic strain.
[0010] Specifically, in S3, the yield strength and elastic modulus are determined as follows: the initial linear segment of the engineering stress-strain curve is read to obtain the slope of the linear fit, which is the elastic modulus E of the material; using the 0.2% offset method, a straight line with a slope of E and an offset of 0.2% is drawn, and the intersection of this straight line with the stress-strain curve is the yield strength A.
[0011] Specifically, in S4, the actual stress after necking is calculated using the Hollom rule and the JIA rule, and the expression is as follows: In the formula, These are weighting coefficients; For neck stress; For equivalent change; For neck strain; This represents the actual stress after necking, where the weighting coefficients are optimized according to the following formula: In the formula, This indicates the number of data points within a uniformly deformed segment. Indicates the index of the data point; Indicates the first The actual stress after correction for each data point; Indicates the first The test stress at each data point.
[0012] Specifically, in step S4, the expressions for obtaining the strain hardening modulus B and the hardening exponent n are as follows: In the formula, Indicates pre-necking stress With necking stress splicing the fitted values; Indicates pre-neck constriction strain The strain values are fitted together with the extrapolated strain values, where the extrapolated strain values are the equivalent strain. , , For equivalent change; It indicates a genuine response.
[0013] Specifically, in S5, the method for obtaining the yield stress data of the material based on the tensile test includes: With the reference temperature kept constant at 298K, four sets of uniaxial tensile tests were conducted at different strain rates, yielding a strain rate of 0.0021 s⁻¹. -1 0.021s -1 0.21s -1 2.1s -1 The yield stress is set below the specified value to conform to the low strain rate environment of PtW7Ir1 alloy. The strain rate is kept constant at 0.0021 s. -1 Two sets of uniaxial tensile tests were conducted at different reference temperatures to obtain the yield stress at temperatures of 773K and 1073K.
[0014] Specifically, in step S5, the yield stress at different strain rates is fitted using the least squares method to obtain the strain rate hardening coefficient C, which is calculated as follows: In the formula, This represents the yield stress at the current strain rate; This represents the yield stress at the reference strain rate; This is the current equivalent plastic strain rate; Reference strain rate; The yield stress at different temperatures is fitted using the least squares method to obtain the thermal softening index m, which is calculated as follows: In the formula, The current temperature; For reference temperature; This is the melting point temperature of the material.
[0015] The beneficial effects of this invention are: This invention targets low strain rates (0.0021 s⁻¹) in PtW₇Ir₁. -1 -2.1s -1 By designing a systematic tensile test covering the actual low and medium strain rate pull-out range and temperature range, the JC constitutive parameters applicable to the alloy were obtained, solving the problem of material behavior distortion caused by parameter missingness.
[0016] Based on the traditional JC model fitting, this invention introduces a weighted fitting method using Hollomon's rule and JIA's rule. By optimizing the weighting coefficient Q with the goal of minimizing the sum of squares of the deviations in the uniform deformation segment, the artifact of the drop in the true stress-strain curve caused by necking in the uniaxial tensile test is effectively corrected. This accurately predicts the true hardening behavior of the material after necking, enabling the constitutive model to more realistically reflect the mechanical response of the material under the cumulative deformation of multiple pull-out passes. Attached Figure Description
[0017] Figure 1 This is a flowchart of the steps of the present invention; Figure 2 This is the engineering stress-strain curve of the room temperature quasi-static tensile test of the present invention; Figure 3 This is the engineering stress-strain curve of the room temperature dynamic tensile test of the present invention; Figure 4 This is the engineering stress-strain curve of the high-temperature quasi-static tensile test of the present invention; Figure 5 The results of the actual stress after necking calculated by the Hollom rule and the JIA rule of this invention; Figure 6 This is the fitting result of the strain hardening modulus B and hardening exponent n of the present invention; Figure 7 This is the fitting result of the strain rate strengthening coefficient C of the present invention; Figure 8 This is the fitting result of the thermal softening index m of the present invention; Figure 9 This is a comparison of the actual stress-strain curves from the plastic stage test and simulation of the present invention. Detailed Implementation
[0018] The present invention will be further described in detail below with reference to specific embodiments.
[0019] This invention addresses the drawing process of PtW7Ir1 alloy wire at medium and low strain rates. It adds weighted fitting of the Hollom rule and JIA rule to the traditional fitting method to predict the true stress-strain curve after necking, providing a new approach for the construction of the Johnson-Cook constitutive model.
[0020] This embodiment uses the PtW7Ir1 alloy ultrafine wire drawing process as the application background. The specific working conditions of this drawing process are: the raw wire diameter is 1.0 mm, the target wire diameter is 0.03 mm, multiple drawing passes are used, and the drawing speed v is set between 1-10 mm / s. According to the drawing geometry and kinematics, the material strain rate corresponding to this drawing speed is in the low to medium strain rate range (approximately 10). -3 s -1~10s -1 ).
[0021] Considering the small deformation per pass during ultrafine filament drawing (approximately 1%-7%), the material mainly undergoes a small-amplitude cyclic loading hardening process, and necking behavior affects the accuracy of fracture prediction. Therefore, the quasi-static uniaxial tensile test described in this invention aims to obtain the basic mechanical response under this low to medium strain rate; the weighted fitting algorithm aims to accurately capture the true stress evolution from small deformation to large necking deformation range, to meet the simulation requirements of the entire process from small deformation accumulation to large deformation in multi-pass drawing.
[0022] like Figure 1 As shown, a fitting method for the Johnson-Cook constitutive model in drawing ultrafine PtW7Ir1 alloy wires includes the following steps: S1. Decouple the standard form of the Johnson-Cook constitutive model and extract the coefficients of each term independently. The specific form of the Johnson-Cook constitutive model is as follows: In the formula, Equivalent flow stress; Yield strength; It is the strain hardening modulus; Equivalent plastic strain; The hardening index; The strain rate strengthening coefficient; This is the current equivalent plastic strain rate; Reference strain rate; The current temperature; For reference temperature; This refers to the melting point temperature of the material. Normalized temperature; The thermal softening index; The standard form of the Johnson-Cook constitutive model is decoupled, and the coefficients of each term are extracted independently, including: Considering only strain hardening, it can be expressed as: ; Considering strain hardening and strain rate strengthening, it can be expressed as: ; Considering strain hardening and temperature softening, it can be expressed as: .
[0023] S2. Design and fabricate a specimen that meets the test conditions, at the reference strain rate. =0.0021s -1 and reference temperature The specimen was subjected to a quasi-static uniaxial tensile test at room temperature at 298K to obtain the engineering stress-strain curve and convert it into the true stress-strain curve. The conversion formulas include: In the formula, Represents actual stress; Represents actual response; The engineering stress-strain curves of the quasi-static tensile test at room temperature are as follows: Figure 2 As shown, the obtained real stress-strain data are used for subsequent necking parameter fitting.
[0024] S3. Determine the yield strength and elastic modulus based on S2; The yield strength and elastic modulus are determined as follows: the initial linear segment of the engineering stress-strain curve is read to obtain the slope of the linear fit, which is the elastic modulus E of the material; using the 0.2% offset method, a straight line with a slope of E and an offset of 0.2% is drawn, and the intersection of this line with the stress-strain curve is the yield strength A. The expression for a straight line is: In the formula, Indicates the strain value; Indicates the elastic modulus; Indicates the strain value; This indicates the offset.
[0025] S4. Calculate the true stress after necking using Hollom's rule and JIA's rule. Obtain the strain hardening modulus B and hardening exponent n from the true stresses before and after necking. The expression is: In the formula, These are weighting coefficients; For neck stress; For equivalent change; For neck strain; This indicates the actual stress after necking. Starting from the necking initiation point, the goal is to minimize the sum of squared deviations between the corrected actual stress and the experimental stress in the uniform deformation segment, and to optimize the weighting coefficients accordingly. : In the formula, This indicates the number of data points within a uniformly deformed segment. Indicates the index of the data point; Indicates the first The actual stress after correction for each data point; Indicates the first The test stress at each data point; The optimal range for the weighting coefficient Q is 0.6 to 0.8. The weighted true stress-strain curve can be extrapolated to the large strain range after necking. The expressions for the strain hardening modulus B and the hardening exponent n are obtained as follows: In the formula, Indicates pre-necking stress With necking stress splicing the fitted values; Indicates pre-neck constriction strain The strain values are fitted together with the extrapolated strain values, where the extrapolated strain values are the equivalent strain. , ; The stress-strain curve obtained by combining the test data before and after necking is shown in the figure. Figure 5 As shown; Linear fitting using the least squares method yields the following results for the strain hardening modulus B and the hardening exponent n: Figure 6 As shown.
[0026] S5. Based on the yield stress data obtained from the tensile test, the strain rate hardening coefficient is calculated using the least squares method. and heat softening index ; Methods for obtaining material yield stress data based on tensile tests include: With the reference temperature kept constant at 298K, four sets of uniaxial tensile tests were conducted at different strain rates, yielding a strain rate of 0.0021 s⁻¹. -1 0.021s -1 0.21s -1 2.1s -1 The yield stress below; The strain rate is kept constant at 0.0021 s. -1 Two sets of uniaxial tensile tests were conducted at different reference temperatures to obtain the yield stress at temperatures of 773K and 1073K. Six specimens conforming to the test conditions were designed and fabricated to obtain stress-strain curves under different conditions, and the yield strength under different conditions was extracted: the first group is the reference test condition, with a tensile rate of 1 mm / min and a corresponding reference strain rate. =0.0021s -1 Reference temperature =298K, a quasi-static tensile test at room temperature, to calibrate the yield strength A, strain hardening modulus B, and hardening exponent n of the Johnson-Cook constitutive model; the second to fourth groups are dynamic tensile tests at room temperature. =298K, with tensile rates set to 10mm / min, 100mm / min, and 1000mm / min, corresponding to a strain rate of 0.021s. -1 0.21s -1 2.1s -1 The strain rate range during the drawing process of PtW7Ir1 alloy wire was covered to calibrate the strain rate strengthening coefficient C of the Johnson-Cook constitutive model; the fifth and sixth groups were quasi-static high-temperature tensile tests with a strain rate of 0.0021 s⁻¹. -1 The thermal softening index m of the Johnson-Cook constitutive model was determined at temperatures of 773K and 1073K, and the results are shown in Table 1. Table 1: Working conditions of the six groups of tensile tests The engineering stress-strain curves of dynamic tensile tests at room temperature are as follows: Figure 3 As shown; the engineering stress-strain curve of the high-temperature quasi-static tensile test is as follows. Figure 4 As shown; The yield stress at different strain rates is fitted using the least squares method to obtain the strain rate hardening coefficient C, which is calculated as follows: In the formula, This represents the yield stress at the current strain rate; This represents the yield stress at the reference strain rate; The fitting results for the strain rate hardening coefficient C are as follows: Figure 7 As shown; The yield stress at different temperatures is fitted using the least squares method to obtain the thermal softening index m, which is calculated as follows: The fitting results for the thermal softening index m are as follows: Figure 8 As shown; The tensile parameter values of the Johnson-Cook constitutive model were obtained through a set of quasi-static tests and three sets of tests at different strain rates and two sets at different temperatures.
[0027] Finally, the parameter values of the Johnson-Cook constitutive model are shown in Table 2; Table 2: Parameter values of the Johnson-Cook constitutive model S6. Verify the rationality of the stretching parameter values of the Johnson-Cook constitutive model using ABAQUS; To verify the present invention, the parameters obtained from S3, S4 and S5 were substituted into the Johnson-Cook constitutive model, and the tensile process was simulated using ABAQUS finite element software. The simulation results were compared with the experimental results to verify the rationality of the model parameters.
[0028] Figure 9 The strain rate is 0.0021 s. -1 The results of the comparison between the actual stress-strain curves during the plastic stage and the simulation results show that the experimental results are in good agreement with the simulation results. This proves that the present invention determined the parameters of the Johnson-Cook constitutive model through a set of quasi-static uniaxial tensile tests, three sets of uniaxial tensile tests with different strain rates, and two sets of uniaxial tensile tests with different temperatures. The values of each parameter of the Johnson-Cook constitutive model were verified by tensile simulation using ABAQUS, and a medium-low speed Johnson-Cook constitutive model suitable for drawing ultrafine wires of PtW7Ir1 alloy was obtained.
[0029] The specific embodiments of the present invention have been described in detail above with reference to examples. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.
Claims
1. A method for fitting the Johnson-Cook constitutive model for drawing ultrafine PtW7Ir1 alloy wires, characterized in that, include: S1. Decouple the standard form of the Johnson-Cook constitutive model and extract the coefficients of each term independently to obtain the constitutive model parameters to be solved. S2. Under a preset environment, a room temperature quasi-static uniaxial tensile test was conducted on the standard PtW7Ir1 alloy processed specimen to obtain its engineering stress-strain curve and convert it into true stress-strain. S3. Determine the yield strength A and elastic modulus of PtW7Ir1 alloy based on S2; S4. Calculate the actual stress after necking using the Hollom rule and the JIA rule. Obtain the strain hardening modulus B and the hardening index n from the actual stress before and after necking. S5. Obtain the yield stress data of the material based on tensile tests and calculate the strain rate hardening coefficient using the least squares method. and heat softening index ; The constitutive model parameters, including yield strength A, strain hardening modulus B, hardening exponent n, strain rate strengthening coefficient C, and thermal softening exponent m, were obtained by fitting using the least squares method, thus completing the fitting of the constitutive model.
2. The fitting method of the Johnson-Cook constitutive model for drawing PtW7Ir1 alloy ultrafine wire according to claim 1, characterized in that: In S1, three items are extracted independently, and each item is represented as follows: Considering only the strain hardening term: ; Consider strain hardening and strain rate strengthening terms: ; Considering strain hardening and temperature softening terms: ; in, Equivalent flow stress; Yield strength; It is the strain hardening modulus; Equivalent plastic strain; The hardening index; The strain rate strengthening coefficient; This is the current equivalent plastic strain rate; Reference strain rate; The current temperature; For reference temperature; This refers to the melting point temperature of the material. Normalized temperature; This is the thermal softening index.
3. The fitting method of the Johnson-Cook constitutive model for drawing PtW7Ir1 alloy ultrafine wire according to claim 1, characterized in that: In S2, the preset environmental condition is: reference strain rate. =0.0021s -1 And reference temperature =298K, at which room temperature quasi-static uniaxial tensile test was conducted.
4. The fitting method of the Johnson-Cook constitutive model for drawing PtW7Ir1 alloy ultrafine wire according to claim 1, characterized in that: In S2, the conversion formula includes: In the formula, Represents actual stress; Represents actual response; This is the equivalent plastic strain.
5. The fitting method of the Johnson-Cook constitutive model for drawing PtW7Ir1 alloy ultrafine wire according to claim 1, characterized in that: In S3, the yield strength and elastic modulus are determined as follows: the initial linear segment of the engineering stress-strain curve is read to obtain the slope of the linear fit, which is the elastic modulus E of the material; using the 0.2% offset method, a straight line with a slope of E and an offset of 0.2% is drawn, and the intersection of this straight line and the stress-strain curve is the yield strength A.
6. The fitting method of the Johnson-Cook constitutive model for drawing PtW7Ir1 alloy ultrafine wire according to claim 1, characterized in that: In S4, the actual stress after necking is calculated using the Hollom-Münden rule and the JIA rule, and the expression is as follows: In the formula, These are weighting coefficients; For neck stress; For equivalent change; For neck strain; This represents the actual stress after necking, where the weighting coefficients are optimized according to the following formula: In the formula, This indicates the number of data points within a uniformly deformed segment. Indicates the index of the data point; Indicates the first The actual stress after correction for each data point; Indicates the first The test stress at each data point.
7. The fitting method of the Johnson-Cook constitutive model for drawing PtW7Ir1 alloy ultrafine wire according to claim 1, characterized in that: In S4, the expressions for the strain hardening modulus B and the hardening exponent n are obtained as follows: In the formula, Indicates pre-necking stress With necking stress splicing the fitted values; Indicates pre-neck constriction strain The strain values are fitted together with the extrapolated strain values, where the extrapolated strain values are the equivalent strain. , , For equivalent change; It indicates a genuine response.
8. The fitting method of the Johnson-Cook constitutive model for drawing PtW7Ir1 alloy ultrafine wire according to claim 1, characterized in that: In S5, the methods for obtaining the yield stress data of the material based on tensile tests include: With the reference temperature kept constant at 298K, four sets of uniaxial tensile tests were conducted at different strain rates, yielding a strain rate of 0.0021 s⁻¹. -1 0.021s -1 0.21s -1 2.1s -1 The yield stress is set below the specified value to conform to the low strain rate environment of PtW7Ir1 alloy. The strain rate is kept constant at 0.0021 s. -1 Two sets of uniaxial tensile tests were conducted at different reference temperatures to obtain the yield stress at temperatures of 773K and 1073K.
9. The fitting method of the Johnson-Cook constitutive model for drawing PtW7Ir1 alloy ultrafine wire according to claim 8, characterized in that: In step S5, the yield stress at different strain rates is fitted using the least squares method to obtain the strain rate hardening coefficient C, which is calculated as follows: In the formula, This represents the yield stress at the current strain rate; This represents the yield stress at the reference strain rate; This is the current equivalent plastic strain rate; Reference strain rate; The yield stress at different temperatures is fitted using the least squares method to obtain the thermal softening index m, which is calculated as follows: In the formula, The current temperature; For reference temperature; This is the melting point temperature of the material.