Method for calculating stress-strain curve by electroplastic tensile test considering skin effect

Abstract

The invention relates to a method for calculating a stress-strain curve by an electroplastic tensile test considering a skin effect, which comprises the following steps: S1, carrying out current density simulation on a tensile sample under the action of introduced pulse current, and determining the current density distribution of the cross section of the tensile sample under the influence of the skin effect; s2, calculating the current density of the surface of the cross section of the tensile sample and the current density of each corresponding position; and S3, improving a previous method for obtaining stress-strain through an electroplastic tensile test according to the results of S1 and S2, and obtaining a scheme for calculating an electroplastic stress-strain curve under the condition of considering the influence of the skin effect. The invention provides a more accurate calculation method for the tensile sample with high-frequency pulse current or large diameter, and the error of the measured test data is smaller.

Description

Technical Field

[0001] The invention belongs to the technical field of material mechanical properties, and in particular relates to a method for calculating a stress-strain curve in an electroplastic tensile test taking into account the skin effect. Background Art

[0002] When a pulse current passes through a metal material, a large number of directional drifting free electrons (electron wind) are generated. The drifting electron group frequently and directionally impacts dislocations, which will generate an electron wind force similar to an external stress on the dislocation segment, promoting the movement of dislocations on their slip planes, thereby improving the plasticity of the metal. Electroplasticity was first discovered by Soviet scholars Troitskii and others who used accelerated electrons to irradiate zinc single crystals. They found that the strain hardening rate of the irradiated zinc samples decreased and the plasticity was significantly improved. Subsequently, Troitskii and others performed point stretching on polycrystalline samples and also found that the tensile force decreased significantly. Hans Conrad conducted a lot of research on the influence of metal flow stress under unidirectional tensile tests under the action of pulse current, laying a theoretical foundation for the theory of electroplastic effect. Xie and others used finite element software to perform finite element simulation under the action of pulse current, and found that pulse current can significantly increase the recrystallization rate of AZ31B magnesium alloy samples and greatly reduce the flow stress of the material.

[0003] When there is alternating current or alternating electromagnetic field in the conductor, the current distribution inside the conductor is uneven, and the current is concentrated in the "skin" part of the conductor, that is, the current is concentrated in the thin layer on the surface of the conductor. The closer to the surface of the conductor, the greater the current density, and the current inside the conductor is actually smaller. As a result, the resistance of the conductor increases, and its power loss also increases. This phenomenon is called the skin effect. Horace Lamb first proposed the concept of skin effect. Limited by the level of science and technology at that time, it was believed that this effect only existed in spherical shell-shaped conductors. Later, Horace Lamb found through a series of studies that the skin effect exists in conductors of any shape. GICostache and others constructed a skin effect model. Then Spanish scholar J.Acero and others proposed an equivalent circular wire skin effect network model. Chen and others used ANSYS finite element simulation software to analyze the skin effect of conductors and gave the final simulation result effect diagram.

[0004] The common electroplastic uniaxial tensile test uses an electronic universal testing machine with the cross-sectional area of ​​the gauge section as the default variable, and does not take into account the uneven current density distribution on the tensile specimen. The experimental data measured by this method have certain differences, especially for large-sized tensile specimens or high-frequency pulse currents, where the current distribution can differ by an order of magnitude due to the skin effect.

[0005] Therefore, a method for calculating the stress-strain curve of the electroplastic uniaxial tensile test considering the skin effect is proposed. Summary of the invention

[0006] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for calculating the stress-strain curve of an electroplastic tensile test taking into account the skin effect. The method uses simulation results and the theoretical formula of the skin effect, combined with the existing electroplastic metal flow dynamics formula, to perform stress refinement on the tensile specimen in the electroplastic tensile test, reduce the error of the experimental data, significantly eliminate the influence of the skin effect, and measure the stress value under a specific current density.

[0007] The present invention solves the technical problem by the following technical solutions:

[0008] A method for calculating a stress-strain curve in an electroplastic tensile test taking into account the skin effect, the method comprising the following steps:

[0009] S1. Use simulation software to simulate the current density of the tensile specimen under the action of pulse current, and determine the current density distribution of the cross section of the tensile specimen under the influence of skin effect according to the simulation results;

[0010] S2. Using the skin effect attenuation law expression, calculate the current density on the cross-sectional surface of the tensile specimen and at each corresponding position;

[0011] S3, the current density distribution obtained by S1 simulation, and the current density on the surface of the tensile specimen and its corresponding parts obtained by S2, are used to improve the previous method of obtaining stress-strain from electroplastic tensile tests using the electroplastic flow stress model, and a solution for calculating the electroplastic stress-strain curve considering the influence of the skin effect is obtained.

[0012] Moreover, the S1 is specifically:

[0013] S11. Click the Maxwell2D screen to create a model, establish a proportional model according to the specific size of the tensile specimen, and create a solution domain in the draw module. Generally, the solution domain range is 100-500 times the size of the model.

[0014] S12. Set the boundary conditions of the model, select the created solution domain and set it as the ballon condition;

[0015] S13. According to the specific material of the tensile specimen, add the relative magnetic permeability, bulk conductivity, Young's modulus, and Poisson's ratio properties of the material in Maxwell;

[0016] S14, setting excitation, applying current magnitude and current frequency conditions to the model according to specific test conditions;

[0017] S15. Draw the skin mesh, select the outer surface of the entire model, and calculate the skin depth according to the material properties of the tensile specimen. The expression for calculating the skin depth is as follows:

[0018]

[0019] Where: ω is the angular frequency, ω=2Πf, f is the magnetic field frequency, μ is the magnetic permeability, P is the resistivity, and σ is the conductivity;

[0020] S16, add analysis command frequency consistent with S14 frequency, select current field analysis as analysis type, and obtain the current density distribution of the cross section of the tensile specimen under the action of pulse current;

[0021] S17. The simulation result is the current density distribution on the cross section of the tensile specimen. The current density distribution is in the form of rings with different radii centered on the center of the tensile specimen, and the number of rings is n.

[0022] Moreover, the S2 is specifically:

[0023] S21. According to the current decay law expression under the influence of skin effect, calculate the current density of the specific part of the cross section of the tensile specimen. The specific expression is as follows:

[0024] J X =J0e -αx

[0025] Where: x is the depth from the surface, J X is the current density at the depth x of the tensile specimen, J0 is the current density on the surface of the tensile specimen, and α is the attenuation coefficient;

[0026] α is the attenuation coefficient and is related to the pulse current frequency, the magnetic permeability and electrical conductivity of the tensile specimen. The specific expression is as follows:

[0027]

[0028] Where: f is the frequency of the pulse current, μ is the magnetic permeability of the tensile specimen, σ is the electrical conductivity of the tensile specimen;

[0029] S22. According to the total current of the pulse current and the current decay law expression under the influence of the skin effect in S21, the current density on the surface of the tensile specimen is calculated. The specific expression is as follows:

[0030]

[0031] Where: R is the radius of the tensile specimen, J X is the current decay law expression in S21, and I is the total current passed through the tensile specimen.

[0032] Moreover, the S3 is specifically:

[0033] S31. The conversion expression of the engineering stress-strain curve obtained from the previous uniaxial tensile test is as follows:

[0034]

[0035] Where: ∈ is the strain of the tensile specimen, σ is the engineering stress of the tensile specimen, F is the load, S is the cross-sectional area of ​​the gauge section, ΔL is the elongation of the gauge section, and L0 is the length of the gauge section of the specimen;

[0036] According to the simulation results of S1 on the current density distribution of the tensile specimen cross section, the expression of engineering stress is improved and its expression is as follows:

[0037]

[0038] Where: 1-n is the flow stress under different current density, S 1-n is the area of ​​the cross section of the tensile specimen occupied by the same current density;

[0039] S32, according to the electroplastic flow stress model, calculate σ 1-n The specific expressions of flow stress under different current densities are as follows:

[0040]

[0041] Where: e is the external stress value when electroplasticity occurs, m is the sensitivity coefficient of flow stress to strain rate, C is a constant, is the strain rate, ξ is the electroplastic constant, J is the current density, σ * is the effective stress;

[0042] For a specific tensile specimen, the current density J is taken as the independent variable, σ e As the dependent variable, this expression is used to calculate the metal flow stress value for different current densities when electroplasticity occurs;

[0043] S33. According to the flow stress values ​​of different current densities obtained in S32, the obtained data are substituted into S31 to obtain the stress value of the tensile specimen.

[0044] The positive effects that the present invention can produce are:

[0045] 1. The present invention provides a calculation method for studying the mechanical properties of alloy materials under the influence of electroplasticity. Through simulation results and theoretical numerical calculations, the current density distribution of the alloy to be measured is calculated, and the flow stress in the areas affected by different current densities is calculated in detail. Compared with the existing calculation method of stress-strain curve, this calculation method has a smaller error in the measured test data. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a current density distribution diagram of the tensile specimen of the present invention;

[0047] Figure 2 This is a schematic diagram of the current density at various locations on the cross section of the tensile specimen of the present invention. DETAILED DESCRIPTION

[0048] The present invention is further described in detail below through specific examples. The following examples are only illustrative and not restrictive, and the protection scope of the present invention cannot be limited thereto.

[0049] The present invention provides a method for calculating a stress-strain curve in an electroplastic tensile test taking into account the skin effect. The current density distribution of the tensile specimen under the action of a pulse current is simulated. Figure 1 Then, according to the theoretical formula of skin effect, the current density of each part on the surface and cross section of the tensile specimen is calculated, and the flow stress under the corresponding current density is calculated using the existing metal flow stress model, which specifically includes the following steps:

[0050] S1. Use simulation software to simulate the current density of the tensile specimen under the action of pulse current, and determine the current density distribution of the cross section of the tensile specimen under the influence of skin effect based on the simulation results.

[0051] Specifically, the MAXWELL simulation software is used to simulate the current density according to the material properties of the tensile specimen and the pulse current frequency during the test, specifically:

[0052] S11. Click the Maxwell2D screen to create a model, establish a proportional model according to the specific size of the tensile specimen, and create a solution domain in the draw module. Generally, the solution domain range is 100-500 times the size of the model.

[0053] S12. Set the boundary conditions of the model, select the created solution domain and set it as the ballon condition;

[0054] S13. According to the specific material of the tensile specimen, add the relative magnetic permeability, bulk conductivity, Young's modulus, and Poisson's ratio properties of the material in Maxwell;

[0055] S14, setting excitation, applying current magnitude and current frequency conditions to the model according to specific test conditions;

[0056] S15. Draw the skin mesh, select the outer surface of the entire model, and calculate the skin depth according to the material properties of the tensile specimen. The expression for calculating the skin depth is as follows:

[0057]

[0058] Where: ω is the angular frequency, ω=2Πf, f is the magnetic field frequency, μ is the magnetic permeability, P is the resistivity, and σ is the conductivity;

[0059] S16, add analysis command frequency consistent with S14 frequency, select current field analysis as analysis type, and obtain the current density distribution of the cross section of the tensile specimen under the action of pulse current;

[0060] S17. The simulation result is the current density distribution on the cross section of the tensile specimen. The current density distribution is in the form of rings with different radii centered on the center of the tensile specimen, and the number of rings is n.

[0061] S2. Using the attenuation law expression of the skin effect and the current density distribution diagram obtained in S1, calculate the current density of the tensile specimen surface and each part of the cross section

[0062] Specifically, firstly, according to the total pulse current, the simulation results of S1, that is, the area occupied by each current density on the cross section of the tensile specimen, and the attenuation law expression of the skin effect are used to calculate the current density on the cross section surface and various parts of the tensile specimen, which is specifically:

[0063] S21, according to the current decay law expression under the influence of the skin effect, calculate the current density of the specific part of the cross section of the tensile specimen, and substitute the calculated value into step S33, the specific expression is as follows:

[0064] J X =J0e -αx

[0065] Where x is the depth from the surface, J X is the current density at the depth x of the tensile specimen, J0 is the current density on the surface of the tensile specimen, and α is the attenuation coefficient;

[0066] S211, α is the attenuation coefficient and is related to the pulse current frequency, the magnetic permeability and electrical conductivity of the tensile specimen. The specific expression is as follows:

[0067]

[0068] Where f is the frequency of the pulse current, μ is the magnetic permeability of the tensile specimen, and σ is the electrical conductivity of the tensile specimen;

[0069] S22. According to the total current of the pulse current and the current decay law expression under the influence of the skin effect in step S21, the current density on the surface of the tensile specimen is calculated. The specific expression is as follows:

[0070]

[0071] Where R is the radius of the tensile specimen, J X is the current decay law expression in step S21, I is the total current passed into the tensile specimen;

[0072] Because J X The expression is a function related to the surface current density J0 of the tensile specimen. The surface current density of the tensile specimen can be calculated based on the expression. Substituting the calculated data into step S33, the flow stress of different current densities can be obtained.

[0073] S3. Based on the data obtained in S1 and S2, the existing metal flow stress model is used to obtain the flow stress at each current density, and then the previous method of obtaining stress-strain in electroplastic tensile test is improved to obtain a method for calculating electroplastic stress-strain curve under the influence of skin effect. The specific process includes:

[0074] S31. The conversion expression of the engineering stress-strain curve obtained from the previous uniaxial tensile test is as follows:

[0075]

[0076] Where, ∈ is the strain of the tensile specimen, σ is the engineering stress of the tensile specimen, F is the load, S is the cross-sectional area of ​​the gauge section, ΔL is the elongation of the gauge section, and L0 is the length of the gauge section of the specimen;

[0077] S32. On the basis of step S31, according to the simulation result of the current density distribution on the cross section of the tensile specimen in S1, the expression of engineering stress is improved, and the expression is as follows:

[0078]

[0079] In the formula, σ 1-n is the flow stress under different current density, S 1-n is the area of ​​the cross section of the tensile specimen occupied by the same current density;

[0080] S321、S 1-nThe specific value of n is obtained by simulating the current density of the tensile specimen under the action of pulse current according to S1;

[0081] S33, according to the electroplastic flow stress model, calculate σ 1-n The specific expressions of flow stress under different current densities are as follows:

[0082]

[0083] Where σ e is the external stress value when electroplasticity occurs, m is the sensitivity coefficient of flow stress to strain rate, C is a constant, is the strain rate, ξ is the electroplastic constant, J is the current density, σ * is the effective stress;

[0084] For a specific tensile specimen, the current density J is taken as the independent variable, σ e As the dependent variable, this expression can be used to calculate the metal flow stress value for different current densities when electroplasticity occurs;

[0085] S34. On the basis of S32, according to the flow stress values ​​of different current densities obtained in S33, the obtained data are brought into S32.

[0086] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will appreciate that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for calculating stress-strain curve in an electroplastic tensile test taking into account skin effect, characterized in that: The steps of the method are: S1. Use simulation software to simulate the current density of the tensile specimen under the action of pulse current, and determine the current density distribution of the cross section of the tensile specimen under the influence of skin effect according to the simulation results; S2. Using the skin effect attenuation law expression, calculate the current density on the cross-sectional surface of the tensile specimen and at each corresponding position; S3, the current density distribution obtained by S1 simulation, and the current density on the surface of the tensile specimen and its corresponding parts obtained by S2, are used to improve the previous method of obtaining stress-strain from electroplastic tensile tests using the electroplastic flow stress model, and a solution for calculating the electroplastic stress-strain curve considering the influence of the skin effect is obtained.

2. The method for calculating stress-strain curve by electroplastic tensile test considering skin effect according to claim 1, characterized in that: The S1 is specifically: S11. Click the Maxwell2D screen to create a model, establish a proportional model according to the specific size of the tensile specimen, and create a solution domain in the draw module. Generally, the solution domain range is 100-500 times the size of the model. S12. Set the boundary conditions of the model, select the created solution domain and set it as the ballon condition; S13. According to the specific material of the tensile specimen, add the relative magnetic permeability, bulk conductivity, Young's modulus, and Poisson's ratio properties of the material in Maxwell; S14, setting excitation, applying current magnitude and current frequency conditions to the model according to specific test conditions; S15. Draw the skin mesh, select the outer surface of the entire model, and calculate the skin depth according to the material properties of the tensile specimen. The expression for calculating the skin depth is as follows: Where: ω is the angular frequency, ω=2Πf, f is the magnetic field frequency, μ is the magnetic permeability, P is the resistivity, and σ is the conductivity; S16, add analysis command frequency consistent with S14 frequency, select current field analysis as analysis type, and obtain the current density distribution of the cross section of the tensile specimen under the action of pulse current; S17. The simulation result is the current density distribution on the cross section of the tensile specimen. The current density distribution is in the form of rings with different radii centered on the center of the tensile specimen, and the number of rings is n.

3. The method for calculating stress-strain curve by electroplastic tensile test considering skin effect according to claim 1, characterized in that: The S2 is specifically: S21. According to the current decay law expression under the influence of skin effect, calculate the current density of the specific part of the cross section of the tensile specimen. The specific expression is as follows: J X =J0e -αx Where: x is the depth from the surface, J X is the current density at the depth x of the tensile specimen, J0 is the current density on the surface of the tensile specimen, and α is the attenuation coefficient; α is the attenuation coefficient and is related to the pulse current frequency, the magnetic permeability and electrical conductivity of the tensile specimen. The specific expression is as follows: Where: f is the frequency of the pulse current, μ is the magnetic permeability of the tensile specimen, σ is the electrical conductivity of the tensile specimen; S22. According to the total current of the pulse current and the current decay law expression under the influence of the skin effect in S21, the current density on the surface of the tensile specimen is calculated. The specific expression is as follows: Where: R is the radius of the tensile specimen, J X is the current decay law expression in S21, and I is the total current passed through the tensile specimen.

4. The method for calculating stress-strain curve by electroplastic tensile test considering skin effect according to claim 1, characterized in that: The S3 is specifically: S31. The conversion expression of the engineering stress-strain curve obtained from the previous uniaxial tensile test is as follows: Where: ∈ is the strain of the tensile specimen, σ is the engineering stress of the tensile specimen, F is the load, S is the cross-sectional area of ​​the gauge section, ΔL is the elongation of the gauge section, and L0 is the length of the gauge section of the specimen; According to the simulation results of S1 on the current density distribution of the tensile specimen cross section, the expression of engineering stress is improved and its expression is as follows: Where: 1-n is the flow stress under different current density, S 1-n is the area of ​​the cross section of the tensile specimen occupied by the same current density; S32, according to the electroplastic flow stress model, calculate σ 1-n The specific expressions of flow stress under different current densities are as follows: Where: e is the external stress value when electroplasticity occurs, m is the sensitivity coefficient of flow stress to strain rate, C is a constant, ε is the strain rate, ξ is the electroplastic constant, J is the current density, σ * is the effective stress; For a specific tensile specimen, the current density J is taken as the independent variable, σ e As the dependent variable, this expression is used to calculate the metal flow stress value for different current densities when electroplasticity occurs; S33. According to the flow stress values ​​of different current densities obtained in S32, the obtained data are substituted into S31 to obtain the stress value of the tensile specimen.

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