Method for establishing constitutive model of electroplastic uniaxial tensile test and its test device

Abstract

The present invention provides a method for establishing an electroplastic uniaxial tensile test constitutive model, and the specific steps include: S1, preparing a tensile specimen, and insulating a fixture and the tensile specimen; S2, respectively making three groups of test devices for room temperature uniaxial tensile, high temperature uniaxial tensile and electroplastic tensile, and clamping the test devices on a universal tensile testing machine, and performing three groups of tensile tests respectively; S3, analyzing the tensile strength and elongation after fracture of the tensile specimen under different states through the test data obtained in S2; S4, combining the uniaxial tensile test data of the three states to establish the constitutive equation of electroplasticity: establishing a Johnson-Cook model for room temperature uniaxial tensile, establishing a high temperature constitutive equation using the Arrhenius model, and obtaining the constitutive equation of electroplasticity by multiple fitting of the electroplastic tensile test data. The present invention is a tensile test method for establishing an electroplastic tensile test and an electroplastic constitutive model for various alloys, and the error of the measured test data is smaller.

Description

Technical Field

[0001] The present invention relates to the field of mechanical properties of materials, and in particular to a method for establishing a constitutive model of an electroplastic uniaxial tensile test and a test device thereof. Background Art

[0002] Traditional uniaxial tensile testing is a common method for testing the mechanical properties of materials. This test reveals the stress-strain relationship under static load, as well as the characteristics and basic laws of three common failure modes, allowing the assessment of the material's basic mechanical properties. However, for some alloys, such as titanium and magnesium alloys, low plasticity at low temperatures leads to poor forming performance and a high risk of cracking and rebound. The mechanical properties derived from traditional uniaxial tensile testing are only applicable to the processing and performance of these alloys at low temperatures.

[0003] The electroplastic effect refers to the phenomenon in which a pulse current or electric field stimulates a metal material undergoing plastic deformation, thereby reducing its deformation resistance and improving its plasticity. The electroplastic effect is divided into a pure electroplastic effect and an additional electroplastic effect. The difference between the two is that the additional electroplastic effect is the Joule heating effect generated by the self-resistance of heat generated by the metal under the action of a pulse current. The new process technology of passing a pulse current through metal materials is called current-assisted processing technology. At this stage, this processing technology only applies the Joule heating generated by the pulse current to the metal material, while the influence of the pulse current itself on the internal electrons of the metal material is often overlooked, which is somewhat one-sided.

[0004] In common electroplastic uniaxial tensile tests, the material temperature is controlled by blowing cold air and setting up a liquid nitrogen environment. As the temperature outside the specimen changes faster than inside, the experimental data obtained using this method has certain errors. Therefore, a method for electroplastic uniaxial tensile testing and the establishment of its constitutive model are proposed. Using a quantitative analysis method, different control groups are set up after the specimen is energized. The stress-strain relationship of the alloy is measured at different temperatures and under both energized and unenergized conditions. By analyzing and processing the experimental data obtained by this method, the true stress-strain curve of the alloy is plotted. The obtained tensile strength and elongation after fracture of the alloy under different conditions are compared, and the influence of the electroplastic effect on the mechanical properties of the alloy is summarized. Summary of the Invention

[0005] In response to the problems existing in the prior art, the present invention provides a method for establishing a constitutive model for an electroplastic uniaxial tensile test and a test device thereof. First, an alloy to be tested is made into a special tensile specimen based on a micro-tensile test standard and applicable under energized conditions, and the tensile specimen is clamped on a universal tensile machine using a homemade non-conductive clamp. Subsequently, three groups of tests are set up: room temperature uniaxial tensile, high temperature uniaxial tensile, and electroplastic uniaxial tensile. The data obtained from the three groups of tests are converted into true stress-strain curves. The three groups of data are compared and analyzed to obtain the primary and secondary relationship between the pulse current size and the duty cycle in the electroplastic effect. Finally, based on the Johnson-Cook model and the Arrhenius model, and through multiple fitting of the electroplastic tensile test data, the constitutive equation of electroplasticity is obtained, thereby providing a theoretical basis for subsequent simulation of electroplastic forming processes.

[0006] The present invention provides a method for establishing a constitutive model for an electroplastic uniaxial tensile test, which specifically comprises the following steps:

[0007] S1. Prepare the tensile specimen and insulate the fixture and tensile specimen;

[0008] S2. Prepare three sets of test devices for room temperature uniaxial stretching, high temperature uniaxial stretching, and electroplastic stretching, respectively. Clamp the test devices on a universal tensile testing machine and perform three sets of tensile tests on each device.

[0009] S3. Analyze the tensile strength and elongation of the tensile specimen under different conditions based on the test data obtained in step S2;

[0010] S4. Combine the experimental data of the three states and establish the constitutive equations under different states:

[0011] S41. Establish the constitutive equation of the tensile specimen in the uniaxial tensile test at room temperature, and add the influence function of the electroplastic effect to obtain the product function of the initial constitutive equation;

[0012] S42. Establish a constitutive model at room temperature based on the Johnson-Cook model:

[0013] S421. Ignore the strain rate in the product function of the initial constitutive equation and obtain the following expression:

[0014]

[0015] Where, is the flow stress corresponding to the reference strain rate, is the reference strain rate, T is the dimensionless temperature term, and g(T) is the thermal softening function;

[0016] S422. Based on the true stress-strain curve of the tensile specimen at room temperature, the Hollomon model is applied to describe the flow stress change of the tensile specimen at room temperature using the hardening index, and the following expression is obtained:

[0017] σ1=A·ε n

[0018] Where ε is the true plastic strain, A is the strength coefficient at room temperature, and n is the strain hardening exponent at room temperature;

[0019] S423. Based on step S421 and step S422, The constitutive equation at room temperature is:

[0020] σ=A·ε n *g(T)

[0021] Where ε is the true plastic strain, A is the strength coefficient at room temperature, n is the strain hardening exponent at room temperature, T is the dimensionless temperature term, and g(T) is the thermal softening function;

[0022] S43. Use the Arrhenius model to establish the high-temperature constitutive equation:

[0023] S431. Based on the Z value characterizing the strain rate and temperature of the high-temperature tensile specimen, the expression of the hyperbolic sine Arrhenius equation modified by the phenomenological constitutive equation is obtained as follows:

[0024]

[0025]

[0026] Where, is the strain rate, B is the material constant, σ2 is the true stress at high temperature, F(σ2) is the stress function, Q is the strain activation energy, R is the gas molar constant 8.314 J / (mol·K), and T is the temperature;

[0027] S432. According to the different expressions of F(σ2) at low stress and high stress levels, under the condition of constant strain rate, the equation about lnσ2-σ2 is obtained;

[0028] S433. Based on step S431 and step S432, according to the expression of the correction value of the strain activation energy Q in the phenomenological thermal deformation constitutive model, the expression of the high-temperature constitutive equation of the tensile specimen is obtained as follows:

[0029]

[0030] Where σ is the flow stress, A is the strength coefficient at room temperature, ε is the true plastic strain, and n is the strain hardening exponent at room temperature. is the strain rate, b1 is the material parameter, d is the material parameter, and T is the temperature;

[0031] S44. Establish the electroplastic constitutive equation:

[0032] S441. Based on the law between effective stress and current in the electroplastic effect, the influence function of the electroplastic effect is obtained. The specific expression is as follows:

[0033]

[0034] Where h is the influence function of the electroplastic effect, j is the current density, and j0 is the material parameter, which is related to temperature;

[0035] S442. Combining the room temperature constitutive equation and the high temperature constitutive equation when no power is applied, the experimental data of electroplastic uniaxial tension are fitted to obtain the constitutive equation when power is applied. That is, the expression of the electroplastic constitutive equation is:

[0036]

[0037] Where σ is the flow stress, A is the strength coefficient at room temperature, ε is the true plastic strain, and n is the strain hardening exponent at room temperature. is the strain rate, b1 is the material parameter, d is the material parameter, T is the temperature, j is the current density, j0 2 (T) is a polynomial function of current density with respect to temperature.

[0038] Preferably, the specific process of step S3 includes:

[0039] S31, converting the test data in the load-displacement curve and the engineering stress-strain curve obtained from the uniaxial tensile test into a true stress-strain curve;

[0040] S32, passing pulse currents of different electrical parameters through the tensile specimen, and measuring different temperature values ​​of the tensile specimen at room temperature using a thermocouple; heating the tensile specimen to a preset temperature, and then keeping the temperature constant to obtain different temperature values ​​of the tensile specimen at high temperature; passing pulse currents of different electrical parameters through the tensile specimen, and measuring different temperature values ​​of the tensile specimen under electroplasticity using a thermocouple;

[0041] S33. By analyzing the comparison graphs of the true stress-strain curves of the tensile specimens under the same pulse current and different duty cycles and the high-temperature true stress-strain curves of the corresponding temperatures, comparison graphs of the tensile strength reduction rate and the elongation after fracture of the tensile specimens under room temperature, high temperature, and electroplasticity are obtained respectively;

[0042] S34. By analyzing the comparison diagram of the true stress-strain curve of the tensile specimen under the same duty cycle and different pulse currents and the high-temperature true stress-strain curve of the corresponding temperature, the tensile strength reduction rate of the tensile specimen under electroplasticity is obtained;

[0043] S35. Compare the tensile strength reduction rates obtained in room temperature, high temperature and electroplastic tensile tests to obtain the primary and secondary relationships between pulse current and duty cycle in electroplasticity.

[0044] Preferably, in step S31, the conversion expression for converting the test data in the load-displacement curve and the engineering stress-strain curve obtained from the uniaxial tensile test into the true stress-strain curve is as follows:

[0045]

[0046]

[0047] Where ε is the true strain of the tensile specimen, σ is the true stress of the tensile specimen, e is the engineering strain of the tensile specimen, s is the engineering stress of the tensile specimen, l0 is the length of the specimen gauge section, Δl is the elongation of the gauge section, P is the load, and A is the cross-sectional area of ​​the gauge section.

[0048] Preferably, in step S41, the expression of the initial constitutive equation multiplicative function is as follows:

[0049] σ=f(ε p )·g(T)·h(j)

[0050] Where σ is the flow stress, ε p is the true plastic strain, j is the pulse current density, f(ε p ) is the constitutive model at room temperature, g(T) is the thermal softening function, and h(j) is the electroplastic effect function.

[0051] Preferably, in step S432, the specific expression of the lnσ2-σ2 equation is as follows:

[0052]

[0053] Where B1, B2, b and c1 are material constants, and σ2 is the true stress at high temperature.

[0054] Another aspect of the present invention provides a test device for establishing the aforementioned electroplastic uniaxial tensile test constitutive model, which includes a silicon nitride rod, a fixture and bakelite. The tensile specimen is a long U-shaped structure with a rectangular cross-section. The fixed end of the tensile specimen is connected to the first end of the bakelite, the second end of the bakelite is connected to the first end of the silicon nitride rod, and the second end of the silicon nitride rod is fixedly connected to the fixture. The silicon nitride rod, the fixture and the bakelite are symmetrically distributed on both sides of the fixed end of the tensile specimen.

[0055] Compared with the prior art, the present invention has the following advantages:

[0056] 1. This paper proposes a tensile testing method to study the electroplasticity of alloys. By comparing room temperature tensile tests, high temperature tensile tests, and electroplastic tensile tests, the effects of electrical parameters such as pulse current and duty cycle on electroplastic mechanical properties are determined. Compared with existing methods for controlling temperature through environmental changes, such as blowing cold air or setting up a liquid nitrogen environment, this testing method produces smaller errors in the measured test data.

[0057] 2. The present invention establishes an electroplastic constitutive model based on the Johnson-Cook model and the Arrhenius model, and establishes a multiplicative function form, that is, an electroplastic constitutive equation of the multiplication of influencing factor functions, which includes temperature and electrical parameters, providing a theoretical basis for the simulation of electroplastic forming process. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A schematic diagram of a tensile specimen in a test apparatus for establishing a constitutive model for an electroplastic uniaxial tensile test according to the present invention;

[0059] Figure 2 A schematic diagram of a test apparatus for establishing a constitutive model for an electroplastic uniaxial tensile test according to the present invention;

[0060] Figure 3a The real stress-strain curves of TC4 titanium alloy under different duty cycles in the method of establishing the constitutive model of electroplastic uniaxial tensile test of the present invention;

[0061] Figure 3b The high-temperature stress-strain curves of TC4 titanium alloy under different duty cycles in the method for establishing the constitutive model of the electroplastic uniaxial tensile test of the present invention;

[0062] Figure 4a A comparison chart of the tensile strength of TC4 titanium alloy under high-temperature tensile test and electroplastic tensile test in the method of establishing the constitutive model of electroplastic uniaxial tensile test of the present invention;

[0063] Figure 4bComparison chart of elongation after fracture of TC4 titanium alloy under high temperature tensile test and electroplastic tensile test respectively in the method of establishing the constitutive model of electroplastic uniaxial tensile test of the present invention;

[0064] Figure 5 The true stress-strain curves of TC4 titanium alloy at different pulse currents with a duty cycle of 20% in the method for establishing the constitutive model of the electroplastic uniaxial tensile test of the present invention;

[0065] Figure 6a-6d A comparison diagram of the true stress-strain of TC4 titanium alloy under high-temperature tensile test and electroplastic tensile test at different temperatures in the method for establishing the constitutive model of electroplastic uniaxial tensile test of the present invention;

[0066] Figure 7 The present invention is a flow chart of the method for establishing a constitutive model for an electroplastic uniaxial tensile test.

[0067] Main reference numerals:

[0068] Silicon nitride rod 1, fixture 2, bakelite 3, tensile specimen 4. DETAILED DESCRIPTION

[0069] To fully describe the technical content, structural features, objectives and effects of the present invention, the following is a detailed description with reference to the accompanying drawings.

[0070] The method for establishing the constitutive model of the electroplastic uniaxial tensile test of the present invention is to draw the true stress-strain curve of the tensile specimen 4 at room temperature, high temperature and electroplastic test under a certain tensile rate, and compare the tensile strength and elongation of the tensile specimen 4 under different states, and summarize the influence of the electroplastic effect on the mechanical properties of the tensile specimen 4, such as Figure 7 As shown, the specific steps include:

[0071] S1. Prepare a tensile specimen 4 and perform insulation treatment on the fixture 2 and the tensile specimen 4.

[0072] Specifically, the clamp 2 is not charged in the working state, and the current flows directly from the first end to the second end of the tensile specimen 4.

[0073] S2. Prepare three sets of test devices for room temperature uniaxial stretching, high temperature uniaxial stretching, and electroplastic stretching, respectively. Clamp the test devices on a universal tensile testing machine, and perform three sets of tensile tests respectively.

[0074] Specifically, the tensile specimen 4 was first clamped on a universal tensile testing machine, and an appropriate strain rate was selected. Then, an SMD-100 CNC bidirectional pulse electroplating power supply was selected to generate a pulse current. A thermocouple was used to measure the temperature and connected to a temperature control box to monitor the temperature change in real time. The thermocouple was made into a patch and fixed to the surface of the gauge section with Teflon tape. Finally, the temperature value change was displayed on the display, and three sets of unidirectional tensile tests were performed.

[0075] At the same time, before the test begins, the pulse current and duty cycle must be selected. Through simulation to guide the specific test, the relationship between the pulse current and the heat generation (temperature) of the test sample is obtained. This temperature is an important control variable for comparison with the high-temperature uniaxial tensile test.

[0076] S3. Analyze and compare the tensile strength and elongation of the tensile specimen 4 under different conditions using the test data obtained in step S2 to determine the influence of the electroplastic effect on the mechanical properties of the tensile specimen 4.

[0077] S4. Combining the experimental data of the three states, the constitutive equations under different states are established through data fitting.

[0078] Specifically, the multiplicative function of the initial constitutive equation is first established, and then based on the Johnson-Cook model and the Arrhenius model, the high-temperature constitutive equation is established by combining the Hollomon model and the phenomenological thermal deformation constitutive model parameters to determine and correct the Q value. Finally, according to the law between the effective stress and current of the electroplastic effect given by Molotskii M, the electroplastic constitutive equation is obtained, and the true stress-true plastic strain curve obtained from the experiment is fitted.

[0079] Furthermore, the specific process of analyzing the tensile strength and elongation after fracture of the tensile specimen 4 under different states in step S3 includes:

[0080] S31. Convert the test data from the load-displacement curve and engineering stress-strain curve obtained from the uniaxial tensile test into a true stress-strain curve. The conversion expression is as follows:

[0081]

[0082]

[0083] Where ε is the true strain of tensile specimen 4, σ is the true stress of tensile specimen 4, e is the engineering strain of tensile specimen 4, s is the engineering stress of tensile specimen 4, l0 is the length of the specimen gauge section, Δl is the elongation of the gauge section, P is the load, and A is the cross-sectional area of ​​the gauge section.

[0084] S32. Pass pulse currents of different electrical parameters through tensile specimen 4 and measure different temperatures of tensile specimen 4 at room temperature using a thermocouple. After heating tensile specimen 4 to a preset temperature, keep the temperature constant to obtain different temperatures of tensile specimen 4 at elevated temperatures. Pass pulse currents of different electrical parameters through tensile specimen 4 and measure different temperatures of tensile specimen 4 under electroplasticity using a thermocouple. Maintain consistency throughout the entire stretching process. The heating furnace heating time is primarily based on the test conditions for tensile specimen 4.

[0085] S33. By analyzing the comparison graphs of the true stress-strain curves of the tensile specimen 4 under the same pulse current and different duty cycles and the high-temperature true stress-strain curves at the corresponding temperatures, comparison graphs of the tensile strength reduction rate and the elongation after fracture of the tensile specimen 4 under room temperature, high temperature and electroplasticity are obtained respectively.

[0086] S34. By analyzing the comparison diagram of the true stress-strain curve of the tensile specimen 4 under the same duty cycle and different pulse currents and the high-temperature true stress-strain curve of the corresponding temperature, the tensile strength reduction rate of the tensile specimen 4 under electroplasticity is obtained.

[0087] S35. Compare the tensile strength reduction rates obtained in room temperature, high temperature and electroplastic tensile tests to obtain the primary and secondary relationships between pulse current and duty cycle in electroplasticity.

[0088] Furthermore, the specific method of establishing the constitutive equations under different states in step S4 is as follows:

[0089] S41. Establish the constitutive equation of tensile specimen 4 in the uniaxial tensile test at room temperature, and add the influence function of the electroplastic effect to obtain the product function of the initial constitutive equation. The specific expression is as follows:

[0090] σ=f(ε p )·g(T)·h(j)

[0091] Where σ is the flow stress, ε p is the true plastic strain, j is the pulse current density, f(ε p ) is the constitutive model at room temperature, g(T) is the thermal softening function, and h(j) is the electroplastic effect function.

[0092] Preferably, the multiplicative function of the initial constitutive equation includes a work hardening model and a thermal softening model.

[0093] S42. Since the Johnson-Cook model can well predict the mathematical form of work hardening of metal materials, a constitutive model at room temperature is established based on the Johnson-Cook model.

[0094] The standard expression of the Johnson-Cook model is as follows:

[0095]

[0096] Where, is the flow stress corresponding to the reference strain rate, c is the material parameter, is the reference strain rate, is the strain rate, and T is the dimensionless temperature term.

[0097] S421. Ignore the strain rate in the product function of the initial constitutive equation, so The following expression is obtained:

[0098]

[0099] Where, is the flow stress corresponding to the reference strain rate, is the reference strain rate, T is the dimensionless temperature term, and g(T) is the thermal softening function.

[0100] S422, flow stress corresponding to reference strain rate According to the true stress-strain curve relationship of tensile specimen 4 at room temperature, the Hollomon model is applied as a full strain extrapolation model, and the hardening index is used to describe the flow stress change of tensile specimen 4 at room temperature. The following expression is obtained:

[0101] σ1=A·ε n

[0102] Where ε is the true plastic strain, A is the strength coefficient at room temperature, and n is the strain hardening exponent at room temperature.

[0103] S423. Based on step S421 and step S422, The constitutive equation at room temperature is:

[0104] σ=A·ε n *g(T)

[0105] Where ε is the true plastic strain, A is the strength coefficient at room temperature, n is the strain hardening exponent at room temperature, T is the dimensionless temperature term, and g(T) is the thermal softening function.

[0106] When the temperature is room temperature, the thermal softening function g(T) of the material is not considered. Therefore, the true stress-plastic strain curve at room temperature is fitted by the formula in S423 to obtain the values ​​of parameters A and n, thereby obtaining the specific expression of the constitutive equation at room temperature.

[0107] S43. Since the Johnson-Cook model lacks consideration of temperature changes, the Arrhenius model is used to establish the high-temperature constitutive equation.

[0108] S431. Based on the Z value characterizing the strain rate and temperature of the high-temperature tensile specimen 4, the expression of the hyperbolic sine Arrhenius equation modified by the phenomenological constitutive equation is obtained as follows:

[0109]

[0110]

[0111] Where, is the strain rate, B is the material constant, σ2 is the true stress at high temperature, F(σ2) is the stress function, Q is the strain activation energy, R is the gas molar constant 8.314 J / (mol·K), and T is the temperature.

[0112] S432. According to the different expressions of F(σ2) at low stress and high stress levels, under the condition of constant strain rate, the equation about lnσ2-σ2 is obtained, the curve of lnσ2-σ2 is drawn, and the slope c is obtained.

[0113] Specifically, the different expressions of F(σ2) at low stress level and high stress level are as follows:

[0114]

[0115] F(σ2)=B2·exp(bσ2

[0116] F(σ2)=B·[sinh(cσ2)] d

[0117] Where B1, c1, B2, b, c, and d are all material constants. The third expression is the expression at the full stress level. Taylor expansion can be performed to obtain the first and second expressions. At the same time, the relationship between c1, b, and c is as follows:

[0118]

[0119] Substituting the different expressions of F(σ2) at low stress level and high stress level into the formula of S431 and taking the logarithm, we get the following expressions:

[0120]

[0121]

[0122]

[0123] For this test, the strain rate is constant. Combining the above equations, we get the following expression:

[0124]

[0125] Where B1, B2, b and c1 are material constants, and σ2 is the true stress at high temperature.

[0126] By testing the peak stress of the alloy at the same strain rate and different temperatures, a lnσ2-σ2 curve was drawn, and the slope c was obtained by fitting the results.

[0127] S433. On the basis of steps S431 and S432, according to the expression of the correction value of the strain activation energy Q in the phenomenological thermal deformation constitutive model, the expression of the high-temperature constitutive equation of the tensile specimen 4 is obtained as follows:

[0128]

[0129] Where σ is the flow stress, A is the strength coefficient at room temperature, ε is the true plastic strain, and n is the strain hardening exponent at room temperature. is the strain rate, b1 is the material parameter, d is the material parameter, and T is the temperature.

[0130] Specifically, the expression of the correction value of the strain activation energy Q in the phenomenological thermal deformation constitutive model is as follows:

[0131] Q=dRb1

[0132] Where b1 is the slope of the ln[sinh(cσ2)]-1000 / T curve, and the value of b1 is obtained by fitting calculation.

[0133] The specific expression of the high-temperature constitutive equation can be obtained by taking the average value of d obtained from the fitting results.

[0134] S44. Establish the electroplastic constitutive equation: The electroplastic constitutive equation is established based on the Johnson-Cook model and the Arrhenius model. It takes into account both the Joule heating effect caused by the self-resistance heating of the metal when it is electrified and the influence of the pulse current. Finally, the electroplastic constitutive equation based on the product function of the initial constitutive equation is obtained.

[0135] S441. Based on the law between effective stress and current in the electroplastic effect, the influence function of the electroplastic effect is obtained. The specific expression is as follows:

[0136]

[0137] Where h is the influence function of the electroplastic effect, j is the current density, and j0 is the material parameter, which is related to temperature.

[0138] Specifically, the expression for the law between effective stress and current in the electroplastic effect is as follows:

[0139]

[0140] Where σ(j) is the effective stress when pulse current is applied, σ is the effective stress when no pulse current is applied, j is the current density, and j0 is a material parameter that is related to temperature.

[0141] S442, due to j0 2 (T) The experimental data of electroplastic uniaxial tension can be fitted by combining the temperatures corresponding to different current densities, the room temperature constitutive equation when no power is applied, and the high temperature constitutive equation to obtain the constitutive equation when power is applied. That is, the expression of the electroplastic constitutive equation is:

[0142]

[0143] Where σ is the flow stress, A is the strength coefficient at room temperature, ε is the true plastic strain, and n is the strain hardening exponent at room temperature. is the strain rate, b1 is the material parameter, d is the material parameter, T is the temperature, j is the current density, j0 2 (T) is a polynomial function of current density with respect to temperature.

[0144] like Figure 1 and Figure 2 As shown, a test device for establishing a constitutive model of an electroplastic uniaxial tensile test includes a silicon nitride rod 1, a fixture 2, and a bakelite 3. Since the tensile specimen 4 needs to be energized, when preparing the tensile specimen 4, the tensile specimen 4 is made into a long U-shaped structure with a thin rectangular cross-section, and the clamping end of the tensile specimen 4 is longitudinally processed into a long U-shape. During the tensile test, power is supplied through the long U-shaped pin; the fixed end of the tensile specimen 4 is connected to the first end of the bakelite 3, the second end of the bakelite 3 is connected to the first end of the silicon nitride rod 1, and the second end of the silicon nitride rod 1 is fixedly connected to the fixture 2. The silicon nitride rod 1, the fixture 2, and the bakelite 3 are symmetrically distributed on both sides of the fixed end of the tensile specimen 4.

[0145] Specifically, the tensile specimen 4 is based on the standard micro-tensile style, and a pin for powering is added to facilitate the electroplastic test; at the same time, in order to prevent power from being passed between the fixture 2 and the tensile specimen 4, the fixture 2 and the tensile specimen 4 are insulated. The fixture 2 uses bakelite 3 and silicon nitride rod 1, which not only has an insulating effect but also meets the bending strength requirements. The material of the fixture 2 is 304 stainless steel, which is resistant to high temperatures and prevents oxidation and rust.

[0146] The following is a further description of a method and test apparatus for establishing a constitutive model for an electroplastic uniaxial tensile test according to the present invention, with reference to an embodiment:

[0147] This specific embodiment takes TC4 titanium alloy material as an example. The TC4 titanium alloy is a plate with a thickness of 1 mm. The mechanical properties of the TC4 titanium alloy are analyzed using this method. The specific implementation process is as follows:

[0148] S1, prepare and process TC4 titanium alloy into Figure 1 The tensile test specimens 4 shown in the figure are processed into 11 pieces in total and marked with numbers 1 to 11. Figure 2 The test was performed using the fixture 2 shown.

[0149] S2. Construct three test apparatuses, one for room temperature uniaxial stretching, one for high temperature uniaxial stretching, and one for electroplastic stretching. For the high temperature uniaxial stretching and electroplasticity parameters, the temperature and electrical parameters were determined as control variables before the test. In this test, the temperatures were set at 80°C, 150°C, 200°C, and 240°C, the electrical currents were set at 6A, 8A, 10A, and 12A, and the duty cycles were set at 15%, 20%, and 30%. The tensile specimen 4 was clamped on a universal tensile testing machine, the strain rate was selected to be 0.01s-1, the SMD-100 CNC bidirectional pulse electroplating power supply was selected to generate the pulse current, a thermocouple was used to measure the temperature and connected to a temperature control box to monitor the temperature change in real time, the thermocouple was made into a patch and fixed on the surface of the gauge section with Teflon tape, the temperature value change was displayed on the display, and three groups of uniaxial tensile tests were carried out, among which No. 1 was the room temperature uniaxial tensile test specimen, No. 2 to No. 5 were the high temperature uniaxial tensile test specimens, and No. 6 to No. 11 were the electroplastic uniaxial tensile test specimens. The entire stretching step was kept consistent as much as possible.

[0150] S3. Using the test data obtained in step S2, the load-displacement curve and the engineering stress-strain curve obtained from the uniaxial tensile test are converted into a true stress-strain curve, and the tensile strength and elongation after fracture of the TC4 titanium alloy under different conditions are analyzed and compared to obtain the influence of the electroplastic effect on the mechanical properties of the alloy.

[0151] S31. Convert the test data in the load-displacement curve and engineering stress-strain curve obtained from the uniaxial tensile test into a true stress-strain curve.

[0152] S32. Determination of the constant temperature tensile test temperature: TC4 titanium alloy tensile specimen 4 is heated by passing a predetermined pulse current through the specimen at room temperature. After the temperature of the specimen stabilizes for 5 minutes, the temperature of the specimen is measured using a thermocouple to obtain the surface temperature of the TC4 titanium alloy under different electrical parameters. The entire tensile step is maintained as consistent as possible, and the heating furnace is set to 20°C per minute.

[0153] S33, by analyzing the comparison diagram of the true stress-strain curve of the tensile specimen 4 of TC4 titanium alloy under the same pulse current and different duty ratios and the high temperature true stress-strain curve of the corresponding temperature, as shown in FIG. Figure 3a and Figure 3b As shown in FIG, the comparison diagrams of the tensile strength reduction rate and the elongation after fracture of TC4 titanium alloy at room temperature, high temperature and electroplasticity are obtained respectively, as shown in FIG. Figure 4a and 4b shown.

[0154] S34, by analyzing the comparison diagram of the true stress-strain curve of tensile specimen 4 under the same duty cycle and different pulse currents and the high temperature true stress-strain curve of the corresponding temperature, as shown in FIG. Figure 5 As shown, the tensile strength reduction rate of TC4 titanium alloy under electroplasticity is obtained.

[0155] S35. The above comparison diagrams are sorted out to draw the real stress-strain comparison diagram of TC4 titanium alloy high temperature uniaxial tensile test and electroplastic uniaxial tensile test, as shown in Figure 3. Figures 6a to 6d As shown, Figures 6a to 6d The comparison diagrams of the real stress-strain curves of uniaxial tensile test at room temperature, 80℃ and 6A, 80℃, 150℃ and 8A, 150℃, 200℃ and 10A, 200℃, and 240℃ and 12A, 240℃ are obtained, and the influence of pure electroplastic effect in the electroplastic effect is obtained, that is, in the electroplastic uniaxial tensile test, the pulse current size (that is, pure electroplastic effect) plays a major role in the decrease in the tensile strength of TC4 titanium alloy, and this effect becomes more obvious with the increase of pulse current.

[0156] S4. Combining the experimental data of the three states, the constitutive equations under different states are established through data fitting.

[0157] S41. Establish the constitutive equation of TC4 titanium alloy in the uniaxial tensile test at room temperature, and add the influence function of the electroplastic effect to obtain the product function of the initial constitutive equation. The specific expression is as follows:

[0158] σ=f(ε p )·g(T)·h(j)

[0159] Where σ is the flow stress, ε p is the true plastic strain, j is the pulse current density, f(ε p ) is the constitutive model at room temperature, g(T) is the thermal softening function, and h(j) is the electroplastic effect function.

[0160] S42. Since the Johnson-Cook model can well predict the mathematical form of work hardening of metal materials, a constitutive model at room temperature is established based on the Johnson-Cook model.

[0161] S421. Ignore the strain rate in the product function of the initial constitutive equation, so The following expression is obtained:

[0162]

[0163] Where, is the flow stress corresponding to the reference strain rate, is the reference strain rate, T is the dimensionless temperature term, and g(T) is the thermal softening function.

[0164] S422, flow stress corresponding to reference strain rate According to the true stress-strain curve relationship of tensile specimen 4 at room temperature, the Hollomon model is applied as a full strain extrapolation model, and the hardening index is used to describe the flow stress change of tensile specimen 4 at room temperature. The following expression is obtained:

[0165] σ1=A·ε n

[0166] Where ε is the true plastic strain, A is the strength coefficient at room temperature, and n is the strain hardening exponent at room temperature.

[0167] S423. Based on step S421 and step S422, The constitutive equation at room temperature is:

[0168] σ=A·ε n *g(T)

[0169] Where ε is the true plastic strain, A is the strength coefficient at room temperature, n is the strain hardening exponent at room temperature, T is the dimensionless temperature term, and g(T) is the thermal softening function.

[0170] When the temperature is room temperature, the thermal softening function g(T) of the material is not considered. Therefore, the true stress-plastic strain curve at room temperature is fitted by the formula in S423 to obtain the values ​​of parameters A and n, and A=1065 and n=0.019 are obtained, thereby obtaining the constitutive equation at room temperature and the specific expression of the constitutive equation at room temperature.

[0171] S43. Since the Johnson-Cook model lacks consideration of temperature changes, the Arrhenius model is used to establish the high-temperature constitutive equation.

[0172] S431. Based on the Z value characterizing the strain rate and temperature of the high-temperature tensile specimen 4, the expression of the hyperbolic sine Arrhenius equation modified by the phenomenological constitutive equation is obtained as follows:

[0173]

[0174]

[0175] Where, is the strain rate, B is the material constant, σ2 is the true stress at high temperature, F(σ2) is the stress function, Q is the strain activation energy, R is the gas molar constant 8.314 J / (mol·K), and T is the temperature.

[0176] S432. According to the different expressions of F(σ2) at low stress and high stress levels, under the condition of constant strain rate, the equation about lnσ2-σ2 is obtained, the curve of lnσ2-σ2 is drawn, and the slope c=0.0012 is obtained.

[0177] S433. On the basis of steps S431 and S432, according to the expression of the correction value of strain activation energy Q in the phenomenological thermal deformation constitutive model, the specific form is as follows:

[0178] Q=dRb1

[0179] Where b1 is the slope of the ln[sinh(cσ2)]-1000 / T curve, and the fitting calculation yields b1=0.4273.

[0180] According to the formula in step S431, the formula for Z can be obtained, where the strain rate is a constant of 0.01s-1. The d values ​​obtained by fitting are 0.22718, 0.21745, 0.20907 and 0.19981, respectively. The average value d=0.213375 is taken. Therefore, the high-temperature constitutive equation of TC4 titanium alloy is constructed as follows:

[0181]

[0182] S44. Establish the electroplastic constitutive equation.

[0183] S441. Since the current frequency has no effect on the mechanical properties, the pulse current density is used to express the electrical coefficient. The electrical coefficient equation is:

[0184] h(j,f)=h(j);

[0185] The expression for the law between effective stress and current in the electroplastic effect is as follows:

[0186]

[0187] Where σ(j) is the effective stress when pulse current is applied, σ is the effective stress when no pulse current is applied, j is the current density, and j0 is a material parameter that is related to temperature.

[0188] According to the law between effective stress and current in the electroplastic effect, the influence function of the electroplastic effect is obtained. The specific expression is as follows:

[0189]

[0190] Where h is the influence function of the electroplastic effect, j is the current density, and j0 is the material parameter, which is related to temperature.

[0191] S442, due to j0 2 (T) The experimental data of electroplastic uniaxial tension can be fitted by combining the temperatures corresponding to different current densities, the room temperature constitutive equation when no power is applied, and the high temperature constitutive equation to obtain the constitutive equation when power is applied. That is, the expression of the electroplastic constitutive equation is:

[0192]

[0193] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A method for establishing a constitutive model for an electroplastic uniaxial tensile test, characterized in that: It specifically includes the following steps: S1. Prepare the tensile specimen and insulate the fixture and tensile specimen; S2. Prepare three sets of test devices for room temperature uniaxial stretching, high temperature uniaxial stretching, and electroplastic stretching, respectively. Clamp the test devices on a universal tensile testing machine and perform three sets of tensile tests on each device. S3. Analyze the tensile strength and elongation of the tensile specimen under different conditions based on the test data obtained in step S2; S4. Combine the experimental data of the three states and establish the constitutive equations under different states: S41. Establish the constitutive equation of the tensile specimen in the uniaxial tensile test at room temperature, and add the influence function of the electroplastic effect to obtain the product function of the initial constitutive equation; S42. Establish a constitutive model at room temperature based on the Johnson-Cook model: S421. Ignore the strain rate in the product function of the initial constitutive equation and obtain the following expression: Where, is the flow stress corresponding to the reference strain rate, is the reference strain rate, u is the dimensionless temperature term, and g(u) is the thermal softening function; S422. Based on the true stress-strain curve of the tensile specimen at room temperature, the Hollomon model is applied to describe the flow stress change of the tensile specimen at room temperature using the hardening index, and the following expression is obtained: σ1=D·e n Where ε is the true plastic strain, D is the strength coefficient at room temperature, and n is the strain hardening exponent at room temperature; S423. Based on step S421 and step S422, The constitutive equation at room temperature is: σ=D·e n *g(u) Where ε is the true plastic strain, D is the strength coefficient at room temperature, n is the strain hardening exponent at room temperature, u is the dimensionless temperature term, and g(u) is the thermal softening function; S43. Use the Arrhenius model to establish the high-temperature constitutive equation: S431. Based on the Z value characterizing the strain rate and temperature of the high-temperature tensile specimen, the expression of the hyperbolic sine Arrhenius equation modified by the phenomenological constitutive equation is obtained as follows: Where, is the strain rate, B is the material constant, σ2 is the true stress at high temperature, F(σ2) is the stress function, Q is the strain activation energy, R is the gas molar constant 8.314 J / (mol·K), and T is the temperature; S432. According to the different expressions of F(σ2) at low stress and high stress levels, under the condition of constant strain rate, the equation about lnσ2-σ2 is obtained; S433. Based on step S431 and step S432, according to the expression of the correction value of the strain activation energy Q in the phenomenological thermal deformation constitutive model, the expression of the high-temperature constitutive equation of the tensile specimen is obtained as follows: Where σ is the flow stress, D is the strength coefficient at room temperature, ε is the true plastic strain, and n is the strain hardening exponent at room temperature. is the strain rate, b1 is the material parameter, d is the material parameter, and T is the temperature; S44. Establish the electroplastic constitutive equation: S441. Based on the law between effective stress and current in the electroplastic effect, the influence function of the electroplastic effect is obtained. The specific expression is as follows: Where h is the influence function of the electroplastic effect, j is the current density, and j0 is the material parameter, which is related to temperature; S442. Combining the room temperature constitutive equation and the high temperature constitutive equation when no power is applied, the experimental data of electroplastic uniaxial tension are fitted to obtain the constitutive equation when power is applied. That is, the expression of the electroplastic constitutive equation is: Where σ is the flow stress, D is the strength coefficient at room temperature, ε is the true plastic strain, and n is the strain hardening exponent at room temperature. is the strain rate, b1 is the material parameter, d is the material parameter, T is the temperature, j is the current density, j0 2 (T) is a polynomial function of current density with respect to temperature.

2. The method for establishing a constitutive model for an electroplastic uniaxial tensile test according to claim 1, wherein: The specific process of step S3 includes: S31, converting the test data in the load-displacement curve and the engineering stress-strain curve obtained from the uniaxial tensile test into a true stress-strain curve; S32, passing pulse currents of different electrical parameters through the tensile specimen, and measuring different temperature values ​​of the tensile specimen at room temperature using a thermocouple; heating the tensile specimen to a preset temperature, and then keeping the temperature constant to obtain different temperature values ​​of the tensile specimen at high temperature; passing pulse currents of different electrical parameters through the tensile specimen, and measuring different temperature values ​​of the tensile specimen under electroplasticity using a thermocouple; S33. By analyzing the comparison graphs of the true stress-strain curves of the tensile specimens under the same pulse current and different duty cycles and the high-temperature true stress-strain curves of the corresponding temperatures, comparison graphs of the tensile strength reduction rate and the elongation after fracture of the tensile specimens under room temperature, high temperature, and electroplasticity are obtained respectively; S34. By analyzing the comparison diagram of the true stress-strain curve of the tensile specimen under the same duty cycle and different pulse currents and the high-temperature true stress-strain curve of the corresponding temperature, the tensile strength reduction rate of the tensile specimen under electroplasticity is obtained; S35. Compare the tensile strength reduction rates obtained in room temperature, high temperature and electroplastic tensile tests to obtain the primary and secondary relationships between pulse current and duty cycle in electroplasticity.

3. The method for establishing a constitutive model for an electroplastic uniaxial tensile test according to claim 2, wherein: In step S31, the test data in the load-displacement curve and the engineering stress-strain curve obtained from the uniaxial tensile test are converted into the true stress-strain curve using the following conversion expression: Where ε0 is the true strain of the tensile specimen, σ0 is the true stress of the tensile specimen, e is the engineering strain of the tensile specimen, s is the engineering stress of the tensile specimen, l0 is the length of the specimen gauge section, Δl is the elongation of the gauge section, P is the load, and A is the cross-sectional area of ​​the gauge section.

4. The method for establishing a constitutive model for an electroplastic uniaxial tensile test according to claim 1, wherein: In step S41, the expression of the initial constitutive equation multiplicative function is as follows: σ=f(ε p )·g(u)·h(j) Where σ is the flow stress, ε p is the true plastic strain, j is the pulse current density, f(ε p ) is the constitutive model at room temperature, g(u) is the thermal softening function, and h(j) is the electroplastic effect function.

5. The method for establishing a constitutive model for an electroplastic uniaxial tensile test according to claim 1, wherein: In step S432, the specific expression of the lnσ2-σ2 equation is as follows: Where B1, B2, b and c1 are material constants, and σ2 is the true stress at high temperature.

6. A test device for establishing a constitutive model for an electroplastic uniaxial tensile test according to any one of claims 1 to 5, characterized in that: The tensile specimen comprises a silicon nitride rod, a fixture and bakelite. The tensile specimen is a long U-shaped structure with a rectangular cross-section. The fixed end of the tensile specimen is connected to the first end of the bakelite, the second end of the bakelite is connected to the first end of the silicon nitride rod, and the second end of the silicon nitride rod is fixedly connected to the fixture. The silicon nitride rod, the fixture and the bakelite are symmetrically distributed on both sides of the fixed end of the tensile specimen.

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