Composite treatment method for regulating residual stress and improving mechanical properties of 2 series aluminum alloys

Through the electro-thermal-magnetic composite treatment method, the problem of difficulty in regulating residual stress in 2-system aluminum alloy is solved, and the effective reduction of residual stress and improvement of mechanical properties of aluminum alloy is achieved, which is specifically manifested as a reduction of 40% to 50%. Residual stress and elongation increased by about 13%.

CN116837303BActive Publication Date: 2025-02-25SICHUAN UNIV
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Patent Information

Application Number
CN202310808487.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-07-03
Publication Date
2025-02-25
Estimated Expiration
2043-07-03

AI Technical Summary

Technical Problem

The prior art is difficult to effectively regulate residual stress in 2-series aluminum alloys, and the traditional methods have problems such as long time, high energy consumption and high production costs.

Method used

Using the electric-thermal-magnetic composite treatment method, the sample model is constructed in COMSOL Multiphysics multiphysics simulation software, the current field and the solid heat transfer field are set, and the steady-state simulation is carried out to calculate the steady-state current, and the electric-thermal-magnetic Pulse current and magnetic processing are performed on the equipment to regulate the residual stress of the aluminum alloy.

Benefits of technology

By the electro-thermal-magnetic composite treatment method, the residual stress of the aluminum alloy can be reduced by 40% to 50%, and the plasticity of the material can be significantly improved, so that its elongation is increased by about 13%.

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Abstract

The present invention discloses a composite treatment method for regulating residual stress of 2 series aluminum alloy and improving mechanical properties, including S1 constructing a sample model and obtaining a sample model diagram; S2 supplementing the physical property parameters of the input sample model; S3 setting a current field in the sample model component; S4 setting a solid heat transfer field in the sample model component; S5 performing steady-state simulation on the heating and heat dissipation of the sample after powering on, and calculating the steady-state current of the sample model; S6 clamping the sample to be processed on an electro-thermal-magnetic device, and performing pulse current treatment with a steady-state current; S7 setting magnetic field parameters, and performing magnetic treatment on the sample; S8 turning off the magnetic field power supply and the electric field power supply. The composite treatment method of the present invention regulates the residual stress of the aluminum alloy, promotes the release of residual stress in the material through the coupling effect of the pulsed magnetic field and the high-frequency current, can reduce the residual stress by 40% to 50%, and improves the plasticity of the material, so that its elongation is increased by about 13%.
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Description

Technical Field

[0001] The invention belongs to the technical field of residual stress regulation, and specifically relates to a composite treatment method for regulating the residual stress of a 2-series aluminum alloy and improving mechanical properties. Background Art

[0002] Aluminum alloy has the characteristics of high strength and low density. It can be used to manufacture mechanical parts and components that bear large loads. It is a non-ferrous metal material widely used in industry. 2 series aluminum alloy is also called Al-Cu alloy. It is a high-strength aluminum alloy. Its specific strength is much higher than that of general high-strength steel. Therefore, it is often used as the main structural material of aircraft. 2 series aluminum alloy is strengthened by solid solution + aging treatment. First, a supersaturated solid solution is obtained by quenching, and then it is kept warm for a period of time at room temperature or low temperature. As time goes by, the supersaturated solid solution decomposes and precipitates the strengthening phase θ (CuAl2), which significantly improves the strength and hardness of the aluminum alloy. Although the strengthening method of solid solution + aging significantly improves the mechanical properties of aluminum alloy, the quenching stage of solid solution treatment is a violent non-equilibrium cooling process. The difference in cooling rate leads to a large temperature difference between the surface and the core of the workpiece. The large temperature gradient brings uneven plastic deformation, and finally leaves a large residual stress inside the material. At the same time, the strengthening phase precipitated at the grain boundary grows and aggregates, resulting in uneven local deformation of the organization, which also increases the internal stress of the material.

[0003] At present, the methods for regulating the internal residual stress of high-strength aluminum alloys can be divided into two categories in principle: mechanical action and thermal action. Mechanical actions include vibration aging, mechanical bulging, cold stretching and pre-deformation, and thermal actions include heat treatment aging, graded heat treatment and cryogenic treatment. Among them, vibration aging has a long cycle and may damage local areas of the workpiece; mechanical bulging and cold stretching are only suitable for parts with simple configurations and have limited regulation effects; heat treatment and cryogenic treatment have the disadvantages of long time consumption, high energy consumption and high production costs.

[0004] At room temperature, the resistivity of copper is only 1.75*10 -8 Ω·m, indicating that copper's electrical conductivity is better than most metals, which is one of the reasons why copper is used as a conductor. In addition, the magnetic permeability of copper is 1.72*10 6 H / m, which is better than most non-ferromagnetic materials. In other words, except for ferromagnetic materials such as iron, cobalt and nickel, copper has a strong magnetic conductivity in a magnetic field. The lower resistivity and higher magnetic permeability of copper determine its significant electric and magnetic effects in electric and magnetic fields. Summary of the invention

[0005] The purpose of the present invention is to provide a composite treatment method for regulating the residual stress of 2 series aluminum alloys and improving the mechanical properties in view of the above-mentioned deficiencies in the prior art, so as to solve the problem of difficulty in regulating the internal residual stress of existing aluminum-copper alloys.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A composite treatment method for regulating residual stress of 2 series aluminum alloy and improving mechanical properties comprises the following steps:

[0008] S1. Input the size parameters of the sample into COMSOL Multiphysics multi-physics field simulation software, build a sample model and obtain a sample model diagram;

[0009] S2. Select aluminum alloy as the material of the sample model, and input additional physical property parameters of the sample model;

[0010] S3, setting a current field in the sample model assembly, including an electric field excitation source, current conservation and insulation conditions;

[0011] S4, setting a solid heat transfer field in the sample model assembly, including boundary conditions for sample heat transfer;

[0012] S5. Perform steady-state simulation on the heat generation and heat dissipation of the sample after power is supplied, and calculate the steady-state current when the sample model temperature is 250°C;

[0013] S6, clamping the sample to be processed onto the electro-thermal-magnetic device, and performing pulse current treatment with the steady-state current in step S5;

[0014] S7, collect the sample temperature in real time, when the temperature reaches 250°C, set the magnetic field parameters, and perform magnetic treatment on the sample;

[0015] S8. After the magnetic treatment is completed, turn off the magnetic field power supply and the electric field power supply, wait for the sample to cool naturally, and obtain the aluminum alloy control component.

[0016] Furthermore, the physical property parameters in step S2 include electrical conductivity 3.53*10^7S / m and thermal conductivity 204W / (mk).

[0017] Further, step S3 includes:

[0018] The definition of current conservation 1 indicates that the entire sample material is homogeneous and has consistent conductivity;

[0019] The current flows into one end of the sample and flows out from the other end. The inflow end is set as terminal 1, and a current with an intensity of I is applied; the outflow end is set as ground 1, and the potential at ground 1 is 0;

[0020] The other surfaces of the sample are set to be electrically insulating 1, that is, no current will flow in or out of the surface;

[0021] The initial value 1 of the whole sample is set to 0, that is, before the experiment starts, there is no voltage and current in the sample.

[0022] Further, step S4 includes:

[0023] Set the entire sample to solid 1 and match the heat transfer equation;

[0024] Set the initial value of sample 1 to 293.15K;

[0025] The two end faces of the sample where current enters and exits are set to thermal insulation 1;

[0026] For the four sides of the sample exposed to air, set the heat flux to 1, select the convection heat flux, the heat transfer coefficient htc, and set the external temperature to 293.15K;

[0027] After power is turned on, the sample heats up and there is radiation heat transfer between the sample and the environment. The states of the four surfaces are set to surface radiation to environment 1, the surface emissivity is the material property, and the environment is room temperature.

[0028] Further, step S5 includes:

[0029] Add domain probe 1, select average value for probe type, select the entire sample as region, and select temperature T as expression;

[0030] Based on the data of domain probe 1, when the current flowing through the sample is 1000A at the initial state, the sample begins to heat up and eventually maintains a stable temperature of 69.87°C; at this time, the heat accumulation caused by the Joule heating effect is balanced with the heat dissipation of the sample to the environment, and the sample no longer heats up;

[0031] Set the parameters to operating current, upper limit 4000A, and plot the relationship between current and sample temperature based on the data obtained from domain probe 1;

[0032] The Nelder-Mead optimization method is used, the objective function is set to abs(comp1.emh1.Tave-523.15), the optimization type is minimum, the control variable is I, the lower limit of I is 1000A, the upper limit is 4000A, the sample temperature is 250℃, and the inverse steady-state current is 2246.9A.

[0033] Furthermore, the parameters of the pulse current in step S6 are: the pulse width of the pulse current is 200 ms, the interval is 20 ms, and the current is 2246A.

[0034] Furthermore, the magnetic field parameters in step S7 are: magnetic field intensity B is 3T, and the interval of magnetic pulses is t=15s.

[0035] The composite treatment method for regulating residual stress of 2-series aluminum alloy and improving mechanical properties provided by the present invention has the following beneficial effects:

[0036] The present invention adopts an electric-thermal-magnetic composite treatment method to regulate the residual stress of aluminum alloy, and promotes the release of residual stress in the material through the coupling effect of pulsed magnetic field and high-frequency current, which can reduce the residual stress by 40% to 50%, and improve the plasticity of the material, thereby increasing its elongation by about 13%.

[0037] The electric-thermal-magnetic composite treatment method of the present invention promotes the depinning and slipping of dislocations inside the aluminum alloy structure through the action of the electromagnetic field (electroplasticity, magnetostriction and other effects), reduces dislocation entanglement, thereby releasing stress and improving the plasticity of the aluminum alloy.

[0038] The present invention utilizes the Joule heating effect of electric current to heat the sample, and the temperature provides an energy basis for the migration of elements in the material. Compared with other heat treatments, the present invention has a short time, a fast temperature rise, and a high energy utilization rate.

[0039] The present invention utilizes the electron wind effect of pulse current and the magnetostrictive effect of aluminum alloy in a magnetic field to promote dislocation slip and vacancy movement in the material and accelerate the release of residual stress with remarkable effect.

[0040] The electric-thermal-magnetic composite treatment method of the present invention strengthens the element diffusion between the second phase and the matrix in the aluminum alloy, promotes the dissolution of the second phase, is beneficial to improving the uniformity of grain boundary energy, releasing internal stress and improving plasticity.

[0041] The method of the present invention can use simulation software to calculate the optimal current and voltage for samples of different sizes, thereby achieving precise control of the experimental temperature; the equipment is easy to operate, the processing process is easy to adjust, and the process method has strong adaptability to parts. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The figure is a flow chart of the processing method of the present invention.

[0043] Figure 2 This is a curve diagram of the relationship between current and sample temperature in Example 1.

[0044] Figure 3 It is an iterative diagram of the steady-state current in Example 1. DETAILED DESCRIPTION

[0045] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0046] Example 1

[0047] refer to Figure 1 This embodiment provides a composite treatment method for regulating residual stress and improving mechanical properties of 2-series aluminum alloys. The treatment object of this method is 2-series aluminum alloys. The second phase in 2-series aluminum alloys is θ (CuAl2), which is a Cu-rich phase, and the aluminum matrix (α-Al) is rich in Al and low in Cu; therefore, the Cu element tends to migrate from the high-concentration area (CuAl2) to the low-concentration area (α-Al). Usually, the above-mentioned element diffusion needs to be carried out at an annealing temperature (>350°C) and lasts for a long time (usually several hours).

[0048] This embodiment utilizes the Joule heating effect of pulse current to achieve spontaneous temperature rise of the material, providing energy for internal element migration; and utilizes the electron wind effect of current pulse and the magnetostrictive effect of magnetic field to promote dislocation slip and vacancy movement inside the material, strengthen the element diffusion of the second phase and the matrix, and is conducive to the homogenization of grain boundary energy and the release of residual stress. It specifically includes the following steps:

[0049] Step S1, inputting the size parameters of the sample into COMSOL Multiphysics multi-physics field simulation software, constructing a sample model and obtaining a sample model diagram;

[0050] In this step, the sample is made by wire cutting of forged 2A02 billet, the sample size is 100*30*5mm, and the residual stress is distributed in the whole sample;

[0051] Step S2, selecting aluminum alloy as the material of the sample model, and inputting additional physical property parameters of the sample model;

[0052] The physical property parameters in this step include but are not limited to electrical conductivity 3.53*10^7S / m and thermal conductivity 204W / (mk).

[0053] Step S3, setting a current field in the sample model assembly, including an electric field excitation source, current conservation and insulation conditions;

[0054] The current field is set as:

[0055] Setting "Current Conservation 1" means that the entire sample material is homogeneous and has consistent conductivity;

[0056] The current flows into one end of the sample and flows out from the other end. The inflow end is set as "Terminal 1" and a current with an intensity of I is applied; the outflow end is set as "Ground 1" and the potential at "Ground 1" is 0;

[0057] Set the other surfaces of the sample to "electrical insulation 1", that is, no current will flow in or out of the surface; set the initial value 1 of the whole sample to 0, that is, before the experiment starts, there is no voltage or current in the sample. Step S4, set the solid heat transfer field in the sample model component, including the boundary conditions for sample heat transfer;

[0058] Specifically, the solid heat transfer field is set as follows:

[0059] Set the entire sample to solid 1 and match the heat transfer equation;

[0060] The heat transfer equation for this step is:

[0061]

[0062] q=-k▽T;

[0063] Cp: ​​specific heat at constant pressure, J / (kg·K);

[0064] ρ: material density, kg / m 3 ;

[0065] u: fluid velocity (vector);

[0066] ▽: gradient operator;

[0067] T: temperature, K;

[0068] q: Conductive heat flux, W / m 2 ;

[0069] Q: heat source, W / m 3 ;

[0070] Q ted: Thermoelastic damping, W / m 3 ;

[0071] k: thermal conductivity, W / (m·K);

[0072] The initial value 1 of the sample is set to 293.15K, i.e. 20°C, which means that the sample is at room temperature before the experiment;

[0073] The two end surfaces of the sample where current enters and exits (i.e., in contact with the electrode) are set to "thermal insulation 1", indicating that the heat transfer behavior of these two end surfaces can be ignored;

[0074] For the four sides of the sample exposed to the air, set "Heat Flux 1", select "Convective Heat Flux", heat transfer coefficient htc, and set the external temperature to 293.15K, which means that the environment where the sample is located is room temperature and there is natural convection heat transfer between the sample and the environment;

[0075] After power is turned on, the sample heats up and there is radiation heat transfer between the sample and the environment. The states of the four surfaces are set to "Surface radiation to environment 1", the surface emissivity is a material property, and the environment is room temperature;

[0076] Step S5, perform steady-state simulation on the heat generation and heat dissipation of the sample after power is supplied, and calculate the steady-state current when the sample model temperature is 250°C, which is specifically:

[0077] Add "Domain Probe 1" to the component, select "Average" for probe type, select the entire sample as the region, and select temperature "T" for expression, that is, use "Domain Probe 1" to track the overall temperature of the sample;

[0078] The steady-state study of the heat generation and heat dissipation of the sample after power is applied is carried out, and the surface temperature of the sample is plotted, specifically:

[0079] Combined with the data from domain probe 1, it can be concluded that: when the current flowing through the sample is in the initial state (1000A), the sample begins to heat up and eventually remains stable at 69.87°C; at this time, the heat accumulation caused by the Joule heating effect is balanced by the heat dissipation of the sample to the environment (natural convection and thermal radiation), so the sample no longer heats up.

[0080] Perform a parametric scan of the study to obtain the relationship between current and sample temperature, refer to Figure 2 , set the parameter to operating current, with an upper limit of 4000A; as can be seen from the figure, as the current increases, the sample temperature gradually increases, and the curve trend is similar to a quadratic function.

[0081] In this example, the current at the equilibrium temperature of 250°C (523.15K) is obtained, and the steady-state study is optimized. The optimization method is Nelder-Mead, the objective function is set to abs(comp1.emh1.Tave-523.15), the optimization type is minimum, the control variable is I, the lower limit of I is 1000A, and the upper limit is 4000A, that is, the sample temperature is 250°C, and the steady-state current is inversely calculated;

[0082] The objective function of this embodiment is:

[0083] Objective function y = abs(comp1.emh1.Tave-523.15)

[0084] Among them: comp1.emh1.Tave represents the body weighted average temperature in K, 523.15 is the Kelvin temperature (K), which represents the target temperature of 250°C (K=273.15+°C), and abs represents the absolute value.

[0085] Therefore, the objective function is to calculate the absolute value of the difference between the simulation temperature and the target temperature (250 degrees Celsius). The optimization type is minimum, that is, to solve the minimum value of the objective function, that is, to find the condition where the simulation temperature is extremely close to the target temperature.

[0086] refer to Figure 3 As can be seen from the figure, after repeated iterative calculations, the objective function is infinitely close to 0. At this time, the current is 2246.9A, that is, the steady-state current is 2246.9A.

[0087] Step S6, clamping the sample to be processed onto the electro-thermal-magnetic device, and performing pulse current treatment with the steady-state current in step S5, that is, setting the pulse width of the pulse current to 200 ms, the interval to 20 ms, and the current to 2246 A, then turning on the current to start the pulse current treatment;

[0088] Step S7, collecting the sample temperature in real time, when the temperature reaches 250°C, setting the magnetic field intensity B to 3T and the interval of the magnetic pulse t=15s, and performing magnetic treatment on the sample;

[0089] Step S8: After the magnetic treatment for 3 minutes, turn off the magnetic field power supply and the electric field power supply, wait for the sample to cool naturally, and obtain the aluminum alloy control panel.

[0090] It should be noted that, in the treatment process of the method of this embodiment, nitrogen protection is used throughout the process to reduce oxidation of the sample; during the electric-thermal-magnetic composite treatment, the pulsed magnetic field and the electric current act on the aluminum alloy workpiece at the same time; before and after the electric-thermal-magnetic composite treatment, residual stress detection is performed on multiple test points on the surface of the workpiece, and the position of the stress test point is the same each time; after the electric-thermal-magnetic composite treatment, a standard tensile sample is prepared from the workpiece for mechanical property testing to evaluate the improvement in plasticity.

[0091] During the processing, the samples were protected by argon atmosphere throughout the process to prevent oxidation of the material; the residual stress was measured according to the national standard GB / T 7704-2017 "Non-destructive Testing X-ray Stress Determination Method".

[0092] The tensile strength and elongation are measured according to the national standard GB / T 228-2002 “Room Temperature Tensile Test Method for Metallic Materials”.

[0093] The performance indicators of 2A02 aluminum alloy after treatment in Example 1 and Comparative Example 1 are listed in Table 1.

[0094] Table 1 Performance comparison of 2A02 in different states

[0095] Processing time Residual stress (MPa) Tensile strength(MPa) Elongation(%) 0 -217 436 11.14 120s -156 431 12.22 240s -117 433 12.64

[0096] It can be seen from the table that after the electric-thermal-magnetic composite treatment, the residual stress of 2A02 aluminum alloy is significantly reduced, with the maximum reduction of about 46.1%, the tensile strength remains basically unchanged, and the elongation increases by about 13.5%. It can be seen that the plasticity of 2A02 aluminum alloy is significantly improved.

[0097] Example 2

[0098] The residual stress of this embodiment is measured according to the national standard GB / T 7704-2017 "Non-destructive Testing X-ray Stress Determination Method".

[0099] The tensile strength and elongation are measured according to the national standard GB / T 228-2002 “Room Temperature Tensile Test Method for Metallic Materials”.

[0100] The performance indicators of 2A14 aluminum alloy after treatment in Example 2 and Comparative Example 2 are listed in Table 2;

[0101] Table 2 Performance comparison of 2A14 in different states

[0102]

[0103] It can be seen from the table that after the electric-thermal-magnetic composite treatment, the residual stress of 2A14 aluminum alloy is significantly reduced, with the maximum reduction of about 54.5%, the tensile strength remains basically unchanged, and the elongation increases by about 13.1%. It can be seen that the plasticity of 2A14 aluminum alloy is significantly improved.

[0104] The present invention adopts an electric-thermal-magnetic composite treatment method to regulate the residual stress of aluminum alloy. It is effective to promote the release of residual stress in the material through the coupling effect of pulsed magnetic field and high-frequency current, which can reduce the residual stress by 40% to 50%, and improve the plasticity of the material, thereby increasing its elongation by about 13%.

[0105] Although the specific implementation of the invention is described in detail in conjunction with the drawings, it should not be understood as limiting the scope of protection of this patent. Within the scope described in the claims, various modifications and variations that can be made by those skilled in the art without creative work still fall within the scope of protection of this patent.

Claims

1. A composite treatment method for regulating residual stress of 2 series aluminum alloy and improving mechanical properties, characterized in that: The following steps are involved: S1. Input the size parameters of the sample into COMSOL Multiphysics multi-physics field simulation software, build a sample model and obtain a sample model diagram; S2. Select aluminum alloy as the material of the sample model, and input additional physical property parameters of the sample model; S3, setting a current field in the sample model assembly, including an electric field excitation source, current conservation and insulation conditions; S4, setting a solid heat transfer field in the sample model assembly, including boundary conditions for sample heat transfer; S5. Perform steady-state simulation on the heat generation and heat dissipation of the sample after power is supplied, and calculate the steady-state current when the sample model temperature is 250°C; S6, clamping the sample to be processed onto the electro-thermal-magnetic device, and performing pulse current treatment with the steady-state current in step S5; S7, collect the sample temperature in real time, when the temperature reaches 250°C, set the magnetic field parameters, and perform magnetic treatment on the sample; S8. After the magnetic treatment is completed, turn off the magnetic field power supply and the electric field power supply, wait for the sample to cool naturally, and obtain the aluminum alloy control panel; The step S3 comprises: Definition Current conservation means that the entire sample material is homogeneous and has consistent conductivity; The current flows into one end of the sample and flows out from the other end. The inflow end is set as the terminal and a current with an intensity of I is applied; the outflow end is set as the ground, and the potential at the ground is 0. The other surfaces of the sample are set to be electrically insulated, that is, no current will flow in or out of the surface; The initial values ​​of the voltage and current of the whole sample were set to 0, that is, before the experiment started, there was no voltage and current in the sample; The step S4 comprises: Set the sample as a solid and match the heat transfer equation; The initial temperature of the sample is set to 293.15K, i.e. 20°C, which means that the sample is at room temperature before the experiment; The two end faces of the sample where current enters and exits are set to be thermally insulated; For the four sides of the sample exposed to the air, set the heat flux, select the convection heat flux, the heat transfer coefficient htc, and set the external temperature to 293.15K; After power is turned on, the sample heats up and there is radiation heat transfer between the sample and the environment. The states of the four surfaces are set to surface radiation to the environment, the surface emissivity is a material property, and the environment is room temperature; The step S5 comprises: Add a domain probe, select average as the probe type, select the entire sample as the region, and select temperature T as the expression; Based on the data from the domain probe, when the current flowing through the sample is 1000A at the initial state, the sample begins to heat up and eventually maintains a stable temperature of 69.87°C; at this point, the heat accumulation caused by the Joule heating effect is balanced with the heat dissipation of the sample to the environment, and the sample no longer heats up; Set the parameters to operating current, upper limit 4000A, and plot the relationship between current and sample temperature based on the data obtained from the domain probe; The Nelder-Mead optimization method is used, and the objective function is set to y=abs(comp1.emh1.Tave-523.15), where comp1.emh1.Tave represents the weighted average temperature of the body in K, 523.15 is in K, representing the target temperature of 250°C, abs represents the absolute value, the optimization type is the minimum value, the control variable is I, the lower limit of I is 1000A, the upper limit is 4000A, and the sample temperature is 250°C. The inverse steady-state current is 2246.9A; The parameters of the pulse current in step S6 are: the pulse width of the pulse current is 200 ms, the interval is 20 ms, and the current is 2246A.

2. The composite treatment method for regulating residual stress and improving mechanical properties of 2-series aluminum alloy according to claim 1, characterized in that: The physical property parameters in step S2 include electrical conductivity of 3.53x10^7 S / m and thermal conductivity of 204W / (mk).

3. The composite treatment method for regulating residual stress and improving mechanical properties of 2-series aluminum alloy according to claim 1, characterized in that: The magnetic field parameters in step S7 are: magnetic field intensity B is 3T, and the interval of magnetic pulses t=15s.

Citation Information

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