rus
Issue #2/2021
E.A.Klimov, M.Yu.Murashkin
Strength estimation of a prospective two-component conductor made of nanostructural aluminum alloys by the finite element method
Strength estimation of a prospective two-component conductor made of nanostructural aluminum alloys by the finite element method
DOI: 10.22184/1993-8578.2021.14.2.150.158
In this paper the finite element method is used to assess the rational design of a prospective two-component conductor made of nanostructured aluminum alloys to ensure the required level of strength.
In this paper the finite element method is used to assess the rational design of a prospective two-component conductor made of nanostructured aluminum alloys to ensure the required level of strength.
Теги: aluminum alloys finite element method intensive plastic deformation strength two-component wire ultra-fine grain structure алюминиевые сплавы двухкомпонентный провод интенсивная пластическая деформация метод конечных элементов прочность ультрамелкозернистая структура
STRENGTH ESTIMATION OF A PROSPECTIVE TWO-COMPONENT CONDUCTOR MADE OF NANOSTRUCTURAL ALUMINUM ALLOYS BY THE FINITE ELEMENT METHOD
E.A.Klimov1, Master, M.Yu.Murashkin1, 2, Cand. of Sci. (Technical), Senior Researcher
DOI: 10.22184/1993-8578.2021.14.2.150.158
Получено: 30.11.2020 г.
In this paper the finite element method is used to assess the rational design of a prospective two-component conductor made of nanostructured aluminum alloys to ensure the required level of strength.
INTRODUCTION
Aluminum is the second conductor after copper in terms of electrical conductivity. Therefore, it is natural that the use of aluminum and aluminum-based alloys as electrical conductors in the last decade has expanded significantly, already accounting for more than 10% of the total consumption of aluminum in the world [1, 2]. Due to a combination of low weight, good electrical conductivity and technological plasticity, as well as high resistance to atmospheric corrosion, aluminum and a number of aluminum-based alloys are increasingly used in power systems and electrical networks, including land and air transport [1–5], displacing heavier and more expensive copper conductor materials. To move forward in this direction, it is necessary to solve a complicated problem of creating new conductive materials based on aluminum, which have strength characteristics comparable to their copper counterparts, as well as electrical conductivity close to pure aluminum.
Nowadays, intensive research is underway to develop high-strength conductors by creating new alloys and composites based on aluminum, as well as methods of their processing [6–10].
Recent studies have shown that a very effective approach, which allows to dramatically improve properties of conductive aluminum alloys, is the formation of regulated nanostructural states in them using the methods of severe plastic deformation (SPD) [11–13]. In order to further improve the complex of properties of nanostructured alloys, studies are currently underway to create two-component conductors on their basis, for example, such as Al/Al, Al/Fe or Cu/Al, in the processing of which such SPD methods are used as equal channel angular pressing (ECAP) [14–16]. However, the selection of the optimal ratio of conductive and reinforcing materials in such conductors, carried out in the course of full-scale experiments, is a very long, technically complex and costly procedure. This paper presents an example of the use of digital technologies – finite element modeling (FEM) to determine the rational design of a two-component conductor made of nanostructured aluminum alloys to ensure the required level of strength.
RESEARCH METHODS
The materials used in this research were alloy 6101 of standard chemical composition (0.59Mg, 0.54Si, 0.07Fe, impurities not exceeding 0.01 wt%, rest Al) as well as aluminum for electrical purposes, grade 1350 (99.5 wt% Al), obtained by the traditional method of combined casting and rolling in the form of 12 mm dia. long rods (wire rod).
Formation of an ultrafine-grained (UFG) structure with specified nanoscale parameters in a wire made of the selected alloys was carried out by the ECAP method according to the Conform scheme (ECAP-K) followed by cold drawing (CD) [12, 13].
Mechanical tensile tests of the wire were carried out on a Shimadzu AG-XD testing machine in accordance with the requirements of GOST 10446-80. Specific electrical resistance was measured by a BSZ-010-2 microohmmeter according to GOST 7229-76.
Microstructure studies were accomplished by transmission electron microscopy on a Jeol JEM-2100 microscope with an accelerating voltage of 200 kV.
The ultimate strength (sВ) of two-component samples was determined by simulating tensile tests with the aid of the finite element method (FEM) and Computer-Aided Engineering (CAE) software package.
When modeling the of sВ value by the FEM use was made of:
The tensile test was simulated on cylindrical billets of a two-component sample made of aluminum alloys: a core diameter of 4 to 1 mm, a 5 mm outer diameter holder and a 150 mm long working section.
RESULTS
As a result of processing by the ECAP-K method, a uniform UFG structure is formed in the wire rod of 1350 and 6101 alloys with an average grain size of 1200 and 670 nm respectively, having a shape close to equiaxial. During SPD a formation of UFG grains in 6101 alloy is accompanied by precipitation of nanosized particles of the Mg2Si phase strengthening from the aluminum solid solution due to strain aging. These changes in the microstructure are characteristic of the aluminum alloys subjected to SPD [11–13]. Subsequent cold drawing (CD) leads to formation of the grains elongated along the drawing axis (Fig.1a, b). Their width in the wire of 1350 and 6101 alloys is 350...600 nm and 150...300 nm, respectively. In the cold-drawn wire cross section the equiaxed grains of the same size range are observed (Fig.1c).
As a result of CD, the nanosized particles of the Mg2Si phase do not undergo any noticeable changes in shape and size; they are located along the drawing axis (Fig.1b), mainly along the grain boundaries formed by SPD. The appearance of the electron diffraction pattern (Fig.1c) indicates that the microstructures formed in the wire of the studied materials as a result of ECAP-K and CD treatment with nanosized precipitates of particles of the hardening phase belong to a grain-type structure formed, predominantly, by a mesh of high-angle boundaries.
As a result of the described above microstructure formation, the ultimate strength of the 1350 and 6101 alloys wire was 218±4 MPa and 426±5 MPa (Fig.2a). In this case, the wire showed a fairly high plasticity (≥ 4%). The electrical conductivity of the wire in 1350 and 6101 alloys was equal to 61.1 and 51.2% IACS, respectively.
An analysis of the experimental results has proved that formation of an UFG structure with nanosized particles made it possible to achieve strength values in a wire of an aluminum 6101 alloy that exceeds the corresponding values of a wire made of copper alloys [11]. However, the conductivity level of high-strength wire is not high enough.
As noted above, one of the ways to effectively control a set of properties, including electrical conductivity, is to create two-component conductors wherein the content of components providing strength or electrical conductivity is selected by results of a physical experiment [15, 16].
To create an aluminum-based conductor with a strength comparable to their copper counterparts (≥400 MPa), simulations of tensile tests of a two-component aluminum wire by the FEM were carried out and their results were used to determine the values of sВ depending on the ratio of the areas of the core made of 1350 alloy with high electrical conductivity and high-strength 6101 alloy. Before simulation, all necessary alloys properties required for the corresponding analysis were established, including the stress-strain curves for each of them and selection of the optimal mesh size for the analysis (Fig.2a).
The Mises model is used to describe the behavior of the material. The yield criterion is presented as:
, (1)
where σ is the effective stress and σy is the yield stress obtained in the tests. Material properties, in particular, modulus of elasticity, yield stress, etc. were obtained from the stress-strain diagram. Simulation of a tensile test on a composite specimen was considered as a non-linear problem. The analysis control method is the load increment according to the Newton-Raphson algorithm. The convergence of the force is used as a scheme for finishing the analysis:
|t+∆t{R}-t+∆t{F}(i)|
<εf|t+∆t{R}-t{F}|, (2)
here t+∆t{R} is the vector of external applied nodal loads, t+∆t{F} is the vector of internal forces generated at the nodes, t+∆t is the time step.
Figure 3 illustrates the stress plots for simulation of tension of two-component aluminum specimens with different ratios of the yoke and core diameters. The ferrule diameter was 5 mm, the core diameter varied from 1 to 4 mm. Based on the simulation results, the strength limits of a two-component nanostructured wire were established, which varied from 294 to 421 MPa depending on the core diameter (Fig.2b).
DISCUSSION
It is shown that the formation of an UFG structure containing nanosized particles of the strengthening phase Mg2Si in the wire samples of the 6101 alloy of the Al–Mg–Si system makes it possible to realize a high-strength state in it (sВ = 426 MPa). The achieved level of strength exceeds the strength of a number of conductors made of copper-based materials [11].
Microstructure refinement also made it possible to achieve good strength (sВ = 218 MPa) in 1350 aluminum, while maintaining the electrical conductivity at a high level (61.1% IACS). The experimentally obtained results indicate that the microstructural design of electrical materials, widely used in various branches of electrical engineering, implemented by processing them and combining the SPD method and CD traditional metal forming can lead to a significant improvement of its properties, for example, strength.
Further improvement of the physical and mechanical properties balance is possible by a study of the two-component conductor on the basis of the research materials.
Modeling the tensile process of a two-component conductor made it possible to establish a dependence of the ultimate strength on the core diameter (see Fig.4) which defines that the core diameter should be 1–2 mm in order to create 5 mm dia. two-component conductors providing for a strength of about 400 MPa at a level comparable to copper alloys.
Based on the results of sВ calculation, by means of the FEM, of a two-component sample consisting of a core and a cage, the following empirical dependence was obtained:
, (3)
here σв(°б) > σв(серд) и δр(°б) ≥ δр(серд).
If δр(°б) < δр(серд), then σв(°б) must be interpolated according to the tension diagram obtained experimentally, where δр=∆l/l – uniform deformation in tension; S – cross-sectional area; σв is the ultimate strength of the material.
CONCLUSIONS
This work has analysed the rational design of a two-component conductor in the form of a wire made of 6101 nanostructured high-strength alloy and aluminum of 1350 electrical aluminum grade by simulating tensile tests with the aid of the finite element method.
Based on the results of the analysis performed by the FE method it was found that to create a two-component conductor consisting of a high-strength shell (alloy 6101) and a core (alloy 1350) with increased electrical conductivity providing strength ≥400 MPa at a level comparable to copper alloys, it is necessary to meet the condition S(серд)/S(пр) ≤ 0.16.
Calculations performed on the simulation test results made it possible to derive an empirical dependence for calculating the ultimate strength of a two-component conductor which can be used for other two-component systems made of metals and alloys for both electrical and structural purposes. ■
ACKNOWLEDGEMENTS
The authors are grateful to the Russian Science Foundation for financial support of the project No. 17-19-01311.
Declaration of competing interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
E.A.Klimov1, Master, M.Yu.Murashkin1, 2, Cand. of Sci. (Technical), Senior Researcher
DOI: 10.22184/1993-8578.2021.14.2.150.158
Получено: 30.11.2020 г.
In this paper the finite element method is used to assess the rational design of a prospective two-component conductor made of nanostructured aluminum alloys to ensure the required level of strength.
INTRODUCTION
Aluminum is the second conductor after copper in terms of electrical conductivity. Therefore, it is natural that the use of aluminum and aluminum-based alloys as electrical conductors in the last decade has expanded significantly, already accounting for more than 10% of the total consumption of aluminum in the world [1, 2]. Due to a combination of low weight, good electrical conductivity and technological plasticity, as well as high resistance to atmospheric corrosion, aluminum and a number of aluminum-based alloys are increasingly used in power systems and electrical networks, including land and air transport [1–5], displacing heavier and more expensive copper conductor materials. To move forward in this direction, it is necessary to solve a complicated problem of creating new conductive materials based on aluminum, which have strength characteristics comparable to their copper counterparts, as well as electrical conductivity close to pure aluminum.
Nowadays, intensive research is underway to develop high-strength conductors by creating new alloys and composites based on aluminum, as well as methods of their processing [6–10].
Recent studies have shown that a very effective approach, which allows to dramatically improve properties of conductive aluminum alloys, is the formation of regulated nanostructural states in them using the methods of severe plastic deformation (SPD) [11–13]. In order to further improve the complex of properties of nanostructured alloys, studies are currently underway to create two-component conductors on their basis, for example, such as Al/Al, Al/Fe or Cu/Al, in the processing of which such SPD methods are used as equal channel angular pressing (ECAP) [14–16]. However, the selection of the optimal ratio of conductive and reinforcing materials in such conductors, carried out in the course of full-scale experiments, is a very long, technically complex and costly procedure. This paper presents an example of the use of digital technologies – finite element modeling (FEM) to determine the rational design of a two-component conductor made of nanostructured aluminum alloys to ensure the required level of strength.
RESEARCH METHODS
The materials used in this research were alloy 6101 of standard chemical composition (0.59Mg, 0.54Si, 0.07Fe, impurities not exceeding 0.01 wt%, rest Al) as well as aluminum for electrical purposes, grade 1350 (99.5 wt% Al), obtained by the traditional method of combined casting and rolling in the form of 12 mm dia. long rods (wire rod).
Formation of an ultrafine-grained (UFG) structure with specified nanoscale parameters in a wire made of the selected alloys was carried out by the ECAP method according to the Conform scheme (ECAP-K) followed by cold drawing (CD) [12, 13].
Mechanical tensile tests of the wire were carried out on a Shimadzu AG-XD testing machine in accordance with the requirements of GOST 10446-80. Specific electrical resistance was measured by a BSZ-010-2 microohmmeter according to GOST 7229-76.
Microstructure studies were accomplished by transmission electron microscopy on a Jeol JEM-2100 microscope with an accelerating voltage of 200 kV.
The ultimate strength (sВ) of two-component samples was determined by simulating tensile tests with the aid of the finite element method (FEM) and Computer-Aided Engineering (CAE) software package.
When modeling the of sВ value by the FEM use was made of:
- model – solid, core material – alloy 1350, cage material – alloy 6101 of the Al–Mg–Si system;
- time increment – auto-step;
- mesh on a solid: four Jacobian points with a maximum (1 mm) and a minimum (0.2 mm) element size;
The tensile test was simulated on cylindrical billets of a two-component sample made of aluminum alloys: a core diameter of 4 to 1 mm, a 5 mm outer diameter holder and a 150 mm long working section.
RESULTS
As a result of processing by the ECAP-K method, a uniform UFG structure is formed in the wire rod of 1350 and 6101 alloys with an average grain size of 1200 and 670 nm respectively, having a shape close to equiaxial. During SPD a formation of UFG grains in 6101 alloy is accompanied by precipitation of nanosized particles of the Mg2Si phase strengthening from the aluminum solid solution due to strain aging. These changes in the microstructure are characteristic of the aluminum alloys subjected to SPD [11–13]. Subsequent cold drawing (CD) leads to formation of the grains elongated along the drawing axis (Fig.1a, b). Their width in the wire of 1350 and 6101 alloys is 350...600 nm and 150...300 nm, respectively. In the cold-drawn wire cross section the equiaxed grains of the same size range are observed (Fig.1c).
As a result of CD, the nanosized particles of the Mg2Si phase do not undergo any noticeable changes in shape and size; they are located along the drawing axis (Fig.1b), mainly along the grain boundaries formed by SPD. The appearance of the electron diffraction pattern (Fig.1c) indicates that the microstructures formed in the wire of the studied materials as a result of ECAP-K and CD treatment with nanosized precipitates of particles of the hardening phase belong to a grain-type structure formed, predominantly, by a mesh of high-angle boundaries.
As a result of the described above microstructure formation, the ultimate strength of the 1350 and 6101 alloys wire was 218±4 MPa and 426±5 MPa (Fig.2a). In this case, the wire showed a fairly high plasticity (≥ 4%). The electrical conductivity of the wire in 1350 and 6101 alloys was equal to 61.1 and 51.2% IACS, respectively.
An analysis of the experimental results has proved that formation of an UFG structure with nanosized particles made it possible to achieve strength values in a wire of an aluminum 6101 alloy that exceeds the corresponding values of a wire made of copper alloys [11]. However, the conductivity level of high-strength wire is not high enough.
As noted above, one of the ways to effectively control a set of properties, including electrical conductivity, is to create two-component conductors wherein the content of components providing strength or electrical conductivity is selected by results of a physical experiment [15, 16].
To create an aluminum-based conductor with a strength comparable to their copper counterparts (≥400 MPa), simulations of tensile tests of a two-component aluminum wire by the FEM were carried out and their results were used to determine the values of sВ depending on the ratio of the areas of the core made of 1350 alloy with high electrical conductivity and high-strength 6101 alloy. Before simulation, all necessary alloys properties required for the corresponding analysis were established, including the stress-strain curves for each of them and selection of the optimal mesh size for the analysis (Fig.2a).
The Mises model is used to describe the behavior of the material. The yield criterion is presented as:
, (1)
where σ is the effective stress and σy is the yield stress obtained in the tests. Material properties, in particular, modulus of elasticity, yield stress, etc. were obtained from the stress-strain diagram. Simulation of a tensile test on a composite specimen was considered as a non-linear problem. The analysis control method is the load increment according to the Newton-Raphson algorithm. The convergence of the force is used as a scheme for finishing the analysis:
|t+∆t{R}-t+∆t{F}(i)|
<εf|t+∆t{R}-t{F}|, (2)
here t+∆t{R} is the vector of external applied nodal loads, t+∆t{F} is the vector of internal forces generated at the nodes, t+∆t is the time step.
Figure 3 illustrates the stress plots for simulation of tension of two-component aluminum specimens with different ratios of the yoke and core diameters. The ferrule diameter was 5 mm, the core diameter varied from 1 to 4 mm. Based on the simulation results, the strength limits of a two-component nanostructured wire were established, which varied from 294 to 421 MPa depending on the core diameter (Fig.2b).
DISCUSSION
It is shown that the formation of an UFG structure containing nanosized particles of the strengthening phase Mg2Si in the wire samples of the 6101 alloy of the Al–Mg–Si system makes it possible to realize a high-strength state in it (sВ = 426 MPa). The achieved level of strength exceeds the strength of a number of conductors made of copper-based materials [11].
Microstructure refinement also made it possible to achieve good strength (sВ = 218 MPa) in 1350 aluminum, while maintaining the electrical conductivity at a high level (61.1% IACS). The experimentally obtained results indicate that the microstructural design of electrical materials, widely used in various branches of electrical engineering, implemented by processing them and combining the SPD method and CD traditional metal forming can lead to a significant improvement of its properties, for example, strength.
Further improvement of the physical and mechanical properties balance is possible by a study of the two-component conductor on the basis of the research materials.
Modeling the tensile process of a two-component conductor made it possible to establish a dependence of the ultimate strength on the core diameter (see Fig.4) which defines that the core diameter should be 1–2 mm in order to create 5 mm dia. two-component conductors providing for a strength of about 400 MPa at a level comparable to copper alloys.
Based on the results of sВ calculation, by means of the FEM, of a two-component sample consisting of a core and a cage, the following empirical dependence was obtained:
, (3)
here σв(°б) > σв(серд) и δр(°б) ≥ δр(серд).
If δр(°б) < δр(серд), then σв(°б) must be interpolated according to the tension diagram obtained experimentally, where δр=∆l/l – uniform deformation in tension; S – cross-sectional area; σв is the ultimate strength of the material.
CONCLUSIONS
This work has analysed the rational design of a two-component conductor in the form of a wire made of 6101 nanostructured high-strength alloy and aluminum of 1350 electrical aluminum grade by simulating tensile tests with the aid of the finite element method.
Based on the results of the analysis performed by the FE method it was found that to create a two-component conductor consisting of a high-strength shell (alloy 6101) and a core (alloy 1350) with increased electrical conductivity providing strength ≥400 MPa at a level comparable to copper alloys, it is necessary to meet the condition S(серд)/S(пр) ≤ 0.16.
Calculations performed on the simulation test results made it possible to derive an empirical dependence for calculating the ultimate strength of a two-component conductor which can be used for other two-component systems made of metals and alloys for both electrical and structural purposes. ■
ACKNOWLEDGEMENTS
The authors are grateful to the Russian Science Foundation for financial support of the project No. 17-19-01311.
Declaration of competing interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Readers feedback
