1. Introduction
Abundant copper demand for electrical applications from various sectors has prompted manufacturers to reduce material costs by replacing this rather expensive and high-density metal partly or entirely. Lower-density and more affordable aluminum-copper (Al-Cu) composite wire is an example of such efforts. The following paragraphs provide a summary of the different features of Al-Cu wires and several other similar composite systems (developed by various techniques) already investigated. The missing aspects and the property of interest to be researched in the current work are then presented at the end of this section. Among those already-studied features are the investigations covering the mechanical behavior and finite element modelling of the manufacture processes of severely cold worked composite systems akin to the one under study in this work. Khosravifard and Ebrahimi [
1] investigated the parameters affecting the interface strength of extruded Al/Cu clad bimetal rods along with FEM analysis of the extrusion process. Feng et al. [
2] examined the compressive mechanical behavior of Al/Mg composite rods with different types of Al sleeve.
Gu et al. [
3] modelled the elastic behavior of architectured and nanostructured Cu–Nb composite wires produced by accumulative drawing and bundling (a severe plastic deformation technique) in a multiscale manner. Priel et al. [
4] did a computational study (validated by experiments) on co-extrusion of an Mg/Al composite billet and suggested a set-up named “Floating Core” as being ideal.
Knezevic et al. [
5] made a comparison between three die designs with a material-based approach towards the extrusion of bimetallic tubes discussing the criteria that are to be met for proper solid-state bonding.
Moreover, a great deal of research has been done addressing the mechanical behavior of metallic and non-metallic fiber-reinforced composites. Ochiai [
6] performed an extensive study on the effect of interface on deformation and fracture behavior of metallic matrix fiber-reinforced composites. Kelly and Lilholt [
7] researched stress-strain curve of a fiber-reinforced composite of tungsten wires embedded in a pure copper matrix. Kelly and Tyson [
8] studied tensile properties of metallic fiber-reinforced composite systems of copper/tungsten and copper-molybdenum. Ebert et al. [
9] analyzed the stress-strain behavior of concentric composite cylinders. Sapanathan et al. [
10] spiral extruded an aluminum/copper composite to study its bond strength and interfacial characteristics. Hao et al. [
11] developed a novel multifunctional NiTi/Ag hierarchical composite, inspired by the hierarchical design of the tendon, by repeated assembling and wire drawing. Tyson and Davies [
12] investigated the shear stresses associated with stress transfer during fiber reinforcement with the help of photoelasticity. Superconducting materials embedded into a copper matrix as multifilaments [
13] and aluminum-steel fiber composites [
14] are the other systems with similarities to the Al-Cu composites under investigation in the current study.
The conventional copper-clad aluminum wire (CCA or single-Al-fiber Al-Cu composite wire) is currently being widely used in the electrical industry [
15]. Architectured copper-clad aluminum wire (ACCA or multi-Al-fiber Al-Cu composite wire), however, has proved to be superior in a variety of areas offering improved thermal diffusivity [
16] and proper electrical conductivity at both low and high frequencies. Moreover, in a previous article, the authors have reported that ACCA samples exhibit rather complex mechanical behavior in both as-drawn and heat-treated states (see [
17] for more details).
The novelty of this work is the investigation of the origin of the understudied mechanical behavior of the novel architectured Cu-Al composite wires and its promising implications in terms of the in-service reliability. The objective of this article is then to better understand the mechanical behavior of Cu-Al wires with different fiber-matrix configurations. Along with the conventional CCA wire, two architectured configurations (ACCA) with different numbers of Al fibers were investigated. A first assessment of the mechanical properties based on the experimental tensile curves is proposed, revealing improved flow stress for architectured configurations.
Numerical simulations of CCA and ACCA configurations were then performed to find the impact of fiber-matrix configurations on the axial stress-strain behavior of these materials. Particularly, the influence of I- transverse interactions and II- processing-induced residual stresses on the mechanical behavior were investigated. The use of finite element analysis is necessary when dealing with the mechanical behaviors that are not easy to understand and interpret experimentally. Crack and fracture behavior are instances of such studies [
18,
19]. A great complexity in the current work is the experimental measurement of radial and circumferential stresses developing at the interface of the fine Al fibers (tens of micron wide) and the Cu matrix during tensile testing of Arcitectured and even conventional Cu-Al wires. The results show that the processing-induced residual stresses most probably explain the exceptional mechanical properties of architectured wires.
2. Material and Experimental Procedure
Copper clad aluminum wires are produced by cold-drawing. For all wires, fully annealed high purity Oxygen Free High Conductivity (OFHC) copper and 99.5% pure Al were employed. For the fabrication of CCA, a copper tube of an outer diameter of 12 mm and inner diameter of 8 mm and an approximately 8 mm-aluminum rod were simultaneously cold-drawn down to 3 mm. For the ACCA drawing, CCA wires were restacked in a copper tube and were further cold-drawn. For these specific architectured wires, two configurations were manufactured, one with 61 restacked 1 mm-CCA wires (labelled ACCA
61) and a second one with 22 restacked 1.7 mm-wires (labelled ACCA
22). All wires were cold-drawn down to 3 mm without inter-operational heat-treatments. For the CCA wires, the aluminum volume fraction is about 50% whereas values of 25% and 32% are associated to the ACCA
61 and ACCA
22, respectively. Details about the manufacturing process can be found in the two previous articles [
15,
17]. The corresponding cross-sections of the three microstructures, imaged via optical microscopy, are illustrated in
Figure 1.
Simulation of the CCA and ACCA behavior under tensile loading requires the stress-strain data of each component (Al and Cu). For that reason, as-drawn samples of both pure Cu and Al with the aforementioned compositions (threes samples each) were prepared for tensile testing to provide the FEA software with the required input. To prepare the above tensile test samples, an aluminum rod and a copper rod of the same initial diameter of 8 mm, heat-treated for three hours at 300 °C and 500 °C respectively, were cold drawn down to 2 mm each. This was to have the same amount of plastic deformation undergone by a 3 mm-CCA composite wire (considered for simulations) stored in pure Al and Cu samples.
The final diameter of the rods was obtained from the following relation for calculating the drawing strain:
where D
0 and D are the initial and final diameters respectively. An MTS Criterion Model 43 10 kN-universal testing machine (MTS, Eden Prairie, MN, USA) was used to perform displacement-controlled tensile tests at room temperature and the strain was measured via a conventional 25 mm-gage length extensometer. Samples were mounted on specialized wire tensile testing grips to minimize stress concentration and were strained at an initial strain rate of 0.004 s
−1 to avoid possible viscous effects.
Engineering stress-strain curves of experimentally tensile-tested pure Al and Cu are plotted in
Figure 2. The following curves were then converted into true stress-strain curves and were used as input for elastoplastic simulation of CCA and ACCA wires.
3. Numerical Procedure
A comprehensive explanation of the simulation approach is presented in the first subsection. The second subsection is devoted to the simulation details.
3.1. Parameters and Methodology
The application of finite element method made it possible to effectively study various parameters involved from a behavioral perspective. Assumptions such as perfect fiber-matrix interface and isotropic behavior were made for the sake of simplicity. As mentioned earlier, the two key factors I- transverse stresses and II- residual stresses (RS) were investigated in a set of numerical simulations. To this end, evolution of transverse (radial and circumferential) stress components under a tensile load was modelled in both elastic and elastoplastic domains for CCA samples.
Tensile elastic-plastic behavior of an ACCA model, created from an actual microstructure, was also studied to discover the potentially distinct development of lateral stresses in this novel configuration. For the sake of conciseness, only the ACCA61 configuration was considered for simulation. The effect of predefined fields of residual stress in both CCA and ACCA wires was also studied independently. The idea was to realize how significant the contribution of lateral and residual stresses could be to the axial stress-strain behavior of these bimetallic composites separately. CCA simulations hold clues to understanding the more complex tensile behavior of the architectured samples (ACCAs).
3.1.1. Transverse Stresses
CCA Elastic Simulations
There are complexities associated with the elastoplastic behavior of these materials, originating from the formation of yield fronts and gradual elastic-to-plastic transition [
9]. In a first attempt to avoid those intricacies, a number of elastic-domain CCA wire simulations were independently run, with the major parameters involved in the evolution of transverse stresses taken into consideration. Those parameters include Young’s modulus and Al/Cu volume fraction.
Therefore, two 10-mm-long CCA samples of the same outer diameter of 3 mm (arbitrary dimensions), containing an aluminum core and a copper case were modelled. One of the two samples contains 75% Al (2.6 mm-Al core) and the other 25% Al (1.5 mm-Al core). The volume fraction of the experimental CCA wire lies in between these two values. This was to account for the role of volume fraction when one of the phases prevails.
It is known from the literature that the elastic behavior of pure copper is largely anisotropic. Its Young’s modulus depends on the texture developments and can range between 60 and 200 GPa as plotted and discussed by Pal-Val et al. [
20] for different crystallographic directions. For that reason, three different Young’s modulus values of 60, 170 and 200 GPa, corresponding to the dominance of [001], [011] and [111] orientations in the order given, were chosen to take account of Young’s modulus effect. Unlike Cu, the elastic behavior of Al is almost isotropic and the Young’s modulus alterations of pure aluminum and many aluminum alloys, following cold working and heat-treatment, vary slightly by 10 percent at most [
21]. Hereby, an average value of 70 GPa was considered for Al. The elastic-domain impact of Poisson’s ratio value difference between the components of bimetallic fiber-composites is generally trivial [
9]. In summary, three Young’s modulus values for Cu and 2 volume fractions were opted for a total number of 6 simulations. The CCA elastic simulations are summarized in
Table 1.
CCA and ACCA Elastoplastic Simulations
It is known that radial and circumferential stresses may become more important in terms of contribution to the axial stress-strain behavior as one of the two phases in a bimetallic cylindrical composite plasticizes first and the other remains elastic within a certain strain range. This is because the already-yielded component could be assumed to have a Poisson’s ratio of 0.5 (due to the incompressible nature of plasticity) and the other would still possess the elastic-domain Poisson’s ratio value. Therefore, the difference between the values of Poisson’s ratio of the two materials would become greater for a certain range of strain before the elastic component begins to behave plastically as well [
9].
Hereby, numerical tensile testing of a set of 3 mm-diameter CCA wires (actual dimension) of four different Al/Cu volume fractions was opted to be modelled with elastic-plastic behavior (without accounting for the Al/Cu interface and residual stresses). Four volume fractions were chosen to have a statistically better approximation of the order of magnitude of transverse stresses. The goal was to discover the degree to which lateral stresses, alone, can possibly influence the tensile behavior.
Table 2 lists all the CCA elastoplastic simulations performed.
Having insights provided from the elastoplastic simulation of CCA wires, a 3-mm diameter ACCA
61 wire was modelled from the actual microstructure of its transversal cross section (see
Figure 3a). The wire contains 61 Al fibers (about 25 percent of the total volume fraction) embedded in a Cu matrix. The corresponding finite element models are presented in
Figure 3a,b.
3.1.2. Residual Stresses
Mechanical residual stresses built up during cold drawing of metals are known to come from the non-uniform nature of plastic deformation in this process. There is a qualitative feature from the literature based on which residual stress simulations are argued in this paper. This feature is the formation of a rather wide range of compressive residual stresses in the central part of a cold-drawn bar and a narrower range of tensile residual stress in its outer part, away from the center. Axial tensile residual stresses forming near the wire surface have detrimental effects on the tensile strength of drawn wires. Modifying the residual profile through the wire cross section by reducing those stresses and boosting the formation of compressive residual stresses favors the yield strength [
22]. Atienza and Elices [
23] suggest such RS distribution for cold drawn steel wires investigated both numerically and experimentally. Ripoll et al. [
24] report a similar RS distribution pattern in their investigation of tungsten wires. Bullough and Hartley [
25] introduce an analytical model for co-deformed Cu-Al rods confirming the above-mentioned RS distribution.
Consistent with the literature on the magnitude and distribution pattern of drawing-induced residual stresses, a behavioral assessment was conducted. One objective was to analyze how the distinct fiber-matrix configuration of an ACCA sample can possibly affect the axial stress-strain behavior of Al-Cu composite wires of the same Al/Cu volume fraction but different architecture.
For the sake of simplicity, this comparison was made irrespective of the fact that ACCA is more strained than CCA and more compressive residual stresses are expected to form in architectured wires. Hereby, the aforementioned 3-mm ACCA sample containing about 25% Al and its corresponding 3-mm CCA sample with 25% Al were considered.
Same-diameter cylinders of compressive residual stress were defined in the center of both wires with hollow cylinders of the same width under tensile residual stress, as illustrated in
Figure 4a,b. Residual stress modelling and analyses were based on the values reported for copper-clad aluminum wires fabricated by hydrostatic extrusion [
25]. The analytical model proposed in [
25] is applicable for both hydrostatic extrusion and wire drawing processes and provides a good first approximation for this behavioral evaluation. Simulation details are presented in the following section. It must be noted that all the above simulations were merely intended to test the assumptions made earlier regarding the role of transverse and residual stresses and no verification of the experimental results was planned. Indeed, the exact development of residual stresses in the architectured composite wires is not straightforward. The simulations were applied towards identifying the potential source of the strengthening effect observed in the architectured Cu-Al wires (reported by [
17]).
3.2. Numerical Modelling Details
The FEA software Abaqus/CAE (ABAQUS Inc., Johnston, RI, USA) was utilized to perform all simulations. All CCA samples were meshed using a mixture of hexahedral elements of type ‘C3D8R’ and wedge elements of type “C3D6′ (both of linear geometric order, from the standard element library) to generate a regular symmetric mesh. However, the ACCA sample was meshed using only hexahedral elements. Independent Al and Cu parts were then assembled by merging the interfacial elements that satisfies the perfect interface assumption and allows the development of transverse stresses. All models were assigned a boundary condition of type “ZSYMM” (symmetry about a constant z-plane) on the fixed end.
An arbitrary displacement of 0.005 mm (0.05% strain—within the reasonable range of elastic domain) was applied on all the CCA elastic models listed in
Table 1. Engineering stress-strain data from tensile testing of the as-drawn pure Al and pure Cu samples were calibrated and converted into true stress-strain curves in Abaqus/CAE as input for elastoplastic simulation of the 3-mm diameter CCA samples mentioned in the previous section.
The elastic-plastic behavior of the aforementioned ACCA sample (≈25% Al) of a gauge length of 25 mm was also studied by straining it up to one percent. The use of CCA input for simulating the tensile testing of ACCA is acceptable to a fairly good approximation due to stress saturation in both Al and Cu at high strains (see [
17]). Chinh et al. [
26] also report stress saturation in highly strained Al.
In order to model the elastic-plastic behavior of CCA and ACCA composite wires in presence of residual stresses, the 25%Al-ACCA wire and its corresponding CCA sample (containing 25% Al) were chosen. Next, for comparison purposes, a cylindrical section of the same diameter of 1.5 mm was defined in the center of both ACCA and CCA samples. As explained in the previous section, residual stress values for simulation were taken from Ref. [
25]. Therefore, predefined stress fields of −90 MPa (compressive) in the central cylinder and +10 MPa (tensile) in the remaining hollow cylinder were defined.
It should be noted that the aforementioned values were considered as single uniform values through the cross section of the wire rather than the actual curved-shape residual stress distributions (see the references presented in
Section 3.1.2 Residual Stresses). This analytical model-based assumption was made for the sake of simplicity and comparison and does not satisfy the residuals stresses’ self-equilibrium requirement. It is however consistent with the literature in terms of the sign of expected residual stresses. Furthermore, to emphasize the favorable impact of compressive residual stresses in the central section of ACCA samples and to reveal its implication for the research problem, a separate simulation with −120 MPs (rather than −90 MPa) and +10 MPa was performed.