1 Introduction

Fastening and resistance spot welding are two of the most widespread processes for producing lap joints in sheets or plates. Fastening belongs to the so-called group of mechanical joining processes [1] and fixes the two sheets together by applying a force directly on the sheet surfaces by means of conventional bolts or rivets (Fig. 1). Resistance spot welding [2] belongs to the group of thermal-based joining process and makes use of a molten nugget that is formed by the passage of a low-voltage, high electric current, between two electrodes to fix the overlapped sheets together (Fig. 1). Resistance element welding and laser welding are examples of other processes that belong to this group and are commonly used to produce lap joints in sheets or plates.

Fig. 1
figure 1

Different types of processes to produce lap joints in sheets or plates. The asterisk refers to the process shown in the schematic drawing

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Despite the widespread use of fastening and resistance spot welding, there are important drawbacks resulting from the development of non-uniform contact pressures on the overlapped surfaces, the self-loosening of bolts, and the weldability problems caused by sheets (or plates) with large thicknesses and made from dissimilar materials [3]. Adhesive bonding (Fig. 1) overcomes some of these problems, but its use in mass production is constrained by additional requirements related to surface preparation, curing time, service temperature, durability, and environmental compliance [4].

Joining by plastic deformation (Fig. 1) belongs to a subset of the mechanical joining group that is characterized by combining plastic deformation with at least one of the three following physical closure mechanisms; (i) form-closure, (ii) force-closure, and (iii) material-closure [5]. Self-pierce riveting and clinching are examples of joining by plastic deformation processes with and without auxiliary elements that make use of form and force-closure mechanisms to produce lap joints in sheets or plates [6]. Cold pressure welding is a joining by plastic deformation process without auxiliary elements that is based on a material-closure physical mechanism [7].

Self-pierce riveting [8] combines plastic deformation with fracture and formation of new surfaces to push a semi-tubular rivet through the upper sheet and flare its end into the lower sheet for assembling the two overlapped sheets together. The process applicability is limited to thin joints, in the range of 1.5 to 4 mm thickness, requires the thinner or softer sheets to be placed on the punch side, and gives rise to material protrusions above and below the sheet surfaces.

Clinching [9] is widely used in mass production of automotive, household appliances, and electronic components, to replace fastening and resistance spot welding. However, it requires sheets to be thin, the harder sheet to be placed on the punch side, and the material to be ductile enough to prevent failure by cracking. The main drawbacks of clinching are related to the contact pressures on the overlapped surfaces, which are not big enough for electrical or high strength mechanical applications, and to the extra space needed to accommodate material protrusions on the die side.

Competition between the different processes belonging to the groups shown in Fig. 1 often leads to situations in which a given process is more suitable than others for achieving the desired goals of a specific application. In energy distribution systems, for example, the commonly used solutions are based on mechanical or thermal based processes involving bolting, laser welding, or friction stir spot welding, but the overall thermo-electrical performance of the resulting joints is much lower than that of an ideal joint. In fact, in a recently published work [10], the authors showed that the electrical resistance of bolted (with 20 Nm torque) and friction stir spot–welded joints of hybrid busbars made from aluminum and copper sheets are 1.4 and 1.6 times higher than that of an ideal joint. This difference increases during service life due to chemical reactions, contaminant films, and unintentional self-loosening that reduces the contact pressures on the overlapped surfaces [11, 12].

In fact, the main reasons for the differences between the electrical resistance of the bolted and friction stir spot–welded joints against that of an ideal joint are attributed to the disturbance in the electrical current caused by the localized contact pressure, the material protrusions of the bolts and nuts, and the keyholes that are left by the rotating tool in the stir zone after being pulled out. Still, most of the electric vehicles make use of fastened busbar joints.

The state of technology and understanding that have been conveyed above stimulate the need for developing a new joining process capable of ensuring good contact pressures and making use of physical closure mechanisms hidden inside the two sheets to avoid material protrusions. In addition, the process to be developed must be also applicable to hybrid busbars made from dissimilar materials (e.g., copper and aluminum).

In view of the above, the aim of this paper is threefold:

  1. (i)

    To present a new joining by plastic deformation process named as “double-sided injection lap riveting” (or, simply, “double-sided ILR”), in which rivets made from a good electrical conductor material that is softer than the busbar sheets are injected by compression into the dovetail ring holes that are previously machined in both sheets to produce an invisible mechanical joint (Fig. 2a). The process is an evolution of the (single-sided) injection lap riveting that was earlier presented by the authors, in which the rivet is visible from one side and the dovetail ring hole is solely machined in the harder busbar sheet [13]

  2. (ii)

    To investigate the working principle of double-sided ILR and characterize the influence of its major geometric parameters (Fig. 2b) on the thermo-electrical performance of the busbar joints by means of experimentation and numerical simulation

  3. (iii)

    To demonstrate the enhanced thermo-electrical performance of the double-sided injection lap riveted joints and their suitability to be used in energy distribution systems by comparing their electrical resistances against those of bolted joints that are included in the presentation for comparison purposes.

Fig. 2
figure 2

Double-sided injection lap riveting. a Schematic representation of the machining and injection stages of the process. b Main geometric parameters of the tubular rivets and dovetail ring holes

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2 Materials and methods

2.1 Materials and mechanical characterization

The choice of busbars made from aluminum is aligned with the ongoing trend of replacing copper by aluminum. This is due to the rising price of copper resulting from its increasing demand in many of today’s existing and advancing technologies in the fields of transportation vehicles, industrial manufacturing, and production and distribution of energy, among others (Fig. 3). The goal is to give aluminum an importance similar to copper as a key material in energy transition and reduction of greenhouse gas emissions.

Fig. 3
figure 3

Price evolution of the copper and aluminum prices per metric ton in the last 2 years (data obtained from [14])

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Despite the lower electrical conductance of aluminum, requiring busbars to be 2.3 times thicker than those made from copper to ensure the same electric current capacity, the tendency is clearly favorable to aluminum busbars because they provide 32% mass reduction and approximately 80% cost savings for the same electrical conductance [15].

Under these circumstances, the investigation was performed in unit cells with 100 mm length and 50 mm width made from 2 and 5 mm thickness aluminum AA6082-T6 sheets that were designed to replicate the fabrication process and the thermo-electrical performance of the busbar joints in service. The mechanical characterization of the AA6082-T6 sheets was carried out in an Instron 4507 universal testing machine by means of tensile tests in specimens that were extracted from the sheets and tested in accordance with the ASTM standards E8/E8 M [16] (Fig. 4a). Table 1 provides a summary of the mechanical properties and of the true stress vs. true strain response after being approximated by means of a Holloman strain hardening model.

Fig. 4
figure 4

Layout and photographs of the equipment used in the a mechanical and b thermo-electrical characterizations of the materials and joints

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Table 1 Mechanical properties of the materials
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The tubular rivets were made from copper C11000 instead of aluminum AA6082-T6 for reasons that will be later discussed in the presentation. The mechanical characterization of copper C11000 was carried out by means of compression tests in specimens with 20 mm height and 20 mm diameter that were extracted from the rods used in the production of the rivets. The mechanical properties of the copper C11000 and the approximation of the true stress vs. true strain response by means of a Holloman strain hardening model are included in Table 1.

The mechanical properties of the medium carbon steel (class 8.8) included in Table 1 refer to the bolts and nuts of the fastened joints that were fabricated and tested for comparison purposes. These properties were retrieved from literature [17, 18].

2.2 Unit cells and thermo-electrical characterization

The unit cells utilized in the investigation are schematically pictured in Table 2. They were designed to replicate the double-sided injection lap riveted joints and the bolted joints.

Table 2 Geometry and process parameters of the unit cells utilized in the investigation
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The double-sided injection lap riveted joints were fabricated by forcing copper C11000 tubular rivets into the dovetail ring holes that were pre-drilled in the overlapped sheets (Fig. 2). Different sheet thicknesses \({t}_{s}\) and inner diameters \({d}_{i}\) were tested, as well as different fixing solutions involving more than one tubular rivet per connection. Other geometric ratios and parameters shown in Fig. 2, like the normalized depth ratio \({d}_{p}/{t}_{s}\), the thickness \(t\), and the inclination \(\alpha\) of the dovetail ring holes, were kept constant to ensure compatibility between the two sheet thicknesses \({t}_{s}\) utilized in the investigation.

The inner \({d}_{i}\) and outer \({d}_{o}\) diameters of the tubular rivets were machined in accordance with the geometry of the dovetail ring holes, whereas their length \(s\) varied to ensure the right amount of material to completely fill the holes.

The bolted joints required pre-drilling through holes of 8.4 mm in both sheets and installation and fastening of M8 hexagonal socket head bolts with 20 Nm tightening torque. Table 2 summarizes the geometric and process parameters utilized in the experiments.

The thermo-electrical characterization of the individual materials and unit cells was carried out in the experimental apparatus developed by the authors that is pictured in Fig. 4b In case of the unit cells shown in the figure, the specimens were held by copper block grippers along their edges and connected to an Oficel AC transformer that supplied an electric current of 1500 A during 10 to 20 min until the temperature of the joint, raised by Joule effect, reached a maximum value \({T}_{\mathrm{max}}=115\)°C. The temperature was measured at the center by means of an infrared Flir E86 camera and required painting the sheets (and the bolts and nuts in case of the bolted joints) in black to ensure the same emissivity values.

The thermo-electrical characterization of the unit cells was carried out during the cooling stage to the ambient temperature and began after reaching a temperature \({T}_{0}=105\) °C to match the limiting temperature established by the IEEE standard [19]. A four-point probe technique [20], using two measuring probes that were 100 mm distance apart and connected to a micro-ohmmeter KoCoS PROMET R600 supplying an electric current of 600 A during approximately 2 s, was used to measure the drop in voltage and determine the electrical resistance.

The electrical resistivity as a function of the temperature for the three different materials utilized in the investigation is given in Fig. 5. Further details on the thermo-electrical characterization procedure and on the determination of the electrical resistivity and electrical resistance are given in a paper that was recently published by the authors [21].

Fig. 5
figure 5

Electric resistivity vs. temperature for the three different materials utilized in the investigation. The values for copper C11000 and aluminum AA6082-T6 are to be read in the left vertical axis while those of medium carbon steel are to be read in the right vertical axis

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After performing the thermo-electrical characterization of double-sided injection lap riveted joints, some unit cells were chosen to be subjected to shear destructive tests for determining the maximum force that the joints can safely withstand. The tests were carried out at ambient temperature in the universal testing machine that was utilized in the mechanical characterization of the materials. Results of these tests are included in Sect. 3.

2.3 Numerical modelling

Numerical modelling of double-sided ILR was carried out in the finite computer program i-form [22] and involved two different mechanical and thermo-electrical types of analysis. Mechanical analysis was focused on the joining by plastic deformation process, in which tubular rivets were forced into the dovetail ring holes that were pre-drilled in the overlapped sheets. Figure 6a shows a cross section of a typical model consisting of three deformable objects and two rigid objects at the beginning and end of the joining process.

Fig. 6
figure 6

Different numerical models utilized in the analysis of the double-sided injection lap riveted unit cells: a Axisymmetric model for the mechanical analysis of the joining by plastic deformation. b Three-dimensional model for the thermo-electrical analysis of the joint in service

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The rivet and neighboring sheet materials were assumed to undergo rotational symmetric plastic deformation, and their cross sections were discretized by means of approximately 8000 quadrilateral elements. The upper and lower compression platens were assumed as rigid and discretized by means of linear contact elements with friction. Typical CPU time for this type of analysis was approximately 3 h in a computer equipped with an Intel Core i7-6950X processor.

The thermo-electrical analysis was focused on the electrical resistance and distribution of electric current in the double-sided injection lap riveted joints for different busbar service temperatures. For this purpose, authors created three-dimensional models like that shown in Fig. 6b that replicate half-width size of the unit cells. The rivet and sheets were discretized with approximately 60,000 hexahedral elements, and the copper block grippers were discretized with spatial triangular surface elements.

An interface layer of 0.05 mm thickness, and discretized by means of hexahedral elements, was also included in the thermo-electrical model. This layer was utilized to impose very high values of electric resistivity due to roughness and oxide films along the overlapped regions where the contact pressure at the end of the joining process is negligible or inexistent.

The overall simulation strategy consisted in creating a digital twin capable of replicating the experimental procedure that had been previously described in Sect. 2.2. For this purpose, an electric current of 1500 A was made to pass through the copper block grippers during a period of 10 to 20 min (depending on the process parameters of the unit cells) to raise the temperature of the sheets at the center up to a maximum temperature \({T}_{\mathrm{max}}=115\) °C. After reaching this temperature, the electric current was set to zero, and the sheets started to cool by convection and radiation to the environment until reaching the first measuring temperature \({T}_{0}=105\) °C. The measuring stage required passing an electric current of 600 A between the two measuring probes for approximately 2 s to determine the drop in voltage and calculate the electrical resistance. This procedure was repeated as many times as in the experiments until reaching the ambient temperature.

The computer program i-form utilized in the numerical modelling is being developed by the authors since the 1980s and performs the mechanical, thermal, and electrical finite element analyses by coupling the weak forms of the three fundamental governing equations,

$${\int }_{V}{\sigma }_{ij}^{\mathrm{^{\prime}}}\delta {D}_{ij}dV+{\int }_{V}K{D}_{v}\delta {D}_{v}dV-{\int }_{{S}_{t}}{t}_{i}\delta {u}_{i}dS=0$$
(1)
$${\int }_{V}{\nabla }^{2}\Phi \delta\Phi dV=0$$
(2)
$${\int }_{V}k\nabla T\nabla \left(\delta T\right)dV-{\int }_{{S}_{q}}{q}_{n}\delta Td{S}_{q}+{\int }_{V}\rho c\frac{dT}{dt}\delta TdV-{\int }_{V}\beta {\sigma }_{ij}{D}_{ij}\delta TdV=0$$
(3)

In the above equations, \(V\) is the control volume of a continuous body bounded by a closed surface \(S\) consisting of a region \({S}_{t}\), where tractions \({t}_{i}\) are applied and a region \({S}_{q}\) where the heat flux \({q}_{n}\) containing the heat dissipated by convection and radiation. The velocity \({u}_{i}\), the electric potential \(\Phi\), and the temperature \(T\) are the primary unknowns of each governing equation, and the remaining symbols are the deviatoric Cauchy stress \({\sigma }_{ij}^{\mathrm{^{\prime}}}\), the rate of deformation \({D}_{ij}\), the volumetric rate of deformation \({D}_{v}\) with the associated penalty function \(K\), the thermal conductivity \(k\), the volumetric heat capacity \(\rho c,\) and the fraction \(\beta\) of plastic work converted into heat.

Further details on the computer implementation of the three fundamental governing equations in the finite element computer program i-form are given in reference [22].

3 Results and discussion

3.1 Working principle of double-sided injection lap riveting

First observation of the double-sided injection lap riveted joints (Fig. 7) recalls those produced by double-sided self-pierce riveting, in which a tubular rivet made from a hard material is placed in between the two sheets to be joined and forced through the sheets by compression to create a mechanical interlocking [23]. However, in contrast to double-sided self-pierce riveting, the working principle of double-sided ILR is solely based on plasticity and friction, without propagation of cracks and creation of new surfaces.

Fig. 7
figure 7

Photograph and finite element computed geometry (at the beginning and end of the process) of the cross sections of double-sided injection lap riveted joints made from aluminum AA6082-T6 sheets with 5 mm thickness with: a one C11000 copper tubular rivet with \({d}_{i}=2\) mm, b one C11000 copper tubular rivet with \({d}_{i}=10\) mm, c one C11000 copper tubular rivet with \({d}_{i}=25\) mm, d two concentric C11000 copper tubular rivets with \({d}_{i}=2\) mm and \({d}_{i}=25\) mm

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The main reason behind this difference is the necessity of pre-drilling dovetail ring holes in double-sided ILR, which paves the way to the use of form-closure interlocks with customized undercuts filled with plastically deformed rivets made from materials that are identical or softer than those of the two overlapped sheets. All these features turn into a huge advantage in the assembly of busbars for energy distribution systems because rivets can be made from materials with good electrical conductivity (e.g., aluminum or copper) instead of being made from harder materials like steel with much poorer electrical conductivity.

Now, focusing our attention on the AA6082-T6 aluminum busbars with 5 mm thickness, it is the purpose of Fig. 7a-d to expose the influence of the inner diameter \({d}_{i}\) of the C11000 copper tubular rivets on the final geometry of the joints fabricated by double-sided ILR. As seen from the cross-sectional photographs and finite element calculations corresponding to the overlapped length \(L=50\) mm (refer to Table 2), the rivets are injected by compression into the dovetail ring holes to obtain near-virtually continuous joints with small, localized gaps along the contact interfaces between the rivets and sheets. The overlapped area subjected to high contact pressures grows with the inner diameter \({d}_{i}\) of the tubular rivets (refer to Fig. 7a-c). In addition, the undercut (defined in Fig. 2a) also increases as the inner diameter \({d}_{i}\) of tubular rivets rises because smaller values (see, for example, Fig. 7a) induce non-negligible deformation of the dovetail ring holes during injection of the tubular rivets.

Figure 7d shows the solution based on the utilization of two concentric rivets with different inner diameters \({d}_{i}\). The length \(s\) of each rivet is different to ensure that both holes are filled. As seen, this solution also creates high pressures along the overlapped contact areas but at the cost of increasing the riveting forces beyond those obtained in the alternative solution based on a single tubular rivet with an inner diameter \({d}_{i}=25\) mm (Fig. 8). The high contact pressures that are observed in Fig. 7c and d give rise to better thermo-electrical performances, as will be seen in the following section of the paper. This is because the increase in contact pressure helps flattening the asperities, breaking up the oxides and increasing the metallurgical bonds by exposure and direct metallic contact along the overlapped sheet surfaces.

Fig. 8
figure 8

Experimental and finite element computed evolutions of the riveting force with displacement for the four different types of double-sided injected lap riveted joints that are shown in Fig. 7

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Regarding the evolutions of the riveting forces with displacement shown in Fig. 8, they all disclose typical closed-die forging trends with two distinct regions separated by a transition zone. The first region labelled as “A” is characterized by a progressive rise in the riveting forces. This is due to an increasing contact with friction between the tubular rivet walls and the dovetail ring hole surfaces at the beginning of deformation, as shown in the finite element predicted cross section included in the top right-hand side of Fig. 8.

The knees at the transition zone (refer to “B” in Fig. 8) correspond to complete filling of the dovetail ring holes by the plastically deformed rivets. This is achieved with a minimum gap left between the upper and lower sheets, as illustrated in the corresponding finite element predicted cross section.

The very steep increase in the forces at the end (region “C”) is caused by full contact between the sheets along their overlapped surfaces, as depicted in the finite element predicted cross section included in the bottom right-hand side of Fig. 8.

Finally, it is worth noting that the differences in total displacement that are observed for the test cases included in Fig. 8 are caused by the various tubular rivet lengths \(s\) needed to be used to ensure complete filling of the dovetail ring holes.

3.2 Thermo-electrical performance

Figure 9 presents the experimental and finite element computed evolutions of the electrical resistance as a function of the service temperature for the double-sided injection lap riveted joints. Results were obtained according to the procedures that had been previously described in Sects. 2.2 and 2.3 and allow concluding that electrical resistance increases linearly with service temperature. An average increase of approximately 22% is found when the service temperature rises from 20 to 105 °C.

Fig. 9
figure 9

Experimental and finite element computed evolutions of the electrical resistance with service temperature for double-sided injection lap riveted and bolted joints

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The best thermo-electrical performance is obtained for the double-sided injection lap riveted joints having two concentric tubular rivets (Fig. 7d) with electrical resistance values close to that of an ideal joint made from two aluminum AA6082-T6 sheets in perfect contact, without auxiliary joining elements and contaminant or oxide films along their overlapped surfaces (refer to the gray dashed line in Fig. 9).

The overall comparison against bolted joints made from AA6082-T6 sheets that were previously ground with emery paper and subjected to a tightening torque \(T\) of 20 Nm shows that the new proposed double-sided injection lap riveted joints provide significant gains in electrical resistance for tubular rivets with \({d}_{i}>10\) mm. This is attributed to the following: (i) larger overlapped regions subjected to high contact pressures than those of bolting; (ii) replacement of steel bolts by tubular copper rivets, with much better electrical conductivity; and (iii) elimination of material protrusions above and below the sheets surfaces that cause disturbance of the electric current. The latter phenomenon can be observed by comparing the distribution of electric current density of Fig. 10c and d against those of Fig. 10e.

Fig. 10
figure 10

Finite element predicted distributions of electric current density (A/mm2) in busbar lap joints made from AA6082-T6 aluminum sheets with 5 mm thickness subjected to a service temperature \({T}_{i}=105\) °C and produced by a double-sided IJR with one C11000 copper tubular rivet with \({d}_{i}=2\) mm, b double-sided IJR with one C11000 copper tubular rivet with \({d}_{i}=10\) mm, c double-sided IJR with one C11000 copper tubular rivet with \({d}_{i}=25\) mm, d double-sided IJR with two concentric C11000 copper tubular rivets with \({d}_{i}=2\) mm and \({d}_{i}=25\) mm, e bolting with one M8 medium carbon steel bolt subjected to 20 Nm of tightening torque, and f bolting with one M8 medium carbon steel bolt subjected to 5 Nm of tightening torque

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The low normal pressures for bolted joints subjected to a tightening torque T of 5 Nm (i.e., near loosened joints) force the electric current to flow mainly through the bolt (Fig. 10f). This observation, combined with the four times higher electric resistivity of the steel bolts and nuts (refer to Fig. 5), gives rise to very poor electrical performances and to electrical resistance values beyond the maximum bound of the vertical axis of Fig. 9.

The two worst electrical performances of the double-sided injection lap riveted joints, making use of tubular rivets with \({d}_{i}\le 10\) mm, are compatible with the high disruption levels of the electric current density that are visible in Fig. 10a and b.

The reason for using copper instead of aluminum tubular rivets made from the same material of the sheets is now clear by comparing the finite element predicted evolutions of the electrical resistance with service temperature for double-sided injection lap riveted joints with copper and aluminum tubular rivets that are given in Fig. 11.

Fig. 11
figure 11

Finite element computed evolutions of the electrical resistance with service temperature for double-sided injection lap riveted joints with copper C11000 and aluminum AA6082-T6 tubular rivets with an inner diameter \({d}_{i}=25\) mm

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As seen, copper tubular rivets provide significant gains in the electrical resistance and, therefore, give rise to better electric current flows. Their values of electrical resistance approach those of ideal busbars, with negligible increases in cost and weight due to the very small percentage of copper utilized in the joints.

3.3 Destructive tests

Figure 12 shows the evolution of the shear destructive force with displacement for three double-sided injection lap riveted joints corresponding to the unit cells showed in Fig. 7a, c, and d. The smallest peak forces (9.9 kN) are found for the single tubular riveted joints with an inner diameter \({d}_{i}=2\) mm, which fail by complete shearing of the rivets with negligible deformation of the overlapped sheets (refer to the top photograph in Fig. 12). Intermediate peak forces (18.2 kN) are obtained for the single tubular riveted joints with an inner diameter \({d}_{i}=25\) mm, which fail by detachment of the rivets with some plastic deformation of the overlapped sheets (refer to middle photograph). The largest peak forces (23.0 kN) were measured for the two concentric tubular riveted joints with \({d}_{i}=2\) mm and \({d}_{i}=25\) mm. In this case, the larger rivet is pulled out after extensive bending and fracture of the overlapped sheets, as seen in the bottom photograph of Fig. 12.

Fig. 12
figure 12

Experimental evolution of the shear destructive force with displacement for double-sided injection lap riveted joints made from aluminum AA6082-T6 sheets with 5 mm thickness using one C11000 copper tubular rivet with \({d}_{i}=2\) mm, one C11000 copper tubular rivet with \({d}_{i}=25\) mm, and two concentric C11000 copper tubular rivets with \({d}_{i}=2\) mm and \({d}_{i}=25\) mm. Photographs showing the unit cells after testing are included

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Because the mechanical loads applied in electric grids are generally low, the peak forces obtained for the three different types of unit cells allow concluding about their adequacy for electrical applications.

3.4 Thermo-electrical sensitivity to sheet thickness

The final section of the paper is focused on the thermo-electrical sensitivity of double-sided injection lap riveted joints to the thickness of the aluminum sheet conductors. The tests were performed in aluminum AA6082-T6 sheets with \({t}_{s}=2\) mm and \({t}_{s}= 5\) mm thickness and made use of copper C11000 tubular rivets having an inner diameter \({d}_{i}=2\) mm. The dovetail ring holes were pre-drilled in both types of sheets with identical leg thickness \(t= 2.3\) mm, inclination \(\alpha = 30^\circ\), and normalized depth ratio \({d}_{p}/{t}_{s}\cong 1.3\) to ensure compatibility between the two sheet thicknesses being compared.

Figure 13 shows cross-sectional photographs and finite element predictions of the double-sided injection lap rivet joints. The differences in the plastically deformed tubular rivet heights result from their initial lengths \(s\) that needed to be different to ensure complete filling of the dovetail ring holes.

Fig. 13
figure 13

Cross-sectional photographs and finite element computed geometries of double-sided injection lap riveted joints made from aluminum AA6082-T6 sheets with a 5 mm and b 2 mm thickness with C11000 copper tubular rivets having an inner diameter \({d}_{i}=2\) mm

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To conclude about the scalability of the new proposed double-sided ILR, it is not sufficient to verify the geometric scalability of the manufacturing process by means, for example, of the result shown in Fig. 13. In fact, it is also necessary to demonstrate the scalability of the thermo-electrical performance of the joints.

This is proved in Fig. 14, in which the evolution of the electrical resistance with service temperature undergoes a translation of 2.5 times up when the sheet thickness reduces from 5 to 2 mm. This result is in good agreement with the 2.5 times reduction in the cross-sectional area of the two different types of sheets and may be further confirmed by referring to the normalized electrical resistance values included in the vertical axis of Fig. 14. Geometrical and thermo-electrical scalability of double-sided ILR opens perspectives for a wide application potential of the new proposed process in electric power grids with very different sizes and energy capacities.

Fig. 14
figure 14

Experimental evolutions of the electrical resistance vs. service temperature for double-sided injection lap riveted joints made from aluminum AA6082-T6 sheets with 2 mm and 5 mm thickness and having copper C11000 tubular rivets with an inner diameter \({d}_{i}=2\) mm

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4 Conclusions

Double-sided injection lap riveting can be successfully used to fabricate invisible lap joints without material protrusions above and below the overlapped sheet surfaces. The working principle of this new joining by plastic deformation process requires pre-drilling dovetail ring holes in both sheets and utilizes tubular rivets that are made from materials identical or softer than the sheets to be joined.

Application of the new process to the joining of aluminum AA6082-T6 busbars with tubular rivets made from softer and better electrically conductive copper C11000 provides up to 25% gains in thermo-electrical performance when compared to conventional fastened joints using steel bolts and nuts that are commonly used in electric power distribution systems. The best performance was achieved with the utilization of two concentric tubular rivets due to its capability to assure larger overlapped areas subjected to high contact pressures than single bolts. The increase in cost and weight resulting from the use of single or concentric copper tubular rivets in electric power grids built upon aluminum busbars is negligible when compared to fastened solutions making used of multiple bolts to obtain larger overlapped areas subjected to high contact pressures.

Double-sided injection lap riveting is also a scalable joining process from both fabrication and thermo-electrical performance points of view. It provides linear increase of electrical resistance with temperature with values that are proportional to the cross-sectional area of the sheet conductors due to minor electric current disturbances caused by the tubular riveting interlock. This last conclusion opens perspectives for the new process being successfully used in electric power grids with very different sizes and energy capacities.