**2. The Principle of Hybrid Welding**

The RUSW system includes a lateral-driven high-power ultrasonic welder and an inverter resistance power supply. The current and ultrasound vibrations act on the workpiece simultaneously. In RUSW, a high pressure creates sufficient contact between the upper and lower workpieces to ensure electrical conductivity between them. The ultrasonic waves from the sonotrode pass through the upper workpiece, causing local relative vibration at the upper/lower specimen interface and thus generating friction. Resistance, friction, and plastic deformation heat cause the interface temperature to rise rapidly, resulting in solid-state joining. Figure 1 shows the schematic diagram of the RUSW process.

**Figure 1.** The principle of resistance heat-assisted high-power ultrasonic welding (RUSW).

In RUSW, the generated heat *Q*RUSW includes one part from ultrasonic vibration *Q*USW and another part from electrical resistance *Q*RSW, as described below:

$$Q\_{\rm RLSW} = Q\_{\rm LSW} + Q\_{\rm RSW} \,. \tag{1}$$

Ultrasonic vibration energy *Q*USW, is converted into friction heat *Q*<sup>f</sup> and plastic deformation heat *Q*q [18], as shown in Equation (2):

$$Q\_{\rm USW} = Q\_{\rm f} + Q\_{\rm g}.\tag{2}$$

*Q*RSW can be expressed as:

$$Q\_{\rm RSW} = I^2 \times R\_{\rm total} \times t \tag{3}$$

where *I* is the electrical current and *t* is the welding time. *R* is the total resistance providing thermal input during the RUSW process. Total resistance *R* involves seven components, as shown in Figure 2, and can be expressed as:

$$R\_{\text{total}} = R\_{\text{st1}} + R\_{\text{c1}} + R\_{\text{c1}} + R\_{\text{c2}} + R\_{\text{AI}} + R\_{\text{c3}} + R\_{\text{a}\nu} \tag{4}$$

where *R*st is the resistance of the sonotrode, *R*Cu is the resistance of Cu plate, *R*Al is the resistance of Al plate, *R*av is the resistance of the anvil, Rc1 is the contact resistance between the sonotrode and the upper specimen, Rc2 is the contact resistance between the upper and the lower specimen, and Rc3 is the contact resistance between the anvil and the lower specimen.

**Figure 2.** Schematic of the resistances in the RUSW system.

In RUSW, material softening arises from two sources: Ultrasonic softening and thermal softening [19]. Thus, the material softening rate in the welding process can be expressed as [18]:

$$
\alpha = \alpha\_{\text{us}} \times \alpha \\
\tau = \alpha\_{\text{us}} \times \frac{\sigma\_T}{\sigma\_{T\_0}} \tag{5}
$$

where, αus and α*<sup>T</sup>* are the ultrasonic softening rate and thermal softening rate, respectively. σ*<sup>T</sup>* and σ*T0* are the yield stresses of material at temperature *T* and room temperature, respectively.

According to the above theory, the interaction between the ultrasonic vibration and the electrical resistance can be described as follows: When the ultrasonic vibration is applied to the RSW, the intensity of the material softening is increased, according to Equation (5). This benefits the breaking of the metal oxide film and promotes the resistance heat. When the resistance heat acts on the ultrasonic metal welding, it promotes the increase in interface temperature according to Equation (1), and thus promotes the metallurgical reaction on the interface. These interactions may potentially increase the weld strength of Cu/Al joints.
