*3.2. Laser Impact Welding Interface Wave*

A periodic wave-like interface is a typical interface morphology in impact welding. On the one hand, the interface wave can increase the area of metallurgical bonding in a limited welding area and increase the welding bonding strength. On the other hand, it can also be mechanically interlocked to improve the strength of the interface. Accordingly, the interface wave characteristics are related to welding parameters such as input energy and impact angle. Figure 8a–c show the interface wave characteristics of explosive welding, magnetic pulse welding and laser impact welding [33]. The wavelength and peak of the interface wave increase with the increase in energy. Due to the low energy input in laser impact welding, the interface wave presents irregular characteristics. It is almost a straight line under the ordinary optical microscope and low-magnification scanning electron microscope, and the undulations of tiny waves can only be seen under the high-magnification electron microscope. Wang et al. [24] studied the relationship between the characteristics of the laser impact welding interface wave and the laser energy density, as shown in Figure 8d, which further confirmed the irregularity of the laser impact welding interface wave.

**Figure 8.** Weld interface morphology of three typical impact welded joints with (**a**) Explosive welding; (**b**) Magnetic pulse welding; (**c**) Laser impact welding; (**d**) Weld wave interface morphology with laser impact welding (reproduced from [24], with permission of Laser Institute of America 2016).

The ideal interface wave can make the welded joint get excellent performance, but the formation mechanism of the interface wave is still controversial. At present, there are mainly the following four theories regarding the formation mechanism of interface waves:

1. Bahrani and Black [34,35] first proposed the flyer flow penetration mechanism (caved mechanism), as shown in Figure 9. Since the stress generated by the impact is much greater than the yield strength of the material, this mechanism regards the flying stream as a fluid with a certain viscosity, and the target is a non-fluid ductile metal. It is believed that the initial impact of

the flyer on the target will cause the target to sink and bulge with plastic deformation. The work hardening caused by deformation makes it more and more difficult for the target to deform, reaching the limit. After periodic action, a wavy interface formed.

**Figure 9.** (**a**–**e**) the process of Bahrani caved mechanism (reproduce from [34], with permission of Royal Society 1967).

2. The Helmholz instability mechanism was proposed by Hunt et al. [36]. This mechanism regards the two metals under high-speed impact as fluids. During the impact and collision, the flyer and the target will have their own characteristics at the interface between the two. The tangential velocities u1 and u2 parallel to the interface, due to that the different properties of the two metals, the different driving forces they receive, and the reflection from the fixed surface of the target, cause the tangential velocities u1 and u2 to be inconsistent. As shown in Figure 10a, the speed difference between the two fluids at the interface position will cause small disturbances. This disturbance will cause the interface to instability and produce a wave-shaped interface. This wave-shaped cloud commonly found in nature is Kelvin–Helmholtz instability. They believe that a similar situation will also occur during the impact, so a wavy interface will be formed.

**Figure 10.** (**a**) Helmholz instability mechanism (reproduced from [37], with permission of Elsevier 2010); (**b**) stress wave mechanism.

3. The stress wave mechanism says that the impact wave generated by the release of energy and the various stress waves reflected from the target superimpose on the interface to produce interface waves as shown in Figure 10b [38,39]. At the collision between the flyer and the target, stress waves generated at the interface and propagate into both the flyer and the target. The higher the input laser energy, the stronger the stress waves are. The waves are reflected when they meet an interface/surface. Until now, no quantitative relationship was built between the wave

characteristics and the stress waves. According to this mechanism, the size of the interface waveform is only related to the thickness of the weldment. However, the size of the waveform will be significantly different under different energy [24]. Therefore, this mechanism is not the main factor affecting the formation of the interface waveform.

4. The vortex street mechanism is also called the vortex flow mechanism. Sherif [40] and Hay [41] drew on the principles of fluid mechanics and regarded the flyer and target as fluids. As shown in Figure 11, according to the vortex mechanism, when the fluid vortex encounters an obstacle, they will rotate in opposite directions from both sides of the obstacle to form a vortex line. Therefore, the flow of the flyer and the target will flow out during the impact welding process. Separation and convergence eventually form a wavy interface. However, in fact, the impact process is not blocked by obstacles.

**Figure 11.** Vortex Street mechanism (reproduced from [42], with permission of Elsevier 2018).

At present, the caved mechanism and the Helmholz instability mechanism are interface wave formation mechanisms accepted by most scholars, especially to explain the periodic interface waves in explosive welding and magnetic pulse welding. The energy input by the two is large, and the interface metal can be approximated as fluid during the impact. The laser impact welding interface presents irregular interface waves or flat interfaces. Whether the Helmholz instability mechanism can accurately predict the shape of the laser impact welding interface still needs to be explored.

At present, the simulation of the wave-shaped interface of impact welding by researchers often regards the material as a fluid and applies the penetration model. The material models adopted by most researchers are the Johnson–Cook materials model [43]. The Johnson–Cook materials model has the following formula.

$$
\sigma = \left( A + B \varepsilon\_{eff}^n \right) \left( 1 + C \ln \dot{\varepsilon} \right) (1 - T^{\star \mathfrak{m}}) \tag{3}
$$

<sup>σ</sup> is flow stress; <sup>ε</sup>*eff* is effective plastic strain; . <sup>ε</sup> <sup>=</sup> <sup>ε</sup>*eff* . ε0 is plastic strain rate; *T*<sup>∗</sup> = *<sup>T</sup>*−*Troom Tmelt*−*Troom* is homologous temperature; *A*, *B*, *C*, *n*, *m* are materials parameters.
