Numerical study of Ti/Al/Mg three-layer plates on the interface behavior in explosive welding

2.1 Strength model

The von Mises strength model is chosen to characterize the mechanical behavior of the materials, which takes the shear modulus and yield strength of materials into accounts. No strain hardening parameters are included in this model. The yield standard is dependent on the classic von Mises equation, as follows:

Here, σ₁, σ₂, and σ₃ are the principal stresses, and Y represents yield strength [22].

2.2 Explosive model

The Jones-Wilkins-Lee state equation, the governing equation, is used to explain the relationship between pressure and volumetric strain of explosive, shown as follows:

Here, P represents pressure, V is the relative volume, E₀ is the initial specific internal energy, and M, N, R₁, and R₂ are shown in Table 1.

2.3 Simulation of explosive welding

The aim of this study was to produce a three-layer plate by adding aluminum alloys between titanium plate and magnesium alloy plate (Shanghai yong super metal materials co., Ltd, China) with the application of explosive welding. The numerical modeling of the explosive welding process was conducted on the platform of AUTODYN-2D (Century Dynamics), analyzing the distribution of jet, velocity, pressure, effective plastic strain, and shear stress. These physical parameters can be calculated precisely for each particle at any time step; meanwhile, the contour or history curve of the above-mentioned parameters can be easily acquired. Flyer 1 is assigned to material property of titanium, flyer 2 is the aluminum alloy, and the baseplate is the magnesium alloy. The parameters used in the von Mises model are listed in Table 2 [23]. The geometric parameters are listed in Table 3. Here, gap 1 (between flyers 1 and 2) and gap 2 (between flyer 2 and the ba seplate) are defined as 0.8 and 0.4 mm, respectively. The SPH processor is used, which is a Lagrangian technique with the potential to be both efficient in modeling material deformation and flexible in terms of the inclusion of specific material models [24]. The particle size plays a great important role in visualizing the interface topography and jet. In this study, the particle size Δr is 20 μm. The number of particles using in the three-layer plates is approximately 345,000. All units adopted in the model are measured in microseconds for time and millimeters for length.

2.4 Experiment model

Titanium (1 mm), 6061 aluminum alloys (0.5 mm), and AZ31B magnesium alloys (5 mm) are used as flyer 1, flyer 2, and baseplate in the experiment, respectively. The scene drawing of explosive welding and the macrofigure of three-layer plates are shown in Figure 1. The detonation is a “slower” powder mix of ammonium nitrate and diesel fuel oil (ANFO), and the thickness of the ANFO explosive layer is approximately 2 mm. A uniform explosive charge is placed on the surface of flyer 1 with a detonator at its edge. The schematic of the explosive welding and the model drawing of three-layer plates in the simulation are shown in Figures 2 and 3.

Figure 1:

The scene drawing and macrofigure of three-layer plates in the experiment. (A) The scene drawing of three-layer plates. (B) The macrofigure of three-layer plates.

Figure 2:

The schematic drawing of the explosive welding.

Figure 3:

The model drawing of Ti/Al/Mg in the simulation.

4.1 Jet formation

The most necessary condition for explosive welding is the appearance of jet, which is essential for a good welding [26]. In respect of the force analysis, it is necessary for the surfaces to be brought together sufficiently close within the range of interatomic attractive forces. Attractive and repulsive forces form the basic strength model, and these two forces are equal at a certain equilibrium distance [27]. The potential energy must reach its minimum value to overcome the repulsive forces at the atomic level, and the distance between two surfaces should be small enough to reach the range of the interatomic attractive forces to obtain the metallurgical bonding. Jet has a remarkable effect on the surface of clearing plates, which is beneficial for achieving a good bonding in the experiment [28].

Jet will appear when the velocity of the collision point is in a subsonic theoretically. The pressure should be sufficiently huge to surpass the dynamic elastic limit of the material so that the deformation degree of the metal surfaces can meet the basic requirement. The formation of jet is shown in the simulation in Figure 4. The low-density plate is inclined to contribute more to the source of jet. In the observation of the entire simulation process, most jets are derived from baseplate (magnesium plate), whereas almost no jet appears between flyers 1 and 2. This is consistent with the theory that a wave interface is always along with jet, and no jet appears in the case of an almost straight interface.

4.2 Velocity distribution

As an index to explore the bonding situation, the Y-direction velocity can be used to investigate the collision and bonding process. Points 4, 11, and 18 on different layers are selected to analyze the variation trend of the Y-direction velocity separately. Although the acceleration produced by the explosive causes flyer 1 to move first, there is a collision between flyers 1 and 2; then flyer 2 starts to move with the kinetic energy absorbed in the collision. Gap 2 is beneficial to speed up the Y-direction velocity of point 11; the peak value of the Y-direction velocity of point 11 is bigger than others, as shown in Figure 9.

Figure 9:

Velocity-time curve along the direction of propagation of detonation: (A) Y-direction velocity curve of the points 4, 11, and 18; (B) X-direction velocity curve of the points 4, 11, and 18.

The X-direction velocity mainly shows the spread direction of wave. As shown in Figure 4, the bonding point on the Al/Mg interface has a delay in the detonation time and location. The detonation time of the Al/Mg interface is slower than that of the Ti/Al interface at approximately 10^-3 ms; at the same time, the detonation location of the Al/Mg interface is slower than that of the Ti/Al interface at approximately 10^-4 m calculated by integral method. As is shown in Figure 9, with the distance away from detonation point increasing, the movement of the selected points starts later, which has proven that the direction of wave spreading is along the X-direction of the three-layer plates. In general, flyer 2 as an interlayer assuages the loss of kinetic energy through the twice collision with flyer 1, which is beneficial for realizing a good bonding for the three-layer plates.

4.3 Pressure distribution

The key point for analyzing pressure is to understand the driving force for bonding the plates. Figure 5 shows the pressure contour of three-layer plates in the simulation at some moment. It can be concluded that the minimum pressure occurs near detonation point. Meanwhile, the pressure around the collision point is the maximum compared with somewhere else in the simulation, which is consistent with the theory that jet forms in the collision point owing to the larger pressure.

The pressure-time curves of the points of three-layer plates are depicted in Figure 10. According to the comparison of the value of these points selected on the three-layer plates, the pressure they bear is declining with the distance away from the increasing ANFO explosive layer. The pressure cannot achieve a steady state in the early stage, and a very low pressure leads to nonbonding under the detonator in the experiment [29]. That is to say, a certain large pressure is necessary for bonding. Humps and hollows both appear in the tendency of pressure on the three curves in Figure 10.

Figure 10:

Pressure-time curve along the direction of propagation of detonation: (A) the upper surface of aluminum alloy plate; (B) the lower surface of aluminum alloy plate; (C) the upper surface of the magnesium alloy plate.

The pressure-time curves of points 4, 11, and 18 on different layers are used for the longitudinal comparison in Figure 11. Considering the yield strength of aluminum and magnesium alloys mentioned in Table 2, the pressure borne by aluminum and magnesium alloys in Figures 10 and 11 is nine times bigger than its own value; thus, a wave interface was obtained in this situation obviously. Meanwhile, the value of pressure on the lower surface of aluminum alloy plate and the upper surface of the magnesium alloy plate (points 11 and 18) is greater than the value on the upper surface of aluminum alloy plate (point 4) owing to the acceleration of velocity.

Figure 11:

Pressure-time curve of points 4, 11, 18.

4.4 Effective plastic strain and shear stress distribution

Just like the theory mentioned by the previous study, high plastic deformation will emerge when confronted with high explosive velocity, which generates a large value of effective plastic strain and a large shear stress on the interface in turn. A narrow band of plastic strain was formed around the collision point. As is shown in Figure 6, an obviously high value of effective plastic strain is shown on the Al/Mg interface compared with the Ti/Al interface, and at the same time, a wave morphology is obtained on the Al/Mg interface. The strain reaches the maximum value of 13 at the collision zone on the Al/Mg interface. We can conclude that the maximum value of effective plastic strain occurs at the collision point with the highest velocity.

Figure 12 depicts the effective plastic strain of points selected on the interface. For the plastic strain on the upper and lower surface of aluminum alloy plate in Figure 12, lower values are presented in comparison with that on the upper surface of the magnesium alloy plate, which is in agreement with the fact that a wave morphology forms on the Al/Mg interface. The highest effective plastic strain is approximately 2.5 on the Al/Mg interface, and it is greater than approximately 1.2 on the Ti/Al interface. This kind of situation is similar with the pressure; large pressure produces large deformation, that is, large plastic strain. A clear distinction for points 4, 11, and 18 on different layers in the vertical direction is shown in Figure 13.

Figure 12:

Effective plastic strain-time curve along the direction of propagation of detonation: (A) the upper surface of aluminum alloy plate; (B) the lower surface of aluminum alloy plate; (C) the upper surface of the magnesium alloy plate.

Figure 13:

Effective plastic strain-time curve of the points 4, 11, and 18.

Figure 7 shows the distribution of shear stress of three-layer plates, it is indicated that the magnitude of the shear stress can be regarded as an index whether good bonding emerges. Figure 14 depicts the shear stress of points on different layers on the interface. In the successful simulation, the shear stress is opposite in sign. The same sign of shear stress means no bonding, which is consistent with Mousavi et al. [29]. As is shown in Figures 14 and 15, the distribution of shear stress of points on different layers holds the same variation trend, whereas different interface morphologies are obtained with the almost equivalent values in the simulation. This can be explained by the fact that aluminum and magnesium alloys have smaller yield strength values than titanium, as shown in Table 2. To clear the process of simulation, the Stress TXY time curve of points 4, 11, and 18 in the vertical direction is shown in Figure 15.

Figure 14:

Stress TXY time curve along the direction of propagation of detonation: (A) the upper surface of aluminum alloy plate; (B) the lower surface of aluminum alloy plate; and (C) the upper surface of the magnesium alloy plate.

Figure 15:

Stress TXY time curve of points 4, 11, and 18.

4.5 The smooth–wavy transition

As is shown in Figure 4, the wave interface was created before the collision point, which is in line with Akbari Mousavi and Al-Hassani [26]. At this stage, people hold different opinions on the formation mechanism of the waves; thus, a uniform conclusion has not been reached. However, one point should be noted that the quantity of jet is related to the formation of the waves, respectively. In this paper, the size of wave along the interface of Al/Mg is inhomogenous in the simulation. In Figure 6, there is an existing threshold of 8.3 when a transition from straight to wavy emerges. It can be observed that the beginning parts of the interface exist with the shallower waves, whereas deeper waves appear in the end. As is known to us, higher plastic strain and shear stress contribute to the wavy interface, and this transition occurs only when the plastic strain surpasses the threshold value of materials under different explosive velocities. Earlier transition will emerge with a higher explosive velocity, and amplitude grows as the value of shear stress increases.