3.1. Influence of capacitance-voltage matching parameters on discharge characteristics
The effect of capacitance-voltage matching parameters on the discharge characteristics of metal wires and its triggering energetic materials is the key link to study the energy release of energetic materials during ETEF process. Under the conditions of two equipment parameters (EPG-A, EPG-B), a metal wire (molybdenum wire with a diameter of 0.2mm and a length of 45 mm) and an EMs cylinder were used as the discharge object, and the discharge voltage U(t) and current I(t) were obtained, as shown in Fig. 3(a-b). According to Eqs. (2) and (3), the waveforms of instantaneous power Pt and the deposited energy Wt were calculated respectively (Fig. 3(c-d)).
According to the current and voltage curves presented in Fig. 3(a-b), at the same electrical pulse generator parameters, the addition of energetic materials resulted in a decrease in the maximum voltage of the wire before breakdown, and the peak value of current waveform decreased significantly after breakdown discharge. Generally, wire explosion will undergo a series of physical changes, that is, the phase transition from solid, liquid, gas to plasma. After the energetic materials were added, the physical process changed, and the plasma formed by wire explosion heated and ignited energetic materials for chemical reaction. In this process, the ignition of energetic materials occurred at the peak of voltage, which reduced the peak of current compared with the Mo wire explosion in water, indicating that the electrical conductivity changed during the ignition of energetic materials by metal wires. There are two reasons that may cause this phenomenon, one is that energetic materials are ignited, the other is that after wire explosion forms plasma, the nearby energetic materials are heated by thermal radiation to form a conductive layer, and the extra conductive layer (gas products produced by vaporization of energetic materials) increases the resistance of the discharge channel . Both of these reasons can reduce the conductivity between electrodes and reduce the current in the circuit. Moreover, based on Eqs (2) and (3), calculated that the introduction of energetic materials reduced the maximum electric power and the electric energy deposited in the discharge channel. This phenomenon may be due to the fact that some energetic materials with high temperature are used as extra conductive substances, which accelerates the breakdown process of the wire vaporization discharge channel, resulting in a decrease in deposition energy. According to Fig. 3(c-d), it can be found that the energy consumed during the ignition of energetic materials was about 200J, so it can be inferred that energetic materials were ignited during the wire explosion, followed by chemical reactions and shock waves. Although energetic materials consumed the energy of plasma in the ignition process, the addition of energetic materials provided an additional shock wave amplitude, namely the secondary shock wave peak effect, which increased the impulse of the whole system, as demonstrated by Zhou et al. . According to our previous studies , compared with pure electrohydraulic forming (discharge voltage 3kV), the bulging height of sheet metal under ETEF condition (3 kV/2 g) increased by 162%, so the shock wave energy produced by energetic materials is the fundamental reason for the significant increase of bulging height of sheet metal.
3.2. Influence of capacitance-voltage matching parameters on sheet bulging
In this section, the influence of energy release from energetic materials triggered by metal wire on sheet bulging is discussed under the matching parameters of capacitance-voltage of electric pulse generator. Fig. 4 presents the changing process of bulging height and deformation speed of sheet metal with time under different equipment parameters. It can be seen that the specimen was rapidly deformed in a short time, and the final bulging height was about 34mm. Under the conditions of two kinds of equipment, the speed of the apex (point A) of the bulged specimen changed with time as follows: the speed of the sheet reached the maximum at about 20μs, then dropped rapidly, and then rose slightly to maintain high speed movement, and the deformation speed was close to zero at about 300μs, finally until the end of deformation. Therefore, under different capacitance-voltage matching equipment parameters, the apex velocity of bulged sheet has the same trend with time in ETEF process. Additionally, according to our previous research , the variation trend of the peak velocity of the specimen obtained in ETEF numerical simulation under the parameter of 3 kV/2.0 g was in good agreement with the experimental results (Fig. 4(a)). Fig. 5 shows the bulged specimen and effective plastic strain under different equipment parameters. In the deformation zone of φ100mm, the distribution trend of effective plastic strain of the sheets under EPG-A and EPG-B equipment was similar, and the maximum effective plastic strain values were 49.3% and 50.4%, respectively. Table 3 lists the final bulging height, maximum deformation speed and maximum effective plastic strain obtained on the sheet under two kinds of equipment parameters, and their values are at the same level.
Table 3 Deformation results of sheets in ETEF under different equipment parameters.
|Electric pulse generator
||Height, H (mm)
||Max velocity, V (m/s)
||Effective plastic strain, (%)
According to the deposition energy curves in Section 3.1 (Fig. 3(c-d)), the deposition energy consumed by the ignition of energetic materials by metal wires was about 200J under different capacitance and voltage matching parameters. Based on our previous studies , the chemical energy per gram of energetic materials was 3.04 kJ. Taking the parameters of EPG-A equipment as an example, in the energy system of 3.0 kV/2.0 g, the energy deposited after the wire triggered the energetic materials was 1.07 kJ. Consequently, the energy released by the energetic materials accounted for 86% of the total energy system, indicating that the bulging height of the sheet was mainly contributed by the chemical energy released by energetic materials. From the perspective of the final bulging height, velocity variation trend and effective plastic strain value, the bulging results obtained under the two equipment parameters were basically consistent. Therefore, we conclude that the initial energy storage of the electric pulse generator can only provide triggering function for energetic materials, and the matching parameters of capacitance-voltage have no effect on the released energy level of energetic materials. In other words, energetic materials were insensitive to the initial equipment conditions of the electrical pulse generator, and had low requirements on the matching parameters of the capacitance-voltage of the equipment. The electric pulse generator can provide enough system triggering energy, which can trigger energetic materials to release energy stably, thus increasing the flexibility of initial equipment condition triggering. This will be beneficial to the popularization and application of ETEF. Subsequently, we select EPG-A equipment parameters to study the deformation of the sheet under ETEF in detail.
3.3. Analysis of deformation results of sheet metal
The bulging height, maximum strain value and maximum thinning rate of the bulged specimen during ETEF were used to analyze the deformation of DP600 sheet, as shown in Table 4. Fig. 6 shows the specimens and profiles obtained from ETEF and QSF tests with the same bulging height (24mm, 29mm). It can be seen that the non-uniform deformation of the QSF specimens occurred in the deformation zone 20–40 mm from the apex of the sheet. While the profile of the specimen under ETEF condition was more uniform. When the energetic materials was triggered by the metal wire to release energy, it would press the surrounding water medium to obtain kinetic energy and push the sheet to complete high-speed deformation. As a flexible “punch”, the water medium has certain fluidity, which improves the profile uniformity of the specimen. The thickness distribution is an important index to measure the deformation uniformity of deformed specimen. Fig. 7 shows the thickness distribution of the bulged specimens. In the deformation zone of φ100mm, the thickness distribution of the specimens under ETEF condition were relatively uniform, and the maximum thinning rate occurred in the apex area of the specimens, which was 15.3% (specimen NO.1) and 23.8% (specimen NO.2), respectively. Under the QSF condition, the thickness distribution of the specimens were deformed unevenly in the deformation zone, which resulted in a very serious thickness reduction, and the maximum values were 22.1% (specimen NO.3) and 27.6% (specimen NO.4), respectively. Therefore, compared with the quasi-static bulged specimens with the same bulging height (24mm, 29mm), the maximum thickness rate of the specimens under the conditions of ETEF/3.0kV/1.0g and ETEF/3.0kV/1.5g were reduced by 30.8% and 13.8%, respectively.
Table 4 Summary of the ETEF and QSF test results.
|Maximum strain (%)
According to Table 4, the maximum major strain and the maximum thinning rate of the specimens obtained under ETEF were lower than those of QSF, which inevitably affected the strain distribution in the deformation zone of the specimens. Fig. 8 exhibits the strain distribution and thinning rate of ETEF/1.5g and QSF/29mm specimens with the same bulging height. The maximum major strain and the maximum minor strain of the specimen under the QSF condition were located 20mm from the apex of the sheet, and their values were 21.6% and 13.7%, respectively, and distributed symmetrically. Clearly, the maximum strain obtained by ETEF was distributed at the apex of the specimen, and its maximum major strain and maximum minor strain were 15.2% and 14.2%, respectively (Fig. 8(a)). In the deformation zone φ 60mm, the strain in two principal in-plane directions was almost equiaxial, therefore, the strain distribution was obviously improved, and the maximum major strain decreased by 29.6% compared with QSF. Moreover, the thinning rate also showed similar distribution characteristics, and the thinning rate of the specimen under ETEF conditions was significantly reduced compared with that of QSF (Fig. 8(b)). According to our previous tests , the specimen also cracked here under quasi-static conditions, mainly because the contact friction between the specimen and punch increased in the deformation zone, which resulted in a large deformation and serious thickness thinning in this zone .Therefore, the maximum strain and thinning rate of ETEF specimens decreased, which significantly improved the uniformity of strain distribution in the deformation zone.
3.4. Dynamic deformation process of sheet metal
LS-DYNA simulation software was adopted to simulate the dynamic deformation process of the sheet in ETEF. A quarter geometric model (including: Mo wire, EMs, water, air, blank, blank holder and liquid chamber) was established based on the test tooling in Fig. 2(a). Then, the energy input in ETEF was preset, including the electrical energy input by metal wire (Fig. 3(c)) and the chemical energy of energetic materials. The former was the electric energy preset by the metal wire through the electric pulse generator, which mainly played the role of igniting energetic materials; the chemical energy of the latter was the energy released by the chemical reaction of energetic materials after being ignited by metal wire. The deformation of the sheet was mainly realized by the chemical energy released by energetic materials. The detailed implementation process of numerical simulation of ETEF can be consulted in our previous work .
According to the description in Section 2.2, energetic materials mainly produce heat energy, light energy and mechanical energy after releasing energy, and form shock waves to work on the surrounding water medium, resulting in plastic deformation of the workpiece. Therefore, the plastic strain energy was used to evaluate the contribution of energy released by energetic materials to the plastic deformation of the blank . Fig. 9 shows the change with time of plastic strain energy of the blank after energy release by energetic materials in ETEF process. It can be found that the addition of energetic materials significantly increased the plastic strain energy of the blank. Compared with the final plastic strain energy of EHF/3kV, the plastic strain energy obtained under the conditions of ETEF/3kV/1.0g and ETEF/3kV/1.5g contributed 60% and 74% to the plastic deformation of the blank, respectively. Specifically, according to the research in Sections 3.1 and 3.2, it was found that the deposition energy consumed by energetic materials during ignition was about 200J, which was relatively small in the whole energy system and even negligible, but it reduced the deposition energy under EHF/3kV conditions. Therefore, the plastic strain energy obtained under the conditions of ETEF/3kV/1.0g and ETEF/3kV/1.5g contributed slightly more than 60% and 74% to the plastic deformation of the blank, respectively. As a result, the energy released by energetic materials in the ETEF process played a major role in the plastic deformation of the blank. Moreover, it can be seen from the changing trend of plastic strain energy of the blank that the increase of plastic strain energy can be divided into two stages. Taking ETEF/3kV/1.5g as an example, the plastic strain energy increased slightly within 60μs, and the plastic strain energy of the blank increased significantly in 60-300 μs. Therefore, after the energetic materials released energy, the shock wave pressure and the stress and strain on the blank must change significantly in different plastic deformation stages.
Figure 10 exhibits the change of the shock wave pressure generated by the elements on the metal wire and energetic materials with time during the ETEF process. Elements A, B, and C were on metal wire, and elements D, E, and F were on energetic materials. After the electric pulse generator discharged, the shock wave pressure of the elements on the metal wire and energetic materials were generated almost simultaneously, and the duration from the generation of the pressure to the rapid drop were about 10 μs. Remarkably, from the peak pressure on the elements, it can be found that the maximum value of the shock wave pressure generated by the elements on the energetic materials were greater than that on the metal wire, indicating that the energetic materials were ignited by the metal wire and increased the peak value of the shock wave. Therefore, according to the analysis in Section 3.1, the addition of energetic materials increased the total energy of the system, that is, increased the pressure of shock wave, which is consistent with the conclusion of Zhou et al. . After 10 μs, the pressure on the elements decreased slowly, only 8 MPa at 50 μs, and close to zero at 60 μs. Therefore, the total duration of the electrical energy of metal wire and the chemical energy generated by energetic materials was 60 μs.
Fig. 11 presents the result velocity and effective stress of the elements on the sheet over time. First, the metal wire and energetic materials released energy within 0-60 μs. At 24 μs, the shock wave pressure was transmitted to the sheet, which caused the effective stress on the sheet to increase rapidly, and the speed of the element L rapidly increased to the maximum value of 188 m/s. Next, due to the weakening of the initial electrical and chemical energy within 24-60 μs, the deformation speed of the sheet decreased. However, the effective stress on the sheet continued to increase, and the increase became slow at 50 μs, and then after 60 μs, the speed of the sheet increased again under the action of water flow pressure and inertia. Eventually, the effective stress decreased rapidly when it increased to 250 μs, and the deformation speed of the sheet also decreased rapidly at 200 μs, and the deformation ended at 300 μs. Therefore, the deformation process of sheet in ETEF can be divided into two stages: (i) the early stage of deformation (within 0-60 μs), and the initial chemical energy action stage of energetic materials; (ii) the late deformation period (within 60-300 μs) belongs to inertia action stage.
Fig. 12 shows the contours/vector of the bulging height (Y-displacement) of the tested specimen during the ETEF process. In the initial chemical energy action stage of energetic materials, the bulging height of the specimen at 60 μs was only 7.5mm, presenting a conical bulging profile, as shown in Fig. 12(a). At 120 μs, the specimen showed an approximately ellipsoidal bulging profile (Fig. 12(b)), and the deformation profile was further improved. At 200 and 300 μs, the profile of the bulged specimen was hemispherical, and the bulging height of the final specimen is 30.1mm, with an error of only 3.8% from the experimental bulging height of 29mm (Table 4). Therefore, in the inertia action stage (within 60-300 μs), the bulging height of the specimen increased by 301% compared with the initial chemical energy action stage of the energetic materials. The inertia effect accounted for 80% of the total deformation time, which significantly increased the bulging height of the sheet metal and played a leading role in the plastic deformation.
The profile change of the bulging specimen during the ETEF process will inevitably affect the distribution of the effective plastic strain. The variation of the effective plastic strain of the deformed specimen at different times is shown in Fig. 13. At 30 μs, the effective plastic strain with elliptical annular distribution appeared on the specimen; At 60 μs, the effective plastic strain presented a rectangular distribution in the central deformation zone of the specimen, at this time, the width of the strain concentration zone was parallel and equal to the geometric dimension of EMs cylinber (Fig. 2(a)). At 100 μs, the effective plastic strain concentration area was elliptical (the ratio of long axis to short axis: 1.6), and the strain distribution was extremely uneven. At 120 μs, the effective plastic strain in the central deformation zone was close to a circle (the ratio of long axis to short axis: 1.1), and the effective plastic strain was significantly improved. Within 200-300 μs, the effective plastic strain in the central deformation zone was uniformly distributed. These results further indicate that the energy released by energetic materials during the ETEF process can significantly improve the distribution of effective plastic strain, which is of great significance for forming axisymmetric parts.