measured with the system is approximately 1200 m/s, limited by the deployed detectors, which is at least two times the radial impact velocity expected for MPW in the given configuration. The analysis of the PDV measurements is performed in the commercial software MATLAB. A short-time Fourier transform allows the determination of a spectrogram for every data point and thus the correlation of the flyer velocity at every time increment. Experiments were conducted on a 32-kJ (0.009-kWh) Bmax pulsedpower generator and workstation. This system has a maximum charging voltage of 20 kV, a capacitance of 160 F, and a discharge frequency of 25 kHz. For the 15-mm coil, working distances lw of 4, 7, 8, 9, 10, 11, 12, 15, and 17 mm were evaluated. A conversion of SI units to U.S. customary units is given in Table 3. For each working length, the initial charging energy was set at 11.5 kJ (0.003 kWh) and increased or decreased for select working lengths depending on initial results. For the 10-mm coil, working distances lw of 4, 5, 6, 7, 8, 9, 10, and 12 mm were evaluated. For each working length, the charging energy was set at 7.7 kJ (0.002 kWh). Experiments Figure 3A and C presents a schematic showing the working lengths and a picture of the experimental setup. Current measurements were conducted for each trial using a Rogowski current probe, CWT 3000 B, from Power Electronic Measurements, Ltd. The current signal triggered the recording of the PDV signal. Two different types of joining experiments were performed. First, the charging energies were chosen to ensure incomplete metallurgical bonding between flyer and parent. That way, after cutting the flyer away, a detailed analysis of the impact surfaces could be performed, allowing for an interpretation of the impact process. After joining, flyers were cut and peeled from the parent to expose the interface. Experiments were conducted under fixed flyer-coil and flyer-parent radial gaps while varying the axial position of the flyer and charging energy. Afterward, experiments with higher charging energies sufficient for Fig. 6 — A — Samples with 10mm working length (15mm coil) at various energies, impact Fig. 7 — Overview and detailed images of samples with working lengths containing the following: A — 4 mm; and B — 7 mm from the 15mm coil. welding were performed, and the obtained welds were examined by metallographic analyses and mechanically tested in an instrumented 90-deg peel testing device. Selected specimens were prepared for visioplastic analysis of the axial elongation or compression by introducing scratch marks in defined intervals of 1 mm onto the original outer flyer surface — Fig. 3B. After the process, the distances between the marks were measured under a microscope. Numerical Simulation Due to the high speed and restrictive conditions of MPW on cylindrical parts, the angles of the welding front are extremely difficult if not impossible to measure directly. For this, coupled mechanical-thermal-electromagnetic numerical calculations mirroring the conditions of the experimental part were conducted. LS-DYNA (version R 7.0) was used; the electromagnetic fields are computed by implicit time integration using a finite element method (FEM) coupled with a boundary element method (BEM) for the surrounding air and insulators (Ref. 16). The mechanical and thermal problems are solved by explicit time integration based on the calculated electromagnetic fields. The rigid coil and parent part as well as the flyer tube (elastic-plastic material model) were modelled in 3D with solid quad elements. At the inner surface of the coil and outer surface of the flyer tube, the element edge length was 0.1 mm to account for the current density distribution, gradually decreasing toward the outside of the coil and inside of the tube, respectively. Recorded current curves from the experiments served as input data. The simulations were calibrated based on PDV data obtained by the authors during welding experiments at Bmax, Toulouse, France. An inverse material characterization approach was used for the identification of the required material parameters. This is a common approach for electromagnetic forming processes, where a direct determination of material parameters for the prevalent high strain rates is elaborate (Refs. 17, 18). To adapt the impact velocities in the simulations to the measured data, the Cowper-Symonds constitutive equation (Equation 1) was used. Here, '0 stands for the dynamic flow stress WELDING RESEARCH 104-s WELDING JOURNAL / MARCH 2016, VOL. 95 areas are marked; B — successful welding at short working length; and C — unsuccessful welding at increased working length. A A B B C
Welding Journal | March 2016
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