at a uniaxial plastic strain rate ε̇, 0 is the associated static flow stress, and D and q are material constants (Ref. 19). ' / 0 = 1+ The quasi-static flow curve was determined by tube tensile testing in combination with the extrapolation approach of Voce (Ref. 20). D and q were chosen in a manner so that the simulated and measured velocity curves of characteristic areas in the flyer tube were comparable. A validation was done by comparing the experiments and simulations of the electromagnetic compression of tubes without parent parts using the same Cowper-Symonds parameters. Beside the radial velocities, the final displacements at the measuring points were also compared — Fig. 4B. The maximum deviation between measured and simulated final necking was approximately 10%. This deviation originates in a slight time shift of the velocity curves. The absolute values of the velocity amplitudes are covered much better, and this is the most important value for the simulation of an MPW process with fixed standoff. Figure 4B also visualizes the reason for the 3D models; the influence of the axial slot in the coil results in an inhomogeneous deformation over the circumference of the tube. This cannot be covered by 2D simulations. Figure 4A shows the obtained strain rate dependency of the aluminum Alloy EN AW-6060, which is used as flyer material. In good accordance with literature (see the overview in Ref. 18), it can be seen for strain rates between 1000 1/s and 10,000 1/s, which are typical for electromagnetic forming, the dynamic flow stress rises significantly. The collision angles were calculated for selected nodes with the coordinates of the nodes in axial and radial Fig. 8 — Measured axial flyer deformation for different working lengths. Fig. 9 — Comparison of experiments and numerical simulation of samples with working lengths of the following: A — 4 mm; and B — 7 mm from the 15mm coil. directions. The LS-DYNA simulation was used to analyze the process regarding the development of the collision angle and prevalent strains and stresses. A bonding between the elements of flyer and parent was not modelled. Beside the kinematic analysis of the process, the thermal component of the process consisting of Joule heating and deformation heating was investigated numerically. For the time-saving simplified, time harmonic calculation of the magnetic field intensity between the coil edge and flyer, the program FEMM 4.2 (Ref. 21) was used. The peak current (500 kA) and dominant frequency (20 kHz) of an exemplary recorded current curve for a charging voltage of 9.7 kJ (0.0027 kWh) was used as input. Results Experimental Results – Varied Working Length For the experiments with incomplete bonding, after performing a peel test to remove the flyer after pulsing, the impact surface was observed. The strength of welds that broke was less than the strength of the aluminum base material (i.e., 222 MPa). The results of experiments are shown in Fig. 5A and B, and the impact surfaces are marked with dashed lines. Both coils exhibit clean welding fronts up to a working length of 7 mm, while at higher working lengths, gray matter begins to appear in the intended welding zone. An increase in working length also increases the in- 0 D 1/q (1) WELDING RESEARCH Table 3 — Conversion of Working Lengths from Metric to U.S. Customary Units mm 4 5 6 7 8 9 10 11 12 15 17 in. 0.16 0.20 0.24 0.28 0.31 0.35 0.39 0.43 0.47 0.59 0.67 MARCH 2016 / WELDING JOURNAL 105-s A B
Welding Journal | March 2016
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