PSI - Issue 50

Alekseev D.I et al. / Procedia Structural Integrity 50 (2023) 17–26 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

20 4

Between the flat conductors, the magnetic pressure Pm is formed, which is directed orthogonally to the current flow in the direction of repulsion of the conductors from each other:

2

1 2        ( ) c i t k c 

( )

m P t

(1)

where i – electric current, c – width of a flat conductor, µ – magnetic permittivity, k c – coefficient reflecting the influence of the geometry of the conductors and the depth of penetration of the magnetic field. If there is a uniform distribution of the current density over the cross-section of the simple MPD conductors (Fig. 2a), then k c = 2/π ‧ atan(c/2h) . If the distance between the conductors h is significantly less than their width c : h << c , then k c → 1 . If the current density is not uniformly distributed over the cross-section of the conductors, then the coefficient k c can be determined by numerical modeling of the magnetic field of flat conductors when a pulsed current flows, as it is shown in Krivosheev et al. (2018). The heating temperature can be determined by the expression (3). The maximum generated magnetic pressure is limited by the thermal stability of the flat conductor material. With a pulse in the form of one half-wave of sinusoidal current with duration T imp , the maximum pressure P max can be determined from the value of the maximum integral of the current J cr :

imp T

T

T

2         m I ch

  

  

2

P

( ) ch

i t

0 

imp

imp

(2)

J

dt

max  



cr

2

2

k h 

c

Exceeding the critical value of the integral leads not only to melting, but can also lead even to an uncontrollable explosion of flat conductors of the MPD. It can be seen from the expression (8) for copper conductor with J cr =0.89 ‧ 10 17 A 2 s ‧ m -4 , shape factor k c =0.5 , pulse duration 5 ms , width h=0.3 mm a pressure pulse up to Pm=1 GPa can be formed without melting, which is sufficient for high strain rate testing of large number of metals. In this case, it is necessary to take into account the possibility of mechanical destruction of flat conductors in the place of bending, see Fig. 2. This loading can be implemented in the schemes Fig. 1a, b, c, d. As it is shown in Krivosheev et al. (2018) this loading was applied to test copper specimens using scheme Fig. 2a and dependencies of relative deformation of samples were obtained, see Fig. 3.

Fig. 3. The magnetic pulse driver (MPD): a) 3D view of the test sample and installed driver, and photos of deformable part; b) Comparison of experimental and numerical calculation relations between magnetic pulse pressure amplitude and relative deformation