PSI - Issue 50

V.V. Titkov et al. / Procedia Structural Integrity 50 (2023) 284–293 Titkov V.V. et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 1. Massive single-turn solenoid cross-section.

Particularly, for a stainless- steel solenoid at pulse duration Tp 100 µs the depth of penetration Δ equals 4 mm. In this case, electromagnetic forces and Joule heating are concentrated near the surface of the conductor in a layer of small thickness Δ. The presence of intense and sharply inhomogeneously distributed impacts creates specific conditions for deformation and heating of the surface layer of the inductor wall, considered in this paper. Volumetric electromagnetic force and heating defined through current density and magnetic induction:

2 / q j   .

j B   ,

(2)

f

The electromagnetic field is described by standard equations for the vector potential of the magnetic field A:

0 t H j B H j E               A B A E

(3)

.

( )

jdS i t

S coil

Stress and strain fields are described by the standard equations of continuum mechanics for the case of small elastic-plastic deformations: 2 2 1 ( ) ( 0 ) 2 u S j B t T u u E T T              . (4) The tensor of mechanical stresses is related to the strain tensor, in accordance with Hooke's law in the linear domain and the model of plastic deformations with the linear hardening law (Fig. 2).