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. 3. Distribution of magnetic induction and electromagnetic forces at the front, at the moment of maximum and at the end of the induction pulse (40 T).

Fig. 4. Induction of the magnetic field in the center of the coil (a), distribution of the Mises stress invariant normalized to the yield strength in the cross section at different time points (b), radial distribution of azimuthal stress in the central plane after cooling (c).

Along with electromagnetic forces proportional to the square of the magnetic field induction, deformations in the solenoid wall are also created due to sharply inhomogeneous heating of the solenoid wall. The thermoelastic stresses arising in this case can be estimated by the formula:

( et E T T E T        . 0 )

(7)

For the studied conditions, the heating temperature of the surface of the inner wall of the inductor is about 300 o C. At the same time, σ et max equals 800 MPa and this exceeds the elastic limit S s0 for steel. Although thermoelastic stresses themselves are not capable of creating residual deformations during unloading, because of cooling and equalization of the thermal field from the plastic state of the surface layer reached by the end of the pulse, residual stresses arise in it (Fig. 4C). As can be seen from Fig. 4C, after each pulse of the magnetic field, a significant area of