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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In our example, length l equals 4R 1 and G equals 0.18μ 0 /R 1 . The relative decrease of the solenoid form factor with small changes in ΔR 1 of the inner radius R 1 will be:

1 G R G R    

1

.

(9)

Thus, the estimation of the solenoid resource for the described conditions can be made based on a 10 % reduction in the form factor, which corresponds to 10 % of the residual tensile deformation on the inner surface of the solenoid. The characteristic values of deformation to fracture for stainless steels are the relative elongation 0.1÷0.2 (I.S. Grigoriev & E.Z. Meilikhov, 1991). Therefore, the permissible reduction of the form factor of the solenoid used here for evaluation coincides with the natural criterion for evaluating its resource by limiting deformation. At the same time, as can be seen from Figs. 5, 6, the value of the resource is very sensitive to the amplitude of the induction pulse. At B m = 40 T, 4 pulses are sufficient to achieve the maximum reduction of the form factor, while at pulses with an amplitude of 30 T of the same form, the calculation of the resource according to this criterion will give a value of about 103 pulses. The threshold nature of the dependence of the monolithic coil resource on the induction amplitude is noted in (Karpova I.M. & Titkov V.V., 1994). 4. Solenoid lifespan evaluation The considered mode of destruction of a single-turn inductor is caused by the residual plastic deformation increasing from pulse to pulse. At the same time, as mentioned above, a mode of mechanical behavior of the inductor, not accompanied by progressive residual deformation, is possible, in which plastic deformations occur cyclically. This is due to the formation of a sharply inhomogeneous temperature profile during the period of exposure to a magnetic induction pulse and its decay in the pauses between pulses. At the same time, the design resource is described within the framework of the Coffin-Manson low-cycle fatigue theory (Hall, 1991), which allows us to estimate the maximum number of cycles involving plastic deformation, leading to the appearance of microcracks of the surface layer, the tops of which are strong concentrators of current density and heating. Under these conditions, an insignificant number of pulses leads to rapid crack growth, known as the "saw" effect (Fig. 7) (Komel’kov V.S., 1970; Krivosheev et al., 2019; Krivosheev S.I. et al., 20 18).

Fig. 7. The "saw" effect of the inner surface of the single-turn solenoid (a), initial defect of the solenoid edge (b), defect configuration after 12 pulses (marker size 0.25×0.25 mm) (c).