PSI - Issue 50

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

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Titkov V.V. et al./ Structural Integrity Procedia 00 (2019) 000 – 000

The critical temperature increment leading to the appearance of a "loop" of plastic deformation in the stress-strain coordinates because of the action of temperature stresses is expressed by the formula (Karpova I.M. & Titkov V.V., 1995):

4 0 (1 ) S s  

Tc  

.

(10)

E



0 C. The condition for the implementation of a "pure" low

The characteristic value for steels ∆T c is 200 – 300 cycle mode of destruction is determined by a system of inequalities:

4 0 (1 )  

2 E Tc S s Bm  



(11)

.

S s



0

2 0 

The temperature increment in the surface layer can be associated with the volumetric density of thermal energy ΔQ, considering the heating adiabatic due to the short duration according to the formula ΔT= ΔQ/γс . For unipolar pulses in the form of a half-period of a sinusoidal function, the maximum heating will be (Shneerson G.A., 1992) ΔQ max = β*B m 2 /μ 0 . For unipolar pulses parameter β equals 1.21. Therefore, the first of the inequalities can be rewritten as: 2 1.21 4 0 (1 ) 0 Bm S s E c         . (12)

Thus, the mode of destruction due to low-cycle fatigue occurs when:

2 B Bm B S s    4 1.21 2 2 0 0 S s    1

(1 ) 0 0  

.

(13)

B



1

B

Particularly for steel B 2 = 30 T, B 1 = 30 T. In this case, inequality (13) is not fulfilled. Therefore, with unipolar induction pulses, the destruction of the solenoid by the mechanism of low-cycle fatigue is not realized. However, in the case of oscillatory pulses, the condition will be:

4

(1 ) 0 0 S s   

.

(14)

Bm







This condition can be performed at significantly lower than B 1 = 25 T values of the induction amplitude B m , since the parameter β f or oscillatory damped pulses can reach several tens, which significantly exceeds the value of 1.21 for a unipolar pulse (Shneerson G.A., 1992). At the same time, for oscillatory damped pulses of magnetic field induction: