PSI - Issue 40

N.A. Makhutov et al. / Procedia Structural Integrity 40 (2022) 264–274 Nikolay A.Makhutov at al. / Structural Integrity Procedia 00 (2022) 000 – 000

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For low cryogenic temperatures achieved during cooling (for liquid hydrogen t min = – 253 °С and oxygen t min = – 183 °С) and high operating temp eratures when the engines are switched on ( t = +620 ÷ 800 °С) at pressures р max up to 32÷ 90 MPa and number revolutions n max up to 50,000 rpm, there are both high ranges Δ t max , Δ р max , Δ n max , and low Δ t , Δ р , Δ n at low frequencies. Low-frequency processes are superimposed on high-frequency ones that are induced by oscillations and pulsations. For the indicated operating temperatures t and structural materials used in the liquid-propellant engine, the basic mechanical properties (yield strength σ y , ultimate st rength σ u ) are determined by the expressions                 0 0 , 1 1 exp , , T T y u y u t u t y       (9) o + t ) and room temperature t 0 = 20°С, respectively; β у and β u are material characteristics depending on σ y 0 and σ u 0 (at 500 ≤ σ у0 ≤ 900 MPa the value of β у decreases from 70 to 40). For cases with self-heating and possible ignition of a metal in an oxygen atmosphere, the term For cases with self-heating and possible ignition of a metal in an oxygen atmosphere, the term (1/ T m -1/ T 0 )- (1/ T m -1/ T )) is used in       0 where σ y t , σ u t , σ y 0 and σ u 0 yield stress and ultimate strength at a given temperature t ( T = 273

equation (9) instead of the term (1/ T m -1/ T 0 ), where T m is the melting temperature. Real loading processes developing in time τ cause strain e at different strain rates the characteristics σ у and σ u are changed with the change of the temperature t :         y u m ,m y u t ue t ye , e e , 0 0 0          ,

 e de d   ; at the same time

(10)

-3 s -1 ; m

where 0 e is the strain rate during standard tests, 0 e = (1 ÷ 5) ∙ 10

y and m u are characteristics of the material's

sensitivity to the dynamic loading. For yield stress at 500 ≤ σ y ≤ 900 MPa, the value of m y decreases 0.045 ≤ m y ≤ 0.010.

The amplitudes of stresses σ а and strains e a , stress ratios r σ and strain ratios r e are estimated according to Fig. 7 and expression (1) for cycles with pressure ranges Δ р and temperature ranges Δ t , maximum and minimum values p max , p min , t max , t min :

  

  









  

  

  

  

  a a ,e 

max

min

max , e e

min

,

(11)



2

2

    r ,r 

  , e e

  max min

max  

.

e

min



Cyclic service life (durability) N at given values { σ а , e a } and { r σ , r e } are determined according to the modified Coffin-Manson-Langer equation for pseudoelastic stresses (Makhutov, 2008; Makhutov, 2011; Makhutov, 2013):

m

t u

   

p     



1

E

,

(12)

e E    a a

, 1 75

e



n

1 1

1 1

r r

r r

 

 

t к

1





  N 4

  N 4

m

m

e e

 





p

e

where E is the modulus of elasticity, ψ с is the relative narrowing at fracture of the laboratory specimen; m p and m e are the characteristics of the material (for σ a ≤ σ u ≤ 1000 MPa, the value of m p increases from 0.5 to 0.6, and the value of m e decreases from 0.12 to 0.08). Plasticity decreases with decreasing temperature t and increasing strain rate e  . When the high-frequency loading is superimposed on the low-frequency one (according to Fig. 7) the service life N n decreases (Makhutov, 2008; Makhutov, 2011; Gadenin, 2018):