PSI - Issue 28

NikolayA. Makhutov et al. / Procedia Structural Integrity 28 (2020) 1347–1359 N.Makhutov, D.Reznikov / Structural Integrity Procedia 00 (2020) 000–000

1353

7

2 K K K  

1  .

(16)

e

t

It should be noted that Neuber's equation (16) does not allow describing the process of elastoplastic deformation in the region of severe strains ( 1 e  ), and accounting for the influence of the strain rate and operating temperatures on the state of stresses and strains of the notched component. Therefore, to solve problems in the field of severe plastic strains (0≤ е ≤1) in the wide ranges of strain rates (0 < e  <10 4 s -1 ), working temperatures (-269 0 C < t <200 0 C ) and stress concentration factors (1≤ K t ≤7) expression (16) was modified (Makhutov, 1981) in the form   2 , , e n t t K K F m K K     . (17)

е     allows writing

A generalization of the design and experimental data for the normalized coordinates

down the following expression for the function F :

       1 1  n m



1/

K

 



1 / (

)

F



n

t





,

(18)

K

t

n

where n is a constant ( n = 0.5). For the elastic material (

1  n  and m =1): F =1 and K σ = K e = K t . Expressions (17) and (18) allow assessing the values of stress K σ and strain K e concentration factors for various K t , σ n , σ y and m .

 2 / (1 ) m n m 

(1 ) / (1 m) m  



1 n   ;

for

(19)

 t n e K K K   t

n

(1 )[1 (

1 )] (1 ) n t K m  

  

2 / (1 ) m 

K

1 n   ;

for

(20)

K



t n m

e





(1 )[1 (

1 )] (1 ) n t K m  

  

K

t n 

 2 / (1 ) m m n m 

K

1 n   ;

for

(21)

K



t





(1 )[1 (

1 )] (1 ) K m m 

   

(1 ) / (1 m) m  

K



t n 

n

t

n

2 / (1 ) m m 

K

1 n   ;

for

(22)

K



t n m







(1 )[1 (

1 )] (1 ) n t K m m  

  

K

t n 

where n n     . For strain hardening materials in the plastic region ( n  is rising and hardening exponent m is decreasing, the stress concentration factor K σ decreases with respect to K t approaching 1 ( K t ≥ K σ ≥1) and the strain concentration factor K e increases approaching K t 2 ( K t ≤ K e ≤ K t 2 ). As it was mentioned above, in order to solve the problem of dynamic low-temperature loading, in addition to accounting for the influence stress concentration it is necessary to bear in mind the effects of low-temperature and dynamic hardening as well as the increase the triaxiality of the state of stresses and strains in the notch zone. / y 1 / n t K   ) when