PSI - Issue 59

Oleksandr Andreykiv et al. / Procedia Structural Integrity 59 (2024) 182–189 O. Andreykiv et al. / Structural Integrity Procedia 00 (2023) 000 – 000

184

3

dt dA

dt dW

d



 

dt

.

(3)

Since external forces p are constant and applied far from the crack, then into account (2), can be rewritten for the crack jump preparation time

0  dA dt . Then equation (3), taking

c t t  in the following form:

  2

dW

  

     c t t

dt dl











  1

0

A W W

pl

  



s

pl

l

dt



(4)

According to the results (Andreikiv et al. (2008, 2017)), we obtain











  1

f pl s A W W Г     

 

t

l



,

(5)

(0) t It

f  is specific fracture energy during crack propagation,

is specific plastic deformation energy in

where



 

t

t  is an averaged normal stresses in the pre-fracture zone, (0) It  is the

the pre-fracture zone near the crack tip,

normal opening of the crack tip. By substituting (5) into (4) and adding initial and boundary conditions, we obtain the complete model for determining the kinetics of creep crack growth in the plate:   t f t t c pl dt dW dt dl            (2)

(6)

0, (0) l

,

, ( )

t

l

t t l t 

l







.

(7)

0

*

*

*

Since the pre-fracture zone will undergo plastic deformation under high stresses t  , we will assume that during crack jump preparation, most of the time will be occupied by steady-state creep, i.e., the rate of strain change const t    , and therefore, the rate of opening of the pre-fracture zone const It    . In that case, the deformation characteristics t   , of the pre-fracture zone near the crack tip for a small period of time c t t  we will express as C t t C (, ,) (0)[( ) ()] 0 0 0 0            , (8) (9) Since under long-term static loading and radiation exposure, we observe a slowed stepwise crack growth, the size of the jump length l  we will define as in the papers by Andreikiv et al. (2012, 2017)): ( , , ) 0 0 0 t C l It     , (10) where 0  is the constant, that is defined by an experiment. Since value l  small enough, then, it is evident that at such a small distance from the crack tip ( , , , ) 0 0 x t C It   changes only slightly, and its approximation by x can be considered a constant, i.e. (0, , , ) ( , , , ) 0 0 0 0 t C x t C It It        l x   0 . The values of plastic deformation energy, considering (9) and the results of Andreikiv et al. (2012), can be expressed as follows: C t 0 t ( , , ) 0 0        C It It It It ( )] (0) [ ( )  0    .