PSI - Issue 16

Zinovij Nazarchuk et al. / Procedia Structural Integrity 16 (2019) 169–175 173 Zinovij Nazarchuk, Olexandr Andreykiv, Valentyn Skalskyi, Denys Rudavskyi / Structural Integrity Procedia 00 (2019) 000 – 000 5

t

, ( ) S S t t S t   ;

; ( ) S K S K  

0, (0)

.



(10)

I

CC

0









Here S 0 is the initial crack area size; S thc is the least size of the creep crack to start growth at the given external load value; S  is the crack critical size. Using the relation (6) the mathematical model (10) can also be written as follows

 

   

t

n 0, (0) 0;

     t t n t , ( )

n



2 1 1 A nA n n n n  m m m thc    t a

m

m m

1



)   

,

.

(11)

/ dt dn

n n

2  

1 (1





thc

Here n  is the SAE pulses critical number before spontaneous fracture which is determined by the formula (7); n thc – the number of the SAE events to form crack area S thc , which does not growth under the given value of external load p ( thc a thc A S n 1 1     ). Integrating the differential equation (11) for given initial and final conditions we obtain the formula (12) to determine the crack subcritical growth period t = t 

n

  

1



 

 

A A n n n m m 1   

n n n n m m m ) 

m



t

dn

0,28

(1

1





.

(12)

t

a

thc

thc

2







0

Thus, since the characteristics m , A 2 t ,  , n thc , A a have been found from the experiment the subcritical period of high-temperature creep crack growth t = t  is given by the formula (12). Along with this the important, for the technical diagnostics of the engineering structures materials, approximate formulas for the current cracks sizes S determination by the SAE parameters (Andreykiv et al. (2017a)) are shown as follows

m

m 0,5(3 1)

m

1 2

t A K 2    1 2 CC

2  

B

A

 

2 m B p n

 ,

.

(13)

0,5( 1)  m

S



a

0

0

Thus, if the material characteristics B 0 , m are known and the SAE intensity n  for a homogeneous load p has been experimentally found, then the crack size in the structural element are approximated by formula (13) in the case when any other SAE sources are not present. 5. Methodology of kinetic diagrams construction of the high-temperature creep cracks growth using the acoustic emission method During the experimental studies of the high-temperature creep cracks growth, in particular for the kinetic diagrams V ~ K I construction, the long-term pure bending load scheme for a beam specimen (cross section h 0 × h 1 ) with a lateral crack (initial length l 0 ) (see Fig. 2, a) is used. For this case, based on the results (Andreykiv et al. (2017a)) the following calculation model with acoustic emission parameters is created   1 2 2 2 1 2 2 2 1 ( )] [1 ( ) ) ( /         dt h K A A K n K K K n dn CC In m thc m In t a m CC ; . , ( ) 0, (0) 0;        t t n t n t n (14)

0 1 / ( ) A n h h S h h a      , ( )) 24,81 23,17 16 4 3    o 1 0 1

dS

dt

A dn a

dt

( ) ( ( ) K S K A n K n In a I I    , )

/

/

 

,

Here

1,5

2    

( ) (6 /  K S M h h I 1

) (1,99 2,47 12,97    

(15)

After integrating equation (14) under given conditions, to determine the high-temperature creep crack period of subcritical growth t = t  in the beam specimen, we obtain the formula