PSI - Issue 16

172 Zinovij Nazarchuk et al. / Procedia Structural Integrity 16 (2019) 169–175 4 Zinovij Nazarchuk, Olexandr Andreykiv, Valentyn Skalskyi, Denys Rudavskyi / Structural Integrity Procedia 00 (2019) 000 – 000

be incorrect. However, the material science justifies the grain size notion (the average grain size value on a certain material surface area). Therefore, in order to simplify the technical diagnostics problems solution, we introduce the microfracture area averaged size s a and the SAE amplitude A a that follows it, that is

n

1   i

a i const A A   ,

S t

s n t a

( ) A A n t

( )

( )



   

.

(6)

i

a

a

b

Fig. 1. (a) scheme of a loaded body with crack; (b) scheme of the body section on the crack plane of the initial a 0 and final a  radii.

On the basis of relations (4) – (6) we find SAE number critical value that corresponds to the spontaneous crack propagation start

T CC a n A p K S        4 4 1 1 2 .

(7)

4. Sack's problem analogue

As mentioned in Andreykiv et al. (2017a), in case of the body pure tension the plane creep crack area change slightly depends on the crack contour configuration and this dependence can be approximated by the rate of the penny-shaped crack area change. Then, let us consider the problem of the creep crack growth subcritical period determination in case of crack with a circle contour L of current radius ( ) a a t  , that is the Sack ’s problem analogue for a high-temperature creep crack (see Fig. 1, a). In this case, the mathematical problem (1) – (2) for the macrocrack is reduced to   2 2 1 2 2 2 2 ) (1 /       I CC m thc m I m t CC dt A K K K K K da , . ; ( ) , ( ) ; 0, (0) 0 CC I t a a t t a t a K a K          (8)

2

p S 2

( ) S S t  is written by the formula

K I

0,72 

Here

and the rate of the circular crack area change

0,28 0,5  

dt da /

dt S dS /

.

(9)

On this basis the mathematical problem (8) is reduced to form

 

   

2  S A S S S S m m m thc t cc

m

m S S

  m

1



,

/ dt dS

2  

1 (1

)



thc

cc