PSI - Issue 39

Dmitry O. Reznikov / Procedia Structural Integrity 39 (2022) 256–265 Reznikov D.O./ Structural Integrity Procedia 00 (2019) 000–000

259

4

with the initial condition at N r =0, a = a 0 . where a is the depth of a surface crack; a 0 is the initial crack depth, С and m are parameters depending on material and loading conditions; N r is the number of loading cycles; R r = S min / S max is the stress ratio; S min and S max are the minimum and maximum stress values in a regular loading cycle, ( ) I K Y a S a     is the range of the stress intensity factor in the loading cycle, Y (a) is a correction function for the crack size and type of loading ; Δ S = S max - S min is the stress range in the regular loading cycle.

Fig. 3. Block diagram of the load history.

After separating the variables in equation (1), we get:

m

S   

a

da

Nr



.

C N  

(2)

 

 

r

0 (

)

1

m

Y a 

R  

a

r

Further, assuming that the correction function Y does not depend on the depth of the surface crack (which is true for a tubular component loaded with internal pressure, when it is possible to take Y = 1.12 (Matvienko,2006; Schijve, 2009) and integrating expression (2), one can get (Matvienko, Kuzmin, Reznikov, et al. 2021):

2

m m

   

   

2



2 1 m Y       

   

2

m





  

,

(3)

1

2 a a N C  

S





0

Nr

r

R



r

where a Nr is the crack depth after N r cycles of constant amplitude loading. Further, the crack depth a Nr reached after the implementation of N r cycles of the first loading block is taken as the initial crack depth when calculating the kinetics of the crack under the action of the second loading block.

m

1 R         I

da

,

(4)

C K

 

dN





k

with the initial condition at N k =0, a = a Nr . Due to the fact that the number of cycles of overloads N k is small in relation to the number of regular load cycles ( N k << N r ), then the cyclic growth of a crack during the action of the second loading block is, as a rule, much less than the growth caused by the first loading block. Since the parameters of overload actions (maximum values and stress