PSI - Issue 36

Nataliya Yadzhak et al. / Procedia Structural Integrity 36 (2022) 401–407 Nataliya Yadzhak, Oleksandr Andreykiv, Yuri Lapusta / Structural Integrity Procedia 00 (2021) 000 – 000

404

4

Taking into account the loading conditions, the strain energy W can be subdivided into two components, responsible for each of applied loadings: II W corresponding to mode II, and III W corresponding to mode III:

(3)

II III W W W = + ,

II W and

III W are defined similarly to W in case of single loading (Andreikiv and Sas

where the components

(2006)):

(1) ip ip W W W l W t = + − . (2) ( ) ( ) i is

(4)

Then, with respect to (3) and (4), the energy rate balance (2) obtains the following form:

(2) dW dW

(2)

IIp

IIIp

+

dl

dN dN

(5)

.

=

 

dN

(

)

 

(1) A W W W W  − − − − −  IIs IIIs IIp

(1)

IIIp

l



Based on the formulas for the energy components

 

(

)

 

(1) A W W W W  − − − − −

(1)

,

( 

IIt  

=

− −



) II III fc +

IIs

IIIs

IIp

IIIp

IIIt

(2) l W N N  = ( )

(6)

(

)



  2 −



2

0 ip it     − it max i





−

min

max

min

ip

ith

ith

adapted from (Andreikiv and Sas (2006)), the right hand side of the expression (5) can be rewritten as follows:

(

)

(

)

(

)

(

)

2

2

2 IIp IIt  

2

2 IIIp IIIt  

2

1

1

R

R



−

−



+



−

−



dl dN

0

max

max

0

max

max

II

II

IIth

III

III

IIIth





(7)

.

=

( 

( 

− −

IIt IIp    

) II III fc II III p + + )

IIIt IIIp

The equation (7) enables the description of small crack growth rate in a thick plate under the mixed mode II+III in terms of the crack tip opening displacements. However, the application of this model requires the values of the critical CTOD ( ) II III fc  + and the average shear stress in the fracture process zone ( ) II III p  + to be available for the given loading conditions of the simultaneous action of transverse and longitudinal shear. In practice, these data can be obtained as a result of an experiment conducted for the material in consideration. However, the experimental data are often unavailable in the publications or documentation, while designing and conducting an experiment may be impossible due to the need for special equipment and funding. For simplification of the model, it is necessary to better understand the nature of mode II and mode III fatigue crack propagation mechanisms. The experimental studies on these mechanisms (Murakami et al. (2003)) were conducted on 0.47% carbon steel specimens containing semi-elliptical cracks by investigating fracture surfaces and dark etching areas of both modes. As result of these experiments, it has been shown that the fatigue fracture mechanisms of mode II and mode III are “ essentially the same ” (Murakami et al. (2003)). These results as well as the mode II and mode III fatigue crack growth curves, obtained by the approach similar to (Lenkovs ’ kyi (2017)), allow us to assume that some experimental constants characterising the material (e.g. 0 , i  , ip  , i R  ( , ) i II III = ), are approximately equal for both modes. This assumption leads to the following equation based on (7):