PSI - Issue 16

Yuri Lapusta, Oleksandr Andreikiv, Nataliya Yadzhak / Structural Integrity Procedia

3

Yuri Lapusta et al. / Procedia Structural Integrity 16 (2019) 105–112

107

Fig. 1. Loading scheme of a plate with a stress riser and a crack on its tip.

2. Formulation of the problem Consider a plate with a prolonged stress riser of the radius r on its tip subject to cyclical loading with amplitude . p A crack of initial length l 0 starts from the tip of the stress riser. This crack can be considered as physically short as it is located in the plastic zone near the tip of the stress riser (Fig. 1). The problem is to determine the period of subcritical crack growth. It is to be noted that no conditions are imposed on the initial crack length 0 l : the initial crack can be a macrocrack, a physically short, mechanically short or even equal to zero. Since our model is valid not only for mechanically short but also for physically short cracks that tends to zero ( 0 0 l  ) it cannot be written using neither crack tip opening  nor stress intensity factor I K , because in that case  and I K will be equal to zero. For that reason, we build the model using deformation parameters  . It is known (Andreikiv and Darchuk (1992)) that the relation between the maximal and critical deformation equals to the relation between the correspondent values of crack tip opening:

max max fc fc     

.

(1)

Having inserted the relation (1) into the equation for a mechanically short crack propagation rate (Andreikiv et al. (2017))

2

2 ) ]

[(  

) ( 











dl dN

t

max min t

th

th

max

min



,

(2)

t fc t t     

max

an equation in deformation parameters  is obtained:

2 max       fc   fc fc

2 th



dl

2

(1 ) R

  

.

(3)

dN

max

The value of maximum tensile deformation is given by the formula (Andreikiv and Darchuk (1992)) depending on the crack size in relation to the plastic zone size: