PSI - Issue 59

4

Ivan Shatskyi et al. / Procedia Structural Integrity 59 (2024) 246–252 Shatskyi et al. / Structural Integrity Procedia 00 (0000) 000 – 000

249

There is an obvious contradiction: y y u h   . In the absence of contact of the crack edges for the same problem |[ ]| [ ]

3

3 h zm l 2

K 



( ) k z 

(7)

;

.

0,

K m l M 



N

1

Results (6), ( Ошибка! Источник ссылки не найден. ) at 0  m are shown in Fig. 1. Due to bending, the stress distribution at the crack front is uneven. The effect of crack closure is manifested in a significant reduction of stresses in the dangerous tensile zone near the crack tip.

h z

/( 1 2 h k m l

2

)

Fig. 1. Stress intensity factor near the crack tip: solid line – including, dashed line – excluding contact

3. Results and discussion 3.1. Criteria for limit equilibrium

Hypothetically, the fracture pattern is represented as follows (Smith and Smith (1970)): at some lower critical load value, steady crack growth begins in the most stressed area; the crack front is curved to become equally stressed. After reaching the upper value of the load (destructive), a crack develops along the entire thickness of the plate. It is clear that such a process of spatial growth of the defect is difficult to model within the framework of the straight normal hypothesis. Therefore, we need to make additional adjustments. First of all, the beginning of steady crack growth can be estimated by the force criterion of linear fracture mechanics (Panasyuk (1968)), applying it to the most stressed areas close to the front surface:

   

   

K



M

max

( )

3

2

k z 1

K

E

(8)











.

N



2

h

h

z

Here   E 2 is a crack resistance of the material,   is a specific surface energy. Further, treating the unequal thickness of the crack growth as a uniform advancement of some equivalent area of the fracture surface, we can calculate the energy flow to the tip of the crack