PSI - Issue 16

Volodymyr Panasyuk / Procedia Structural Integrity 16 (2019) 3–10 Volodymyr Panasyuk / Structural Integrity Procedia 00 (2019) 000 – 000

5 3

Griffith and Irwin formulas have become the basis of materials linear fracture mechanics when the prefracture zone near the crack tip (∆ l ) is small in comparison with crack size (Fig. 1 c ). 3. Generalization of Griffith – Irwin concept In the 60 th of the last century, Panasyuk et al. (1965) generalized Irwin criterion (2) for the case when the cracked plate is in the complex stressed state (a plate with an arbitrary orientated crack), i.e. when SIF values equal   I0 , 0  K p l ,   II0 , 0  K p l ,   III0 , 0  K p l . The hypothesis (   -criterion) was adopted for determining the direction of the crack initial propagation in the θ θ   plane (plane y 0 x , Fig. 2) for which the coefficient of normal tensile stresses intensity factor (   ) attains its maximum value in a small vicinity of the crack tip.

Fig. 2. Local system of coordinates at the crack front (line Oz ) and components (I, II, III) of the vector of crack edges displacement.

Using this approach the limiting-equilibrium equation of a plate with an arbitrary orientated crack was established for the first time (Panasyuk et al. (1965)):

θ

θ

  

  

3

K p l

II0 K p l ( , α, ) 

I c K ,

(3)

cos

( , α, ) 3tg 







I0



2

2

2   K K K K I0 I0 8 4

2

II0

2 π sin α

 K p l

II0  K p l

π sinαcosα

,

I0 0  K ,

II0 0  K ,

,

.

(4)

θ 2arctg 

I0



II0

Here θ  is the angle of the initial direction of the crack growth;  is the angle of initial crack orientation relative to load direction р (Fig. 3).

Fig. 3. The tension of a plate with an arbitrarily oriented crack