PSI - Issue 81

Mykola Stashkiv et al. / Procedia Structural Integrity 81 (2026) 143–150

148

Fig. 8. The dependence of the mode I SIF K І on the crack length L

Traditionally, the mathematical expression for determining the mode I SIF of a K І is written as:

( ) L F    =    ,

(1)

I K

where σ is maximum normal stresses in the cross-section of an element without a defect, MPa. L is crack length, m. F(ε) is dimensionless correction function. For the considered case, the correction function equation takes the following form: ( ) 2 3 4 1.039 1.421 5.306 12.959 15.822 F      = −  +  −  +  ,

(2)

where

) 2 2( 2 ) 2 L  − + − +



=

.

(

W w h

b

The equation of the correction function was obtained by applying polynomial regression (with the polynomial degree equal to 4) to the simulation data, followed by the corresponding mathematical transformations. The correction function is shown graphically in Fig. 9.

Fig. 9. Graphical representation of the correction function.

The error of the obtained correction function equation does not exceed 1% within the range 0 ≤ ε ≤ 0,5. The dependence of the SIF of the mode I K І on the dimensionless parameter ε is shown graphically in Fig. 10.