PSI - Issue 81

Oleh Yasniy et al. / Procedia Structural Integrity 81 (2026) 244–250

246

Fig. 1. Crack initiation nuclei.

Eq. (1) was derived from experimental data obtained for 21CrMoV5-7 steel tested in air under thermo-fatigue conditions with a triangular temperature cycle (Yasniy et al., 2009) 408 63lg a N    . (2)

  ( ) i D N of that nucleus satisfied

A crack of length 0.2 mm was assumed to initiate at a given nucleus if the damage measure

the following inequality:   ( )

( ) i i D N R  ,

(3)

where   i R denotes the resistance of the i-th nucleus to crack initiation. This resistance was treated as a uniformly distributed random variable within the interval (0, 1), reflecting the inherent material heterogeneity and the stochastic nature of microstructural defects. The orientation of newly initiated cracks was selected to be perpendicular to the direction of the maximum principal stress, in accordance with fracture mechanics principles. In the case of equibiaxial tension, where the principal stresses are equal and no preferential direction exists, the crack orientation was assigned randomly. This formulation enables a realistic representation of both the probabilistic character of crack nucleation and the variability of crack orientation under different stress states, thereby enhancing the physical fidelity of the thermo-fatigue damage model.

2.2. Fatigue crack growth The initiated cracks were assumed to grow at a rate,

/ dc dN , which was calculated using the following Paris law equation

(Yasniy et al., 2009):

d с

11     9.26 10

4.09

(4)

,

K

I

dN

where the crack growth rate is expressed in mm/cycle, and the stress intensity factor (SIF) is in MPa m . Here, I K  represents the range of the normal opening mode SIF, which was evaluated using the boundary element method (Pasternak et al., 2013), taking into account the interaction between cracks. The crack growth was simulated by adding a short straight segment (a new boundary element), the length of which was determined according to Eq. (4). It was assumed that cracks could change their propagation direction according to the so-called max   (or Erdogan – Sih) criterion (Erdogan & Sih, 1963). According to this criterion, the change in the crack growth angle  was calculated by substituting the mode I ( I K ) and mode II ( II K ) stress intensity factors into the following equation:

   

   

2 II K K K K K K    2 II 2 3 9 I

2

3

I

1

cos



(5)





.

2 II

I