PSI - Issue 68

Stefan Fladischer et al. / Procedia Structural Integrity 68 (2025) 486–492 S. Fladischer et al. / Structural Integrity Procedia 00 (2024) 000–000

489

4

3.0

[ ]

0

0

2.5

d

a

2.0

d

2 a

0

0

1.5

1.0

0.5

distance between cracks

0.0

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

a)

b)

crack size

[mm]

a

0

Fig. 3. Simulated crack configurations: (a) simulated ( a 0 , d 0 ) combinations; (b) single, interacting and convex hull analysis case.

4

2.50

2.0

4

<

<

<

1

2

3

4

3

2.25

1.9

2

]

2.00

m

]

1.8

1

m

1.75

[MPa

0

1.7

x [mm]

th

4

K [MPa

K , K

3

1.50

1

2

1.6

1

2

1.25

K

th ,

lc

1.5

(

a )

K

th

3

1.00

K

th ,

eff

1.4

4

1

2

0

b)

a)

10

2 1 0 1 2

10

10

[mm]

y

crack extension

[mm]

a

Fig. 4. Exemplary interaction crack growth simulation results for a 0 = 1 . 5mmand d 0 = 1 . 5 mm: (a) crack diving forces ∆ K along the interaction axis at di ff erent load levels ∆ σ 1 < ∆ σ 2 < ∆ σ 3 =∆ σ NPC < ∆ σ 4 ; (b) through-propagation crack evolution for ∆ σ TPC =∆ σ 4 , containing a limited selection of simulated crack growth steps for visual clarity.

corresponding to reaching the intrinsic ∆ K th , ef f and the long crack ∆ K th , lc crack growth threshold in the initial crack configuration, respectively. The latter may be limited by the fatigue limit of the plain specimen ∆ σ LLF , alike the cut-o ff of the KT-diagram for small defect sizes. Interaction e ff ects are quantified in terms of the degradation of the computed fatigue limit with respect to crack size and proximity.

2.3. Geometry factor evaluation

Further evaluation of interacting crack simulations is performed by extracting SIF results at the crack growth path along the axis connecting the crack centers. This yields a series of ( ∆ a , ∆ K ) value pairs, one for each simulated iteration of the crack front, as exemplified in Fig. 4, where ∆ a is the crack extension relevant for the built-up of crack closure, starting from the initial crack contour of radius a 0 . Normalization with respect to applied load level ∆ σ and current crack size a = a 0 +∆ a according to equation (3) results in geometry factor trajectories Y ( ∆ a ).

∆ K ∆ σ √ π ( a 0 +∆ a )

(3)

Y ( a 0 , d 0 , ∆ a ) =

In order to include crack elongations up to coalescence, these geometry factors are evaluated utilizing results at the minimum through-propagating load level ∆ σ TPC =∆ σ NPC + 1MPa.