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

490

5

Y

data

Y

0,fit

2.00

Y

fit

1.75

1.00

0.95

[ ]

1.50

+ a )

0.90

0.85

1.25

K

0

( a

0.80

0.75

1.00

[mm]

0.70

0

Y =

a

0.65

0.75

0.60

0.0

0.50

0.5

1.0

0.25

1.0

1.5

0.8

[ ]

2.0

0.6

0

0.00

d

0

a

0.4

2

2.5

a

d

0.2

[ ]

0

3.0

0.0

d 0 a 0

Fig. 5. Geometry factor for interacting cracks Y ( a 0 , d 0 , ∆ a ) over 2 ∆ a d and

including fitted curves

2.4. Experimental validation procedure

To verify the interaction e ff ects as determined by short crack growth simulations, a fatigue test series using spec imens containing internal artificial flaws is carried out. Crack-like, penny-shaped voids are additively manufactured at the critical cross section of tensile specimens by selective laser melting. Fatigue tests are performed under fully reversed constant amplitude loading on a SincoTec ™ Power Swing MAG150 resonance testing rig, running at ap proximately 127 Hz. The load level is step-wise increased for run-outs at ten million load cycles. The test results are summarized in terms of maximum run-out load levels ∆ σ RO . Fractography analysis aids in the interpretability of crack growth occurrence and non-propagating crack formation of each printed sample.

3. Results and Discussion

3.1. Geometry factors

The geometry factor trajectories of all simulated interacting crack configurations at their respective ∆ σ TPC load levels can be summarized in one three-dimensional diagram over the normalized crack growth increment 2 ∆ a / d and the normalized distance between cracks d 0 / a 0 , as presented in Fig. 5. For cracks in their initial configuration, the geometry factor Y 0 = Y | ∆ a = 0 at large interaction distances d 0 > 2 a 0 corresponds to the geometry factor of a single circular crack Y circ 0 . 635. For smaller spacings, increasing interaction e ff ects lead to an o ff set of Y 0 > Y circ . Additionally, the geometry factors Y ( ∆ a ) increases with the crack growth increment ∆ a . A fitted curve Y 0 ( d 0 / a 0 ) and a fitted surface Y ( 2 ∆ a / d 0 , d 0 / a 0 ) were added to Fig. 5 to emphasize these trends. A slight dependence of the geometry factor on the initial crack size a 0 is observed. Further data is encouraged for a more distinctive analysis on the influence of crack size e ff ects in relation to the length scale of the cyclic R-curve. Per definition the geometry factor is material independent. However, the simplified parametrization of Y ( a 0 , d 0 , ∆ a ) does not describe the precise crack front evolution, which is based on a material dependent short crack growth simu lation at a specific load level. Therefore, material and load level dependencies are implicitly included in the evaluated geometry factors. Nevertheless, the geometry factors are assumed to be transferable to similar materials, due to the normalization in the geometry factor evaluation, as the cyclic loading level is linked to the crack growth threshold lev els. Therefore, these geometry factors facilitate the transferability of interaction e ff ect results to di ff erent load ratios and materials by cyclic R-curve analysis.

3.2. Interaction e ff ects

To summarize the resultant interaction e ff ects of all simulated crack configurations, the fatigue limits ∆ σ NPC , normalized by the corresponding single crack reference case ∆ σ NPC , single , are shown in Fig. 6. As expected, the interaction e ff ects are increasingly severe for d 0 ≤ 2 a 0 , whereas farther spaced cracks behave like individual ones.