PSI - Issue 68

Fatigue limit (endurance limit): for load cycles

to reach a NDT threshold of 1mm

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

487

Kitagawa-Takahashi diagram Degradation of

2

with increasing defect size

wer

•

Franc3D static SIF analysis

uncracked FE-model

SIFs

Interacting defects effective size? fatigue limit?

pre-processing

crack front propagation

END

crack front contour points

post-processing

Python routine

a)

b)

MONTANUNIVERSITÄT LEOBEN

6

Fig. 1. Methodical approach: (a) Demonstration of the degradation of the fatigue limit subject to defects based on their size as described by the Kitagawa-Takahashi diagram. Interaction e ff ects need to be considered for adjacent flaws; (b) Flow chart of the short crack growth simulation as iterative forward integration of the modified NASGRO equation. Franc3D is invoked for static SIF analysis of each crack front iteration. User defined Python scripts handle the pre- and post-processing of results as well as the actual crack front propagation.

© CHAIR OF MECHANICAL ENGINEERING /

MONTANUNIVERSITÄT LEOBEN

20

as demonstrated by Fig. 1a, if the distance between two flaws is less than the extent of the smaller one (Murakami, 2019; Åman et al., 2020). Most non-experimental investigations consider static geometric defect configuration, whose results are only indi rectly applicable to fatigue strength assessment. Thus, the present study focuses on the numerical short crack growth simulation of neighboring cracks, subject to crack closure, accounting for crack extensions developing at and above the intrinsic crack growth threshold ∆ K th . ef f , in order to quantify conservative defect interaction e ff ects on the fatigue limit of defect a ffl icted specimens.

2. Methodology

2.1. Short crack growth simulation

The short crack growth simulation is based on the iterative forward integration of the modified NASGRO equation, introduced by Maierhofer et al. (2014) to incorporate crack closure, and the accurate computation of stress intensity factors for arbitrary crack geometries utilizing the analysis software Franc3D ™ . Franc3D allows for the insertion and automatic re-meshing of crack geometries into an uncracked finite element model. After numerical solution via standard finite element solvers like Abaqus ™ , Franc3D computes mode I, II and III stress intensity factors along the crack fronts. While Franc3D includes automatic crack growth routines, short crack growth and especially partial crack growth arrest along a crack front are not supported (Franc3D version 8.3.7). Therefore, user-defined Python scripts are employed, which invoke only the Franc3D static stress intensity factor analysis for each step of the short crack growth simulation. Pre- and post-processing of the crack fronts and SIF results as well as the actual crack front propagation, accounting for locally varying crack closure for any point along the crack front, is implemented in a custom Python package. This workflow is summarized in Fig. 1b. The modified NASGRO equation of the form

∆ K

m 1 −

p

∆ K th

da dN

= C · F · ∆ K

(1)

describes the transition from short crack growth to stable crack growth in the Paris region, neglecting the region of unstable crack growth towards the fracture toughness K IC . ∆ K th incorporates the buildup of crack closure, described