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Multiscale Fatigue Crack Growth Modeling for Welded Stiffened Panels

  • Ž. Božić
  • S. Schmauder
  • M. Mlikota
  • M. Hummel
Living reference work entry

Abstract

The influence of welding residual stresses in stiffened panels on effective stress intensity factor values and fatigue crack growth rate is studied in this paper. Interpretation of relevant effects on different length scales such as dislocation appearance and microstructural crack nucleation and propagation is taken into account using molecular dynamics (MD) simulations as well as a Tanaka-Mura approach for the analysis of the problem. Mode I stress intensity factors (SIFs), K I, were calculated by the finite element method (FEM) using shell elements and the crack tip displacement extrapolation technique. The total SIF value, K tot, is derived by a part due to the applied load, K appl, and by a part due to welding residual stresses, K res. Fatigue crack propagation simulations based on power law models showed that high tensile residual stresses in the vicinity of a stiffener significantly increase the crack growth rate, which is in good agreement with experimental results.

Keywords

Dislocation Microstructurally small cracks Fatigue crack growth rate Residual stress 

Nomenclature

a

half crack length

a0

initial crack length

afin

final crack length

C

material constant of the Paris equation

CRSS

critical resolved shear stress

d

slip band length

da/dN

crack growth rate

E

Young’s modulus

\( F\left(\overrightarrow{r},t\right) \)

interatomic force

Fmax

maximum applied force

Fmin

minimum applied force

G

shear modulus

K

stress intensity factor (SIF)

Kappl

stress intensity factor due to the applied load

Kres

stress intensity factor due to welding residual stresses

Kth

stress intensity factor threshold

Ktot

total stress intensity factor

m

atomic mass

m

material constant of the Paris eq.

N

number of stress cycles for the fatigue crack propagation

Nf

number of stress cycles for fatigue failure

Ng

number of stress cycles required for crack nucleation in a single grain

Nini

number of stress cycles needed for the initiation of a small crack

R

stress ratio

Reff

effective stress intensity factor ratio

\( U\left(\overrightarrow{r}\, ,t\right) \)

interatomic embedded atom method (EAM) pair potential

Wc

specific fracture energy per unit area

ΔF

applied force range

ΔK

stress intensity factor range

ΔKeff

effective stress intensity factor range

Δσ

average applied stress range

\( \Delta \overline{\tau} \)

average shear stress range on the slip band

σ0

yield stress

Notes

Acknowledgments

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. Schm 746/132-1 and as part of the Collaborative Research Centre SFB 716 at the University of Stuttgart and by the Croatian Science Foundation Grant No. 120-0362321-2198. The support is gratefully acknowledged.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Ž. Božić
    • 1
  • S. Schmauder
    • 2
  • M. Mlikota
    • 2
  • M. Hummel
    • 2
  1. 1.Faculty of Mechanical Engineering and Naval ArchitectureUniversity of ZagrebZagrebCroatia
  2. 2.IMWFUniversity of StuttgartStuttgartGermany

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