PSI - Issue 5

Jesús Toribio et al. / Procedia Structural Integrity 5 (2017) 1299–1303 Jesús Toribio et al./ Structural Integrity Procedia 00 (2017) 000 – 000

1302

4

3. Numerical results

Figs. 3 and 4 show the evolution of the crack aspect ratio a / b with the relative crack depth a / t , during the fatigue grow of corner and surface cracks with initial geometries ( a / t ) 0 = {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7} and ( a / b ) 0 = {0.2, 1, 2} placed at the root of a semicircular notch (of radius r / t = 1) in a plate subjected to cyclic tensile loading. Material was characterized by means of an exponent m = 3 of the Paris law. Fatigue crack shape evolutions from different initial geometries tend towards a preferential propagation path ( a / b - a / t ) P , that associated with an initially very shallow crack of circular shape a / b  1. The convergence (approach between different fatigue crack propagation curves a / b – a / t ) is quicker for corner cracks than for surface defects.

2.0

2.0

1.5

1.5

1.0

1.0

a/b

a/b

0.5

0.5

0.0

0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 a/t

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 a/t

(a)

(b)

Fig. 3. Aspect ratio evolution during fatigue crack propagation in a notched plate with r / t = 1 for: (a) corner cracks; (b) surface cracks.

4. Conclusions

In plates with semi-circular notches subjected to cyclic tension loading, corner or surface elliptical cracks with different initial geometries approach to each other during fatigue crack growth toward a preferential propagation path , the convergence being quicker for corner cracks than for surface defects.

Acknowledgements

The authors wish to acknowledge the financial support provided by the following Spanish Institutions: Ministry for Science and Technology (MICYT; Grant MAT2002-01831), Ministry for Education and Science (MEC; Grant BIA2005-08965), Ministry for Science and Innovation (MICINN; Grant BIA2008-06810), Ministry for Economy and Competitiveness (MINECO; Grant BIA2011-27870) and Junta de Castilla y León (JCyL; Grants SA067A05, SA111A07 and SA039A08).

References

Jergéus, H.Ǻ., 1978 . A simple formula for the stress intensity factors of cracks in side notches. International Journal of Fracture 14, R113 – R116. Lin, X.B., Smith, R.A., 1997. Stress intensity factors for semi-elliptical surface cracks in semicircularly notched tension plates. Journal of Strain Analysis 32, 229 – 236. Newman Jr., J.C., Wu, X.R., Venneri, S.L., Li, C.G., Small-crack effects in high-strength aluminum alloys: NASA Reference Publication 1309, Hampton, 1994. Paris, P.C., Erdogan, F., 1963. A critical analysis of crack propagation laws. Journal of Basic Engineering 85D, 528 – 534. Schijve, J., The stress intensity factor of small cracks at notches: Delft University of Technology Report LR-330, Delft, 1981.