13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- Acknowledgements The authors wish to acknowledge the financial support provided by the following Spanish Institutions: Ministry for Science and Technology (MCYT; Grant MAT2002-01831), Ministry for Education and Science (MEC; Grant BIA2005-08965), Ministry for Science and Innovation (MICINN; Grants BIA2008-06810 and BIA2011-27870), Junta de Castilla y León (JCyL; Grants SA067A05, SA111A07 and SA039A08). References [1] A. Carpinteri, Shape change of surface cracks in round bars under cyclic axial loading. Int J Fatigue, 15 (1993) 21–26. [2] Y.-S. Shih, J.-J. Chen, Analysis of fatigue crack growth on a cracked shaft. Int J Fract, 19 (1997) 477–485. [3] N. Couroneau, J. Royer, Simplified model for the fatigue growth analysis of surface cracks in round bars under mode I. Int J Fatigue, 20 (1998) 711–718. [4] X.B. Lin, R.A. Smith, Shape growth simulation of surface cracks in tension fatigued round bars. Int J Fatigue, 19 (1997) 461–469. [5] X.B. Lin, R.A. Smith, Fatigue growth simulation for cracks in notched and unnotched round bars. Int J Mech Sci, 40 (1998) 405–419. [6] C.S. Shin, C.Q. Cai, Evaluating fatigue crack propagation properties using a cylindrical rod specimen. Int J Fatigue, 29 (2007) 397–405. [7] J. Toribio, J.C. Matos, B. González, J. Escuadra, Numerical modelling of crack shape evolution for surface flaws in round bars under tensile loading. Eng Fail Anal, 16 (2009) 618–630. [8] M.A. Astiz, An incompatible singular elastic element for two- and three-dimensional crack problems. Int J Fract, 31 (1986) 105–124. [9] A. Carpinteri, Elliptical-arc surface cracks in round bars. Fatigue Fract Eng Mat Struct, 15 (1992) 1141–1153. [10]A. Levan, J. Royer, Part-circular surface cracks in round bars under tension, bending and twisting. Int J Fract, 61 (1993) 71–99. [11] C.S. Shin, C.Q. Cai, Experimental and finite element analyses on stress intensity factors of elliptical surface crack in a circular shaft under tension and bending. Int J Fract, 129 (2004) 239–264. [12]L. Rubio, B. Muñoz-Abella, G. Loaiza, Static behaviour of a shaft with an elliptical crack. Mech Syst Signal Process, 25 (2011) 1674–1686. [13]J. Toribio, J.C. Matos, B. González, J. Escuadra, Compliance evolution in round cracked bars under tensile fatigue. Eng Fract Mech, 78 (2011) 3243–3252. [14]P.C. Paris, F. Erdogan, A critical analysis of crack propagation laws. J Basic Eng, 85D (1963) 528–534. [15]C.Q. Cai, C.S. Shin, A normalized area-compliance method for monitoring surface crack development in a cylindrical rod. Int J Fatigue, 27 (2005) 801–809.
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