Prediction of fatigue crack initiation lives at elongated notch roots using short crack concepts Jaime Tupiassú Pinho de Castro a,⇑ , Marco Antonio Meggiolaro a , Antonio Carlos de Oliveira Miranda b , Hao Wu c , Abdellatif Imad d , Noureddine Benseddiq d a Mechanical Engineering Department, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rio de Janeiro, RJ 22451-900, Brazil b Department of Civil and Ambiental Engineering, University of Brasília, SG-12 Building, Darcy Ribeiro Campus, DF 70910-900, Brazil c The Parading Center of Mechanics Laboratory of Ministry of Education, Tongji University, Shanghai 200092, China d Laboratoire de Mécanique de Lille (CNRS UMR 8107), Université Lille1, Villeneuve D’Ascq, France article info Article history: Available online 7 November 2011 Keywords: Notch sensitivity Short cracks Non-propagating cracks Fatigue life prediction Short crack tolerance abstract Re-initiation lives of fatigue cracks departing from stop-holes roots, previously introduced at the tip of deep cracks on modified SE(T) specimens, have been satisfactorily predicted using their properly calcu- lated notch sensitivity factor q, considering the notch tip stress gradient influence on the fatigue behavior of mechanically short cracks. This is an indispensable detail, since traditional q estimates are only appli- cable to semi-circular notches, whereas elongated slits can have q values which also depend on their shape, not only on their tip radius. Based on this experimental evidence, a criterion for acceptance of short cracks is proposed. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The notch sensitivity factor 0 6 q 6 1 is widely used in struc- tural design to quantify the difference between K t , the linear elastic stress concentration factor (SCF) of a notch, and K f , its correspond- ing fatigue SCF, which quantifies the actual notch effect on the fa- tigue strength of structural components [1]. The SCF K t is equal to r max /r n , where r max is the maximum (linear elastic) stress at the notch root caused by r n , and r n is the nominal stress that would act at that point if the notch did not affect the stress field around it. The fatigue SCF is usually defined by K f ¼ 1 þ qðK t  1Þ¼ S L =S Lntc ð1Þ where S L and S Lntc are the material fatigue limits (or their fatigue strengths at a convenient very long life) measured on standard (smooth and polished) and on notched test specimens, respectively. But, as the fatigue process depends on two parameters, Eq. (1) can be generalized considering that K f may depend e.g. on R= r min /r max , by writing K f (R)= S L (R)/S Lntc (R). It is well known that q can be associated with the relatively fast generation of tiny non-propagating fatigue cracks at notch roots, see Fig. 1. Indeed, according to Frost et al. [2], early experimental evidence that small non-propagating fatigue cracks are found at notch roots when S L /K t < r n <S L /K f goes back as far as 1949. Hence, it is certainly reasonable to expect that such tiny cracks can be used to quantitatively explain why K f 6 K t and, consequently, that the notch sensitivity can be analytically predictable from the fatigue propagation behavior of short cracks emanating from the notch tip. It is demonstrated below that in fact this can be done using relatively simple but sound mechanical principles, which do not require heuristic arguments, or arbitrary fitting parameters. To associate the notch sensitivity to the transition between the non-propagating and propagating states of short fatigue cracks, first the influence of stress field gradients around notch roots on their propagation behavior is studied. Knowing that for stress anal- ysis purposes the behavior of notches with depth b and tip radius q can be well simulated by elliptical notches with semi-axes b and c and tip radius q =c 2 /b, it is shown that, for any given material, q depends not only on the notch tip radius q, but also on its depth b [3,4]. In other words, the crack shape, characterized by its tip ra- dius to depth q/c ratio (or by the semi-axes c/b ratio), has a strong influence on its effect on fatigue strength. This means that shallow and elongated notches of same tip radius q may have quite differ- ent notch sensitivities q. It is also shown that the material influence on the notch sensi- tivity depends on its propagation threshold for (long) fatigue cracks DK th (R) and on its fatigue limit for crack initiation from a 0142-1123/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2011.10.010 ⇑ Corresponding author. Tel.: +55 21 3527 1642; fax: +55 21 3527 1665. E-mail addresses: jtcastro@puc-rio.br (J.T.P. Castro), meggi@puc-rio.br (M.A. Meggiolaro), acmiranda@unb.br (A.C.O. Miranda), wuhao@tongji.edu.cn (H. Wu), abdellatif.imad@polytech-lille.fr (A. Imad), noureddine.benseddiq@univ-lille1.fr (N. Benseddiq). International Journal of Fatigue 42 (2012) 172–182 Contents lists available at SciVerse ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue