Short crack threshold estimates to predict notch sensitivity factors in fatigue Marco Antonio Meggiolaro * , Antonio Carlos de Oliveira Miranda, Jaime Tupiassu ´ Pinho de Castro Department of Mechanical Engineering, Pontifical Catholic University of Rio de Janeiro, Rua Marque ˆs de Sa ˜o Vicente 225, 22453-900 Ga ´ vea, Rio de Janeiro, RJ, Brazil Received 18 December 2006; received in revised form 4 February 2007; accepted 5 February 2007 Available online 2 March 2007 Abstract The notch sensitivity factor q can be associated with the presence of non-propagating fatigue cracks at the notch root. Such cracks are present when the nominal stress range Dr n is between Dr 0 /K t and Dr 0 /K f , where Dr 0 is the fatigue limit, K t is the geometric and K f is the fatigue stress concentration factors of the notch. Therefore, in principle it is possible to obtain expressions for q if the prop- agation behavior of small cracks emanating from notches is known. Several expressions have been proposed to model the dependency between the threshold value DK th of the stress intensity range and the crack size a for very small cracks. Most of these expressions are based on length parameters, estimated from DK th and Dr 0 , resulting in a modified stress intensity range able to reproduce most of the behavior shown in the Kitagawa–Takahashi plot. Peterson or Topper-like expressions are then calibrated to q based on these crack propagation estimates. However, such q calibration is found to be extremely sensitive to the choice of DK th (a) estimate. In this work, a generalization version of El Haddad–Topper–Smith’s equation is used to evaluate the behavior of cracks emanating from circular holes and semi-elliptical notches. For several combinations of notch dimensions, the smallest stress range necessary to both initiate and propagate a crack is calculated, resulting in expressions for K f and therefore for q. It is found that the q estimates obtained from this generalization, besides providing a sound physical basis for the notch sensitivity concept, better correlate with experimental data from the literature. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Notch sensitivity; Short cracks; Fatigue crack growth threshold; Non-propagating cracks 1. Introduction The purpose of this paper is to verify if and when the classical Peterson-like notch sensitivity factors, still widely used all over the world for designing mechanical compo- nents by the classical SN methodology [1–3], can be repro- duced from notch stress analysis and Topper-like short crack concepts, assuming the material can be modeled as linear, elastic, isotropic and homogeneous. The empirical notch sensitivity factor q was introduced to quantify the difference between K t , the geometric (or lin- ear elastic) stress concentration factor of the notch, and its actual effect in the fatigue limit, K f =1+ q(K t 1) = Dr 0 / Dr f , where K f is the so-called fatigue (stress) concentration factor, and Dr 0 and Dr f are the fatigue limits of smooth and notched SN specimens, respectively. Small non-propa- gating fatigue cracks that are found at the notch roots when Dr 0 /K t < Dr n < Dr 0 /K f , where Dr n is the nominal stress range applied in the notched piece [4] can, at least in some cases, explain why K f 6 K t . Therefore, in such cases it should in principle be possible to analytically 0142-1123/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2007.02.022 * Corresponding author. Tel.: +55 21 3527 1638; fax: +55 21 3527 1165. E-mail addresses: [email protected] (M.A. Meggiolaro), amiranda @tecgraf.puc-rio.br (Antonio Carlos de Oliveira Miranda), jtcastro@mec. puc-rio.br (J.T.P. de Castro). www.elsevier.com/locate/ijfatigue International Journal of Fatigue 29 (2007) 2022–2031 International Journalof Fatigue
Short crack threshold estimates to predict notch sensitivity factors in fatigue
Jun 29, 2023
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