Issue 41

V.M. Machado et alii, Frattura ed Integrità Strutturale, 41 (2017) 236-244; DOI: 10.3221/IGF-ESIS.41.32 237 For design purposes, q -values are traditionally estimated by fitting semi-empirical models to data from fatigue tests of notched components. However, q has long been associated to non-propagating short cracks that start at the notch tips but stop after growing for a small distance [2-4]. Consequently, q -values can also be analytically modeled by studying the behavior of those short fatigue cracks. In particular, the model proposed in [5-7] estimates q -values for fatigue loading conditions using sound mechanical principles and well-defined mechanical properties, without the need for any additional data-fitting parameter. Moreover, it allows the notch sensitivity concept to be extended to environmentally-assisted cracking (EAC) problems as well, and its predictions have been validated under liquid metal embrittlement conditions by testing notched Al samples in a Ga environment [8], as well as under hydrogen embrittlement conditions by testing similar steel samples in aqueous H 2 S environments [9]. This versatile notch sensitivity model is extended in this work to deal with elastoplastic (EP) problems using J -integral techniques properly adapted to consider the short crack behavior near the notch tips. I NFLUENCE OF SHORT CRACKS IN THE FATIGUE LIMIT OF NOTCHED STRUCTURAL COMPONENTS atigue cracks are very sensitive to local load conditions, so they usually initiate at notch tips due to the stress concentration effects induced by the notch. A similar behavior occurs under EAC conditions as well. However, it is less well-known that short cracks initiated at notch tips can stop to grow if the stress gradient ahead of the tip is steep enough. In fact, albeit such non-propagating cracks induce damage, they can be tolerated whenever the loading conditions cannot induce the higher local stresses needed to restart their growing process. Moreover, this apparently odd behavior can be easily explained by the competition between the opposing effects of the decreasing stress  ahead of the crack tip (due to the stress gradient that acts there) and of the increasing crack size a on its stress intensity factor (SIF) K I   (  a ), which can be seen as the crack driving force under LE conditions. To make the crack size dependent SIF compatible with a fatigue limit when a  0 , El-Haddad, Topper, and Smith (ETS) redefined the SIF range acting in a Griffith plate by [10-11]       0 K a a ( ) (1) where a 0  ( 1/  )(  K 0 /  S 0 ) 2 is the short crack characteristic size,  K th0 is the long fatigue crack growth threshold and  S L0 is the fatigue limit at R   min /  max  0 , both well-defined material properties that can be measured by standard procedures. This simple but clever trick reproduces the correct limits  ( a  0 )   S 0 for very short cracks and  K ( a  a 0 )   K th0 for long cracks, as well as the data trend in a Kitagawa-Takahashi  a diagram by predicting that cracks do not grow whenever    K th0 /  ( a  a 0 ) [4]. Since cracks that depart from notches are driven by the local stress field around their tips, if the geometry factors g(a/w) used in their SIFs K I   (  a )  g(a/w) include K t effects, as usual, it is convenient to split it into two parts, g(a/w)  (a) . In this way  (a) quantifies stress gradient effects near the notch and tends towards K t at its tip,  (a  0)  K t ; whereas  accounts for other effects that affect the SIF, like the free surface, for instance. Moreover, since the SIF is a crack driving force, it should be material-independent. So, the a 0 effect on the short-crack behavior should be used to modify the fatigue crack growth (FCG) threshold  K th (R) , which is a material property, instead of the loading parameter  K , making it a function of the crack size and of the fatigue limits, a trick that is quite convenient for operational purposes. In this way, the FCG threshold for pulsating loads  K th (a, R  0)  K th0 (a) is given by:                       ( ) ( ) ( ) ( ) ( ) ( ) 0 0 0 0 th 1 2 th th 0 th 0 0 K a a g a w a K K a 1 a a K a a a a g a w (2) However, since FCG depends both on  K and K max , Eq. (2) should be modified to consider the K max (or the R -ratio) effect on the short crack behavior. Moreover, it can also be seen as just one of the models that obey the long-crack and the microcrack limits, so it can include a data fitting parameter  [5]. So, if  K thR   K th ( a >> a R , R ) is the FCG threshold for long cracks and  S LR   S L ( R ) is the fatigue limit of the material, both measured (or estimated) at the desired R -ratio, then: F