Issue 41

V.M. Machado et alii, Frattura ed Integrità Strutturale, 41 (2017) 236-244; DOI: 10.3221/IGF-ESIS.41.32 238            R R 1 2 th th R K a K 1 a a / ( ) ( ) , where   R R 2 R th L a (1 ) K S            (3) Equation (3) reproduces the ETS model when  2 , and the bi-linear limits in Kitagawa-Takahashi diagrams as well, see [4] for details. But much more important, it can be used to answer questions that are quite important in practical applications. This model can be used for practical applications. For example, it can check if it is possible to replace a central circular hole with diameter d  20mm by an elliptical one with axes 2b  20mm (perpendicular to  n ) and 2c  2mm , in a large notched steel plate with tensile strength S U  600MPa , S L  200MPa , and  K th0  9MPa  m , which works under a constant fatigue load  n  100MPa and R  1 . Neglecting buckling to start with, using classic SN design procedures [12-14], the circular hole would have a safety factor  F  S L /K f  n  200/150  1.33 against fatigue crack initiation, since due to its large radius it has K f  K t  3 . However, since the much sharper elliptical hole tip radius  c 2 /b  0.1mm  K t  2b/c  21  K f  1  q  (K t  1)  7.33 (as, according to the traditional Peterson’s estimate, q  ( 1  )  1  [ 1  0.185  (700/600)/0.1 ]  1  0.32 [15]), it should fail by classic SN procedures. Indeed, it would work under a stress amplitude  a  K f   n  367MPa > S L . Nevertheless, since this K f value is larger than the K f < 4 typically obtained from notched coupons fatigue data [4], it is worthwhile to reevaluate this prediction. This can be done assuming e.g.  K th0 (a)  K th0 / [ 1  (a 0 /a) ] 0.5 (by ETS), the steel fatigue limit S L  S U /2 (as usual, noticing that S L is an amplitude whereas  S L is a range),  S L0  S U /1.5 (by Goodman), and a 0  ( 1/  )(  K th0 /  S L0 ) 2  ( 1/  )( 1.5  K th0 /1.12  S U ) 2  0.13mm . Using these estimates, then the SIF ranges  K I (a) estimated for the two holes by the procedures developed in [5] are compared to the short-crack threshold  K th0 (a) in Fig. 1. Notice that crossings between the  K I loading and the  K th (a) resistance curves in this figure define crack arrest, so the largest tolerable crack sizes. Hence, considering the effect of the stress gradient ahead of the notch tip on the growth behavior of short cracks, this model predicts that both the circular and the elliptical holes could support the nominal load range  n without failing by fatigue. Figure 1 : According to the short crack model, cracks should not initiate at the circular hole (which tolerates cracks a tol < 1.52mm ), while the crack that initiates at the elliptical hole tip should stop when reaching a size a st  0.33mm . It is interesting to emphasize the practical usefulness of modeling the short crack behavior in notched components. The classic SN and  N methodologies are very much used to analyze and to design supposedly crack-free structural components in engineering applications, even though it is impossible to guarantee that they are really free of cracks smaller than the guaranteed detection threshold of the non-destructive inspection method used to identify them. In fact, although large cracks may be detected and dealt with in practice, microcracks and short cracks are practically undetectable by traditional non-destructive inspection methods. Nevertheless, most components are still designed against fatigue crack initiation using procedures that do not recognize such unavoidable small flaws. So, their service life expectancy may become unreliable when such tiny defects are introduced by any means during manufacturing or service. Therefore, structural components that must last for long fatigue lives should be designed not only to avoid crack initiation, but also to be tolerant to undetectable short cracks. Indeed, continuous work under fatigue loads cannot be guaranteed if any of the flaws that they might have (because they could not be or have not been detected) can somehow