Issue 44

M. Ciavarella et alii, Frattura ed Integrità Strutturale, 44 (2018) 49-63; DOI: 10.3221/IGF-ESIS.44.05 59 The limit case is when the stress concentration is high enough that K t >F K /F R in which case the limit ratios is obtained between the static and the fatigue limits, and consequently from (18)         R lim K k F k F Log Log (21) which is clearly the highest slope compatible to our criteria and the material properties ratios. The more general equation analogous to Eq. (20) could be obtained by using K t >F K /F R in (20) or combining eqt(21) with Eq. (6-7), obtaining in any case                    lim c a th a N N k m v v 0 Log Log (22) which clearly seems to link the limit generalized Wöhler slope to the Paris slope and the position of the key points in the Wöhler and Paris laws, as it is correct since the limit generalized Wöhler slope is indeed significant in the region where life would be mainly given by propagation. In fact, turning back to the standard assumptions for the key points ( th a v , c a v =10 -6 , 10 -2 mm/cycle and, perhaps with less generality, N ∞ =10 7 and N 0 =10 3 cycles), we re-obtain the comforting result that the limiting Wöhler coefficient coincides numerically with the Paris coefficient:        lim k m m ' 7 3 2 6 (23) as it was obtained independently from integrating Paris’ law in (8). Turning back to our classification, we have finally a 4 th region, where a*<a< a* S where the slope starts to increase again towards the original value, k, which then remains constant in the fifth region. This is not too hard to interpret, given that a very large blunt notch basically behaves as a standard specimen subject to a nominal stress K t -times higher than the remote stress. In other words, we suggest that we start from the basic Wöhler curve behaviour, we move towards Paris with increasing notch size, but we then return to the original Wöhler behaviour again, for very large blunt notches. Notice that only the Wöhler curves corresponding to the key sizes are reproduced in Fig.6, whereas also some intermediate ones are included in Fig.7 with lighter line. For Case (a), F K >F R but K t <F K /F R the limiting slope is not reached, and we only obtain the minimum slope as (18) or (20). We then decrease slope in the fourth region and return to the original one in the fifth. The case (b) is somehow contrived and would correspond to an abrupt transition from Wöhler towards Paris and back to Wöhler , the abrupt transition being particularly evident because of the schematic form of the criterion. W ÖHLER CURVES USING E L H ADDAD n the previous paragraph, we used the schematic version of the static and infinite life Atzori-Lazzarin criteria. Here, we shall use the El Haddad Eqs. (10) and the corresponding static case. Notice we can put these two equations in the form of a reduction fatigue K f in fatigue, and the corresponding K S reduction static factor               f t a for a a a K K for a a * 0 * 1 ,       ,      (24) and I