Issue 43

F. Berto et alii, Frattura ed Integrità Strutturale, 43 (2018) 1-32; DOI: 10.3221/IGF-ESIS.43.01 11                 2 0 0 (1 )(5 8 ) 4 th K R (9) When ν =0.3, Eq. (4) gives R c = 0.845 a 0 , where      2 0 0 (1/ )( / ) th a K is the El Haddad-Smith-Topper parameter [106]. Under plane stress conditions, simple algebraic considerations give:               2 0 0 (5 3 ) 4 th K R (10) so that we have now R 0 =1.025 a 0 when the Poisson’s ratio ν is 0.3. Fig. 11 exactly fits the Kitagawa diagram plotting fatigue strength of a material in the presence and absence of cracks [103]. The plateau on the left hand side of Fig. 2 is due to the fact that the small cracks are fully embedded in the elementary structural volume, so that the value of 1 W coincides with that of the plain specimens (under plane strain conditions). The transition crack size a 0 has been employed as an empirical parameter to account for the differences between long and short fatigue cracks. In particular El Haddad et al. [106] suggested to add in the SIF range definition the fictitious crack length a 0 to the crack amplitude a. Doing so, the fatigue limit Δ σ th of cracked components was correlated to plain specimen fatigue limit by means of the expression:       0 0 1 1 / th a a (11) By observing Fig. 11, when a >> R 0 , it is possible to write:       Re Re 1 1 Re 1 1 0 0 1 0 1 1 1 ( ) 1 / 1 / (1 / ) f f f W W W a aI R a a W aI R (12) where   Re 2 0 1 / 2 f W E is the reference value. The analogy with Eq.(11) is evident. Figure 12: Fatigue behavior of a material weakened by notches or cracks (log-log scale).