Issue 48

A.C. de Oliveria Miranda et alii, Frattura ed Integrità Strutturale, 48 (2019) 611-629; DOI: 10.3221/IGF-ESIS.48.59 616         24 2 4.5 0.89 1 1.09 0.09 14 1 , c t 0.2 0.65 0.04 0.09 , c s t c t c t c t c M c t c t c t c t t                   (15)       1.65 1.65 1 1.464 , c t 1 1.464 , c t t c Q c t c t           (16)     , 1.45, c t 1.1 0.35 , c t s c F c t c t         (17) , 1.1 s a F   (18) To guarantee continuity of the K I (c) expression, Eqs. (10) and (12) should be equivalent at the end of the 2D/1D transition zone (when a’  2.3  t ), resulting in   ,1 , ' 2.3 ( ) ( ) '( ) ( ) 1 I I D s s c a t K c K M c t Q c t t c F c t              (19) Notice that Eq. (19) is a function of c/t only, having a unique solution for c/t  1.23. Therefore, if the ratio c/t is replaced in Eqs. (12-18) by a function r’(c/t, a’/t) that tends to 1.23 as a’ tends to 2.3  t , then continuity of the SIF is guaranteed. So, from Eq. (3), r’ is expressed as       2.3 1.3 , 1.23 1.23 a t r c t a t c t      (20) and the SIF during the transitioning period is then modeled replacing c/t by r’ in Eqs. (12-18). When the imaginary crack depth a’ reaches 2.3  t , Eq. (15) is then used to model the subsequent 1D crack growth. Fig. 4 plots the ratio between the transition and the 1D SIFs calculated using the proposed approach, to show their smooth transition. Figure 4 : Ratio between the transition and 1D SIF calculated using the proposed approach. Two main improvements are achieved using this approach. First, the effect of c/t on K I (c) is much better modeled by Newman-Raju’s equations than by the expressions used by Johnson. Second, continuity in the K I (c) function is guaranteed