Issue 48

A.C. de Oliveria Miranda et alii, Frattura ed Integrità Strutturale, 48 (2019) 611-629; DOI: 10.3221/IGF-ESIS.48.59 614 Castro and Meggiolaro [10] proposed in their 2016 book improved equations for 2D-1D crack transitions, which are inspired on Johnson’s approach but use much improved Newman-Raju’s solutions for the 2D crack SIFs [18-22]. However, their proposed equations have not been properly checked by experimental data. To verify them, in this paper 2D-1D FCG transitions are measured in two different materials, 4340 steel and polycarbonate (PC), in order to present suitable crack size and shape data, and the corresponding numbers of cycles spent in the 2D-1D transition zones, as discussed in the following. These studies were done only for plate-like geometries. Some authors have worked with different geometries, like the pipes studied in [23-24], for example. I MPROVED MODELS FOR THE TRANSITION FROM SURFACE TO THROUGH CRACKS ewman-Raju’s equations are adapted to model the transition from surface semi-elliptical or corner quarter elliptical 2D cracks to through-the-thickness 1D cracks. In addition to the effects of the back face magnification and crack shape parameter, Newman-Raju’s expressions also model the specimen width and front surface effects. To model the 2D/1D transition zone, the basic hypothesis of ellipsoidal geometry preservation is assumed. Therefore, as illustrated in Fig. 3 [10], Johnson’s criterion c’  0.9  c for the end of the 2D/1D transition zone is equivalent to   2 2 ' 1 ' 1 0.9 2.3 a t c c t t      (2) Figure 3 : Gradual model for the 2D/1D surface-to-through-crack transition in the plate. In other words, the 2D/1D transition zone starts when the crack depth equals the specimen thickness ( a’  a  t ), and is assumed to end when the imaginary crack depth a’ reaches 2.3  t . Using this result, continuity of the width SIF expressions for the transitioning period, K I (c) , and for the 1D crack growth regimen, K I,1D , can be achieved replacing all occurrences of c/t by a parameter     2.3 1.3 ( ) a t r c t        (3) where  is the value of c/t that satisfies K I (c)  K I,1D . Note that r’  c/t in the beginning of the 2D/1D transition zone (when a’  t ), and r’  a when the transition ends and the crack finally becomes a 1D through-the-thickness crack with a’  2.3  t . The application of this approach for the transition from surface (semi-elliptical) cracks to through-cracks is presented next. Transition from 2D semi-elliptical surface cracks to 1D through-cracks Newman and Raju modeled the SIF on the width and depth directions of surface cracks under uniaxial tension  , respectively K I (c) and K I (a) , by N