Issue34

M. Goto et alii, Frattura ed Integrità Strutturale, 34 (2015) 427-436; DOI: 10.3221/IGF-ESIS.34.48 433 Figure 8 : Orientation Imaging Microscopy orientation for sub-surface microstructure in the zx -plane: (a ) original microstructure before stressing; (b) after constant stressing at  a = 240 MPa; (c) after constant stressing at  a = 90 MPa F i (α) = K i (α)/ K i E (α) i = I, II, III (1) where, K i (  ) is SIF along the crack front and K i E (  ) is SIF of an elliptical crack [29]. The location along a crack front was defined by the eccentric angle of the ellipse,  , defined as the angle for mapping a semi-circle illustrated with a dashed line in Fig. 9c. Namely, the actual position of a semi-elliptical crack at a given  value in Fig. 9c is indicated by a point A for the zx -plane crack ( b < a ), and point B for the xy -plane crack ( a < b ). Here, a and b are the half lengths and depth of a semi-elliptical crack measured along the crack face, respectively (Fig. 9c). The crack front at the surface and the deepest point are shown by  = 0 and 90°, respectively. However, the DL-SIF values at the surface were evaluated by the values Figure 9: Inclined semi-elliptical surface-cracks in a semi-infinite body subjected to tension load in the x -direction at infinity: ( a and b ) a model for crack on the zx - and xy -planes; (c) the definition of  , and actual position for the zx - and xy -plane crack fronts. at  = 1° instead of  = 0°, because in 3-dimensional surface cracks, the point where the crack front intersects a free surface is known as a corner point. The stress singularity at this point is different from that of an ordinary crack [30]. Generally, it has been difficult to obtain smooth distributions of SIFs along the crack front accurately.