Issue 48

M. K. Hussain et alii, Frattura ed Integrità Strutturale, 48 (2019) 599-610; DOI: 10.3221/IGF-ESIS.48.58 601             sin 2 sin 2 0 sin 2 sin 2 0 I I n n II II n n (3)              0 2 0 2 1 1 1 ; sin ; ( cos ) 2 2 2 I II II R R R u A u B r v B B r G G G (4) where 0 A and 0 B are Williams’ coefficients corresponding to the rigid body translation and 2 B is Williams’ coefficient corresponding to the rigid body rotations. Figure 1: A notch geometry with a local coordinate system. Mode I and mode II NSIFs can be defined as [10]                                                    1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 lim 2 0 2 1 cos 2 cos 2 lim 2 0 2 1 cos 2 cos 2 I II I I I I I y r II II II II II xy r K r A K r B (5) Considering only the singular terms and constant displacement terms, the displacement field at any nearby point    , P r under any arbitrary in-plane loading can be given as [14]                                                   1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 2 1 cos 2 cos 2 cos cos 2 2 2 1 cos 2 cos 2 sin sin 2 sin 2 2 I II I I I I I II II II II II A u A r G G B r B r G G (6)                                                  1 1 1 1 1 1 1 0 1 1 1 1 1 1 2 1 cos 2 cos 2 sin sin 2 2 2 1 cos 2 cos 2 cos cos 2 cos 2 2 I II I I I I I n II II II II II A v r B G G B r B r G G (7) where 1 A and 1 B are Williams coefficients for the singular terms for mode I and mode II, respectively. It can be shown that the notch opening displacement (NOD) can be written as [29]                                           1 1 1 1 1 1 1 1 1 1 cos 2 cos 2 sin 2 2 2 2 sin 2 I I I I I I I I I I A v v v v r A C r G (8)