numero25

C. J. Christopher et alii, Frattura ed Integrità Strutturale, 25 (2013) 161-166; DOI: 10.3221/IGF-ESIS.25.23 163 1 1 1 2 2 2 y r r r i 1 1 2 2 1 1 1 2 2 2 r r i x r 1 1 5 1 5 (A cos B B sin 2 2 2 2 2 2 2 1 5 5 E 4B 8E)r r cos r sin r ln(r ) cos sin ) 4B 8E)r r c 5cos 5sin O(r 2 2 2 2 2 1 1 5 1 5 (A cos B B os r si 7sin 2 2 n 2 2 2 2 2                                                                     1 1 2 2 1 1 2 2 xy r r i 1 1 2 2 1 5 5 E 3cos 3sin C O(r 2 2 2 2 2 1 5 1 5 r B B r cos 3cos 2 2 2 2 2 2 3 3 E ln(r )cos sin O r ln(r ) cos sin ) A sin s (r 2 2 in r sin )                                                                       (3) F K is defined from the asymptotic limit of y  as x 0   , along y 0  , i.e. towards the crack tip from the front along the crack line: r 0 1 2 F y r r K lim 2Er ln(r )) 2 r( (A 3B 8E) 2                 (4) R K was obtained by evaluating x  in the limit as x 0   , along y 0  , i.e. towards the crack tip from behind along the crack flank: R i r x 0 2 r K lim (2B E 2 4 )              (5) S K is derived from the asymptotic limit of xy  as x 0   , along y 0  , i.e. towards the crack tip from behind along the crack flank: S 0 xy r r r 2 r K l A ) im ( B 2            (6) The +ve sign indicates y 0  , and a –ve sign that y 0  . The quantity II K characterizes mode II loading, and is derived from the asymptotic limit of xy  as x 0   , along y 0  , i.e. towards the crack tip from the front along the crack line: xy I i I r 0 2 r 2 B K lim 2           (7) T-stress is the transverse stress which is added to x  as a constant term and is given by T C   (8) The new five-parameter model can be solved for displacement fields: