Interaction of longitudinal wave with a penny-shaped crack at the interface of two bonded dissimilar elastic solids-II

✍ Scribed by K. N. Srivastava; R. M. Palaiya; O. P. Gupta

• Publisher: Springer Netherlands
• Year: 1979
• Tongue: English
• Weight: 398 KB
• Volume: 15
• Category: Article
• ISSN: 1573-2673
• DOI: 10.1007/bf00019925

✦ Synopsis

The paper deals with the problem of finding the stress distribution near a penny-shaped crack situated at the interface of two bonded dissimilar elastic solids. The crack is opened by the interaction of plane harmonic longitudinal elastic wave, incident normally on the crack. The problem is first reduced to a set of simultaneous dual integral equations which are further transformed to a set of simultaneous singular integral equations. These are solved numerically by reducing them to a set of algebraic equations. The solution is used to calculate the stress-intensity factors and the size of the overlapping zones at the edge of the crack. Applying the operators Air, AI, A 2 ( O ) r and Az(O/Or) to Eqns. (3.5)-(3.8) Int. Yourn. of Fracture, 15 (1979) 591-599 m~(~) = -(n20 + G)(1 + n~0G) x [k2G!~-l{a~'(2!~ 2 -kZ~) 2 -4/32~ 2} + k ~-' { a ~1(2~2 -k2) z -4 / 3 ~ 2} + {(-t/z0 + G)(1 + "ql0G)}-l{(~/10 + 1)G + ('02o + 1)}/76] + F 6 , Kt(x, u) = rn(~) sin ~:x cos {~u d~, i0 o Kz(x, u ) = n(~) sin ~x sin ~u d~, o~ml(~) COS ~x cos ~U d~,

w h e r e ~i (i = 1, 2) is t h e P o i s s o n ' s ratio of t h e m a t e r i a l of the r e g i o n z > 0 a n d z < 0 r e s p e c t i v e l y a n d ai, ¢ii, hi, k; are d e f i n e d in (2.11).