qfiR (0 )P (0 ) Id i ,
For the subsonic case in which the crack-tip speed is less than the Rayleigh-wave speed, the stress intensity factor of a mode-I crack is defined by:
= lim£-hO f2m cjyte y=0)
However,It is apparent from eqs.(2.2), (3.1), and (3.6) that for the transonic case the stress field has singularities with the order of -(l/2+H(s-2) ), instead of -1/2. Therefore, we defined the stress intensity factor for the transonic case as:
Kj = lim e-»0
„ l/2+H(s"2) (27te) a y(e,,y=o)}
After some manipulations, the dynamic stress intensity factor for the transonic case is found as:
s V - 2 s-2)2 w "-2'
(1 +2H(s*2> j Vs
■wr J-, 3 >H(S‘2) l*(b’ « T T ( 0Kt = qV7ist (tcs t) I s'2-a-2 J
where J is given in eq.(3.6) and is negative. Since y (s-2) and H(s-2) are all positive when the crack-tip speed s is in the transonic range, the value of Kx is therefore negative for positive load q. A graph of the ratio Kj/qVrcst (n s3t)H<s 2> versus s/a is shown in FIGURE 2 for the Pwave speed a = 6326 m/sec and die S-wave speed b = 3463 m/sec. FIGURE 2 shows that the
value of Kj/qVrcst (k s3t)H^s 2) is approximated to -0.5 when s = b, stays about -0 when b < s < a, and approaches to - when s = a. From the viewpoint of physics, the negative stress intensity factor means a healing crack. However, when a crack is subjected to a tensile external load, the crack surface is going to open, not to close. This means that the mode-I crack propagating with transonic velocity is impossible, which independently agrees with the Broberg's study.