Issue34

Y. Sumi, Frattura ed Integrità Strutturale, 34 (2015) 42-58; DOI: 10.3221/IGF-ESIS.34.04 50 Figure 4 : Comparison of the crack path stability [12]. As can be seen from the condition (43), the present concept of crack path stability includes the length parameter h / L s and the stability may depend on the range of the crack growth length considered. An initially unstable crack growth path may recover its straight direction with increasing crack length under the condition (iv) in (43). On the other hand, if condition (iii) holds, the crack path may become unstable in the range h / L s >  (  */  * ) 2 . The Cotterell and Rice theory [4] is based on the first term of the condition (40), leading to the following criterion for crack path stability: * 0 : stable / 0 : unstable      , (44) which is equivalent to 0 : stable 0 : unstable T    (45) This may be considered as a local stability criterion for the branched and curved crack extension, while the condition (43) may be regarded as an intermediate range of stability concept, in which the stability conditions change with increasing crack length. This theoretical prediction is borne out by experimental observations. A double-cantilever beam specimen is shown in Fig. 5, where the length L equals 6 B . The characteristic length is L s = B . The numerical values of  */  and  */  are given in Fig. 6, which show the condition * * / 0 and / 0,       (46) except for an extremely long initial crack. In this case the value of D s , given by (40), is always positive, so that an unstable crack path is expected. On the contrary, when the initial crack is extremely long and the crack tip is very close to the right- hand edge of the specimen, we have * * / 0 and / 0,       (47) where the intermediate range of stability may exist. The experimental results [12, 24], are shown in Fig. 7, where sharp crack curving is observed and the final break-off of the specimen may occur at either the upper or the lower surfaces. However, if the initial straight crack is extremely long and its tip is close to the right-hand edge of the specimen, crack curving is stabilized after some crack extensions as predicted by the theory.