Crack paths in three-dimensional elastic solids. ii: three-term expansion of the stress intensity factors—applications and perspectives

This work continues the calculation of the stress intensity factors\ as a function of position s along the front of an arbitrary "kinked and curved# in_nitesimal extension of some arbitrary crack on some three! dimensional body[ More precisely\ o denoting a small parameter which the crack extension length is proportional to\ what is studied here is the third term\ proportional to o0 o and noted K"0#"s#o\ of the expansion of these stress intensity factors at the point s of the crack front in powers of o[ The novelties with respect to previous works due to Gao and Rice on the one hand and Nazarov on the other hand\ are that both the original crack and its extension need not necessarily be planar\ and that a kink "discontinuity of the tangent plane to the crack# can occur all along the original crack front[ Two expressions of K"0#"s# are obtained^ the di}erence is that the _rst one is more synthetic whereas the second one makes the in~uence of the kink angle "which can vary along the original crack front# more explicit[ Application of some criterion then allows to obtain the a priori unknown geometric parameters of the small crack extension "lengthkink angle\ curvature parameters#[ The small scale {{segmentation|| of the crack front which is observed experimentally in the presence of mode III is disregarded here because a large scale point of view is adopted^ this phenomenon will be discussed in a separate paper[ It is shown how these results can be used to numerically predict crack paths over arbitrary distances in three dimensions[ Simple applications to problems of con_gurational stability and bifurcation of the crack front are _nally presented[ 0887 Elsevier Science Ltd[ All rights reserved