Note on the Energy Release Rate for a Crack Starting from the Apex of a Wedge.
CARNEGIE-MELLON UNIV PITTSBURGH PA DEPT OF MATHEMATICS
Pagination or Media Count:
Griffith was apparently the first to employ the energy release rate G as a critical condition of crack extension. In this note we will show, however, that if a crack starts from the apex of a wedge, the initial value of G is zero, although the stresses at the crack tip are unbounded. This example suggests that you cannot use the initial energy release rate as a critical condition of crack extension unless the opening-angle of the crack faces in the reference is precisely zero. Since the order of the singularity of the strain energy density is less than one, this result may be predicted mathematically but it is not trivial physically. We confine our problem to a simple mode II crack the given solutions are then simple and of closed-form so that we can examine the precise dependence of G on the crack length a. To the authors knowledge, no such closed-form solutions for an arbitrary crack length a have been presented. Author