  In this paper we provide necessary and sufficient conditions in order to
guarantee the energy-dissipation balance of a Mode III crack, growing on a
prescribed smooth path. Moreover, we characterize the singularity of the
displacement near the crack tip, generalizing the result in [S.Nicaise,
A.M.Sandig - \textit{J. Math. Anal. Appl.} 2007] valid for straight fractures.
