Mode III near and far fields for a crack lying in or along a joint

Matched asymptotic expansions allow one to give, at two scales, a description of the solution to the antiplane problem of two di€erent elastic substrates bonded together by a thin elastic adhesive layer with a crack lying inside or even outside at a short distance of it. The leading term is the classical solution obtained, by ®nite elements for instance, when perfect transmission conditions are assumed through the line modelling the interface. The corrections depend on the relative sti€nesses of the components and on the thickness of the joint. It also depends on the crack location, within the joint or outside. Two kinds of Mode III stress intensity factors are de®ned, a ®ctitious and an actual one, they are so-called far and near (or remote and local) by the authors. The ®ctitious one is meaningless and must be rescaled by an appropriate coecient to give the actual one.