The Half-plane with an Edge Crack in Plane Elastostatics

The Wiener-Hopf technique is applied to the problem of a half-planewith a crack perpendicular to its edge. A closed solution isobtained giving the stress and displacement fields in the formof eigenfunction expansions, valid over the whole region, exceptthe neighbourhood of the tip of the crack. The behaviour inthis region is obtained by an asymptotic technique. The coefficientsof the expansions involve a generalized factorial function,and a method for the computation of this function is given,thus enabling numerical values of the stresses and displacementsto be obtained for the given cases of stretching and bendingthe half-plane.     

The Wedge with a Symmetric Crack at the Vertex in Plane Elastostatics

A closed solution of the biharmonic equation under boundaryconditions appropriate to the wedge with a symmetric crack atthe vertex is found by using the Wiener-Hopf technique. Thestress and displacement fields are given as integrals whichmay be readily expressed as eigenfunction expansions. An expression is obtained for the stress intensity factor atthe tip of the crack using an asymptotic method, and is verifiedby a consideration of the stran-energy.