Saint-Venants principle and the plane elastic wedge

The stress _eld due to self!equilibrating loading on the inner or outer arc of a plane strain elastic wedge sector is a}ected by two agencies] a geometric e}ect of increasing or decreasing area\ and decay as anticipated by Saint!Venant|s principle "SVP#[ When the load is applied to the inner arc the two e}ects act in concert ^ however\ when the load is applied to the outer arc the two e}ects act in opposition and for a wedge angle in excess of the half!space\ 1a p\ for the symmetric case\ and for 1a 0[32p for the asymmetric case\ the geometric e}ect is dominant over Saint!Venant decay and stress level increases as one moves away from the outer arc\ con_rming the inapplicability of SVP[ This is additional to previously reported di.culties at these angle when a self!equilibrated load on the inner arc decays at the same rate as does a concentrated momentand is explained in terms of the interaction of a near!_eld geometric e}ect and a far!_eld stress interference e}ect at a traction!free edge[ For wedge angle 1a 1p the unique Modes I and II inverse square root stress singularities at the crack tip\ which are at the heart of Linear Elastic Fracture Mechanics "LEFM#\ can be attributed to this inapplicability for just one symmetric and one asymmetric eigenmode[ 0887 Elsevier Science Ltd[ All rights reserved