A tale of two saints: St. Venant and ‘St. Nick’ — does St. Venantʹs principle apply to bi-material straight-edge and wedge-singularity problems?

A rigorous approach is presented to investigate the applicability of St. Venantʹs principle to the class of bi-material straight edge stress singularity problems, first investigated by Pipes and Pagano in the special case of a free edge and anti-plane shear loading. A recently developed eigenfunction expansion method is utilized to obtain three-dimensional asymptotic stress field in the vicinity of a point located at the bimaterial wedge front, subjected to free-free, clamped-clamped and clamped-free wedge-side boundary conditions. The present study considers the straight edge as a special case of a bi-material wedge, consisting of two isotropic materials, with half the aperture angle View the MathML source. The present study is devoted to establishment of rigorous conditions as to whether the presence of bi-material straight edge (free or otherwise) singularity can validate or invalidate the assumption implicit in St. Venantʹs principle that more or less guarantees the occurrence of tensile or compressive failure in the gauge section of a carefully prepared test specimen. This is accomplished by applying Cherepanovʹs general approach to the solution of canonically singular problems, based on the concept of proper boundary-value problem and the theorem of homogeneous solutions, and classification of boundary value problems (BVP) of three-dimensional elasticity theory into class S (St.Venant) or class N (non-St. Venant or ‘St. Nickʹ). It is concluded that the class of bimaterial straight edge (free-free, clamped-clamped and clamped-free) stress singularity problem belongs to class N, which explains the frequent occurrence of end tab failures in tensile (or compressive) laminate test specimens.