On estimating the tensile strength of an adhesive plastic layer of arbitrary simply connected contour

Two approaches for ®nding three-dimensional kinematically admissible velocity ®elds in a ¯at layer of an ideal rigid±plastic material subjected to tension (compression) are proposed. The layer is assumed to have a simply connected but otherwise arbitrary in-plane cross section. The kinematically admissible velocity ®elds are based on a uniform strain rate ®eld appropriate for a layer without friction and on such a ®eld combined with the asymptotic behavior required of a real velocity ®eld near a velocity discontinuity surface (surface with maximum shear stress). Both of these kinematically admissible velocity ®elds are used to determine upper bounds on the limit load for layers with quite general yield criteria. Using these limit load solutions, an approach is proposed for estimating the distribution of tensile stresses on the symmetry plane of the layer and, in particular, the value of maximum tensile stress. The latter is of importance for understanding fracture within the layer. A practical application of this analysis is estimation of the strength of adhesive joints. Numerical calculations are made for an elliptical layer with the Mises yield criterion and for a circular layer with the Tresca yield criterion. The results compare very favorably with available slip line solutions for plane strain and axial symmetry