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

Two approaches for finding three-dimensional kinematically admissible veloc ity fields in a flat layer of an ideal rigid-plastic material subjected to tension (compression) are proposed. The layer is assumed to have a simply c onnected but otherwise arbitrary in-plane cross section. The kinematically admissible velocity fields are based on a uniform strain rate field appropr iate for a layer without friction and on such a field combined with the asy mptotic behavior required of a real velocity field near a velocity disconti nuity surface (surface with maximum shear stress). Both of these kinematica lly admissible velocity fields are used to determine upper bounds on the li mit load for layers with quite general yield criteria. Using these limit lo ad solutions, an approach is proposed for estimating the distribution of te nsile stresses on the symmetry plane of the layer and, in particular, the V alue of maximum tensile stress. The latter is of importance for understandi ng fracture within the layer. A practical application of this analysis is estimation of the strength of a dhesive joints. Numerical calculations are made for an elliptical layer wit h the Mises yield criterion and for a circular layer with the Tresca yield criterion. The results compare very favorably with available slip line solu tions for plane strain and axial symmetry. (C) 1999 Published by Elsevier S cience Ltd. All rights reserved.