Pure plastic bending of sheet laminates under plane strain condition

Abstract

Pure plastic bending of two- and three-ply laminates in plane strain condition has been investigated. Rigid-strain hardening material behavior has been assumed. For fibers which have been overtaken by the neutral axis and have experienced load reversal, a linear \\ ̄ gs − \\ ̄ ge relationship has been adopted. Different deformation zones have been recognized and relevant equations for the distributions of radial and tangential stresses in terms of material parameters and unknown variables have been determined. In each case, from continuity of radial stress at interlaminate boundaries, an expression for the current location of the neutral axis, in terms of the relative curvature, χ, and the relative thickness, η, has been obtained. A numerical scheme for the simultaneous solution of this expression, along with a thickness equation, has been developed. As a result, distributions of radial and tangential stresses, fiber movements, and bending moments have been calculated. The effect of material properties in terms of core/clad strength differential, and rate of strain hardening has been determined. Also, the influence of laminate geometry in two-ply, as well as symmetric and non-symmetric three-ply laminates, has been investigated.