fnr. 1. Engng Sci. Vol. 31, No. 9, pp. 1301-1307, 1993 MM-7225193 $4.00 f 0.00 P&led in Great Britain. All rights reserved Copyright @ 1993Pergamon Press Ltd STRESS DISTRIBUTION IN AN ELASTIC PERFECTLY PLASTIC PLATE SUBJECTED TO CORROSIVE ENVIRONMENTAL LOADS A. KADIC-EALEB and R. C. BATRA Department of Mechanical and Aerospace E~gin~ring and Engineering Mechanics, University of Missouri-Rolla, Rolta, MO 65401-0249, U.S.A. Abstract-We analyse deformations of an isotropic elastic/perfectly plastic plate subjected to environmental effects such as the corrosive forces exerted by the surrounding medium. It is found that for the bounding surfaces of the plate to deform plastically, the corrosion process must propagate to a point whose distance from the outer bounding surface exceeds one third the half-thickness of the plate, and for the central unaffected material to also deform plastically the half-thickness of the corroded layer must exceed five eighths the half-thickness of the plate. INTRODUCTION The mecbani~l behavior of materials subjected to reactive environments is of interest in many industries such as the electronics industry wherein dies are etched by dipping the body in a reactive chemical solution. Often, one deals with small scale structures, and the surrounding medium can cause severe adverse effects leading to its eventual failure. If the forces exerted by the environment on the structure could be estimated with some certainty, then the problem of analyzing deformations of the structure will reduce to solving an initial-boundary-value problem. However, such information is generally lacking. Therefore, we use here a semi-inverse approach in the sense that we represent deformations caused by the corrosive medium by an eigenstrain, motivate a reasonable expression for it, and ascertain conditions under which the body will deform elastically and/or plastically. Here we consider a flat plate made of an isotropic elastic/pe~ectly plastic material. We envisage that the plate is initially stress free and is exposed to a reactive environment. The corrosion process affects the faces of the plate by, for example, selective removal of atoms so that pores are generated within the plate, and the pore concentration varies through the thickness, being highest at the outermost surface layer in contact with the environment and gradually decreasing to zero. An example of such a process is the preferential dissolution of copper from Cu,Al alloy in NaCl solution [l]. The corrosion affected layer tends to contract. Here we analyze the stress distribution within the plate because of the differential contraction of various layers. FORMULATION OF THE PROBLEM In order to simplify the problem, we consider an infinite plate of thickness 2h and made of an isotropic elastic/perfectly plastic material. We use rectangular Cartesian coordinates with origin at the mid surface of the plate and x,-axis perpendicular to its faces. The bounding surfaces x3 = fh of the plate are exposed to a corrosive environment and are presumed to be traction free. The plate layer in contact with the environment deforms because of the exchange of particles between the plate and the environment. These deformations induce stresses in the plate. We assume that the plate deforms quasistatically so that inertia effects are negligible, a state of plane stress prevails within the plate, corrosive forces cause only normal stresses, the defo~ations of the plate are in~nitesimal in the sense that linear kinematical relations can be 1301