The End Problem for a Laminated Elastic Strip — II. Differential Expansion Stresses

Abstract

A plane elasticity solution is presented for the state of stress resulting from differential expansion in a composite made up of two rectangular strips bonded on an interface. The stress field that has long been known to exist in the middle of such a laminated strip (to the St. Venant approximation) includes neither normal nor shear traction on the bonded interface. These stress components are shown to be significant only within a distance from each end equal to the total thickness, and their distribution is determined for a wide range of elastic moduli and strip dimensions.It is found that the distribution of normal stress at the interface is quite sensitive to the modulus and thickness ratios of the laminae. By making use of the form of this dependence, it may be possible to design bonded structures to withstand curing and/or temperature changes which would otherwise cause failure.