Realistic Modeling of Edge Effect Stresses in Bimaterial Elements

A classic paper by Timoshenko in 1925 dealt with thermal stresses in bimetal thermostats and has been widely used for designing laminated structures, and in contemporary studies of stresses in electronic devices. Timoshenko’s analysis, which is based on strength of materials theory, is unable to predict the distribution of the interfacial shear and normal stresses known to exist based on more sophisticated analyses involving the theory of elasticity (Bogy (1970) and Hess (1969)). Suhir (1986) has recently provided a very insightful approximate method whereby these interfacial stresses are estimated by simple closed-form formulas. The purpose of the present paper is to compare three independent methods of predicting the interfacial normal and shear stresses in bimaterial strips subjected to thermal loading. These are: 1.) Theory of elasticity via an eigenfunction expansion approach proposed by Hess, 2.) Extended strength of materials theory proposed by Suhir, 3.) Finite element stress analysis. Two material configurations which figure prominently in the electronics area have been studied. These are the molydeneum/aluminum and aluminum/silicon material systems. It has been discovered that when the two layers are nearly the same thickness, the approximate methods adequately predict the peak values of the interfacial stresses but err in a fundamental manner in the prediction of the distribution of stress. This may not be of concern to designers who are interested mainly in maximum stress alone. However, it has been shown that if one layer is relatively thin compared to the other, the approximate methods have difficulty in predicting both the peak value of stress and its associated distribution.