An alternative model for elastic thermal stresses in two materials joined by a graded layer

The elastic stress distribution resulting from thermal mismatch in a film/graded layer/substrate system is a critical issue. Recently by a three-variable method Hsueh and Lee formulated a closed-form analytical solution [Hsueh CH, Lee S. Modeling of elastic thermal stresses in two materials joined by a graded layer. Composites: Part B 2003;34:747–52] in order to overcome the complexity of the traditional analytical models. The paper is devoted to developing an alternative analytical model for graded beams by Zhang’s two-variable method for multilayered beams. To illustrate applications of the present solution, specific results are calculated for the GaAs/graded GaAs–Si/Si systems. The transition phenomenon between tensile stress and compressive stress in the graded beam is investigated in detail for different graded parameters or different thickness. The present results agree well with existing analytical results. The differences between the present two-variable model and Hsueh’s three-variable model are also discussed.