Modeling of thermal stresses in joining two layers with multi- and graded interlayers

The technique of introducing interlayers has been used extensively to mitigate residual thermal stresses in joining dissimilar materials. Finite-element analyses have often been used to quantify thermal stresses in these layered structures in case-by-case studies. Recently, simple analytical models containing only three unknowns have been developed to derive closed-form solutions for elastic thermal stresses in both multilayer systems and two layers joined by a graded junction. The analytical solutions are exact for locations away from the free edges of the system. Application of these solutions is shown here to provide a systematic study of thermal stresses in Si3N4 and Al2O3 layers joined by various sialon polytypoid-based multi- and graded interlayers. The effects of the thickness, stiffness, and coefficient of thermal expansion of the interlayer on thermal stresses in the system are examined. The differences in thermal stresses resulting from multi- and graded interlayers are shown.