Simulation and empirical equation for thermal stress in Al ₂ O ₃ /Si ₃ N ₄ ceramic joints brazed to Kovar/Monel metal alloys

Abstract This study presents a simulation methodology to choose the optimal material combination before constructing a ceramic‒metal composite joint. Two types of joint assemblies/structures designed with and without pores and eight material combinations are tested. The finite element discretization of the model is implemented using Abaqus. The effect of thermal stress is functionally evaluated by Von Mises Stress (VMS) and average volumetric stress as a decision parameter. The joint assembly with Al 2 O 3 /Ag‒Cu‒Ti/Kovar composite material is found to have a relatively larger limit to get fractured. The thermal strain rate for optimal material combination is 3.77 × 10 −6 K ‒1 (with pores) and 6.11 × 10 −6 K ‒1 (without pores), respectively. The porous joint structure's average thermal stress is (∼30%‒50%) lower than the non‐porous joint structure. The analysis concludes that pores do not always deteriorate joint performance. An empirically fit equation is derived to estimate the VMS value for any pore's shape, size, location, porosity, and material properties. The equation can be used to predict the VMS value for any ceramic‒metal composite material combinations. An empirical linear equation is also derived to predict effective coefficient of thermal expansion as a function of microstructure (shape, size, location, and porosity) and material type (effective molecular mass).