A three-dimensional theoretical model for estimating the thermal residual stresses in micro multilayer ceramic capacitors

A three-dimensional theoretical model is proposed to estimate the thermal residual stresses in multilayer ceramic capacitors (MLCCs) based on the effective medium method in micromechanics of composites. The MLCC is first decomposed into some sub-blocks with different material properties, and then the classical lamination theory and the combined Voigt’s and Reuss’ assumptions are adopted to calculate the residual stress distributions. The results obtained from this theoretical model show a good agreement with the numerical results of finite element method. The effects of such key factors as the dielectric layer thickness, the number of dielectric layers, the cover layer sizes, as well as the length and width creepage paths on the distributions of residual stresses are all examined. The suggested theoretical method provides a convenient tool for estimating the residual stresses in MLCCs as a function of characteristic sizes and manufacturing process parameters and, therefore, is helpful for the optimal design of MLCCs with enhanced performance.