The Influence of Edge Boundary Conditions and Cracks on Vibrational Modes of Multilayer Ceramic Capacitors

Abstract

Electrical failure of layered capacitors is often a limiting factor in the design of many important electronic devices. Manufacturing processes, soldering, and service conditions have been shown to induce cracks in the dielectric material of the capacitor, providing conductive pathways that result in electrical leakage. In addition to the crack itself, edge boundary conditions can cause modal stress concentrations in a particular region of the capacitor that can initiate new cracks or propagate existing ones. Small but potentially damaging cracks can be very difficult to detect, and their presence may only become evident when they grow large enough to impact the capacitor’s performance. Recent experimental studies have demonstrated that cracks in layered capacitors can be detected nondestructively by measuring a shift in the resonant frequency of the structure via ferroelectric transduction. This study seeks to extend these recent findings by developing finite element models of layered capacitors in order to determine the level of influence that cracks and edge boundary conditions have on their frequency spectrum and their localized stress fields. Of particular interest is determining if ferroelectrically excited modes will be sensitive to cracks that can commonly appear near either restrained or traction-free corners. Computational investigation is intended to supplement future experiments on these structures, with the eventual goal of merging and analyzing the results from theoretical predictions and physical measurements. Specifically, three different crack types were simulated (endcap crack, inner crack, corner crack) along with three boundary conditions (free-free, fixed surface, and soldered). Results indicated that a fractured capacitor yielded lower natural frequency values in comparable modes to an uncracked capacitor, and that this shift in natural frequency values could be magnified depending on the applied boundary conditions. This finding is an important contribution toward the effort of non-destructively detecting cracks in the MLCCs and for future research to confidently utilize MLCCs in future applications.