A Curvature-Based Interpretation of the Steinberg Criterion for Fatigue Life of Electronic Components

Abstract

The “Steinberg Criterion” is a well-known method for determining the fatigue life of Printed Circuit Board (PCB) components based on the deflection of the PCB. It has been adopted as a de facto industry standard for the fatigue analysis of electronic components, and has been successfully used on many programs. However it has some limitations. Steinberg derived this equation to describe the behavior of rectangular PCBs simply supported on all sides. In this configuration the deformed shape of the first mode of a PCB under vibratory loads is assumed by Steinberg to be described by two perpendicular half sine waves. Unfortunately many PCBs have distorted mode shapes as a result of clamped or asymmetric edge constraints, stiffeners, or irregular PCB outline. Finite Element Models (FEMs) can be used to predict mode shapes for these PCBs, but there has been no clear way to use Steinberg's equation to determine the fatigue margin for components on such boards. The traditional method (when the discrepancy is addressed) is to use a value for PCB length in the equation based on an approximation of the length of an equivalent half sine wave superimposed on the predicted mode shape. This approach, while better than ignoring the problem, can lead to inconsistency in results or the overlooking of localized effects, and in the case of extremely odd mode shapes can be nearly impossible. This paper presents a method of using FEM data for curvature as well as deflection at a single location to eliminate the shape and location variables from the Steinberg criterion, allowing it to be applied confidently to PCBs and Printed Wiring Assemblies (PWAs) with any shape and boundary conditions. Test cases are described that show equivalence between this method and the existing Steinberg criterion. Lastly the methodology used to extract phase-consistent curvature and deflection results from FEM analysis is briefly discussed.