Predicted Size of an Inelastic Zone in a Ball Grid Array Assembly

Abstract

A simple and easytouse analytical (“mathematicalâ€‌) predictive model has been developed for the assessment of the size of an inelastic zone, if any, in a ballgridarray (BGA) assembly. The BGA material is considered linearly elastic at the strain level below the yield point and ideally plastic above the yield strain. The analysis is carried out under the major assumptions that, as far as the estimated size of an inelastic zone is concerned, (1) the inhomogeneous (“discreteâ€‌) BGA structure can be substituted by a homogeneous (continuous) bonding layer of the same thickness (height) and (2) only the longitudinal crosssection of the packagesubstrate assembly can be considered. The numerical example carried out for a 30 mm long surfacemount package and a 200 خ¼m thick leadfree solder indicated that, in the case of a high expansion PCB substrate, about 7.5% of the interface's size experienced inelastic strains, while no such strains could possibly occur in the case of a low expansion ceramic substrate. The suggested model can be used to check if the zone of inelastic strains exists in the design of interest and, if inelastic strains cannot be avoided, how large this zone is, before applying a CoffinMansontype of an equation (such as, say, Anand's model in the ANSYS software) with an objective to evaluate the BGA material lifetime.