A simple and easy-to-use analytical (“mathematical”) predictive model has been developed for the assessment of the size of an inelastic zone, if any, in a ball-grid-array (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 (“discrete”) BGA structure can be substituted by a homogeneous (continuous) bonding layer of the same thickness (height) and (2) only the longitudinal cross-section of the package-substrate assembly can be considered. The numerical example carried out for a 30 mm long surface-mount package and a $200 μm$ thick lead-free 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 Coffin-Manson-type of an equation (such as, say, Anand's model in the ANSYS software) with an objective to evaluate the BGA material lifetime.

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