Predicted size of the inelastic zone in a ball-grid-array (BGA) assembly

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 solder material is considered linearly elastic at the strain level below the yield point and ideally plastic above this level. The numerical example carried out for a 30mm long surface-mount package with a 200 micrometer thick lead-free solder has indicated that, in the case of a high expansion PCB substrate, about 7.5% of the interface's length experiences inelastic strains, while no such strains occur in the case of a low expansion ceramic substrate. The FEA computations confirmed this result. The suggested model can be used to check if a zone of inelastic strains exists indeed in the design of interest, and if inelastic strains can be avoided by using a low expansion board or by some other means (say, by using different bonding material at the assembly ends). If not, the model can be used to determine the size of the inelastic zone. It is advisable that such an assessment is carried out prior to the application of a Coffin-Manson-type of an equation (such as, e.g., Anand's model employed in the ANSYS software) aimed at the evaluation of the BGA material lifetime.