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A thorough understanding of the mechanics of lead-free solder joint in a ball grid array (BGA) assembly under expected operating conditions is essential in developing reliable life prediction models. In this respect, accurate deformation response of Sn-4Ag-0.5Cu (SAC405) solder under varying temperature cycles and straining rates is established using unified inelastic strain theory. The mechanics of the solder joint is then quantified through finite element modeling of a typical BGA assembly. The 3D quarter-model of the test assembly consists of silicon die, FR-4 substrate and printed circuit board (PCB), copper traces, intermetallics layer (IMC) and SAC405 solder joints in an area array. Reflow temperature profile consists of cooling from the assumed stress-free temperature of 220 to 25°C. Temperature cycles in the range between 125 and -40°C with dwell time at peak temperature levels are simulated. Results show that residual von Mises stress of 48.7 MPa and the corresponding inelastic strain of 0.031 are predicted in the critical solder joint at 25°C following solder reflow cooling. Additional inelastic strains accumulates continuously in the solder throughout the temperature cycles. Solder stress relaxation with accompanying inelastic strain occurs during dwell-time periods at both -40 and 125°C due viscoplastic and creep effects, respectively. In the critical solder joint, both high stress and strain gradients are localized in a small edge region at the solder-IMC interface near the component (SMD) side of the assembly. A new fatigue life model with unified inelastic strain theory defined for SAC405 solder joints is proposed based on accumulated inelastic strains and plastic work density of the critical solder joint.