Anand model calibration for SAC305 solder joints based on the evolution of the shear stress and strain hysteresis loops for different thermal cycling conditions

Since 2006 and the introduction of the RoHS legislation preventing the use of lead in electronic assemblies, lead-free solder alloys have gained interest amongst the industry and academics with the introduction of new solder alloy compositions. Solder joint durability has been widely studied, especially the SAC305 solder composition, one of the most common lead-free alloy used in electronic equipment. Assessing solderjoint durability can consists in performing Accelerated Temperature Cycling (ATC) tests to measure durability data. Finite Element Analysis (FEA) can also be performed in order to correlate a thermomechanical fatigue criterion, such as the inelastic strain energy density, with the durability data for different test configurations to develop a fatigue model. However, accurately calculating the inelastic strain energy density dissipated in solder interconnections during thermal cycling requires knowledge of the solder material’s behavior law. Under thermal cycling conditions, SAC305 solder behaves as a highly viscoplastic material and is often described using the Anand model.This study presents the methodology considered to determine the Anand viscoplastic model representative of actual SAC305 solder joints. The experimental procedure which consists of a custom-made 76 I/O Ceramic Ball Grid Array (CBGA76) assembly instrumented with four strain gauges and subjected to three different thermal cycling conditions is described $(\triangle \mathrm{T}=[-25^{\circ}\mathrm{C}, 125^{\circ}\mathrm{C}], [0^{\circ}\mathrm{C}, 100^{\circ}\mathrm{C}]$ and [−40°C, 85°C]). The strain gauges allow to determine the shear stresses and shear strains applied on the critical solder balls during temperature cycles. The obtained experimental shear stress and strain hysteresis loops are compared with the numerical hysteresis loops determined with the FEA. By assessing the effect of each Anand parameter on the shape of the hysteresis loop plotted for the thermal cycle between −25°C to 125°C, the best-fit parameters for the Anand viscoplastic model was derived. The model was then validated considering the temperature cycles between −40°C to 85°C and 0°C to 100°C.