Size Effects on Overall Deformation Behavior of SAC Samples

SAC alloys are the most widely used lead-free materials to fabricate solder joints in electronic packaging industries. Almost 97% weight percentage is
$\boldsymbol{\beta}-\mathbf{Sn}$
which is a highly directional material in terms of elastic modulus (E) and coefficient of thermal expansion (CTE). Since
$\boldsymbol{\beta}-\mathbf{Sn}$
is a crystalline material, deformation beyond the elastic limit is described by various atomic planes and directions, which are termed as slip systems together. Ten different slip families have been recognized in literatures for
$\boldsymbol{\beta}-\mathbf{Sn}$
body-centered tetragonal (BCT) crystals. When external loads are applied on solder balls, plastic deformation is dictated by the movement of dislocations and direction of deformation is defined by slip systems. Crystal plasticity theory has proved to be an accurate way of predicting crystalline material response when samples are significantly small. In this study, a crystal plasticity-based DAMASK code was used to explain the mesoscale deformation behavior of polycrystal beta-tin samples. Polycrystalline beta-tin samples were obtained using Voronoi tessellation in NEPER with random grain orientations, which is the case for real samples. Tensile simulations were performed for a sample with reasonably large number of grains. The model was then calibrated with experimental stress-strain data for a reflowed SAC305 alloy to determine a set of beta-tin slip properties. Subsequently, multiple polycrystalline models were generated with varying number of Sn grains, and a spectral solver was used to determine the sample responses under tensile loads along three orthogonal directions. Samples with large number of grains exhibited isotropic deformation behavior. However, samples with fewer number of grains demonstrated anisotropic behavior. This study determined the overall average grain size to sample size ratio at which isotropic behavior breaks down.