Characterizing and Modelling the Viscoplastic Anisotropy of Tin Single Crystals Using CPFEM

The reliability of electronic assemblies heavily depends on the durability of Sn-based solder joints grids. Due to their sub-millimeter scale, these joints solidify into nearly single-crystal dendritic β-Sn structures (over 90% in mass), with Cu and Ag-containing intermetallic particles. The low symmetry of the tetragonal ($\beta$) tin lattice induces a pronounced thermo-elastic and viscoplastic anisotropy, and since the solder joints undergo both cyclic and sustained stresses at high homologous temperatures ($T/T_m$ > 0.50 at room-temperature), they exhibit highly orientation-dependent service lives, due to a combination of creep, ratchetting, and fatigue [1]. Characterizing the viscoplastic anisotropy of pure tin, through tests run on a sufficiently wide range of crystal orientations, and then capturing the observed behaviors through a Crystal Plasticity (CP) model, should be the first steps towards reliable modelling of the multiphase solder joints behavior. However, the corresponding literature is limited. Moreover, some authors tested directionally-grown tin single crystals in tension [2] or made nanoindentation tests on individual grains in tin polycrystals [3], these methods face some limitations: directional solidification mostly yields crystal orientations near [110] restricting the investigated range of orientations, while the complex stress field in nanoindentation often masks anisotropy. In this study, a large set of single crystal dogbone-shaped tin specimens, with sufficiently varied orientations, ensuring the independent activation of most of the 10 potential slip families, were solidified, polished, and submitted to tensile cyclic or creep tests at room temperature. A combined analysis of the surface slip lines, and the strain fields measured by Digital Image Correlation or obtained by CPFEM simulations, the type of activated slip systems could be determined for most tests, and the hardening and viscous parameters of each one was identified. Such dialog between experimental data and CPFEM simulations showed that the hardening parameters are highly dependent on the type of active slip system which was not the case for the viscous parameters. Viscous stress exponents $n$ are all between 3 and 5, which appears consistent with common underlying creep mechanisms: dislocation glide and climb plus cross-slip

References

1. A. Bleuset and E. Charkaluk, Creep behavior of SAC305 quasi-single crystals at 185 °C, EMMC19, Madrid, Spain, 2024, May 29-31.
2. J. Weertman, Creep of tin single crystals, J. Appl. Phys., 27, 1956.
3. B. Ernst, On the anisotropic indentation modulus and anisotropic creep behavior of β-Sn characterized by nanoindentation methods, Mater. Sci. Eng. A, 848, 2022.