Measurement of anisotropic coefficients of thermal expansion of SAC305 solder using surface strains of single grain with arbitrary orientation

Abstract

The anisotropic coefficient of thermal expansions (CTEs) of SAC305 grain are measured using a full-field in-plane displacement measurement technique. Theoretical relationships among (1) the transversely-isotropic CTEs, (2) the surface strains of a specimen containing a single grain with arbitrary orientation, and (3) the direction of a grain orientation are derived first. Cube shape specimens that contain a single SAC305 grain are fabricated by controlling cooling rates. Thermally-induced displacements fields with a sub-micron resolution are documented on two perpendicular surfaces of the specimen as a function of temperature, and the engineering strains are calculated from the displacement fields. Two directional CTE values are determined from the theoretical relationships. The direction of the c-axis is also obtained during CTE calculations. The validity of the measurement is corroborated by comparing the c-axis direction obtained from the experiment with a grain orientation measured by the electron backscatter diffraction (EBSD) method.