Molecular dynamics calculations and nanoindentation testing of the strain-rate and size dependent material properties of Cu<inf>3</inf>Sn IMC

Abstract

The aims of investigation are to evaluate the strain, strain-rate and size dependent material properties of orthorhombic Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn crystals by way of the proposed molecular dynamics (MD) simulation model based on the modified embedded atom method (MEAM). The study starts from theoretical assessments of the elastic stiffness coefficients of a variety of single crystal orthorhombic Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn as a function of both applied strain and size, followed by the exploration of their strain-rate effects. To the authors' best knowledge, this would be the first paper discussing the issue using an MD method. Furthermore, experimental testing using nanoindentation with continuous stiffness measurement technique is performed to verify the validity of the proposed MD simulation model. For effective comparison with the published experimental data and the present nanoindentation findings, the polycrystalline elastic moduli are estimated by using the Voigt-Reuss (VR) bounds and Voigt-Reuss-Hill (VRH) average based on the single crystal data. The results show that the calculated single crystal and polycrystalline elastic stiffness coefficients of the orthorhombic Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn crystal present not only high elastic anisotropy but also great size, applied strain and strain rate dependence as the applied strain is under the necking point and the nominal strain rate larger than about 0.07-0.08%ps <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . Specifically, a larger strain rate would increase the elastic stiffnesses over the threshold range while an increasing applied strain would decrease them. As the strain approaches the necking point, these elastic stiffness coefficients tend to converge to a constant value. It is also shown that the ultimate tensile strength and shear strength of stress-strain curves for the Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn crystal all change significantly with strain rate, increasing with an increasing strain rate. The calculated polycrystalline elastic properties are very comparable to the present nanoindentation findings and the published theoretical and experimental data.