Anisotropic steady-state creep behavior of Single-crystal β-Sn: A continuum constitutive model based on crystal viscoplasticity

Abstract

Body-center tetragonal (BCT) β-Sn crystals exhibit highly anisotropic properties such as stiffness and thermal expansion, which significantly affect their thermal-mechanical behavior. The homologous temperature of β-Sn is relatively high under common applications due to its low melting point, which renders Sn and Sn-based alloys viscoplastic even at room temperature. The orientation-dependent creep behavior of β-Sn specimens have been previously measured by different research groups. A dislocation mechanics based crystal viscoplasticity model is applied in this study to describe this anisotropic steady-state creep behavior of β-Sn single crystals. The model constants are calibrated with single-crystal creep test results available in the literature. The resulting creep behavior of β-Sn single-crystal is also represented with a homogenized continuum-scale finite element approach based on the use of a combined Hill-Norton approach where the creep anisotropy is represented with Hill's anisotropic potential and the creep flow rule is represented with Norton's power-law model. Estimation of the six Hill's constants for β-Sn requires multiple creep tests under specific stress states, for single crystals along crystal principal directions. In this study, these physical creep tests are replaced with ‘virtual tests’ conducted with the developed dislocation-based crystal-viscoplasticity model. To assess the ability of the Hill-Norton finite element approach to represent dislocation creep, the finite element simulation results are compared with results of: (i) physical tests on single crystal specimens reported in the literature; and (ii) crystal-viscoplasticity modeling along many crystal orientations (beyond the fundamental calibration cases conducted along crystal principal directions). In future studies, this approach will be used for anisotropic finite element modeling of creep in polycrystalline specimens.