Effective Superelastic Domains of Schwarz Primitive Shape Memory Alloy Lattices Subjected to Cyclic Loading

This work investigates the evolution of effective phase transformation thresholds in superelastic shape memory alloy (SMA) lattice architectures subjected to cyclic loading. The investigation is carried out by means of finite element analysis and numerical homogenization methods, considering Schwarz primitive triply periodic minimal surface (TPMS) SMA unit cells subjected to periodic boundary conditions. The results are reported for relative densities between 10% and 50%. It is shown that, in all the cases considered, the loading surfaces governing both forward and reverse phase transformations have an ellipsoidal shape that can be reasonably well represented using an extended Hill's criterion that accounts for the influence of hydrostatic pressure. Moreover, by considering polynomial expressions of the coefficients of Hill's criterion in terms of martensite volume fraction and cumulated fraction, the evolution of the loading surfaces as a consequence of functional fatigue is reasonably well approximated. The results suggest that an extended Hill's criterion with variable coefficients can well be used to simulate effective phase transformation and functional fatigue in architected TPMS SMAs.