A thermo-mechanical, viscoelasto-plastic model for semi-crystalline polymers exhibiting one-way and two-way shape memory effects under phase change

A finite strain phenomenological model is developed to simulate the shape memory behavior of semi-crystalline polymers under thermo-mechanical loading. The polymer is considered to be a composite of crystalline and amorphous phases with constant volume fractions. While the amorphous phase is stable, the crystalline phase is considered to change phase with temperature. Therefore, the crystalline phase is considered further to be composed of two phases, whose volume fractions are controlled by a temperature and strain dependent function: the melted phase which is soft, and the crystallized phase which is stiff.A pressure dependent viscoelasto-plastic behavior is considered for the constitutive model of the different phases. In addition to pressure dependent plasticity, additional deformation measures are applied to the crystalline phase to model temporary (imperfect shape fixity) and permanent (imperfect shape recovery) deformations in a thermo-mechanical loading cycle. Formulating a compressible plastic flow during the phase changes yields the possibility to capture both one-way and two-way shape memory effects. As a consequence, the load-dependent and anisotropic thermal expansion observed experimentally in semi-crystalline polymers during phase change is naturally captured.The model is validated within a test campaign performed on nano-composite having a semi-crystalline polymer as a base material. It is shown that the model gives close results with the tests and it is able to capture the shape fixity and shape recovery behaviors of the polymer, for both one-way and two-way shape memory effects.