Homogenization of phase transforming materials: The concept of phase-morphology and variable scale separations
Vincent von Oertzen, Bjöern Kiefer · Journal of the Mechanics and Physics of Solids · 2024
Phase transforming solids are in focus of modern engineering applications due to their promising mechanical properties, which originate from a change of microstructure in stress- and temperature induced loading scenarios. The transition of respective evolution laws, describing these characteristic phase changes, between several spatial (and temporal) scales through appropriate homogenization techniques is the key to understand and simulate large scale behavior of these materials. Whereas in most of the relevant literature the microstructure is only analyzed in the relaxed and thus fully transformed system state, this work aims to derive the effective material behavior during the phase evolution process. More specifically, a homogenization theory is presented for systems in which the conventional notion of scale separation changes over time. This involves the introduction of new concepts of so-called phase-morphology and variable scale separation . The developed homogenization theory is applied to the material ZrO 2 in order to derive its effective driving force at variable scales and macroscopic elastic properties , both as a function of the temporally changing microstructural topology. Moreover, the martensite re-orientation during undercooling simulations is analyzed, thus demonstrating that the concept of phase-morphology can also serve as an indicator for the stationarity of phase distributions during a transformation process. The results agree with those obtained from one- and two-dimensional finite element simulations up to a negligible tolerance, which proves the validity of the outlined homogenization approach.