Multi-scale material modelling of glass-ceramics

Although the new material class of glass-ceramics with excellent capacitor propertieshas already been discovered in the 1960s , the microscale interactions between the glassmatrix and the ferroelectric particles are so far unexplored. Knowing the correlationbetween microstructure and material properties would help to improve the capacity andstorage density of the dielectric material.In this presentation an electro-mechanical model developed by Peter Neumeister forsimulating lead zirconate titanate will be explained to describe the piezoelectric behaviorof ferroelectric barium titanate. This model will be adapted to glass-ceramic material inthe future.The model uses three different scales to characterize the properties and the physical vari-ables of the unit cell, the grain and the microstructure. To model the domain interactionswithin one grain, the percentage of unit cells polarized in one of the six orientation di-rections is represented as volume fraction. Out of those volume fractions the materialtensors of each grain are calculated. A Finite element software computes the local loads ateach grain, which are further used together with an energy-based switching criterion todetermine the volume ow between the volume fractions. Using this electro-mechanicalmaterial model a simulation of the strain - stress curve, the electric Field - polarizationcurve and the electric Field - strain curve has been achieved. Those curves are in verygood agreement to experimental curves, which is very promising for the simulation ofthe glass-ceramic material.