A microstructure-based approach to modeling electrostriction that accounts for variability in spatial locations of domains

Abstract The discovery of polyvinylidene fluoride (PVDF) based family of relaxor ferroelectric (RFE) polymers has attracted attention due to their high electrostrictive strain and relatively low hysteresis loss. These RFE polymers exhibit complex microstructures containing both crystalline domains and amorphous domains; the interactions of the crystalline domains drive the electrostrictive behavior of these EAPs, while the amorphous domains dictate the mechanical behavior of the materials. Furthermore, the crystalline domains are spatially and orientationally distributed across the amorphous medium, further complicating the morphology of RFE polymers. Although a number of studies have focused on experimental and computational investigation of the interaction among different crystalline phases of this family of RFE, electrostriction models that represent the variabilities in the microstructure of biphasic RFE polymers are lacking. The proposed model aims to link the semicrystalline microstructure to the observed electromechanical coupling. An energy density function is constructed for a representative volume element (RVE) of the EAP, including a term for each phase, crystalline and amorphous. The interaction of the crystalline domains is based on the Coulomb interaction energy between a pair of dipoles. The responses of the amorphous domains are predicted by a modified hyperelastic stress–stretch eight-chain model. The total free energy is then analyzed under constitutive laws for an isothermal electromechanical deformation to determine the stresses generated in the RVE. The strain versus electric field, i.e. the electrostriction, relationship is calculated from a self-equilibrium condition of the Cauchy stress. The microstructure of the material is taken into account by applying the dipolar energy to a semicrystalline network model, in which a dipole that represents a crystalline domain is surrounded by an amorphous medium. The semicrystalline RVE experiences interactions with neighboring crystallites, which drives the electrostriction of the material. Two basic cases of the semicrystalline network model are explored to study the effects of spatial variation of crystalline domain locations relative to each other. Furthermore, higher fidelity descriptions of spatial location are introduced through the addition of a probability density function (PDF) of dipoles around a central dipole. Comparing the model to experimental results from the literature allows best-fit determination of the model parameters describing the PDF, e.g. aspects of microstructure, itself. These results, which agree well with experimental data, imply that the model has an ability to infer key information about the microstructure of the material by fitting the distribution of dipoles with a single adjustable parameter. The model is unique in that its descriptions of the crystalline domains is amenable to direct measurement by spectroscopic scattering techniques. Consequently, adjustable parameters in the model are linked to physical characteristics that are quantifiable, such as magnitudes of dipole moments and spatial distribution parameters.The model may also be used to elucidate aspects of network morphology using best fit of these physically meaningful adjustable parameters to experimental data, possibly providing a link between processing-structure-property relationships for future researchers.