Micromechanics models for non-linear behavior of piezo-electric fiber reinforced composite materials

Abstract

Abstract Two non-linear micromechanics models, referred to as `XY piezo-electric fiber reinforced composite (PFRC) non-linear model' and `YX PFRC non-linear model', are proposed for predicting the non-linear behavior of unidirectional PFRC materials, which are subjected to a high monotonic electric field. These two models are developed following the similar procedures for the XY model and YX model, proposed previously for the linear properties of woven composite materials. Emphasis in this paper is placed on the lowest order of non-linearities, that is, dependent variables depend quadratically on independent variables. The required closed-form formulas for the effective electroelastic constants of PFRC materials are obtained using the non-linear constitutive equations for purely piezo-electric materials and the iso-field assumptions. The single- and double-loading conditions are introduced when deriving these closed-form formulas. For the sake of validating the present non-linear micromechanics models, a numerical study is carried out for four different types of materials including LiNbO3/piezo-polymer polyvinylidene fluoride (PVDF), PZT-5H/PVDF, PZN-4.5%PT/PVDF and PZT-7A/Araldite D PFRC materials. It is noted that the predicted variation trends of T3, D3 with S3 and E3 for the first three PFRC materials are consistent with those for the corresponding purely piezo-electric ceramics or crystals. For the effective properties along the fiber direction, the relevant closed-form formulas obtained using the present non-linear models are exactly the same as those derived based on the rule of mixtures. The effective linear constants C11, C12, C13, C22, C23, e31, e32, e33 and e33 predicted using the present models are consistent with those proposed by other researchers. For PZT-7A/Araldite D PFRC materials, the predicted results of S11+S12 and e33T/eo correlate well with the measured results available in the literature.