铁电陶瓷宏细观本构模型

A MACROSCOPIC-MICROSCOPIC CONSTITUTIVE MODEL FOR FERROELECTRIC CERAMICS 1)

在居里温度以下，铁电陶瓷呈铁电相，具有许多取向不同的铁电畴，取向分布函数描述了铁电畴的取向分布情况文中推广了经典的内变量理论，采用宏细观相结合的方法，建立了铁电陶瓷的宏观行为与细观结构的关系，给出了铁电陶瓷的屈服条件。

Ferroelectric ceramics are an important class of modern engineering materials and have received increasing attention for their distinctive properties and applications For example, they are used as modulators, deflectors, optical memories imaging devices and so on With the wider use of the materials and harsher requirement of their performances, the study of coupling electric and mechanical behavior has attracted great interests The main effort of this paper is to obtain the constitutive relation of ferroelectric ceramics It is well known that ferroelectric ceramics take on ferroelectric phases when the temperature is below the Courier point Domains appear during the ferroelectric transformation Experiments have shown that domain switching is the main source of nonlinearity in ferroelectric ceramics, which is also the base of the theory proposed in this paper In the model, ferroelectric ceramics are treated as an agglomerate of domains, and each grain is supposed to be a single domain and assumed as an inclusion The Orientation Distribution Function, or noted as ODF, is used to describe the domain patterns The Helmholtz free energy and the complementary Helmholtz free energy of a constituent element are obtained by expanding the Mori-Tanaka mean field theory The classic internal variable theory was also extended and applied to analyze the constitutive relations of ferroelectric ceramics Finally a theoretical constitute law in terms of the internal functional theory was developed to describe the nonlinearities and hysteresis in the ferroelectric behavior By way of taking ODF as Fourier's expansion, we obtained the yielding conditions and the evolution equations of ODF The proposed constitute relation is simplified to an in-plane problem in the paper, so that ODF can be simplified as one dimensional Fourier′s expansion Two simple loading cases, electric field loading and compressive stress loading, are considered for the numerical calculation Numerical results based on the theory are compared to the experimental results, which indicates that the theory is reasonable and applicable The theoretical results give insight into the evolution of the microstructures associated with domain switching and into the source of the observed hysteresis of ferroelectric ceramics In this model, there are two contributions to the nonlinearities One is the direct effect of domain switching induced by either stress or electric field, and the second is the dependence of the macroscopic piezoelectric coefficients of the ceramics on the overall polarization of the ferroelectric materials It must be pointed out that the constitutive law was only compared with the uniaxial experimental data, therefore, it must be substantiated by the multiaxial loading data though so far there are not any available data from multiaxial testing for the ferroelectric ceramics