THE EFFECTIVE PROPERTIES OF PIEZOCOMPOSITES, PART Ⅱ: THE EFFECTIVE ELECTROELASTIC MODULI

Since piezoelectric ceramic/polymer composites have been widely used as smart materials and smart structures, it is more and more important to obtain the closed-from solutions of the effective properties of piezocomposites with piezoelectric ellipsoidal inclusions. Based on the closed-from solutions of the electroe- lastic Eshelby's tensors obtained in the part I of this paper and the generalized Bu- diansky's energy-equivalence framework, the closed-form general relations of effective electroelastic moduli of the piezocomposites with piezoelectric ellipsoidal inclusions are given. The relations can be applicable for several micromechanics models, such as the dilute solution and the Mori-Tanaka's method. The difference among the various models is shown to be the way in which the average strain and the average electric field of the inclusion phase are evaluated. Comparison between predicted and exper- imental results shows that the theoretical values in this paper agree quite well with the experimental results. These expressions can be readily utilized in analysis and design of piezocomposites.

The symmetry and loading-independency of multiple inclusions enclosing uniform stresses in an infinite elastic plane

The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials.In anti-plane shear and plane deformations,certain sufficient conditions have been established in the literature which guarantee uniform internal stresses inside multiple interacting inclusions displaying various symmetries when the matrix is subjected to specific uniform remote loading.Correspondingly,sufficient conditions which allow for the design of multiple interacting inclusions independent of any specific form of(uniform)remote loading have also been established.In this paper,we demonstrate rigorously that,in all cases,these sufficient conditions are also necessary conditions and indeed allow for the identification of all possible collections of such inclusions.

Three-Dimensional Growth of Coherent Ferrite in Austenite: A Molecular Dynamics Study

Coherent second phase often exhibits anisotropic morphology with specifi c orientations with respect to both the second and the matrix phases.As a key feature of microstructure,the morphology of the coherent particles is essential for understanding the second-phase strengthening eff ect in various industrial alloys.This letter reports anisotropic growth of coherent ferrite from austenite matrix in pure iron based on molecular dynamics simulation.We found that the ferrite grain tends to grow into an elongated plate-like shape,independent of its initial confi guration.The fi nal shape of the ferrite is closely related to the misfi t between the two phases,with the longest direction and the broad facet of the plate being,respectively,consistent with the best matching direction and the best matching plane calculated via the Burgers vector content(BVC)method.The strain energy calculation in the framework of Eshelby’s inclusion theory verifi es that the simulated orientation of the coherent ferrite is energetically favorable.It is anticipated that the BVC method will be applicable in analysis of anisotropic growth and morphology of coherent second phase in other phase transformation systems.