Research On Effective Elastic Properties Of Quasicrystal Composites

A quasicrystal is a solid substance having a regular convex polyhedron shape,but distinct from a crystal.Quasicrystals have the unique properties of being hard and elastic,abrasion-resistant and very smooth,but have poor electrical and thermal conductivity.These properties of quasicrystals have great potential in engineering applications of composite materials and are of great significance to the development of applications of quasicrystals in structural materials and new composite materials.The study of effective elastic properties of quasicrystal composites is helpful to promote the development of mechanics of quasicrystal composites and provide theoretical basis for functional design and application of quasicrystal composites.In this paper,the effective elastic properties of quasicrystals are analyzed by combining the structural characteristics,anisotropy properties and phonon-phase field coupling.The influence of inclusion shape and volume fraction on the effective elastic modulus of quasicrystals composites is revealed.By introducing Eshelby tensor into quasicrystals,the problem of ellipsoidal inclusions in one-dimensional hexagonal quasicrystals is analyzed.The Eshelby tensor of one-dimensional hexagonal quasicrystals composites is obtained,and the Eshelby tensor of ellipsoidal inclusions in one-dimensional hexagonal quasicrystals is discussed in special cases,such as spheroid,elliptic cylindrical,ribbon-like,penny-shaped and circular cylinder inclusions.The analytical expression of effective elastic properties is obtained by Mori-Tanaka method.In particular,a numerical example of one-dimensional hexagonal quasicrystal composites with cylindrical holes is given,and the effect of inclusion volume fraction on the elastic properties of one-dimensional hexagonal quasicrystal composites is discussed.The explicit expression of Eshelby tensor of two dimensional decagonal composites is obtained by using Green's function method.The Eshebly tensors of two-dimensional decagonal quasicrystal composites with spheroid,elliptic cylindrical,ribbon-like,penny-shaped and circular cylinder inclusions embedded in the matrix are discussed.The variation of Eshelby tensor with inclusions aspect ratio in two dimensional quasicrystal composites is studied.Based on the intrinsic strain formula and Mori-Tanaka theory,the effective elastic properties of two-dimensional decagonal composites is obtained.The effect of inclusion shape on the effective elastic properties of two-dimensional decagonal composites is discussed.The influence of inclusion volume fraction on elastic properties of two-dimensional decagonal composites is also discussed when the aspect ratio of the inclusion is constant.