Evolution Of An Inclusion In Orthotropic Material And Influence Exerted By Inclusion On Material Creep Rate

The composite widely used in various fields, not only to study the macroscopic properties, but also need to study the micro law of the damage. Conductor chip packaging interconnect thin film circuits, silicon dioxide insulating substrate and the circuit chip package comprising a composite material structure can be considered, the macroscopic mechanical properties of the orthotropic material. A variety of composite structures in the middle of forming and processing often present a variety of defects are. Inclusion is a typical defect. Also for some ceramic materials, macro-mechanical properties of materials can be improved through the inclusion or particles. In the study, various composite structures are often considered to be dealt with orthotropic materials. The research for evolution of an inclusion in orthotropic material and influence exerted by inclusion on ma material creep rate has important theoretical significance and practical application reference value.This paper established in gradient stress the mechanical model of evolution of inclusion in orthotropic materials, and then based on Lekhnitskii theory of inclusion in orthotropic materials, solve the stress expression, and through gradient overlay way to get the equivalent load of stress expressions, and then analytical solution of migration rate of inclusion in orthotropic materials are given. The example shows that there is a x - x0 (for the ellipse center in the overall coordinate system coordinates), can make the migration rate to 0; At that time x - x0, x the smaller the migration rate is negative and larger; At that time x - x0, x the greater the migration rate is positive and Greater. At the same time,β(with the inclusion of matrix elastic modulus ratio) is, the faster the migration rate of change. With the change of oval shape parameter m, m is larger, the rate of change is faster.Second, we set the inclusion in orthotropic materials with periodic microstructure, which is the basic unit of a cross-sectional model. Based on the interface diffusion theory and mass conservation law, we gives the inclusion expression of the creep rate. The example shows that, regardlessβ> 1orβ> 1, creep rate> increases with f v (inclusion with the matrix volume ratio) increasing. At that timeβ> 1, creep rate is positive, increasing in positive direction with the increase of the rate; at the time > > 1, the creep rate is negative, increasing in negative direction with the increase of the rate.βis closer to 1, that is, elastic constants of inclusion and the matrix is closer, the smaller the creep rate is. Study shows the law for the different key parameters on the evolution of inclusions in orthotropic materials and inclusion on the creep characteristics. The study provides some theoretical basis and engineering applications for micro-and macro-mechanical properties of orthotropic materials containing a inclusion.