Theoretical Studies On The Effective Properties Of Multiphase Materials

There have been a lot of studies on the effective properties of multiphase materials widely used in industry. But various existing methods have their own drawbacks, some even ambiguous in concepts. This dissertation focuses on the theoretical study of some problems associated with the effective properties of multiphase materials, and compared the results with the enormous numerical works accomplished by the research group of Prof. Zheng. The specific works finished are listed below:1.Developed the following new methodsIDD and Effective self-consistent method: Starting from the topological structure and spatial distribution, a new micromechanical method-interaction direct derivation (IDD) was developed, which accounts for inclusion shapes and spatial distribution, suitable for multiphase and anisotropic materials, while having the precision up to the second order of volume fraction. Comparison with various numerical and experimental results showed that IDD indeed has excellent precision and it can expected to replace the widely used Mori-Tanaka method. At the same time, IDD is applicable for the estimation of various effective linear physical properties. This dissertation gives the IDD estimation for elasticity, electric conductivity and thermoelasticity specifically.Equivalent loading method: In combination with IDD, this method can use simple semi-analytic method to analyze the spatial distribution induced interactions among defects and to give more precise local fields. This method is an paradigm of micro-macro correlation, as an application, it gives effective strength quite easily.Double interaction model: Based on IDD estimate, the concept of double interaction was proposed for micro-quasi-periodic composites with multi-level topological structure. As an example, this concept is used to analyze Zr-2.5Nb used in nuclear industry. This concept also provides a new approach for analyzing a wide class of advanced materials, in contrast with traditional micro -mechanical models which can only deals with simple spatial distributions.2.Pointed out and revised the several essential drawbacks of existing method:A series of properties of Eshelby tensor were proved. Based on these properties, the problems associated with the kind of method similar to pseudo tractionmethod for both finite and infinite composites were analyzed, simple revisions were proposed correspondingly.The consistency between the generalized self-consistent method and the independence theorem was confirmed. The concept of intrinsic was proposed, which utilizes the independence properties, this concept can both guarantee the independence of the numerical simulation results and simplify the results.The plane version of Cauchy-Voigt dispute was discussed. It is proved that for certain plane piezoelectricity problem, Cauchy's view is correct. As a byproduct, the essence of the CLM invariant transformation was discovered.