Study Of Multiscale Methods For Polymer Matrix Composites

According to the scale characteristic of material internal structure, the mechanical properties of polymer matrix composites are studied from multilevels (macroscopic, microscopic and nanoscopic levels) in this work. Microscopic structure of polymer matrix composites is assumed to be periodic or approximately periodic. The finite element method is combined with multiscale successive homogenization theory based on asymptotic expansion. Microscopic and nanoscopic base cells analysis models are established. A computational program based on multiscale homogenization method is written by FORTRAN language. The relation between macroscopic mechanical properties of polymer matrix composites and microscopic structure is studied. Local variation rule of microscopic stress is researched.The computed model for predicting the effective properties of polymer matrix composites is established based on multiscale asymptotic homogenization theory and finite element analysis technology. The influence of ratio of modulus of particle and polymer matrix, particle Poisson's ratio, shape, volume fraction on effective elastic constants of polymer matrix composites is studied. Uniaxial tension experiment is simulated by finite element analysis technology to validate macroscopic effective elastic constants of polymer matrix composites computed by homogenization method. Experiment results show the accordance with computed results.Based on homogenization theory, the analyzed models of macroscopic stress field and the microscopic unit cell local field are established in this work. The relation between microscopic local stress of polymer matrix composites and ratio of modulus, particle shape, Poisson's ratio and volume fraction is investigated. The microscopic failure modes of polymer matrix composites are qualitatively analyzed. The effect of ratio of modulus and volume fraction on microscopic local stress concentration at macroscopic stress concentration location is analyzed. Mesh adaptive analysis technique is combined with the finite element method to study local stress problem. Mesh superposition technique is constructed and combined with homogenization method to research the effect of heterogeneity on macroscopic stress field and unit cell microscopic local stress field of polymer matrix composites. Some available results are obtained.The effective elastic constant prediction model of polymer matrix composites with imperfect interface is established by integrating three phase model with interface displacement jump assumption. The theoretical predicting formulae of effective bulk modulus and effective shear modulus have been derived. The effect of interface parameters on the effective elastic constants of polymer matrix composites is discussed. The predicted results in this paper have the generality and universality. The model is simplified as perfect interface case when interface parameter C is equal to 1 and as debonding interface case when interface parameter C is equal to O.Crystalline polymer-inorganic nanocomposites present a multiscale complex structure system. The model of multiscale successive asymptotic homogenization theory is applied. Based on the experiment analysis of crystalline polymer-inorganic nanocomposites, from a microscopic structure characteristic of material point of view, a multiscale analysis computing model of crystalline polymer-inorganic nanocomposites is established. Internal structure of crystalline polymer-inorganic nanocomposites is described by multilevels(macroscopic, microscopic and nanoscopic levels). The finite element method is combined with multiscale successive homogenization theory based on asymptotic expansion for predicting effective modulus of crystalline polymer-inorganic nanocomposites. Two nanoscopic level homogenizations and one microscopic homogenization are used. The effect of crystal degree of polymer, elastic modulus of crystal inclusion, elastic modulus of nanoparticle and volume fraction of nanoparticle on the effective elastic modulus of polymer-inorganic nanocomposite is discussed respectively. Some valuable results are obtained.This work may be used to supply guidelines for the modifying design of polymer matrix composites.