Two-scale Asymptotic Analysis For Thermal/mechanical Properties Of Composite Materials

With the rapid development of space technology, the investigations on macroscopic properties'characterization and broken-down mechanism of composite material structures under thermo-elasticity coupling condition are extremely desired. The multi-scale modeling and computation for composite materials is coincident with the intrinsic nature of physical world, so it can more exactly characterize properties of composites and predict the response of composites under certain loading (or working) condition. Moreover, it supplies a method to optimize microstructure of composites for the best properties. That is, based on multi-scale modeling and computation, we can design the microstructure of composites and determine the processing before preparation of composites.Among many multi-scale methods known, two-scale asymptotic analysis method is a general, efficient and accurate method which is suitable for properties'characterization and response analysis of composites with periodic configuration. Its main idea is that the computation for properties of composites is presented with two-scale homogenization in the process from mesoscopic to macroscopic, and then the local fluctuations of physical and mechanical fields are described with two-scale asymptotic technique in the process from macroscopic to mesoscopic. In this paper, based on two-scale asymptotic method principally, the effective thermal/mechanical properties of composites are characterized as well as the responses of composite structures in multiple scales under certain loading (or working) condition are computed.Firstly, two-scale asymptotic formulae of the temperature and the mechanical fields are derived on the base of the basic equations of thermo-elasticity coupling problem, and then the expressions of effective thermal conductivities, stiffness and thermal expansion coefficients of composites are deduced. Whereafter, combining with finite element method, the numerical computing procedure of two-scale method is established.Secondly, the validity of two-scale method for characterizing the effective properties of composites is evaluated by numerical experiments. The changes of the effective properties of composites resulting from the variations of the volume fraction and shape of inclusion and the interaction of the inclusions are analyzed. After that, the validity and efficiency of two-scale method for describing the temperature and mechanical fields of composite structure are validated by numerical experiments.Thirdly, two-scale asymptotic method is employed in the field of ZrB2-SiC ultra high temperature ceramics (UHTCs) to implement multi-scale characterization and simulation which links micro-, meso- and macro-scale. The thermal response of ZrB2-SiC is computed and the influences of the size and the location of SiC inclusion on microstructure of ZrB2-SiC are analyzed. Furthermore, the unit cell of carbon fibre toughened UHTCs matrix composite is modeled, the response of the composite under certain working condition is computed, and the maximal stress in the composite and its location are determined.Fourthly, considering the influence of the tiny size of interphase on the computation, a dual two-scale method is proposed. 3-D stress distributions of unidirectional-fibre reinforced composites with interphase under macroscopic axial uniform tension, transversal uniform tension and transversal uniform shear are respectively calculated and the maximal stress and their locations are determined. The influence of different interphases on the distributions of stress fields is discussed. The results show that arithmetical transition of the properties of fibre, interphase and matrix is beneficial to abate stress concentration of fibre which occurs near the interphase under macroscopic axial uniform tension.Finally, different failure criteria are introduced according to different attributes of components of unidirectional composite to establish a two-scale method for predicting the axial strength of unidirectional-fibre reinforced composites. When applying the method to predict the axial tensile strength, the concept of fibrous effective tensile strength is defined to relate the progressive damage with the method. The calculated values have a good agreement with the experiment results which verifies the validity of this method.