Numerical Simulation Of Homogenization Methods To Particle Reinforced Amorphous Alloy Composites Equivalent Modulus And Viscoelastic Property

Bulk amorphous alloys(BAAs),which has aroused widespread concern in the industry due to their superior mechanical and physical properties,are very promising structural or functional materials.Unfortunately,BAAs fail catastrophically at room temperature uniaxial tension or compression.This seriously limits their further developments and wide applications.In order to improve their plasticity and/or ductility,the reinforcing phase is added to BAAs.Recent advances in BAAs and amorphous alloy matrix composites(AAMCs)were reviewed from the following four aspects:(1)the development of amorphous alloys,(2)the mechanical behaviors of amorphous alloys and their deformation mechanism,(3)the development of amorphous alloy matrix composites,and(4)a review on the calculation of effective elastic modulus in a composite.In this paper,based on the homogenization method,finite element analysis and microstructure in particle reinforced AAMCs,the effective elastic moduli and viscoelastic responses of particle reinforced AAMCs were calculated or simulated.Some of the main results and conclusions are listed following:1.Particle reinforced AAMCs are supposed to be composed of a homogeneous macrostructure and a heterogeneous periodic microstructure.Based on the properties of the component materials and the structure characteristics in particle reinforced AAMCs,the effective properties of the composites with periodicity were investigated by the two-scale asymptotic homogenization method.According to the displacement expansion of the small parameter ?,a series of perturbation equations were derived by applying the perturbation method to the control equations of linear elasticity,and the basic theoretical formula was obtained by introducing the eigendisplacement and the homogenization coefficient;The finite element solution of the characteristic function was derived from the control formulas of the homogenization equations in terms of the principle of the minimum potential energy,and the boundary force method was further proposed to solve the characteristic function;the boundary force method can be realized based on the unit node information obtained in the finite element software,and therefore the effective elastic modulus of particle reinforced AAMCs can be simulated by finite element method.2.The effective elastic modulus of various particle reinforced AAMCs isanalyzed by combining the three-dimensional finite element method with progressive homogenization and some meaning results were obtained :(1)Compared with the Mori-Tanaka method,Halpin-Tsai equation method and Hashin-Shrikman model,homogenization theory is a strictly mathematical-based,efficient and practical approach on the calculation of the effective composite modulus,and can also be used to predict Poisson's ratio of composites;(2)A combined approach of the homogenization theory and the finite element in this study was applied to reach elastic modulus of particle reinforced AAMCs with different reinforcement volume fraction,its predictive value falls in between series model and parallel model,however,based on this method,the predictive modulus value of fiber-reinforced AAMCs is close to that of the parallel model;(3)For Cu particle reinforced Cu50Zr45Al5 AAMCs,their predictive modulus values is 1%-3% higher than the corresponding experimental results due to the interfacial reaction between the Cu particle and Cu50Zr45Al5 amorphous matrix,on the other hand,their predictive Poisson's ratio values are very close to the experimental values;(4)Compared with the other particle reinforced AAMCs investigated here,the combined approach of the homogenization theory and the finite element can be most effectively used to predict elastic modulus of diamond particle reinforced AAMCs with different reinforcement volume fraction;(5)Based on the relationship between the predictive Poisson's ratio value and the experimental plastic strain of the composite,it is found that when the volume fraction of the reinforced phase is relatively small(<10%),the Poisson's ratio value is inversely proportional to the plastic strain,on the other hand,when the volume of the reinforced phase is increased to a certain degree,this trend will change and the plastic strain will decrease sharply.3.Based on the homogenization theory,a mechanical model to calculate the viscoelastic properties of Cu or W particle reinforced AAMCs with periodic microstructure was formulated.The results show that a combined approach of the homogenization theory and the finite element formulation can effectively anticipate the viscoelastic properties of these materials with periodic microstructure,and thus provide basis for effective optimization of this kind of composites.