Abstract: Metal matrix composites combine the advantages of metal structural materials and reinforcement as matrix, and have the characteristics of high strength, high elastic modulus and good fatigue performance. Due to the relatively simple manufacturing process and low price, particle reinforced metal matrix composites show wide commercial value. Metal matrix composites were first used in the aerospace field, and with the continuous reduction of their prices, they were more and more widely used in automobile, electronics, machinery and other industrial fields. For this reason, the research and application development of it by major companies and research institutions around the world are being carried out at multiple levels and in large areas. The author has read a lot of relevant literature, and then summarized the research on metal matrix composites by domestic and foreign scholars in recent years, which has certain practical significance.
1. Study on Effective Properties of Metal Matrix Composites with Random Particle Distribution
In the mid-1990s, Bovik and Gousev proved that the whole composite can be modeled by a representative volume element with a finite volume, thus establishing the quantitative relationship between the macroscopic properties of the composite and the properties and microstructure of its constituent materials.
With the rapid development of computer technology, numerical analysis method has become an indispensable tool in the mechanical analysis of composite materials. When doing numerical simulation, establishing a suitable mathematical model is the basis of numerical simulation to calculate the equivalent properties of composite materials.
Multi-scale equivalent performance calculation based on finite element method is an effective and important method to study the relationship between microstructure and macro-mechanical behavior of composites. The premise of adopting this method is to establish the finite element model of composite materials, including geometric modeling and mesh generation of random particle distribution areas, and then multi-scale calculation can be carried out.
Various numerical methods for calculating the equivalent properties of composites have been developed at home and abroad. Generally speaking, it can be divided into back analysis and direct analysis. The essence of back analysis method is to inverse the mechanical parameters of composite materials according to the field observation results. The back analysis method mainly depends on the measured displacement of the material path, the constitutive model and the assumption of material parameters. Due to the influence of objective conditions and ignorance of composite materials, the assumptions of model and material parameters are often quite different from the actual situation, so this method has encountered some difficulties in practical application. Therefore, people try to choose another way-direct analysis method to predict the mechanical parameters of composite materials. Because the discrete element method can not solve the error of the calculation results of discrete composites well, there is little research on the calculation of macro-mechanical parameters based on discrete element method. At present, the numerical analysis method is mainly based on finite element method, and the calculation process is to establish the statistical model of granular materials first, and then simulate the composite "specimens" with different scales; The composite "specimen" obtained in this way can be regarded as composed of matrix and reinforced particles, and its mechanical parameters can be determined separately in the laboratory, and then the statistical mechanical parameters of the particles can be obtained by finite element analysis. The correctness of the calculation results of this method depends on the correctness of particle statistical model and the rationality of finite element algorithm. Although there is an error in this process, the error will not be greater than the in-situ measurement. The disadvantage of this method is that in order to avoid the size effect, the calculation cost is increased when simulating "specimens" with different scales, and when the calculation scale is increased, the number of particles in "specimens" increases obviously, which brings difficulties to finite element division and calculation.
Some scholars have studied the equivalent properties of particle reinforced composites based on finite element method and equivalent viewpoint, that is, according to certain equivalence principle, the influence of particles on the mechanical properties of materials is considered macroscopically, and the whole particle reinforced composites are homogenized and continuous, and then the equivalent mechanical properties are obtained through finite element calculation. However, there are still some limitations, such as the size effect of equivalent body. As a new method to study the macroscopic properties of composite materials, mathematicians have done a lot of research, such as A.Bensousson, J.L.Lion, etc. The concept of homogenization material coefficient is given for the step-by-step analysis of small period structure problems. O.A.Oleinik and others have deeply studied the homogenization theory and the first-order asymptotic analysis theory with small periodic structure; On this basis, Hou He gave a theoretical estimate of the first-order progressive expansion finite element. Cui Junzhi and others proposed a two-scale mutation algorithm for small periodic structures. For the basic element with symmetry, the higher-order asymptotic formula and finite element estimation are given, and this method is applied to engineering calculation, so that the theoretical analysis to numerical calculation is homogenized. The stage and practical application stage make it possible to calculate the macroscopic mechanical parameters of heterogeneous materials with complex microstructure, and a two-scale method for calculating the equivalent mechanical parameters of periodically braided composites is given.
In equivalent calculation, it is necessary to establish cell models of materials, such as two-dimensional cell model, two-dimensional multi-particle cell model, three-dimensional cell model, three-dimensional multi-particle cell model and representative cell model. Professor Qu Pengcheng from Wuhan University of Technology, etc. According to the cross section of SEM sample, the finite element model is established, and the equivalent elastic-plastic mechanical properties characteristic curve of SiC particle reinforced aluminum matrix composites is successfully predicted. According to the volume content of 10%Al2O3, Soppa enhanced the experimental micrograph of 606 1Al matrix composites, and made the finite element analysis model of the components to observe the influence of residual thermal stress on the deformation and failure of PRMMCs. Han et al. used a three-dimensional multi-particle cell model to study the mechanical properties and crack generation of PRMMCs.
2. Research on topology optimization of composite microstructure.
Structural topology optimization is the development of structural shape optimization and an aspect of layout optimization. When the shape optimization gradually matured, the new concept of structural topology optimization began to develop, and now topology optimization is becoming a new hot spot in the international structural optimization field. With Roderick Lakes( 1987, 1993) as the symbol, this paper expounds the foam materials with negative Poisson's ratio coefficient and the new discovery that extreme material characteristics (such as zero expansion coefficient and zero shear performance) incomparable to any single-phase material can be obtained by compounding materials with different components, and brings the optimization design of material microstructure into the field of topology optimization. Especially put forward by Sigmund in the mid-1990s, it has become one of the frontier topics in the field of materials research. At the 9th AIAA Annual Meeting in 2002, Kalidindi and others put forward the concept of "MSD- microstructure sensitive design", which further improved and developed the idea and system of microstructure configuration and composition optimization design. These pioneering works have laid a solid foundation for topology optimization design of composite materials and structures, and further promoted the optimization design of material microstructure.
Macroscopic properties of composites can be obtained by homogenization technology of microstructure cells, and composites with good characteristics can be obtained by topological optimization design of microstructure cells, such as piezoelectric materials with negative Poisson's ratio, negative thermal expansion coefficient, zero shear performance and good piezoelectric properties. For the topological optimization design of single cell, the problems can be divided into two categories: one is the problem that the minimum volume percentage of constitutive modulus is equal to a given value; The other is the extreme material constant problem that satisfies a series of volume constraints and symmetry conditions. Silva developed the optimal design of two-dimensional and three-dimensional piezoelectric materials with ultimate performance based on homogenization method. In China, Yuan Zhen and Wu Changchun carried out the optimal design of elastic materials with extreme properties, and Yang Wei and others used the optimization criterion method to design the microstructure with specific properties and realized the material design with negative Poisson's ratio. At present, the optimization design of microstructure based on heat transfer performance is still in its infancy. Zhang et al. predicted the heat transfer performance of materials based on homogenization method, and designed composite materials under a given amount of materials to obtain composite materials with extreme heat transfer performance.
Topological optimization has the complexity of both size optimization and shape optimization, and the final topological form of microstructure is unknown. The honeycomb structure obtained by microstructure topology optimization with minimum flexibility as the objective function is a standard regular hexagonal honeycomb structure.
Three. abstract
Metal matrix composite is a new type of high-tech engineering material developed rapidly in recent years, and it has been highly valued at home and abroad for its superior properties. SiC particle reinforced aluminum matrix composite is one of the most striking systems in composite materials at present, and it is an ideal research object of composite materials both theoretically and experimentally. In this paper, the effective properties research and microstructure topology optimization of metal matrix composites at home and abroad are reviewed, which is of certain significance to the research of metal matrix composites.