| Metal matrix composites(MMCs) have many excellent characteristics, such as specific strength, specific modulus and good high temperature stability, good thermal and electricity conductivity and anti-radiation. They have been widely used in the fields of building construction, aerospace, urban rail transit, medical equipment and so on. MMCs not only bear various complicated mechanical loadings in practical applications, but also influenced by all kinds of environmental factors, such as temperature. These loadings and environmental factors make the prediction of material properties, mechanical performance and failure mechanism become complicated. The traditional micromechanics model and calculation method of MMCs most are based on different specific assumptions, which have more or less deflects. Hence, it is urgent to construct a mechanics model and solving algorithm for MMCs, which have good precision, high efficiency and dispense with specific assumptions.In this graduation thesis, a micromechanics model for MMCs with periodic micro structure is established based on the variational asymptotic method. The accuracy of this model is verified by compared with finite element analysis and theoretical data. Then, the elasto-plastic and thermo- elasto-plastic properties of MMCs are simulated by the model. Firstly, the total energy incremental equations are established based on the generalized energy principle. Secondly, the solving of the total energy incremental equations under constrained conditions(geometric equations, the displacement continuity conditions, etc.) are converted into solving the stationary value problem of energy functional. Thirdly, in order to establish the solving method for single unit cell, we replace the large calculation with small scale computation. The leading items of energy functional are obtained by constructing difference function, which is obtained by the exact value minus the average value. In order to homogenize the boundary conditions for variational analyzing the leading items of energy functional, the difference function is characterized by the fluctuation function, and the stationary value problem defined in the unit cell is obtained. Finally, it is implemented by using finite element numerical method and the local stress-strain fields are recovered.The main conclusions obtained from the predicting elasto-plastic and thermo-elasto-plastic properties of MMCs by this micromechanics model are as follows:(1)The initial yield surface simulated by this micromechanical model agree well with ABAQUS results; when the fiber volume fraction is larges, the tress-strain curves predicted by this micromechanical model are almost the same as those of ABAQUS and experimental results.(2)Under off-axis loading, when ?(28)45,70,90? ? ?and the fiber volume fraction is small,the stress-strain curves of MMCs are almost identical to that of matrix. When ?(28)0,20? ?, the effect of fiber volume fractions on the global elastic performance is very small. The flexibility of MMCs firstly increase with the increase of off-axis load angle, then decreases with the sustained increase of off-axis load angle, and reach the maximum value at ?(28)45?.(3)Under uniaxial cyclic loading, the simulated stress-strain curves along the fiber direction are almost the same as those of other models; while the simulated stress-strain curves along the transverse direction have good agreement only in the positive direction of loading and unloading path and most negative direction of loading path.(4)The bauschinger effect appears in both axial and transverse direction, and the bauschinger effect in the axial direction is more noticeable. Under a cycle of the same strain, the compressive stress is greater than the tensile stress. At a constant strain range [-0.5%,0.5%], the stress constantly increases with the increase of cycling time, which can result in the cyclic hardening phenomenon.(5)With the temperature increases and under two transverse loads, the position of initial yield surface will shift along the corresponding equivalient normal stress direction; the temperature changes will not affect the critical stress that convert the elasto-plastic behavior of MMCs.(6)When the mechanical loading and temperature changes in same phase, the elastic stiffness and hardening stiffness is smaller than that in reversed phase. The added tress value in each cyclic is smaller than that in reversed phase. The yield strength will decrease, while the elastic stage of boron/aluminum composite will increase. When the mechanical loading and temperature changes in reversed phase, the yield strength increases, but the elastic stage of the boron/aluminum composite can be reduced.This innovation points in this graduation thesis are as follows:(1)To solve the elasto-plastic problem of MMCs, the generalized incremental energy functional is established from the point of view of energy. The corresponding micromechanical model is established based on the variational asymptotic homogenization method for unit cell. The fixed solution problem for elasto-plastic properties of MMCs is converted into the extreme value problem for functional, which can avoid specific defects existed in the traditional micromechanical model based on different specific assumptions. It has certain innovative in the application of the method.(2)The combination variational asymptotic theory with finite element method makes full use of the advantages of both methods, making up for the faults that traditional approximate method cannot predict very well the effective properties of complex microstructure. Meanwhile, it can effectively simulate behavior of MMCs under different thermal/loading conditions and l boundary conditions.(3)The local field distribution is recovered by using the simple algebraic operation of fluctuation function and global response, which breaks through the limitation of the traditional reprocessing that need to introduce the average stress and strain to recover the local fields. The theoretical result is a breakthrough in the micromechanics development, which can provide a broader perspective for mechanical development. |
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