Nonlinear Finite Elements Analyzing Of Tensile Mechanical Properties Of Nano-crystal Materials

The mechanical properties of nanocrystalline (NC) materials have been the subject of intensive investigations in reacent years. The numerical simulation is an impotant method to study mechanical properties of nanostructured materials. In order to investigate the uniaxial deformation of NC materials and the effects of grain size and porosity on the constitutive model, the atomic simulation technology in conjunction with the traditional finite element analysis method was employed. First we assume that NC materials is a composite constitutive model to consist of equiaxed grains (or crystalline) surrounded by interfaces consisting mostly of grain boundaries and triple junctions. As a further step in advancing the phase mixture model, we develop constitutive models for the crystalline phase and grain boundary phase which can account for the microstructural characteristics and the mechanism of deformation. In the paper, the many-body potential function based on the approximate local density and the approximate budiansky momentum was used to simulate the nonlinear constitutive model of grain boundary phase of NC silver.Finite element model of NC materials was built according to constitutive relation, and finite element programs were generated based on the given differential equation of evry phase and the nonlinear increament iterative algorithm by means of finite element program automatic generate system-FEPG. Two nonlinear problems including the nonlinearity of the material, the nonlinearity of the large gemetrical deformation was caculated by the numerical simulation system. Especially when the deformation of the grain biundary in nonlinear elasticity was simulated using NFEA, negtive value of the stiffness appeared often, which resulted the analysis stop. This was due to the decline of the loads-displacements curve. In this paper, the numerical simulation system has been used to solve the problem. The mixed problem of positive and negtive value of the stiffness was solved. At last, the results show that the contour of stress-strain distribution curve was determined in the gross at the nonlinear elastic stage.The calculated numerical simulation results show that the effects of grain size and porosity on the elastic modulus of nanocrystalline materials are very much large. With the decease of crystalline size, volume percent of grain boundary increased, it was found that nonlinear constitutive characteristic of NC silver and iron became more and more obvious, and the extension rate of materials was augmented. The intensity of NC matels was lower while the value of extension rate was greater. The value of extension rate of the pure and compact NC silver with 2nm is about 2 times of that with 100nm. The finial results show that the effect of porosity on intensity is the primary factor. For example, the intensity of NC silver with 2nm and 25% porosity reduces 43.88% than that of the pure and compact NC silver. Compared the numerical analysis results with the experimentation results of other scholars, it is shown that the theory and model in this article were feasible. Dates from different scholars exists difference through experimentations due to the restriction of preparation methods and test methods, etc. So it is necessary to prepare pure, compact and uniformity grain block in order to embody excellent properties of NC materials.