Study On The Elastic Constants And Size Effect Of Solid Based On Microscopic Particle

At present,to MEMS,size effect is an unprecedented science difficult problem. After mechanical being miniaturized,the problem that should be answered at first is the differences between the mechanical properties of the micro-component and the traditional component's.In recent years,the experiments have revealed that there is strong size effect in metal materials in micrometer scale.On the ground of elasticity,continuum mechanics,solid state physics,potential function theory and so on,orienting the plane solid thin plate toward research object, the plate is composed of a single layer of particles that are homologous and can be replaced by ball model approximately,the model of "the Continuous Medium Two-dimensional Model based on Interparticle Force"("PF-CM-2D" model) is built. Based on the model,the elastic properties,elastic constants and size effect of pure solid material(mainly is pure metal) are studied.The major works and conclusions can be summarized as follow.To whichever triangle regional of the "PF-CM-2D" model,the calculation formulas of the elastic coefficients and of the initial stresses are deduced.The elastic constitutive equation in whichever triangle regional of the model is obtained,and the equation is anisotropic while the special cases do not be considered.The conclusions are drawn:there are not the unified totality elastic coefficients and the unified totality elastic constitutive equation to the integer of the model,the integral elastic behavior of the model is anisotropic while the special cases do not be considered.The concept of the ideal micro structure is presented.While the micro structure of the "PF-CM-2D" model is ideal micro structure,the calculation formulas of the initial stresses,the totality elastic coefficients,the elastic modulus,the poisson ratio and the totality elastic constitutive equation are deduced.From these calculation formulas,it can be known that the poisson ratio is a constant(the value is equal to 1/3) and only one of 6 totality elastic constants is independent.The unique existence of elastic isotropic is proved.The conclusion is given:size effect has not influence on the totality elastic coefficients,the elastic modulus and the poisson ratio while the micro structure of the "PF-CM-2D" model is ideal micro structure.The concepts of the actual micro structure,the equivalent interparticle distance, the actual average density,the monolayer homogeneity particle ideal average density and so on are presented.While the micro structure of the "PF-CM-2D" model is actual micro structure,the calculation formulas of the equivalent interparticle distance, the approximate totality elastic coefficients,the approximate elastic modulus,the approximate poisson ratio are deduced and the approximate totality elastic constitutive equation are deduced.The influence of size effect on the approximate totality elastic coefficients,the approximate elastic modulus and the approximate poisson ratio are studied.Taking pure copper as an example,the elastic modulus and the elastic constitutive equation are solved according to the ideal micro structure of the "PF-CM-2D" model,and the equivalent interparticle distance and the elastic modulus are solved according to the actual micro structure of the model.Moreover some curves are given.With the square pure copper thin plate as an example,whenρ_s(ρ_s is actual average density) is 5500kg/m~3 and 5400kg/m~3 respectively,the influence of size effect on the elastic modulus is studied.To the standard involute cylindrical spur gear with complex geometry,the calculation formula of the ratio of the end-face contour total length to the end-face area is deduced.While the addendum coefficient is 1,the tip clearance coefficient is 0.25,the diameter of the gear inner hole is 0 and the actual average density is 5500kg/m~3,the relation curves between the elastic modulus and the module are given when the tooth number is respectively 20,40,60,100,and the relation curves between the elastic modulus and the tooth number are given when the module is respectively 0.01mm,0.1mm,1mm,2mm.From the curves,the conclusion is obtain that size effect has obvious influence on the elastic modulus of the pure copper with the geometry of the standard involute cylindrical spur gear when the pitch circle diameter of gear is less than about 300μm.