Study On Mechanical Properties Around The Hole In Micro Devices

The basic characteristics of the microelectronic mechanical system is miniaturization.Compared with the traditional mechanical system,their size is smaller,the maximum is no more than one centimeter,even just for a few microns.In microelectronic mechanical system,due to the miniaturization of length,physical and mechanical quantities of micro devices are significantly different than traditional mechanical systems,which is known as the size effect.Size effect makes the existing results of the research of macro phenomenon can not be directly applied to the micro situation.The existing study about size effect indicates that,the main reason of different mechanical properties in macroscale and microscale is uniformity and continuity hypothesis.The classic elastic mechanics consider that object is continuous uniform.It is believed that this assumption is usually accurate enough for macro circumstances,but under the condition that device size is close to the material internal length scale,this assumption is wrong.However,on the condition of the maintaining continuity and uniformity hypothesis,generalized elastic mechanics can explain the size effect of microstructures.The main work of the paper is as follows:(1)From the aspects of geometric description,conservation equation,constitutive relation and so on,the generalized elastic theory is distinguished from the classical elastic theory.The finite element equation of generalized elastic mechanics theory is established,and the programming is solved by Matlab.(2)The results of ANSYS finite element software are used to represent the classical elasticity theory.Comparing with the generalized elasticity Matlab programming results,the correctness of the generalized elasticity Matlab program is proved in the macroscopic dimension,but in the microcosmic dimension they are different,which reflects the size effect of microstructure.(3)Taking the uniaxial tension of the Single hole plate as an example,the calculation results of classical elasticity and generalized elastic theory in macroscopic size are compared.The distribution of corner,curvature,and couple stress which are not mentioned in the classical elasticity theory is given.The stress concentration factor and the couple stress magnitude of the tip of the hole from macro to microscopic dimensions are extracted to show the size effect of the structure.(4)Take the center circle radius of 1 mm to represent the macro size and take the center circle radius of 10 μm to represent the macro size.The calculation results of the nodes on the axis of the plate are compared in macroscopic and microscopic dimensions.The stress concentration factor and the couple stress magnitude are compared in macroscopic and microscopic dimensions,which is further illustrates the size effect of the orifice problem.(5)The stress symmetry is defined to illustrate the asymmetry of stress.The stress symmetry of the nodes along the edge of the circular hole is calculated,and the stress symmetry is maintained at 100% in the macroscopic dimension,but in the microscopic dimension,the stress symmetry of some nodes at the edge of the hole is not 100%.The size effect of stress symmetry is described in detail by taking one of the nodes as an example.In macroscopic size,the stress in the generalized elastic theory is approximately symmetrical,while in microscopic size,the proportion of the anti-symmetrical part of the total stress increases,the stress is no longer symmetrical.(6)The stress concentration factor of the uniaxial tension of the central elliptical hole plate is calculated.Comparing with the calculation results of the center circular hole plate,the greater the change in the cross-sectional dimension of the structure,the more serious the stress concentration is.Comparing the magnitude of the couple stress in the two cases,the more the even stress is obtained,the magnitude of the couple stress increases as the cross-sectional dimension changes more drastically.(7)Taking the double-hole plate structure as an example,the structural influence between one hole and the other one is discussed.The stress concentration factor of different hole margins in macroscopic size is compared.Whether in classical elastic mechanics or generalized elastic mechanics,the stress concentration factor of the double-hole plate is larger than that of the single-hole.And the stress concentration effect increases with the decrease of the hole margin.With the decrease of the double-hole margin,the difference between classical and generalized elastic mechanics increases.The generalized elastic stress concentration can not reach the high value as the classical elasticity.(8)In the microscopic size,the size effect of the stress concentration of the double-hole plate uniaxial tension still exists.With the structural dimension decreasing from centimeter to micrometer,the stress concentration factor decreases and the couple stress magnitude increases,which is consistent with the conclusion of the single-hole plate.(9)The problem of uniaxial tension of double elliptical hole plate is discussed.It is concluded that the stress concentration factor of the uniaxial tension of double elliptical hole plate is larger than that of the double circular hole plate,and the couple stress magnitude is larger than that of the double circular hole plate.The trend of the stress concentration and the magnitude of couple stress of the double elliptical hole plate is the same as that of the double circular hole plate.