In this paper,the material removal mechanism of copper chemical mechanical polishing was studied by the quasicontinuum method that integrated molecular dynamics and the finite element method.By analyzing the abrasive ...In this paper,the material removal mechanism of copper chemical mechanical polishing was studied by the quasicontinuum method that integrated molecular dynamics and the finite element method.By analyzing the abrasive process of different particle sizes on single crystal copper,we investigated the internal material deformation,the formation of chips,the stress distribution,and the change of cutting force.Results showed that shear band deformation was generated along the cutting direction at approximately 45° inside the workpiece material.The deformation was accompanied by dislocations and sliding phenomena in the shear band region.Smaller abrasive particle size led to poor quality of the workpiece,while a larger particle size led to better quality.However,larger particle size resulted in greater plastic deformation and deeper residual stress inside the workpiece.Size change of abrasive particles had little effect on the tangential cutting force.展开更多
In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the stra...In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the strain energy for the nano-sized plate under tension and bending, the relationship between the elastic modulus and the plate thickness is found. Size effects of the elastic modulus are displayed by the relative differences of the elastic modulus between the nano-sized plate sample and the bulk sample. By comparing the present results with those of others, the effectiveness of the Cauchy-Born rule model in studying the size effects of material properties are shown.展开更多
A quasi-continuum model of plate-type nanomaterials with the face-centered cubic crystal structures is proposed in this paper.The fundamental governing equations for the nonlinear bending of the nanoplates are given b...A quasi-continuum model of plate-type nanomaterials with the face-centered cubic crystal structures is proposed in this paper.The fundamental governing equations for the nonlinear bending of the nanoplates are given by using the principle of minimum potential energy.Specifically,the analytical solution is derived for cylindrical bending deformation of the structure under uniform transverse loading fixed at two sides based on the modified iterative method.A lattice finite element model is established to verify the present quasi-continuum model.Meanwhile,the corresponding solution by adopting the classical continuous plate theory is presented,in which two cases are considered for use of bulk values(limit values)and nanovalues of both elastic modulus and Poisson's ratio.The difference among the quasi-continuum and continuous models are discussed by computation.展开更多
A dynamic quasi-continuum model is presented to analyze free vibration of plate-type cubic crystal nano-materials.According to the Hamilton principle,fundamental governing equations in terms of displacement components...A dynamic quasi-continuum model is presented to analyze free vibration of plate-type cubic crystal nano-materials.According to the Hamilton principle,fundamental governing equations in terms of displacement components and angles of rotations are given.As an application of the model,the cylindrical bending deformation of the structure fixed at two ends is analyzed,and a theoretical formula evaluating the fundamental frequency is obtained by using Galerkin's method.Meanwhile,the solution for the classical continuous plate model is also derived,and the size-dependent elastic modulus and Poisson's ratio are taken in computation.The frequencies corresponding to different atomic layers are numerically presented for the plate-type NaC l nano-materials.Furthermore,a molecular dynamics(MD)simulation is conducted with the code LAMMPS.The comparison shows that the present quasi-continuum model is valid,and it may be used as an alternative model,which reflects scale effects in analyzing dynamic behaviors of such plate-type nano-materials.展开更多
基金The authors greatly appreciate the financial support from National Natural Science Foundation of China
文摘In this paper,the material removal mechanism of copper chemical mechanical polishing was studied by the quasicontinuum method that integrated molecular dynamics and the finite element method.By analyzing the abrasive process of different particle sizes on single crystal copper,we investigated the internal material deformation,the formation of chips,the stress distribution,and the change of cutting force.Results showed that shear band deformation was generated along the cutting direction at approximately 45° inside the workpiece material.The deformation was accompanied by dislocations and sliding phenomena in the shear band region.Smaller abrasive particle size led to poor quality of the workpiece,while a larger particle size led to better quality.However,larger particle size resulted in greater plastic deformation and deeper residual stress inside the workpiece.Size change of abrasive particles had little effect on the tangential cutting force.
基金Project supported by the National Natural Science Foundation of China(Nos.11021262,10932011 and 91216108)the National Basic Research Program of China(2012CB937500)
文摘In the present research, a simple quasi-continuum model, the Cauchy-Born rule model, is used to investigate the size effects of elastic modulus for fcc metals. By considering a nanoplate model and calculating the strain energy for the nano-sized plate under tension and bending, the relationship between the elastic modulus and the plate thickness is found. Size effects of the elastic modulus are displayed by the relative differences of the elastic modulus between the nano-sized plate sample and the bulk sample. By comparing the present results with those of others, the effectiveness of the Cauchy-Born rule model in studying the size effects of material properties are shown.
文摘A quasi-continuum model of plate-type nanomaterials with the face-centered cubic crystal structures is proposed in this paper.The fundamental governing equations for the nonlinear bending of the nanoplates are given by using the principle of minimum potential energy.Specifically,the analytical solution is derived for cylindrical bending deformation of the structure under uniform transverse loading fixed at two sides based on the modified iterative method.A lattice finite element model is established to verify the present quasi-continuum model.Meanwhile,the corresponding solution by adopting the classical continuous plate theory is presented,in which two cases are considered for use of bulk values(limit values)and nanovalues of both elastic modulus and Poisson's ratio.The difference among the quasi-continuum and continuous models are discussed by computation.
文摘A dynamic quasi-continuum model is presented to analyze free vibration of plate-type cubic crystal nano-materials.According to the Hamilton principle,fundamental governing equations in terms of displacement components and angles of rotations are given.As an application of the model,the cylindrical bending deformation of the structure fixed at two ends is analyzed,and a theoretical formula evaluating the fundamental frequency is obtained by using Galerkin's method.Meanwhile,the solution for the classical continuous plate model is also derived,and the size-dependent elastic modulus and Poisson's ratio are taken in computation.The frequencies corresponding to different atomic layers are numerically presented for the plate-type NaC l nano-materials.Furthermore,a molecular dynamics(MD)simulation is conducted with the code LAMMPS.The comparison shows that the present quasi-continuum model is valid,and it may be used as an alternative model,which reflects scale effects in analyzing dynamic behaviors of such plate-type nano-materials.
