The micropolar(MP) and strain gradient(SG) continua have been generally adopted to investigate the relations between the macroscopic elastic constants and the microstructural geometric parameters. Owing to the fact th...The micropolar(MP) and strain gradient(SG) continua have been generally adopted to investigate the relations between the macroscopic elastic constants and the microstructural geometric parameters. Owing to the fact that the microrotation in the MP theory can be expressed in terms of the displacement gradient components, we may regard the MP theory as a particular incomplete SG theory called the MPSG theory,compared with the existing SG theories which are deemed complete since all the SGs are included. Taking the triangular lattice comprising zigzag beams as an example, it is found that as the angle of the zigzag beams increases, the bending of the beams plays a more important role in the total strain energy, and the difference between the results by the two theories gradually decreases. Finally, the models are verified with the pure bending and simple shear of lattices by comparing with the results obtained by the finite element method(FEM)-based structure analyses.展开更多
利用纳米硬度仪研究了在Cu基底上的Cu／Cr梯度膜的机械性能。梯度膜是通过将Cu靶和Cr靶同时溅射到Cu基底材料上,但两个靶的相对溅射功率随溅射时间变化而制备。利用Oliver and Pharr方法得到了膜随其厚度变化的硬度和弹性模量。然后利...利用纳米硬度仪研究了在Cu基底上的Cu／Cr梯度膜的机械性能。梯度膜是通过将Cu靶和Cr靶同时溅射到Cu基底材料上,但两个靶的相对溅射功率随溅射时间变化而制备。利用Oliver and Pharr方法得到了膜随其厚度变化的硬度和弹性模量。然后利用加载／卸载／再加载的方法得到了在不同深度(即膜的厚度)压头平均压力与相对压入深度之间的关系曲线,在此曲线上可以明显反映出材料的屈服特性。展开更多
We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is p...We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing.Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice,resulting in a novel SG model.For various kinds of diatomic lattices,the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone,manifesting the robustness of the present model.Based on this SG model,we have conducted the following discussions.(Ⅰ)Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials,which is very helpful for the design of metamaterials.(Ⅱ)The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted.Without doing so,the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy.The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone.(Ⅲ)The effects of the nonlocal interactions are analyzed.The nonlocal interactions reduce the workable range of the well-known long-wave approximation,causing more local extrema in the dispersive diagrams.The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing,i.e.,when the long-wave approximation is no longer valid.For the convenience of band gap designs,we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.展开更多
Coarse-grained（CG） metals strengthened by nanotwinned（NT） regions possess high strength and good ductility. As such, they are very suitable for applications in bullet-proof targets. Here, a numerical model based o...Coarse-grained（CG） metals strengthened by nanotwinned（NT） regions possess high strength and good ductility. As such, they are very suitable for applications in bullet-proof targets. Here, a numerical model based on the conventional theory of strain gradient plasticity and the Johnson–Cook failure criterion is employed to study the influences of volume fraction of NT regions on their ballistic performance.The results show that in general a relatively small twin spacing（4–10 nm） and a moderate volume fraction（7%–20%） will lead to excellent limit velocity and that the influences of volume fraction on limit displacement change with the category of impact processes.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 11972174)。
文摘The micropolar(MP) and strain gradient(SG) continua have been generally adopted to investigate the relations between the macroscopic elastic constants and the microstructural geometric parameters. Owing to the fact that the microrotation in the MP theory can be expressed in terms of the displacement gradient components, we may regard the MP theory as a particular incomplete SG theory called the MPSG theory,compared with the existing SG theories which are deemed complete since all the SGs are included. Taking the triangular lattice comprising zigzag beams as an example, it is found that as the angle of the zigzag beams increases, the bending of the beams plays a more important role in the total strain energy, and the difference between the results by the two theories gradually decreases. Finally, the models are verified with the pure bending and simple shear of lattices by comparing with the results obtained by the finite element method(FEM)-based structure analyses.
文摘利用纳米硬度仪研究了在Cu基底上的Cu／Cr梯度膜的机械性能。梯度膜是通过将Cu靶和Cr靶同时溅射到Cu基底材料上,但两个靶的相对溅射功率随溅射时间变化而制备。利用Oliver and Pharr方法得到了膜随其厚度变化的硬度和弹性模量。然后利用加载／卸载／再加载的方法得到了在不同深度(即膜的厚度)压头平均压力与相对压入深度之间的关系曲线,在此曲线上可以明显反映出材料的屈服特性。
基金Project supported by the National Natural Science Foundation of China(Nos.11972174 and 11672119)。
文摘We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing.Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice,resulting in a novel SG model.For various kinds of diatomic lattices,the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone,manifesting the robustness of the present model.Based on this SG model,we have conducted the following discussions.(Ⅰ)Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials,which is very helpful for the design of metamaterials.(Ⅱ)The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted.Without doing so,the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy.The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone.(Ⅲ)The effects of the nonlocal interactions are analyzed.The nonlocal interactions reduce the workable range of the well-known long-wave approximation,causing more local extrema in the dispersive diagrams.The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing,i.e.,when the long-wave approximation is no longer valid.For the convenience of band gap designs,we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.
基金supported by the National Natural Science Foundation of China(11372214)the opening project of State Key Laboratory of Explosion Science and Technology(Beijing Institute of Technology)(KFJJ17-10M)+1 种基金the support of the NSF Mechanics of Materials Program under CMMI-1162431the support from the Advanced Engineering Programme and School of Engineering,Monash University Malaysia
文摘Coarse-grained（CG） metals strengthened by nanotwinned（NT） regions possess high strength and good ductility. As such, they are very suitable for applications in bullet-proof targets. Here, a numerical model based on the conventional theory of strain gradient plasticity and the Johnson–Cook failure criterion is employed to study the influences of volume fraction of NT regions on their ballistic performance.The results show that in general a relatively small twin spacing（4–10 nm） and a moderate volume fraction（7%–20%） will lead to excellent limit velocity and that the influences of volume fraction on limit displacement change with the category of impact processes.
