Recent advances in additive manufacturing have enabled the construction of metallic lattice structures with tailored mechanical and functional properties.One potential application of metallic lattice struc-tures is in...Recent advances in additive manufacturing have enabled the construction of metallic lattice structures with tailored mechanical and functional properties.One potential application of metallic lattice struc-tures is in the impact load mitigation where an external kinetic energy is absorbed by the deformation/crushing of lattice cells.This has motivated a growing number of experimental and numerical studies,recently,on the crushing behavior of additively produced lattice structures.The present study overviews the dynamic and quasi-static crushing behavior of additively produced Ti64,316L,and AlSiMg alloy lattice structures.The first part of the study summarizes the main features of two most commonly used additive processing techniques for lattice structures,namely selective-laser-melt(SLM)and electro-beam-melt(EBM),along with a description of commonly observed process induced defects.In the second part,the deformation and strain rate sensitivities of the selected alloy lattices are outlined together with the most widely used dynamic test methods,followed by a part on the observed micro-structures of the SLM and EBM-processed Ti64,316L and AlSiMg alloys.Finally,the experimental and numerical studies on the quasi-static and dynamic compression behavior of the additively processed Ti64,316L,and AlSiMg alloy lattices are reviewed.The results of the experimental and numerical studies of the dynamic properties of various types of lattices,including graded,non-uniform strut size,hollow,non-uniform cell size,and bio-inspired,were tabulated together with the used dynamic testing methods.The dynamic tests have been noted to be mostly conducted in compression Split Hopkinson Pressure Bar(SHPB)or Taylor-and direct-impact tests using the SHPB set-up,in all of which relatively small-size test specimens were tested.The test specimen size effect on the compression behavior of the lattices was further emphasized.It has also been shown that the lattices of Ti64 and AlSiMg alloys are relatively brittle as compared with the lattices of 316L alloy.Finally,the challenges associated with modelling lattice structures were explained and the micro tension tests and multi-scale modeling techniques combining microstructural characteristics with macroscopic lattice dynamics were recommended to improve the accuracy of the numerical simulations of the dynamic compression deformations of metallic lattice structures.展开更多
Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications r...Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications requiring a compromise among lightness and suited mechanical properties,like improved energy absorption capacity and specific stiffness-to-weight and strength-to-weight ratios.A dedicated modeling strategy to assess the energy absorption capacity of lattice structures under uni-axial compression loading is presented in this work.The numerical model is developed in a non-linear framework accounting for the strain rate effect on the mechanical responses of the lattice structure.Four geometries,i.e.,cubic body centered cell,octet cell,rhombic-dodecahedron and truncated cuboctahedron 2+,are investigated.Specifically,the influence of the relative density of the representative volume element of each geometry,the strain-rate dependency of the bulk material and of the presence of the manufacturing process-induced geometrical imperfections on the energy absorption capacity of the lattice structure is investigated.The main outcome of this study points out the importance of correctly integrating geometrical imperfections into the modeling strategy when shock absorption applications are aimed for.展开更多
In this paper,the numerical simulation method is used to study the ballistic performances of hourglass lattice sandwich structures with the same mass under the vertical incidence of fragments.Attention is paid to eluc...In this paper,the numerical simulation method is used to study the ballistic performances of hourglass lattice sandwich structures with the same mass under the vertical incidence of fragments.Attention is paid to elucidating the influences of rod cross-section dimensions,structure height,structure layer,and rod inclination angle on the deformation mode,ballistic performances,and ability to change the ballistic direction of fragments.The results show that the ballistic performances of hourglass lattice sandwich structures are mainly affected by their structural parameters.In this respect,structural parameters optimization of the hourglass lattice sandwich structures enable one to effectively improve their ballistic limit velocity and,consequently,ballistic performances.展开更多
An efficient binomial lattice for pricing Asian options on yields is established under the affine term structure model. In order to reconnect the path of the discrete lattice,the technique of D. Nelson and K. Ramaswam...An efficient binomial lattice for pricing Asian options on yields is established under the affine term structure model. In order to reconnect the path of the discrete lattice,the technique of D. Nelson and K. Ramaswamy is used to transform a stochastic interest rate process into a stochastic diffusion with unit volatility. By the binomial lattice and linear interpolation,the prices of Asian options on yields can be obtained. As the number of nodes in the tree structure grows linearly with the number of time steps, the computational speed is improved. The numerical experiments to verify the validity of the lattice are also provided.展开更多
The electronic structures of pure V, Nb and Ta metals with bcc structure were determined by one atom (OA) theory. According to the electronic structures of these metals, their potential curves, cohesive energies, latt...The electronic structures of pure V, Nb and Ta metals with bcc structure were determined by one atom (OA) theory. According to the electronic structures of these metals, their potential curves, cohesive energies, lattice parameters, elasticity and the dependence of linear thermal expansion coefficients on temperature were calculated. The electronic structures and characteristic properties of these metals with fcc and hcp structures and liquid states were studied.展开更多
The electronic structures of pure Ti, Zr and Hf metals with hcp structure were determined by one atom (OA) theory. According to the electronic structures of these metals,their potential curves, cohesive energies, latt...The electronic structures of pure Ti, Zr and Hf metals with hcp structure were determined by one atom (OA) theory. According to the electronic structures of these metals,their potential curves, cohesive energies, lattice constants, elasticities and the temperature dependence of linear thermal expansion coefficients were calculated. The electronic structures and characteristic properties of these metals with bcc and fcc structures and liquids were also studied. The results show that the electronic structures of Ti, Zr and Hf metals are respectively [Ar](3d n) 0.481 0 (3d c) 2.085 7 (4s c) 1.000 0 (4s f) 0.433 3 , [Kr](4d n) 0.396 8 (4d c) 2.142 8 (5s c) 1.262 0 (5s f) 0.198 4 , [Xe](5d n) 0.368 0 (5d c) 2.041 4 (6s c) 1.406 6 (6s f) 0.184 0 . It is explained why the pure Ti, Zr and Hf metals with hcp and bcc structures can exist naturally, while those with fcc structure can not.展开更多
Based on the empirical electronic theory of solids and molecules （EET）, the actual model for unit cell of cementite （0-FeaC） was built and the valence electron structures （VES） of cementite with specified site a...Based on the empirical electronic theory of solids and molecules （EET）, the actual model for unit cell of cementite （0-FeaC） was built and the valence electron structures （VES） of cementite with specified site and a number of Fe atoms substituted by alloying atoms of M （ M=Cr, V, W, Mo, Mn ） were computed by statistical method. By defining P as the stability factor, the stability of alloyed cementite with different numbers and sites of Fe atoms substituted by M was calculated. Calculation results show that the density of lattice electrons, the symmetry of distribution of covalent electron pairs and bond energy have huge influence on the stability of alloyed cementite. It is more stable as M substitutes for FeE than for Fe1. The alloyed cementite is the most stable when Cr, Mo, W and V substitute for 2 atoms of Fe2 at the sites of Nos. 2 and 3 （or No. 6 and No. 7）. The stability of alloyed cementite decreases gradually as being substitutional doped by W, Cr, V, Mo and Mn.展开更多
基金the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 101034425 for the project titled A2M2TECHThe Scientific and Technological Research Council of Türkiye (TUBITAK) with grant No 120C158 for the same A2M2TECH project under the TUBITAK's 2236/B program
文摘Recent advances in additive manufacturing have enabled the construction of metallic lattice structures with tailored mechanical and functional properties.One potential application of metallic lattice struc-tures is in the impact load mitigation where an external kinetic energy is absorbed by the deformation/crushing of lattice cells.This has motivated a growing number of experimental and numerical studies,recently,on the crushing behavior of additively produced lattice structures.The present study overviews the dynamic and quasi-static crushing behavior of additively produced Ti64,316L,and AlSiMg alloy lattice structures.The first part of the study summarizes the main features of two most commonly used additive processing techniques for lattice structures,namely selective-laser-melt(SLM)and electro-beam-melt(EBM),along with a description of commonly observed process induced defects.In the second part,the deformation and strain rate sensitivities of the selected alloy lattices are outlined together with the most widely used dynamic test methods,followed by a part on the observed micro-structures of the SLM and EBM-processed Ti64,316L and AlSiMg alloys.Finally,the experimental and numerical studies on the quasi-static and dynamic compression behavior of the additively processed Ti64,316L,and AlSiMg alloy lattices are reviewed.The results of the experimental and numerical studies of the dynamic properties of various types of lattices,including graded,non-uniform strut size,hollow,non-uniform cell size,and bio-inspired,were tabulated together with the used dynamic testing methods.The dynamic tests have been noted to be mostly conducted in compression Split Hopkinson Pressure Bar(SHPB)or Taylor-and direct-impact tests using the SHPB set-up,in all of which relatively small-size test specimens were tested.The test specimen size effect on the compression behavior of the lattices was further emphasized.It has also been shown that the lattices of Ti64 and AlSiMg alloys are relatively brittle as compared with the lattices of 316L alloy.Finally,the challenges associated with modelling lattice structures were explained and the micro tension tests and multi-scale modeling techniques combining microstructural characteristics with macroscopic lattice dynamics were recommended to improve the accuracy of the numerical simulations of the dynamic compression deformations of metallic lattice structures.
文摘Modern additive manufacturing processes enable fabricating architected cellular materials of complex shape,which can be used for different purposes.Among them,lattice structures are increasingly used in applications requiring a compromise among lightness and suited mechanical properties,like improved energy absorption capacity and specific stiffness-to-weight and strength-to-weight ratios.A dedicated modeling strategy to assess the energy absorption capacity of lattice structures under uni-axial compression loading is presented in this work.The numerical model is developed in a non-linear framework accounting for the strain rate effect on the mechanical responses of the lattice structure.Four geometries,i.e.,cubic body centered cell,octet cell,rhombic-dodecahedron and truncated cuboctahedron 2+,are investigated.Specifically,the influence of the relative density of the representative volume element of each geometry,the strain-rate dependency of the bulk material and of the presence of the manufacturing process-induced geometrical imperfections on the energy absorption capacity of the lattice structure is investigated.The main outcome of this study points out the importance of correctly integrating geometrical imperfections into the modeling strategy when shock absorption applications are aimed for.
基金supported by the Defense Industrial Technology Development Program(Grant No.JCKY2018604B004)the National Natural Science Foundation of China(Grant No.11972007)。
文摘In this paper,the numerical simulation method is used to study the ballistic performances of hourglass lattice sandwich structures with the same mass under the vertical incidence of fragments.Attention is paid to elucidating the influences of rod cross-section dimensions,structure height,structure layer,and rod inclination angle on the deformation mode,ballistic performances,and ability to change the ballistic direction of fragments.The results show that the ballistic performances of hourglass lattice sandwich structures are mainly affected by their structural parameters.In this respect,structural parameters optimization of the hourglass lattice sandwich structures enable one to effectively improve their ballistic limit velocity and,consequently,ballistic performances.
文摘An efficient binomial lattice for pricing Asian options on yields is established under the affine term structure model. In order to reconnect the path of the discrete lattice,the technique of D. Nelson and K. Ramaswamy is used to transform a stochastic interest rate process into a stochastic diffusion with unit volatility. By the binomial lattice and linear interpolation,the prices of Asian options on yields can be obtained. As the number of nodes in the tree structure grows linearly with the number of time steps, the computational speed is improved. The numerical experiments to verify the validity of the lattice are also provided.
文摘The electronic structures of pure V, Nb and Ta metals with bcc structure were determined by one atom (OA) theory. According to the electronic structures of these metals, their potential curves, cohesive energies, lattice parameters, elasticity and the dependence of linear thermal expansion coefficients on temperature were calculated. The electronic structures and characteristic properties of these metals with fcc and hcp structures and liquid states were studied.
基金TheNaturalScienceFoundationofHunanProvince (No .99JZY10 0 5 )
文摘The electronic structures of pure Ti, Zr and Hf metals with hcp structure were determined by one atom (OA) theory. According to the electronic structures of these metals,their potential curves, cohesive energies, lattice constants, elasticities and the temperature dependence of linear thermal expansion coefficients were calculated. The electronic structures and characteristic properties of these metals with bcc and fcc structures and liquids were also studied. The results show that the electronic structures of Ti, Zr and Hf metals are respectively [Ar](3d n) 0.481 0 (3d c) 2.085 7 (4s c) 1.000 0 (4s f) 0.433 3 , [Kr](4d n) 0.396 8 (4d c) 2.142 8 (5s c) 1.262 0 (5s f) 0.198 4 , [Xe](5d n) 0.368 0 (5d c) 2.041 4 (6s c) 1.406 6 (6s f) 0.184 0 . It is explained why the pure Ti, Zr and Hf metals with hcp and bcc structures can exist naturally, while those with fcc structure can not.
基金Project(2014CFB801)supported by Natural Science Foundation of Hubei Province of ChinaProject(11304236)supported by the National Natural Science Foundation of China
文摘Based on the empirical electronic theory of solids and molecules （EET）, the actual model for unit cell of cementite （0-FeaC） was built and the valence electron structures （VES） of cementite with specified site and a number of Fe atoms substituted by alloying atoms of M （ M=Cr, V, W, Mo, Mn ） were computed by statistical method. By defining P as the stability factor, the stability of alloyed cementite with different numbers and sites of Fe atoms substituted by M was calculated. Calculation results show that the density of lattice electrons, the symmetry of distribution of covalent electron pairs and bond energy have huge influence on the stability of alloyed cementite. It is more stable as M substitutes for FeE than for Fe1. The alloyed cementite is the most stable when Cr, Mo, W and V substitute for 2 atoms of Fe2 at the sites of Nos. 2 and 3 （or No. 6 and No. 7）. The stability of alloyed cementite decreases gradually as being substitutional doped by W, Cr, V, Mo and Mn.
