With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezo...With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezoelectric quasicrystals,an elliptical hole model under different boundary conditions is established.The analytical expressions of generalized stress intensity factors(GSIFs)are obtained,respectively,for four general cases:a Griffith crack with generalized remote uniform loading,arbitrary loading on the crack surface,concentrated loading at any position of the crack surface,and multiple collinear periodic cracks under uniform loading at infinity.Numerical examples are given,and the effects of crack length,loading position,loading condition,and crack period on GSIFs are discussed.The derived analytical solutions of cracks play a significant role in understanding the phonon-phason and electromechanical coupled behavior in quasicrystals,and they also serve as criteria for fracture analysis.展开更多
A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) ...A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.展开更多
Mg-6Zn-1Y(at.%)ribbons with strengthening precipitates of multi-type nanoquasicrystals were prepared by melt-spinning followed by aging treatments.Microstructural evolution of the rapidly solidified ribbons during iso...Mg-6Zn-1Y(at.%)ribbons with strengthening precipitates of multi-type nanoquasicrystals were prepared by melt-spinning followed by aging treatments.Microstructural evolution of the rapidly solidified ribbons during isothermal aging was comprehensively studied using various electron microscopy techniques.Two new kinds of decagonal quasicrystals were formed in aged ribbons,in addition to precipitation of nanometer icosahedral quasicrystals.Atomic-resolution observations reveal that both decagonal quasicrystals can be modeled by quasiperiodic tiling with decagonal clusters of 2.5 nm in diameter,but overlap of neighboring clusters in both decagonal quasicrystals is different from the Gummelt model observed in other quasicrystals.A shell composed of complex Laves Mg-Zn domains was formed surrounding each decagonal quasicrystal precipitate upon prolonged aging.In addition,all kinds of nanoprecipitates exhibit excellent structure and size stability at 573 K.Our findings may have implications for not only fundamental studies about quasicrystals,but also microstructural manipulation of high-performance Mg alloys.展开更多
Aim To study dislocation elasticity theory in quasicrystals. Methods A dislocation was separated into pure edge part and pure screw part and their superposition was used to find the elastic field. Results and Conclu...Aim To study dislocation elasticity theory in quasicrystals. Methods A dislocation was separated into pure edge part and pure screw part and their superposition was used to find the elastic field. Results and Conclusion The elastic solution of a straight dislocation parallel to the quasiperiodic axis in 1D hexagonal quasicrystals was obtained and the generalized Peach Koehler force on a dislocation in quasicrystals was given.展开更多
Based on the fundamental equations of piezoelasticity of quasicrystal media, using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional（1D）hexagonal quasicrystals is invest...Based on the fundamental equations of piezoelasticity of quasicrystal media, using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional（1D）hexagonal quasicrystals is investigated and the piezoelasticity problem of 1D hexagonal quasicrystals is decomposed into two uncoupled problems, i.e., the classical plane elasticity problem of conventional hexagonal crystals and the phonon–phason-electric coupling elasticity problem of1 D hexagonal quasicrystals.The final governing equations are derived for the phonon–phasonelectric coupling anti-plane elasticity of 1D hexagonal quasicrystals.The complex variable method for an anti-plane elliptical cavity in 1D hexagonal piezoelectric quasicrystals is proposed and the exact solutions of complex potential functions, the stresses and displacements of the phonon and the phason fields, the electric displacements and the electric potential are obtained explicitly.Reducing the cavity into a crack, the explicit solutions in closed forms of electro–elastic fields,the field intensity factors and the energy release rate near the crack tip are derived.展开更多
By constructing a new conformal mapping function, we study the surface effects on six edge nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional (1D) hexagonal piezoelectric quasicrystals under a...By constructing a new conformal mapping function, we study the surface effects on six edge nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional (1D) hexagonal piezoelectric quasicrystals under anti-plane shear. Based on the Gurtin–Murdoch surface/interface model and complex potential theory, the exact solutions of phonon field, phason field and electric field are obtained. The analytical solutions of the stress intensity factor of the phonon field, the stress intensity factor of the phason field, the electric displacement intensity factor and the energy release rate are given. The interaction effects of the nano-cracks and nano-hole on the stress intensity factor of the phonon field, the stress intensity factor of the phason field and the electric displacement intensity factor are discussed in numerical examples. It can be seen that the surface effect leads to the coupling of phonon field, phason field and electric field. With the decrease of cavity size, the influence of surface effect is more obvious.展开更多
Based on the fundamental equations of piezoelasticity of quasicrystal material,we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal ...Based on the fundamental equations of piezoelasticity of quasicrystal material,we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal quasicrystals.Explicit analytical solutions are obtained for stress and electric displacement intensity factors of the crack,as well as the force on dislocation.The derivation is based on the conformal mapping method and the perturbation technique.The influences of the wedge angle and dislocation location on the image force are also discussed.The results obtained in this paper can be fully reduced to some special cases already available or deriving new ones.展开更多
The present study is to determine the solution of a strip with a semi-infinite crack embedded in decagonal quasicrystals,which transforms a physically and mathematically daunting problem.Then cohesive forces are incor...The present study is to determine the solution of a strip with a semi-infinite crack embedded in decagonal quasicrystals,which transforms a physically and mathematically daunting problem.Then cohesive forces are incorporated into a plastic strip in the elastic body for nonlinear deformation.By superposing the two linear elastic fields,one is evaluated with internal loadings and the other with cohesive forces,the problem is treated in Dugdale-Barenblatt manner.A simple but yet rigorous version of the complex analysis theory is employed here,which involves a conformal mapping technique.The analytical approach leads to the establishment of a few equations,which allows the exact calculation of the size of cohesive force zone and the most important physical quantity in crack theory：stress intensity factor.The analytical results of the present study may be used as the basis of fracture theory of decagonal quasicrystals.展开更多
The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjecte...The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors is presented.展开更多
The stress potential function theory for the plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving the elasticity of octagonal quasicrys...The stress potential function theory for the plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving the elasticity of octagonal quasicrystals are reduced to a single partial differential equation. Furthermore, we develop the complex variable function method （Lekhnitskii method） for anisotropic elasticity theory to that for quasicrystals. With the help of conformal transformation, an exact solution for the elliptic hole of quasicrystals is presented. The solution of the Griffith crack problem, as a special case of the results, is obtained. As a consequence, the phonon stress intensity factor is derived analytically.展开更多
Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement fiel...Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral A1-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral A1-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of pbonon-phason coupling effect on the icosahedral A1-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.展开更多
The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to a...The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation,and then general solutions are presented through an operator method.By virtue of the Almansi′s theorem,the general solutions are further established,and all expressions for the phonon,phason and thermal fields are described in terms of the potential functions.As an application of the general solution,for a steady point heat source in a semi-infinite quasicrystal plane,the closed form solutions are presented by four newly induced harmonic functions.展开更多
In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact pr...In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact problem.The analytic expressions of contact stresses in the phonon and phason fields were obtained for a flat rigid punch,which showed that：（1） for the finite frictional contact problem,the contact stress exhibited power-type singularities at the edge of the contact zone;（2） for the adhesive contact problem,the contact stress exhibited oscillatory singularities at the edge of the contact zone.The distribution regulation of contact stress under punch was illustrated;and the low friction property of quasicrystals was verified graphically.展开更多
Double-well potentials are used for molecular dynamics simulation in monatomic systems. The potentials change as their parameters are adjusted, resulting in different structures. Of particular interest, we obtain deca...Double-well potentials are used for molecular dynamics simulation in monatomic systems. The potentials change as their parameters are adjusted, resulting in different structures. Of particular interest, we obtain decagonal and dodecagonal quasicrystals by simulations. We also verify the results and explain the formation of quasicrystals from the perspective of potential energy.展开更多
Plane elasticity theory of one-dimensional hexagonal quasicrystals with point group 6 is proposed and established. As an application of this theory, one typical example of dislocation problem in the quasicrystals is i...Plane elasticity theory of one-dimensional hexagonal quasicrystals with point group 6 is proposed and established. As an application of this theory, one typical example of dislocation problem in the quasicrystals is investigated and its exact analytic solution is presented. The result obtained indicates that the stress components of (elastic) fields of a straight dislocation in the quasicrystals still first order singularity, which is the same as the (general crystals,) but are related with the Burgers vector of phason fields, which is different from the general (crystals.)展开更多
Icosahedrons in supercooled liquids and glasses are considered to be of significance for the glass formation in alloy systems. Starting from the similarity of the local structure of quasicrystals to the icosahedrons i...Icosahedrons in supercooled liquids and glasses are considered to be of significance for the glass formation in alloy systems. Starting from the similarity of the local structure of quasicrystals to the icosahedrons in metallic glasses, a scheme is put forward to prepare metallic glasses based on a well-known quasicrystal Zr40Ti40Ni20. A series of （Zr4o Ti40Ni20 ）lOO-x Cos metallic glasses are fabricated, and the optimized glass forming composition is determined at （Zr40 Ti40Ni20 ）92 Cos. The results show that the glass-forming ability of the alloys is c10sely related to the quasicrystalline phases. The mechanism of the enhanced glass-forming ability is discussed.展开更多
Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With th...Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With the aid of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is obtained. The solution of the mode II Griffith crack as a special case is constructed. The stress intensity factor and energy release rate have been also obtained as a direct result of the crack solution.展开更多
A method to evaluate some Fourier integrals is extended from two-dimensional (2-D) and three dimensional (3-D) spaces ton-dimensional (n-D) space, which are often used in the elasticity theory of dislocations in quasi...A method to evaluate some Fourier integrals is extended from two-dimensional (2-D) and three dimensional (3-D) spaces ton-dimensional (n-D) space, which are often used in the elasticity theory of dislocations in quasicrystals. Some key formulae have been given.展开更多
The detailed atomic structure of quasicrystals has been an open problem for decades. Here we present a quasilattiee-conserved optimization method （quasi-OPT）, under particular quasiperiodic boundary conditions. As t...The detailed atomic structure of quasicrystals has been an open problem for decades. Here we present a quasilattiee-conserved optimization method （quasi-OPT）, under particular quasiperiodic boundary conditions. As the atomic coordinates are described by basic cells and quasilattices, we are able to maintain the self-similarity characteristics of qusicrystals with the atomic structure of the boundary region updated timely following the relaxing region. Exemplified with the study of decagonal Al-Co-Ni （d-Al-Co-Ni）, we propose a more stable atomic structure model based on Penrose quasilattice and our quasi-OPT simulations. In particular, rectangle-triangle ruIes are suggested for the local atomic structures of d-Al-Co-Ni quasicrystals.展开更多
The discoveries of so-called quasicrystals have broken through the theoretic foundation set up by the classical crystallographic group theory since 1891 and proposed new topics for study of solid structures. Electron ...The discoveries of so-called quasicrystals have broken through the theoretic foundation set up by the classical crystallographic group theory since 1891 and proposed new topics for study of solid structures. Electron diffraction patterns (EDP' s) and high-resolution microscopic (HREM) images have proved invaluable tools of studying the structures of crystals. The recognition and determination of EDP's and HREM images of a real-structure play a key role for understanding the structure. This paper will introduce some new developments about crystallographic group theory and new image processing methods on EDP's and HREM images. Contrary to popular beliefs, the research shows that quasicrystals can be understood (perturbed) complex periodic structures.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12272402,12102458,and 11972365)the China Agricultural University Education Foundation(No.1101-2412001).
文摘With the assistance of Stroh formalism,the general solutions satisfying the basic laws of linear elastic theory are written in complex variable forms.To analyze the fracture behavior of two-dimensional decagonal piezoelectric quasicrystals,an elliptical hole model under different boundary conditions is established.The analytical expressions of generalized stress intensity factors(GSIFs)are obtained,respectively,for four general cases:a Griffith crack with generalized remote uniform loading,arbitrary loading on the crack surface,concentrated loading at any position of the crack surface,and multiple collinear periodic cracks under uniform loading at infinity.Numerical examples are given,and the effects of crack length,loading position,loading condition,and crack period on GSIFs are discussed.The derived analytical solutions of cracks play a significant role in understanding the phonon-phason and electromechanical coupled behavior in quasicrystals,and they also serve as criteria for fracture analysis.
文摘A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.
基金supported by the National Natural Science Foundation of China (grant number: 51771202, 51971225, 52001225)Key Research of Frontier Science, Chinese Academy of Science (grant number: QYZDY-SSW-JSC207)+1 种基金Ji Hua Laboratory (X210141TL210)Guangdong Province (2021B0301030003)
文摘Mg-6Zn-1Y(at.%)ribbons with strengthening precipitates of multi-type nanoquasicrystals were prepared by melt-spinning followed by aging treatments.Microstructural evolution of the rapidly solidified ribbons during isothermal aging was comprehensively studied using various electron microscopy techniques.Two new kinds of decagonal quasicrystals were formed in aged ribbons,in addition to precipitation of nanometer icosahedral quasicrystals.Atomic-resolution observations reveal that both decagonal quasicrystals can be modeled by quasiperiodic tiling with decagonal clusters of 2.5 nm in diameter,but overlap of neighboring clusters in both decagonal quasicrystals is different from the Gummelt model observed in other quasicrystals.A shell composed of complex Laves Mg-Zn domains was formed surrounding each decagonal quasicrystal precipitate upon prolonged aging.In addition,all kinds of nanoprecipitates exhibit excellent structure and size stability at 573 K.Our findings may have implications for not only fundamental studies about quasicrystals,but also microstructural manipulation of high-performance Mg alloys.
文摘Aim To study dislocation elasticity theory in quasicrystals. Methods A dislocation was separated into pure edge part and pure screw part and their superposition was used to find the elastic field. Results and Conclusion The elastic solution of a straight dislocation parallel to the quasiperiodic axis in 1D hexagonal quasicrystals was obtained and the generalized Peach Koehler force on a dislocation in quasicrystals was given.
基金supported by the National Natural Science Foundation of China (Nos.11262012, 11462020, 10761005 and 11262017)the Scientific Research Key Program of Inner Mongolia University of Technology of China (No.ZD201219)+1 种基金the Natural Science Foundation of Inner Mongolia Department of Public Education of China (No.NJZZ13037)the Inner Mongolia Natural Science Foundation of China (No.2013MS0114)
文摘Based on the fundamental equations of piezoelasticity of quasicrystal media, using the symmetry operations of point groups, the linear piezoelasticity behavior of one-dimensional（1D）hexagonal quasicrystals is investigated and the piezoelasticity problem of 1D hexagonal quasicrystals is decomposed into two uncoupled problems, i.e., the classical plane elasticity problem of conventional hexagonal crystals and the phonon–phason-electric coupling elasticity problem of1 D hexagonal quasicrystals.The final governing equations are derived for the phonon–phasonelectric coupling anti-plane elasticity of 1D hexagonal quasicrystals.The complex variable method for an anti-plane elliptical cavity in 1D hexagonal piezoelectric quasicrystals is proposed and the exact solutions of complex potential functions, the stresses and displacements of the phonon and the phason fields, the electric displacements and the electric potential are obtained explicitly.Reducing the cavity into a crack, the explicit solutions in closed forms of electro–elastic fields,the field intensity factors and the energy release rate near the crack tip are derived.
基金Project supported by the National Key R&D Program of China (Grant No. 2017YFC1405605)the Innovation Youth Fund of the Ocean Telemetry Technology Innovation Center of the Ministry of Natural Resources, China (Grant No. 21k20190088)+1 种基金the Natural Science Foundation of Inner Mongolia, China (Grant No. 2018MS01005)the Graduate Students' Scientific Research Innovation Program of Inner Mongolia Normal University (Grant No. CXJJS19098).
文摘By constructing a new conformal mapping function, we study the surface effects on six edge nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional (1D) hexagonal piezoelectric quasicrystals under anti-plane shear. Based on the Gurtin–Murdoch surface/interface model and complex potential theory, the exact solutions of phonon field, phason field and electric field are obtained. The analytical solutions of the stress intensity factor of the phonon field, the stress intensity factor of the phason field, the electric displacement intensity factor and the energy release rate are given. The interaction effects of the nano-cracks and nano-hole on the stress intensity factor of the phonon field, the stress intensity factor of the phason field and the electric displacement intensity factor are discussed in numerical examples. It can be seen that the surface effect leads to the coupling of phonon field, phason field and electric field. With the decrease of cavity size, the influence of surface effect is more obvious.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11262017,11262012,and 11462020)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2015MS0129)+1 种基金the Programme of Higher-level Talents of Inner Mongolia Normal University(Grant No.RCPY-2-2012-K-035)the Key Project of Inner Mongolia Normal University(Grant No.2014ZD03)
文摘Based on the fundamental equations of piezoelasticity of quasicrystal material,we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal quasicrystals.Explicit analytical solutions are obtained for stress and electric displacement intensity factors of the crack,as well as the force on dislocation.The derivation is based on the conformal mapping method and the perturbation technique.The influences of the wedge angle and dislocation location on the image force are also discussed.The results obtained in this paper can be fully reduced to some special cases already available or deriving new ones.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10972035)
文摘The present study is to determine the solution of a strip with a semi-infinite crack embedded in decagonal quasicrystals,which transforms a physically and mathematically daunting problem.Then cohesive forces are incorporated into a plastic strip in the elastic body for nonlinear deformation.By superposing the two linear elastic fields,one is evaluated with internal loadings and the other with cohesive forces,the problem is treated in Dugdale-Barenblatt manner.A simple but yet rigorous version of the complex analysis theory is employed here,which involves a conformal mapping technique.The analytical approach leads to the establishment of a few equations,which allows the exact calculation of the size of cohesive force zone and the most important physical quantity in crack theory：stress intensity factor.The analytical results of the present study may be used as the basis of fracture theory of decagonal quasicrystals.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11072104,11272053,and 11262017)the Key Project of Chinese Ministry of Education(Grant No.212029)+3 种基金the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2013MS0114)the Natural Science Foundation of Inner Mongolia Department of Public Education,China(Grant No.NJZZ13037)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region,China(Grant No.NJYT-13-B07)the Program for Higher-Level Talents of Inner Mongolia University,China(Grant No.125125)
文摘The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors is presented.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11026175, 11262017, and 10761005)the Key Project of Ministry of Education of China (Grant No. 212029)+1 种基金the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2009MS0102 and 2009BS0104)the Natural Science Foundation of Inner Mongolia Department of Public Education, China (Grant Nos. NJzy08024 and NJ10047)
文摘The stress potential function theory for the plane elasticity of octagonal quasicrystals is developed. By introducing stress functions, a large number of basic equations involving the elasticity of octagonal quasicrystals are reduced to a single partial differential equation. Furthermore, we develop the complex variable function method （Lekhnitskii method） for anisotropic elasticity theory to that for quasicrystals. With the help of conformal transformation, an exact solution for the elliptic hole of quasicrystals is presented. The solution of the Griffith crack problem, as a special case of the results, is obtained. As a consequence, the phonon stress intensity factor is derived analytically.
基金Project supported by the National Natural Science Foundation of China(Grant No.11172319)the Scientific Fund of Chinese Universities(Grant Nos.2011JS046 and 2013BH008)+1 种基金the Opening Fund of State Key Laboratory of Nonlinear Mechanics,Program for New Century Excellent Talents in University,China(Grant No.NCET-13-0552)the National Science Foundation for Post-doctoral Scientists of China(Grant No.2013M541086)
文摘Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral A1-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral A1-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of pbonon-phason coupling effect on the icosahedral A1-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.
基金supported by the National Natural Sci-ence Foundation of China(11172319)the Chinese Univer-sities Scientific Fund(2011JS046,2013BH008)+2 种基金the Opening Fund of State Key Laboratory of Nonlinear Mechanicsthe Program for New Century Excellent Talents in Univer-sity(NCET-13-0552)the National Science Foundation for Post-doctoral Scientists of China(2013M541086)
文摘The thermoelastic plane problems of two-dimensional decagonal quasicrystals(QCs)are systematically investigated.By introducing a displacement function,the problem of thermoelastic plane problems can be simplified to an eighth-order partial differential governing equation,and then general solutions are presented through an operator method.By virtue of the Almansi′s theorem,the general solutions are further established,and all expressions for the phonon,phason and thermal fields are described in terms of the potential functions.As an application of the general solution,for a steady point heat source in a semi-infinite quasicrystal plane,the closed form solutions are presented by four newly induced harmonic functions.
基金Project supported by the National Natural Science Foundation of China(Nos.11362018,11261045 and 11261401)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116401110002)
文摘In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact problem.The analytic expressions of contact stresses in the phonon and phason fields were obtained for a flat rigid punch,which showed that：（1） for the finite frictional contact problem,the contact stress exhibited power-type singularities at the edge of the contact zone;（2） for the adhesive contact problem,the contact stress exhibited oscillatory singularities at the edge of the contact zone.The distribution regulation of contact stress under punch was illustrated;and the low friction property of quasicrystals was verified graphically.
基金Supported by the National Natural Science Foundation of China under Grant No 11674102
文摘Double-well potentials are used for molecular dynamics simulation in monatomic systems. The potentials change as their parameters are adjusted, resulting in different structures. Of particular interest, we obtain decagonal and dodecagonal quasicrystals by simulations. We also verify the results and explain the formation of quasicrystals from the perspective of potential energy.
文摘Plane elasticity theory of one-dimensional hexagonal quasicrystals with point group 6 is proposed and established. As an application of this theory, one typical example of dislocation problem in the quasicrystals is investigated and its exact analytic solution is presented. The result obtained indicates that the stress components of (elastic) fields of a straight dislocation in the quasicrystals still first order singularity, which is the same as the (general crystals,) but are related with the Burgers vector of phason fields, which is different from the general (crystals.)
基金Supported by the National Basic Research Program of China under Grant No 2010CB731604the National Natural Science Foundation of China under Grant Nos 51131002,51071138 and 51271160the Program of Qinhuangdao Science and Technology Bureau under Grant No 201401A051
文摘Icosahedrons in supercooled liquids and glasses are considered to be of significance for the glass formation in alloy systems. Starting from the similarity of the local structure of quasicrystals to the icosahedrons in metallic glasses, a scheme is put forward to prepare metallic glasses based on a well-known quasicrystal Zr40Ti40Ni20. A series of （Zr4o Ti40Ni20 ）lOO-x Cos metallic glasses are fabricated, and the optimized glass forming composition is determined at （Zr40 Ti40Ni20 ）92 Cos. The results show that the glass-forming ability of the alloys is c10sely related to the quasicrystalline phases. The mechanism of the enhanced glass-forming ability is discussed.
基金Project supported by the National Natural Science Foundation of China(Grant No.10761005)the Natural Science Foundation of Inner Mongolia of China(Grant Nos.2009MS0102,2009BS0101 and 2009BS0104)+1 种基金the Natural Science Foundation of Inner Mongolia Normal University(Grant No.QN07034)the Natural Science Foundation of Inner Mongolia Department of Public Education(Grant No.NJzy08024)
文摘Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With the aid of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is obtained. The solution of the mode II Griffith crack as a special case is constructed. The stress intensity factor and energy release rate have been also obtained as a direct result of the crack solution.
基金Supported by the Natural Science Foundation of Hubei( 992 0 p30 7)
文摘A method to evaluate some Fourier integrals is extended from two-dimensional (2-D) and three dimensional (3-D) spaces ton-dimensional (n-D) space, which are often used in the elasticity theory of dislocations in quasicrystals. Some key formulae have been given.
基金Supported by the National Natural Science Foundation of China under Grant No 11174082
文摘The detailed atomic structure of quasicrystals has been an open problem for decades. Here we present a quasilattiee-conserved optimization method （quasi-OPT）, under particular quasiperiodic boundary conditions. As the atomic coordinates are described by basic cells and quasilattices, we are able to maintain the self-similarity characteristics of qusicrystals with the atomic structure of the boundary region updated timely following the relaxing region. Exemplified with the study of decagonal Al-Co-Ni （d-Al-Co-Ni）, we propose a more stable atomic structure model based on Penrose quasilattice and our quasi-OPT simulations. In particular, rectangle-triangle ruIes are suggested for the local atomic structures of d-Al-Co-Ni quasicrystals.
文摘The discoveries of so-called quasicrystals have broken through the theoretic foundation set up by the classical crystallographic group theory since 1891 and proposed new topics for study of solid structures. Electron diffraction patterns (EDP' s) and high-resolution microscopic (HREM) images have proved invaluable tools of studying the structures of crystals. The recognition and determination of EDP's and HREM images of a real-structure play a key role for understanding the structure. This paper will introduce some new developments about crystallographic group theory and new image processing methods on EDP's and HREM images. Contrary to popular beliefs, the research shows that quasicrystals can be understood (perturbed) complex periodic structures.
