The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattic...The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .展开更多
A glassy(G)phase was formed for Zr-rich Zr70-75(Al,Ni,Cu,Ag)25-30(atomic percent,at.%)melt-spun alloy ribbons.These glassy alloys exhibit the glass transition,followed by a supercooled liquid region and then three-sta...A glassy(G)phase was formed for Zr-rich Zr70-75(Al,Ni,Cu,Ag)25-30(atomic percent,at.%)melt-spun alloy ribbons.These glassy alloys exhibit the glass transition,followed by a supercooled liquid region and then three-stage crystallization.The glass transition temperature and the onset temperature for the first-stage crystallization(Tx1)decrease from 630 to 668 K,respectively for the 70Zr alloy to 619 and 652 K,respectively for the 75Zr alloy.The first-stage exothermic peak is due to the precipitation of an icosahedral quasicrystal(IQ)phase.The IQ particle size decreases from 10 nm to 6 nm with increasing Zr content from 70 at.%to 74 at.%.The[G+IQ]phases change to Zr2 Ni+Zr2(Cu,Ag)phases after the second exothermic peak and then Zr2 Ni+Zr2(Cu,Ag)+Zr5 Al3 phases after the third stage.It is noticed that the as-spun glassy alloy ribbons as well as the annealed[G+IQ]phase ribbons exhibit good bending plasticity.Furthermore,the 70Zr thicker ribbons also exhibit high tensile fracture strength of 1090-1187 MPa and plastic elongation of 0.17%-0.42%.The fracture mode is similar to that of ordinary bulk metallic glasses.The Vickers hardness(H v)is 480 for 70Zr alloy and decreases to 436 for 75Zr alloy.The precipitation of IQ phase causes a significant increase in H v to about 554.The formations of glassy alloys with high Zr contents of 70 at.%-75 at.%by melt spinning as well as the[G+IQ]phase alloys with good bending plasticity by annealing hold promise for the creation of a new type of engineering material,transcending mere academic novelty.展开更多
Al_(65)Cu_(20)Fe_(15)bulk is synthesized with the high-pressure synthesis(HPS)method.Various analytical techniques,such as single crystal x-ray diffraction(SXRD),scanning electron microscopy equipped with energy-dispe...Al_(65)Cu_(20)Fe_(15)bulk is synthesized with the high-pressure synthesis(HPS)method.Various analytical techniques,such as single crystal x-ray diffraction(SXRD),scanning electron microscopy equipped with energy-dispersive x-ray spectroscopy,and transmission electron microscopy,are employed to characterize the sintered bulk and confirmed its quasicrystalline structure.The electrical resistivity of the HPS quasicrystal specimen is measured from 2 K to 300 K,revealing a significantly elevated value in comparison to samples prepared via alternative methods.Nanoindentation testing demonstrates exceptional hardness and elastic modulus of our Al_(65)Cu_(20)Fe_(15)quasicrystal,consistent with existing results.The ratio of hardness to elastic modulus further highlight the potential superior wear resistance of the Al_(65)Cu_(20)Fe_(15)quasicrystal.Differential scanning calorimetry measurement conducted on the HPS Al_(65)Cu_(20)Fe_(15)quasicrystals reveal a high melting point of 877℃.展开更多
In this paper,the mechanical response of a one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)thin film is analyzed under electric and temperature loads.Based on the Euler-Bernoulli beam theory,a theoretical ...In this paper,the mechanical response of a one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)thin film is analyzed under electric and temperature loads.Based on the Euler-Bernoulli beam theory,a theoretical model is proposed,resulting in coupled governing integral equations that account for interfacial normal and shear stresses.To numerically solve these integral equations,an expansion method using orthogonal Chebyshev polynomials is employed.The results provide insights into the interfacial stresses,axial force,as well as axial and vertical deformations of the PQC film.Additionally,fracture criteria,including stress intensity factors,mode angles,and the J-integral,are evaluated.The solution is compared with the membrane theory,neglecting the normal stress and bending deformation.Finally,the effects of stiffness and aspect ratio on the PQC film are thoroughly discussed.This study serves as a valuable guide for controlling the mechanical response and conducting safety assessments of PQC film systems.展开更多
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
In this paper,we investigate the interfacial behavior of a thin,penny-shaped,one-dimensional(1D)hexagonal functionally graded(FG)piezoelectric quasicrystal(PQC)film bonded on a temperature-dependent elastic substrate ...In this paper,we investigate the interfacial behavior of a thin,penny-shaped,one-dimensional(1D)hexagonal functionally graded(FG)piezoelectric quasicrystal(PQC)film bonded on a temperature-dependent elastic substrate under thermal and electrical loads.The problem is modeled as axisymmetric based on the membrane theory,with the peeling stress and bending moment being disregarded.A potential theory method,combined with the Hankel transform technique,is utilized to derive the displacement field on the substrate surface.With perfect interfacial bonding assumption,an integral equation governing the phonon interfacial shear stress is formulated and numerically solved by the Chebyshev polynomials.Explicit expressions are derived for the interfacial shear stress,the internal stresses within the PQC film and the substrate,the axial strain,and the stress intensity factors(SIFs).Numerical simulations are conducted to investigate the effects of the film's aspect ratio,material inhomogeneity,material mismatch,and temperature-dependent material properties on its mechanical response.The results provide insights for the functional design and reliability assessment of FG PQC film/substrate systems.展开更多
The Mg-Zn-Y quasicrystal-reinforced AZ91 D magnesium matrix composites were prepared by squeeze casting process. The effects of applied pressure on microstructure and mechanical properties of the composites were inves...The Mg-Zn-Y quasicrystal-reinforced AZ91 D magnesium matrix composites were prepared by squeeze casting process. The effects of applied pressure on microstructure and mechanical properties of the composites were investigated. The results show that squeeze casting process is an effective method to refine the grain. The composites are mainly composed of α-Mg, β-Mg17Al12 and Mg3Zn6Y icosahedral quasicrystal phase（I-phase）. With the increase of applied pressure, the contents of β-Mg17Al12 phase and Mg3Zn6 Y quasicrystal particles increase, further matrix grain refinement occurs and coarse dendritic α-Mg transforms into equiaxed grain structure. The composite exhibits the maximum ultimate tensile strength and elongation of 194.3 MPa and 9.2% respectively when the applied pressure is 100 MPa, and a lot of dimples appear on the tensile fractography. Strengthening mechanisms of quasicrystal-reinforced AZ91 D magnesium matrix composites are chiefly fine-grain strengthening and quasicrystal particles strengthening.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
The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so t...The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.展开更多
As a new structure of solid matter quasicrystal brings profound new ideas to the traditional condensed matter physics, its elastic equations are more complicated than that of traditional crystal. A contact problem of ...As a new structure of solid matter quasicrystal brings profound new ideas to the traditional condensed matter physics, its elastic equations are more complicated than that of traditional crystal. A contact problem of decagonal two? dimensional quasicrystal material under the action of a rigid flat die is solved satisfactorily by introducing displacement function and using Fourier analysis and dual integral equations theory, and the analytical expressions of stress and displacement fields of the contact problem are achieved. The results show that if the contact displacement is a constant in the contact zone, the vertical contact stress has order -1/2 singularity on the edge of contact zone, which provides the important mechanics parameter for contact deformation of the quasicrystal.展开更多
The structures and electrochemical properties of the Ti1.4V0.6Ni ribbon before and after heat treatment are investigated systematically. The structure of the sample is characterized by X-ray powder diffraction analysi...The structures and electrochemical properties of the Ti1.4V0.6Ni ribbon before and after heat treatment are investigated systematically. The structure of the sample is characterized by X-ray powder diffraction analysis. Electrochemical properties including the discharge capacity, the cyclic stability and the high-rate discharge ability are tested. X-ray powder diffraction analysis shows that after heat treatment at 590 °C for 30 min, all samples mainly consist of the icosahedral quasicrystal phase (I-phase), Ti2Ni phase (FCC), V-based solid solution phase (BCC) and C14 Laves phase (hexagonal). Electrochemical measurements show that the maximum discharge capacity of the alloy electrode after heat treatment is 330.9 mA?h/g under the conditions that the discharge current density is 30 mA/g and the temperature is 30 °C. The result indicates that the cyclic stability and the high-rate discharge ability are all improved. In addition, the electrochemical kinetics of the alloy electrode is also studied by electrochemical impedance spectroscopy (EIS) and hydrogen diffusion coefficient (D).展开更多
Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were appli...Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.展开更多
The review is devoted to introduce the recent development of the study in mathematical theory and methods of mechanics of quasicrystals, respectively. The mechanics of quasicrystalline materials includes elasticity, p...The review is devoted to introduce the recent development of the study in mathematical theory and methods of mechanics of quasicrystals, respectively. The mechanics of quasicrystalline materials includes elasticity, plasticity, defects, dynamics, fracture etc. In the article some relevant measured data are collected for some important quasicrystal systems, which are necessary for understanding physics and applications of the materials. It is very interesting that the mathe-matical theory and solving methods of the mechanics of quasicrystals have developed rapidly in recent years, which is strongly supported by the experiments and applications. The theoretical development strongly enhances the understanding in-depth the physics including mechanics of the materials. The mathematical theory and computational methods provide a basis to the applications of quasicrystals as functional and structural materials in practice as well. More recently the quasicrystals in soft matter are observed, which challenge the study of based on the quasicrystals of binary and ternary alloys and greatly enlarge the scope of the materials and have aroused a great deal attention of researchers, an introduction about this new phase and its mathematical theory is also given in the review.展开更多
The microstructure of an as-cast Mg-Zn-Er alloy was investigated through scanning electron microscopy （SEM） and transmission electron microscopy （TEM） equipped with energy dispersive spectroscopy （EDS）. The resu...The microstructure of an as-cast Mg-Zn-Er alloy was investigated through scanning electron microscopy （SEM） and transmission electron microscopy （TEM） equipped with energy dispersive spectroscopy （EDS）. The results indicate that two different second phases, one with eutectoid-lamellar morphology and the other with granular shape, distribute in the α-Mg matrix. The coexistence of the face-centered icosahedral quasicrystalline phase （I-phase） and W-phase with the face-centered cubic structure is found in the as-cast alloy. The coexistence of I-phase and W-phase in the Mg-Zn-Er alloy is because the W-phase is the primary phase and the I-phase forms by peritectic reaction during solidification.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
The serrated phenomena of the quasicrystalline phase reinforced Mg-4%Li-6%Zn-1.2%Y alloy after the extrusion,solid solution treatment and aged treatment have been investigated at different temperatures.The result show...The serrated phenomena of the quasicrystalline phase reinforced Mg-4%Li-6%Zn-1.2%Y alloy after the extrusion,solid solution treatment and aged treatment have been investigated at different temperatures.The result shows that when the temperature is above 100℃,the serrated phenomenon becomes weak and all the serrated amplitudes are lower than 1 MPa.Among them,the serrated amplitude of samples in aged condition is the lowest and the value is only 0.1-0.2 MPa.The underneath mechanism for the lower plastic instability at higher temperature(≥100℃)can be ascribed to the weak pining effect of solute atoms on the movement of dislocation and release of the pile-up dislocations.展开更多
Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is in...Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is investigated systematically. The gov- erning equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the opera- tor method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form so- lutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.展开更多
Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For th...Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.展开更多
The axisymmetric elasticity theory of cubic quasicrystal was developed in Ref. [1]. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introd...The axisymmetric elasticity theory of cubic quasicrystal was developed in Ref. [1]. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function, based on which, the exact analytic solutions for the elastic field of an axisymmetric contact problem of cubic quasicrystalline materials are obtained for universal contact stress or contact displacement. The result shows that if the contact stress has order - 1/2 singularity on the edge of the contact domain, die contact displacement is a constant in the contact domain. Conversely, if the contact displacement is a constant, the contact stress must have order - 1/2 singularity on the edge of die contact domain.展开更多
To effectively reduce the field concentration around a hole or crack,an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional(1D)hexagonal piezoelectric ...To effectively reduce the field concentration around a hole or crack,an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)is investigated subject to remotely mechanical and electrical loadings.The surface effect and dielectric characteristics inside the hole are considered for actuality.By utilizing the technique of conformal mapping and the complex variable method,the phonon stresses,phason stresses,and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions.Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack.Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer,the aspect ratio of the hole,and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip.The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack,which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.展开更多
文摘The geometric theory of quasicrystal structure is an important subject in quasicrystal research. The authors deduce the quasicrystal plane geometric lattices from the stereograms of quasicrystal space geometric lattice , and put them together to form the geometric lattices of quasicrystal structures . The general characteristics of quasicrystal geometric lattices , the relation between structural models and geometric lattices , and the relation formula (k=0 , 2 , 4 , 6 , 8, 10,12) of the symmetric axis between quasicrystal and crystal are discussed based on the quasicrystal space geometric lattices. This is of significant in quasicrystal research .
基金support from the China Postdoc-toral Science Foundation(No.2023M730905)Hebei Province High-level Talent Funding Project(No.A20231001)Scientific Research Fund of Dezhou University(No.2022xjrc407).
文摘A glassy(G)phase was formed for Zr-rich Zr70-75(Al,Ni,Cu,Ag)25-30(atomic percent,at.%)melt-spun alloy ribbons.These glassy alloys exhibit the glass transition,followed by a supercooled liquid region and then three-stage crystallization.The glass transition temperature and the onset temperature for the first-stage crystallization(Tx1)decrease from 630 to 668 K,respectively for the 70Zr alloy to 619 and 652 K,respectively for the 75Zr alloy.The first-stage exothermic peak is due to the precipitation of an icosahedral quasicrystal(IQ)phase.The IQ particle size decreases from 10 nm to 6 nm with increasing Zr content from 70 at.%to 74 at.%.The[G+IQ]phases change to Zr2 Ni+Zr2(Cu,Ag)phases after the second exothermic peak and then Zr2 Ni+Zr2(Cu,Ag)+Zr5 Al3 phases after the third stage.It is noticed that the as-spun glassy alloy ribbons as well as the annealed[G+IQ]phase ribbons exhibit good bending plasticity.Furthermore,the 70Zr thicker ribbons also exhibit high tensile fracture strength of 1090-1187 MPa and plastic elongation of 0.17%-0.42%.The fracture mode is similar to that of ordinary bulk metallic glasses.The Vickers hardness(H v)is 480 for 70Zr alloy and decreases to 436 for 75Zr alloy.The precipitation of IQ phase causes a significant increase in H v to about 554.The formations of glassy alloys with high Zr contents of 70 at.%-75 at.%by melt spinning as well as the[G+IQ]phase alloys with good bending plasticity by annealing hold promise for the creation of a new type of engineering material,transcending mere academic novelty.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.52173231 and 51925105)the Natural Science Foundation of Hebei Province,China(Grant No.E2022203182)+1 种基金The Innovation Ability Promotion Project of Hebei supported by Hebei Key Laboratory for Optimizing Metal Product Technology and Performance(Grant No.22567609H)supported by the grants from Slovak National Agencies(Grant Nos.VEGA 2/0144/21,APVV19-0369,and APVV-20-0124)。
文摘Al_(65)Cu_(20)Fe_(15)bulk is synthesized with the high-pressure synthesis(HPS)method.Various analytical techniques,such as single crystal x-ray diffraction(SXRD),scanning electron microscopy equipped with energy-dispersive x-ray spectroscopy,and transmission electron microscopy,are employed to characterize the sintered bulk and confirmed its quasicrystalline structure.The electrical resistivity of the HPS quasicrystal specimen is measured from 2 K to 300 K,revealing a significantly elevated value in comparison to samples prepared via alternative methods.Nanoindentation testing demonstrates exceptional hardness and elastic modulus of our Al_(65)Cu_(20)Fe_(15)quasicrystal,consistent with existing results.The ratio of hardness to elastic modulus further highlight the potential superior wear resistance of the Al_(65)Cu_(20)Fe_(15)quasicrystal.Differential scanning calorimetry measurement conducted on the HPS Al_(65)Cu_(20)Fe_(15)quasicrystals reveal a high melting point of 877℃.
基金Supported by the National Natural Science Foundation of China (Nos. 11902293 and 12272353)。
文摘In this paper,the mechanical response of a one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)thin film is analyzed under electric and temperature loads.Based on the Euler-Bernoulli beam theory,a theoretical model is proposed,resulting in coupled governing integral equations that account for interfacial normal and shear stresses.To numerically solve these integral equations,an expansion method using orthogonal Chebyshev polynomials is employed.The results provide insights into the interfacial stresses,axial force,as well as axial and vertical deformations of the PQC film.Additionally,fracture criteria,including stress intensity factors,mode angles,and the J-integral,are evaluated.The solution is compared with the membrane theory,neglecting the normal stress and bending deformation.Finally,the effects of stiffness and aspect ratio on the PQC film are thoroughly discussed.This study serves as a valuable guide for controlling the mechanical response and conducting safety assessments of PQC film systems.
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.
基金Project supported by the National Natural Science Foundation of China(Nos.11902293 and 12272353)。
文摘In this paper,we investigate the interfacial behavior of a thin,penny-shaped,one-dimensional(1D)hexagonal functionally graded(FG)piezoelectric quasicrystal(PQC)film bonded on a temperature-dependent elastic substrate under thermal and electrical loads.The problem is modeled as axisymmetric based on the membrane theory,with the peeling stress and bending moment being disregarded.A potential theory method,combined with the Hankel transform technique,is utilized to derive the displacement field on the substrate surface.With perfect interfacial bonding assumption,an integral equation governing the phonon interfacial shear stress is formulated and numerically solved by the Chebyshev polynomials.Explicit expressions are derived for the interfacial shear stress,the internal stresses within the PQC film and the substrate,the axial strain,and the stress intensity factors(SIFs).Numerical simulations are conducted to investigate the effects of the film's aspect ratio,material inhomogeneity,material mismatch,and temperature-dependent material properties on its mechanical response.The results provide insights for the functional design and reliability assessment of FG PQC film/substrate systems.
基金Projects(5120414751274175)supported by the National Natural Science Foundation of China+3 种基金Projects(2011DFA505202014DFA50320)supported by the International Cooperation Program from the Ministry of Science and Technology of ChinaProject(20123088)supported by the Foundation for Graduate Students of Shanxi ProvinceChina
文摘The Mg-Zn-Y quasicrystal-reinforced AZ91 D magnesium matrix composites were prepared by squeeze casting process. The effects of applied pressure on microstructure and mechanical properties of the composites were investigated. The results show that squeeze casting process is an effective method to refine the grain. The composites are mainly composed of α-Mg, β-Mg17Al12 and Mg3Zn6Y icosahedral quasicrystal phase（I-phase）. With the increase of applied pressure, the contents of β-Mg17Al12 phase and Mg3Zn6 Y quasicrystal particles increase, further matrix grain refinement occurs and coarse dendritic α-Mg transforms into equiaxed grain structure. The composite exhibits the maximum ultimate tensile strength and elongation of 194.3 MPa and 9.2% respectively when the applied pressure is 100 MPa, and a lot of dimples appear on the tensile fractography. Strengthening mechanisms of quasicrystal-reinforced AZ91 D magnesium matrix composites are chiefly fine-grain strengthening and quasicrystal particles strengthening.
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.
文摘The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.
文摘As a new structure of solid matter quasicrystal brings profound new ideas to the traditional condensed matter physics, its elastic equations are more complicated than that of traditional crystal. A contact problem of decagonal two? dimensional quasicrystal material under the action of a rigid flat die is solved satisfactorily by introducing displacement function and using Fourier analysis and dual integral equations theory, and the analytical expressions of stress and displacement fields of the contact problem are achieved. The results show that if the contact displacement is a constant in the contact zone, the vertical contact stress has order -1/2 singularity on the edge of contact zone, which provides the important mechanics parameter for contact deformation of the quasicrystal.
基金Project (20112216120001) supported by the Doctoral Program of Tertiary Education of the Ministry of Education of ChinaProject(21215141) supported by the Natural Science Foundation of Jilin Province, China+3 种基金Project (20921002) supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of ChinaProjects (21073179, 61106050) supported by the National Natural Science Foundation of ChinaProject (BE2012047) supported by Scientific and Technological Supporting Program of Jiangsu Province of China and GS Yuasa Corporation of JapanProject (11KZ38) supported by and Scientific and Technological Pillar Project of Changchun, China
文摘The structures and electrochemical properties of the Ti1.4V0.6Ni ribbon before and after heat treatment are investigated systematically. The structure of the sample is characterized by X-ray powder diffraction analysis. Electrochemical properties including the discharge capacity, the cyclic stability and the high-rate discharge ability are tested. X-ray powder diffraction analysis shows that after heat treatment at 590 °C for 30 min, all samples mainly consist of the icosahedral quasicrystal phase (I-phase), Ti2Ni phase (FCC), V-based solid solution phase (BCC) and C14 Laves phase (hexagonal). Electrochemical measurements show that the maximum discharge capacity of the alloy electrode after heat treatment is 330.9 mA?h/g under the conditions that the discharge current density is 30 mA/g and the temperature is 30 °C. The result indicates that the cyclic stability and the high-rate discharge ability are all improved. In addition, the electrochemical kinetics of the alloy electrode is also studied by electrochemical impedance spectroscopy (EIS) and hydrogen diffusion coefficient (D).
文摘Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.
文摘The review is devoted to introduce the recent development of the study in mathematical theory and methods of mechanics of quasicrystals, respectively. The mechanics of quasicrystalline materials includes elasticity, plasticity, defects, dynamics, fracture etc. In the article some relevant measured data are collected for some important quasicrystal systems, which are necessary for understanding physics and applications of the materials. It is very interesting that the mathe-matical theory and solving methods of the mechanics of quasicrystals have developed rapidly in recent years, which is strongly supported by the experiments and applications. The theoretical development strongly enhances the understanding in-depth the physics including mechanics of the materials. The mathematical theory and computational methods provide a basis to the applications of quasicrystals as functional and structural materials in practice as well. More recently the quasicrystals in soft matter are observed, which challenge the study of based on the quasicrystals of binary and ternary alloys and greatly enlarge the scope of the materials and have aroused a great deal attention of researchers, an introduction about this new phase and its mathematical theory is also given in the review.
基金supported by the National Major Fundamental Research Program of China (No. 2007CB613706)
文摘The microstructure of an as-cast Mg-Zn-Er alloy was investigated through scanning electron microscopy （SEM） and transmission electron microscopy （TEM） equipped with energy dispersive spectroscopy （EDS）. The results indicate that two different second phases, one with eutectoid-lamellar morphology and the other with granular shape, distribute in the α-Mg matrix. The coexistence of the face-centered icosahedral quasicrystalline phase （I-phase） and W-phase with the face-centered cubic structure is found in the as-cast alloy. The coexistence of I-phase and W-phase in the Mg-Zn-Er alloy is because the W-phase is the primary phase and the I-phase forms by peritectic reaction during solidification.
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This work was supported by the National Natural Science Foundation of China projects under Grant Nos.51171192,51271183 and 51301172the National Basic Research Program of China(973 Program)project under Grant No.2013CB632205 and the Innovation Fund of Institute of Metal Research(IMR),Chinese Academy of Sciences.
文摘The serrated phenomena of the quasicrystalline phase reinforced Mg-4%Li-6%Zn-1.2%Y alloy after the extrusion,solid solution treatment and aged treatment have been investigated at different temperatures.The result shows that when the temperature is above 100℃,the serrated phenomenon becomes weak and all the serrated amplitudes are lower than 1 MPa.Among them,the serrated amplitude of samples in aged condition is the lowest and the value is only 0.1-0.2 MPa.The underneath mechanism for the lower plastic instability at higher temperature(≥100℃)can be ascribed to the weak pining effect of solute atoms on the movement of dislocation and release of the pile-up dislocations.
基金Project supported by the National Nature Science Foundation of China(Nos.11262012,11262017,11462020,and 10761005)the Scientific Research Key Program of Inner Mongolia University of Technology(No.ZD201219)
文摘Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is investigated systematically. The gov- erning equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the opera- tor method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form so- lutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.
基金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Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.
基金the National Natural Science Foundation of China(No.19972011)
文摘The axisymmetric elasticity theory of cubic quasicrystal was developed in Ref. [1]. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function, based on which, the exact analytic solutions for the elastic field of an axisymmetric contact problem of cubic quasicrystalline materials are obtained for universal contact stress or contact displacement. The result shows that if the contact stress has order - 1/2 singularity on the edge of the contact domain, die contact displacement is a constant in the contact domain. Conversely, if the contact displacement is a constant, the contact stress must have order - 1/2 singularity on the edge of die contact domain.
基金supported by the National Natural Science Foundation of China(Nos.12072166,11862021)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(No.NJYT-19-A06)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(No.2020MS01006)。
文摘To effectively reduce the field concentration around a hole or crack,an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)is investigated subject to remotely mechanical and electrical loadings.The surface effect and dielectric characteristics inside the hole are considered for actuality.By utilizing the technique of conformal mapping and the complex variable method,the phonon stresses,phason stresses,and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions.Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack.Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer,the aspect ratio of the hole,and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip.The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack,which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.
