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
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
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
This paper employes variable function method and the technique of conformal mappingto discuss the anti-plane problem of a circular hole with three unequal cracksin a one-dimensional （1D） hexagonal piezoelectric quas...This paper employes variable function method and the technique of conformal mappingto discuss the anti-plane problem of a circular hole with three unequal cracksin a one-dimensional （1D） hexagonal piezoelectric quasicrystal. Based on the piezoelectricityfundamental equations of quasicrystal materials and the symmetry of1D hexagonal quasicrystal and its linear piezoelectricity effect, 1D hexagonal quasicrystalcontrol equations of anti-plane problem are derived. Applying Cauchyintegral formula, the analytical expressions for the crack tip filed intensity factorsare presented with the assumption that the crack are electrical impermeable andelectrical permeable. With the variation of the hole-size and the crack length, someof the new model of crack are obtained. In the absence of the electric load, theresults match with the classical ones. The numerical results indicate the effects ofgeometric parameters on the field intensity factors. It is verified that the horizontalcrack length and the circle radius can easily promote crack growth. Researchon such issues will provide reliable theoretical value for the engineering materialspreparation and application.展开更多
The dynamic response of an icosahedral Al-Pd Mn quasicrystal with a Griffith crack to impact loading is investigated in this paper. The elastohydrodynamic model for the wave propagation and diffusion together with the...The dynamic response of an icosahedral Al-Pd Mn quasicrystal with a Griffith crack to impact loading is investigated in this paper. The elastohydrodynamic model for the wave propagation and diffusion together with their interaction is adopted. Numerical results of stress, displacement and dynamic stress intensity factors are obtained by using the finite difference method. The effects of wave propagation, diffusion and phonon-phason coupling on the quasicrystal in the dynamic process are discussed in detail, where the phason dynamics is explored particularly.展开更多
By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions o...By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.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
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
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
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 the plane elasticity theory of icosahedral quasicrystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components o...The complex variable method for the plane elasticity theory of icosahedral quasicrystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.展开更多
Diffusion controlled phase transformations and tribological properties and hardness of Al 65 Cu 20 Cr 15 quasicrystal particles(QC p)/Al matrix composites have been studied. The mixtures of the quasicrystal particles ...Diffusion controlled phase transformations and tribological properties and hardness of Al 65 Cu 20 Cr 15 quasicrystal particles(QC p)/Al matrix composites have been studied. The mixtures of the quasicrystal particles with volume fractions of 15%, 20%, 25% , 30% and pure Al powder were hot pressed at 600, 650, 700 ℃. During the diffusion controlled phase transformation induced by hot pressing, a simple cubic icosahedric quasicrystal (SIQC) phase transforms into stable Θ phase with the microstructure of monoclinic of Al 13 Cr 2 through a transitional faced cubic icosahedric quasicrystal (FIQC), a decagonal quasicrystal (DQC) and an approximant of decagonal quasicrystal (DA) phases. And G. P. zones and Al Cu precipitates, θ′ Al 2Cu and θ Al 2Cu, are separated out from the Al matrix respectively after hot pressing. The QC p/Al composites have double strengthening effect after hot pressing. One is the strengthening of the particles that reinforce the matrix Al; the other is the dispersion strengthening of the precipitates in the Al matrix. The hardness of the composites increases with increasing volume fraction of quasicrystal particles. The maximum hardness reaches 1 200 MPa, being 4 times that of Al. The frictional coefficient and the wear rate of the QC p/Al are lower than those of Al. In comparison with SiC p/Al matrix composites, QC p/Al composites have higher hardness and lower frictional coefficient.展开更多
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 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.
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.
文摘This paper employes variable function method and the technique of conformal mappingto discuss the anti-plane problem of a circular hole with three unequal cracksin a one-dimensional （1D） hexagonal piezoelectric quasicrystal. Based on the piezoelectricityfundamental equations of quasicrystal materials and the symmetry of1D hexagonal quasicrystal and its linear piezoelectricity effect, 1D hexagonal quasicrystalcontrol equations of anti-plane problem are derived. Applying Cauchyintegral formula, the analytical expressions for the crack tip filed intensity factorsare presented with the assumption that the crack are electrical impermeable andelectrical permeable. With the variation of the hole-size and the crack length, someof the new model of crack are obtained. In the absence of the electric load, theresults match with the classical ones. The numerical results indicate the effects ofgeometric parameters on the field intensity factors. It is verified that the horizontalcrack length and the circle radius can easily promote crack growth. Researchon such issues will provide reliable theoretical value for the engineering materialspreparation and application.
基金supported by the National Natural Science Foundation of China (Grant Nos 10672022 and 10372016)
文摘The dynamic response of an icosahedral Al-Pd Mn quasicrystal with a Griffith crack to impact loading is investigated in this paper. The elastohydrodynamic model for the wave propagation and diffusion together with their interaction is adopted. Numerical results of stress, displacement and dynamic stress intensity factors are obtained by using the finite difference method. The effects of wave propagation, diffusion and phonon-phason coupling on the quasicrystal in the dynamic process are discussed in detail, where the phason dynamics is explored particularly.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11462020,11262017,and 11262012)the Key Project of Inner Mongolia Normal University,China(Grant No.2014ZD03)
文摘By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.
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 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 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the National Natural Science Foundation of China (Grant Nos. 10372016 and 10761005)the Natural Science Foundation of Inner Mongolia of China (Grant No. 200607010104)the Natural Science Foundation of Inner Mongolia Normal University (Grant No. QN07034)
文摘The complex variable method for the plane elasticity theory of icosahedral quasicrystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.
文摘Diffusion controlled phase transformations and tribological properties and hardness of Al 65 Cu 20 Cr 15 quasicrystal particles(QC p)/Al matrix composites have been studied. The mixtures of the quasicrystal particles with volume fractions of 15%, 20%, 25% , 30% and pure Al powder were hot pressed at 600, 650, 700 ℃. During the diffusion controlled phase transformation induced by hot pressing, a simple cubic icosahedric quasicrystal (SIQC) phase transforms into stable Θ phase with the microstructure of monoclinic of Al 13 Cr 2 through a transitional faced cubic icosahedric quasicrystal (FIQC), a decagonal quasicrystal (DQC) and an approximant of decagonal quasicrystal (DA) phases. And G. P. zones and Al Cu precipitates, θ′ Al 2Cu and θ Al 2Cu, are separated out from the Al matrix respectively after hot pressing. The QC p/Al composites have double strengthening effect after hot pressing. One is the strengthening of the particles that reinforce the matrix Al; the other is the dispersion strengthening of the precipitates in the Al matrix. The hardness of the composites increases with increasing volume fraction of quasicrystal particles. The maximum hardness reaches 1 200 MPa, being 4 times that of Al. The frictional coefficient and the wear rate of the QC p/Al are lower than those of Al. In comparison with SiC p/Al matrix composites, QC p/Al composites have higher hardness and lower frictional coefficient.
