ON CORE STRUCTURE PROPERTIES AND PEIERLS STRESS OF DISSOCIATED SUPERDISLOCATIONS IN ALUMINIDES: NiAl AND FeAl

<正>The study of dislocation properties in B2 structure intermetallics NiAl and FeAl is crucial to understand their mechanical behaviors.In this paper,the core structure and Peierls stress of collinear dissociated〈111〉{110} edge superdislocations in NiAl and FeAl are investigated with the modified P-N dislocation equation.The generalized stacking fault energy curve along〈111〉direction in {110} slip plane contains two modification factors that can assure the antiphase energy and the unstable stacking fault energy to change independently.The results show that the core width of superpartials decreases with the increasing unstable stacking fault energy,and increases with the increasing antiphase boundary energy.The calculated Peierls stress of〈111〉{110} edge superdislocations in NiAl and FeAl are 475 MPa and 3042 MPa,respectively.The values of Peierls stress in NiAl is in accordance in magnitude with the experimental and the molecular statics simulations results.     

EXTENDED CORE STRUCTURE OF DISSOCIATED EDGE DISLOCATIONS IN FCC CRYSTALS WITH CONSIDERATION OF DISCRETENESS

The extended core structure of the dissociated edge dislocation in Al, Au, Ag, Cu and Ni is determined within lattice theory of dislocation. The 2D dislocation equation governing the displacements is coupled by the restoring forces that are determined by the parameterization of the generalized stacking fault energies. The Ritz variational method is presented to solve the dislocation equation and the trial solution is constituted by two arctan-type functions with two undetermined parameters. The core widths of partial dislocations are wider than that obtained in generalized Peierls-Nabarro model due to the consideration of discreteness of crystal.     

THERMODYNAMIC VARIATIONAL APPROACH FOR CLIMB OF AN EDGE DISLOCATION

A general thermodynamic variational approach is applied to study the force on an edge dislocation, which drives the dislocation to climb. Our attention is focused on the physical mechanism responsible for dislocation climb. A dislocation in a material element climbs as a result of vacancies diffusing into or out from the dislocation core, with the dislocation acting as a source or a sink for vacancy diffusion in the material element. The basic governing equations for dislocation climb and the climb forces on the dislocation are obtained naturally as a result of the present thermodynamic variational approach.     

Interaction between a screw dislocation and a circular nano-inhomogeneity with a bimaterial interface

The problem of a screw dislocation interacting with a circular nano-inhomogeneity near a bimaterial interface is investigated. The stress boundary condition at the interface between the inhomogeneity and the matrix is modified by incorporating surface/interface stress. The analytical solutions to the problem in explicit series are obtained by an efficient complex variable method associated with the conformal mapping function. The image force exerted on the screw dislocation is also derived using the generalized Peach–Koehler formula. The results indicate that the elastic interference of the screw dislocation and the nano-inhomogeneity is strongly affected by a combination of material elastic dissimilarity, the radius of the inclusion, the distance from the center of inclusion to the bimaterial interface, and the surface/interface stress between the inclusion and the matrix. Additionally, it is found that when the inclusion and Material 3 are both harder than the matrix( μ_1 μ_2 and μ_3 μ_2), a new stable equilibrium position for the screw dislocation in the matrix appears near the bimaterial interface; when the inclusion and Material 3 are both softer than the matrix( μ_1 μ_2 and μ_3 μ_2), a new unstable equilibrium position exists close to the bimaterial interface.     

A SCREW DISLOCATION IN A THREE-PHASE COMPOSITE CYLINDER MODEL WITH INTERFACIAL RIGID LINES

The problem of the elastic interaction between a screw dislocation and a three-phase circular inclusion with interracial rigid lines （anti-cracks） is investigated. An efficient and concise method for the complex multiply connected region is developed, with which explicit series form solutions of the complex potentials in the matrix, and the interphase layer and inclusion regions are derived. Based on the complex potentials, the image force on the screw dislocation is then calculated by using the Peach-Koehler formula. The equilibrium position of the dislocation is discussed in detail for various rigid line geometries, interphase layer thicknesses and material property combinations. The main results show that the interracial rigid lines exert a significant perturbation effect on the motion of the screw dislocation near the circular inclusion surrounded by an interphase layer.     

Electroelastic interaction between piezoelectric screw dislocation and circularly layered inclusion with imperfect interfaces

The interaction between a piezoelectric screw dislocation and an interphase layer in piezoelectric solids is theoretically investigated.Here,the dislocation located at arbitrary points inside either the matrix or the inclusion and the interfaces of the interphase layer are imperfect.By the complex variable method,the explicit solutions to the complex potentials are given,and the electroelastic fields can be derived from them.The image force acting on the dislocation can be obtained by the generalized PeachKoehler formula.The motion of the piezoelectric screw dislocation and its equilibrium positions are discussed for variable parameters.The important results show that,if the inner interface of the interphase layer is imperfect and the magnitude of degree of the interface imperfection reaches the certain value,two equilibrium positions of the piezoelectric screw dislocation in the matrix near the interface are found for the certain material combination which has never been observed in the previous studies(without considering the interface imperfection).     

MODE III 2-D FRACTURE ANALYSIS BY THE SCALED BOUNDARY FINITE ELEMENT METHOD

The scaled boundary finite element method （SBFEM） is a novel semi-analytical technique that combines the advantages of the finite element method and the boundary element method with unique properties of its own. This method has proven very efficient and accurate for determining the stress intensity factors （SIFs） for mode I and mode II two-dimensional crack problems. One main reason is that the SBFEM has a unique capacity of analytically representing the stress singularities at the crack tip. In this paper the SBFEM is developed for mode III （out of plane deformation） two-dimensional fracture anMysis. In addition, cubic B-spline functions are employed in this paper for constructing the shape functions in the circumferential direction so that higher continuity between elements is obtained. Numerical examples are presented at the end to demonstrate the simplicity and accuracy of the present approach for mode Ⅲ two-dimensional fracture analysis.     

Atomic resolution in noncontact AFM by probing cantilever frequency shifts

Rutile TiO2 （001） quantum dots （or nano-marks） in different shapes were used to imitate uncleaved material surfaces or materials with rough surfaces. By numerical integration of the equation of motion of cantilever for silicon tip scanning along the [110] direction over the rutile TiO2 （001） quantum dots in ultra high vacuum （UHV）, scanning routes were explored to achieve atomic resolution from frequency shift image. The tip-surface interaction forces were calculated from Lennard-Jones （12-6） potential by the Hamaker summation method. The calculated results showed that atomic resolution could be achieved by frequency shift image for TiO2 （001） surfaces of rhombohedral quantum dot scanning in a vertical route, and spherical cap quantum dot scanning in a superposition route.2007 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V.     

THE PERIODIC CRACK PROBLEM IN BONDED PIEZOELECTRIC MATERIALS

The problem of a periodic array of parallel cracks in a homogeneous piezoelectric strip bonded to a functionally graded piezoelectric material is investigated for inhomogeneous continuum.It is assumed that the material inhomogeneity is represented as the spatial varia- tion of the shear modulus in the form of an exponential function along the direction of cracks. The mixed boundary value problem is reduced to a singular integral equation by applying the Fourier transform,and the singular integral equation is solved numerically by using the Gauss- Chebyshev integration technique.Numerical results are obtained to illustrate the variations of the stress intensity factors as a function of the crack periodicity for different values of the material inhomogeneity.     

Interaction of a screw dislocation in the interphase layer with the inclusion and matrix

The interaction of a screw dislocation in the interphase layer with the circular inhomogeneity and matrix was dealt with . An efficient method for multiply connected regions was developed by combining the sectionally subholomorphic function theory, Schwatz symmetric principle and Cauchy integral technique. The Hilbert problem of the complex potentials for three material regions was reduced to a functional equation in the complex potential of the interphase layer, resulting in an explicit series solution . By using the present solution the interaction energy and force acting dislocation were evaluated and discussed.     

Quantitative study on interactions between interfacial misfit dislocation networks and matrix dislocations in Ni-based single crystal superalloys

The interactions between the moving dislocation within matrix channel and the interfacial misfit dislocation networks on the two-phase interfaces in Ni-based single crystal superalloys are studied carefully via atomic modeling, with special focus on the factors influencing the critical bowing stress of moving dislocations in the matrix channel. The results show that the moving matrix dislocation type and its position with respect to the interfacial misfit dislocation segments have considerable influences on the interactions. If the moving matrix dislocation is pure screw, it reacts with the interfacial misfit dislocation segments toward dislocation linear energy reduction, which decreases the critical bowing stress of screw dislocation due to dislocation linear energy release during the dislocation reactions. If the moving matrix dislocation is of 60°-mixed type, it is obstructed by the interaction between the mixed matrix dislocations and the misfit interfacial dislocation segments. As a result, the critical bowing stress increases significantly because extra interactive energy needs to be overcome. These two different effects on the critical bowing stress become increasingly significant when the moving matrix dislocation is very close to the interfacial misfit dislocation segments. In addition, the matrix channel width also has a significant influence on the critical bowing stress, i.e. the narrower the matrix channel is, the higher the critical bowing stress is. The classical Orowan formula is modified to predict these effects on the critical bowing stress of moving matrix dislocation, which is in good agreement with the computational results.     

Torsion of elastic shaft of revolution embedded in an elastic half space

The problem of torsion of elastic shaft of revolution embedded in an elastic half space is studied by the Line-Loaded Integral Equation Method (LLIEM). The problem is reduced to a pair of one-dimensional Fredholm integral equations of the first kind due to the distributions of the fictitious loads "Point Ring Couple (PRC) "and "Point Ring Couple in Half Space (PRCHS) "on the axis of symmetry in the interior and external ranges of the shaft occutied respectively. The direct discrete solution of this integral equations may be unstable, i.e. an ill-posed case occurs. In this paper, such an ill-posed Fredholm integral equation of first kind is replaced by a Fredholm integral equation of the second kind with small parameter, which provides a stable solution. This method is simpler and easier to carry out on a computer than the Tikhonov’s regularization method for ill-posed problems. Numerical examples for conical, cylindrical, conical-cylindrical, and parabolic shafts are given.     

EFFECT OF SURFACE ENERGY ON DISLOCATION-INDUCED FIELD IN HALF-SPACE WITH APPLICATION TO THIN FILM-SUBSTRATE SYSTEMS

In this work the elastic field of an edge dislocation in a half-space with the effect of surface energy has been obtained. The elastic field is then used to study the image force on the dislocation, the critical thickness for dislocation generation in epitaxial thin films with strain mismatch and the yielding strength of thin films on substrates. The results show that the image forces on the dislocation deviate from the conventional solutions when the distance of the dislocation from the free surface is smaller than several times of the characteristic length. Also due to the effect of surface energy, the critical thickness for dislocation generation is smaller than that predicted by the conventional elastic solutions and the extent of the deviation depends on the magnitude of mismatch strain. In contrast, the effect of surface energy on the yielding strength for many practical thin films can be neglected except for some soft ones where the characteristic length is comparable to the thickness.     

FIXED STREAM-TUBE METHOD FOR SOLVING TWO-PHASE PLANE FLOW PROBLEMS AND ITS THEORETICAL ANALYSIS

The fixed stream-tube method widely adopted in engineering field for giving anapproximate solution to the two-dimensional problems of two-phase flow through porousmedia is summarized and an improvement has been made in this paper.Its core part,i.e.,thefluid displacement within a one-dimensional stream tube with variable cross-sectional areaunder a given pressure difference across the tube is thoroughly studied.The existence anduniqueness of solution are proved the exact solution,numerical solution and itsconvergence.stability analyses are given in this paper.     

Second mode unstable disturbance measurement of hypersonic boundary layer on cone by wavelet transform

Experimental investigation of hypersonic boundary layer instability on a cone is performed at Mach number 6 in a hypersonic wind tunnel.Time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface in the streamwise direction to investigate the development of the unstable disturbance.Wavelet transform is employed as a mathematical tool to obtain the multi-scale characteristics of fluctuating surfacethermal-flux both in the temporal and spectrum space.The conditional sampling algorithm using wavelet coefficient as an index is put forward to extract the unstable disturbanceThe generic waveform for the second mode unstable disturbance is obtained by a phase-averaging technique.The development of the unstable disturbance in the streamwise direction is assessed both in the temporal and spectrum space.Our study shows that the local unstable disturbance detection method based on wavelet transformation offers an alternative powerful tool in studying the hypersonic unstable mode of laminar-turbulent transition.It is demonstrated that,at hypersonic speeds,the dominant flow instability is the second mode,which governs the course of laminar-turbulent transition of sharp cone boundary layer.     

MOVING SCREW DISLOCATION IN CUBIC QUASICRYSTAL

The elasticity theory of the dislocation of cubic quasicrystals is developed. The governing equations of anti-plane elasticity dynamics problem of the quasicrystals were reduced to a solution of wave equations by introducing displacement functions, and the analytical expressions of displacements, stresses and energies induced by a moving screw dislocation in the cubic quasicrystalline and the velocity limit of the dislocation were obtained. These provide important information for studying the plastic deformation of the new solid material.     

A screw dislocation near one open inhomogeneity and another closed inhomogeneity both permitting constant interior stresses

We prove that the interior stresses within both a non-parabolic open inhomogeneity and another interacting non-elliptical closed inhomogeneity can still remain constant when the matrix is simultaneously under the action of a screw dislocation and uniform remote anti-plane stresses.The constancy of interior stresses is realized through the construction of a conformal mapping function for the doubly connected domain occupied by the surrounding matrix.The mapping function is endowed with the information describing the screw dislocation via the incorporation of two specifically defined logarithmic terms.The constant interior stress fields are observed to be independent of the specific open and closed shapes of the two inhomogeneities and the existence of the screw dislocation.In contrast,the existence of the neighboring screw dislocation significantly affects the open and closed shapes of the two inhomogeneities.     

Template-free synthesis and characterization of K-phillipsite for use in potassium extraction from seawater

Kbphillipsite was prepared using a hydrothermal method. Soluble glass and sodium aluminate were used as raw materials in the absence of an organic template. Investigations regarding the K＋ ions were con- ducted at room temperature to determine the ion-exchange capacity in the seawater sample and the selectivity coefficient of the mixed K＋-Na~ solution. The sample was characterized by X-ray diffraction （XRD）, scanning electron microscopy （SEM）, and energy dispersion spectroscopy （EDS）. The K＋ ion- exchange capacity is 51 mg/g in seawater and the selectivity coefficient is 75.1 in the mixed K＋-Na＋ solution. The sample has a selectivity preference for K＋, and therefore can be used to selectively extract potassium from seawater. The sample composed of Si, Al, K, Na, and O exhibits a cross-like shape and is a typical K-phillipsite structure.     

Dislocation stability in three-phase nanocomposites with imperfect interface

Interface imperfection can significantly affect the mechanical properties and failure mechanisms as well as the strength and toughness of nanocomposites. The elastic behavior of a screw dislocation in nanoscale coating with imperfect interface is studied in the three-phase composite cylinder model. The interface between inner nanoin- homogeneity and intermediate coating is assumed as perfectly bonded. The bonding between intermediate coating and outer matrix is considered to be imperfect with the assumption that interface imperfection is uniform, and a linear spring model is adopted to describe the weakness of imperfect interface. The explicit expression for image force acting on dislocation is obtained by means of a complex variable method. The analytic results indicate that inner interface effect and outer interface imperfection, simultaneously taken into account, would influence greatly image force, equilibrium position and stability of dislocation, and various critical parameters that would change dislocation stability. The weaker interface is a very strong trap for glide dislocation and, thus, a more effective barrier for slip transmission.     

INTERACTION OF A DISLOCATION DIPOLE WITH A MODE III INTERFACE CRACK

Interaction between a screw dislocation dipole and a mode III interface crack is investigated. By using the complex variable method, the closed form solutions for complex potentials are obtained when a screw dislocation dipole lies inside a medium. The stress fields and the stress intensity factors at the tip of the interface crack produced by the screw dislocation dipole are given. The influence of the orientation, the dipole arm and the location of the screw dislocation dipole as well as the material mismatch on the stress intensity factors is discussed. The image force and the image torque acting on the screw dislocation dipole center are also calculated. The mechanical equilibrium position of the screw dislocation dipole is examined for various material property combinations and crack geometries. The results indicate that the shielding or anti-shielding effect on the stress intensity factor increases abruptly when the dislocation dipole approaches the tip of the crack. Additionally, the disturbation of the interface crack on the motion of the dislocation dipole is also significant.