Strain anisotropy models for refined diffraction line profile analysis in cubic metals

The present work examined the anisotropy magnitudes obtained from different elastic models of cubic metals(Cu,5383 Al alloy,FCC austenite steel and BCC steel)to explore the origin of strain anisotropy.The results showed that stable intersections were observed from the modeled and experimental plots of the reciprocal elastic modulus(1/Ehkl)and orientation parameter(Γ).The effectiveness of quasi elasto-plastic model based method in correcting strain anisotropy was further verified in cold-worked specimens.For the important input parameters in dislocation model based diffraction line profile analysis methods,the average diffraction contrast factors(■)of dislocations were observed to depend on elastic constants.Interesting intersections were found from linear dependence of■onΓ.The conventional input■values indicated distinct dependencies on given elastic constants in diffraction line profile analysis.Accordingly,a refined approach was proposed by adopting the optimized intersections as input values,by which more reliable results could be obtained in practical applications.

Acoustic focusing effect of composite metamaterial column in air

The acoustic focusing effect of metamaterial has a wide range of applications in medicine,acoustic imaging,signal detection,etc.This paper presents an acoustic metamaterial applied to the acoustic focusing effect.The formation of acousticmetamaterial is designed into a cylindrical structure with three layers of ludox,cork and fluid rubber,which can produce a focusingphenomenon when acoustic waves propagate in air.For these strange phenomena,a scientific description is given theorietically.It can also be concluded that when the frequency of the incident acoustic wave increases?the number of peripheral bandsoutside the focusing poles will increase periodically.Besides,there are numerous groups of multipolar focusing phenomena inhigh frequency.The design of this acoustic metamaterial is successful through theorietical and experimental verification,therefore,it can be applied to acoustic communication and test.

Visualization of pullout behaviour of geogrid in sand with emphasis on size effect of protrusive junctions

Geogrid has been extensively used in geotechnical engineering practice due to its effectiveness and economy. Deep insight into the interaction between the backfill soil and the geogrid is of great importance for proper design and construction of geogrid reinforced earth structures. Based on the calibrated model of sand and geogrid, a series of numerical pullout tests are conducted using PFC^(3D) under special considerations of particle angularity and aperture geometry of the geogrid. In this work, interface characteristics regarding the displacement and contact force developed among particles and the deformation and force distribution along the geogrid are all visualized with PFC^(3D) simulations so that new understanding on how geogrid-soil interaction develops under pullout loads can be obtained. Meanwhile, a new variable named fabric anisotropy coefficient is introduced to evaluate the inherent relationship between macroscopic strength and microscopic fabric anisotropy. A correlation analysis is adopted to compare the accuracy between the newly-proposed coefficient and the most commonly used one. Furthermore, additional pullout tests on geogrid with four different joint protrusion heights have been conducted to investigate what extent and how vertical reinforcement elements may result in reinforcement effects from perspectives of bearing resistance contribution, energy dissipation, as well as volumetric response. Numerical results show that both the magnitude and the directional variation of normal contact forces govern the development of macroscopic strength and the reinforcing effects of joint protrusion height can be attributed to the accelerated energy dissipation across the particle assembly and the intensive mobilization of the geogrid.

Numerical Simulation of the Whole Three-Dimensional Flow in a Stirred Tank with Anisotropic Algebraic Stress Model

In accordance to the anisotropic feature of turbulent flow, ananisotropic algebraic stress model is adopted to predict theturbulent flow field and turbulent characteristics generated by aRushton disc turbine with the improved inner-outer iterativeprocedure. The predicted turbulent flow is compared with experimentaldata and the simulation by the standard k-ε turbulence model. Theanisotropic algebraic stress model is found to give better predictionthan the standard k-ε turbulence model. The predicted turbulent flowfield is in accordance to experimental data and the trend of theturbulence intensity can be effectively reflected in the simulation.

Active earth pressure acting on retaining wall considering anisotropic seepage effect

This paper presents a general solution for active earth pressure acting on a vertical retaining wall with a drainage system along the soil-structure interface. The backfill has a horizontal surface and is composed of cohesionless and fully saturated sand with anisotropic permeability along the vertical and horizontal directions. The extremely unfavourable seepage flow on the back of the retaining wall due to heavy rainfall or other causes will dramatically increase the active earth pressure acting on the retaining walls, increasing the probability of instability. In this paper, an analytical solution to the Laplace differential governing equation is presented for seepage problems considering anisotropic permeability based on Fourier series expansion method. A good correlation is observed between this and the seepage forces along a planar surface generated via finite element analysis. The active earth pressure is calculated using Coulomb's earth pressure theory based on the calculated pore water pressures. The obtained solutions can be degenerated into Coulomb's formula when no seepage exists in the backfill. A parametric study on the influence of the degree of anisotropy in seepage flow on the distribution of active earth pressure behind the wall is conducted by varying ratios of permeability coefficients in the vertical and horizontal directions,showing that anisotropic seepage flow has a prominent impact on active earth pressure distribution. Other factors such as effective internal friction angle of soils and soil/wall friction conditions are also considered.

Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.

Impact of anisotropic growth on kinetics of solid-state phase transformation

Based on the statistical analysis of blocking effect arising from anisotropic growth,the anisotropic effect on the kinetics of solid-state transformation was investigated.The result shows that the blocking effect leads to the retardation of transformation and then a regular behavior of varying Avrami exponent.Following previous analytical model,the formulations of Avrami exponent and effective activation energy accounting for blocking effect were obtained.The anisotropic effect on the transformation depends on two factors,non-blocking factor γ and blocking scale k,which directly acts on the dimensionality of growth.The effective activation energy is not affected by the anisotropic effect.The evolution of anisotropic effect with the fraction transformed is taken into account,showing that the anisotropic effect is more severe at the middle stage of transformation.

Softening response under undrained compression following anisotropic consolidation

Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical state theory of soil mechanics.Based on experimental data on different types of clay,a simple double-surface model was developed considering explicitly the location of critical state by incorporating the density state into constitutive equations.The model was then used to simulate undrained triaxial compression tests performed on isotropically and anisotropically consolidated samples with different stress ratios.The predictions were compared with experimental results.All simulations demonstrate that the proposed approach is capable of describing the drained and undrained compression behaviors following isotropic and anisotropic consolidations.

Equivalent strain hardening exponent of anisotropic materials based on spherical indentation response

Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element (FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.

Quantum Nucleation of Antiferromagnetic Bubbles with Tetragonal and Hexagonal Symmetries

We study the quantum nucleation in a nanometer-scale antiferromagnet placed in a magnetic field at an arbitrary angle. We consider the magnetocrystalline anisotropy with tetragonal symmetry and that with hexagonal symmetry, respectively. Different structures of the tunneling barriers can be generated by the magnitude and the orientation of the magnetic field. We use the instanton method in the spin-coherent-state path-integral representation to calculate the dependence of the rate of quantum nucleation and the crossover temperature on the orientation and strength of the field for bulk solids and two-dimensional films of antiferromagnets, respectively. We find that the rate of quantum nucleation and the crossover temperature from thermal-to-quantum transitions depend on the orientation and strength of the external magnetic field distinctly, which can be tested by use of existing experimental techniques.

Dynamic strength characteristics and failure criteria of anisotropically consolidated silt under principal stress rotation

In order to identify the critical properties and failure criteria of in-situ silt under vehicle or wave loading, anisotropically consolidated silt under undrained cyclic principal stress rotation was studied with hollow cylinder dynamic tests. The results show that for the slightly anisotropically consolidated samples with consolidation ratios no larger than 1.5, the structure collapses and the deviator strain and pore pressure increase sharply to fail after collapse. For the highly anisotropically consolidated samples with consolidation ratios larger than 1.5, the strain increases steadily to high values, which shows characteristics of ductile failure. 4% is suggested to be the threshold value of deviator stain to determine the occurrence of collapse. The normalized relationship between pore pressure and deviator strain can be correlated by a power fimction for all the anisotropically consolidated samples. Based on it, for the highly anisotropically consolidated samples, the appearance of inflection point on the power function curve is suggested to sign the failure. It can be predicted through the convex pore pressure at this point, whose ratio to the ultimate pore pressure is around linear with the consolidation ratio in spite of the dynamic shear stress level. And the corresponding deviator strain is between 3% and 6%. The strain failure criterion can also be adopted, but the limited value of stain should be determined according to engineering practice. As for the slightly anisotropically consolidated samples, the turning points appear after collapse. So, the failure is suggested to be defined with the occurrence of collapse and the collapse pore pressure can be predicted with the ultimate pore pressure and consolidation ratio.

Effect Analysis of High Strain Rate and Anisotropy on Tension⁃Compression Asymmetry of Aluminum Alloy 7050

Using the devices of split Hopkinson tension bar(SHTB)and split Hopkinson pressure bar(SHPB),the dynamic tension and compression experiments in three typical forming directions(rolling direction(RD),transverse direction(TD)and normal direction(ND))were carried out at strain rates of 1000,2000 and 4000 s-1,respectively.From the microscopic point of view,the effect of strain rate and anisotropy on tension compression asymmetry of aviation aluminum alloy 7050 was studied by scanning electron microscope(SEM),metallographic microscope and electron backscatter diffraction(EBSD).The results showed that there was obvious asymmetry between tension and compression,especially that the yield strength of the material in tension was higher than that in compression.The asymmetry in the elastic stage of tension-compression was weaker and the asymmetry in the strengthening stage was stronger with the increase of strain rate.At the same strain rate,the changing trend of the flow stress was distinct under different orientations of tension and compression,which was related to the stress direction of the grains.According to EBSD grain orientation analysis and raw material texture pole figure analysis,it was found that the larger the difference in the degree of grain refinement during tension and compression,the larger the macro-flow stress difference.

Influence of Ground State Spin of Projectile-Target on Fission Anisotropies

Fission fragment anisotropies have been investigated for various systems produced in heavy-ion reactions at near and sub-barrier energies. In particular, special attention has been paid to the entrance channel dependence of fragment angular anisotropies. The results of our analysis of the fragment angular anisotropies induced by boron, carbon, and oxygen ions on Thorium and Neptunium targets as well as Fluorine ions on Neptunium target indicate strong dependence of fragment anisotropies on the channel spin, in consistence with the predication of the pre-equilibrium model.

Adaptive Finite Element Modeling of Marine Controlled-Source Electromagnetic Fields in Two-Dimensional General Anisotropic Media

In this paper, we extend the scope of numerical simulations of marine controlled-source electromagnetic (CSEM) fields in a particular case of anisotropy (dipping anisotropy) to the general case of anisotropy by using an adaptive finite element approach. In comparison to a dipping anisotropy case, the first order spatial derivatives of the strike-parallel components arise in the partial differential equations for generally anisotropic media, which cause a non-symmetric linear system of equations for finite element modeling. The adaptive finite element method is employed to obtain numerical solutions on a sequence of refined unstructured triangular meshes, which allows for arbitrary model geometries including bathymetry and dipping layers. Numerical results of a 2D anisotropic model show both anisotropy strike and dipping angles have great influence on the marine CSEM responses.

Anisotropic Lattice Strain of Composite Materials of LiMnO2 and H/D-Substituted Chiral Cyanide-Bridged Ni（Ⅱ）-Fe（Ⅲ） Coordination Polymers

Composite materials composed of LiMnO2, a typical electrode material for lithium ion battery, and a chiral cyanide-bridged Ni（Ⅱ）-Fe（Ⅲ） coordination polymer [NiL2][Fe（CN）6]·4H2O （Ni-Fe, H-form） （L = （1R,2R）-（-）-1,2-cyclohexane-diamine） or its deuterium isomer, [NiL2][Fe（CN）6]·4D2O （Ni-Fe, D-form） have been prepared by the various ratios （w/w） of Ni-Fe：LiMnO2 = 10：0 （pure Ni-Fe）, 9：1, 8：2, 7：3, 6：4, 5：5, 4：6, 3：7, 2：8, 1：9 and 0：10 （pure LiMnO2）. Gradual shift of IR （infrared） spectra by changing the ratios and losing difference between H-form and D-form of Ni-Fe due to isotope effects revealed adsorption of Ni-Fe onto LiMnO2 to form composite materials. Formation of composite materials of Ni-Fe and LiMnO2 could be also proved losing ferromagnetic behavior of LiMnO2 on increasing of the ratios of Ni-Fe in each composite. In contrast to smoothly positive thermal expansion of pure LiMnO2 along the crystallographic b axis, variable temperature powder XRD （X-ray diffraction） patterns at 100-300 K of the composite materials exhibited thermally-accessible lattice distortion along the b axis with different ratios. It is also proved deviation of ideal linear correlation of an evaluation function, In K = a/T ＋ b （where, K = （d（T） - d（0））/d（T）, d（T） denotes nλ/（sin 2θ） at T （K））.

Redistribution and magnitude of stresses around horse shoe and circular excavations opened in anisotropic rock

In this paper numerical analysis of underground structures, taking account the transverse isotropy system of rocks, was done using CAST 3M code by varying the shape of excavation and the coefficient of earth pressure k. Numerical results reveal that the anisotropy behavior, the shape of hole and the coefficient of earth pressure k have significant influence to the mining induced stress field and rock deformations which directly control the stability of underground excavation design. The magnitude of horizontal stress obtained for the horse shoe shape excavation(25.2 MPa for k = 1; 52.7 MPa for k = 2)is lower than the magnitude obtained for circular hole(26.4 MPa for k = 1; 59.5 MPa for k = 2).Therefore, we have concluded that the horse shoe shape offers the best stability and the best design for engineer. The anisotropy system presented by rock mass can also influence the redistribution of stresses around hole opened. Numerical results have revealed that the magnitude of redistribution of horizontal stresses obtained for transverse isotropic rock(12.1 MPa for k = 0.5; 25.2 MPa for k = 1 and52.7 MPa for k = 2) is less than those obtained in the case of isotropic rock(27.6 MPa for k = 1;48.6 MPa for k = 2 and 90.81 MPa for k = 2). The more the rock has the anisotropic behavior, the more the mass of rock around the tunnel is stable.

Stress sensitivity of coal samples in terms of anisotropy

The permeability and porosity of coal seams are anisotropic, and the variation of confining stress may induce deformation in coal samples. In order to study these characteristics, experiments and model analyses were conducted to understand the behaviors of anisotropic stress sensitivity of lean coal samples. The results showed as the closure of cleats and the generation of micro-cracks, the strong stress sensitivity of coal samples and the discrete changes in porosity were caused by confining pressure changes. In the compression period, the anisotropy trend first increased, and then decreased. In the direction perpendicular to the bedding plane, the permeability decrease rate and the irreversible damage rate were the highest. In the direction parallel to the cleats, permeability recovery rate was higher and the irreversible damage rate was lower along butt cleats. Compared to the cube root of permeability to porosity, a 1/6 power relationship was proved to be closer to the experiment results, the new relationship had the highest fit level in the face cleat direction, and the lowest fit level in the vertical direction

Ferrimagnetic Properties of Bond Dilution Mixed Blume-Capel Model with Random Single-Ion Anisotropy

We study the ferrimagnetic properties of spin 1/2 and spin-1 systems by means of the effective field theory. The system is considered in the framework of bond dilution mixed Blume-Capel mode/ （BCM） with random single-ion anisotropy. The investigation of phase diagrams and magnetization curves indicates the existence of induced magnetic ordering and single or multi-compensation points. Special emphasis is placed on the influence of bond dilution and random single-ion anisotropy on normal or induced magnetic ordering states and single or multi-compensation points. Normal magnetic ordering states take on new phase diagrams with increasing randomness （bond and anisotropy）, while anisotropy induced magnetic ordering states are always occurrence no matter whether concentration of anisotropy is large or small. Existence and disappearance of compensation points rely strongly on bond dilution and random singleion anisotropy. Some results have not been revealed in previous papers and predicted by Néel theory of ferrimagnetism.

Formability of the AMS 5596 Sheet in Comparison with EDDQ Steel Sheet

Some materials form better than others, moreover, a material that has the best formability for one stamping may behave very poorly in a stamping of another Configuration. The forming limit of a metal sheet is generally given in terms of the limiting principal strains under different loading conditions and represented by the so-called FLD （forming limit diagram）. In view of the difficulty to experimentally determine the forming limits, many researchers have sought to predict FLD. The formability of sheet metal has frequently been expressed by the value of strain hardening exponent and plastic anisotropy ratio. The stress-strain and hardening behaviour of a material is very important in determining its resistance to plastic instability. For these reasons, extensive test programs are often carried out in an attempt to correlate material formability with value of some mechanical properties. In this study, mechanical properties and the FLD of the AMS 5596 sheet metal was determined by using uniaxial tensile test and Marciniak＇s flat bottomed punch test respectively.