Application of ultrasonic methods to determine elastic anisotropy of polycrystalline copper processed by equal-channel angular pressing

Anisotropy of elastic properties of ultrafine-grained polycrystalline copper after one, two and four passes of equal-channel angular pressing (ECAP) is investigated by means of ultrasonic methods. For each material, Young’s and shear moduli in the principal processing directions are evaluated and the symmetry and orientation of the anisotropy are identified. The relation between the determined symmetry and the processing mechanisms is discussed. It is shown that the material after one and two passes of ECAP exhibits a measurable anisotropy, while the material after the fourth pass behaves isotropically. Within the discussion, it is shown that the origin of the observed anisotropy may be attributed to the spatial arrangement of grain boundaries rather than to the crystallographic texture. In the light of this conclusion, the obtained results correspond well with optical and transmission electron microscopy observations of the microstructures of ECAPed materials documented in the literature.     

金属板材弹性性质与塑性性质关联性的数值验证

金属材料的宏观弹性和塑性性质均与晶粒对称性和晶粒取向分布(材料的织构)有关,因此弹性常数和塑性参数间具有关联性。该文在已有文献对金属板材弹性性质与塑性关系的关联性做了大量理论研究工作的基础上,利用ADINA软件,通过一立方晶粒正交集合金属板材不同方向的试样拉伸数值模拟实验,对多晶体材料的弹性与塑性关联性进行数值验证。验证结果较好的吻合了其弹塑性关系的理论公式,为该理论的进一步研究和应用提供了有效的验证方法。     

Determination of texture and estimation of anisotropie properties of metallic uranium rods by neutron diffraction

Textures of metallic uranium rods were measured by neutron diffraction. From experimentally measured single and composite pole figures, the crystallite orientation distribution function (ODF) was determined by the harmonic method using a computer program developed for the fiber texture with orthorhombic crystal symmetry. The composite pole figures measured at overlapped peak positions of the diffraction pattern were assumed to be a linear combination of several neighboring single pole figures. The calculated results show that the harmonic method based on this conjecture well recovers the experimentally measured composite pole figures. Anisotropie physical properties such as thermal expansion coefficients and elastic constants due to the texture were evaluated by numerically averaging the second and fourth rank tensors with the calculated ODF, respectively.     

Elastic properties of double layered manganites R_（1.2）Sr_（1.8）Mn_2O_7（R=La,Pr, Nd,Sm）

The polycrystalline colossal magnetoresistive double-layered manganite samples R1.2Sr1.8Mn2O7(R = La Pr, Nd, Sm) were prepared by the sol–gel method and their room temperature elastic behavior was investigated by ultrasonic pulse transmission technique at 1 MHz. The values of elastic constants were calculated from longitudinal and shear velocities and they were corrected to zero porosity using Hasselman and Fulrath's formulae. The elastic constants of the samples were also estimated by Modi's heterogeneous metal-mixture rule which is based on the metal ions present in the samples. The measured,corrected, and estimated values of elastic moduli are found to increase with decreasing rare earth ion size. The variation of elastic moduli with the size of the rare earth ion is interpreted in terms of strength of interatomic bonding.     

Stiffness properties and stiffness orientation distributions for various paper grades by non-contact laser ultrasonics

The stiffness properties, especially flexural rigidity (FR), out of plane shear rigidity (SR), and stiffness orientation distributions (SOD) are characterized for various paper grades, by a laser ultrasonics instrument. Laser ultrasonics generation is achieved through thermal dilatation by point focusing of a pulsed laser beam onto the surface of the specimen. By probing the excited broadband ultrasound propagating in the samples, the velocities dispersions are obtained and the materials properties are extracted. The measured FR and SR along machine direction (MD) and cross direction (CD) are presented for 10 paper samples ranging from thin copy papers to heavy linerboards. The SOD polar diagrams for some of the samples are also presented and discussed. The relationships of FR, SR, Young's and shear moduli with basis weight are discussed. It is observed that both the Young's and shear moduli tend to decrease significantly when the basis weight increases, going from copy paper to linerboard grades. We also found that SR reaches a maximum value and then decreases when the basis weight increases to 150 g/m² and above. This unusual behavior of SR can be explained by the noticeable reduction of shear modulus for heavy linerboards.     

Velocities of elastic waves and the elasticity moduli of nickel-base superalloys and of the 60N21 alloy

Measurements of velocities of elastic waves have been performed in polycrystalline samples of an intermetallic compound Ni₃Al, this intermetallic compound alloyed with niobium or cobalt, superalloys ZhS36 and VKNA-4U, and the 60N21 alloy. Elasticity moduli have been calculated, namely, Young’s modulus, shear modulus, bulk modulus, and the Poisson ratio. The results obtained are compared with those calculated from the tensor of the elasticity moduli obtained for single crystals. The calculations have been performed in the Voigt and Reuss approximations.     

Orientation dependence of elastic properties and internal stresses in sub-microcrystalline copper produced by equal channel angular pressing

The orientation characteristics of the elastic properties of sub-microcrystalline copper produced by equal channel angular pressing (ECAP) were studied by measuring the velocities of the longitudinal and transverse ultrasonic waves in different spatial directions. It was shown that the effect of an “anomalous” reduction in the elastic moduli observed after ECAP treatment reflects a strong spatial anisotropy of the material. Internal stresses arising in copper as a result of ECAP processing were determined by means of X-ray diffraction line broadening analysis. An appreciable anisotropy of the internal stresses was also found. Possible mechanisms responsible for the anomalies of the elastic properties are discussed.     

A method for measuring single-crystal elastic moduli using high-energy X-ray diffraction and a crystal-based finite element model

This paper presents a method – based on high-energy synchrotron X-ray diffraction data and a crystal-based finite element simulation formulation – for understanding grain scale deformation behavior within a polycrystalline aggregate. We illustrate this method by using it to determine the single-crystal elastic moduli of β21s, a body-centered cubic titanium alloy. We employed a polycrystalline sample. Using in situ loading and high-energy X-rays at the Advanced Photon Source beamline 1-ID-C, we measured components of the lattice strain tensor from four individual grains embedded within a polycrystalline specimen. We implemented an optimization routine that minimized the difference between the experiment and simulation lattice strains. Sensitivity coefficients needed in the optimization routine are generated numerically using the finite element model. The elastic moduli that we computed for the β21s are C₁₁ = 110 GPa, C₁₂ = 74 GPa and C₄₄ = 89 GPa. The resulting Zener anisotropic ratio is A = 5.     

Quantitative estimation of material properties of porous ceramics by means of composite micromechanics and ultrasonic velocity

This paper describes a nondestructive method for the quantitative estimation of property variations due to porosity in advanced ceramics. The method employs a composite micromechanics which accounts for the effective density and elastic stiffness of a porous composite medium with a measurement of ultrasonic velocity. When the measured velocity is coupled with the theoretically predicted velocity, the unknown pore volume fraction is solved, from which other material properties are determined. The micromechanics model based on the Mori-Tanaka theory can handle ellipsoidal pores with a certain orientation distribution. Given the zero-porosity matrix moduli and the pore aspect ratio, the oblate spheroidal theory is first applied to hot pressed silicon carbide (SiC) samples in the range of about 85–100% of theoretical density and then extended to sintered samples in the density range of 93.6–97.6%. It is shown that the bulk density and elastic modulus of porous ceramics can be estimated accurately by the proposed method.     

First-principles density functional calculations of physical properties of orthorhombic Au2Al crystal

The study attempts to perform a systematical investigation of the thermodynamic, mechanical and electronic properties of orthorhombic Au₂Al crystal by using first-principles calculations incorporated with a quasi-harmonic Debye model. In addition, their temperature, hydrostatic pressure and direction dependences are also addressed. The investigation begins with evaluation of the equilibrated lattice constants and elastic constants of Au₂Al single crystal. Next, the mechanical features of the single crystal, such as ductile-brittle characteristic and elastic anisotropy, are assessed based on the Cauchy pressures, shear anisotropy factors and directional Young's modulus. Alternatively, the pressure-dependence of polycrystalline mechanical properties of Au₂Al, including bulk, shear and Young's moduli, and ductility, brittleness and microhardness characteristics are also estimated. Furthermore, the study also characterizes the temperature-dependence of thermodynamic properties of Au₂Al single crystal, namely, Debye temperature and heat capacity. At last, electronic characteristic analysis is carried out to predict the electronic band structures and density of states profiles of the crystal.The calculation results indicate that Au₂Al crystal is an elastically anisotropic material at zero pressure and a highly ductile material with low stiffness. In addition, the Young's moduli of the crystal would be markedly enhanced with the increase of the hydrostatic pressure. It is also found that the heat capacity of Au₂Al at low temperature strictly sticks to the Debye T³ law.     

Simulation of faceted film growth in two-dimensions: microstructure,morphology and texture

A series of simulations of the growth of polycrystalline, faceted films from randomly oriented nuclei in two spatial dimensions was performed. The simulations track the motion of all corners where facets from the same grain and different grains meet. Results are presented on the temporal evolution of the mean grain size, grain size distribution, surface roughness, crystallographic texture and growth zones as a function of α, a parameter describing the relative facet velocities. The mean grain size and r.m.s. surface roughness are shown to be a parabolic function of the film thickness, in agreement with experiment and theoretical results. The grain size distribution is temporally self-similar when scaled by the mean grain size and has the form of a gamma distribution. The crystallographic orientation distribution (i.e. texture) is Gaussian, peaks at an α-dependent orientation and the peak sharpens during film growth. The peak position is well described by the largest radius vector of the appropriate idiomorph in two and three dimensions. The grain size, roughness and texture evolution are intimately linked. This type of simulation may be used to examine the evolution of the microstructure of any film which exhibits faceted growth with prescribed facet velocities.     

Measurements of local elastic moduli by amplitude and phase acoustic microscope

A new method is suggested for the nondestructive measurement of elastic moduli in a localized area, 100–400 μm in diameter, by the complex V(z) curve using an amplitude and phase acoustic microscope. The inverse Fourier transform of the complex V(z) curve contains the reflectance function of a liquid-specimen interface. Therefore, the longitudinal, transverse and Rayleigh wave velocities for the specimen are simultaneously obtained by the inversion of the complex V(z) curve. The elastic moduli for glass obtained from wave velocities by acoustic microscope agree fairly well with those by other methods. The present method is applied to aluminium alloy, and it is shown that this method is useful in measuring the microscopic characteristics in inhomogeneous materials.     

Deformation and creep modeling in polycrystalline Ti–6Al alloys

This paper develops an experimentally validated computational model for titanium alloys accounting for plastic anisotropy and time-dependent plasticity for analyzing creep and dwell phenomena. A time-dependent crystal plasticity formulation is developed for hcp crystalline structure, with the inclusion of microstructural crystallographic orientation distribution. A multi-variable optimization method is developed to calibrate crystal plasticity parameters from experimental results of single crystals of α-Ti–6Al. Statistically equivalent orientation distributions of orientation imaging microscopy data are used in constructing the polycrystalline aggregate model. The model is used to study global and local response of the polycrystalline model for constant strain rate, creep, dwell and cyclic tests. Effects of stress localization and load shedding with orientation mismatch are also studied for potential crack initiation.     

Prediction of intergranular strains in cubic metals using a multisite elastic-plastic model

A novel approach is adopted for determining the elastic and plastic strains of individual grains within a deformed polycrystalline aggregate. In this approach, termed “multisite modeling”, the deformation of a grain does not merely depend on the grain lattice orientation. It is also significantly influenced by the interaction with one or several of the surrounding grains. The elastic-plastic constitutive law is integrated by identifying iteratively which dislocation slip systems are activated within the grains, and the local stress tensor is shown to be the solution of a linear equation set. Several micro–macro averaging schemes are considered for the distribution of the macroscopic load over the polycrystalline aggregate. These averaging schemes are tested by simulating the development of intergranular strains during uniaxial tension of MONEL-400 as well as commercial purity aluminium. Neutron diffraction measurements of the elastic lattice strains are used as a reference in order to discriminate between the various predictions. The results demonstrate the relevance of “multisite” grain interactions in f.c.c. polycrystals.     

Work-hardening/softening behaviour of b.c.c. polycrystals during changing strain paths: I. An integrated model based on substructure and texture evolution,and its prediction of the stress–strain behaviour of an IF steel during two-stage strain paths

For many years polycrystalline deformation models have been used as a physical approach to predict the anisotropic mechanical behaviour of materials during deformation, e.g. the r-values and yield loci. The crystallographic texture was then considered to be the main contributor to the overall anisotropy. However, recent studies have shown that the intragranular microstructural features influence strongly the anisotropic behaviour of b.c.c. polycrystals, as revealed by strain-path change tests (e.g. cross effect, Bauschinger effect). This paper addresses a method of incorporating dislocation ensembles in the crystal plasticity constitutive framework, while accounting for their evolution during changing strain paths. Kinetic equations are formulated for the evolution of spatially inhomogeneous distributions of dislocations represented by three dislocation densities. This microstructural model is incorporated into a full-constraints Taylor model. The resulting model achieves for each crystallite a coupled calculation of slip activity and dislocation structure evolution, as a function of the crystallite orientation. Texture evolution and macroscopic flow stress are obtained as well. It is shown that this intragranular–microstructure based Taylor model is capable of predicting quantitatively the complex features displayed by stress–strain curves during various two-stage strain paths.     

Directional thermoelectric properties of Ru2Si3

The orthorhombic compound Ru₂Si₃ is currently of interest as a high-temperature thermoelectric material. In order to clarify the effects of crystal orientation on the thermoelectric properties of Ru₂Si₃, we have examined the microstructure, Seebeck coefficient, electrical resistivity, and thermal conductivity of Ru₂Si₃ along the three principal axes, using these measured quantities to describe the relative thermoelectric performance as a property of crystal orientation. Ru₂Si₃ undergoes a high temperature (HT)→low temperature (LT) phase change and polycrystalline Si platelet precipitation during cooling, both of which are expected to effect the thermoelectric properties. The HT tetragonal→LT orthorhombic phase transformation results in a [010]//[010], [100]//[001] two-domain structure, while polycrystalline Si precipitation occurs on the (100)_LT and (001)_LT planes. The [010] orientation is found to posses superior thermoelectric properties (with the dimensionless figure of merit, ZT_[010]/ZT_[100]>4 at 900 K), due principally to the larger Seebeck coefficient along the [010] direction. The effect of the domain structure on the thermoelectric properties is discussed.     

First-principle calculations of structural,elastic and thermodynamic properties of Fe–B compounds

The structural, elastic and thermodynamic properties of FeB, Fe₂B, orthorhombic and tetrahedral Fe₃B, FeB₂ and FeB₄ iron borides are investigated by first-principle calculations. The elastic constants and polycrystalline elastic moduli of Fe–B compounds are usually large especially for FeB₂ and FeB₄, whose maximum elastic constant exceeds 700 GPa. All of the six compounds are mechanically stable. The Vickers hardness of FeB₂ is estimated to be 31.4 GPa. Fe₂B and FeB₂ are almost isotropic, while the other four compounds have certain degree of anisotropy. Thermodynamic properties of Fe–B compounds can be accurately predicted through quasi-harmonic approximation by taking the vibrational and electronic contributions into account. Orthorhombic Fe₃B is more stable than tetrahedral one and the phase transition pressure is estimated to be 8.3 GPa.     

Crystal Plasticity Finite Element Simulations for Single Phase Titanium Alloys: Effect of Polycrystalline Aggregate Features on the Mechanical Response

基于率相关晶体塑性理论,以滑移作为主要的变形机制,建立了描述多晶钛合金室温拉伸变形行为的本构模型。并采用三维Voronoi几何模型仿真初始组织创建了多晶集合体。利用该数值模型,探讨了多晶集合体特征对合金宏观力学响应的影响。研究结果表明,多晶集合体三边的尺寸差异将导致集合体的应力应变关系沿3个方向出现各向异性,同时在长度方向上易发生颈缩现象。此外,多晶集合体中的晶粒形貌与取向分布对合金的宏观应力应变响应也有重要的影响。针对单相钛合金建立的晶体塑性有限元模型为钛合金组织控制技术的发展以及加工工艺的优化提供了重要的技术途径。     

Synthesis and on-line ultrasonic characterisation of bulk and nanocrystalline La0.68Sr0.32MnO3 perovskite manganite

La_0.68Sr_0.32MnO₃ perovskite manganite samples were prepared using sonochemical reactor and solid state reaction technique. The ultrasonic velocity, attenuation and elastic moduli of samples were measured using ultrasonic through transmission method, at a fundamental frequency of 5 MHz over a wide range of temperatures. The temperature dependence of the ultrasonic parameters shows an interesting anomaly in all the compositions. The observed dramatic softening and hardening in sound velocities or attenuation is related to phase transitions. The linear magnetostriction effect is more dominant in the perovskite than volume magnetostriction effect which is evident from the observed anomalous in both longitudinal and shear velocities and attenuation. Further, a decrease in grain size in the sintered sample leads to a shift in the ferromagnetic transition temperature (T_C) from 375 to 370 K.     

Structural investigation and simulation of acoustic properties of some tellurite glasses using artificial intelligence technique

The developments in the field of industry raise the need for simulating the acoustic properties of glass materials before melting raw material oxides. In this paper, we are trying to simulate the acoustic properties of some tellurite glasses using one of the artificial intelligence techniques (artificial neural network). The artificial neural network (ANN) technique is introduced in the current study to simulate and predict important parameters such as density, longitudinal and shear ultrasonic velocities and elastic moduli (longitudinal and shear moduli). The ANN results were found to be in successful good agreement with those experimentally measured parameters. Then the presented ANN model is used to predict the acoustic properties of some new tellurite glasses. For this purpose, four glass systems xNb₂O₅-(1 − x)TeO₂, 0.1PbO-xNb₂O₅-(0.9 − x)TeO₂, 0.2PbO-xNb₂O₅-(0.8 − x)TeO₂ and 0.05Bi₂O₃-xNb₂O₅-(0.95 − x)TeO₂ were prepared using melt quenching technique. The results of ultrasonic velocities and elastic moduli showed that the addition of Nb₂O₅ as a network modifier provides oxygen ions to change [TeO₄] tbps into [TeO₃] tps.