Orientation Distribution Coefficients Research Articles

Influence of surface ultrasonic impact treatment on texture evolution and elastic properties in the volume of Zr1Nb alloy

The study is devoted to examination of the features of influence of ultrasonic impact treatment (UIT) on the evolution of texture and the changes of elastic parameters in the volume of specimens of Zr1Nb alloy with preliminary-formed strong crystallographic texture. In this case the bulk-wave ultrasonic velocities (vij) in the orthogonal directions in the different sections of the specimens were measured by the automatic US apparatus in initial state (after high-temperature rolling) and after UIT. The density (ρ) of the specimens was also measured in initial and deformed states. Based on the obtained results orientation distribution coefficients (Wij0) were calculated, complete pole figures were plotted, relative intensity of diffraction lines of the basal plane (ΔІ(0001)) and Kearns parameters (fi) were determined. The extreme values of Young (E) and shear (G) moduli, Poisson ratio (η) and their anisotropy were also calculated for different sections of the treated specimens. It is shown that UIT in applied regime changes the texture and elastic parameters in all specimen volume. Pole figures (0001) after UIT keep the view typical for rolled HCP alloys with ratio c/a < 1.633. The clear qualitative correlation between the texture and elastic parameters of the specimens in initial state and after UIT in their different sections is defined. The revealed features indicate that the evolution of crystallographic texture of Zr1Nb alloy specimens is a result of the depth nonuniformity of plastic deformation accumulated during the UIT process. The results are in agreement with available literature data. The effectiveness of applied US method and equipment for layer-by-layer analysis of the texture and elastic characteristics in the volume of spatially inhomogeneous materials subjected to directional surface thermomechanical treatment is shown.

Controlling orientational order in block copolymers using low-intensity magnetic fields

The interaction of fields with condensed matter during phase transitions produces a rich variety of physical phenomena. Self-assembly of liquid crystalline block copolymers (LC BCPs) in the presence of a magnetic field, for example, can result in highly oriented microstructures due to the LC BCP's anisotropic magnetic susceptibility. We show that such oriented mesophases can be produced using low-intensity fields (<0.5 T) that are accessible using permanent magnets, in contrast to the high fields (>4 T) and superconducting magnets required to date. Low-intensity field alignment is enabled by the addition of labile mesogens that coassemble with the system's nematic and smectic A mesophases. The alignment saturation field strength and alignment kinetics have pronounced dependences on the free mesogen concentration. Highly aligned states with orientation distribution coefficients close to unity were obtained at fields as small as 0.2 T. This remarkable field response originates in an enhancement of alignment kinetics due to a reduction in viscosity, and increased magnetostatic energy due to increases in grain size, in the presence of labile mesogens. These developments provide routes for controlling structural order in BCPs, including the possibility of producing nontrivial textures and patterns of alignment by locally screening fields using magnetic nanoparticles.

Theory and application of laser ultrasonic shear wave birefringence measurements to the determination of microstructure orientation in transversely isotropic, polycrystalline graphite materials

Laser ultrasonic line source methods have been used to study elastic anisotropy in nuclear graphites by measuring shear wave birefringence. Depending on the manufacturing processes used during production, nuclear graphites can exhibit various degrees of material anisotropy related to preferred crystallite orientation and to microcracking. In this study, laser ultrasonic line source measurements of shear wave birefringence on NBG-25 have been performed to assess elastic anisotropy. Laser line sources allow specific polarizations for shear waves to be transmitted – the corresponding wavespeeds can be used to compute bulk, elastic moduli that serve to quantify anisotropy. These modulus values can be interpreted using physical property models based on orientation distribution coefficients and microcrack-modified, single crystal moduli to represent the combined effects of crystallite orientation and microcracking on material anisotropy. Ultrasonic results are compared to and contrasted with measurements of anisotropy based on the coefficient of thermal expansion to show the relationship of results from these techniques.

Ultrasonic studies of texture inhomogeneities in pressure vessel steel subjected to ultrasonic impact treatment and shock compression

Abstract Specimens of Cr-Ni-Mo-V pressure vessel steel 15Kh2NМFА were cut from the achieve wall of the WWER-1000 reactor and were then deformed either using ultrasonic impact treatment (UIT) inducing low energy multiple impacts or by drop-hammer inducing high energy shock compression (HESC). With the aim of texture evaluation comprehensive ultrasonic measurements and X-ray texture analysis were carried out in different sections of the deformed specimens. A nondestructive quantitative analysis of the crystallographic texture in various layers of the deformed specimens was performed on the base of precise measurements of the bulk-wave ultrasonic velocities ( v ij ) by means of the pulse-echo method using a home-made automated apparatus. The mass densities ( ρ ) of the deformed specimens and their cut sections were also precisely measured. The obtained data allowed calculating orientation distribution coefficients ( W 4 i 0 ) of crystallites and to construct ultrasonic pole figures for different specimen layers and cut sections. The ultrasonic pole figures correlate well to the X-ray pole figures registered in the cut sections of the specimens. It is found that maximal pole intensities (Δ I [ ijk ] ) and spatial inhomogeneities of these textures depend on the used regimes of UIT and HESC. The revealed peculiarities of the texture formation correlate well to the depth distributions of microhardness and strain extents. The higher the strain extent or the longer the treatment time, the more intensive texture is registered and the deeper the textured layer is observed. The ultrasonic method applied is shown to be useful and efficient for non-destructive examination of elastically heterogeneous systems, particularly the materials with mechanically treated surfaces.

Estimates of Nonlinear Elastic Constants and Acoustic Nonlinearity Parameters for Textured Polycrystals

In this article, expressions are derived for the Voigt, Reuss, and Hill estimates of the third-order elastic constants for polycrystals with either cubic or hexagonal crystal symmetry and orthorhombic physical symmetry. General forms of the fourth- and sixth-rank elastic stiffness and compliance tensors for crystal and physical symmetries are given. Explicit expressions are reduced from these tensors for the case of polycrystals exhibiting orthorhombic sample symmetry with either cubic or hexagonal crystallites. The estimated third-order elastic constants of the textured polycrystal are obtained in terms of second- and third-order single-crystal elastic constants and orientation distribution coefficients (ODCs), which are used to account for anisotropic physical symmetry. The acoustic nonlinearity parameter, $\bar{\beta}$ , is defined through combinations of the second- and third-order Voigt, Reuss, and Hill estimates of the elastic constants for a textured polycrystal. The model predicts that $\bar{\beta}$ is dependent on the type of averaging scheme used and the texture-defining ODCs. The model is quantitatively evaluated for polycrystalline iron, aluminum, and titanium using second- and third-order single-crystal elastic constants and experimentally measured ODCs. The interrelation between $\bar{\beta}$ and polycrystalline anisotropy offers potential for techniques associated with quantitative texture analysis.

Texture analysis of low-carbon steel under annealing conditions using non-contact ultrasound

The ability to rapidly and non-destructively detect crystallographic changes in sheet metals under annealing conditions has potential uses in the strip manufacturing industry. Ultrasonic Lamb wave velocity measurements as a function of the in-plane angle were taken on a number of steel sheets and an aluminium sheet of a nominal thickness of I mm. A number of thermal annealing steps in air were performed on all these sheets and subsequent ultrasonic measurements of the same Lamb wave velocities were taken. The first three crystallographic texture orientation distribution coefficients (ODCs) were inferred from the ultrasonic velocity data. These ODCs were used to construct 'simulated pole figures', illustrating crystallographic texture changes that occurred in the steel and aluminium sheets during the annealing processes. The changes (including those relative to the material's melting point) were found to be much more pronounced in the case of the aluminium sheet. The steel sheets showed a gradual shift from fourfold to twofold symmetry under anneals of increasing temperature, whereas the aluminium sheet showed a much more extreme shift, with a reversal of the ultrasonic fast axes implying substantial recrystallisation

The accuracy of acoustic birefringence shear wave measurements in sheet metal

In rolled metal sheet the through thickness shear wave energy is steered into two orthogonal polarizations, parallel and perpendicular to the sheet’s rolling direction. Ultrasonic velocity measurements used to determine the orientation distribution coefficients in thin sheets can be obtained from the fast Fourier transform of the time domain signal. It is observed that the data obtained using a linearly polarized electromagnetic acoustic transducer (EMAT) do not correspond with that obtained using a radially polarized EMAT. An analytical model has been developed, which explains the source of this effect from the using the fast Fourier transform.

Prediction of Elastic Modulus + Anisotropy Using X-Ray and Electron Backscattered Diffraction Texture Quantification and Ultrasonic (Electromagnetic Acoustic Transducer) Measurements in Aluminum Sheets

Crystallographic texture is generally measured using X-ray diffraction, performed off-line using small samples determining near-surface texture only; electron backscattered diffraction (EBSD) can also be used, but only samples relatively small areas. Ultrasonic methods determine elastic property anisotropy and texture, via orientation distribution coefficients (ODCs), and while there is substantial literature comparing ultrasonically determined properties with X-ray or neutron diffraction texture, there is little discussion about texture inhomogeneity (place to place in a sheet or through thickness) and sampling volume effects (X-ray compared to EBSD) on the accuracy of the correlations. In this article, the crystallographic texture of nominally pure aluminum and commercial aluminum alloy sheets has been determined by X-ray diffraction and EBSD and used to calculate the elastic anisotropy, which is then compared to ultrasonic electromagnetic acoustic transducer (EMAT) velocity anisotropy taking into account through-thickness texture variations. Significant and consistent spatial variability in texture occurs in the aluminum sheet samples (sheet edge to center and through thickness). Predictions of elastic anisotropy based on surface texture determination, as characterized by X-ray diffraction or surface EBSD, gave poor correlations with EMAT velocity anisotropy when the sample contained significant through thickness texture variations; however, accounting for this using multiple EBSD scans through thickness gave good correlations.

Characterizing texture in polycrystalline materials by ultrasonic waves

A method for characterizing texture from measurements of ultrasonic wave velocities is proposed. In polycrystalline aggregates, ultrasonic wave velocities are strongly affected by orientation distribution coefficients (ODCs), which are usually used to describe the degree of preferred grain orientation in textured materials. In this work, velocities of longitudinal and transverse waves propagating into aluminum alloy 6061 were measured under pure shear, simple shear and uniaxial tension. From the measured ultrasonic wave velocities, the ODCs W 400 and W 420 were calculated to infer the deformation-induced texture. The predicted pole figures, obtained using ultrasonic velocities, were in good qualitative agreement with the finite element polycrystal model analyzed pole figures.

Molecular Orientation Distributions in the Crystalline and Amorphous Regions of Uniaxially Oriented Isotactic Polypropylene Films Determined by Polarized Raman Spectroscopy

Molecular orientation distributions in both the crystalline and amorphous regions of uniaxially oriented isotactic polypropylene (it.PP) films were determined by polarized Raman spectroscopy. By comparing polarized Raman scattering intensities of a highly oriented film for different polarization scattering geometries, the form of Raman tensor was determined for the Raman bands of it.PP. Orientation distribution coefficients, P l00, for the Raman bands were combined with the results of wide angle x‐ray diffraction (WAXD) and birefringence measurements in order to determine their tilt angle, Ω, which is the angle between the principal axis of a Raman tensor and the molecular chain axis. The angles, Ω, were determined for the first time for Raman bands assigned to both the crystalline and amorphous regions. It was shown that the molecular orientation distributions in the crystalline regions and in the amorphous regions can be determined fully by polarized Raman spectroscopy, once the tilt angle, Ω, was obtained first for a Raman band assigned to the crystalline regions only and then for one assigned to both the crystalline and amorphous regions. The study of uniaxially oriented it.PP films with different sample draw ratios (DR) revealed that the development of high molecular orientation in the crystalline regions took place up to DR=7.5. Compared to the crystalline regions, a lower degree of molecular orientation was observed in the amorphous regions, and there was a slight increase of molecular orientation above DR=7.5. Dedicated to Professor John L. Stanford on the occasion of his 60th birthday.

Attenuation of ultrasonic waves in rolled metals

Scattering of ultrasonic waves in polycrystals with texture is studied in this article. The attenuations of the three wave modes are determined as a function of dimensionless frequency and propagation direction, respectively, for given orientation distribution coefficients (ODCs). The calculation is done in the case of a statistically orthorhombic sample made up of cubic crystallites. The wave propagation and scattering model is formulated by the Dyson equation using an anisotropic Green's function approach. Within the limits of the first-order smoothing approximation, the Dyson equation is solved in the spatial Fourier transform domain. The results presented are shown to be directional dependent, frequency dependent, and especially dependent on the texture coefficients (ODCs) for the quasilongitudinal and two quasishear waves. The theoretical results presented may be used to improve the understanding of the microstructure during recrystallization processes.

Development of an automated non-contact ultrasonic texture measurement system for sheet metal

We report on the further development of an automated PC-based system for determination of the crystallographic texture of sheet metals by ultrasonic measurement of the zero-order symmetric (S0) Lamb wave mode velocity. Measuring the in-plane anisotropy of S0 mode velocities gives information on the crystallographic texture of the sheet. This can be used as an indication of the suitability of the metal for cold forming techniques. Currently, texture information is determined by x-ray pole figure measurements, which are slow, expensive and unsuitable for online quality control. The effect of coil geometry on the electromagnetic acoustic transducer (EMAT) generated S0 mode has been investigated. Developments in the EMAT design have led to considerable improvements in performance over our previous work, allowing measurements to be made at increased stand-offs of up to several millimetres on an increased range of metal sheets including up to 3 mm thick steel with pulse repetition rates of up to 60 Hz. Using 360° velocity scans reveals texture asymmetry in certain aluminium sheets which would not be detected by limiting the scan to velocities in one 90° quadrant. This asymmetry is shown to lead to significantly different crystallite orientation distribution coefficients (ODCs) depending which quadrant is looked at.

Scattering of elastic waves in textured media

The investigation of wave propagation and scattering of elastic waves in heterogeneous, anisotropic media is of substantial interest to quantitative nondestructive evaluation and materials characterization. The scattering of elastic waves in polycrystalline media is primarily due to interaction with the grains. Knowledge of wave velocity and attenuation may be used to infer material texture in polycrystalline aggregates. In this presentation, a model for wave propagation and scattering in polycrystalline materials with texture is presented. Attenuations and wave velocities are discussed for a general orthorhombic material made up of cubic crystallites. The attenuations of each wave type are derived as a function of dimensionless frequency and wave propagation direction, respectively, for given orientation distribution coefficients (ODCs). The ODCs are, in essence, the coefficients of an expansion of crystallite of orientation distribution function (ODF) in terms of a series of generalized spherical harmonics. A relationship between the phase velocity and recrystallization variables, such as annealing time, is also investigated for specific examples. Finally, numerical results are presented and discussed in terms of the relevant dependent parameters. The results are anticipated to advance the field of materials characterization of statistically anisotropic media. [Work supported by DOE.]

Evolution of crystal orientation distribution coefficients during plastic deformation

A general methodology is developed to model the texture evolution of polycrystalline materials during mechanical processing. The methodology is based on the conservation of texture volume as proposed by Bunge. One of the interesting features of the formulation is that the texture coefficients can be predicted for each processing path using a sixth rank tensor. The range of validity for this methodology is investigated using a set of input data predicted by a crystal plasiticity model based on Taylor.

On-line measurement of texture, thickness and plastic strain ratio using laser-ultrasound resonance spectroscopy

Laser-ultrasound resonance spectroscopy, a non-contact ultrasonic technique, was used to determine reliably and rapidly the crystallographic texture, the average plastic strain ratio, and the thickness of sheet metal on the production line. As with laser-ultrasonics, a short laser pulse is used to generate a wide-band pulse of ultrasound and a laser interferometer is used for its detection. In this paper, a large number of echoes are collected and analyzed together using Fourier techniques to measure the natural resonance frequencies in the thickness of the sheet. One longitudinal and two shear resonance frequencies were measured together with their harmonics. From these frequencies, two crystallographic orientation distribution coefficients, W 400 and W 420, are obtained, as well as a highly accurate measurement of the sheet thickness that is corrected for changes in ultrasonic velocity caused by texture variations. Using these coefficients, the average and in-plane twofold and fourfold variations of the plastic strain ratio, respectively r̄, Δ 2 r, and Δ 4 r, can be evaluated. These parameters are indications of the formability of metals sheets, which is of industrial interest. Measurements on 1 mm thick, low carbon steel sheets have shown the following measurement accuracies: r̄ to within ±0.08, Δ 2 r, and Δ 4 r to within ±0.1, and thickness to better than ±1 μm. On-line tests at LTV Steel Company showed that the sensitivity of the apparatus is sufficient to detect systematic variations in texture along the length of similar production coils and that the on-line repeatability for r̄ was of order ±0.02.

Ultrasonic measurement of the kearns texture factors in zircaloy, zirconium, and titanium

Texture, developed during the processing of zirconium and zirconium alloys, e.g., ZIRCALOY, plays an important role in determining the properties and performance of the resultant structural components. Extending the work done on cubic metals, ultrasonic velocity measurements were used to nondestructively characterize the texture in hexagonal sheet metals. A theory is developed relating the texture coefficients WLMN (L≤4, found in an expansion of the crystallite orientation distribution function (ODF) in terms of generalized spherical harmonics) to industrially measured Kearns factors, which predict the fraction of basal poles aligned in a particular sample reference direction. Ultrasonic characterization of texture has been performed on three sheets of zirconium (one pure, two ZIRCALOY) and on one sheet of titanium. These results are compared to the Kearns factors, measured by X-ray diffraction (for the two ZIRCALOY sheets) and to the WLMN value measured by neutron diffraction (for the pure zirconium and the titanium). Results show that ultrasonics predict both the orientation distribution coefficients (ODCs) and the Kearns factors very well.

Non-destructive evaluation of formability of zinc-coated steel sheets using electromagnetic acoustic transducer

An ultrasonic technique for evaluation of the formability of zinc-coated steel sheets has been developed. The technique is based on the dispersion relation, which correlates the velocity anisotropy of the S 0-mode Lamb wave to the texture defined by orientation distribution coefficients. In cold rolled steel sheets, we have already developed the evaluation system and installed it on two continuous annealing production lines. In this paper, we describe how to remove the effect of the zinc-coated layer from the measured velocity and the evaluation results of the formability for zinc-coated steel sheets. The coating induced a decrease in the S 0-mode Lamb wave velocity. The change in ultrasonic velocity due to the zinc-coated layer has been shown to be compensated by using a simple correction curve, which enables the correction for the effect of zinc coating from the known coating/substrate thickness ratio. The test results indicate that the monitoring of the formability for zinc-coated steel sheets as well as for cold rolled steel sheets is quite feasible.

Method for the simultaneous determination of anisotropic residual stresses and texture by x-ray diffraction

A method is developed that yields the residual stress, the orientation distribution coefficients, the average crystallite dimension, the microstrain, and the crystal structure parameters from x-ray diffraction data in a single-step procedure. To this end, a general approach is introduced that combines the equations of micromechanics with the harmonic description of texture. All relationships are cast into a Rietveld-like format, which incorporates a microstructure model derived from line-broadening methods. In this manner, data collected over the whole x-ray-diffraction pattern at different tilting of the sample can be fitted directly. The associated fitting parameters are the crystal structure and microstructure, the texture coefficients, and the micromechanical properties and fields.

Third-order stiffness constants of textured hexagonal crystallite aggregates with an orthotropic macroscopic symmetry

Voigt-type averaging is carried out to obtain the effective second- and third-order elastic stiffness constants of textured hexagonal (6/mmm, 6̄m2 or 6mm point group) crystallite aggregates with orthotropic macroscopic symmetry. The second-order constants agree with previously reported results. The third-order constants are presented in a compact formula. The formula relates the effective third-order stiffness constants to the crystallite orientation distribution coefficients (CODCs) and the single-crystal third-order stiffness constants. If any two of these three sets of parameters are known, information of the third set can be inferred. The sensitivity of the effective third-order stiffness constants to changes of the CODCs is also given.

Ultrasonic measurement of sheet steel texture and formability: Comparison with neutron diffraction and mechanical measurements

Ultrasonic measurements were made on a set of thin steel sheets, using the lowest-order shear horizontal mode (SH0-mode) and lowest-order symmetric Lambwave mode (S0-mode). The velocities of these modes were measured as a function of angle relative to the sheet rolling direction. From the data reduction it is, in theory, possible to (1) partially characterize the texture of the sheet, and (2) predict the plastic strain ratio (r-value). The plate texture can be completely characterized by quantities known as orientation distribution coefficients (ODCs). The lowest-order ODCs can be obtained from our measurements; these were compared with ODCs measured by neutron diffraction, with good agreement for the dominant ODC. The r-value is a commonly used measure of sheet formability. It is typically measured mechanically with uniaxial tension specimens subjected to large plastic strain. Therefore, the r-value test is destructive and time consuming. We found a good correlation between S0-mode velocity measurements and\(\bar r\), the average in-plane r-value. Consequently, the use of noncontacting electromagnetic-acoustic transducers (EMATs) may offer an online nondestructive measurement of sheet formability.