Methodological aspects of the quantitative texture analysis of HCP Alloy (Ti,Zr) sheet semiproducts

The specific features of the existing methods of quantitative texture analysis of semiproducts and products made of titanium and zirconium alloys are analyzed. A technique is proposed to determine the Kearns coefficients (f parameters) for sheets made of hcp-metal-based alloys with allowance for the weighting factor of each reflection in the standard stereographic triangle. The f parameters calculated for sheets made of a zirconium alloy and various titanium alloys using different techniques are compared. The accuracy of measuring the Kearns coefficients by the inverse pole figure method is estimated.     

Characterization of formability in cold-rolled steel sheets using electromagnetic acoustic tranducers

An ultrasonic technique for evaluating the formability of cold-rolled steel sheets is developed. The technique is based on the generalized dispersion relation, which correlates the velocity anisotropy of ultrasonic plate modes guided in the sheet plane to the texture defined by orientation distribution coefficients. Electromagnetic acoustic transducers (EMAT’s), constructed of permanent magnets and meander-line coils, allow the accurate and easy measurement of transit times of theS _o (fundamental symmetric) mode. The planar average of the transit times shows a close correlation with both the planar average of plastic strain ratios (r value), obtained through tensile tests and the pole intensities, measured with the X-ray diffraction method. These favorable comparisons with the destructive tests indicate a good possibility of texture monitoring with the noncontacting EMAT’s.     

A comparison of ultrasonic and X-ray determinations of texture in thin Cu and Al plates

Ultrasonic techniques for determining the orientation distribution coefficients (ODC’s), which define the preferred orientation of polycrystals, are discussed. The theory is reviewed for thin plates of cubic crystallites for which the texture information is deduced from the velocity anisotropy of guided modes. Experimental ultrasonic and X-ray predictions of the ODC’s of up to an order of 4 are compared for plates of commercially pure electrolytic tough pitch (ETP) copper and aluminum. ForW ₄₂₀ andW ₄₄₀ in both samples andW ₄₀₀ in copper, the predictions agree to |ΔW|∼10^-3. However, considerably greater differences are reported for the predictions ofW ₄₀₀ in aluminum. Interpretation of these comparisons is assisted by a detailed error analysis for the ultrasonic technique and reference to a number of other recent comparisons of ultrasonic and neutron or X-ray predictions of ODC’s Possible applications of the ultrasonic technique during the production and forming of metal sheet are indicated. S. S. LEE, formerly a Graduate Student with Ames Laboratory     

The Formation of the {112}<111> Shear Texture in Hot-Rolled Sheets of Electrical Steels

Due to the friction between rolls and sheet surface, shear texture inevitably occurs in the surface layer of the hot-rolled sheets in electrical steel. The shear texture contains Goss texture {110}<001>, brass texture {110}<112>, and copper texture {112}<111>. The existence of shear texture and its corresponding microstructure affect the texture distribution in the subsequent normalized sheets, cold-rolled sheets, and final sheets. Electron backscattered diffraction and reaction stress model are used herein to study the formation conditions of {112}<111> orientation in the hot-rolled sheets. The results show that initial rotated cube orientation tends to rotate around transverse direction to the copper orientation during hot rolling due to the shear action. Different shear orientations can be formed in different regions of an initial coarse columnar grain during hot rolling, because of the change in surrounding environment reaction and the difference of the shear strain at different thickness positions. The thinner the hot-rolled sheet is, the smaller the dynamic recrystallization region with shear orientation, and there is almost no copper texture in the thinnest hot-rolled sheet. The simulation results show that the copper texture is easy to form under the action of σ₂₃ and σ₂₂ reaction stresses.     

Relationship between contractile strain ratioR and texture in zirconium alloy tubing

The crystallographic textures of zirconium alloy tubing used as cladding in nuclear reactor fuel are commonly characterized by the quantitative texture numbersF (Källström) and f_r (Kearns) which are derived from the direct and inverse pole figures. The texture numbers of zircaloy 2 and 4 tubes have been correlated experimentally with the value of the contractile strain ratioR which is a measure of the plastic anisotropy of the tube. The correlations were based on the results of 20 different tubing lots. Thef _r-R correlation shows much less data scatter than theF-R correlation. By assuming a simple plastic deformation model for zirconium alloys the following relations between texture and anisotropy are obtained:F=R- 1/R+1 and f_r = R/R+1 The theoretically derived relations are in good agreement with the experimental data. The procedure of correlating texture with plastic anisotropy is not limited to zirconium alloy tubing, but should be equally applicable to textured sheet and plate materials and other alloys with a limited number of slip systems.     

Deformation and fracture behavior of beams composed of alumium foam core and ceramic Al<Subscript>2</Subscript>O<Subscript>3</Subscript> under monolithic bending

Deformation and fracture mechanisms of sandwich and multilayer beams composed of aluminum foam core and ceramic face sheets under four-point bending condition were investigated in situ by surface displacement analysis (SDA) software. The toughening mechanism of the beams was discussed and a model was given for the computation of the fracture energy of the beams. Beams containing foam core with 5-, 10-, and 20-mm thickness and Al₂O₃ face sheets of 0.5-and 1-mm thickness were prepared. The results show that collapse of the beams is by two basic modes, indentation (ID) and face plate failure (PF). The SDA results illustrated that indentation is localized compression on the portion of the beam adjacent to the loading rollers, where displacement and strain are at the maximum. In PF, the beam entirely bends. It is also found that before collapse of the beams with pure PF mode, the foam core undergoes uniform compressive deformation, which contributes most to the fracture energy of the beams. As for the beams with ID characteristic, the localized compressive deformation plays a key role rather than the uniform compressive deformation in the fracture energy of the beam. The total fracture energy W of a beam under bending condition is proposed as W=W _UC+W _LC+W _CB+W _PF where W _UCis the energy of uniform compressive deformation of the foam core, W _LCis the energy of localized compression of the foam core and W _CBand W _PFare the bending fracture energy of the monolithic foam core and ceramic face sheet, respectively. For the beams with pure PF mode, W _LCis zero. The estimated values of the fracture energy are in good agreement with the measured fracture energy of the beams.     

Effects of transformation on texture and iodine stress corrosion cracking resistance of zircaloy sheet

A two-step heat treatment was developed as a means of maximizing the basal texture of Zircaloy-4 sheet. The heat treatment, consisting of a brief beta heat treatment and subsequent controlled cooling, resulted in a Kearns number (f_n) of 0.83 with a microstructure of uniformly fine grains and high hardness. The texture component, as determined by the crystallite orientation distribution function (CODF), was (0002)(10−10). The result was discussed in terms of phase transformation, either diffusional or martensitic, incurred by controlled cooling. The rate of stress corrosion cracking (SCC) of the alloy was evaluated with constant deflection tests in an iodine environment. The exponentn of the relationshipda/dt = C · (K_l ⁿ was found to correlate with f_n for K_I, ranging from 4 to 17 MPa√m. Formerly Graduate Student, Department of Metallurgical Engineering, Inha University.     

Prediction of yield surfaces of textured sheet metals

To predict the yield surfaces of textured sheet metals, two methods were conducted. The first method (crystallographic yield surface) is based on the Taylor-Bishop-Hill (TBH) polycrystal model, using the orientation distribution function (ODF) of the material as an input. The second method (phenomenological yield surface) makes use of phenomenological yield functions based on mechanical test data. Anisotropic properties for six texture components typical of aluminum alloy sheets were examined and the results based on crystal plasticity were compared with the results based on phenomenological yield functions. The experimental anisotropy measurements obtained for an AA6xxx sheet were also compared to crystallographic and phenomenological predictions.     

Deformation and fracture behavior of beams composed of aluminum foam core and ceramic Al<Subscript>2</Subscript>O<Subscript>3</Subscript> under monolithic bending

Deformation and fracture mechanisms of sandwich and multilayer beams composed of aluminum foam core and ceramic face sheets under four-point bending condition were investigated in situ by surface displacement analysis (SDA) software. The toughening mechanism of the beams was discussed and a model was given for the computation of the fracture energy of the beams. Beams containing foam core with 5-, 10-, and 20-mm thickness and Al₂O₃ face sheets of 0.5- and 1-mm thickness were prepared. The results show that collapse of the beams is by two basic modes, indentation (ID) and face plate failure (PF). The SDA results illustrated that indentation is localized compression on the portion of the beam adjacent to the loading rollers, where displacement and strain are at the maximum. In PF, the beam entirely bends. It is also found that before collapse of the beams with pure PF mode, the foam core undergoes uniform compressive deformation, which contributes most to the fracture energy of the beams. As for the beams with ID characteristic, the localized compressive deformation plays a key role rather than the uniform compressive deformation in the fracture energy of the beam. The total fracture energy W of a beam under bending condition is proposed as

R values of fiber-textured tantalum plates

Computations have been made of the effect of crystallographic texture on the R values in sheets of bcc metals with an upper-bound model based on t<111t> pencil glide. Sheets having [111] and [100] textural components with rotational symmetry about the sheet normal were considered. The predicted R values increase with the fraction [111] component up to a maximum of about 3 for pure [111]. Experiments were made on disks of tantalum produced by upsetting of rods, which produced textures having rotational symmetry about the disk normal. X-ray diffraction showed mixed [111] and [100] textures, with the fraction of [111] varying from about 34 to 96 pct. R values were measured in tension and compression tests on these sheets, and their dependence on fraction [111] agrees very well with the theoretical predictions.     

X-Ray elastic constants in textured Zr-base materials

A general method for the calculation of the X-ray elastic constants (XREC) for textured hexagonal close-packed (hcp) materials was developed by using the orientation distribution function (ODF) and the Reuss hypothesis. This method was applied to textured zirconium (Zr) sheets and zircaloy 4 (Zry 4) extruded tubes. For these samples, where the elastic anisotropy is not very strong, an “isotropic approximation” method is proposed using the ODF data. In that case, the classical XREC 1/2S₂ and S₁ values are calculated and experimentally verified for {10-14} diffracting planes. Theoretical XREC values are also given for different hkil that could be chosen according to the experimental conditions, considering texture effects on diffracting peak intensities. Formerly with ENSAM     

Correlation of Surface Roping with Through-Thickness Microtextures in an AA6xxx Sheet

Strain-induced surface roughness was quantitatively correlated with microtexture spatial distributions from the surface to the midthickness of a strongly roping AA6016 sheet. The microtexture variations through the sheet were measured by acquiring a series of large area electron backscatter diffraction (EBSD) scans at intervals of about the grain size. The orientations of the different layers were translated into out-of-plane strains using a crystal plasticity model for comparison with the surface roping. The spatial distributions (particularly the characteristic wavelengths) of the microtexture layers were determined by areal auto-correlation functions, and quantitatively compared to the surface appearance by correlation coefficients. The results show that texture banding of Cube/Goss components along the rolling direction is present from the surface to midthickness but with significant variations from one grain layer to another. The wavelength correlation coefficient exhibits a maximum at about 55 μm, or 2 grain thicknesses, below the surface. It is shown that the spatial distribution of Cube/Goss components of the first three or four surface grain layers plays an important role in strong roping of AA6016 sheets.     

Acoustoelastic determination of the higher order orientation distribution function coefficients up tol = 12 and their use for the on-line prediction ofr-value

The higher order orientation distribution function (ODF) coefficients up tol = 12 in cold-rolled and annealed sheet steels were evaluated and calculatednondestructively from the anisotropy of the ultrasonic velocities of the lowest order symmetrical Lamb (S₀) and shear horizontal (SH ₀) waves propagating in the rolling plane. The elastic energy method was employed, together with a decomposition of the texture into the principal preferred orientations, following a procedure originally developed for Young’s modulus data obtained destructively. Plastic strain ratios are estimated using the series expansion method, in conjunction with a relaxed constraint (pancake) grain interaction model. Ther- value predictions based on the ODF coefficients obtained in this study are compared with tensile data and with empirical predictions made using the Modul-r approach. Formerly with the Department of Metallurgical Engineering, McGill University     

Structural states of aluminum-lithium alloy 1469 sheets

The texture and microstructure of the central layers in alloy 1469 sheets and the orientations of hardening T₁-phase precipitates are studied by X-ray diffraction, optical microscopy, and transmission electron microscopy. These studies and X-ray diffraction performed in asymmetric geometry demonstrate that the texture of the material is formed by the broadening of the orientations located near a β skeleton line. The contribution to an X-ray diffraction pattern from two of the four possible versions of the orientations of hardening T₁-phase plates that are caused by a brass-type texture component in the matrix and the orientation relationships between the matrix and the T₁-phase lattices is separated. The microstructure of the sheets is shown to have a two-level character. It is formed by extended (up to several millimeters long) regions fragmented into grains several microns in size. The structural states of the sheet material are discussed in their relation to the crystallographic character of fatigue crack propagation.     

The Effect of Heat Treatment on the Mechanical Behavior of Commercially Pure Titanium and Zirconium Under Quasi-static and Dynamic Loading

The mechanical properties (stress–strain behavior) of three hexagonal metals, two grades of commercially pure titanium (CP-Ti) and zirconium (CP-Zr), are systematically characterized before and after heat treatment. Those materials are investigated under quasi-static (< 1 s⁻¹) and dynamic (> 2000 s⁻¹) tension, compression, dominant, and pure shear to draw general conclusions as to the effect of the same heat treatment and, specifically, dynamic shear failure propensity in those hexagonal materials. The results do not reveal any consistent influence of the texture on the overall quasi-static and dynamic mechanical (stress–strain) response of the investigated materials. However, when the propensity to dynamic shear failure is specifically considered, it appears that texture variations of the CP-Ti grades have more influence than purely microstructural changes resulting from the heat treatment for both materials. When no other changes than grain growth are induced, such as in the case of CP-Zr, it appears that grain growth does not significantly affect the dynamic shear failure toughness of this material. It therefore seems like no general conclusions can be drawn as to the effect of heat treatment and associated texture changes of these three hexagonal metals on their mechanical and failure properties. Thus, despite their common crystallographic features, those materials must be considered individually rather than as belonging to the general family of hexagonal metals.

     

Diffusion of titanium in copper

Interdiffusion coefficients in copper-titanium alloys have been determined by Matano's method in the temperature range between 973 and 1283 K on (pure Cu)-(Cu-1.98 at. pct Ti alloy) and (pure Cu)-(Cu-2.91 at. pct Ti alloy) couples. Temperature dependence of the impurity diffusion coefficient of titanium in copper, determined by extrapolation of the concentration dependence of the interdiffusion coefficient to zero mole fraction of titanium, is expressed by the following Arrhenius equation along with the probable errors:D _Ti/Cu=(0.693 _−0.135 ^+0.169 )×10⁻⁴exp[−(196±2)kJ mol⁻¹/RT] m²/s. The difference in the activation energies for the impurity diffusion of the 3d-transition metals and self-diffusion in copper has been calculated by applying LeClaire's model with the oscillating potential of the impurity atom in copper. The calculated values agree well with the experimental values including the present one. Kazutomo Hoshino, formerly Graduate Student, Tohoku University     

Evaluation of the normal anisotropy coefficient in AZ31 alloy sheets

The Taylor-Bishop-Hill model of plastic deformation is used to determine the dependence of normal anisotropy coefficient R on angle α in the sheet plane (α = 0 in the rolling direction) from texture in the form of the coefficients of expansion of an orientation distribution function into a series in generalized spherical functions for AZ31 magnesium alloy sheets. The calculated values of R(α) are compared to the experimental values obtained during tensile tests under normal conditions (20°C) and at 180°C.     

Microtexture Development of Niobium in a Multilayered Ti/Al/Nb Composite Produced by Accumulative Roll Bonding

Multilayered Ti/Al/Nb composites were produced by the accumulative roll bonding (ARB) process utilizing pure Ti, Al, and Nb element sheets. Up to four cycles of ARB were applied to the composites. The microstructure and texture evolution on the Nb phase were studied by X-ray diffraction (XRD), transmission electron microscopy, scanning electron microscopy, and electron backscattered diffraction. Nb and Ti layers necked and fractured as the number of ARB passes increased. After four ARB cycles, a nearly homogeneous distribution of Nb and Ti layers in Al matrix was achieved. As-received Nb sheet exhibited a fully lamellar structure and had a strong cold-rolling texture. After subjecting to ARB, slight grain refining was observed and the high-angle boundary fraction was increased. The intensity of the α-fiber was weakened, while that of the γ-fiber was strengthened during ARB. The texture evolution was attributed to partial recrystallization during the ARB process as a result of adiabatic heating.