Structure of deformed polycrystalline zirconium carbide

Numerous studies have been conducted on the transition metal carbides for establishing the regularities of their plastic deformation [1, 2]. However, the relationship between the evolution of the deformation microstructure, the structural changes occurring at the micro-and the macrolevels, and the mechanical properties of the polycrystalline materials has not been investigated in sufficient detail. In view of this, we studied the dislocation structure of ZrC_x at different stages of deformation and over a wide range of temperatures and related the structural characteristics with the changes occurring in certain mechanical properties.Translated from Poroshkovaya Metallurgiya, No. 12 (360), pp. 72–77, December, 1992.     

The recrystallization characteristics of moderately deformed aluminum

The early stage of isothermal recrystallization of moderately deformed, polycrystalline alloys of zone-refined aluminum containing 20 and 45 at. ppm of Au has been studied by quantitative metallography. The basic structural parametersX _v , the volume fraction recrystallized, andS _v , the grain boundary area per unit volume, were measured on specimens annealed for different times at specific temperatures in the range 80° to 187°C. Both the maximum, G _m , and the average, \(\bar G\) , growth rates of the recrystallizing grains were also determined. All results could be interpreted in terms of a site-saturated, matrix grain edge nucleation at zero time with subsequent two-dimensional growth perpendicular to the nucleated edge controlling recrystallization kinetics. An equation relatingS _v toX _v was derived and found to describe the experimental data quite well. Experimentally, the ratio \(G_m /\bar G\) was 2.6 and the activation energy for growth was 25,700 cal per mole.     

The basic concepts of texture investigation in polycrystalline materials

Polycrystalline materials consist of grains which may have different sizes, shapes and arrangements to be observed under the microscope as well as different crystal orientations observed by diffraction methods. The orientation parameters of the crystallites are subsumed under the term texture. The main textural quantities are the orientation distribution function ODF of the crystallites and the misorientation distribution function MODF of grain- and phase boundaries. Textures are being formed in materials by all kinds of anisotropic solid state processes and they have influence on all kinds of anisotropic material properties. Textures can be measured grain-by-grain or using polycrystal diffraction methods. The appropriate radiations are X-rays, electrons and neutrons. Finally, some examples are given concerning martensitic transformation in FeNi-alloys, shape memory alloys, cross-rolling of Armco-iron, biaxially stretched polyethylene, and HT_c superconductors.     

Deformation texture of channel-die deformed aluminum bicrystals with S orientations

The evolution of crystal lattice orientations in two aluminum bicrystals with S orientations, during channel die compression has been studied in detail. The boundary planes of the bicrystals were parallel to the plane of compression. The textures developed in each component crystal and at the boundary between the two crystals were examined as a function of deformation. In one of the bicrystal assemblies, the initial orientations of the component crystals were found to be unstable. They rotated to a common orientation. Hence, the bicrystal boundary, initially high angle in nature, became a low angle boundary. In the other bicrystal, the initial orientations of the component crystals were found to be largely stable. Except for some minor orientation adjustments, they remained essentially in their initial orientations, and the bicrystal boundary retained its high angle misorientation. Results of theoretical analyses using a numerical model appear to explain the texture development and the behavior at the boundary of the bicrystals very satisfactorily.     

Observation of cold-rolling texture and partially recrystallized texture in polycrystalline 3 pct Si-Fe by high-resolution electron backscattered diffraction

Cold-rolling texture and partially recrystallized texture of polycrystalline 3 pct Si-Fe were investigated using high-resolution electron backscattered diffraction (EBSD) method. From the measurement on a deformed grain with {211}〈011〉∼{111}〈011〉 orientations, deformation bands with {12 4 1}〈014〉 orientation were found. It turned out that the orientation rotation relationship between deformation bands and surrounding deformed grain can be explained by the activation of the slip system, which has a common slip plane with an adjacent grain. Oriented nucleation of recrystallized grains with {12 4 1}〈014〉 orientation was observed in a deformed grain with {211}〈011〉∼{111}〈011〉 orientation. Exactly the same orientation relationship that was observed between deformed grain and the deformation bands was also observed between the deformed grain and the recrystallized grain. A hypothesis that recrystallization nuclei are generated directly from the deformation bands formed by an activation of the slip system that has a common slip plane of neighboring deformed grains was proposed from the present experimental results.     

X-ray diffraction study of a bulk,polycrystalline Ag-9 at. pct Sn alloy deformed in compression

An analysis was made of X-ray powder pattern peaks from a bulk, polycrystalline Ag-9at. pct Sn alloy that was plastically deformed by compression. The shapes and positions of all available (hkl) reflections were recorded using the focusing, Bragg-Brentano X-ray geometry. Fourier analysis of the profiles were carried out on (111)–(222), (200)–(400), and (220)–(440) pairs of reflections. The effective particle sizesD _e (hkl) decreased rapidly with increasing deformation and reached values ofD _e (111)=110Å,D _e (100)=40Å, andD _e (110)=90Å beyond 20 pct reduction in thickness. The anistropy of the particle sizes is interpreted as a consequence of faulting in the deformed alloy. The mean square strains in the [111] direction were of the order of 10^?5 after more than 20 pct reduction in thickness. Lattice parameter measurements yield the deformation fault probability (α≈0.02), and the residual stresses. The variation of the true lattice parametera _o with increasing deformation indicated that segregation occurred in the deformed alloy. From the ratio of 〈ε²〉/α (≈ 6 × 10^?4), a nominal stacking fault energy of 6 erg per sq cm was calculated.     

A variant selection model for predicting the transformation texture of deformed austenite

The occurrence of variant selection during the transformation of deformed austenite is examined, together with its effect on the product texture. A new prediction method is proposed based on the morphology of the austenite grains, on slip activity, and on the residual stresses remaining in the material after rolling. The aspect ratio of pancaked grains is demonstrated to play an important role in favoring selection of the transformed copper ({311}〈011〉 and {211}〈011〉) components. The extent of shear on active slip planes during prior rolling is shown to promote the formation of the transformed brass ({332}〈113〉 and {211}〈113〉) components. Finally, the residual stresses remaining in the material after rolling play an essential part by preventing growth of the {110}〈110〉 and {100}〈uvw〉 orientations selected by the grain shape and slip activity rules. With the aid of these three variant selection criteria combined, it is possible to reproduce all the features of the transformation textures observed experimentally. The criteria also explain why the intensities of the transformed copper components are sensitive to the pancaking strain, while those of the transformed brass are a function of the cooling rate employed after hot rolling.     

Dislocation structure and work hardening in polycrystalline ofhc copper rods deformed by torsion and tension

The dislocation structure during work hardening in copper deformed by torsion and tension is investigated by X-ray line broadening and TEM. In the case of torsion the equivalent tensile flow stress and the rate of work hardening is lower than that obtained in tensile experiments. At the same time the dislocation density at the same equivalent strain is considerably larger in the torsionally deformed material and the TEM microstructure indicates a double-slip deformation mechanism. In the tensile deformed samples asymmetric X-ray line broadening indicates long-range internal stresses with relatively lower dislocation densities. In this mode of deformation multiple slip takes place. The lower equivalent flow stress and the smaller rate of work hardening in the torsionally deformed material is correlated with the restricted number of slip systems and the absence of strong long-range internal stresses, which leads to the relative ease of generating high dislocation densities.     

Microstructure and texture effect on the thermal expansion of a variously aged polycrystalline superalloy IN738LC

Thermal-expansion measurements of a suitably heat-treated and aged polycrystalline superalloy, IN738LC, with various γ′ (Ni₃(A1, Ti, Nb)) precipitate microstructures and annealing textures, were carried out using procedures given in ASTM E228. The preferred orientation (PO) and elasticity modulus of the alloy under the different microstructural conditions are correlated to the thermal expansivity obtained. Thermal expansion was found to decrease with decreasing γ′ precipitate size. The microstructures with coarse and medium-sized precipitates, with the 〈100〉-PO (soft directions in the fcc Ni-based alloys) and low elasticity modulus values, yield the highest thermal expansion. The microstructure with fine-sized precipitates has a lower expansion coefficient at all temperatures, while the duplex-size (fine + medium) precipitate microstructure and the single-phase solution-treated, supersaturated solid solution (SSS) condition show the lowest expansion coefficients. The low expansivity is attributed to the prevalence of the 〈111〉 and/or 〈131〉 POs in these specimens for the matrix phase and the expansion being along these relatively harder directions. Internal constraints to expansion, which determine dα/dT, are postulated to result from dislocation substructures present in the microstructural constituents and at the precipitate-matrix interface.     

An electron-backscattered diffraction study of the texture evolution in a coarse-grained AZ31 magnesium alloy deformed in tension at elevated temperatures

Electron-backscattered diffraction (EBSD) has been used to investigate the texture evolution during tensile deformation at temperatures between 673 and 773 K of a coarse-grained commercial AZ31 magnesium alloy. A weak (0001) fiber texture was initially present in the hot-rolled magnesium alloy plate. The [0001] directions of the grains spread 0 to 45 deg around the normal direction (ND) of the magnesium alloy plate. This pre-existing weak texture evolved during tensile deformation into a strong texture close to the {0001} 〈1 00〉. The [0001] directions of the grains rotated toward the orientations perpendicular to the tension axis of the samples, indicating that the 〈11 0〉 slip system appeared to be the most active slip system, especially in the early stages of deformation. The EBSD Schmid-factor analysis revealed that, however, with an increase in strain and the rotation of the (0001) slip plane, the {11 2} 〈11 〉 slip system appeared to be more favorable. The {1 00} 〈11 0〉 and {1 01} 〈11 0〉 slip systems remained favored throughout the strains investigated, indicating that {1 00} and {1 01} are two important slip planes for cross slip using the 〈11 0〉 slip vector. It is found that the misorientation across one coarse grain (as high as 38.2 deg) is accommodated by low-angle grain boundaries (LAGBs). The formation of these LAGBs may be an intermediate stage of the coarse grain refinement that occurred during deformation. This article is based on a presentation made in the symposium entitled “Processing and Properties of Structural Materials,” which occurred during the Fall TMS meeting in Chicago, Illinois, November 9–12, 2003, under the auspices of the Structural Materials Committee.     

Effects of symmetry,texture and topology on triple junction character distribution in polycrystalline materials

Studies of triple junctions in f.c.c. polycrystalline material were carried out analytically and by computer modelling. An analysis of triple junction symmetry identified a group of triple junctions having at least a common axis, along with a subgroup of triple junctions having symmetry axes as common axes. Frequencies of occurrence of Coincident Axial Direction and Coincident Site Lattice triple junctions are assessed in both randomly oriented and fibre textured materials. Distributions of I- and U-line triple junctions are evaluated in randomly oriented and fibre textured materials, and in polycrystalline materials composed of CSL grain boundaries. Finally, and optimal three-dimensional polycrystalline material is proposed from a topological point of view.     

Apparent contrast and spatial frequency of local texture elements

We measured the apparent contrast and spatial frequency of a parafoveal Gabor signal located at the center of an array of Gabor signals as a function of both element density and the direction of contrast and spatial frequency of the surrounding elements. The target Gabor appeared lower in contrast and higher in spatial frequency when the elements were in close proximity, regardless of the direction of contrast and spatial frequency of the surrounding elements. Overall, the evidence suggests that the appearance of a parafoveal target is strongly affected by its visual context. These findings provide additional support for the existence of spatial interactions among neurons implicated in textural processing.     

Effects of grain interactions on deformation and local texture in polycrystals

Detailed simulations of grain deformation and crystal orientation evolution in a small region at the interior of polycrystal have been performed. The finite element model accounts for deformation by crystallographic slip and for crystal lattice rotation with deformation. The initial shapes and orientations of the grains and the crystal hardening relations were determined from polycrystalline aluminum samples. The results clearly demonstrate the effects of grain interaction on local deformation and texture evolution. A comparison of the predicted lattice orientations with results from plane strain compression experiments shows good agreement for some of the grains and little agreement for others. Part of the discrepancy results from kinematic restrictions which were necessary to model the 3D microstructure with 2D models. The model shows very nonuniform strain fields and provides detailed information on grain interactions.     

Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning

The face number, the volume, and the surface area (boundary area) of grains are measured in recrystallized α-iron by serial sectioning coupled with quantitative microstructural analysis on two-dimensional (2-D) sections. The sampling volume contained approximately 1000 grains whose mean grain size was ∼15 μm. The grain volume distribution decreased monotonously with increasing grain volume, whereas the surface area had a peak around one-half of the average. The distribution of the sphere equivalent radii significantly deviated from the log-normal distribution and distributions predicted from mean field theories. The peak and the mean of the face number distribution were f=11 and 12.1, respectively. The linear relationship between the face number of a central grain and the mean face number of surrounding grains, known as the Aboav-Weaire law, was observed in three dimensions. The mean radius of f-faced grains was not proportional to the face number (perimeter law in 3-D), but appeared to be related by a curve convex upward. This article is based on a presentation made at the symposium “Characterization and Representation of Material Microstructures in 3-D” held October 8–10, 2002, in Columbus, OH, under the auspices of ASM International’s Phase Transformations committee.     

Recovery of heavily cold-rolled aluminum: Effect of local texture

Commercial-purity aluminum, AA1200, was cold-rolled to a true thickness strain of 2 and annealed at low temperatures. The microstructural evolution and the changes of the rolling, cube, Goss, and other texture components were characterized thoroughly by transmission electron microscopy. Both the deformation microstructure and the annealing behavior were found to be texture dependent. In the deformed structure, texture components other than the rolling, cube, and Goss showed a broader orientation spread as well as a larger content of stored energy. Structural coarsening took place during the annealing and depended on the local texture environment. Other texture components showed more pronounced coarsening than the rolling components. The orientational heterogeneity in the deformed structure influenced the heterogeneous structural coarsening during the recovery.     

A new approach in texture research: local orientation determination with EBSP

A new technique for convenient measurement of crystallographic orientation of small volumes in bulk samples is introduced. It makes use of electron back scattering patterns (EBSP) in the SEM. The principle of pattern formation as well as measuring and evaluation procedure are introduced. The method offers a viable procedure for obtaining information on the spatial arrangement of orientations, i.e. on orientation topography and thus, provides a new level of information on crystallographic texture. The application of EBSP is demonstrated by two examples, namely for investigation of nucleation of recrystallization and microstructure evolution during high-temperature fatigue.     

Characterization of the spatial-frequency spectrum in the perception of shape from texture

The major cue to shape from texture is the compression of texture as a function of surface curvature [J. Exp. Psychol. 13, 242 (1987); Vision Res. 33, 827 (1993)]. A number of computational models have been proposed in which compression is measured by detection of changes in the spatial-frequency spectrum [Comput. Graphics Image Process. 5, (1976)]. We propose that the visual system uses a strategy of characterizing the frequency spectrum by a simple set of measures and of tracking the changes in this characterization rather than determining changes in the shape of the actual spectra. Our evidence is based on a number of psychophysical demonstrations that use stimuli with specifically tailored frequency spectra, constructed from white noise filtered in the frequency domain. Our evidence suggests that the visual system determines the average peak frequency of the spectrum and uses this measure as its characterization. Changes in fp are strongly correlated with the degree of surface curvature, and, over a range of stimuli, fp takes account of the variance in local estimates of the frequency spectrum. One computes fp by determining the peak frequency at each spatial location and then averaging these frequency values over a local spatial region. We show that fp is related to the second-order moment but is more biologically plausible and shows superior ability to function in the presence of noise. As a test of this model, we have constructed a neural network architecture for computing shape from texture. Our model is limited to orthographically projected, homogeneous textures without in-surface rotation. The early stages of the model consist of multiple simple-cell units tuned to different orientations and spatial frequencies. We show that these simple cells are inadequate for the determination of compression but that the outputs of complex-cell-like units after normalization generate estimates of surface slant and tilt. The network shows qualitative agreement with human perception of shape from texture over a wide range of real and artificial stimuli.