studies of deformation-induced texture development in sheet materials using diffraction techniques

$: Studies of deformation-induced texture development in sheet materials using diffraction techniques$
Materials Science and Engineering A 380 (2004) 155–170

Studies of deformation-induced texture development insheet materials using diffraction techniques

S.W. Banovica,∗, M.D. Vaudinb, T.H. Gnaeupel-Heroldc, D.M. Saylorb, K.P Rodbelld

a Metallurgy Division, Department of Commerce Gaithersburg, National Institute of Standardsand Technology Technology Administration, Gaithersburg, MD 20899, USA

b Ceramics Division, Department of Commerce Gaithersburg, National Institute of Standards andTechnology Technology Administration, Gaithersburg, MD 20899, USA

c Center for Neutron Research, Department of Commerce Gaithersburg, National Institute of Standards andTechnology Technology Administration, Gaithersburg, MD 20899, USA

d IBM, T.J. Watson Research Ctr. MS 05/225/P.O. Box 218 Yorktown Heights, NY 10598, USA

Received 4 September 2003; received in revised form 18 March 2004

Abstract

Crystallographic texture measurements were made on a series of rolled aluminum sheet specimens deformed in equi-biaxial tension up toa strain level of 0.11. The measurement techniques used were neutron diffraction with a 4-circle goniometer, electron backscatter diffraction,conventional powder X-ray diffraction (XRD), and XRD using an area detector. Results indicated a complex texture orientation distributionfunction which altered in response to the applied plastic deformation. Increased deformation caused the{1 1 0} planes, to align parallel to theplane of the sheet. The different techniques produced results that were very consistent with each other. The advantages and disadvantages ofthe various methods are discussed, with particular consideration of the time taken for each method, the range of orientation space accessible,the density of data that can be obtained, and the statistical significance of each data set with respect to rolled sheet product.© 2004 Elsevier B.V. All rights reserved.

Keywords:Crystallographic texture; Neutron diffraction; X-ray diffraction; Electron backscatter diffraction; Sheet metals; Formability

1. Introduction

As many physical and mechanical properties of polycrys-talline materials are highly dependent upon the orientationdistribution of the crystallites in the bulk, it is importantto understand the evolution of preferred crystallographicorientation, or texture, due to processing conditions. Un-derstanding this is also crucial in optimizing subsequentprocessing procedures to help predict and improve finalproduct performance. Preferred orientation or crystallo-graphic texture, which strongly influences the anisotropyof material properties, frequently develops as a result ofmechanical deformation and thermal heat treatments. Asobserved in rolled sheet products, both morphological andcrystallographic anisotropy can be observed. Morphologi-

∗ Corresponding author.E-mail address:[email protected] (S.W. Banovic).

cal anisotropy is caused by variations in the grain size orshape, while crystallographic anisotropy arises from pre-ferred orientations of these constituents. These microstruc-tural anisotropies have been found to affect the propertiesof rolled sheet product in terms of the forming limits[1–4],drawability (e.g., earring)[4–7], as well as various sur-face characteristics[1,8–11]. Many different techniques areavailable to analyze the texture of materials using variousdiffraction methods, including neutron, X-ray, and electronsystems. The choice of technique is typically chosen basedupon what is available within the facilities, the cost of theanalysis, the physical and chemical characteristics of thespecimen, and the objective of the examination (surfaceversus bulk texture). The goal of this work is two-fold: (i) todetermine experimentally the influence of in-plane strainingon the evolution of texture development in aluminum sheetmetal; and (ii) to compare the results obtained betweenthree different methods of texture analysis: neutron diffrac-tion, X-ray diffraction (XRD), and electron backscatterdiffraction.

0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.msea.2004.03.084

156 S.W. Banovic et al. / Materials Science and Engineering A 380 (2004) 155–170

2. Description of techniques

The crystallite orientation data collected in this study areprimarily in the form of pole figures, which describe thedistribution of a specified crystal plane with respect to afixed sample coordinate system. When possible, data arerepresented in multiples of random distribution (MRD). TheMRD at a particular point is simply the ratio of the volumeof grains oriented such that the (h k l) pole coincides withthe direction of the scattering vector to the volume expectedif the grains were randomly distributed. To express the data,it is necessary to define the angles and coordinate systems.Throughout this paper, an attempt has been made to use aconsistent set of names to limit confusion, as the various ex-perimental techniques discussed traditionally employ differ-ent symbols for the various angles of importance. Rotationabout the sample normal is designated byϕ. Rotation aboutan axis in the sample plane has been denoted by many dif-ferent symbols (e.g.,χ, ω, ψ), depending on the orientationof the axis relative to the diffractometer.ω has been chosenfor this angle (the so-called polar angle). The sample coor-dinate system is defined as having thex-axis parallel to therolling direction (RD), they-axis parallel to the transversedirection (TD), and thez-axis parallel to the normal direc-tion (ND) of the sheet material.

2.1. Neutron diffraction technique

The neutron diffraction technique quantifies the textureby measuring the distribution of diffracted intensity from aparticular crystal plane (h k l) depending on the orientationof the specimen. The crystal plane is selected by positioningthe detector at the angle 2θ as given by Bragg’s law

nλ = 2dhkl sinθ (1)

wheredhkl is the (h k l) plane spacing,λ is the neutron wave-length, andn is an integer. For this technique, the reflectedintensity is proportional to the total illuminated volume ofgrains that are oriented such that the normal of the plane(h k l) coincides with the direction of the scattering vector.The scattering vector is in the direction of the bisector of theangle between the incident and the reflected neutron beam.The size of the incident beam is such that the specimenis completely bathed in the beam at all specimen orienta-tions. The reflected beam intensity is measured using a posi-tion sensitive proportional counter capable of recording theentire peak profile simultaneously. For the aluminum cubespecimen, 5 mm on a side, used as the example throughoutthis paper, the absorption is negligible so that effectively allgrains of that specific orientation contribute to the diffractedintensity at that orientation.

As neutrons interact relatively weakly with matter, theycan easily penetrate through many millimeters of material.Thus, the diffracted signal is weak, requiring fairly long mea-surement times. However, the entire specimen contributesto the signal, so that the average texture of the entire spec-

imen is measured. For a sample with an ASTM grain sizeof 7.5, the number of possible contributing grains is >106

in neutron diffraction. Additionally, there are no correctionsfor defocusing required because the diffracted intensity orig-inates from the entire volume of the specimen rather thanits surface. This also implies that in neutron diffraction ev-ery angle, includingω = 90◦ is accessible. The use of amulti-wire detector simplifies the measurement even further,because it captures the entire diffraction peak plus the back-ground regions on both sides of the peak. The backgroundis determined individually for each orientation (ω, φ) by apeak fitting procedure. The intensity value is equal to thetotal number of counts minus the background counts.

If a homogeneous specimen can be produced with a suffi-cient volume and a clearly defined specimen reference frame(for this case, RD, TD, and ND), then neutron diffractionhas hardly any disadvantages. There are no special sam-ple preparation techniques required. For sheet metal, how-ever, individual pieces must be stacked together to obtainenough scattering volume. Small misalignments betweenthese pieces are likely and may results in very sharp tex-tures being “washed out” if the misalignment is significant.As the minimum sample volume is≥8 mm3, this techniqueis unsuitable for thin films or thin sheets.

2.2. Electron backscatter diffraction technique

Electron backscattered diffraction (EBSD)[12,13] istypically performed using a scanning electron microscope(SEM). This technique involves focusing a narrow beamof low energy electrons, similar to that used for imaging,onto a grain on a polished specimen surface. Followingone or more quasi-elastic collisions within the sample, thebackscattered electrons emerge from the surface to form apattern that can be imaged on a phosphorus screen withinthe SEM chamber. This EBSD pattern is produced whenseveral pairs of diffraction cones, whose cone axes arenormal to the diffracting planes in the analyzed crystal,intersect the screen in a series of geometrically arrangedbands, also referred to as Kikuchi bands. A camera locatedoutside the chamber is used to import the image into oneof numerous commercially developed software programs.The geometry of the Kikuchi bands is then determinedautomatically by the software through the use of a Hough(or Radon) transform. Finally, using the band geometry,the software solves for a set of three Euler angles (φ) [14]which specify the orientation of the crystallite with respectto the sample coordinate system.

One important attribute of this technique is the ability toconduct orientation analyses of specific microstructural fea-tures. This is due to the ability to direct a relatively smallprobe (�100 nm diameter) onto the sample and determinethe orientation of a single element within a polycrystallinematerial. In addition to the single point analysis, raster scanscan be conducted automatically over large areas of the mi-crostructure, which allows the microtexture of the sample’s

S.W. Banovic et al. / Materials Science and Engineering A 380 (2004) 155–170 157

surface to be quantified. Depending upon the software uti-lized, various methods of displaying the crystal orientationdata are possible, ranging from orientation maps to direct orinverse pole figures to full orientation distribution functions(ODFs).

The time required to process and index an individual pointhas decreased with an increase in software capabilities andcomputing power. The analysis directly depends upon thesoftware parameters set to analyze and index the pattern,with typical times being considerably less than 1 s per pat-tern. One factor that can effect the analysis time is the qual-ity of EBSD patterns, which is strongly dependent uponthe condition of the surface. As the information from thediffracted electrons comes from within the top few hundrednanometers of surface material, the preparation of the speci-men surface prior to analysis is extremely important and ma-terial dependent. For this analysis, it was observed that alu-minum is one of the more difficult materials to prepare duein part to: (1) the low hardness of aluminum which yieldsa deeper deformation layer near the surface subsequent tobeing worked, and (2) its lower density which allows fordeeper penetration of the electrons into the specimen and,consequently, fewer backscattered electrons.

2.3. XRD technique

A technique has been developed at NIST for quantitativemeasurement of texture using scans performed on a con-ventional 2-circle diffractometer[15]. Similar to the proce-dures employed in many other texture analysis methods, aθ scan from the textured specimen is divided by aθ scanfrom an untextured sample of the same material. This givesthe texture profile in MRD as a function of the polar an-gle,ω, given byω = θ − θB, whereθB is the Bragg angleof the peak. The innovative aspect of the new data analysismethod is that theh k l θ scan from the untextured sampleis calculated, not measured, thus, removing the need for theuntextured sample, which is frequently difficult to obtain.The data required for the untexturedθ scan calculation arethe optics of the diffractometer and aθ to 2θ scan of theh k l peak taken from the textured sample. The calculationaccounts for the following: purely geometrical factors, suchas the variation in irradiated area with incident beam angleand the effect of absorption; and the effect of defocusing,which is the variation in scattering angle at different parts ofthe irradiated specimen surface when the specimen is tiltedout of the symmetrical orientation. Thus, the random inten-sity at a particularθ is proportional to an integral over theBragg peak scan, with the integration limits 2θ− and 2θ+being functions ofω and 2θB. The experimentalθ scan fromthe textured sample is divided by the calculatedθ scan froma random specimen. Then,θ is transformed to the polar an-gle,ω, thus, giving theω texture profile of the sample whenrotated about the axis of the diffractometer.

Since, the technique employs a 2-circle diffractometer,for which 0< θ < 2θB, ω is limited to an angular range of

−θB to θB. Thus, it is best suited to the analysis of relativelysharp axisymmetric (fiber) texture, although the selection ofa high angle Bragg peak allows a relatively large orientationrange to be probed. In the case of rolled Al sheet, where thetexture is complex and not sharply peaked, the main advan-tages offered by the method are its speed (on the order ofhalf an hour total data collection time per correctedω scan),precision, and ease of application. The method allows for alarge number of data points to be collected in a limited re-gion of orientation space in a relatively short time. Typicalω steps, are 0.2◦ as opposed to 5◦ for neutron and X-ray4-circle diffractometry. The software used to perform thecalculations was developed at NIST and is presently avail-able on the World Wide Web in a Windows-based packagecalled TexturePlus[16].

3. Experimental procedure

Table 1gives the chemical composition of the commer-cially available aluminum alloy 5052 H32 sheet (1 mm nom-inal thickness) that was obtained for testing. Straining ofthe as-received sheet was conducted under an equi-biaxialmode using a modified Marciniak in-plane stretching test. Adetailed description of the experimental equipment[17] andprocedure[8] can be found elsewhere. Varying amounts ofin-plane stretching were obtained by setting the limit con-trol of the central ram (Marciniak tooling) to predetermineddeflections. The true in-plane strain was determined by mea-suring the change in diameter of a stenciled circle alongthree directions lying in the rolling plane: parallel, perpen-dicular, and 45◦ to the RD of the sheet. The texture of thesheets was evaluated using techniques that employ three dif-ferent probing radiations: (1) neutron diffraction; (2) EBSD;and (3) XRD.

For the neutron diffraction studies, experiments were con-ducted at the NIST Center for Neutron Research. Samplesizes were 5 mm on a side, stacked five high, which resultedin the beam irradiating approximately 125 mm3 of mate-rial. The samples were mounted in the center of a 4-circlediffractometer with the RD parallel to the beam. The beamhad a wavelength of 1.884 Å. Pole figure data for three re-flections, 1 1 1, 2 0 0, and 2 2 0, were collected over an entirehemisphere of sample orientations ranging from 0◦ to 355◦in the azimuthal angle,φ, and 0◦–90◦ in the polar angle,ω,each in 5◦ steps[4]. Once the background had been sub-tracted from the raw data, the value at each observation pointwas normalized such that the values were represented inMRD.

Table 1Alloy composition, as mass fractions× 100, for aluminum alloy 5052H32

Mg Fe Cr Si Cu Mn Ni Ti Zn Al

2.50 0.40 0.22 0.23 0.10 0.09 0.01 0.05 0.06 Bal


Table 2Experimental conditions for X-ray machines

Machine Tube electric current (mA) Tube electric voltage (kV) Beam width (mm) Incident slit (◦) Receiving slit (◦) Diffracting radius (mm)

D500 30 40 8 0.68 0.6 200D5000 40 45 12 0.68 0.53 217

For the EBSD technique, the samples were first metallo-graphically prepared to 0.3�m alumina by hand, followedby 7 min of vibratory polishing in a slurry of 0.05�m col-loidal silica. Subsequent etching in Keller’s reagent for upto 30 s was conducted to improve pattern quality. A JEOL6400 scanning electron microscope, with a LaB6 tungstenfilament, was used to analyze the samples which were tilted68◦ with respect to the beam. Microscope conditions wereas follows: 20 kV accelerating voltage, magnification of 700times, and working distance of 28 mm. A 10× 10 matrixof single mapping scans, each consisting of a grid of 100points on a side with a step size of 1�m, were collectedand stitched together to form a single large dataset. This re-sulted in approximately 1× 106 analyzed points coveringapproximately 1800 grains in both the as received and de-formed samples. Total collection times were typically lessthan 8 h per sample, and the percentage of acceptable pat-terns ranged from 85 to 92%. Using these data, pole figuresfor the<1 1 1>,<2 0 0>, and<2 2 0> crystal directions weregenerated using a discrete binning approach. To accomplishthis, the range of spherical angles (ω, φ), representing thesample directions of the pole figure, are first divided intoequal sized angle bins (5◦). Next, for each orientation obser-vation, the sample direction parallel to the specified crystaldirection is determined, and the bin corresponding to thatsample direction is incremented by 1. This is performed forall of the symmetrically equivalent crystal directions. Theentire process is repeated until all successfully indexed ob-servation points in the raster scans have been added to the

Fig. 1. Cross-sectional micrograph of the sample with strain level of 0.104 showing the planes analyzed normal to the sheet.

appropriate bins. Once normalized for variations in cell area,the accumulated cell values give the relative volume of crys-tallites corresponding to each discrete pole figure direction.In other words, they are equivalent to the intensities deter-mined from neutron or XRD. Finally, as with the neutrondiffraction data, the intensities are renormalized such thatthe values in each bin is in units of MRD.

XRD experiments were conducted on three different ma-chines located in two laboratories. For data collected in theCeramics Division at NIST,θ to 2θ scans, andθ scans wereobtained on Siemens D500 and Siemens D5000 diffractome-ters. The former was equipped with a focusing Ge incidentbeam monochromator tuned to Cu K�1 radiation, whereasthe D5000 has a standard Cu K�1/�2 source. The experimen-tal conditions for operation of the two machines are found inTable 2and the particulars of the experiment are describedin detail elsewhere[15]. In both cases, collection steps of0.25◦ were used. These parameters resulted in a sampledarea of approximately 1 cm on a side with a maximum depthof approximately 50�m, thus allowing for a large area ofthe surface to be analyzed. Rocking curves, orω scans, forthe 1 1 1, 2 0 0, and 2 2 0 reflections were obtained by cor-recting theθ scans for defocusing and absorption using theTexturePlus software program described inSection 2.3. Thespecimen was oriented with the RD both in the diffractionplane and normal to it.

X-ray texture measurements were also performed at theT.J. Watson Research Center, using a Bruker GADDS (Gen-eral Area Diffraction Detector System), with a Cu K� ro-


tating anode source operating at 40 kV and 100 mA (BrukerAnalytical X-ray Systems, Madison, WI, USA). The BrukerGADDS system uses a stationary area detector to acquireX-ray intensities as the sample is rotated about the substratenormal. Gobel mirrors (crossed) were used to collimate theincident radiation to a beam diameter of 800�m. The valueof ω, the effective tilt angle during a normal texture mea-surement (Bragg–Brentano geometry), varied along the De-bye arcs of X-ray intensity. By combining information fromseveral measurements in whichφ is varied, a pole figure forthe diffraction peak of interest may be obtained. Fiber tex-ture plots were calculated from the pole figures by averagingthe pole figure information about the substrate normal andnormalizing the X-ray intensity such that the random grainorientation corresponded to a value of one MRD.

Serial polishing of the sheet was conducted to measurethe through thickness texture variation normal to the planeof the sample.Fig. 1 shows a metallographic cross-sectionindicating the various planes of the Al sheet that were ana-lyzed. Analysis of these planes, was achieved by removingapproximately 100�m of material parallel to the plane ofthe sheet using a tripod polisher and 6�m diamond paste ona low nap cloth. The samples were subsequently cleaned inacetone and rocking curves collected at each depth on theD500 diffractometer using the method described above.

The grain structure of the sheet was revealed through aconventional anodizing technique using a solution of 98 ml

Fig. 2. Normalized pole figure plots obtained via neutron diffraction for strain levels of: (a) 0 and (b) 0.104. The rolling and transverse directions areindicated. The lines A–B and A–C indicate the slices of data acquired by the X-ray diffraction technique for samples aligned parallel and perpendicularto the beam, respectively.

water and 2 ml of fluoboric acid (HBF). A stainless steelcathode was used with a pre-set voltage of 35 V dc. This re-sulted in an approximate current density of 2.0× 103 A/m2.The grain size was determined by a linear intercept method.The transverse aspect ratio was calculated by dividing thelength of the grain parallel to the transverse direction by thewidth of the grain parallel to the normal direction.

4. Results

4.1. Characterization of the Al sheet

The as-received microstructure consisted of grains thatwere relatively equiaxed in the plane of the sheet and elon-gated when viewed in the transverse direction.Table 3gives the average planar grain size and the transverse as-pect ratio. From these data, the geometric anisotropy of the

Table 3Average planar grain size and transverse aspect ratio, with standard de-viations, for samples of various strain levels

Strain level Average planar grainsize (�m)

Transverse aspect ratio

0.0 (as-received) 31± 9 1.9 ± 0.50.104 35± 13 4.0± 0.5


sheet is clearly evident. Second phase constituents werefound dispersed throughout the matrix as well as at thegrain boundaries. While the particles were not analyzed,the size, shape, and color suggested that they were mostlikely (FeCr)3SiAl12, Mg2Si, and other intermetallic phases[18]. Deformation of the sheets via the Marciniak in-planestretching test resulted in samples with true in-plane strainlevels of 0.000, 0.018, 0.036, and 0.104. The individual levelfor each sample was found to be extremely uniform with nostatistically significant difference along the three directionsmeasured parallel, perpendicular and 45◦ to the RD (i.e.,the initial stencil remained circular). After deformation, thegrains in the sheet were found to have further elongatedin the transverse direction.Table 3 shows that while theaverage planar grain size did not change dramatically, thetransverse aspect ratio was found to increase significantly.

4.2. Neutron diffraction analysis

Fig. 2 displays the normalized pole figure plots ob-tained from the neutron diffraction technique for strainlevels of 0.000 and 0.104. These plots reveal the overallchange in texture due to mechanical deformation underan in-plane, equi-biaxial mode. The as-received material,Fig. 2a, displayed a strong{2 0 0} component, typical ofa thermo-mechanically treated aluminum alloy sheet[19].With increasing strain in the material, the development ofa prominent{2 2 0} component and the decrease of the

Fig. 3. Normalized pole figure plots obtained using EBSD for strain levels of: (a) 0 and (b) 0.104. The rolling and transverse directions are indicated.

{1 1 1} and {2 0 0} components were observed. In addi-tion, {2 0 0} type planes were found to be more uniformlydispersed perpendicular to the sample normal after defor-mation (Fig. 2b). In all plots, near perfect orthorhombicsample symmetry was observed.

4.3. Electron backscatter diffraction analysis

The pole figure calculations based on the EBSD data werebased on approximately 1800 grains for both samples. Basedon the 5◦ tessellation of the vector space representing eachpole figure, there were 1296 distinct cells (from 360/5×90/5). Thus, there were only about 1.4 unique observationsper cell. However, because the neutron data show almostperfect orthorhombic sample symmetry, we can enforce thissymmetry in the EBSD pole figures. This reduces the uniquedomain of the vector space that we need to consider to 1/4its original size, and so, after enforcing orthorhombic sam-ple symmetry, there were about 5.5 unique observations percell. To enforce the symmetry, each point on the pole figureis taken as the average of the four symmetrically equivalentcells within the tessellated vector space.Fig. 3 shows thenormalized pole figures obtained from the EBSD data. Goodqualitative agreement is observed when the EBSD derivedpole figures are compared with those obtained using neutrondiffraction. As observed in the neutron diffraction results,the as-received material showed the cube{1 0 0}<0 0 1>rolling texture component, which typically develops dur-


ing the thermo-mechanical processing of fcc sheet materials[19]. As the material is deformed, the grains are observedto rotate towards positions along the alpha-fiber, defined ascommon orientations with<1 1 0> normal to the plane ofthe sheet. There also appears to be a high frequency of ori-entations near the Brass{1 1 0}<1 1 2> component.

One point to note here was the considerable amount oftime that was spent in obtaining relatively good, indexablepatterns from the samples. Numerous preliminary experi-ments were conducted in order to eliminate the deforma-tion layer (damage to the crystal lattice) at the free surface.Patterns were collected on samples subsequent to just handpolishing, hand polishing in conjunction with vibratory pol-ishing, and finally, these steps combined with a subsequentetch in Keller’s Reagent, before relatively good quality pat-terns were obtained. Before the etching step, pattern index-ing was typically below 60%.

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4.4. XRD analysis

Figs. 4 and 5 show the ω scans aligned parallel and per-pendicular, respectively, to the RD of the sheet for the 1 1 1,2 0 0, and 2 2 0 reflections obtained using the D500. Thescans in Figs. 4 and 5 correspond directly to the lines A–Band A–C, respectively, indicated in the pole figure of Fig. 2afor the 2 2 0 poles. As discussed in Section 2.3, when usinga powder diffractometer, data can only be collected over alimited range of ω (e.g., between the ranges of 0◦ to ±31◦for the 2 2 0 peak) and not the full scans along the linesA–B and A–C (0◦–90◦) as acquired for the neutron diffrac-tion analysis. Very good symmetry can be observed in thescans about the diffraction orientation of ω = 0◦. In termsof the relative shapes and intensities of the curves, the trendsare similar to the neutron and EBSD results on a qualitativebasis. Again, as the amount of deformation in the material


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increased, the fraction of grains oriented with {1 1 1} and{2 0 0} parallel to the plane of the sheet decreased, whilethe overall number of grains with their {2 2 0} parallel tothe sheet plane increased.

4.4.1. Reproducibility with different machinesWhen comparing the rocking curves obtained from the

different X-ray machines (D500, D5000, Bruker GADDS),similar texture profiles were observed. Fig. 6 shows overlaidω scan curves from the two Siemens machines for the threereflections, 1 1 1, 2 0 0, and 2 2 0. Fig. 7 compares the inten-sity data in the RD with that of the GADDS data. The shapeof the texture profiles are quite similar; the actual intensitiesincrease from the GADDS measurements to the D500 to theD5000. Results along the transverse direction also show agood agreement between observations from the two differ-ent machines.

4.4.2. Through thickness texture evaluationExperiments were also conducted to observe the texture

variations normal to the plane of the sample. Both theas-received sheet and a deformed specimen with a strain

level of 0.104, were serial polished approximately every100 �m from the surface to the mid-plane of the sheet(Fig. 1) and rocking curves were collected at each depth.The observations on each layer were within a standard devi-ation for a given plane. Thus, the through-thickness textureof the sheets was relatively homogeneous. The results fromthe deformed sample are shown in Fig. 8 and display therelatively uniform texture normal to the plane of the sheet.

4.4.3. Surface finish evaluationThe effect of surface finish on the texture evaluation was

also conducted. Undeformed sheets with four different sur-face conditions were tested. In order of decreasing rough-ness, the surface preparations were: (1) ground to 600 grit,(2) the as-received surface, (3) polished to 6 �m diamond,and (4) polished to 0.05 �m colloidal silica. Rocking curveswere obtained for each surface and are displayed in Fig. 9.Varying amounts of plastic deformation in the near surfaceof the material occurs as a result of grinding/polishing withdifferent particle sizes, as well as the deformation from theprocessing of the sheet. The effect of this near surface defor-mation is important as the X-ray beam will typically sample


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from the first two to three layers of surface grains (about50 �m depth) in the aluminum sheet. The results show thatthe sample ground to 600 grit was most affected relative tothe as-received sheet. This grit size is on the order of 15 �mand it is estimated that plastically deformed material canbe found from 20 to 40 �m below the root of the surfacescratches (induced by the grinding process). Therefore, theoriginal texture of the as-received surface appears to havebeen significantly altered, as shown in Fig. 9. Between thetwo polished samples, no measurable difference was notedas the deformed layer beneath the surface of each sampleis less than 1 �m for both particle sizes. However, there isa slight and reproducible difference between the polishedand as-received surfaces, which can clearly be observed inFig. 9.

5. Discussion

5.1. Development of strain-induced texture

During deformation of the sheet, mis-match strains at thegrain boundaries will develop due to the different orienta-

tions of slip systems in adjacent grains [1,2,20–25]. To ac-commodate these strain incompatibilities, individual grainswill rotate with respect to each other to become orientedin more stable positions for deformation to occur alongthe {1 1 1}<1 1 0> slip systems in aluminum [10]. Optimalslip behavior under balanced biaxial conditions requires the<1 1 0> direction of the grain to be parallel to the sheetnormal. This aligns the {1 1 1} slip planes of the crystal(grain) with the sample plane for which the resolved shearstress on the slip planes would be maximized. From the re-sults obtained in this research (Fig. 4), the strength of the{1 1 0} component was observed to increase with strain, in-dicating that the grains are rotating to meet this condition.Further, as seen in Figs. 2 and 3, the initial texture com-ponents of the sheet, such as cube and copper, were foundto decrease and the intensity of texture components withinthe alpha-fiber was observed to increase. This observation isconsistent with other studies that show the main texture com-ponent that evolves during equi-biaxial stretching in Al-basealloys as<1 1 0> parallel to the normal direction of the sheet[19,26–29].

In addition, measurements showed that the texture wasconsistent throughout the thickness of the as-received mate-


0

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ps

)

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220

ωoωo

ωo

(a) (b)

(c)

Fig. 7. Rocking curves obtained using X-ray diffraction for the three reflections: (a) 1 1 1, (b) 2 0 0, and (c) 2 2 0. Results from the GADDS machinehave been multiplied by the factor shown. The sample has a strain level of 0.106 and the RD is aligned parallel to the beam.

rial and that the texture development with straining appearsto have evolved homogeneously. Modeling efforts have pre-dicted that textures near the surface of a rolled sheet are dif-ferent from those located at the mid-plane [30]. During pro-cessing of the sheet, friction at the roll/sheet interface wasshown to result in the elements at the surface being moredistorted by shear deformation than those in the middle. Thediscrepancy was not observed here in the initial texture ofthe sheet and may be explained by the fact that the modeledsheets were cold rolled to their final thickness while thoseobtained for this study underwent a modest heat treatmentduring the processing. Further, it does not appear that a gra-dient in the constraint on grain rotation existed through thethickness of the sheet during the straining operation (such agradient would imply that constraint is greater at the centerof the sheet than at the free surface). This would be due to ad-jacent grains constraining activation of the crystallographicslip required for grain rotation in the sheet interior. Again,the measurements showed that the texture continued to berelatively homogeneous through the thickness of the sheet,Fig. 8, possibly indicating that the thinness of the sheet al-lowed for constraint to be relatively equivalent throughoutthe material.

5.2. Comparison between diffraction techniques

Based on the results in Section 4, conclusions can bedrawn about the reproducibility and applicability of texturemeasurements (with respect to rolled sheet product), usingdifferent experimental techniques. Complete pole figures,shown in Figs. 2 and 3, were obtained using both neutrondiffraction and EBSD, respectively. Therefore, direct com-parison between these two techniques was possible. How-ever, a similar direct comparison with the XRD data wasnot as the XRD data could not be collected over the entirehemisphere of sample orientations (the ω scans are simplythe values of the pole figure at constant φ along either theRD (φ = 0◦) or the TD (φ = 90◦) over a restricted range ofω). Thus, the information required to scale the data to MRDcould not be obtained. In order to circumvent this problem,the neutron diffraction data were used as a baseline. Alongthe direction of the ω scan, the average value of the neutrondiffraction distribution over the range of angles covered bythe XRD ω scan was found. The X-ray intensities were thenscaled such that their average was equal to this value. By ex-tracting similar data along the RD and TD from the neutrondiffraction and EBSD pole figures, a direct comparison can


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µm

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ωo

ωo ωo(a) (b)

(c)

Fig. 8. Rocking curves obtained using X-ray diffraction for the three reflections: (a)1 1 1, (b) 2 0 0, and (c) 2 2 0. Where possible, the various planes analyzednormal to the surface are indicated for the sample with a strain level of 0.104. Results are from the D500 with the RD of the sheet parallel to the beam.

now be made. Figs. 10 and 11 show the texture comparisonbetween the three techniques, using different probing radi-ations, for samples with strain levels of 0.0 and 0.104, re-spectively. Scans oriented along both the RD and TD of thesheet are shown. Only XRD results from the D500 are dis-played as the data from the D5000, Fig. 6, and the GADDStechnique, Fig. 7, indicated that these data sets were verysimilar.

5.2.1. Crystallographic texture comparisonWith the apparent lack of depth dependence and the vast

number of grains sampled, neutron diffraction provides themost statistically significant probe of bulk preferred orienta-tion. Therefore, these data will be used as an initial baselinewith which to compare the texture results from the othertwo techniques. Through a visual inspection of the completepole figures, Figs. 2 and 3, a strong similarity between theresults from neutron diffraction and EBSD techniques wasobserved. The differences between the two techniques werewithin ±0.9 MRD over 95% of the area of the analyzed polefigures. The curves obtained by EBSD appear significantlynoisier than both the neutron and XRD data. This is due tothe relatively small number of grains (1800) used to obtainthe EBSD data compared to the entire scattering volume

sampled by the neutron diffraction technique. Typically, alower limit of 10 on the average number of grains per bin(or cells) is considered adequate to provide data with rea-sonably low noise. As discussed above, with a 5◦ bin size,there are 1296 bins and applying orthorhombic sample sym-metry reduces this to 324. Thus, to obtain an average of 10grains per bin, 3240 grains must be analyzed.

Even with this number of grains, the EBSD data will beconsiderably noisier than the neutron data. There are re-gions in the EBSD data (e.g., Fig. 10, 1 1 1 RD) wherethe differences appear to be statistically significant whencompared to both of the other data sets. This may indi-cate that grains sampled in a single region of the specimenmay not completely reflect the texture of the whole sam-ple. To avoid this problem when using EBSD to charac-terize texture, one approach is to measure the orientationof as many locations in as large an area of the microstruc-ture as possible, possibly by using a random sampling tech-nique. Although one of the main strengths of EBSD is spa-tially resolved orientation measurements for microstructuralmapping, clearly this is not compatible with random sam-pling. Care must be taken when using information froma small number of mapped areas to draw global textureconclusions.


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6 µm polish

As-received surface

As-received surface

600 grit

600 grit

600 grit

ωoωo

ωo

(a) (b)

(c)

Fig. 9. Rocking curves obtained using X-ray diffraction for the three reflections: (a) 1 1 1, (b) 2 0 0, and (c) 2 2 0. Where possible, the various surfacefinishes are indicated. Results are from the D500 with the RD of the sheet parallel to the beam.

Relatively good agreement between the neutron and XRDdiffraction data was observed. The XRD profiles, were muchsmoother than those produced with the other techniques asrelatively high intensity, low noise data from a large numberof grains was obtained. The profiles provided more detailedinformation as data were collected every 0.25◦ during theω scans. The worst agreement was for the data collectedfor the 1 1 1 peak, particularly for the as-received specimen(Fig. 10), where significant differences between the XRDand the neutron and EBSD distributions were observed atthe limits of the ω angle range.

When using XRD analysis for texture measurements, adiffractometer equipped with an area detector has significantadvantages over conventional powder diffractometers. Sucha machine, can obtain data in parallel over an area of orien-tation space, thus, collecting data orders of magnitude fasterthan a conventional powder diffractometer. However, overthe limited range of the ω scans, the conventional diffrac-tometers produce results that are essentially equivalent tothe GADDS data (Fig. 7). When analyzing a bulk sample(as in these experiments), an area detector must be used inreflection mode, and thus, is still limited in its angular range,although less so than a 2-circle powder diffractometer.

The two different powder diffractometers used differ inthat the D500 has a Ge incident beam monochromator thatproduces a divergent beam tuned to the Cu K�1 wavelength,whereas the D5000 has a standard Cu K�1/�2 source. De-spite this difference, the data from the two machines arepractically indistinguishable (Fig. 6). This is significant asthe defocusing corrections that are applied to the raw dataare very large (factors as large as 10) and depend on integra-tions over the Bragg peak profiles, which are significantlydifferent for the two machines. This shows that the perfor-mance of the NIST developed algorithm does not depend ona particular wavelength profile for the incident beam.

5.2.2. Suitability of techniquesAs observed, there was relatively good agreement between

the EBSD and neutron diffraction data sets. Both methodsproduce pole figures that are equally suited for further cal-culations of earring, formability limits, or elastic anisotropy.The advantage to using neutron diffraction is the larger scat-tering volume which makes this technique the most suitablewhen considering the texture of a bulk sample. Additionally,there was less noise content in the neutron data as a highernumber of grains are sampled to characterize the texture with


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Along TD Along RD

ωo ωo

ωoωo

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90

9090

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Fig. 10. Comparison between texture measurement as-received sample, 0.0 strain level, showing both rolling (RD) and transverse directions (TD).


111 peak0.104, RD

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90

90

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ωo ωo

ωoωo

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90

Fig. 11. Comparison between texture measurement of the 0.104 strain level, showing both rolling (RD) and transverse directions (TD).


neutrons compared to EBSD. Finally, the labor required forsample preparation is minimal, and there are no surface fin-ish requirements. However, problems arise if a lack of mate-rial is encountered, as in this case in the normal direction ofthe sheet. In addition, there may be a significant limitationon the access to an experimental nuclear reactor. Thus, thistechnique is not suitable for routine measurements or for ahigh throughput of samples.

The advantage that the EBSD technique has is the greateravailability of an SEM outfitted with an EBSD system whencompared to obtaining beam time on a nuclear reactor. Addi-tionally, this technique is more suitable when measuring tex-ture in large grained samples, when diffraction-based tech-niques produce data with large intensity spikes because thenumber of grains being irradiated is not sufficiently large togive good statistics. Finally, the ability to directly link tex-ture data with the microstructure is very attractive and use-ful, a feature neither of the two other techniques have. Adrawback is that this method is extremely sensitive to sur-face preparation in which a relatively undeformed surface isneeded to obtain good patterns.

For the XRD technique, X-ray rocking curves were ob-served to produce similar texture results compared to theother methods. Although, the technique has limited angularranges and measures one “component” at a time, it is ca-pable of much higher resolution in a more reasonable timeframe relative to the EBSD and neutron techniques. Thus,the XRD method appears well suited for limited, everydaytexture measurements, particularly sharp axisymmetric tex-tures typically observed in thin films. Furthermore, surfacefinish was unimportant unless a gross amount of superficialdeformation was applied; even then, the differences were mi-nor. Finally, with its rapid turn around time (a total of 30 minper ω scan), the powder XRD method was more suitableto verify that the texture was uniform through the thicknessof the sheet. However, if a powder diffractometer is used,there is the limitation that complete pole figures cannot beobtained. With the limited angular range of the technique,the data necessary to normalize the intensity values to MRDcannot be collected.

6. Summary

For characterizing the crystallographic texture of sheetmaterials, the techniques analyzed in this work have bothadvantages and drawbacks. The EBSD technique is good formicro-textural work of the surface, such as analyzing highlylocalized textures, quantifying texture gradients, or spatiallyanalyzing the microstructure. However, sample preparationcan be extensive and data collection times relatively long.The XRD analyses demonstrated the techniques robustnesswith different machines and experimental conditions, in ad-dition to its cost-effective and rapid collection of data. How-ever, the lack of angular range does not allow for the acquisi-tion of complete pole figures. Neutron diffraction, appeared

to be the most reliable in terms of determining the bulk tex-ture, with inherently better grain statistics of the sheet asthe entire volume was included in the measurement. How-ever, access to an experimental beam line may not alwaysbe available. Nevertheless, it was shown that if the limita-tions of each technique are understood, then any one of thesemethods is suited for textural analyses of sheet materials.

7. Disclaimer

Identification of any equipment or software is for the pur-pose of describing the experimental techniques and does notimply recommendation or endorsement by NIST, the De-partment of Commerce, or the US Government, nor does itimply that the identified equipment or software is the bestavailable.

Acknowledgements

T. Foecke is recognized for his helpful discussions con-cerning the formability results.

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studies of deformation-induced texture development in sheet materials using diffraction techniques

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