typical textures in sheet metals

8/7/2019 Typical Textures in Sheet Metals

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pical Textures in Sheet Metals

p://archive.uky.edu/bitstream/10225/437/11chap1.htm[2011-02-0712:46:45]

Chapter One

Introduction

1.1 Overview

In many alloy systems the interrelation between microstructure and properties contains the key informaestablishing the strategies for material development. Texture is an essential part of the microstructure and cadominant role when the anisotropy of the material is large and crucial. Texture and anisotropy is a traditionalmaterials science that has continuously expanded for about 70 years. It will continue to grow at an increasingto the progress made in this area, particularly during the last two decades:

Experimental techniques for the rapid determination of texture on macroscopic and microscopic scales haimproved considerably and are widely available in many laboratories.

Methods of texture representation and texture analyses have been perfected.

Physical concepts for modeling texture evolution in laboratory tests and in industrial processes are develorapidly.

Measured texture data can be used, on a routine basis, as input for computer codes to evaluate and quant predict anisotropic material behavior.

This coincides with an enormous increase of manufactured materials in number and complexity, where at time demands are strong to achieve optimal material behavior by the adequate design of microstructure. Thorientation distribution in a polycrystal is the result of the manufacturing process and thus texture containsinformation about the production history of a work piece. On the other hand, texture has a strong effect on pso that it contains easily accessible information on the interrelation between processing parameters and mperformance. In this context, texture evaluation and application provides many highly important aspectsinterrelation between microstructure and properties for process control and material performance and for idenof the controlling mechanisms.

Two of the main uses of aluminum alloys are for beverage container bodies and automotive body panels. Eformability in aluminum sheet products used in stamping of automotive panels follows from control of texturecontrol of the production processes. Quantitative texture analysis provides the essential feedback for tunthermomechanical history on the basis of detailed insight into controlling mechanisms, thereby leading toproperties in the finished product. Economic savings through control of texture can be significant. Due to production volume of sheet material, such as aluminum can body stock, great savings can be achieved thrreduction of scrap causes by earing tear offs.

1.1.1 Crystallographic anisotropy of aluminum alloys

Crystallographic anisotropy of aluminum alloys is generally characterized by earing behavior which hextensively investigated either experimentally or theoretically. It has been found that earing is strongly determcrystallographic textures. The relation between earing and texture is thus of great interest both to acadindustry. Minimizing the earing of products has always been the object of the can industry. The industry also the prediction of product earing based on the original hot band earing. Thus a total understanding of earingduring cold rolling is a prerequisite for a satisfactory prediction. A large amount of research work has been dto this purpose. It is well known that a recrystallization texture causes 90 earing and that a deformation texture resultin 45 earing. With increasing cold reduction, the intensity of the recrystallization texture of the hot band dewhile that of the deformation texture increases. Correspondingly, the 90 earing of the hot band decreases with colrolling and eventually changes to 45 earing in the final product. It is also found that a strong recrystallization texof the hot band is good for a stable and minimal earing behavior during cold rolling.


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These qualitative results have been a great help in the control of thermomechanical processes and of producHowever, a more quantitative relation is highly desired and is required for automatic process control andmonitoring of the formability of aluminum alloys. This is usually characterized as a relation between forparameters (r-value, percent earing) and orientation intensity/volume fraction or the ODF (Orientation DisFunction) coefficients, Wlmn. In this paper this relation is expressed as the percent earing and the orientation intof the texture components. In addition, influence of the rolling process has also been investigated and discusse

1.1.2 Luders bands of aluminum alloys

The pressure on the automotive industry to produce lighter cars with reduced fuel consumption causes a denew materials able to replace steel for car body panels. Some of the materials considered for this applicaaluminum alloys, especially Al-Mg alloys of the 5xxx series. Although they combine a reasonable strength wcorrosion resistance and formability, their mechanical properties are still inferior to those of steel andimprovement is thus required. Therefore a deeper understanding of the processes taking place during preheand cold rolling and annealing of Al-Mg rolled sheets is of crucial importance.

One striking problem of Al-Mg alloys (5xxx) is the surface roughening caused by Luders bands. The appeLuders bands is usually related to the Portevin -Le Chatelier (PLC) effect (serrated yielding) which is gascribed to the effect of dynamic strain ageing ---the dynamic interaction between solute atoms and dislocations. A lot of work has been performed on the parameters which could influence the interaction of dis

and solute in alloys. These include the effects of strain rate, deformation temperature, solute concentration,treatment and precipitation. Serrated yielding normally occurs after a critical strain, ec, and when the strain ratesensitivity , reaches a negative value. The effect is found to increase with increasing Mg content. Qsamples after solution treatment are more likely to cause the PLC effect since more solute is kept in solid Processes that cause precipitation, which decrease the solute in solid solution, will decrease the PLC effect.

When the alloy and the deformation temperature or strain rate do not favor the formation of Luders banddetection of the Portevin -Le Chatelier effect, there still exists at least three causes for flow localization:thermal, textural or structural softening. It is easy to determine if local heating is responsible for the observbanding. This occurs when large strain rates are associated with low thermal conductivity. By contrast, when heating may be reasonably neglected, it is not straightforward to distinguish textural from structural origin

localization. The former, sometimes called geometrical softening, is related to crystallographic rotations whichto optimize the orientation of slip systems in the majority of grains. The latter process is illustrated by the piworks on latent hardening performed on single crystals and is frequently invoked when a change of straininvolved. Structural softening is mainly related to the decrease of the strength of barriers to the glide of dislwhich in the case of change of strain path constitutes alien dislocations.

Because of the close association of crystal deformation mechanisms with surface roughening, the crystalltexture and local crystal lattice misorientations are expected to have an effect on roughness, and also on teffect. The texture effect on surface roughening or on the PLC effect has been little studied [1,2]. In aluminuma notable difference in the Taylor factor, computed for a state of balanced biaxial tension, exists between distinct crystallographic bands [3,4]. Etching techniques reveal grooves that are populated with colonies ohaving near-cube orientation [3]. The formation of a groove indicates that the cube-oriented colonies haveaverage) lower through-thickness strength than the surrounding material. This supports the notion that meinhomogeneity arising from the spatial segregation of crystallographic texture can promote direction rouwhich eventually leads to local failure. Experiments on copper sheets with a high cube texture suggest tharoughening may be reduced for materials with certain strong crystallographic texture [5]. This is becdeformation incompatibility between neighboring grains is reduced. However, the cube orientation is not finite strains, and intense strain localization can development at a lower strain than for a randomly textureSince the traditional x-ray techniques can only catch the texture information on a macroscopic scale (a smeaning), they do not give the detailed orientation distribution of each grain, which is considered essentiainvestigation for the effect of texture on the PLC effect. With the Electron Back Scattering Pattern (EBSP), whappeared in the early 90's, it is now possible to obtain the orientation for each grain. Several works [1,6] hav


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that the orientation distribution of grains is not random. The grains with similar orientations have a trendtogether to form a "texture clustering". This phenomena has been found most recently both in SC and DC alalloys by Liu et al [7], and he has named it "texture continuity". Since the Luders bands are the proinhomogeneous deformation, which is closely related to the local lattice orientation, the orientation distribgrains is expected to have an effect on their formation. In this regard, the phenomenon of texture clustering ipossible effect on the PLC effect. This has been considered and is a totally different concept from the convidea, and deserves more investigation.

1.1.3 Age softening behavior

Age softening of strain -hardened Al- Mg alloys is of particular commercial significance, because it leads to of the heavily worked Al-Mg alloys when they are held for increasing times at room temperature. The age effect increases with increasing cold work and with increase in Mg content. Since the PLC effect is also very Al-Mg alloys and increases in intensity with increase in Mg content it is reasonable to deduce that the PLCalso involved in the age softening behavior. The PLC effect which induces Mg clusters around dislocations leincrease in strength during cold working of these alloys. This increase in strength is greater than if the PLCabsent. Thus, it could be assumed that a part of the age softening behavior is associated with the lodecomposition of the Mg clusters that are bound to the dislocations. Strain energy would be released by this ea relaxation of the tangled dislocation structure would occur. It is recognized that Al-Mg solid solutions deaccording to the reaction S.S. b '' b ' b and that this reaction is in part the driving force for the Mg cluste

change with time in their characteristics and behavior.It is to be expected that texture and anisotropy will gain increasing interest in all sorts of transformation p(such as recrystallization, precipitation and martensite formation). It is also assumed that the effect of interphalocal orientation arrangements on evolution of microstructure and texture will play an important role and sincorporated routinely in most of the investigations of the mechanical properties and formability durinprocesses.

1.2 Texture measurements and representations

1.2.1 The representation of orientations and textures

The orientation of a crystal may be characterized in a great many different ways with respect to the sample aof the most frequently used representations of an orientation is to specify the crystal direction which is parallsheet normal direction (ND) and the one parallel to the rolling direction (RD)

g = (hkl)[uvw].

For the sake of symmetry it is now convenient to include the third perpendicular direction namely the trdirection (TD) and to specify the crystal direction in a matrix.

RD TD ND

where the components are the Miller indices of RD, TD, ND. It is usually normalized to 1 as:


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where

For practical manipulations of orientations, the Euler angles have been introduced for these representations.rotations of the axes, the sample frame is rotated to coincide with that of the crystal. There are two different given by Bunge [8] and Roe [9]. Here the Roe's method is adopted, which is shown asFigure1.

1. Rotate about z-axis by an angle Y.

2. Rotate about the new y'-axis by an angle Q.

3. Rotate about the new z''-axis by an angle F.

The orientation g is thus defined by

which is simplified as

Under the sample coordinates, the orientation g is represented by the matrix

Or

Comparing Eq.2 with Eq.3 one obtains the interrelation between the Euler angles and the direction cosinerolling and normal directions and thus the relation between the Euler angles and the Miller indices.

1.2.2 Texture measurements

The preferred orientation of polycrystallities is usually determined by pole figure measurements. X-ray diffrmost commonly applied and will be discussed here. But other techniques, such as Neutron diffraction anddiffraction using TEM or SEM, are also used for this purpose.

X-ray diffraction was first employed by Wever [10] to investigate the preferred orientation in metals. Howe
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with the introduction of the pole figure goniometer and the use of Geiger counters by Decker & al [11] an[12] has it become a quantitative method. Many aspects of pole figure goniometry have been discussed in somby Schulz [13,14]. Bragg's law for monochromatic radiation is applied. It has two conditions. The first is thatplane (hkl) diffracts if it is in a reflection position between the incident and diffracted x-rays. The second conthat lattice planes with a spacing dhkl obey the law

where 2q is the angle between incident and diffracted beams, and l is the monochromatic x-ray wavelength n aninteger defining the order of diffraction. The principle is simple (Figure2). In order to determine the orientation of given lattice, (hkl), of a single crystallite, the detector is first set at the proper Bragg angle, 2q, of the diffractof interest, then the sample is rotated in a goniometer until the lattice plane (hkl) is in the reflection conditionnormal to the lattice plane or diffraction vector is the bisectrix between the incident and diffracted beagoniometer rotations are related to the angular coordinates which define a sample orientation. In the capolycrystalline sample, the intensity recorded at a certain sample orientation is proportional to the volume frcrystallites with their lattice planes in reflection geometry.

Two methods of analysis are generally used: Determination of texture can be done on a sample of large thicka plane surface on which x-rays are reflected (reflection) or on a thin slab of thicknesst which is penetrated by x-rays(transmission). Since x- rays are strongly absorbed by matter, the transmission method is only applicable on foils or wires (


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spherical harmonic functions:

In this equation Qlm are coefficients to be determined, Plm(cosa ) eimb is a spherical harmonic function (P is anassociated Legendre polynomial), andl and m are integers that govern the shape of the function (these would beangular momentum and magnetic quantum numbers in the solution for the hydrogen atom);l is often called the 'order'

of the spherical harmonic function. This is an infinite series, but it is clear that truncation at some finite valul isnecessary in practice, limited by the number of data points measured. This limits the resolution of the metleads to termination or truncation errors in the results. The coefficients are, in principle, complex, but symmthe material often reduce the imaginary parts to zero, while the complex exponents in Eq. 5 can be reduced tfunctions.

Because the functions are orthogonal, the coefficients can easily be obtained from the experimental dintegration:

It is assumed that the ODF can be similarly expanded in a series of generalized spherical harmonic fuspecifically:

where Wlmn are the coefficients of this series, and Zlmn are Jacobi polynomials. The problem becomes one of findthe relation between the unknown Wlmn and the experimentally accessible. By substituting Eqs. 5 and 7 in Eqintegrating, and making use of the Legendre addition theorem, we obtain

Here x and h are the polar coordinates of the (hkl) pole in the crystal coordinate system.

Equation 8 is a linear equation relating the pole figure coefficients with the ODF coefficients. By measurinpole figures from geometrically independent poles, we obtain a set of linear simultaneous equations that can bfor the Wlmn. The Wlmn can then be substituted in Eq. 7 to obtain the ODF.

The number of pole figures that must be measured depends on the number of independent unknowns in Eq. turn depends on the order l to which we intend to compute the series. Symmetry in the crystal Laue group will rthe number of independent Wlmn and the number of required pole figures. For example, cubic crystal symmdictates that W2mn=0 (and therefore Q2m=0), and in fact allows all the independent coefficients to be determined tl =22 from only two pole figures [9].

Once the Wlmn have been found Eqs. 8 and 5 can be used to re-calculate pole figures, even for pole figures thnot measured or used in the analysis.

The simple calculation of pole figure coefficients, Qlm, from the experimental data using Eq. 6 is a consequence oforthogonality of the spherical harmonic functions over the surface of the sphere. With the available expe


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methods, however, it is difficult in many cases to obtain complete pole figures, or at least, it requires a muexperimental effort than the determination of incomplete pole figure for example in the back -reflection ranEquation 6 cannot, therefore, be used as it stands with incomplete pole figures. Two ways have been used to othis difficulty. One of these [17] uses a least-squares analysis to find the ODF coefficients that best fit the expedata.

A second method is much easier to implement, and involves an initial extrapolation from the known to thepart of the pole figures, usually with a third-order polynomial. For materials with cubic crystal symm

requirement that Q2m=0 can be used to properly normalize the values in this extrapolation [18]. Equations 6 anthen used to calculate a first estimate of the Wlmn. These values are used to recalculate the missing parts of the pfigure (from Eqs. 8 and 5). Any physically meaningless negative values are replaced with zeros. These recparts contain information derived from, and crystallographically consistent with, the real experimental drecalculated values are, therefore, much better estimates than the original extrapolated values, and are substthem. The process is repeated, each iteration improving the reliability of the estimate of the missing parts,self-consistency of the data is judged satisfactory. Dahms & Bunge [19] suggest that even better resultobtained by recalculating additional (non-measured) pole figures, correcting for any negative values, aincorporating these into the iterative process.

1.3 Typical textures in sheet metals

1.3.1 Deformation textures in fcc metals

The textures that have been most thoroughly investigated in metallurgy have been those in rolled sheets, or rrecrystallized sheets, of materials of cubic lattice structure. Some textures are well described by 'composuperposition of a small number of single crystals, with some spread (which may be quantified by Gaussians)Others can be idealized as 'fiber' in orientation space, in which a single angle can be used to specify an orwithin the fiber (although it may not be simply one of the Euler angles). Thus the analyzing of rolling texusually been approached in a simplified manner: (1) using texture components and (2) using fibers. The aimtexture components is to reduce the representation of the orientation distribution into a small set of specific orior texture components. Table 1 lists the Euler angles and Miller indices of the texture components that appeafcc metals.

Table 1 Rolling texture components: Indices and Euler angles [22]

Name Indices Bunge

(j 1,F ,j2)

Kocks

(y ,Q ,f )

Copper 90, 35, 45 0, 35, 45

S1 59, 29, 63 149, 29, 27

S2 47, 37, 63 137, 37, 27

S3* 59, 37, 63 149, 37, 27

Brass 35, 45, 0 55, 45, 0

Taylor {4 4 11}

90, 27, 45 0, 27, 45


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Goss 0, 45, 0 90, 45, 0

* This particular orientation is often quoted as 'the' characteristic S orientation. Nevertheless, there is sigvariation in the literature as to which precise orientations are labeled as 'S'.

The other approach for studying rolling textures uses the concept of partial fibers, where a fiber is a orientations limited to a single degree of (rotational) freedom about a fixed axis [23]; some fibers are defined of an axis in sample space, and some in terms of crystal coordinates. The appearance of a fiber in ODF plots

a line, which may or may not lie entirely in one section. There are two fibers typically used for fcc metals: thfibers. The b fiber runs (in orientation space) from the 'copper' to the 'brass' component. The 'S' orientationintermediate locations along this fiber. The a fiber runs from 'brass' to 'Goss'. The b fiber is generally promrolling textures. Ideally, these fibers should always correspond to regions of high intensity in the oriedistribution. However, the location of the maximal values in any given ODF may vary significantly from tThis has led to definitions of fibers that are not fixed in position ('skeleton lines') [17].

It is often assumed that the texture of a polycrystal rolled to a high reduction will give essentially the same texpolycrystal rolled to a lower reduction only stronger. While a higher reduction will generally produce atexture, the character of the texture may change significantly.3 shows (111) pole figures for copper rolincreasing reductions [23]. In this figure, the texture sharpens with increasing strain, as would be expected

general features of the texture remain relatively constant as well. However, the locations of the peaks in figures shift considerably in orientation space. As discussed below, this means that caution is required when atextures in terms of fibers that are fixed in orientation.

The variation in rolling texture with material has been well documented by previous researchers. It is convregard the 'copper' texture and the 'brass' texture as the opposite extremes of 'pure metal' and 'alloy' textures (s1 for definitions). The effect of increasing the amount of zinc in copper is shown in4[24]. This set of (111) pofigures shows the transition from the pure metal to the alloy type texture over a range of Zn content in which is not generally observed. The figure shows that there is a transition to the alloy texture at about 15% zinc. Hthis transition can also be achieved with the addition of only a few percent of phosphorus [25].

Similarly, elevated deformation temperatures tend to lead to the pure metal texture, whereas low temperatures opposite effect. For example, rolling copper at liquid nitrogen temperature yields a brass texture [26], and rolliat high temperature shifts the texture toward that of Al [27,28].Figure5 [29] shows the effect of temperature on texturevolution in 95% rolled plutonium with 9.6 atomic percent gallium. These pole figures show that the transitthe pure metal to the alloy type texture can be achieved by decreasing the deformation temperature. A rather table is available in Dillamore & Roberts [25] summarizing the texture data for most fcc alloy systems.

It is also worth noting the controversy in the literature concerning the role of microstructure on the formatialloy or brass texture. Although brass itself twins readily at small strains, it is not clear that additional twinninat higher strains (greater reductions in thickness) during rolling at which the brass component becomes strongthe brass component appears without twinning in many cases; for example, this component is often domaluminum-lithium alloys [30], obviously for different reasons.

1.3.2 Recrystallization texture in rolled fcc metals

The topic of recrystallization texture is not merely of academic interest since the properties of many commercdepend critically on the control of the recrystallization texture. Examples abound in the literature on siliconsteels, used for their magnetic properties, and aluminum sheet for beverage cans. On the other hand, recrysttextures in rolled copper have been investigated most thoroughly from a fundamental point of view. Coppeeasily obtained in high purity whereas aluminum very often has significant levels of both insoluble andimpurities.

As an illustration of the wide variety of recrystallization textures that can be obtained in fcc materials,Figure6 shows
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the (111) pole figures of the recrystallization textures of Al, Cu, Brass, and an aluminum alloy. Recrystaltextures (just like rolling textures) show significant material dependence, especially the effect of stacking-fau(SFE). In materials of relatively high SFE (Al, Ni, Cu), a cube component often plays a major role. In additicube component, Al and Al alloys often exhibit a component close to the typical rolling texture S-ori(Fig.6a)[31]. In Ni and Cu, recrystallization twinning leads to minor intensities of the cube orientationgeneration twin. (Fig.6b). In contrast to these examples, low-SFE materials (Ag, brass, austenitic steels) genexhibit much weaker recrystallization textures, which are characterized by the so-called brass recrystaorientation {236}(Fig.6c).

In comparison to rolling textures, recrystallization textures are much more complicated. In addition to the depon SFE, the following conditions of the deformed state, the annealing temperature, and particularly the prestate are known to exert strong influences on the recrystallization behavior and, consequently, on the recrystatextures [32]. As an example, the recrystallization texture of an Al-Mn alloy (AA3104), which was pretrcontain large (>1m m) constituent particles, is shown inFig.6d. In comparison to pure Al (Fig.6a), the texture of thetwo-phase material is much less pronounced, which is caused by the additional, nearly random nucleatideformation zones around the second-phase particles ('particle stimulated nucleation') [33].

One overriding feature of recrystallization textures that has yet to be quantitatively understood is the develohigh symmetry components, such as cube ({100}) and Goss ({110}), after rolling [34]. As an exrecent research on recrystallization in copper [23],Figure7shows the evolution of the texture from the standard f

rolling texture, after 90% reduction in thickness by rolling, to a fully recrystallized condition. The initial textuoxygen-free-electrical conductivity (OFE) copper before rolling had a weak cube component. The final texrolling and annealing is an extremely strong cube texture with a very small volume fraction of a twin-related dof the cube. This evolution is of considerable practical interest to the suppliers of aluminum sheet to the bindustry because the balance between deformation textures and annealing textures is crucial to controlling beverage can stock. It happens that the anisotropy of interest, most easily characterized in terms of the variatvalue with direction in the rolling plane has the same symmetry (four ears), but is turned by 45 , for the rolling and thecube textures. Thus, it can happen that the texture in the partially recrystallized state (Fig.7b-e) is far from random, yetthe anisotropy of interest is nearly absent. This point is a caution against using any particular test of meisotropy as a diagnostic test for texture.

A more detailed analysis of the evolution of texture during recrystallization is shown inFigure8. This figure shows thevariation in volume fraction with fraction recrystallized for both the deformation and the recrystallization comThe first thing to note in this figure is that the volume fractions of the deformation components decrease unThis indicates that no particular rolling component is depleted faster than any other during recrystallization. Tdecrease in the deformation components is in contrast to the non-linear increase observed for the cube compovolume fractions in this case were calculated by first representing the orientation distribution by sets of wdiscrete orientations [35]. The volume fraction for a specific component was then calculated by adding up theof all of the weighted discrete orientations which were within 7.5 of the particular component and dividing this suby the weights of all of the discrete orientations in the set. (These results compared closely with volume calculated by integrating the intensity of the orientation distribution over a 15 15 15 volume around eachcomponent.).

Another interesting aspect of texture evolution during recrystallization is the dependence on the deformFigure9shows the variation in the cube component volume fraction with prior rolling strain, expressed here in the von Mises equivalent strain. Note that four different criteria have been used for the spread in the cube coand that, at high pre-strains, most of the cube component oriented material is within 7.5 of the ideal position. Theresults indicate that there is a marked transition from very little cube at pre-strains less than 2.0, to cube-domstrains over about 3.0. Many other scalar measures of texture are available for these sorts of investigationtextures are to be compared with microscopy then volume fractions of components are more approprintensities.

Lastly grain growth can also lead to changes in texture because of variations of grain boundary energy and
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associated with specific texture components [36].

1.4 Anisotropy and formability of aluminum alloys

Enhanced formability in aluminum sheet products used in stamping of automotive panels follows from cotexture through control of the production processes. Quantitative texture analysis provides the essential feedtuning the thermomechanical history on the basis of detailed insight into controlling mechanisms, thereby ledesired properties in the finished product. Economic savings through control of texture can be significant. Dlarge production volume of sheet material, such as aluminum can body stock, great savings can be achieved

the reduction of scrap caused by earing.1.4.1 Anisotropy behavior of aluminum sheets for can body

One of the main uses of aluminum alloys is for beverage containers. During the deep drawing process, undulthe rim of the formed article may be found. The high points are called "ears" and the general phenomenon"earing". Minimizing earing is an important objective when producing rolled alloys that have to be subsequedrawn. A randomly oriented material would be ideal for this purpose, since it would not show earing. Thiachieved through multidirectional rolling or by small rolling reductions and frequent intermediate heat treatmthis is neither a practical nor an economical proposition.

Table 2. The effect of processing variables on earing of finally annealed materials

Fabrication variable Comments on effect of variable

Method of casting and castingconditions (DC vs. SC)

Increased solidification rate tends to producemore 45 earing and increase the range. Bothinitial texture of cast product and ingot geometrywill influence the subsequent fabrication practice.

Composition of material In dilute alloys decreasing (increasing Fecontent) purity produces more 45 earing; lower Fe/Si content reduces the range. Minor additionscan influence earing in either directiondependent on the Fe and Si contents.

Homogenization and preheating

Precipitation of supersaturated elementsincreases 45 earing. In commercial puritymaterials 45 earing increases with increasingtemperature up to ~570 C.

Hot rolling Conditions that give rise to recrystallization

increase 90 earing.Interannealing (including hotmill slab)

Normally increases 90 earing. The effect isreduced on repeated interannealing.

Cold rolling Increasing heavy reductions promote 45 earing.After interannealing, results depend on thedegree of subsequent cold reduction.

Table 2 [37] summarizes some of the main factors in processing sheet aluminum, which can influence the eari


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final product. Because the fabrication of sheet materials involves a series of processes (casting, homogehot/cold rolling, annealing, etc.), it follows that almost every change in practice can potentially influence theearing behavior of aluminum alloys. Therefore, the earing of aluminum alloys products can be controlled, textent, by the chemical composition, the casting process, ingot/strip homogenization, hot and cold rolling pracfinal annealing operations. Table 2 is not comprehensive and there are many more factors which have been obinfluence earing behavior [38,39]. It is generally accepted that earing results from the presence of preferred orin the metal being fabricated.

A number of factors influence the earing behavior of aluminum alloys by affecting directly or indirectly the porientation of the materials. In aluminum alloys, the earing has two main forms: (1) 45 earing, which is associatedwith deformation type textures, and (2) 90 earing, which is associated with recrystallization type textures. The conof earing in aluminum alloys depends therefore in a large measure on the balance between these two types ofin order to produce "earing -free" material. The combined effect of deformation and recrystallization microstructure of a work piece is due to a complex interplay between the different physical processes of defand recrystallization, which is not easily treated theoretically but, nevertheless, offer a wide range of possibimanipulation of texture. For metallurgical applications an enormous amount of empirical knowledge has beenand has led to standardized treatment schemes. In practice, when the hot band is to be cold rolled, the texmicrostructure have essentially already been determined. It is in this sense that cold rolling determines the prthe final products. Understanding the earing behavior during cold rolling is not only essential for prediresultant formability, but also gives an insight into the thermomechanical processes needed to obtain a suitablehot band condition.Earing behavior of aluminum alloys has been extensively investigated either experimentally or theoretically45]. It has been found that earing is strongly determined by crystallographic textures. The quantitative relationearing and texture is thus of much interest both to academy and industry. Minimizing the earing of prodalways been the objective of the can industry. The industry also demands the prediction of product earing baseoriginal hot band earing. Thus a total understanding of earing behavior during cold rolling is a prerequissatisfactory prediction. A large amount of research work has been dedicated to this purpose [46,47]. It is wethat the recrystallization textures cause 90 earing and that the deformation textures result in 45 earing. Withincreasing cold reduction, the intensity of the recrystallization textures of hot band decreases while thadeformation textures increases. Correspondingly, 90 earing of the hot band decreases with cold rolling and eventu

changes to 45 earing in the final product. It is also found that a strong recrystallization texture of the hot bdesirable for a stable earing behavior during cold rolling [46]. The can industry considers that 0/90 earing is moreharmful in the final sheet material and more easily causes an unacceptable number of defects than does 45 earing.Therefore an investigation of the evolution of crystallographic textures of aluminum alloys and their earisignificant importance both to the can industry and for texture theory.

1.4.2 The Portevin-Le Chatelier (PLC) effect of aluminum alloys

In order to increase the ratio of strength/weight, replacing most of the steel with aluminum alloys is the currfor the automotive industry. Al-Mg alloys (5xxx) are most suitable for this purpose and currently are extinvestigated. The striking problem is the surface quality caused by Luders bands. Luders bands forming in a

alloys has been known for many years. The 5xxx series alloys (Al-Mg) of Al are most prone to this behavior.appearance of Luders bands, the materials present a serrated yielding in the strain-stress curve which is desigPortevin-Le Chatelier (PLC) effect.

The occurrence of the Portevin -Le Chatelier effect (serrated yielding) is generally ascribed to the effect of strain ageing ---the dynamic interaction between solute atoms and mobile dislocations. It normally occurcritical strain ec and when the strain rate sensitivity D s / D ln reaches a negative value. Former work has shoexistence of three types of serrated yielding, characterized by both the form of serrations, as evidenced onstrain curve, and the strain rate or temperature dependence of the critical strain, ec. At low and intermediatetemperatures or high strain rates in the serration range, ec is found to increase with increasing strain and decreasi


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temperature. In this region the solute mobility, which is initially insufficient to form atmospheres, is increvacancy production during deformation while the dislocation velocity decreases, allowing the locking conditmet at ec. At ec the dislocations are effectively locked and further deformation requires dislocation breakawmultiplication, as evidenced on a stress-strain curve by an abrupt rise in flow stress followed by a discontinback to or below the level of the curve [48-50]. Such serrations are called locking serrations as they originatelocking of initially mobile dislocations. In addition to vacancy concentrations produced by deformation, quevacancy supersaturations have also been found to influence the strain at the onset of serrated flow [51].

At high temperatures and low strain rates, ec is often found to increase with decreasing strain rate and increastemperature [51-58]. In this region the form of the serrations is found to differ from the locking serrations inleast initially, no increase in flow stress is observed prior to the discontinuous yield drop. Although little wbeen done in this region, it has been shown that the dislocation velocity is low enough initially for the dislocbe aged from the start of deformation. The serrations appear to be due to the breakaway and multiplication oaged dislocations and are termed unlocking serrations. Thomas [58] has shown that each unlocking scorresponds to the initiation of a local Luders band.

Some experimental results have revealed a decreasing ec with increasing temperature [59-62], whereas some haalso shown that ec decreases initially to a minimum then increases with temperature [63-65]. Regardless difference in critical strain behavior, there exists a temperature range in which ec decreases with increasing

temperature. In this temperature range, the serration stress amplitude, D s , increases with increasing strtemperature [59,61,62] and decreases with increasing grain size [61,66,67]. Grain size plays a majordetermining the strain to the onset of serrated yielding in a polycrystalline aluminum-3% magnesium alloy [52

Various models [68-73] for dynamic strain ageing have been developed to account for the occurrence of serrat temperatures where solute diffusivity is extremely low, and for the observations of a critical straindependence on strain rate and temperatureT and of the dependence of strain rate sensitivity of flow stress on stor stress. The vacancy model [69,70] considers the enhancement of the diffusion coefficient by the vacancies gduring plastic flow [68], the increase in mobile dislocation density with strain [52] and the ageing of dislduring their waiting time at discrete obstacles [69,74]. In addition, the critical strain is interpreted in terms of at which the strain rate sensitivity becomes zero [70]. Negative strain rate sensitivity as a crucial factor for theserrated flow is now recognized in all the models.In the models of Van den Beukel [70] and Mulford and Kocks [71] it is held that any solute mobility makes acontribution to the total strain rate sensitivity and that this negative contribution increases with strain; whenstrain rate sensitivity becomes negative, plastic flow becomes unstable. In arriving at the strain dependencstrain rate sensitivity Van den Beukel [70] retains the notions of a strain-dependent solute diffusion coefficstrain dependent mobile dislocation density from the older models. Mulford and Kocks [71], on the othdescribe the strain rate sensitivity in terms of the flow stress s which is the sum of two components---the frictis f and the dislocation flow stress sd ; solute mobility affects sd , the strain hardening component of the flow stresThey contend that the rate sensitivity of sd is negative, which in turn causes serrated flow. This interpretationcritical strain does not rely on the production of vacancies for explaining the onset of serrated flow, instead it the diffusion of solute atoms along dislocations at forest intersections. In a joint paper, Van den Beukel an[72] have arrived at a unified approach which enables the negative strain rate sensitivity to arise as a conseqthe influence of solute mobility on both s f (by decreasing the obstacle spacing along the dislocation) and sd (byincreasing the strength of dislocation junctions). However, it should be mentioned that the vacancy concentranot significantly affect the initiation of jerky flow [54,75-77]. In some models [71,73,74,78-80] the critical the occurrence of jerky flow may be explained without any assumption that vacancies created during defocontribute to the diffusion process. More recently, Kubin and Estrin [73] have proposed a model explaining thstrains for the appearance of plastic instability in terms of the strain dependence of the densities of mobile andislocations. In their model, the explanation of experimentally observed strain ranges of the PLC effeconnected directly to the particular choice of a model for dynamic strain ageing. Though there are objectio


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against the models which rely on the vacancies generated during plastic flow, the vacancy model cannot be rethis would cause serious problems in explaining the differences in observed ec vs variation between interstitial andsubstitutional solid solutions.

The various investigations on the serrated flow suggest that the measurement of ec and its dependence on andT isessential in order to understand the underlying mechanisms. This dependence is generally expressed [69,81] a

(9)

where m and b are the respective exponents in the relations for the variation of vacancy concentrationC v and of mobile dislocation density r m with plastic strain (C v e m; r e b ), K' is a constant,Q is the activation energy,k andT have their usual meanings. One can obtain the exponent (m+b ) as the slope in the plot of ln vs lnec at a constanttemperature.

Because of the close association of crystal deformation mechanisms with surface roughening, the crystalltexture and local crystal lattice misorientations are expected to have an effect on roughness. Experiments osheets with a high cube texture suggest that surface roughening may be reduced for materials with certai

crystallographic textures [5]. This is because the deformation incompatibility between neighboring grains isHowever, the cube orientation is not stable at finite strains and intense strain localization can develop at lowethan for a randomly textured sheet.

Another factor known to interact with surface roughening is small -scale strain localization near the surfaceFormation of bands of localized deformation can enhance roughening by increasing the depths of the valaltering the surface strain distribution. Models formulated to capture shear bands near a free surface have assuexistence of a vertex at the loading point of the yield surface [84] or that the bands are related to the presporosity [85].

1.5 Proposed work

Based on the aforementioned literature work this paper does not intend to study the formability of aluminum ase. It will, however, investigate different factors which affect the formability of aluminum alloys basicallyalloys. Therefore, the following work will be carried out.

1.5.1 Texture and anisotropy of aluminum alloys

The crystallographic texture of aluminum alloys has been thoroughly investigated for different thermomeprocesses. The anisotropy and formability of aluminum alloys have also been extensively studied eitherdependence on crystallographic texture or for their direct dependence on different thermomechanical procequalitative relation between texture and anisotropy has been well developed. However, the need for an automline control of texture and formability is highly desired by industry and this requires a more quantitative

between texture and formability for certain processes. This is usually characterized as a relation between foparameters (r -value, percent earing) and orientation intensity/volume fraction [46,38] or the ODF coefficienlmn[39,86-88]. In this work this relation is expressed as the percent earing and the orientation intensity of the text

For the can industry, when the hot band is ready to be cold rolled its microstructure and texture have alredetermined. In addition the final product formability is significantly determined by the cold rolling process. Sounderstanding of the earing behavior and texture evolution during cold rolling is very important for on- lincontrol. Thus, we want to perform work on the earing behavior and texture evolution during cold rolling. Tpurpose is to try to find an analytical relation between texture and earing. In addition, influence of the rollingwas also investigated and discussed.


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1.5.2 PLC effect on Al-Mg alloys

The PLC effect on aluminum alloys has been extensively studied by the appearance of yielding serrations,intensity of the serrations, the onset of serrations, types of serrations, the magnitude of the stress drop as wfrequency. Many factors, i.e., temperature, strain rate, heat treatment process, composition, have also been sturegard to their effect on these parameters. Most of those investigations are based on the theory of dynamiageing---dynamic interaction between solute atoms and mobile dislocations first presented by Cottrell. Howevthe alloy and the deformation temperature or strain rate do not favor the formation of Luders bands or the PoChatelier effect, there still exists at least three causes for flow localization: namely thermal, textural or softening. It is rather easy to determine if local heating is responsible for the observed shear banding. This occif large strain rates are associated with low thermal conductivity. By contrast, when adiabatic heatingreasonably neglected, it is not straightforward to distinguish textural from structural origins of flow localizaformer, sometimes called geometrical softening, is related to crystallographic rotations which are able to optiorientation of slip systems in the majority of grains [89]. The latter process is illustrated by the pioneeringlatent hardening performed on single crystals [90] and is frequently invoked when a change of strain path is [91-93]. Structural softening is mainly related to the decrease of the strength of the barriers to the glide of dislwhich in the case of change of strain path constitutes alien dislocations. Most recently, Lopes et. al have shtextural instability in pure aluminum [94]. R. Becker has also shown that grain structure and texture has an the surface roughening during sheet forming [2].

It is proposed that this study of the PLC effect be carried out in relation to the age softening behavior and tinhomogeneity of texture on Al-Mg (5xxx) alloys by chemical composition variations (alloy effect) as wethermomechanical process variations (homogenization, solution treatment, annealing, deformation, etc.). Twill incorporate both Direct Chill Cast (DC) material as well as Strip Cast (SC) material.

Copyright 2000 Xiang-Ming Cheng


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typical textures in sheet metals

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