Textural Development of AA 5754 Sheet Deformed under

In-Plane Biaxial Tension

S.W. BANOVIC, M.A. IADICOLA, and T. FOECKE

Crystallographic texture evolution was quantified as a function of biaxial strain level and strain

path for AA5754-O sheet metal in an effort to provide a physical description of grain rotation

resulting from in-plane stretching. Samples were incrementally deformed to near-failure in three

strain states (equibiaxial, plane strain, and uniaxial modes) with the rolling direction (RD) and

transverse direction (TD) of the sheet parallel to the major stress axis for the latter two cases.

The macrotextures were measured using X-ray diffraction techniques. Results showed that for a

given strain path similar deformation textures developed in the two material sets (RD- and

TD-oriented samples), though the evolution of the deformed texture was not homogeneous over

the entire strain range. These variations in orientation intensities were related to the feeder

components found in the initial texture and the availability of these components to rotate

toward the more stable orientations under the particular mode of deformation. The nonuniform

texture development of the sheet along different directions appears to contribute to the anisotropic mechanical response of the sheet during stretching as measured in the evolving multiaxial

flow surfaces.

DOI: 10.1007/s11661-008-9547-9

 The Minerals, Metals & Materials Society and ASM International 2008

I. INTRODUCTION

OVER the past three decades, aluminum alloys have

been increasingly used to replace conventional Fe-base

components in automotive applications. Their light

weight and excellent corrosion properties make them

suitable for both internal structural members and outerbody panels. However, some obstacles to widespread

use of these alloys exist, which include unfavorable

mechanical response (lower forming limit strains compared to Fe-base counterparts, serrated yielding, and

yield plateaus), forming defects (wrinkling and tearing),

and macroscopic surface imperfections (orange peel and

ridging/roping lines).

Another issue restricting their application concerns

numerical modeling presently used to determine the

appropriate processing parameters of a given alloy for a

specific part. The predictions of multiaxial behavior are

largely inaccurate as these models are based on extrapolations or predictions from basic uniaxial tension

tests.[1] Further, the constitutive equations available

for use in the models and the data used to develop them

are limited in the strain states measured, the level of

strains achieved, and accuracy of the measurement.

Recent work by this research group has shown that this

barrier is being overcome as multiaxial flow surfaces can

be experimentally determined, out to failure of the sheet,

using an in-situ X-ray diffraction technique.[2,3]

Typically, in-plane anisotropy is seen in the mechanical response of rolled sheet, with different uniaxial

behavior parallel and perpendicular to the rolling

direction (Figure 1(a)). These effects are not limited to

the uniaxial case, as shown in Iadicola et al.[3] for

AA5754-O sheet subjected to biaxial in-plane straining. The plane strain (Figure 1(b)) and equibiaxial

(Figure 1(c)) stress-strain data show that typically

assumed isotropic (von Mises) transverse responses

(i.e., half the first principal stress and equal biaxial

stress, respectively) do not actually occur. However, it

was seen that by comparing contours of equal plastic

work (based on work values at specific values of plastic

strain in the uniaxial rolling direction) in stress space

(Figure 1(d), for 1, 5, 10, and 15 pct plastic strain) that

the initial anisotropy decreased above 4 and 7 pct strain,

for plane strain and equibiaxial tension, respectively.

Barlat and Richmond[4] have shown that this material

anisotropy may be a result of the preferred crystallographic orientation in the as-received sheet. Using the

Taylor–Bishop–Hill model, materials with strong initial

textures of Goss f g 011 h i 100 and Brass (B) 011 f gh i 211

components developed flow surfaces similar to that

observed early in the deformation process. However,

with increasing plastic strain, the distortion along the

rTD direction was further intensified, and did not agree

with the experimental results shown in Figure 1(d). One

explanation may be that the model used by Barlat and

Richmond did not account for the continually evolving

texture that is developed in the sheet as deformation

progresses and the subsequent effect that this will have

on the flow surface.

While the basic understand of texture changes in

aluminum sheet during in-plane forming operations

have been studied for uniaxial,[5,6] plane strain,[5,7–9]

S.W. BANOVIC, M.A. IADICOLA, and T. FOECKE, Materials

Research Engineers, are with the Metallurgy Division, Technology

Administration, Department of Commerce, National Institute of

Standards and Technology, Gaithersburg, MD 20899. Contact e-mail:

swbanovic@nist.gov.

Manuscript submitted October 19, 2007.

Article published online May 17, 2008

U.S. GOVERNMENT WORK

NOT PROTECTED BY U.S. COPYRIGHT

2246—VOLUME 39A, SEPTEMBER 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
and equibiaxial[5,7–12] stretching, absent in these works

was a detailed analysis of the quantitative development

of texture modification with incremental plastic straining, particularly in the lower strain regime associated

with the sheet metal stamping process. Instead, the

greater majority of the work focused on the effect of

the initial texture on that of the evolved. Further, only

Savoie et al.[6] analyzed the crystallographic development along both the rolling direction (RD) and

transverse direction (TD) of an aluminum sheet under

a single deformation mode (uniaxial). Unfortunately, a

corresponding analysis of the mechanical behavior of

the materials was not conducted to indicate if the

change in sheet orientation, with respect to the major

stress axis, had an effect on the properties. Therefore,

to help provide a physical description of the evolving

yield surfaces throughout the deformation process,

investigation of the crystallographic texture development of the material tested by Iadicola et al.[3] was

initiated. This study characterizes the texture modification as a function of strain level of AA5754-O, which

has been deformed along both the sheet RD and TD

under three in-plane straining modes (equibiaxial,

plane strain, and uniaxial). These results will be used

to validate future polycrystal plasticity simulation

work.

Fig. 1—Multiaxial true stress–true strain data determined through X-ray diffraction[3] for (a) uniaxial, (b) plane strain, and (c) equal biaxial

strain. Plane strain stress data for near zero strain direction (and the associated von Mises predicted curve) are plotted using the first principal

strain for visibility in (b). (d) Derived points of equal plastic work plotted in stress space, with von Mises’ isotropic yield loci (solid curves) and

isotropic strain paths (dashed lines).

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, SEPTEMBER 2008—2247
II. EXPERIMENTAL TECHNIQUES

A. Materials and Deformation Procedures

The material used in this investigation was industrially processed AA5754-O sheet, nominally 1-mm thick,

with composition given in Table I. Figure 2 shows the

as-received microstructure of the commercial sheet

material. The grains are relatively equiaxed in the

rolling plane (Figure 2(a)) and slightly elongated along

the RD (Figure 2(b)). This is indicative of a recrystallized microstructure associated with the O-temper. The

nominal grain diameter in the rolling plane was approximately 40 lm. Constituent particles observed in the

polished cross section (Figure 2(c)) were well dispersed

and identified via energy dispersive spectroscopy as

primarily Al-Fe-Mn particles.

Samples were cut to appropriate dimensions for

testing and deformed in three strain states, indicated

by their principal strain ratio (q)

q 1⁄4 e2

e1

1⁄21

where e1 and e2 are the major and minor strains

measured within the plane of the sheet, respectively.

Standard test methods were used for uniaxial tension

(q = -0.5) with the rolling direction of the sheet aligned

both parallel and perpendicular to the major stress axis.

For plane strain (q = 0) and equibiaxial (q = 1)

tension, a technique based upon the Raghavan[13]

modification of the Marciniak in-plane biaxial stretching test[14] was employed; the specialized tooling is a

cylindrical ram and binder.[15] Mild steel was used as a

washer (driver blank) to prevent failure in the sidewall

of the aluminum test sheet; lubricant was applied to

those faces in contact with the tooling. The load of the

hold-down ring was maintained at approximately

340 kN, so that movement of material inward over the

draw bead was restricted while being deformed at a

constant central ram speed of 1.0 mm/s. Varying

amounts of stretching were obtained by setting the limit

control of the central ram to predetermined deflections.

The true in-plane strain was determined using a calibrated biaxial extensometer. Similar to uniaxial deformation, plane strain testing was conducted with the

sheet RD parallel and perpendicular to the main stress

axis. Under all modes, samples were produced approximately every 5 pct true strain to near-failure of the

plate, Table II. The through thickness strain, e3, was

determined through physical measurement of the thickness change. The effective strain, eeff, for equibiaxial and

Fig. 2—Microstructures of as-received sheet material: (a) and (b) differential interference contrast images showing grain size along different directions, and (c) SEM showing second phase (white).

Table II. Strain Levels (Percent) Achieved during In-Plane

Deformation*

Nominal Strain Level e1 e2 e3 eeff

Equibiaxial

5 5.1 4.9 -10.6 10.4

10 9.7 9.7 -21.6 21.0

15 13.9 14.0 -27.8 27.9

20 19.9 20.0 -41.2 40.8

Plane strain

5 4.9 -0.4 -3.5 4.9

10 9.8 -0.7 -8.6 10.7

15 14.2 -0.3 -12.7 14.7

Uniaxial

5 5.6 -2.3 -3.1 5.6

10 11.6 -4.7 -5.1 11.6

15 16.0 -6.5 -9.5 16.0

*Effective strains for equibiaxial and plane strain modes were calculated using the von Mises criterion.

Table I. Chemical Composition of As-Received AA5754-O

Determined Using ASTM E227

Element Mass Fraction · 100

Mg 3.75

Mn 0.29

Fe 0.24

Si 0.06

Cr, Cu, Pb, Ni, Sn, Ti, Zn individually <0.05

Aluminum balance

2248—VOLUME 39A, SEPTEMBER 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
plane strain modes was calculated using the von Mises

criterion

eeff 1⁄4

ffiffiffi

2

p

3 ð Þ e1 e2

2

þð Þ e2 e3

2

þð Þ e3 e1

2 h i1=2

1⁄22

B. Crystallographic Texture Evaluation

The macrotextures of the samples were measured

using an X-ray diffraction technique on a conventional

diffractometer with quarter Eulerian cradle. Samples

were illuminated using Cu Ka radiation. In order to

eliminate any possible gradients associated with the

surface layer, the samples were polished by hand to the

midplane of the sheet with a final step of 0.05 lm

alumina. An area detector was used to collect three

incomplete pole figures {111}, {200}, and {220} with 0

deg £ a £ 65 deg. The samples were oscillated over an

area of 6.4 cm2

. The data were corrected for background intensity.

For quantitative texture analysis, the three-dimensional orientation distributions (ODs) were calculated

from the pole figures using the arbitrary defined cell

(ADC) method based upon the work of Pawlik and

Pospiech[16] and Li.[17] Orientations were expressed by

Euler angles, u1, F, and u2 in Bunge’s notation,[18]

which relates the cubic crystal frame to the orthotropic

sample frame given by the normal direction (ND), the

RD, and the TD. To facilitate interpretations of

textures, ODs were represented by plotting iso-intensity

lines in sections of constant u2 through a subset of the

Euler angle space with 0 deg £ u1, F, u2 £ 90 deg. As

the textures were weak for the both the initial and

deformed materials, recalculated pole figures were

derived from the ODs and presented as a substitute of

the raw data.

Volume fractions of specific orientations were calculated using the following equation:

dV

V 1⁄4 fðgÞdg 1⁄23

with

dg  dðu1; U; u2Þ 1⁄4 1



8p2 sin UdUdu1du2 1⁄24

Integrating all orientations that have their misorientation, with respect to the given ideal orientation, less

than the given tolerance yields the volume fraction.

III. CRYSTALLOGRAPHIC TEXTURE

DEVELOPMENT

The following convention was used in the presentation of the texture data. Samples were tested with either

the rolling direction (RD-oriented material) or transverse direction (TD-oriented material) of the sheet

parallel to the major stress axis. For analysis of the

{111} pole figures, the major stress axis was aligned

parallel to the North-South poles.

A. {111} Pole Figures

Figure 3 shows the recalculated pole figures from the

as-received materials for both RD- and TD-oriented

materials. For the RD sample (Figure 3(a)), the sheet

displays a low degree of texture (peak intensity of

2 times random) with a combination of recrystallization

(cube f g 001 h i 100 , R f g 124 h i 211 ) and retained deformation (B f g 011 h i 211 , copper f g 112 h i 111 ) components,

typical of an O-temper material. Comparing the pole

figure from the TD-oriented material (Figure 3b), the

two are nearly identical, though rotated 90 deg about

the sheet ND. For the TD sample, the cube orientation

was also observable due to its four-fold symmetry.

Other secondary components were 90 deg rotations

about the sheet ND of components noted in the

RD-oriented pole figure: rotated (RND)-R (approximately 123 f gh i 341 ), P f g 011 h i 566 (90 deg rotation of

B orientation), and RND-copper 112 f gh i 110 .

Fig. 3—{111} recalculated pole figures of as-received sheet material:

(a) RD-oriented material, positions of the ideal orientations are

shown (cube n, R , Brass ¤, S D, copper :); and (b) TD-oriented

material.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, SEPTEMBER 2008—2249
Figures 4 and 5 show the development of the recalculated {111} pole figures as a function of deformation

mode and strain level schematically shown in stress

space for the RD- and TD-oriented material, respectively. In both material sets, equibiaxial straining

(q = 1) produced a nonuniform, ringlike pole distribution with maxima readily noted near the B (RD-sample

set) and P (TD-sample set) positions. For plane strain

(q = 0) and uniaxial (q = -0.5) modes, deformation

universally sharpened the majority of as-received texture

components, as well as the S orientation 123 f gh i 634 , in

the RD-oriented material. The TD-oriented material

also saw a strengthening of the cube orientation as well

as the development of a strong P component under

plane strain. Both cube and P orientations also

increased under uniaxial straining, however, preservation of the original texture was stronger in the uniaxial

case than in the plane strain condition toward the higher

strain level. The degree of texture increased only slightly

after the in-plane stretching compared to the as-received

material in both RD and TD material sets.

B. Orientation Distributions

1. As-received material

Recrystallization and retained deformation components are readily observed in the OD of the RD-oriented

material (Figure 6(a)). The texture was mainly concentrated around the cube orientation, though it was not

exceedingly sharp as spread was observed about all three

directions (ND, RD, and TD). Additionally, the R

component (recrystallization component close to the

former rolling texture component, S) was present at

about one third of the intensity of the cube (f(g)cube =

6.0, f(g)R = 1.9). Retained rolling components (B and

copper orientations) located in the b fiber were also

noted. For the TD-oriented material, the OD was

similar, but showed a 90 deg rotation about the ND

with maxima observed near the cube and P components.

Orientation intensity values for these components were

similar to their nonrotated counterparts. While no

evidence of a retained b fiber, with respect to the tensile

axis, was found, components in the RND-b fiber were

observed (P and RND-copper).

2. Equibiaxial deformation

Three u2 sections (u2 = 45, 60, and 90 deg) were

chosen to highlight the evolution of texture across the

strain range for each deformation mode. Figure 7 shows

these sections for both materials sets strained under

equibiaxial conditions. As no distinct major stress axis

occurred under this mode of deformation, the material

was first analyzed with the X-ray beam perpendicular to

the RD of the sheet and then rotated 90 deg about the

ND for the TD analysis. In general, deformation

resulted in the weakening of the as-received components

with strengthening of all orientations along the u1 axis

at F = 45 deg in the u2 = 90 deg section. For the

RD-oriented material, a maximum was observed near

the B orientation, while the P component developed for

the TD case.

3. Plane strain deformation

The u2 sections for the samples deformed under plane

strain mode are shown in Figure 8. Nearly all orientations found in the as-received RD-oriented material

strengthened with deformation with the exception of the

copper component (Figure 8(a)). The most substantial

change occurred for the cube component, though

the spread about this orientation was found to be

Fig. 4—Change in {111} recalculated pole figure with strain path

and strain level for the RD-oriented material where the plane strain

and uniaxial samples have their RD parallel to the major stress axis.

Fig. 5—Change in {111} recalculated pole figure with strain path

and strain level for the TD-oriented material where the plane strain

and uniaxial samples have their RD perpendicular to the major

stress axis.

2250—VOLUME 39A, SEPTEMBER 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
inhomogeneous with reduction in the scatter noted

along the ND and TD but increased along the

RD. Some of the components in the b fiber, specifically

S, were also observed to increase. Similarly, the

TD-oriented material had an overall strengthening of

the cube orientation, with an increase in the P component (Figure 8(b)). All other orientations decreased.

4. Uniaxial deformation

Texture evolution under uniaxial deformation

resulted in similar trends as found under plane strain

conditions (Figure 9). For the RD-oriented material,

the cube component and the majority of orientations

found within the b fiber strengthened significantly

(Figure 9(a)), while only the cube and P orientations

increased for the TD case (Figure 9(b)).

C. Volume Fraction Calculations of Texture Components

The volume fractions of major texture components

were calculated for numerous tolerance angles (x0) from

1 deg up to 20 deg from the ideal position. As the trends

were consistent at all x0, a tolerance angle of 10 deg was

chosen to represent the data to ensure that overlap of

texture components did not occur during the calculations.

From Figure 6(a), it appears that the cube orientation

of the RD-oriented material is the much stronger

recrystallization texture component in the as-received

material (f(g)cube = 6.0, f(g)R = 1.9). However, volume

fraction calculations indicate that the material contains

a higher fraction of R-oriented grains (4.5 pct than cube

(2.4 pct)), as seen in Table III for the strain level of zero.

The difference between orientation intensities and volume fraction results has previously been reported by

Engler[19]

and is due to the higher symmetry of the cube

orientation compared to the R orientation. Similarly,

the orientation intensities for B and copper components

in the as-received material are weaker than for cube

(f(g)B = 2.9, f(g)copper = 2.4), but volume fraction

calculations show that they were nearly equivalent

(B = 2.7 pct, copper = 2.2 pct).

Fig. 6—Orientation distribution for as-received material: (a) RD-oriented material with positions of ideal orientations (cube, R, Goss, Brass, S,

copper) and (b) TD-oriented material with positions of ideal orientations (cube, RND-R, RND-Goss, P, RND-S, RND-copper).

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, SEPTEMBER 2008—2251
With equibiaxial deformation, the volume fraction of

Goss and B-oriented grains in the RD-sample set

increased, while the major recrystallization and most

other retained deformation components decreased

(Table III). Volume fraction calculations for plane

strain and uniaxial deformation indicated that the most

significant increase was for the S orientation. All other

orientations either increased slightly or stayed approximately the same.

In the TD-oriented as-received material, the cube,

P, and RND-copper have similar volume fractions

(Table IV). The RND-R position had the highest volume

fraction. Equibiaxial deformation resulted in the increase

in volume fraction of P and RND-Goss oriented grains;

all others decreased. Under plane strain and uniaxial

modes, RND-R and RND-copper decreased and the

RND-Goss component appeared to have little change.

While volume fractions of cube and P orientations

increased for both types of deformation, there was a

more notable increase under uniaxial conditions.

IV. DISCUSSION

A. Crystallographic Texture Evolution

As the crystallographic anisotropy of the starting

aluminum sheet used in this investigation was relatively

weak, the deformation-induced textures of the two

sample sets for a given straining mode may be expected

to be similar. Furthering this argument, one of the

major texture components of the sheet is the cube

f g 001 h i 100 orientation, which has fourfold symmetry

and should respond similarly when the material is

rotated by 90 deg. Therefore, the observed anisotropy of

the material during stretch forming is primarily a result

of the other texture components that have lower

crystallographic symmetry. From the results of this

work, it was found that even though the initial texture of

the as-received material was weak, it still had a

significant effect on the evolved texture as a result of

deformation along perpendicular directions for each

straining mode.

Fig. 7—/2 sections at given strain levels under equibiaxial conditions (q = 1): (a) RD-oriented material and (b) TD-oriented material.

2252—VOLUME 39A, SEPTEMBER 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
Metallic sheet materials develop a preferred crystallographic orientation due to their thermomechanical

processing. Industrially produced sheet metal typically

has a combination of deformation and recrystallization

textures subsequent to the rolling and heat treating

practices used to obtain an O-temper.[20]

For the Al-Mg

alloy studied in this investigation, the starting texture of

the RD-oriented material contained recrystallization

components comprised of cube 001 f gh i 100 and R

f g 124 h i 211 orientations, while the retained rolling

textures were copper 112 f gh i 111 and B f g 011 h i 211 .

Of the three strain states evaluated, equibiaxial

stretching produced the strongest modification of the

initial texture as this mode of deformation resulted in

the largest effective strains (Table II). In both sets of

samples, grains rotated toward stable orientations

located in the 011 h iND fiber (along the /1 axis at

F = 45 deg, /2 = 90 deg), a result previously

shown experimentally[5,10,12] and theoretically[7–9,11] on

fcc materials. Reviewing these works as a whole indicates

that regardless of the alloy composition, starting texture,

or technique producing deformation (pure in-plane

tension vs in-plane tension with out-of-plane bending),

texture evolution of fcc materials under equibiaxial

conditions is similar. Further, the development of the

h i 011 ND fiber appears to have increased uniformly as a

result of the deformation in these previous studies.

From the incremental straining of the sheet during

this investigation, the 011 h iND fiber development was

inhomogeneous (Figure 10). This was a consequence of

the different reorientation rates of the individual texture

components across the strain range and the availability

of unstable feeder components to rotate toward the

more stable orientations. At the onset of straining the

RD-oriented material, cube grains, and those located

between cube and Goss components, rapidly flowed

along the F-axis toward the Goss position (Figure 6(a)).

Physically speaking, this is a rotation about the sheet

RD that significantly increased the Goss component

during the early stages of deformation. The orientation

density near the B position also increased in this strain

regime, though to a lesser extent than Goss, as grains

flowed along the b fiber toward B. Both reorientations

align the 110 h i direction of previously unstable grains

parallel to the sheet ND, establishing optimum slip

conditions along their slip system 111 f gh i 110 under

equibiaxial conditions. With further deformation to

10 pct strain, a significant increase in the orientation

density near the B position resulted as flow along

the b fiber continued to deteriorate the fiber itself

(Figure 11(a)). Rotations toward the Goss position

slowed considerably as cube-oriented grains have been

depleted from earlier deformation. Higher levels of

straining resulted in a more homogeneous intensity

Fig. 8—/2 sections at given strain levels under plane strain conditions (q = 0): (a) RD-oriented material and (b) TD-oriented material.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, SEPTEMBER 2008—2253
increase along the entire length of the 011 h iND fiber as

unstable grains from across the orientation space

continue to flow toward the fiber. The flux of orientations in this manner gives the general result of a

uniformly strengthened 011 h iND fiber compared to the

as-received texture.

As no distinct major stress axis occurs under equibiaxial deformation, a similar trend was observed for the

TD-oriented material, with similar rotations with

respect to the sample coordinate system. For this sample

set, the starting material displayed the cube component

and 90 deg rotations about the sheet ND of those

orientations observed for the RD-oriented material.

Upon straining, rotations around the sheet RD lead to

strengthening of the RND-Goss component initially, with

additional deformation strengthening 011 h iND fiber and,

in particular, the P orientation 011 f gh i 566 .

The dissimilar maxima that developed in the two data

sets (e.g., development of the strong B vs P orientations)

Fig. 9—/2 sections at given strain levels under uniaxial conditions (q = -0.5): (a) RD-oriented material and (b) TD-oriented material.

Table III. Volume Fraction Calculations of Various Texture

Components for RD-Oriented Material (x0 = 10 Deg)

Mode

Nominal

Strain Level Cube Goss B R/S Copper

Initial 0 2.4 0.6 2.7 4.5 2.2

Equibiaxial 5 2.0 1.1 3.0 4.0 1.4

10 1.5 1.1 3.4 3.6 1.3

15 1.2 1.2 3.9 3.2 1.0

20 1.0 1.2 4.1 2.9 0.9

Plane strain 5 2.7 0.8 2.7 5.2 2.4

10 2.9 0.8 2.9 5.9 2.7

15 2.8 0.8 3.0 5.8 2.2

Uniaxial 5 3.0 0.9 2.7 5.0 2.2

10 2.8 0.9 2.8 5.5 2.4

15 2.8 0.8 3.0 5.9 2.9

Table IV. Volume Fraction Calculations of Various Texture

Components for TD-Oriented Material (x0 = 10 Deg)

Mode

Nominal

Strain Level Cube

RNDGoss P

RNDR/SRNDCopper

Initial 0 2.4 0.6 2.7 4.9 2.2

Equibiaxial 5 2.0 1.0 3.1 4.0 1.4

10 1.5 1.1 3.4 3.6 1.3

15 1.2 1.1 3.9 3.2 1.0

20 1.0 1.2 4.1 2.8 0.9

Plane strain 5 2.9 0.7 2.7 4.2 1.7

10 2.8 0.7 3.0 3.6 1.1

15 2.7 0.7 3.3 3.1 1.0

Uniaxial 5 3.1 0.7 2.9 4.6 1.5

10 3.1 0.6 3.7 4.3 1.2

15 3.4 0.5 4.0 4.2 1.1

2254—VOLUME 39A, SEPTEMBER 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
were dictated solely by the presence or absence of

texture components found in the as-received sheet and

not related to stability considerations of the individual

components. In an isotropic material, ‘‘feeder’’ components (i.e., those in the b fiber or cube) would be

homogeneously distributed at all inclinations with

respect to the sheet RD. Under pure equibiaxial stress

conditions where no major stress axis exists, maxima

would not develop in the 011 h iND fiber as the fiber

would strengthen uniformly regardless of crystal direction. This development was modeled by Zhou and

Neale[8] using a rate-sensitive crystal plasticity model

together with full Taylor constraint theory indicating

that any orientation with an 011 h i parallel to the sheet

ND is stable under equibiaxial conditions. However, as

components populated the retained b fiber for the asreceived material of the RD-sample set, the B orientation was strengthened due to rotations through the b

fiber that feed this particular texture component in the

h i 011 ND fiber. For the TD-oriented material, feeder

components within the b fiber were not observed in the

as-received texture (Figure 5(b)), resulting in no grains

available to rotate along the fiber toward the B

component during deformation. As a result, the B

component was not observed to develop. Instead, the P

orientation was strengthened through rotations of

orientations in the RND-b fiber present in the TD-asreceived material. Thus, while the initial texture would

be considered weak, the difference in starting components, such as those in the retained b fiber, was enough

to result in dissimilarly evolved textures along the two

straining directions under equibiaxial straining, with the

strength of the components related to the level of plastic

deformation.

Under plane strain and uniaxial stretching, deformation of the material was significantly less than in the

equibiaxial case, eeff, of Table II. When compared to

balanced biaxial stretching, with two equal orthogonal

in-plane strains, the thickness strain to maintain constant volume in uniaxial or plane strain tension is on the

order of one half as large. Concurrently, a less dramatic

change was observed in the evolved texture from the

as-received material.

In general, significant sharpening of the major starting texture components was observed in both sets of

samples, with the additional development of the deformation component S f g 123 h i 634 in the RD-oriented

material, under both modes of deformation. For the

RD-oriented material, straining favored the formation

of 100 h i fiber parallel to the major stress axis (occupation along the F-axis at /1 = 0 deg in the /2 = 90 deg

section in Figures 8(a) and 9(a)) and, to a lesser extent,

h i 111 fiber parallel to the major stress axis. Alignment of

the grains in this manner is in agreement with previous

works[5,6,21] that show the 110 h i direction as being

Fig. 10—Orientation intensity plot of 011 h iND fiber under equibiaxial

straining conditions for RD-oriented material. Ideal positions for

Goss 011 f gh i 100 and Brass 011 f gh i 211 are indicated.

Fig. 11—Orientation intensity plots of b fiber under various straining conditions for RD-oriented material. Ideal positions for copper

f g 112 h i 111 , S f g 123 h i 634 , and Brass 011 f gh i 211 are indicated: (a)

equibiaxial and (b) uniaxial.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, SEPTEMBER 2008—2255
unstable under these deformation modes, with grain flux

toward the other two directions. However, strengthening in the 100 h i direction appears to be greater for both

cases. This can be attributed to the relative distribution

of orientations in the initial texture as the starting

material of this work is favored toward the 100 h i.

Wassermann and Grewen have previously shown a

similar influence by the starting texture on that of the

evolved.[22] Further, development of a 100 h i fiber

parallel to the major stress axis attempts to maximize

the resolved shear stress experienced by the four slip

planes of the crystal. The maximum resolved shear stress

occurs when the {111} planes are inclined at 45 deg to

the tensile axis. For grains with their 100 h i parallel

to the tensile axis, all four {111} slip planes are at 35.3

deg, very near the position of maximum stress. The

TD-sample sets also saw a significant increase in the

cube position, but did not have a similar spread about

the tensile axis (Figure 9(b)). Instead, a strong P

component emerged increasing the orientations with

h i 111 or near 111 h i parallel to the major stress axis.

The influence of the starting texture on the evolved

texture can be observed when comparing the results

obtained between the two data sets. Again, if the material

was isotropic, the texture development observed along the

RD and TD would be similar. However, the RD-oriented

material showed an increase for the S f g 123 h i 634 orientation and other components in the b fiber (Figure 11(b)),

whereas the b fiber did not develop for the TD-oriented

material. Similar to the equibiaxial case, this was again

due to the lack of feeder components of the TD-oriented

material in and around the b fiber that would strengthen

these texture components during deformation. As orientations in the RND-b fiber were observed in the starting

texture, development of the P orientation was seen in the

evolved texture due to rotation and flow of the retained

deformation components (RND-R and RND-copper) in the

as-received material.

Savoie et al.[6] also performed uniaxial experiments

with the tensile axis parallel to both the sheet RD and

TD of an experimental 5XXX series alloy. Analysis of

RD-oriented material showed strengthening of the cube

f g 001 h i 100 , S f g 113 h i 574 , P f g 011 h i 111 , and Goss

f g 011 h i 100 components observed in the as-received

texture. Comparable to the results of this work, they

also showed that similar textures developed for the

TD-oriented material. However, while fibers consisting

of 111 h i and 100 h i parallel to the tensile axis evolved, the

R and Goss orientations were weak or missing in the

deformation texture as grains oriented near these

components were not observed in the starting texture

of the TD-oriented material. Based upon the results of

Savioe et al., as well as the results of this present study,

it can also be concluded that texture development of a

weakly textured sheet is anisotropic under plane strain

and uniaxial straining.

B. Influence of Texture on Mechanical Behavior

The mechanical response of the sheet to a given

imposed strain state will be dictated by the aggregate

plastic behavior of the grains in the polycrystal. The

initial yield stress will be controlled in part by the initial

texture, and the hardening behavior in part by how the

texture evolves with increasing multiaxial plastic strain.

With a dataset that includes both the evolution of the

yield surface with strain and the corresponding texture

evolution, it can be determined what, if any, characteristics of the multiaxial stress-strain behavior can be

explained by the developing crystallographic texture. A

complete treatment using a Taylor-type analysis is

ongoing, but some characteristics of the flow behavior

can be modeled by comparing the experimental results

to the numerical yield surface predictions of Barlat and

Richmond[4] of idealized textured microstructures.

Barlat and Richmond calculated flow surfaces of fcc

rolled sheets containing grains having 50 pct of one of

the specified crystallographic orientations (copper, B, S,

cube, and Goss) with the remainder uniformly distributed over the remaining orientations. An isotropic case

was also considered. The yield surfaces were then

plotted in stress space after being normalized on the

uniaxial yield stress in the rolling direction for each

texture component. According to these calculations, the

isotropic case, cube and S textured sheets showed yield

surfaces that were symmetric about the 45 deg (i.e.,

identical yield behavior parallel and perpendicular to the

rolling direction), where cube had a slightly larger flow

stress in plane strain. Essentially all three orientations

behaved very similarly. Compared to the isotropic

results, the sheet containing the copper orientations

exhibited a strength decrease for plane strain in the

transverse direction and an increase for plane strain in

the longitudinal direction. The two remaining sheets,

with orientations of B and Goss, show very asymmetric

yield surfaces, with Goss producing a 50 pct increase in

plane strain yield stress in the transverse direction

compared to the longitudinal. The values of the respective normalized flow stresses measured from the plots in

Reference 4 are given in Table V.

A reasonable first approximation of the behavior of

the sheets in the present study is a linear combination of

the flow stresses predicted in Reference 4, weighted by

the volume fraction of grains with each crystallographic

orientation at each multiaxial strain level (Table III).

This in effect treats the sheet as a composite made up of

a matrix of grains, which average to relatively isotropic

properties and a dispersion of grains, each with one of

the specified crystallographic orientations, of the appropriate measured volume fraction. The trend of these

values can then be compared to the experimentally

determined flow stresses.

The values calculated in Reference 4 were each

normalized to the uniaxial flow stress of that particular

texture component. In order to combine them into a

composite flow stress, they must be renormalized to a

common flow stress. This is accomplished by calculating

the uniaxial RD Schmid factors for the various possible

slip planes for the texture components of interest, and

dividing each normalized strength by its corresponding

maximum uniaxial Schmid factor (Table V). While this

does not give an absolute value of the flow stress that

can be directly compared to experiments, it gives relative

values that will be used to compare to trends in the data.

2256—VOLUME 39A, SEPTEMBER 2008 METALLURGICAL AND MATERIALS TRANSACTIONS A
The composite flow stress for a given strain level and

state due to the texture is then given by

rYS 1⁄4 XrBR  1

SFRD;Uniaxial

 Vf 1⁄25

summed over all texture components including the

isotropic matrix, where rBR is the Barlat–Richmond

predicted multiaxial yield stress, SFRD,Uniaxial is the

maximum Schmid factor for the slip planes of the

texture component in uniaxial tension in the rolling

direction, and Vf is the measured volume fraction of

each texture component. For biaxial strain states (plane

strain, PS and equibiaxial, BB), the ratio of the stress in

the transverse direction to that in the rolling direction is

calculated, and compared to ideal isotropic results from

von Mises yield theory, the fcc isotropic case of Barlat

and Richmond,[4] and to the experimental observations

of this study (for nominally 5 pct strain). Note: For the

random texture, the SFRD,Uniaxial value is not known,

but the values of Vf,Random (the remainder of the

volume) and rBR (symmetric in RD and TD) are known.

The calculated ratios reported in Table VI neglect this

term (i.e., Vf,Random = 0). The other extreme would be

to calculate the ratio values for Vf,Random = 1 from

Table V (where the SF values being the same will divide

to 1), which would result in the values labeled as

‘‘Isotropic case.’’

In Table VI, the experimental ratios (calculated from

Figure 1(d)) are distinctly different from the von Mises’

isotropic predictions for the three strain states shown,

but the isotropic case from Barlat and Richmond

deviate from these values for plane strain in the

direction of the experimental results. The calculated

values using the previous equation tend to move the

ratio values closer to the experimental values for all

three biaxial strain states. This would suggest that a

polycrystal model would be able to capture some of the

changes in mechanical behavior if the texture changes

are included (especially for the specific components

considered here), and since the mechanical behavior and

texture both change with increased deformation, the

model used must include and properly predict the

texture evolution. Additionally, the model will have to

account for other factors, such as the work hardening

characteristics of the various texture components and

grain morphology. This might explain the remaining

difference between numerical and experimental results.

Therefore, modeling efforts are currently underway

using a Taylor-type analysis that will admit texture

evolution and work hardening, unlike the Taylor–

Bishop–Hill model used by Barlat and Richmond.[4]

V. CONCLUSIONS

The presented work provides the physical description

of texture evolution of a solution-strengthened Al-Mg

alloy whose flow surfaces were previously measured.[3]

From the results, it was observed that the change in

texture with in-plane stretching is considerably less

significant compared to other deformation processes of

aluminum alloys where through-thickness strains are

well in excess of unity (rolling, equal channel extrusion).

However, investigation of this lower strain regime is

necessary, as these strains are on the same order as those

observed during stamping operations. Further, as sheet

materials are rarely isotropic and deformation of sheet

metal typically does not occur exclusively along one

direction, it is necessary to investigate the mechanical

properties and subsequently evolved texture along

numerous directions to fully understand the behavior

of the material. From the results of this work, it was

found that similar textures developed in the two

material sets (RD- and TD-oriented samples) under

each mode of deformation, however, the strength of

specific orientations depended upon the amount of

deformation and intensity of components in the

as-received material. The differences were primarily

related to the flow of retained deformation components

located in the b fiber during straining of the sheet; the b

fiber was observed for the RD-oriented material but not

for the TD-oriented material. This nonuniform texture

development of the deformed sheet appears to contribute to the anisotropic mechanical response of the sheet

during stretching.

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Table V. Values of Normalized Yield Stresses from

Reference 4*

Direction Cube Goss B S Copper Isotropic

BB-RD 1.00 1.00 1.10 1.00 0.90 1.00

BB-TD 1.00 1.40 1.20 1.00 0.85 1.00

PS-RD 1.10 1.10 1.10 1.10 1.10 1.10

PS-RDM 0.50 0.60 0.50 0.45 0.40 0.50

PS-TD 1.10 1.50 1.20 1.10 0.95 1.10

PS-TDM 0.50 0.75 0.75 0.50 0.30 0.50

U-RD 1.00 1.00 1.00 1.00 1.00 1.00

U-TD 1.00 1.40 1.10 0.95 0.90 1.00

Schmid factor 0.41 0.41 0.41 0.43 0.27 0.40

*Note ‘‘M’’ denotes plane strain minor stress. Values are for theoretical mixtures of 50 pct isotropic and 50 pct respective texture

component. Also shown are the maximum Schmid factors calculated

for each orientation in uniaxial tension in the RD.

Table VI. Values of Yield Stress Ratios (Transverse over

Rolling Direction) after 5 Pct Multiaxial Prestrain

PS-TD PS-RD BB

Von Mises’ isotropic 2.00 0.50 1.00

fcc isotropic case[4] 2.20 0.45 1.00

Calculated (Eq. [5]) 2.27 0.43 1.01

Experimental (Fig. 1(d)) 2.71 0.31 1.12

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, SEPTEMBER 2008—2257
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