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Experimental study of aluminum sheet surface roughness using optical interferometry

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Title:
Experimental study of aluminum sheet surface roughness using optical interferometry
Creator:
Lucachick, Glenn Arthur
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English
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xii, 57 leaves : illustrations ; 28 cm

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Subjects / Keywords:
Sheet-metal ( lcsh )
Aluminum ( lcsh )
Surface roughness -- Measurement ( lcsh )
Optical interferometers ( lcsh )
Aluminum ( fast )
Optical interferometers ( fast )
Sheet-metal ( fast )
Surface roughness -- Measurement ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 56-57).
General Note:
Department of Mechanical Engineering
Statement of Responsibility:
by Glenn Arthur Lucachick.

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Source Institution:
University of Colorado Denver
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Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
747705349 ( OCLC )
ocn747705349
Classification:
LD1193.E55 2011m L82 ( lcc )

Full Text
EXPERIMENTAL STUDY OF ALUMINUM SHEET SURFACE
ROUGHNESS USING OPTICAL INTERFEROMETRY
by
Glenn Arthur Lucachick
B.S., University of North Dakota, 2008
A thesis submitted to the
University of Colorado Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Mechanical Engineering
2011


This thesis for the Master of Science
degree by
Glenn Arthur Lucachick
has been approved
by
Atousa Plaseied
^0 / 2.0
Date


Lucachick, Glenn Arthur (M.S., Mechanical Engineering)
An optical interferometry investigation of the evolution of surface roughness
during manufacturing process simulations
Thesis directed by Associate Professor Rafael Sanchez
ABSTRACT
During sheet metal forming, the surface finish changes as the sheet
slides, bends, and stretches against the tools. Specially engineered surface
finishes have been developed by automakers to improve forming consistency
and painting quality. This study assessed the evolution of surface parameters
on aluminum sheet surface finishes during manufacturing processes.
The scope of this work is experimental. Two surface finish conditions
were studied, mill finish (MF) and electro discharge texture (EDT). The 3D
Surface roughness conditions were determined for these materials in both the
longitudinal and the transverse rolling directions of the sheet. The sheets were
tested using several tests (i) three pin Draw Bead Simulator (DBS) tests, with
tests run under fix and roller conditions, (ii) pure bending moment tests, (iii)
and tensile tests. A 3-D Wyko profilometer was used to take the surface
roughness measurements.
The changes in surface roughness due to bending effects, tension
effects, and contact effects are investigated for both material types and rolling


directions. The results indicate that the creation of new surface features during
tensile straining under both bending and tension are more significant in
influencing surface textures in MF sheet than in EDT sheet. During the initial
change in curvature for DBS and pure bending moment tests from flat to
concave the MF samples experienced an average increase in roughness 390%
greater than EDT. This trend is observed in similar strain directions
undertaken during the cycles investigated. Conversely, the effects of contact
pressure and friction were found more influential for EDT surface textures
than in MF at the middle pin. At that location, the transition from an un-
contacted convex surface to a concave surface under DBS contact pressure
results in a surface roughness 10% less than the starting value for EDT
samples, whereas MF returns to approximately the original value.
This study showed changing trends on the surface roughness of sheet
metal under bending and tension. It also shows a methodology to assess those
roughness changes. The understanding of the contact effects on surface
roughness for sheet textures may provide insight for further texture
optimization and to the understanding of friction itself.


This abstract accurately represents the content of the candidates thesis. I
recommend its publication.


ACKNOWLEDGEMENT
Great thanks to my advisor Dr. Rafael Sanchez for guiding and encouraging
me in this research. Also thanks to Melanie Nelson and Nicholas Williams for
their contributions in the laboratory for my data processing. Thanks to the
CAPT center, and the help of director Larry Scherrer in training me to use the
Wyko Interferometer. Also, thanks to General Motors for providing the
materials and inspiration for the research.


TABLE OF CONTENTS
LIST OF FIGURES.....................................................x
LIST OF TABLES....................................................xii
1. Introduction.....................................................1
1.1 Motivation......................................................1
1.2 Manufacturing background........................................2
1.3 Drawbead Simulator..............................................4
1.3.1 Fixed Drawbead................................................4
1.3.2 Roller Drawbead...............................................5
2. Prior Work.......................................................7
2.1 Surface Strain..................................................7
2.2 Contact Pressure...............................................11
3. Methods of Experimentation and Data Collection..................12
3.1 Surface Texture Characterization...............................12
3.1.1 Amplitude Parameters.........................................12
3.1.2 Volume Parameters............................................13
3.1.3 Spatial Parameters...........................................13
3.2 Tested Materials...............................................14
3.2.1 Surface Types................................................15
Vll


3.3 Material Processing..............................................19
3.3.1 DBS Sample Preparation..........................................19
3.3.2 DBS Processing..................................................19
3.3.3 Uniaxial Tensile Processing.....................................22
3.3.4 Pure Bending Moment Processing..................................23
3.4 Optical Interferometry..........................................27
4. Results and Discussion.............................................29
4.1 DBS Friction Results.............................................29
4.2 Roughness Amplitude Results......................................31
4.2.1 Uniaxial Tensile Sa Results.....................................31
4.2.1.1 EDT Uniaxial Tensile Roughness Results........................32
4.2.1.2 MF Uniaxial Tensile Roughness Results.........................34
4.2.1.3. Uniaxial Tensile Interpretation..............................35
4.2.2 Pure Bending Moment Results...................................36
4.2.2.1 EDT Pure Bending Roughness Results............................36
4.2.2.2 MF Pure Bending Roughness Results.............................41
4.2.2.3 Pure Bending Moment Interpretation............................41
4.2.3 DBS Results...................................................43
4.2.3.1 MF Transverse DBS Results.....................................43
4.2.3.2 MF Longitudinal DBS Results...................................45
Vlll


4.2.3.3 EDT Transverse DBS Results......................................46
4.2.3.4 EDT Longitudinal DBS Results....................................49
4.3 Plasticity Index Results............................................52
5. Summary and Conclusions..............................................53
Bibliography............................................................56
LIST OF FIGURES
IX


Figure
1. Drawbead Schematic and Finished Part..............................3
2. Fixed Bead Drawbead Schematic.......................................4
3. DBS by Sanchez......................................................5
4. Roller Drawbead Schematic...........................................6
5. Processed Sample with Locations Labeled...........................5
6. DBS Sample Strain Histogram.......................................10
7. MF Textures in both Longitudinal and Transverse Orientations......16
8. EDT Textures in both Transverse and Longitudinal Orientations.....18
9. Schematic and Photograph of EDM Dissection........................21
10. Pure Bending Moment Device.......................................24
11. Razor Etched Interferometer Image................................27
12. Wyko NT-2000 Optical Interferometer...............................28
13. Interferometer Objective Lens in Scanning Mode...................29
14. EDT Uniaxial Tensile Sa Results..................................32
15. MF Uniaxial Tensile Sa Results...................................35
16. MF Transverse Pure Bending Roughness Evolution...................38
17. MF Longitudinal Pure Bending Roughness Evolution.................40
18. EDT Transverse Pure Bending Roughness Evolution..................41
19. MF Transverse Sa Roughness Evolution.............................44
x


20. MF Longitudinal Sa Roughness Evolution.............................46
21. EDT Transverse Sa Roughness Evolution..............................47
22. EDT Longitudinal Sa Roughness Evolution............................50
LIST OF TABLES
xi


Table
I. Friction Table.................................................30
II. Sa Values vs. Tensile Strain..................................33
III. Sample Thickness Changes During Pure Bending Sequence........39
IV. Plasticity Index for Uncontacted 3B...........................53
xii


1. Introduction
1.1 Motivation
The continued improvement of sheet metal forming requires careful
analysis of the surface topography of the sheet metal. The characterization of
the surface texture of aluminum alloy sheets is an important parameter
influencing formability, friction, and painted appearance for the forming of
automotive parts [1]. This characterization is especially important as new
surface textures and patterns are introduced, electro discharge textures (EDT)
are credited with improving painting and formability and their use is
becoming more extensive in Europe[l,2], while traditional mill finish (MF)
textures remain popular in North America. While the factory surface finish
qualities for these sheets are well known, surface roughness changes affected
by forming practices are also of great importance in manufacturing and are of
primary interest in this study.
The introduction of non-contact 3d optical interferometer technology
allows defining surface parameters to extents not allowed with conventional
2d interferometer techniques. In their studies of sheet metal surfaces, M.
Pfestorf et al [3] showed the significant advantages offered by 3D instruments.
Optical interferometry is particularly useful for studying contact and friction
1


phenomena and investigating changes due to the complex interactions with the
tooling, lubricants and sheet metal. An extensive presentation of
characterization techniques and their applications can be found in [4]. In this
study, 3D non contact interferometry is used to measure changes in texture for
aluminum alloy sheet under plane strain cyclic bending with stretching and
compressing. These modes of deformation are predominant in the forming of
automotive parts, and are simulated in this study by the passage of the sheet
through cylindrical drawbeads. Other tests, such as the Pure Bending Test, and
the Tensile Test, were performed in order to provide fundamental data
important to the understanding of the cyclic bending with tension case.
1.2 Manufacturing Background
Controlling the flow of material into die cavities during stamping and
forming operations is important for controlling overfeeding of the sheet,
wrinkling, and material thinning. This control can be accomplished with the
use of blank holders that use friction, or a combination of friction and
deformation. In many cases, friction from flat clamping binders is not
sufficient to control the flow of the material[5]. In these cases, a drawbead is
used (figure 1.).
2


Figure 1. Drawbead Schematic and Finished Part
Drawbeads provide the material with back-tension due to both friction and
deformation mechanisms. The contribution to back-tension from the force
required to deform the material around the drawbead is several times greater
than the force of friction imparted by the drawbead. This gives the benefit of
smaller blank holder forces, reduced contact pressure, more consistency and
reduced friction on the part during forming operations verses entirely friction-
based flat blank holder surfaces.
3


1.3 Drawbead Simulator
1.3.1 Fixed Drawbead
The drawbead forming process is replicated using a Drawbead Simulator
(DBS) patterned after H. Nine [5]. The sheet metal is pulled at constant rate
between three fixed cylindrical pins. While the pins can be positioned with
axes non-coplanar, most manufacturing conditions as well as this study are
conducted with axes aligned along the same plane. Figure 2 shows a
schematic of a three-pin, circular drawbead.
Sheet
Metal
4


A DBS designed and fabricated by Sanchez was the device utilized for this
study(Figure 3.).
Figure 3. DBS by Sanchez
1.3.2 Roller Drawbead
As mentioned earlier, most of the force required to draw the sheet through
the DBS is used to deform the material, however the force due to friction is
not insignificant. Substituting the fixed drawbeads for rolling drawbeads, the
beads are allowed to roll freely with the material (Figure 4.). As the
5


coefficient of friction for the ball bearings supporting the roller beads is on the
order of .002, friction can be considered negligible for this condition.
Figure 4. Roller Drawbead Schematic
The forces are recorded during the drawing process and the material is
tested using both the fixed and roller drawbeads. The pulling and clamping
forces are recorded by load cells on the test fixture. The coefficient of friction
is determined using the following equation (1)[5].
6


F
1 Pull, Roller
1
M = -
x
Pull, Fix
Clamp, Fix
0)
2. Prior Work
2.1 Surface Strain
Surface straining is one of the two primary mechanisms for affecting
surface texture. The DBS process is unique in deforming the sheet under
cyclic plastic plane strain. Each test sample is strained in three reversing
cycles. The total accumulated strain (the summation of the absolute value of
all cumulative strains) at the sheet surface is over 30%(see Figure 5) for
typical DBS samples. Resultant strains in the most strained locations can be as
much as 20%. The net strain upon exit from the fixed pins depends on friction,
but is typically 10%, and approximately the same for both sides. Five
locations (Figure 5) were identified as the most significant to our study. The
evolution of the surface roughness on the outer layers was investigated in
those five positions, on both the concave and convex sides.
7


3B
In the discussion that follows, it is important to note that the pulling force
(the resultant force pulling the sheet through the pins) increases from zero at
the inlet to a maximum at the outlet. This implies that the amount of stretching
superimposed to bending is different for each pin. Upon entering the DBS,
side A is subjected to a compressive strain typically around 9% (region 2) as it
bends to conform to the first pin. While side A is concave, and under
compressive strains, side B is subjected to tensile strains of similar magnitude
to side A. At location 2, the material has bent to contact with the first
drawbead pin. The sheet has undergone bending plastic deformation. Since the
inlet force is zero, the amount of net pulling force was not significant at this
location. This is evidenced by the similar strains on both compressive and
8


tensile sides seen in Figure 5. During the change in curvature that occurs in
between the first and second pins of the drawbead(region 3), the curvature of
the sheet is completely reversed within a gap between pins equal to only 0.003
inches plus sheet thickness. The material experiences high strain rates as the
sheet passes it inflexion point. Strain rates two orders of magnitude larger than
standard uniaxial tensile testing are normal. Nevertheless, aluminum sheets
are not strain rate dependent and are unaffected by this rapid curvature
change. During this reversal from pinl(location 2) to middle pin (location 3),
side A goes from compressive straining to tensile straining, a total change of
around 16%. Side B undergoes an opposite, but similar straining mechanism.
The net compressive strain on side B at location 3 is smaller than that for side
A at location 2, because of the additional effect of the tensile pulling force
acting on the cross section. In between the second and the third pin, the sheet
undergoes another full reversal as it conforms to the curvature of the third pin
(region 4). At this location, side A is on the compressive side, however, the
compressive strains are not large. The pulling tension becomes significant at
this location and significantly reduces the amount of compressive straining (to
about 4% for the case shown in Figure 6.)[7]. The neutral axis has shifted
closer to the compressive outer fiber because of this superimposed pulling
tension. Upon exiting the DBS at region 5, the sheet is unbent. Strains in side
9


A become tensile, while those in side B are reduced upon unbending. The net
resultant strain (around 9%) are close for both sides, but not equal. Strains at
side B remain slightly higher, as the sheet was not unbent past its point of
inflection. This results on a noticeable final curvature in section 5 typical of
aluminum samples.
10


2.2 Contact Pressure
The contact pressure on the sheet is a function of two phenomena.
Describing the first, the sheet wraps around the respective drawbead pins in an
arc described by the term sliding angle. The net tensile force at the end of this
sliding angle is resolved by the effect of friction caused by the contact
pressure against the sheet. For the frictionless case, the pulling tension does
not increase through this sliding angle, as the sheet rolls along with the
drawbead pin. For the friction case, the tension increases, and thus the contact
pressure increases. Because the thickness of the sheet is significant compared
to the radius of the drawbead, describing the contact pressure as resolved
entirely by the net tensile loads exerted on the sheet following a membrane
model is not adequate. As the sheet reverses in curvature at the beginning and
ends of the sliding angle, there is a large transverse shear force that must be
supported by the pin to execute the bending or unbending. This results in a
spike in the contact pressure that represents the most severe contact pressure
experienced by the pin[7]. While the analytical model developed by Sanchez
does determine the shear forces present on pin entrance and exit, further
experimental studies are necessary to assess the actual size of the contact areas
for those localized shear effects.
11


3. Methods of Experimentation and Data Collection
The surfaces parameters under investigation are the 3-Dimensional
Roughness average (Sa), normalized volume, RMS roughness (Rq), and
various spatial parameters. The roughness average and volume parameters
were primary indicators of the effect of the DBS on the sheet surface features
and are the parameters discussed here. Other spatial parameters are used to
predict the changes on the surface due to contact forces.
3.1 Surface Texture Characterization
3.1.1 Amplitude Parameters
There are a myriad of surface texture parameters that can be used to
characterize a surface. Amplitude parameters provide information relating to
the height differences in surface valleys and asperities. Sa or surface
roughness arithmetic average is a common amplitude parameter used in
manufacturing (Equation 2.).
(2)
12


The variable Y is the distance of a surface point from a plane defined as the
mean of the surface.
RMS or RQ roughness is a measure of the standard deviation of the
surface. High asperities and Valleys are given greater weight than in Sa
calculations(Equation 3.). This parameter is important in performing contact
analysis.
3.1.2 Volume Parameters
Surface volume data defines the volume of empty space between the
lowest valley of the surface to the top of the highest peak. This parameter is
evaluated in this study because it is used in evaluating mean lubricant film
thickness, deformation of local maxima, and lubricant containment.
3.1.3 Spatial Parameters
Amplitude parameters do not supply any information related to the spatial
characteristics of features. Two surfaces represented by sine waves can have
(3)
13


equal amplitudes and Sa values but vastly different shapes given by different
frequencies. Surface deformation and friction characteristics are dependent
not only on amplitude parameters, but also spatial-dependent parameters such
as asperity radius and asperity frequency No is the number of zero crossings
per unit length. Np is the number of local maxima per unit length, where a
local maxima is defined as any point where the adjacent points are lower. Rp
is asperity tip radius.
3.2 Tested Materials
The material under investigation for this study is 6000 series cold-rolled
sheet aluminum. Although the material of choice for automotive application is
sheet steel (lower cost), aluminum is increasingly considered a material of
choice for automotive applications due to its more advantageous weight and
strength characteristics. Aluminum is strain rate insensitive, but it is more
prone to surface damage such as scoring and galling. Also, while steel is more
isotropic, the mechanical properties of aluminum show dependence on the
direction of the grain and its behavior is more orthotropic.
14


3.2.1 Surface Types
The two surface types under investigation are created with two
different methods. Mill Finish (MF) textures are the standard rolled surfaces
created by the rolling process. The rollers are tangentially ground, imprinting
directional grain effects on the sheet. They have relatively low roughness, but
exhibit different frictional properties along different directions. The roughness
inherent to the sheet is a byproduct of the elongation and deformation of the
grain structure under the finish roller. Figure 7 shows a 3D surface roughness
texture typical of mill finish. The anisotropic roughness is noted along the
longitudinal and the transverse directions.
15


Figure 7. MF Textures in Both Longitudinal and Transverse Orientations
Electro-Discharge Textures (EDT) are created by rolling the sheet using a
special roller that has been textured by an electrodischarge process. The
texture of the drum is impressed onto the rolled sheet. EDT textures are more
16


expensive to produce than MF textures. In this study, EDT surfaces will be
analyzed in both the longitudinal and transverse directions. EDT textures
(Figure 8) do not show a preferential pattern with direction.
17


I***-'-
Figure 8. EDT Textures in Both Transverse and Longitudinal
Orientations.
18


3.3 Material Processing
3.3.1 DBS Sample Preparation
DBS samples of dimensions 2xl6x sheet thickness were cut from a
large blank with a power shear, and the edges were de-burred with a hand
tool. These samples were scrubbed with a combination of isopropyl alcohol
and P-xylene to remove all debris and packing grease. The samples were
immersed in a bath of Enviro-Tech N-solv solvent with a solute of MP404
prelube in a carefully controlled concentration. The solvent was allowed to
dry leaving a film of oil weighing 1 gram per square meter. The proper mass
application of oil was verified using a precision scale.
3.3.2 DBS Processing
Once the samples are cut, cleaned, and lubricated, they were subjected to
testing in the DBS. A PDAQ data acquisition system used with Labview data
processing software enabled the collection of data. The samples were loaded
into the DBS, the bottom was clamped using hydraulic grips, and the center
drawbead was moved into place with a hydraulic ram, forcing the part to
conform to the contours of the drawbeads. A large power screw was actuated
electronically and the hydraulic grips pulled the sample through the beads at a
rate of 85 mm/s (200 ipm). The pulling force and the clamping force were
19


recorded during the entirety of the process. An initial transient condition is
present due to the inertia of the device components and the static friction that
is overcome at the start of the process. Pulling and clamping data were
collected around mid-stroke, where the data typically exhibit a plateau. Data
from the plateau are used in the friction and load calculations. The sample is
carefully removed from the apparatus and packaged in order to prevent
surface damage. The sample is then dissected into five small sections using an
EDM wire cutting machine (Figure 9), allowing the interferometer lens access
to the areas of interest. This process was repeated for all samples using both
the roller drawbeads and the fixed drawbeads.
20


3B
3A
Figure 9. Schematic and Photograph of EDM Dissection
The outer layer for side A can be seen to evolve from flat to concave
(location 2) to convex (location 3) to concave (location 4) to (approximately)
flat at the exit (location 5).
21


Correspondingly, the outer layer of side B becomes convex at location 2,
concave at 3, convex at 4 and unbent to -flat at 5.
It is noted that the contact sections at which friction is operative are given
by the concave outer layers, locations 2 and 4 side A, and location 3, side B.
At those locations, the resulting amount of compressive straining depends on
the contribution of the amount of pulling tension at the location. The resulting
Sa roughness values may depend on this resultant straining, added to peak
flattening resulting from sheet and tool contact.
In an effort to isolate the combined effect described, two additional tests
were included in the surface roughness tests: the uniaxial tension test, and the
pure bending moment test.
3.3.3 Uniaxial Tensile Processing
Uniaxial samples were processed on an Instron test fixture. These samples
were razor etched perpendicular to the direction of tension for tracking strain
data after processing. The samples were strained monotonically. It should be
noted that the strains from the tensile test are uniaxial, while the strains from
the DBS are plane strain, with approximately zero strain along the width
(since the sample width remains constant). The uniaxial tension test follows
22


the ASTM E8 standard for sheet metal. It is universally used and no further
details are given here.
3.3.4 Pure Bending Moment Processing
The pure bending moment device was developed by Sanchez to
investigate plane strain pure bending, Bauschinger Effect and springback
phenomena. It is noted that the plastic strains from this test are plain strain, as
are the strains from the DBS tests. A major difference to the DBS is the zero
pulling tension under pure bending. Figure 10 shows the working mechanisms
of this device.
23


Sheet
Specimen
Torque load
cell
Pulley
Bearing
Carriage
Figure 10. Pure Bending Moment Device
24


The sheet is held between two clamps. One clamp is mounted to a rigid
frame and the other is mounted to a moving mechanism consisting of a load
cell, a pulley and a moving carriage. The pulley is supported by a bearing and
rotates freely on the moving carriage. The carriage is supported on linear
bearings and the pulley can rotate and translate in the horizontal plane with
minimum friction. Weights hanging on cords (not shown) apply the couple
shown by the arrows in Figure 10. The couple is opposed by the resistance of
the sheet to bend and it is monitored by the torque load cell. The load is
removed during unloading. Reverse loading is applied by wrapping the strings
on the opposite direction, inverting the direction of the load applied to the
pulley.
Before processing in the pure bending moment device, the samples were
cut to 2x2 size and marked with a razor etched grid in the center of the
bending area (Figure 11). This grid was used to track the strain of the outer
fibers of the material. The use of strain gauges on pure bending moment
samples is difficult and laborious due to strain gage requirements for large
deformations. To achieve strains similar to that of the DBS, the sample has to
be bent in a very narrow region, and the maximum strains either require
plastic strain gages that are difficult to mount and require high oven
25


temperatures and large curing times. Furthermore, strain gages must be
discarded under reverse bending due to hardening effects.
The device was carefully loaded in a two person team. Weights are slowly
added to both sides of the machine in tandem to ensure the only load on the
sample is a bending moment. Weights are added until the sample reaches a
curvature of the same radius as the drawbeads on the DBS. Achieving levels
of strain similar to that of the DBS was the goal in order to investigate the
effect of tensile and compressive strain in the absence of contact forces. The
part was then carefully removed from the device, scanned in the
interferometer, and returned to the device to perform a reversal of the bending
cycle that was executed prior. A total of three bends and rebends were
performed, replicating the cyclical bending of the DBS machine. Surface data
was also captured for strains between the two bending reversals (flat surface
between bending reverse bending).
26


Figure 11. Razor Etched Interferometer Image
3.4 Optical Interferometery
For this study a Wyko NT-2000 optical interferometer (Figure 12.) was
used for 3d surface data collection. The interferometer was operated in VSI
(vertical scanning interferometry) mode. The scan area was 2.432mm by
1.852 mm with a lateral resolution of 3.31 pm and a vertical resolution of .1
27


nm. This resolution was more than adequate to capture the features of the
aluminum sheet.
Figure 12. Wyko NT-2000 Optical Interferometer
To scan the data, the sample was places squarely under the objective
lens(Figure 13). The curved samples were positioned such that the scan
occurred at the center of their arc. The interferometer scans from the top
down, capturing the highest features first and then scanning down towards the
lowest points of the surface. The vertical scanning distance was adjusted from
25 pm for flat surfaces to up to 180 pm for curved sections.
28


Figure 13. Interferometer Objective Lens in Scanning Mode
The result of the scan is an optical file representing the surface of the
samples.
4. Results and Discussion
4.1. DBS friction results
The friction results gathered by the DBS test device are created using
samples cut from the same blank, and are created using averages from at least
ten samples. This ensures the roller DBS samples and the fixed bead DBS
29


samples will possess the same mechanical properties and surface texture. The
friction and load results are as follows (Table I)
Table I. Friction results for EDT samples and MF for two suppliers
Material Surface Finish Rolling Direction Roller Force N DBS Friction Coefficient
AA6022 Mill Finish Longitudinal 3273 0.078
Mill Finish Transverse 3120 0.048
GMW15192 Mill Finish Longitudinal 3212 0.088
Mill Finish Transverse 3078 0.031
GMW15192 EDT Longitudinal 3114 0.122
EDT Transverse 2944 0.115
Although for these materials Mill Finish texture has the lowest friction
characteristics for both longitudinal and transverse directions verses the EDT
samples, this is not necessarily more desirable. EDT textures offer close to
isotropic friction, with very small difference between longitudinal and
transverse directions. MF instead, has significant differences on friction along
the longitudinal and transverse directions. The trend of reduced friction in the
transverse direction verses the longitudinal direction has also been reported in
other sliding friction studies. It is believed that transverse roughness
characteristics promotes larger film thicknesses than longitudinal surfaces in
similar conditions [6]. It is interesting to note that the tensile pulling forces
30


reported for the Roller in Table I, results on stresses around 10 000 psi, which
are significantly smaller than the yield of the material. The combined bending
and stretching mechanism allows for the plastic deformation under DBS
testing.
4.2 Roughness Amplitude Results
Roughness average Sa is a common measure of surface roughness in the
automotive industry. The effects of the DBS process are evident in the study
of the evolution of the surface Sa roughness as it travels through the DBS. To
develop a fundamental understanding of the effects of material processing on
the samples, the results from the simpler uniaxial tension and pure bending
moment tests are presented before the DBS results
4.2.1 Uniaxial Tensile Sa Results
The uniaxial tensile test is a common test used to evaluate the strength and
hardening properties of material. Our material was strained in two steps. The
material was strained to around 10% elongation, since most of our testing is
around this magnitude of strain. One side of the tensile test sample was
selected and scanned for roughness data. The test sample was then replaced in
31


the uniaxial tester and strained to failure. The at-failure samples are then
scanned for roughness data.
4.2.1.1 EDT Uniaxial Tensile Roughness Results
The results for both longitudinal and transverse orientation EDT samples are
plotted in Figure 14.
1.2 4
0% elongation 10% elongation elongated to fracture
Sample Condition
Figure 14. EDT Uniaxial Tensile Sa Results
32


It is observed that the evolution of the surface roughness in the tensile test
was linear with tensile strain tor the EDT along the transverse direction (T) ,
and non-linear along the longitudinal direction (L). Sa is smaller for the
longitudinal sample than for the transverse sample at 10% strain. However,
the trend reverses for the L sample at fracture. It should be noted that the
longitudinal sample fractured at 28.3% elongation where the transverse
sample fractured at 22.25% elongation. The increase in roughness for the
longitudinal sample may be due to reaching larger strains. Of interest here are
the Sa values around 10% strain (Table II).
Table II. Sa values vs. Tensile Strains
Condition Tensile Strain Sa (pm)
EDT L 10% 1.56
EDT T 10% 1.47
MF L 10% .77
MF T 10% .80
EDT L Fracture at 28.3% 2.1425
EDT T Fracture at 22.25% 1.8075
MF L Fracture at 28.2% 1.415
MF T Fracture at 28.75% 1.57
33


Although the effect of tensile strain on Sa is considerable at fracture
(around 40% and 50% at T and L, respectively), it is much less pronounced at
10% strains, with (10% along L and 18% along T)
4.2.1.2 MF Uniaxial Tensile Roughness Results
The results for the MF samples exhibit similar monotonic increases in
surface roughness under tensile strains (Figure 15.)- The transverse sample
achieves a higher roughness than the longitudinal case. However, the
difference is small and may be equivalent at 10% strain. The fracture strains
are 28.75% for the transverse case and 28.2% for the longitudinal case.
These results show high sensitivity of Sa values to mill finish tensile
straining. At fracture, Sa increased from an average of .35 pm to 1.4 -1.6 pm
Sa. This represents an Sa increase to tensile strains at fracture of more than
300%. This number compares to 40-50% increase on Sa for the EDT
samples.
34


I E
w
3
O
cc
TJ
m
tD
l/>
i
Mill Finsh Uniaxial Tension Sa Roughness
0% elongation
10% elongation
elongated to fracture
MF
Longitudinal
MF Transverse
Sample Condition
Figure 15. MF Uniaxial Tensile Sa Results
4.2.1.3 Uniaxial Tensile Interpretation
Previous studies indicate that the increase in surface roughness due to
intrinsic surface defects occur as a result of surface displacement fields that
occur as a result of microstructural dynamics during tensile plastic straining
[8,9]. Earlier studies have shown surface roughness to increase linearly during
low-strain conditions [10], and to become increasingly non-linear for greater
strains [11]. Surface roughness increases linearly and monotonically for
tensile strains from 0 to 10%, as shown in Table I.
35


4.2.2 Pure Bending Moment Results
The results for the pure bending moment give important insights on the
mechanisms influencing surface roughness in the DBS test that the uniaxial
test simply cannot give. The pure bending moment device allows the
investigation of roughness changes for compressive and tensile strain under
cyclic loading. The compressive strains develop as free surfaces, and do not
include contact or friction effects. While the literature reports extensive Sa
values in terms of tensile strains, compressive strains on sheet metals are
largely missing. In addition, pure bending strains are plane strains, which is
also the mode of deformation in DBS testing.
As shown in Table I, DBS friction for MF samples are significantly
different for the L and T directions, but close to isotropic for EDT. Sa
evolution under cyclic pure bending was determined for the MF sheets along
the longitudinal and the transverse directions, but limited to the transverse
direction for the EDT material.
4.2.2.1 MF Pure Bending Roughness Results
The Pure Bending Sa values for the MF Transverse texture are shown in
Figure 16. Starting from the originally flat sample, the Sa values for side A
and Side B are identical during the first bend in which side A is concave. Bent
36


from flat, Sa increased from 0.4 to ~ 0.84 pm for both sides. This implies that
the compressive (concave side) and tensile strains (convex side) had an
equivalent influence in Sa. This is significant, since under tensile strains new
surface opens up, and the surface reduces under compression. Upon
unbending the Sa roughness decreases to close the original values for both
sides.
Since the tensile strains effects on Sa under tensile testing are equivalent
for the L and T directions, these results correlate well for this first cycle under
pure bending. It shows an equivalent Sa behavior under both tensile and
compressive strains.
37


0.2 i
Flat Bent-A concave Unbent to flat Rebent-A Rebent_flat Rerebent-A RerebentJIat
convex Concave
Sample Condition
Figure 16. MF Transverse Pure Bending Roughness Evolution
The Sa values evolve differently after the first bend-unbend. This behavior
depended on which side was bent first. For Side B (convex first) Sa exhibits a
regularly increasing pattern during the sequence rebending- flat-second
bending-flat. Sa values consistently increased under tensile strains (convex
side) and compressive strains (concave side).
38


The Sa values depart from the pattern above for side A (concave first).
When rebent from flat to convex after the first bent, side A is under tensile
strains and Sa increased. From convex to flat Sa decreased, but not to the
extent anticipated. The difference on Sa values between the two sides
becomes significant.
Sa values for side A departs from previous trends when changing from flat
to concave for the second time. Under the compressive strains, Sa actually
decreased substantially, resulting on the largest Sa difference between the
sides. This difference becomes smaller, but still significant, upon the last
unbending to flat.
An explanation to this behavior must take into account the changes on
sheet thickness during this cyclic bending sequence. The degree of bending is
severe, and these thickness changes are not small, as shown in Table III.
Table III. Sample Thickness Changes During Pure Bending Sequence
Sample Direction Flat First bend Flat Rebend
Mill Finish T 0.0386 0.0386 0.03815 0.0378
L 0.0385 0.0385 0.0382 0.03785
EDT L 0.0378 0.03775 0.03755 0.03735
T 0.0378 0.03775 0.0375 0.03715
39


The change of thickness imposes a net stretching effect on the sample. It is
noted that this stretching operates under pure bending. Potential contributions
due to out of equilibrium forces, or device misalignment are not present.
Furthermore, the forces (weights) used in the Pure Bending test are extremely
small (around 6 -7 lbs).
The trends for Sa values described above for MF along T apply directly to
Pure Bending Sa values along the longitudinal direction (Figure 17).
Mill Finish Pure Bending Sa Roughness Longitudinal Direction
0.2
0
Flat
Bent-A concave Unbent to flat Rebent-A Rebent.flat Rerebent-A RerebentJlat
convex Concave
Sample Condition
side A
Side B
Figure 17. MF Longitudinal Pure Bending Roughness Evolution
40


The pattern replicates for all cycles and similar discussions apply. Sa
differences between directions mostly occur during the last two bends, when
side A goes from flat to second concave. These differences are taken as
distinctive to the texture differences between the L and the T directions.
4.2.2.2 EDT Pure Bending Roughness Results
The results for the EDT transverse sample are given in Figure 18.
EDT Pure Bending Sa Roughness Transverse Direction
Sample Condition
Side A
l"'Side B
Figure 18. EDT Transverse Pure Bending Roughness Evolution
41


Some general trends show similarities with those shown for the MF
samples. For Side B (convex first) Sa exhibits a regularly increasing pattern
during the sequence rebending- flat-second bending-flat. Sa values (side B)
consistently increased under tensile strains (flat to convex side) and
compressive strains (flat to concave side).
EDT Sa values between the first tensile (convex) and compressive
(concave) sides were different. Sa values were smaller under tensile strains.
These results depart from the MF samples for which both sides had equivalent
Sa (Figures 16, 17). This behavior shows as related to the EDT texture, which
under Pure Bending the compressive side (concave) becomes rougher at the
first bend.
Given the increased pattern for the Sa values for side B, Sides Sa
differences decrease as side A goes from flat to convex. Once again, Sa side
differences become pronounced at the last flat to second concave. As for the
MF samples, this effect is attributed to the stretching mechanism operating
under Pure Bending under severe plastic deformation.
It is noted that Sa changes for EDT textures are less pronounced than
those for MF texture. Furthermore, as EDT samples start from a Sa value
significantly higher (1.45 ) than for MF samples (0.35 ) the percent Sa change
42


for EDT samples is around 30%, and compares to higher than ~ 200% change
for MF textures,
4.2.3. DBS Results
4.2.3.I. MF Transverse DBS Results
The results showing the evolution of Sa as the sheet slides through the
DBS are shown in Figure 19 for the fixed (black) and the roller pins (blue).
Solid lines represent side A and dashed lines correspond to side B.
The sheet is bent to the first pin at location 2, with side A concave and
side B convex. As the sheet bends, it contacts the pin and exerts contact
pressure. However, the back pulling force is zero at the inlet, and the strains
are mostly due to bending. The A and B surfaces increase equally in the same
manner as the equivalent pure bending operation and they correlate with Pure
Bending results given in Figure 15.
The equivalency to pure bending ends with the samples contact at the
second pin in section 3B. The contact pressure is sufficient to flatten the
material to starting roughness. The same trend is observed at point 4A, where
maximum contact pressure is expected at this location.
43


Sa Roughness Average (iim)
3B
MILL Finish Roughness TRANSVERSE Direction
'Side A Fixed
Bead T
Side B fixed
beadT
diSide A roller
beadT
iSide Broiler
beadT
Figure 19. MF Transverse Sa Roughness Evolution
44


The Sa values for the roller device closely follow the results for the
MF Transverse up to location 3. This is expected, as the friction coefficient
for MF Transverse is very low ( 0.031). Differences are more evident at the
exit pin 3 (location 4), and at unbending (location 5). The pulling tension is
significantly greater than the roller for the MF sample at those locations.
4.2.3.2. MF Longitudinal DBS Results
The MF Longitudinal DBS sample showed quite similar results to the
MF Transverse sample (Figure 20). The exceptions are the free surface tensile
strain (convex side) roughness values, which are significantly lower than
those for the transverse sample at locations 4 and 5. Recent studies by
Mahmudi and Mehdizadeh showed that increased non-homogeneity in the
strain direction of a transverse rolling structure exhibited more pronounced
roughening than in the longitudinal direction for tensile straining (materials
processing technology citation). This may explain the decreased roughness in
tensile locations compared to the transverse MF case despite the higher total
load as a result of increased friction and orthotropic hardness.
45


Sample Location
Side A Fixed
Bead
' Side B fixed
bead
""**Side A roller
bead
Side B roller
bead
Figure 20. MF Longitudinal Sa Roughness Evolution
4.2.3.3. EDT Transverse DBS Results
EDT textures are credited with improving paint and finishing quality, at a
greater cost than MF textures. EDT textures have a Sa roughness amplitude
over four times greater than MF. Sa data has been recorded at the five
positions along the sample and presented in line graph form in Figure 21. The
starting surface roughness values are slightly different for the four starting
positions sides A and B on both roller bead and fixed bead samples. For
46


comparison purposes, this was eliminated arithmetically, effectively
translating each of the four curves up or down to a common starting position.
Side A Fixed
Bead
^ Side B fixed
bead
'^Side A roller
bead
-A-Side Broiler
bead
Figure 21. EDT Transverse Sa Roughness Evolution
During the passage of the sample over the first drawbead, both sides
increase in roughness. It is interesting to note that the concave side A
47


increased in roughness by a much larger factor with its negative strain than the
positively strained convex side B, even while under contact pressure from the
first pin. As stated above for MF samples, the first pin correlated with Pure
Bending results. This trend for EDT at the first bend is also shown to
correlated with the corresponding Pure Bending result given in Figure 18.
As the sample contacts the second pin, the now convex side A is strained
in the opposite direction, achieving a net positive strain, and reaching an even
higher roughness value, while the now concave side B is strained negatively,
and subjected to contact pressure. It falls far below its initial value. It is
obvious that the effect of contact pressure is now a significant factor in
affecting the surface roughness. As the material comes into contact with the
third pin, the now convex side B strains in the positive direction and
experiences a drastic increase in surface roughness. It should be noted that this
location is subjected to the most extreme tensile stress and strain of any point
during the entire operation. The now concave side A experiences a huge drop
in surface roughness as it is strained negatively, returning to nearly starting
roughness (slightly lower for fixed bead, slightly higher for roller bead).
Contact forces are at their highest levels at this point, due to the occurrence of
maximum net tensile force. At location 5, both sides are now free from
contact with the third pin. Side B is strained negatively, although not enough
48


to give it a net negative strain. Side A is strained positively. Both sides are left
with a net positive strain as the sample is now loaded with maximum total
tensile stress. Side A experiences a huge increase in surface roughness, while
side B falls slightly, which was at first unexpected in the absence of contact
pressure.
4.2.3.4. EDT Longitudinal DBS Results.
The EDT Longitudinal results closely mirror the EDT Transverse result
with a two noticeable exceptions (Figure 22). The drop in surface roughness
for side B upon going from flat to convex in the transition from position 1 to 2
is unlike that of the EDT Transverse case. The drop in surface roughness for
side A in going from convex to concave in the transition from 2 to three is
also unlike that of the EDT transverse case. This observation may be
explained by the bulk mechanical properties of the material and by variations
on the EDT texture itself. The designation Longitudinal or Transverse is
explained by the rolling direction at the steel mill. A longitudinal sample is
DBS processed in the same direction as the direction of rolling. A transverse
sample is processed at a 90 degree angle to that. This rolling process hardens
the material anisotropically, making it more difficult to strain (stronger) in the
49


direction of rolling than in the transverse direction. This effect explains the
increase in drawing load for longitudinal samples vs. transverse samples.
EDT Finish Roughness Logitudinal Direction
Same initial Sa for all samples for comparison purposes
Side A Fixed
Bead
Side B fixed
bead
HirSide A roller
bead
ASide Broiler
bead
Figure 22. EDT Longitudinal Sa Roughness Evolution
The decrease in surface roughness for side B for the fixed bead case may
also be influenced by the contact pressure exerted by the backup roller as it
50


reacts the moment created by bending the sample around the first pin. This
contact pressure is larger than in the Transverse case because of the
anisotropic hardening effect. There is an additional superimposed moment for
the fixed case vs. the roller case created by the friction resisting the travel of
the sample as it touches the first pin.
The second noticeable effect is the dropping of surface roughness as side
A transitions from concave to convex as it moves from position 2 to position
3. The pure bending moment results suggest that the roughness will increase
at this point. This may also be explained due to the increased contact force
required to resolve the moment required to execute that bend. This contact
force is more significant in flattening the surface features than the tensile
straining is in promoting roughness.
4.3. Plasticity Index Results


A measure of the degree of plasticity inherent with the contact between
two surfaces was developed by Bhushan [12]. It is expressed with equation 4.
Â¥ =
( E*^|
\~H J
2 V
(4)
Where E* is the effective modulus of the two surfaces in contact, H is the
hardness of the material, Op is the standard deviation of peak heights, and Rp
is the effective peak radius. Lower plasticity indices indicate that a surface is
less likely to undergo plastic deformation. It can be observed that an increase
in material hardness or effective peak radius will lower the plasticity index.
The pure bending moment device gives us the opportunity to replicate the
condition of the surface of the concave side 3B in the absence of contact
pressure. The fourth datapoint in the pure bending data is the pure bending
equivalent of concave side 3b having followed the same bending sequence. It
was originally flat, then bent to convexe, then bent to concave. We can
evaluate the plasticity index of this region for the EDT and MF samples. This
will allow us to gain insight into the potential for influence of roughness at
these points due to contact pressure (Table III). The plasticity indices for the
EDT textures are much higher than for the MF textures. This is reflected in
52


the reduction in surface roughness to levels below the starting roughness for
DBS EDT samples.
Table IV. Plasticity index for uncontacted 3B
Condition
EDT L 25.1432693
EDT T 29.0202701
MF L 16.4089938
MF T 14.9394187
5. Summary and Conclusions
This study investigated the evolution of surface roughness during DBS
testing, pure bending moment testing, and uniaxial tensile testing. Friction
results for DBS testing were also established.
The finding that friction for EDT textures was both larger, and more
isotropic than EDT textures has been previously established by extensive
testing. EDT drawing friction varied by only 6% from longitudinal to
transverse directions. MF texture drawing friction varied by over 60% from
longitudinal to transverse directions. The uniform directional friction
characteristics make it a superior drawing material at a higher cost.
53


The primary mechanisms affecting surface roughness were proven to be
tensile and compressive straining in addition to contact pressure. Friction
effects were the least significant factor, with Sa differences between roller and
fixed beads mostly unnoticeable.
The pure bending moment device offers capabilities that are especially
unique in surface texture studies. Specific to the study of the DBS forming
process, It is especially in useful in its ability to isolate certain strain
conditions. The ability to subject materials to cyclic and compressive allows
the investigation of new phenomena such as reversible roughening effects is
also an important quality. Subjecting a MF longitudinal sample to a 10%
compressive/tensile strain, the pure bending device causes an average increase
in surface Sa value of 203%. Reversing the bend and returning the sample to a
flat condition reduces the increase in Sa roughness to a mere 12%. This
indicates a large degree of reversibility in the displacement field surface
structure, which would otherwise be unrealized without using a device
capable of such large reversing strains.
The behavior of EDT samples in pure bending was suprising in
comparison to the behavior of MF textures. Subjecting a MF sample to pure
bending causes both tensile and compressive sides to increase in surface
roughness equally. Subjecting an EDT sample to pure bending causes an
54


average increase in roughness on the compressive side of 27%, but only a
13% increase on the tensile side. A through thickness orthotropy could be the
source of this discrepancy. Further testing should be undertaken to study this
effect.
The high flattening behavior of EDT textures in DBS contact areas in
relation to MF involves both spatial and amplitude factors. The plasticity
index evaluation indicates that the susceptibility of the EDT texture to contact
flattening is a result asperity peak RMS and asperity peak radius. The
plasticity index increases proportionately to the asperity peak RMS. The
plasticity index is inversely proportional to the asperity peak radius. This
suggests that the plasticity index could be reduced without decreasing the Sa
roughness giving EDT textures their superior paintability. Increasing the
asperity tip radius and more carefully controlling the asperity height
distribution could reduce the plasticity index. This would allow EDT textures
to retain more of their factory surface roughness while maintaining the friction
and textural isotropy for which they are prized.
55


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Appearance of Aluminum Sheet Material, Proceedings of the International
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[5] Nine H., Draw bead forces in sheet metal forming, Wang Koistinen,
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58