Paper Number 2005-01-0500

Evaluating The Relationships Between Surface Roughness

And Friction Behavior During Metal Forming

M. R. Stoudt

J. B. Hubbard

S. P. Mates

Materials Science & Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-8553, USA

D. E. Green

Mechanical Engineering Department

University of Windsor

Windsor, Ontario, N9B 3P4, Canada

Copyright © 2005 SAE International

ABSTRACT

The inhomogeneous distribution of surface asperities

generated by deformation induces variability in the

friction and initiates strain localizations during metal

forming. The friction literature generally does not

account for the strong influence localized variations in

material properties have on the friction behavior. A

prototype apparatus was developed that measures the

friction behavior under simulated forming conditions and

enables detailed characterization of the influences of the

microstructure and the topographical conditions that

occur under those conditions. The results demonstrate

that the measurement system can resolve subtle realtime changes in the dynamic friction coefficient, and that

a correlation could exist between the largest surface

asperities and the largest variations in the measured

friction coefficient. 

INTRODUCTION

The property differences that exist between traditional

automotive steel alloys and many of the new alloys

designed to improve automotive fuel economy pose a

significant challenge to our understanding of metal

formability. The inhomogeneous surface roughening

and variability in the deformation behavior [1-3] often

initiate strain localizations that promote necking, tearing,

or wrinkling in stamped metallic components. 

During metal stamping, the flow of the work piece into

the die cavity is usually controlled with a binder (holding)

clamp and a drawbead. Appropriate drawbead shapes

and clamping forces on the sheet stock have been

effective in preventing wrinkling and tearing in the

stamping [4]. However, deviations from the predicted

deformation behavior around the drawbead or in the

binder clamp may result in insufficient or excessive

clamping forces that can increase wrinkling or tearing.

Furthermore, the increased sensitivity to variations in

alloying content and metallurgical processing conditions

exhibited by many of the newer alloys cause

inconsistencies in the metal properties that exacerbate

the forming difficulties [5]. Recent studies have resulted

in better drawbead designs [6], as well as in new

approaches to locally monitor and control the clamping

forces on the binder [7, 8]. While successful to some

degree, these studies still heavily rely on the quality of

the empirical friction data used in the finite element

analysis (FEA) predictions. 

Many investigators [9-12] have successfully measured

frictional forces under a range of simulated metal forming

conditions and a wealth of data is available in the

literature. However, the literature also shows that the

coefficients of friction are highly dependent upon the

parameters used in the friction test (e.g., sliding time,

indentation force, strain rate, and test environment) [13-

15]. Traditional friction measurements tend to strictly

focus on the mechanics of friction and do not account for

the dynamic response of the material during the

deformation process. Most of these data do not account

for the strong influences that variations in metallurgical

conditions have on the material properties. For this

reason, the friction values selected for an FEA simulation

may not be entirely representative of the actual metal

behavior under those particular conditions. Since the

traditional approaches cannot provide the essential data,

there is a need for new approaches that a) evaluate both

the static and the dynamic properties for the materials of

SAE Trans. J. Mater. & Manu., 2006, vol. 114-5, pp. 183-90. 
interest, and b) provide a more broad-based

understanding of the relationships between the friction

behavior and the microstructural variations that affect the

properties during metal forming.

A prototype friction testing apparatus is being developed

as part of a test protocol that produces friction data under

a wide range of loading and strain rate conditions in

response to this need. The principal advantage of this

protocol is that it enables direct assessment of the

relative influence of metallurgical variables, such as

composition, grain size and orientation effects,

strengthening mechanisms, slip homogeneity, as well as

changes in the microstructures that are produced under

conditions closely emulating those encountered in

industrial forming operations. These measurements can

then be used to guide the development of improved

finite element models that predict the shape of the

formed part after each forming operation. This particular

study focuses on the suitability of the design to produce

and measure the friction under different surface

conditions. 

EXPERIMENTAL

MATERIAL- Hot-dipped galvanized DQSK steel is a

relatively common automotive alloy that demonstrates

good formability so it was selected as the material for this

evaluation. The steel sheet had an initial thickness of 1

mm with a zinc coating of approximately 170 μm.

Metallographic analysis revealed that the average grain

size of the DQSK steel was 20 μm ± 7 μm. This is

substantially smaller than the microstructure observed in

the zinc layer shown in Figure 1. 

Figure 1. SLCM image of the surface of the hot-dipped galvanized DQSK

steel in the as-received condition. Note that the grain structure of the zinc

layer is substantially different from that of the underlying steel.

Pre-strained channel sections were provided for these

experiments by IRDI. An A/SP channel draw die formed

each blank into an open-ended channel section (Figure

2). During the forming of the channel, the floating binder

maintained a constant pressure against the upper die by

means of pressure pins that were connected to a

pressure cushion positioned beneath the press bolster.

Four “kiss blocks” mounted on the binder ensured a

constant clearance between the binder and the upper

die. The material on either side of the central punch then

flowed through a drawbead and over the die entry radius

(inserts B & C in Figure 3). The drawbeads used for the

straining had the following configuration: The male

beads were round with a 4.0 mm profile radius. The

female insert had a width of 10.8 mm, and a profile radius

of 4.0 mm. The horizontal clearance on each side of the

male bead was 1.4 mm and the vertical clearance

between the binder and the upper die was equivalent to

material thickness plus approximately 0.4 mm. The die

entry radius was 12.0 mm. Prior to forming channel

sections in the draw die, blanks were sheared

lengthways across the width of the coil so that straining

occurred in the transverse direction of the coil (i.e., ⊥ to

the rolling direction). The blanks were 254 mm (10 in)

wide and approximately 1067 mm (42 in) long. A 2.54

mm (0.1 in) diameter circle grid was electro-etched on the

surface of the blanks to facilitate measurement of the

strain. After forming, the channel sections were placed

and stored on edge to avoid any modifications of the

shape. Additional details regarding the procedure used

to form the channel sections can be found in reference

[16].

Figure 2: A channel section formed in the A/SP channel draw die (courtesy

of IRDI).

Friction specimens with nominal dimensions of 30 mm x

80 mm were cut from the DQSK sheet stock in the asreceived condition such that the long dimension of the

specimen was orientated parallel to the rolling direction.

Pre-strained specimens of the same geometry were also

cut from sidewall sections of the pre-strained channel

produced with a 100 % bead penetration. This condition

generated an approximate strain level of 21.5 % in the

sidewall section. (Note that the long dimensions of the

100 μm

SAE Trans. J. Mater. & Manu., 2006, vol. 114-5, pp. 183-90. 
pre-strained specimens were in a perpendicular

orientation to the strain direction.) 

FRICTION EXPERIMENTS- A schematic diagram of the

apparatus used to evaluate the friction behavior is shown

in Figure 4. The apparatus was designed for use in

conjunction with a high-speed, servo-hydraulic testing

platform. As shown in the figure, the friction apparatus

consists of an upper, mobile grip that is attached the

actuator; and a lower, stationary grip frame that is

attached to the load cell of the servo-hydraulic testing

platform. One end of the test specimen is attached to

the upper grip and the other is held between two 6.35

mm diameter ball indenters. Hardened tool steel balls

were used for the indenters for two reasons: First, the

force interactions between a flat sheet of a “soft” material

and a hard spherical surface are well studied and many

force models are available in the literature. Second, most

of the dies used in automotive metal forming operations

are machined from hardened steel. Using a similar

material for the indenters will allow for examinations of

any possible interactions between steel and the surfaces

created during an experiment. The normal force was

applied to the sample via the indenters and two small

load cell/lever arm assemblies. The load cells that

monitor the normal forces are mounted in the large, rigid

steel supports of the stationary grip frame to eliminate

any rotational, or side loading that could occur during the

test. 

Figure 3: Sketch of the channel draw die with location of drawbead inserts

(courtesy of IRDI).

The large pressure reservoirs in the servo-hydraulic

testing platform produce immediate actuator motion at

the pre-programmed displacement rate; making the time

required to reach a steady-state velocity effectively zero.

In addition, the actuator moved continuously under

closed-loop position control at that displacement rate

until the pre-determined endpoint was achieved. Thus,

any variability in the applied load that could be

transmitted to the specimen was effectively eliminated.

The total displacement for these experiments was 12.5

mm (0.5 in) at a fixed displacement rate of 25.4 mm/s (1.0

in/s). The indentation forces used for these experiments

were 500 N (112.4 lbf) and 1250 N (281 lbf). The friction

behavior was evaluated under both unlubricated and

lubricated conditions. Light paraffin oil was used as the

lubricant for these experiments.

An experiment consisted of a minimum of three tests for

each load/lubrication condition. A balanced indentation

force was applied to the sample via the two load cell

assemblies after which it was pulled through the

indenters by a single continuous actuator displacement.

The actuator motion at the test start triggered the

computer-controlled digital data acquisition system.

Once triggered, the system continuously acquired the

outputs of the two normal force load cells, the stationary

load cell, and the actuator position with a minimum

sampling frequency of 50 MHz until the end of the test. 

Figure 4. Schematic diagram of the prototype test apparatus used for the

friction measurements.

SURFACE ROUGHNESS MEASUREMENTS- The

topographies of both the initial surfaces and the wear

scars created during the friction experiments specimen

surface were examined with the SLCM. Details

pertaining to the operation of the SLCM used for in study

can be found in references [17-19]. All of the images in

this analysis were created with a 635 nm laser optical

source (λ), a 10x objective lens and a z-scan range of

approximately 20 μm. These parameters generated

intensity images of the surface with outstanding

resolution and optical depth of field and with (x, y, z)

dimensions of 1000 μm x 800 μm x 20 μm respectively.

The spacing between the individual focal planes in each

image was approximately 100 nm. Topographic maps

were generated from the intensity images by the

controlling software [17]. A series of linear roughness

profiles with a typical length of 750 μm were collected

from the topographic maps. Each profile contained a

minimum of 2400 data points, resulting in an approximate

sampling interval of 300 nm. A roughness measurement

Fixed

Punch

Movable

Binder

Interchangeable

Drawbead

Inserts

Upper

Die

CD AB

High Capacity

Load Cell

Sample

Stationary

Grip Frame

Servo-hydraulic

Actuator 

Sliding Velocity

Control

Load Cells

Wear Scar Interchangeable Indenters 

Load Cell

Support Arms

Indenter Gap

Setting Screws

Hinge Pins

Mobile Upper Grip

To Computer Data

Acquisition System

SAE Trans. J. Mater. & Manu., 2006, vol. 114-5, pp. 183-90. 
consisted of a minimum of five, randomly placed profiles

in the parallel orientation followed by five profiles in the

perpendicular orientation with respect to the rolling

direction of the sheet. Additional roughness

measurements were performed along the length of the

wear scars. These measurements consisted of several

sequential 1000 μm profiles taken along a consistent

feature in the scar.

RESULTS AND DISCUSSION

The results from a basic assessment of the initial surface

roughness are shown in Table 1. The values in the table

are averages of the measurements taken in the parallel

and perpendicular directions. As expected, both the rms

average roughness (Rq), the maximum peak height

(Rmax) and the associated measurement uncertainty

values are considerably larger for the pre-strained

condition. 

Table 1. Initial surface roughness of the DQSK steel

Surface

Condition

Rq

[μm]

Unc.

[2σ]

Rmax

[μm]

Unc.

[2σ]

As-received 0.775 0.047 2.408 0.366

Pre-strained 1.527 0.222 4.719 0.726

A basic frictional force, F, can be defined for any loading

situation as the force normal to an interface between two

bodies that resists the motion produced by the action of

an externally applied force [13, 14]. A dimensionless

coefficient of friction, μ, can be defined from the basic

frictional force as the ratio between the force required to

produce movement and the normal force, N, that resists

motion (i.e., μ = F/N). This general definition can then

be used to define both a coefficient of static friction (μs)

from the force that is just sufficient to resist the onset of

the relative motion (Fs) and a coefficient of sliding friction

(μk) from the force that resists relative motion after sliding

has initiated (Fk). As noted by Blau [14], these

coefficients are simple quantities that only express the

proportionality between two forces and, as noted earlier,

all coefficients of friction are a function of the test

parameters including sliding time, indentation force,

strain rate, and the test environment.

An example of the typical friction behavior observed

during the experiments is shown in Figure 5. Three

distinct regimes are exhibited in this figure: the fully static

(i.e., zero actuator velocity), the steady-state dynamic

(i.e., sliding), and the transition between the static and

dynamic regimes. In some literature accounts, the

transition regime is referred to as the “run-in.” However,

this term generally describes the initial period where the

surface roughness changes during sliding in a test

where the same surfaces repeatedly slides over one

another (e.g., a pin on disk test). Considering that this

test protocol consisted of a single-pull through the

indenters, and that the surfaces interacted only once,

“run-in” is not an appropriate term. Therefore, this

section of the curve will be referred to as the “transient”

regime. 

Figure 5. Variation in friction coefficient as a function of time for lubricated

DQSK steel under a 1250 N indentation force.

A summary of an analysis of the friction data is presented

as a function of the surface roughness condition in Table

2. Several friction parameters can be derived from a test

of this type. For brevity, only the average normal force

(N), the average coefficient of steady-state friction (μk)

and the uncertainty associated with the friction

coefficients are presented. Note that the average normal

force values shown in the table are one-half the

maximum indentation force. The basis for this being, the

measured indentation force is actually the sum of the

absolute values of the two equal and opposing normal

forces acting on the surface of the specimen (i.e., Find =

2 FN).

Overall, the results from this set of experiments appear to

be reasonable with respect to the values reported in the

literature for mild steel [3, 20-22]. The friction

coefficients acquired from the tests in the unlubricated

condition are somewhat higher than those acquired from

the lubricated condition. Similarly, the coefficients

acquired from the pre-strained surfaces are consistently

higher than those acquired from the as-received

surfaces. However, the friction coefficients at the two

normal forces in the unlubricated pre-strained conditions

are essentially the same. This implies that the steadystate friction coefficient may have become insensitive to

the normal force for this lubrication/surface roughness

condition. While the increase in the friction coefficients

between the lubricated as-received and the lubricated

pre-strained conditions might appear unusual, this trend

also agrees 

-0.02

0

0.02

0.04

0.06

0.08

0.1

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Friction Coefficient

Elapsed Time, s

“Transient” “Steady-state”

“Static“

SAE Trans. J. Mater. & Manu., 2006, vol. 114-5, pp. 183-90. 
Table 2. Friction data obtained for DQSK steel.

As-received Pre-strained

Avg. N

[N]

Lubricity Avg. μk Unc.

[2σ]

Avg. N

[N]

Lubricity Avg. μk Unc.

[2σ]

250 None 0.0616 0.013 250 None 0.1135 0.012

625 None 0.0939 0.005 625 None 0.1110 0.010

250 Paraffin oil 0.0335 0.006 250 Paraffin oil 0.0614 0.002

625 Paraffin oil 0.0454 0.011 625 Paraffin oil 0.0698 0.007

with the literature. An increase in friction in the lubricated

state can be attributed to several effects including

interactions between bare surfaces (i.e., micro-scale

galling) [23] as well as to the influence of localized

variations in the hardness produced during bulk

deformation that alter the fractional area of contact

around the indenter [24, 25]. An additional source for

this behavior may be the interactions between the steel

indenter and the softer zinc coating on the surface. As a

result, additional analyses are in progress to ascertain the

relative influence of the zinc coating on the friction

behavior of the DQSK steel.

Assessing the character of the roughness in the wear

scar created during a friction experiment can be a

challenging measurement. However, the linear wear

track produced by this test methodology easily allows for

detailed characterizations of the surfaces in the SLCM. 

The images shown in Figure 6 are topographies of a

typical wear scar acquired from the DQSK steel (at a

indentation load of 1250 N) by the SLCM. Figure 6a

shows the surface conditions at the initiation of the test.

The circle indicates the initial position of the indenter (i.e,

the static regime in Figure 5) and the dashed lines reflect

the evolution of the wear scar (i.e., the initial segment of

the transient regime). Figure 6b shows the topography

of the wear scar after the transient friction developed into

the steady-state mode (i.e., the sliding regime). The

solid line in both figures represents the location of the

continuous surface roughness measurement taken

along the length the wear scar with the SLCM. This

measurement was created from a series of sequential

topographic images taken along the length of the wear

scar. The roughness profile at the maximum depth of the

wear scar is shown in Figure 7. Note that while the total

length of the scar was 12.5 mm, only the first 6.75 mm

(i.e., 21,000 data points) are shown in this figure. The

profile was cropped to accentuate the resolution of the

closely spaced height variations that would have been

suppressed had the entire profile been presented. The

profile in Figure 7 consists of both the steady-state and

the transient regimes and the transition appears to occur

at approximately 2.8 mm. The dashed line in the figure

indicates the transition point. 

Figure 6. SLCM topographic images of the wear scar produced in

lubricated DQSK steel under a1250 N indentation force.

Because this technique was intended to measure both

the friction behavior and the roughness character in the

wear scar at virtually any point during the test, it is then

reasonable to determine whether any correlations exist

between the features in the two profiles. While the

behaviors in both the transient and the steady-state

regimes have significance in a metal forming operation,

sliding friction has been better characterized in the

literature. With this in mind, it was appropriate to

A

B

SAE Trans. J. Mater. & Manu., 2006, vol. 114-5, pp. 183-90. 
Figure 7. Corresponding roughness profile of the wear scar shown in

Figure 6.

ascertain the degree of correlation in the steady-state

regime. The large number of data points in the

roughness profile required additional reduction to

facilitate data manipulation. Thus, the roughness data

was cropped to correspond with the friction data in the

time interval between 0.25 s and 0.4 s (see Figure 5). A

simple, straightforward analysis was performed to match

both profiles to centered Gaussian distributions. This

was achieved by fitting the data from the two profiles to a

normal Gaussian probability density function in the same

manner shown in references [19] and [26]. The results

are presented in Figure 8. The PDF of the roughness

data is shown as Figure 8a and the PDF of the force data

is shown as Figure 8b. The two figures were plotted on

different axes to accentuate the similarities between the

two data sets. Had the data sets been plotted on the

same set of axes, the range of the roughness data would

have been compressed to the extent where these

similarities would not be apparent. However, the quality

of a Gaussian fit is characterized by the values of the

higher central moments about the mean. The skew (σ3)

is a measure of the asymmetry in the overall shape of the

distribution and the kurtosis (σ4) characterizes the shape

of the tails of the distribution. The ideal Gaussian shape

is characterized by a skew (σ3) of zero and by a kurtosis

(σ4) of three [27, 28]. The skew and kurtosis values for

the roughness probability density function are –0.8520

and 2.5979 respectively, whereas the skew and kurtosis

values for the friction probability density function are

–0.7706 and 2.5951. The fact that the skew values for

the two distributions are within 10 % of each other

indicates that the general shapes of the distributions are

quite similar. Furthermore, the kurtosis values are

essentially identical which indicates that the extremes of

the two distributions are closely related. Clearly, further

analysis is required before any causal relationship can be

established between these two distributions; but it has

been suggested that the extremes in the distribution of a

surface roughness profile may produce larger variations

in the contact area; and thereby, have a stronger

influence on the friction than the mean roughness. This

relationship does imply that a correlation may exist

between the largest asperities present in the wear scar of

the DQSK steel and the local maxima in the friction

coefficient profile. 

Figure 8. Probability density functions of the steady-state friction behavior.

a) the surface roughness profile (Figure 7), b) friction coefficient (Figure 5).

CONCLUSION

A prototype test apparatus has been developed as part

of a test protocol designed to address the need for

friction measurements that provide a more broad-based

understanding of the complex relationships between the

friction behavior and the microstructural variations that

affect the properties during metal forming. The principal

advantage of this protocol is that it enables direct

assessment of the relative influence of metallurgical

variables, such as composition, grain size and orientation

effects, strengthening mechanisms, slip homogeneity,

as well as changes in the microstructures that are

0

1

2

3

4

5

6

7

8

0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Transient Steady-State

Wear Scar Length, mm

Height Profile, μm

0

0.1

0.2

0.3

0.4

-4 -2 0 2 4 6

Normalized Heights

Probability Density

A

σ3= - 0.8520

σ4= 2.5979 

0

0.5

1

1.5

2

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Normalized Friction Coefficient

Probability Density

B

σ3= - 0.7706

σ4= 2.5951 

SAE Trans. J. Mater. & Manu., 2006, vol. 114-5, pp. 183-90. 
produced under conditions closely emulating those

encountered in industrial forming operations. 

A series of single-pull friction experiments were

conducted on hot-dipped DQSK steel under two normal

forces, in two surface roughness conditions, and under

two lubricities. The resulting surfaces were examined

with the SLCM. The goal of this particular study was to

determine whether this prototype measurement

apparatus could produce friction data that are

comparable to those obtained under actual automotive

metal forming conditions, and enable detailed

characterizations of the surfaces created under those

experimental conditions.

The results demonstrated that: 

• The friction coefficients calculated from the force data

are within the range of values reported in the literature for

steel. Considering that all friction coefficient data are

dependent upon parameters used in the test, the

reasonable agreement is an indication that the

measurement sensitivity is appropriate for the intended

purpose.

• The test apparatus can easily distinguish the transition

from the static to the sliding state and that the magnitude

of the friction coefficients can be determined in real time

in the steady-state and in the transient friction regimes

for any condition.

• The wear scars are suitable for detailed surface analysis

in the SLCM. The linear shape of the wear scar facilitated

detailed surface characterization in the SLCM. The

combination of high-resolution topographic analysis and

roughness measurements in the wear scar enabled a

thorough assessment of the character of the surface

asperities.

• The measurement sensitivity is such that the quality of

the resulting data is amenable to detailed statistical

analysis. A simple analysis of the distributions of the

steady-state friction coefficient and the surface

roughness of the wear scar in the same region revealed

that a correlation could exist between the largest

asperities and the local maxima in the friction coefficient

profile. 

Based on the results, it was concluded that the

prototype successfully met the design criteria for the

experimental technique and that the measurement

protocol is appropriate for further development. As a

result, a wide range of experiments are planned to

further evaluate the influences of initial surface

roughness, strain path and asperity distribution, indenter

shapes, as well as indentation forces, strain rates and

surface lubricants.

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CONTACT

Mark. R. Stoudt, Steven P. Mates, and Joseph B.

Hubbard- Materials Performance Group, Materials

Science and Engineering Laboratory. Email:

mark.stoudt@nist.gov , steven.mates@nist.gov ,

joseph.hubbard@nist.gov .

Daniel E. Green, Assistant Professor, Mechanical,

Automotive & Materials Engineering Department,

University of Windsor. dgreen@uwindsor.ca .

DEFINITIONS, ACRONYMS,

ABBREVIATIONS

A/SP: Automotive/Steel Partnership

DQSK: Draw Quality, Semi-Killed Steel

FEA: Finite Element Analysis

IRDI: Industrial Research & Development Institute

N: Normal Force equal to the (Indentation Force /2) in

Newtons

PDF: Probability Density Function

SLCM: Scanning Laser Confocal Microscope

Rq: Root Mean Squared (rms) Roughness

Rmax: The maximum peak height in a roughness

profile.

UNC: The statistical uncertainty equal to 2 standard

deviations (σ) of the mean.

λ: Wavelength of the laser source in the SLCM.

μk: Coefficient of Steady-state (Dynamic) Friction

(dimensionless)

σ3: (Skew) A measure of the symmetry of the PDF.

σ4: (Kurtosis) A measure of the shape of the tails of the

PDF.

SAE Trans. J. Mater. & Manu., 2006, vol. 114-5, pp. 183-90.