metals

Article

Investigation on Friction and Wear of Cold RolledHigh Strength Steel against an AISI52100 Counterpart

Jiwon Hur and Kyungmok Kim *

School of Aerospace and Mechanical Engineering, Korea Aerospace University, 76 Hanggongdaehang-ro,Deogyang-gu, Goyang-si, Gyeonggi-do 412-791, Korea; jiwooun107@naver.com* Correspondence: kkim@kau.ac.kr; Tel.: +82-2-300-0288

Academic Editor: Filippo BertoReceived: 2 February 2017; Accepted: 6 March 2017; Published: 10 March 2017

Abstract: This article investigates the friction and wear of cold rolled high strength steel at variousdisplacement amplitudes. Reciprocal sliding tests are carried out using a ball-on-flat testing apparatus.The tangential force occurring at the contact surface between a high strength steel specimen and anAISI52100 ball is measured during the tests. After each test, the worn surface profile on the steelspecimen is determined. Experimental results show that the ratio of the maximum tangential tothe normal force remains at 0.7 after an initial rapid increase, and the ratio does not greatly changeaccording to the imposed displacement amplitudes (in the range of 0.05 mm and 0.3 mm). The wearvolume loss on the steel specimen increases according to the number of cycles. It is determined thatthe wear rate of the specimen changes with respect to the imposed displacement amplitude. That is,the wear rate rapidly increases within the displacement amplitude range of 0.05 mm to 0.09 mm,while the wear rate gradually increases when the displacement amplitude is greater than 0.2 mm.The obtained results provide the friction and wear behaviors of cold rolled high strength steel infretting and reciprocal sliding regimes.

Keywords: fretting; sliding; friction; wear; cold rolled high strength steel; AISI52100

1. Introduction

Use of cold rolled high strength steel sheets is widespread in the automotive industry dueto their outstanding mechanical properties [1,2]. The steel is used for automobile body panels,bumpers, and door panels. In addition, these steel sheets are often used for tribo-components suchas automotive seat sliding tracks. A typical automotive seat sliding track consists of two rails andmetallic balls (or cylindrical rollers). The metallic balls enable the movement of the upper rail on thelower rail. The rails are usually coated using an electro-deposition method. The anti-friction propertyof an electro-deposited coating has been studied by determining the coefficient of kinetic friction [3].The coefficient was determined to be approximately 0.3 under fretting and reciprocal sliding regimes.The coating lifetime was much shorter than those of other automotive seat components because thepurpose of the electro-deposition on the surfaces of the rails is focused on anti-corrosion. For thisreason, semi-solid lubricants such as grease are applied onto the coating surface. The deteriorationof semi-solid lubricants brings about the frictional contact between cold rolled high strength steeland AISI52100 steel. Thus, this frictional contact without coatings and lubricants needs to be studied.That is, studies on the frictional behavior of the contact between the substrate (i.e., cold rolled highstrength steel) and an AISI52100 counterpart are needed under reciprocal sliding conditions. When anAISI52100 steel counterpart slides on a high strength steel plate, wear volume loss mostly occurs on thesurface of the steel sheet because the hardness of AISI52100 steel is higher than that of the cold rolledhigh strength steel. Considering that the wear on the high strength steel sheet significantly affects theentire performance of the seat sliding track, the wear and friction behaviors of the steel sheet are of

Metals 2017, 7, 90; doi:10.3390/met7030090 www.mdpi.com/journal/metals

Metals 2017, 7, 90 2 of 11

practical interest. However, little is found in the literature related to the wear rate of cold rolled highstrength steel and the friction between the steel and AISI52100 steel.

Reciprocal sliding motions and fretting (small amplitude oscillatory motions) between two solidsurfaces lead to wear and friction. The relative displacement between two contacting bodies is takeninto account as an important parameter resulting in material volume loss and cracking. If the relativedisplacement leads to a partial slip at contact, cracks occur in the vicinity of the contact edges (knownas fretting fatigue) [4]. If the relative displacement results in a gross slip at the entire contact zonebetween two bodies, wear occurs in the contact zone (fretting wear) [5–8]. In a gross slip regime, thewear rate per unit sliding has been found to increase with the relative displacement amplitude [6–8].Meanwhile, within a reciprocal sliding regime, the wear rate per unit sliding has been shown to bealmost constant without regard to the relative displacement. The transition from a gross slip to areciprocal sliding regime has been observed in hundreds of displacement amplitudes. For example, thecritical displacement amplitude for the transition was found to be 0.1 mm for self-mating mild steel [7],and 0.3 mm for structural steel [8]. Difficulties remain regarding a stringent definition of the relativedisplacement at the transition because of the complexity of the fretting process including the effectsof the contact conditions (e.g., contact geometry, normal force, and frequency) [8]. Thus, in order todetermine the transition between two regimes, reciprocal sliding tests are typically employed withvarious displacement amplitudes. The wear rate is then measured using a series of worn specimens.Several studies have investigated the effects of the relative displacement on a fretting wear volumeand a friction coefficient evolution [9–11]. In one study, the evolution of the friction coefficient of athermally-sprayed coating was evaluated at various imposed displacements [9]. It was observed thatthe friction coefficient did not change according to displacement amplitude. Another study investigatedthe effect of displacement amplitude on electro-deposited steel plates [10]. It was found that the steadyfriction coefficient value was almost constant regardless to the imposed displacement amplitudewithin the range of 0.05–0.3 mm. However, the duration of the coating failure varied according tothe displacement amplitude. This indicated that the wear rate of the coating layer changed with thedisplacement amplitude. Meanwhile, in a third study, the ratio of the maximum tangential force tonormal force changed according to the imposed displacement amplitude at the contact surface betweenInconel 600 alloys and AISI52100 steels [11]. The fretting wear volume gradually increased as thedisplacement amplitude increased, which was attributed from the transformation of a fretting mode(from adhesion to full sliding).

In this study, friction and wear behaviors between cold rolled high strength steel and AISI 52100steel were investigated for the use on automotive seat slide tracks. Frictional forces were measuredat various imposed displacement amplitudes. Then, the effect of the displacement amplitude onthe frictional force was identified. The wear rates in a gross slip fretting regime and a reciprocalsliding regime were determined at the loading condition similar to those of actual seat tracks. Finally,the change of the wear rate in a gross slip regime was identified.

2. Materials and Methods

Figure 1 shows a reciprocal linear sliding test apparatus using ball-on-flat contact geometry.For each test, a ball and a flat specimen were used. The specimen was fixed on a moving table ina linear stage. The linear stage made the specimen move at a pre-described displacement amplitude.The ball was inserted in a ball holder and gripped by a screw to prevent rotation in the ball holder.The ball holder was then placed in a rigid arm. In the rigid arm, the ball holder was allowed to movevertically. Deadweights were placed onto the ball holder to apply normal force at the contact surfacebetween the flat specimen and the ball. The rigid arm was attached to a fixed support via a load cell(Interface, Inc. Atlanta, GA, USA). The load cell continuously measured the tangential force occurringat contact during reciprocal sliding. For the purpose of measuring the relative displacement betweenthe flat specimen and the ball holder, a laser displacement sensor (Model LK-081 (resolution: 3 µm,linearity = ±0.1%), Keyence Corp., Itasca, IL, USA) was attached to the carriage of a linear stage.

Metals 2017, 7, 90 3 of 11

The measured tangential force was recorded according to the relative displacement during each test,and the ratio of the maximum tangential force to normal force was subsequently computed.

Metals 2017, 7, 90 3 of 11

tangential force was recorded according to the relative displacement during each test, and the ratio

of the maximum tangential force to normal force was subsequently computed.

Figure 1. Illustration of a reciprocal linear sliding test apparatus using ball-on-flat contact geometry.

A cold rolled high strength steel (material designation: SPFC 440, provided by POSCO P & S Co.

Ltd., Seoul, Korea) plate was prepared as the specimen. Its surface roughness was controlled with No.

2000 emery paper. The arithmetic average of roughness (Ra) of the flat specimen after polishing with

the emery paper was found to be 0.4 µm. A commercial AISI52100 steel ball (Φ5 mm) was used as the

flat specimen’s counterpart. The initial roughness (Ra) of the ball was approximately 0.025 µm

(provided by KOPECO Co. Ltd., Incheon, Korea). The chemical compositions and mechanical

properties of the flat specimen and the ball are shown in Tables 1 and 2, respectively. Elastic modulus

and Poisson’s ratio of the cold rolled high strength steel were similar to those of AISI52100 steel.

Meanwhile, the hardness of the steel was lower than that of the AISI52100 steel.

Table 1. Chemical compositions (wt %) of cold rolled high strength steel and AISI 52100 steel provided

by the manufacturers.

Material C Mn P S Si Al Cr

Cold rolled high strength steel 0.18 1.5 0.08 0.03 0.3 0.02 -

AISI52100 0.95–1.10 0.05 0.025 0.025 0.15–0.35 - 1.3–1.6

Table 2. Mechanical properties of cold rolled high strength steel and AISI 52100 steel provided by the

manufacturers.

Material Elastic Modulus, GPa Poisson’s Ratio Vickers Hardness, HV

Cold rolled high strength steel 205 0.28 ~153 1

AISI52100 ~200 0.27–0.3 789

1 The hardness was measured in this study.

In this study, displacement amplitudes of 0.05 mm, 0.07 mm, 0.09 mm, 0.2 mm, and 0.3 mm were

selected. In actual automotive seat slide rails, the displacement amplitude between the rail and the

ball is found to vary. For example, while seat position is being adjusted, reciprocal sliding or rolling

of a ball occurs. If the seat position remains fixed, fretting could be induced by external force or

vibration. Thus, different displacement amplitudes from 0.05 mm to 0.3 mm were selected.

A normal force of 50 N and a fixed frequency of 1 Hz were induced at contact. A normal force

of 50 N was selected under the assumption that a loaded seat of 800 N maintained two sliding rails

with 16 balls (each rail came in contact with 8 balls). All tests were conducted at room temperature

of 25 C and relative humidity of 60%.

3. Results and Discussion

Rigid arm

Ball holder

Flat specimen

Ball

Moving table

Ball holder

Laser

Displacement

sensor

Fixed

block

Deadweight

Rigid arm

Load cell

Linear stage

Figure 1. Illustration of a reciprocal linear sliding test apparatus using ball-on-flat contact geometry.

A cold rolled high strength steel (material designation: SPFC 440, provided by POSCO P & S Co. Ltd.,Seoul, Korea) plate was prepared as the specimen. Its surface roughness was controlled with No. 2000emery paper. The arithmetic average of roughness (Ra) of the flat specimen after polishing with theemery paper was found to be 0.4 µm. A commercial AISI52100 steel ball (Φ5 mm) was used as the flatspecimen’s counterpart. The initial roughness (Ra) of the ball was approximately 0.025 µm (providedby KOPECO Co. Ltd., Incheon, Korea). The chemical compositions and mechanical properties of theflat specimen and the ball are shown in Tables 1 and 2, respectively. Elastic modulus and Poisson’s ratioof the cold rolled high strength steel were similar to those of AISI52100 steel. Meanwhile, the hardnessof the steel was lower than that of the AISI52100 steel.

Table 1. Chemical compositions (wt %) of cold rolled high strength steel and AISI 52100 steel providedby the manufacturers.

Material C Mn P S Si Al Cr

Cold rolled high strength steel 0.18 1.5 0.08 0.03 0.3 0.02 -AISI52100 0.95–1.10 0.05 0.025 0.025 0.15–0.35 - 1.3–1.6

Table 2. Mechanical properties of cold rolled high strength steel and AISI 52100 steel provided bythe manufacturers.

Material Elastic Modulus, GPa Poisson’s Ratio Vickers Hardness, HV

Cold rolled high strength steel 205 0.28 ~153 1

AISI52100 ~200 0.27–0.3 7891 The hardness was measured in this study.

In this study, displacement amplitudes of 0.05 mm, 0.07 mm, 0.09 mm, 0.2 mm, and 0.3 mm wereselected. In actual automotive seat slide rails, the displacement amplitude between the rail and theball is found to vary. For example, while seat position is being adjusted, reciprocal sliding or rolling ofa ball occurs. If the seat position remains fixed, fretting could be induced by external force or vibration.Thus, different displacement amplitudes from 0.05 mm to 0.3 mm were selected.

A normal force of 50 N and a fixed frequency of 1 Hz were induced at contact. A normal force of50 N was selected under the assumption that a loaded seat of 800 N maintained two sliding rails with16 balls (each rail came in contact with 8 balls). All tests were conducted at room temperature of 25 ◦Cand relative humidity of 60%.

Metals 2017, 7, 90 4 of 11

3. Results and Discussion

Reciprocal sliding tests with a cold rolled high strength steel specimen were conducted in dryconditions. The imposed displacement amplitudes were 0.05 mm, 0.07 mm, 0.09 mm, 0.2 mm and0.3 mm; the displacement amplitude of 0.09 mm was similar to the Hertz contact radius calculatedbetween a Φ5 mm ball and a cold rolled high strength steel plate. Note that the Hertz contact radiusis 0.094 mm at a given contact condition (as described in Appendix A). It has been suggested thatfretting is defined as occurring when the displacement amplitude is lower than the Hertz contactradius [12]. Thus, the selected imposed displacement amplitudes produce fretting and reciprocalsliding, respectively.

Figure 2 shows the ratio of the maximum tangential force to induced normal force at thedisplacement amplitude of 0.09 mm. The maximum tangential force was selected on a measuredforce-displacement loop, as presented in Figure 3. Figure 3 shows the tangential force versusdisplacement loops found at the 4000th cycle. Force peaks were found near contact edges dueto the ploughing effect. In order to obtain worn surfaces interrupted at various numbers of cycles,sliding tests were terminated at different numbers of cycles, as shown in Figure 2. In the figure, it wasobserved that the ratio increased rapidly up to 500 cycles, followed by a steady-state sliding stage.The initial increase on the ratio was called the initial running-in period. From 500 cycles to 4000 cycles,the ratio was almost stable in the range of 0.7 and 0.78.

Metals 2017, 7, 90 4 of 11

Reciprocal sliding tests with a cold rolled high strength steel specimen were conducted in dry

conditions. The imposed displacement amplitudes were 0.05 mm, 0.07 mm, 0.09 mm, 0.2 mm and 0.3 mm;

the displacement amplitude of 0.09 mm was similar to the Hertz contact radius calculated between a

Φ5 mm ball and a cold rolled high strength steel plate. Note that the Hertz contact radius is 0.094 mm

at a given contact condition (as described in Appendix A). It has been suggested that fretting is defined

as occurring when the displacement amplitude is lower than the Hertz contact radius [12]. Thus, the

selected imposed displacement amplitudes produce fretting and reciprocal sliding, respectively.

Figure 2 shows the ratio of the maximum tangential force to induced normal force at the

displacement amplitude of 0.09 mm. The maximum tangential force was selected on a measured force-

displacement loop, as presented in Figure 3. Figure 3 shows the tangential force versus displacement

loops found at the 4000th cycle. Force peaks were found near contact edges due to the ploughing

effect. In order to obtain worn surfaces interrupted at various numbers of cycles, sliding tests were

terminated at different numbers of cycles, as shown in Figure 2. In the figure, it was observed that the

ratio increased rapidly up to 500 cycles, followed by a steady-state sliding stage. The initial increase on

the ratio was called the initial running-in period. From 500 cycles to 4000 cycles, the ratio was almost

stable in the range of 0.7 and 0.78.

Figure 2. The ratio of the maximum tangential force (Qmax) to normal force (50 N) according to number

of cycles at the displacement amplitude of 0.09 mm.

Figure 3. Tangential force versus displacement loops found at the 4000th cycle for various initial

displacement amplitudes (δamp).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Rat

io o

f th

e m

ax. ta

ngen

tial

forc

e to

norm

al f

orc

e

Number of cycles

by 100 cycles

by 500 cycles

by 1000 cycles

by 2000 cycles

by 4000 cycles

δamp=0.09 mm

-50

-40

-30

-20

-10

0

10

20

30

40

50

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Tangential force, Q (N)

Displacement, δ

(mm)

δamp=0.3 mm

δamp=0.2 mm

δamp=0.09 mmδamp=0.07 mm

δamp=0.05 mm

Figure 2. The ratio of the maximum tangential force (Qmax) to normal force (50 N) according to numberof cycles at the displacement amplitude of 0.09 mm.

Metals 2017, 7, 90 4 of 11

Reciprocal sliding tests with a cold rolled high strength steel specimen were conducted in dry

conditions. The imposed displacement amplitudes were 0.05 mm, 0.07 mm, 0.09 mm, 0.2 mm and 0.3 mm;

the displacement amplitude of 0.09 mm was similar to the Hertz contact radius calculated between a

Φ5 mm ball and a cold rolled high strength steel plate. Note that the Hertz contact radius is 0.094 mm

at a given contact condition (as described in Appendix A). It has been suggested that fretting is defined

as occurring when the displacement amplitude is lower than the Hertz contact radius [12]. Thus, the

selected imposed displacement amplitudes produce fretting and reciprocal sliding, respectively.

Figure 2 shows the ratio of the maximum tangential force to induced normal force at the

displacement amplitude of 0.09 mm. The maximum tangential force was selected on a measured force-

displacement loop, as presented in Figure 3. Figure 3 shows the tangential force versus displacement

loops found at the 4000th cycle. Force peaks were found near contact edges due to the ploughing

effect. In order to obtain worn surfaces interrupted at various numbers of cycles, sliding tests were

terminated at different numbers of cycles, as shown in Figure 2. In the figure, it was observed that the

ratio increased rapidly up to 500 cycles, followed by a steady-state sliding stage. The initial increase on

the ratio was called the initial running-in period. From 500 cycles to 4000 cycles, the ratio was almost

stable in the range of 0.7 and 0.78.

Figure 2. The ratio of the maximum tangential force (Qmax) to normal force (50 N) according to number

of cycles at the displacement amplitude of 0.09 mm.

Figure 3. Tangential force versus displacement loops found at the 4000th cycle for various initial

displacement amplitudes (δamp).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Rat

io o

f th

e m

ax. ta

ngen

tial

forc

e to

norm

al f

orc

e

Number of cycles

by 100 cycles

by 500 cycles

by 1000 cycles

by 2000 cycles

by 4000 cycles

δamp=0.09 mm

-50

-40

-30

-20

-10

0

10

20

30

40

50

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Tangential force, Q (N)

Displacement, δ

(mm)

δamp=0.3 mm

δamp=0.2 mm

δamp=0.09 mmδamp=0.07 mm

δamp=0.05 mm

Figure 3. Tangential force versus displacement loops found at the 4000th cycle for various initialdisplacement amplitudes (δamp).

Metals 2017, 7, 90 5 of 11

Figure 4 shows the ratio of the maximum tangential force to normal force at the displacementamplitudes of 0.05 mm, 0.07 mm, 0.2 mm, and 0.3 mm. At each given displacement amplitude, threetests were interrupted after 500, 2000, and 4000 cycles, respectively. The three evolutions of the ratiomeasured at the same displacement amplitude were found to be similar to each other.

Metals 2017, 7, 90 5 of 11

Figure 4 shows the ratio of the maximum tangential force to normal force at the displacement

amplitudes of 0.05 mm, 0.07 mm, 0.2 mm, and 0.3 mm. At each given displacement amplitude, three

tests were interrupted after 500, 2000, and 4000 cycles, respectively. The three evolutions of the ratio

measured at the same displacement amplitude were found to be similar to each other.

(a) (b)

(c) (d)

Figure 4. The ratio of the maximum tangential force to normal force at various displacement amplitudes:

(a) 0.05 mm; (b) 0.07 mm; (c) 0.2 mm; (d) 0.3 mm.

Figure 5 shows the average ratio of the maximum tangential force to normal force measured at

the tests terminated after 4000 cycles. The ratios between 500 and 4000 cycles were averaged. The

error bars in the plot showed a 95% confidence interval. The average ratio varied from 0.68 to 0.72. It

was determined that the average ratio did not significantly change according to the imposed

displacement amplitude.

Figure 5. The average ratio of the maximum tangential force (Qmax) to normal force (P) at different

displacement amplitudes. Error bars show a 95% confidence interval.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Rati

o o

f th

e m

ax.

tan

gen

tial

forc

e to

norm

al

forc

e

Number of cycles

by 500 cycles by 2000 cycles by 4000 cycles

δamp=0.05 mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Ra

tio

of

the

ma

x. ta

ng

enti

al

forc

e to

no

rma

l fo

rce

Number of cycles

by 500 cycles by 2000 cycles by 4000 cycles

δamp=0.07mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Ra

tio

of

the

ma

x. ta

ng

enti

al

forc

e to

no

rma

l fo

rce

Number of cycles

by 500 cycles by 2000 cycles by 4000 cycles

δamp=0.2mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Ra

tio

of

the

ma

x.

tan

gen

tia

l fo

rce

to

no

rma

l fo

rce

Number of cycles

by 500 cycles by 2000 cycles by 4000 cycles

δamp=0.3mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

P

Qmax

Imposed displacement amplitude (mm)

Figure 4. The ratio of the maximum tangential force to normal force at various displacement amplitudes:(a) 0.05 mm; (b) 0.07 mm; (c) 0.2 mm; (d) 0.3 mm.

Figure 5 shows the average ratio of the maximum tangential force to normal force measuredat the tests terminated after 4000 cycles. The ratios between 500 and 4000 cycles were averaged.The error bars in the plot showed a 95% confidence interval. The average ratio varied from 0.68 to0.72. It was determined that the average ratio did not significantly change according to the imposeddisplacement amplitude.

Metals 2017, 7, 90 5 of 11

Figure 4 shows the ratio of the maximum tangential force to normal force at the displacement

amplitudes of 0.05 mm, 0.07 mm, 0.2 mm, and 0.3 mm. At each given displacement amplitude, three

tests were interrupted after 500, 2000, and 4000 cycles, respectively. The three evolutions of the ratio

measured at the same displacement amplitude were found to be similar to each other.

(a) (b)

(c) (d)

Figure 4. The ratio of the maximum tangential force to normal force at various displacement amplitudes:

(a) 0.05 mm; (b) 0.07 mm; (c) 0.2 mm; (d) 0.3 mm.

Figure 5 shows the average ratio of the maximum tangential force to normal force measured at

the tests terminated after 4000 cycles. The ratios between 500 and 4000 cycles were averaged. The

error bars in the plot showed a 95% confidence interval. The average ratio varied from 0.68 to 0.72. It

was determined that the average ratio did not significantly change according to the imposed

displacement amplitude.

Figure 5. The average ratio of the maximum tangential force (Qmax) to normal force (P) at different

displacement amplitudes. Error bars show a 95% confidence interval.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Rati

o o

f th

e m

ax.

tan

gen

tial

forc

e to

norm

al

forc

e

Number of cycles

by 500 cycles by 2000 cycles by 4000 cycles

δamp=0.05 mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Ra

tio

of

the

ma

x. ta

ng

enti

al

forc

e to

no

rma

l fo

rce

Number of cycles

by 500 cycles by 2000 cycles by 4000 cycles

δamp=0.07mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Ra

tio

of

the

ma

x. ta

ng

enti

al

forc

e to

no

rma

l fo

rce

Number of cycles

by 500 cycles by 2000 cycles by 4000 cycles

δamp=0.2mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Ra

tio

of

the

ma

x.

tan

gen

tia

l fo

rce

to

no

rma

l fo

rce

Number of cycles

by 500 cycles by 2000 cycles by 4000 cycles

δamp=0.3mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

P

Qmax

Imposed displacement amplitude (mm)

Figure 5. The average ratio of the maximum tangential force (Qmax) to normal force (P) at differentdisplacement amplitudes. Error bars show a 95% confidence interval.

Metals 2017, 7, 90 6 of 11

Figure 6a shows the worn surface image of a cold rolled high strength steel plate at thedisplacement amplitude of 0.09 mm. The surface image was captured after 4000 cycles. Severe damagewas observed at the contact surface (dark area in the image). A cross-sectional profile on the A-A’axis was measured with a 2D surface profiler (SJ-210, Mitutoyo Corp., Takatsuku, Kawasaki, Japan).Figure 6b shows the worn surface profiles after different numbers of cycles. The area below zero onthe vertical axis is associated with wear volume loss. It was identified that the wear depth and widthon the steel plate increased as the number of cycles increased.

Metals 2017, 7, 90 6 of 11

Figure 6a shows the worn surface image of a cold rolled high strength steel plate at the

displacement amplitude of 0.09 mm. The surface image was captured after 4000 cycles. Severe

damage was observed at the contact surface (dark area in the image). A cross-sectional profile on the

A-A’ axis was measured with a 2D surface profiler (SJ-210, Mitutoyo Corp., Takatsuku, Kawasaki,

Japan). Figure 6b shows the worn surface profiles after different numbers of cycles. The area below

zero on the vertical axis is associated with wear volume loss. It was identified that the wear depth

and width on the steel plate increased as the number of cycles increased.

(a) (b)

Figure 6. Worn surface and profile of a cold rolled high strength steel plate at the displacement

amplitude of 0.09 mm: (a) Wear scar after 4000 cycles; (b) The cross-sectional profile of a scar.

Figure 7 shows the cross-sectional profile of a wear scar on a cold rolled high strength steel plate

at the displacement amplitudes of 0.05 mm, 0.07 mm, 0.2 mm, and 0.3 mm. The size of the area below

zero on the vertical axis was calculated. The cross-sectional area size according to the number of

cycles was presented in Appendix B (Figure B1). Figure 8 shows the growth rate of the cross-sectional

area. The growth rate of the cross-sectional area was determined to increase with the imposed

displacement amplitude up to 0.09 mm. After the imposed displacement amplitude of 0.2 mm, the

growth rate was almost steady.

(a) (b)

(c) (d)

Figure 7. The cross-sectional profile of a wear scar on a cold rolled high strength steel plate at various

displacement amplitudes: (a) 0.05 mm; (b) 0.07 mm; (c) 0.2 mm; (d) 0.3 mm.

A

A´

Sliding direction

300µm

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

100 cycles500 cycles1000 cycles2000 cycles4000 cycles

Height (µm)

Position (mm)

δamp=0.09 mm

A A´

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 cycles

2000 cycles

4000 cycles

Height (µm)

Position (mm)

δamp=0.05 mm

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 cycles

2000 cycles

4000 cycles

Height (µm)

Position (mm)

δamp=0.07 mm

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 cycles

2000 cycles

4000 cycles

Height (µm)

Position (mm)

δamp=0.2 mm

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 cycles

2000 cycles

4000 cycles

Height (µm)

Position (mm)

δamp=0.3 mm

Figure 6. Worn surface and profile of a cold rolled high strength steel plate at the displacementamplitude of 0.09 mm: (a) Wear scar after 4000 cycles; (b) The cross-sectional profile of a scar.

Figure 7 shows the cross-sectional profile of a wear scar on a cold rolled high strength steel plateat the displacement amplitudes of 0.05 mm, 0.07 mm, 0.2 mm, and 0.3 mm. The size of the area belowzero on the vertical axis was calculated. The cross-sectional area size according to the number of cycleswas presented in Appendix B (Figure A1). Figure 8 shows the growth rate of the cross-sectional area.The growth rate of the cross-sectional area was determined to increase with the imposed displacementamplitude up to 0.09 mm. After the imposed displacement amplitude of 0.2 mm, the growth rate wasalmost steady.

Metals 2017, 7, 90 6 of 11

Figure 6a shows the worn surface image of a cold rolled high strength steel plate at the

displacement amplitude of 0.09 mm. The surface image was captured after 4000 cycles. Severe

damage was observed at the contact surface (dark area in the image). A cross-sectional profile on the

A-A’ axis was measured with a 2D surface profiler (SJ-210, Mitutoyo Corp., Takatsuku, Kawasaki,

Japan). Figure 6b shows the worn surface profiles after different numbers of cycles. The area below

zero on the vertical axis is associated with wear volume loss. It was identified that the wear depth

and width on the steel plate increased as the number of cycles increased.

(a) (b)

Figure 6. Worn surface and profile of a cold rolled high strength steel plate at the displacement

amplitude of 0.09 mm: (a) Wear scar after 4000 cycles; (b) The cross-sectional profile of a scar.

Figure 7 shows the cross-sectional profile of a wear scar on a cold rolled high strength steel plate

at the displacement amplitudes of 0.05 mm, 0.07 mm, 0.2 mm, and 0.3 mm. The size of the area below

zero on the vertical axis was calculated. The cross-sectional area size according to the number of

cycles was presented in Appendix B (Figure B1). Figure 8 shows the growth rate of the cross-sectional

area. The growth rate of the cross-sectional area was determined to increase with the imposed

displacement amplitude up to 0.09 mm. After the imposed displacement amplitude of 0.2 mm, the

growth rate was almost steady.

(a) (b)

(c) (d)

Figure 7. The cross-sectional profile of a wear scar on a cold rolled high strength steel plate at various

displacement amplitudes: (a) 0.05 mm; (b) 0.07 mm; (c) 0.2 mm; (d) 0.3 mm.

A

A´

Sliding direction

300µm

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

100 cycles500 cycles1000 cycles2000 cycles4000 cycles

Height (µm)

Position (mm)

δamp=0.09 mm

A A´

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 cycles

2000 cycles

4000 cycles

Height (µm)

Position (mm)

δamp=0.05 mm

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 cycles

2000 cycles

4000 cycles

Height (µm)

Position (mm)

δamp=0.07 mm

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 cycles

2000 cycles

4000 cycles

Height (µm)

Position (mm)

δamp=0.2 mm

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 cycles

2000 cycles

4000 cycles

Height (µm)

Position (mm)

δamp=0.3 mm

Figure 7. The cross-sectional profile of a wear scar on a cold rolled high strength steel plate at variousdisplacement amplitudes: (a) 0.05 mm; (b) 0.07 mm; (c) 0.2 mm; (d) 0.3 mm.

Metals 2017, 7, 90 7 of 11Metals 2017, 7, 90 7 of 11

Figure 8. Growth rate of the cross-sectional area of a wear scar on a cold rolled high strength steel

specimen according to the imposed displacement amplitude. R indicates the quality of curve fitting

with linear regression.

In this study, the wear volume was calculated with the measured cross-sectional profiles. Figure 9

shows the schematic diagram of a worn surface and a profile, where 2ac denotes the actual contact

width and dp is the average wear depth. The total wear volume corresponds to the sum of Parts I and

II in Figure 9. The wear volume for Part I can be assumed as semi-ellipsoid. Thus, the total wear

volume (Vw) is given as

222

3w ac c pV A a d (1)

where A is the measured cross-sectional area and δac denotes the actual sliding amplitude. The actual

sliding amplitude could be determined on a tangential force versus displacement loop; the actual

sliding amplitude was defined as the displacement in which a tangential force comes to zero.

Figure 9. Schematic diagram of a worn surface and a profile to calculate the wear volume. dp denotes

the average wear depth, ac is the actual contact radius, and δac is the actual sliding amplitude.

Figure 10 shows the calculated wear volume according to the number of cycles. Markers show

the calculated data and the solid lines denote fitted curves with a linear form. As shown in the figure,

the wear volume increased according to the number of cycles. Table 3 shows the results of the curve

fitting. The slope of the linear fit equals to the wear rate. The wear rate of the steel at the displacement

amplitude of 0.3 mm was found to be ten times greater than the calculated one at 0.05 mm.

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400

Imposed displacement amplitude, δamp (µm)

Chan

ge

rate

of

cross

-sec

tional

are

a

size

, A

(µm

2/c

ycl

e)920

460020

.R

..A amp

2δac

B

B

B´

B´

2ac

dp

I II I

Contact area

(grey)

Figure 8. Growth rate of the cross-sectional area of a wear scar on a cold rolled high strength steelspecimen according to the imposed displacement amplitude. R indicates the quality of curve fittingwith linear regression.

In this study, the wear volume was calculated with the measured cross-sectional profiles. Figure 9shows the schematic diagram of a worn surface and a profile, where 2ac denotes the actual contactwidth and dp is the average wear depth. The total wear volume corresponds to the sum of Parts Iand II in Figure 9. The wear volume for Part I can be assumed as semi-ellipsoid. Thus, the total wearvolume (Vw) is given as

Vw = 2 · δac · A +23π · a2

c · dp (1)

where A is the measured cross-sectional area and δac denotes the actual sliding amplitude. The actualsliding amplitude could be determined on a tangential force versus displacement loop; the actualsliding amplitude was defined as the displacement in which a tangential force comes to zero.

Metals 2017, 7, 90 7 of 11

Figure 8. Growth rate of the cross-sectional area of a wear scar on a cold rolled high strength steel

specimen according to the imposed displacement amplitude. R indicates the quality of curve fitting

with linear regression.

In this study, the wear volume was calculated with the measured cross-sectional profiles. Figure 9

shows the schematic diagram of a worn surface and a profile, where 2ac denotes the actual contact

width and dp is the average wear depth. The total wear volume corresponds to the sum of Parts I and

II in Figure 9. The wear volume for Part I can be assumed as semi-ellipsoid. Thus, the total wear

volume (Vw) is given as

222

3w ac c pV A a d (1)

where A is the measured cross-sectional area and δac denotes the actual sliding amplitude. The actual

sliding amplitude could be determined on a tangential force versus displacement loop; the actual

sliding amplitude was defined as the displacement in which a tangential force comes to zero.

Figure 9. Schematic diagram of a worn surface and a profile to calculate the wear volume. dp denotes

the average wear depth, ac is the actual contact radius, and δac is the actual sliding amplitude.

Figure 10 shows the calculated wear volume according to the number of cycles. Markers show

the calculated data and the solid lines denote fitted curves with a linear form. As shown in the figure,

the wear volume increased according to the number of cycles. Table 3 shows the results of the curve

fitting. The slope of the linear fit equals to the wear rate. The wear rate of the steel at the displacement

amplitude of 0.3 mm was found to be ten times greater than the calculated one at 0.05 mm.

0

0.5

1

1.5

2

2.5

3

0 100 200 300 400

Imposed displacement amplitude, δamp (µm)

Chan

ge

rate

of

cross

-sec

tional

are

a

size

, A

(µm

2/c

ycl

e)920

460020

.R

..A amp

2δac

B

B

B´

B´

2ac

dp

I II I

Contact area

(grey)

Figure 9. Schematic diagram of a worn surface and a profile to calculate the wear volume. dp denotesthe average wear depth, ac is the actual contact radius, and δac is the actual sliding amplitude.

Figure 10 shows the calculated wear volume according to the number of cycles. Markers showthe calculated data and the solid lines denote fitted curves with a linear form. As shown in the figure,the wear volume increased according to the number of cycles. Table 3 shows the results of the curvefitting. The slope of the linear fit equals to the wear rate. The wear rate of the steel at the displacementamplitude of 0.3 mm was found to be ten times greater than the calculated one at 0.05 mm.

Metals 2017, 7, 90 8 of 11Metals 2017, 7, 90 8 of 11

Figure 10. Calculated wear volume on a cold rolled high strength steel plate according to the number

of cycles.

Table 3. Curve fitting results of calculated wear volume (Vw) on a cold rolled high strength steel plate.

R indicates the quality of curve fitting with linear regression.

Displacement

Amplitude

(mm)

CNV)N(V ww

wV : wear rate, N: number of cycles, C: constant

wV (µm3/cycle) C (µm3) R

0.05 320.05 6.08 × 105 0.99

0.07 441.07 1.19 × 106 0.96

0.09 1053.70 5.04 × 105 0.98

0.2 2711.00 1.11 × 106 0.95

0.3 3287.20 1.03 × 106 0.96

Figure 11 shows the wear rate of a cold rolled high strength steel plate. When the imposed

displacement amplitude was lower than 0.09 mm (or when the actual sliding amplitude was lower

than 0.062 mm), the calculated wear rate of the high strength steel specimen rapidly increased as the

displacement amplitude increased; the increase rate was 18.34 µm3/cycle per unit displacement

amplitude. This wear rate could be used for indicating the wear behavior of the steel in a gross slip

regime. The transition on the increase of the wear rate was found between 0.09 mm and 0.2 mm in

displacement amplitude. From Figures 8 and 11, it could be suggested that sliding at an imposed

displacement amplitude of lower than 0.09 mm should be considered fretting. Given that the imposed

displacement amplitude of 0.09 mm was similar to the Hertz contact radius, it can be identified that

the fretting occurred when the imposed displacement was lower than the Hertz contact radius during

the sliding between cold rolled high strength steel and AISI52100. In order to identify the apparent

transition from fretting to reciprocal sliding regimes, additional sliding tests are needed in the

displacement amplitude range of 0.09 mm and 0.2 mm. In addition, direct measurements of the wear

volume on a cold rolled high strength steel specimen would be useful in determining the accurate

wear rate.

0

2

4

6

8

10

12

14

16

0 1000 2000 3000 4000 5000

Number of cycles, N

Wea

r v

olu

me,

Vw

(µm

3)

x106

0.3 mm

0.2 mm

0.05 mm

0.07 mm

0.09 mm

Figure 10. Calculated wear volume on a cold rolled high strength steel plate according to the numberof cycles.

Table 3. Curve fitting results of calculated wear volume (Vw) on a cold rolled high strength steel plate.R indicates the quality of curve fitting with linear regression.

DisplacementAmplitude (mm)

Vw(N) =.Vw × N + C

.Vw: wear rate, N: number of cycles, C: constant

.Vw (µm3/cycle) C (µm3) R

0.05 320.05 6.08 × 105 0.990.07 441.07 1.19 × 106 0.960.09 1053.70 5.04 × 105 0.980.2 2711.00 1.11 × 106 0.950.3 3287.20 1.03 × 106 0.96

Figure 11 shows the wear rate of a cold rolled high strength steel plate. When the imposeddisplacement amplitude was lower than 0.09 mm (or when the actual sliding amplitude was lowerthan 0.062 mm), the calculated wear rate of the high strength steel specimen rapidly increased asthe displacement amplitude increased; the increase rate was 18.34 µm3/cycle per unit displacementamplitude. This wear rate could be used for indicating the wear behavior of the steel in a gross slipregime. The transition on the increase of the wear rate was found between 0.09 mm and 0.2 mm indisplacement amplitude. From Figures 8 and 11, it could be suggested that sliding at an imposeddisplacement amplitude of lower than 0.09 mm should be considered fretting. Given that the imposeddisplacement amplitude of 0.09 mm was similar to the Hertz contact radius, it can be identifiedthat the fretting occurred when the imposed displacement was lower than the Hertz contact radiusduring the sliding between cold rolled high strength steel and AISI52100. In order to identify theapparent transition from fretting to reciprocal sliding regimes, additional sliding tests are needed inthe displacement amplitude range of 0.09 mm and 0.2 mm. In addition, direct measurements of thewear volume on a cold rolled high strength steel specimen would be useful in determining the accuratewear rate.

Metals 2017, 7, 90 9 of 11Metals 2017, 7, 90 9 of 11

Figure 11. Wear rate on a cold rolled high strength steel plate with the imposed displacement

amplitude. δac denotes the average value of the actual sliding amplitude during a test, and δamp is the

imposed displacement amplitude. R indicates the quality of curve fitting with linear regression.

4. Conclusions

The following conclusions have been drawn.

The ratio of the maximum tangential to normal force was independent of the imposed

displacement amplitude (between 0.05 mm and 0.3 mm). The ratio between the cold rolled high

strength steel and AISI52100 steel was determined to be about 0.72 in dry conditions.

The cross-sectional area size of the wear scar increased as the number of cycles increased. The growth

rate of the cross-sectional area size increased according to imposed displacement amplitude up

to 0.09 mm.

The approximate wear volume on the cold rolled high strength steel specimen increased according

to the number of cycles. A rapid increase in the wear rate occurred at imposed displacement

amplitudes lower than 0.09 mm. The increase in the wear rate was found to transition from rapid

to gradual between displacement amplitudes of 0.09 mm and 0.2 mm. In other words, the

transition from fretting to reciprocal sliding regimes was identified between 0.09 mm and 0.2 mm.

The obtained values of the friction and the wear rate could be used for indicating tribological

properties of cold rolled high strength steel. In addition, the wear rate can be used to predict the

lifetime of an automotive seat slide track. Further work needs to include the measurement of accurate

wear volume after a series of tests with additional displacement amplitudes (between 0.09 mm and

0.2 mm). In this study, only AISI52100 steel counterparts were considered. Thus, other counterparts

such as ceramics and stainless steel balls need to be used to determine the wear rate of the cold rolled

high strength steel.

Acknowledgments: This work was supported by the National Research Foundation of Korea (NRF) grant

funded by the Korea government (MSIP) (No. 2016R1C1B1008483).

Author Contributions: J.H. and K.K. conceived and designed the experiments; J.H. performed

the experiments; J.H. and K.K. analyzed the data; J.H. and K.K. contributed reagents/materials/analysis tools;

K.K. wrote the paper.

Conflicts of Interest: The authors declare no conflict of interest.

Appendix A

The maximum contact pressure ( 0p ) between a sphere and a plate is calculated from Hertz

contact theory [13]

0

500

1000

1500

2000

2500

3000

3500

4000

0 50 100 150 200 250 300 350

Imposed displacement amplitude, δ (µm)

Wea

r ra

te, V

(µ

m3/c

ycl

e)

930

956783418

.R

..V amp

960

521476118

.R

..V ac

.

Figure 11. Wear rate on a cold rolled high strength steel plate with the imposed displacement amplitude.δac denotes the average value of the actual sliding amplitude during a test, and δamp is the imposeddisplacement amplitude. R indicates the quality of curve fitting with linear regression.

4. Conclusions

The following conclusions have been drawn.

• The ratio of the maximum tangential to normal force was independent of the imposeddisplacement amplitude (between 0.05 mm and 0.3 mm). The ratio between the cold rolledhigh strength steel and AISI52100 steel was determined to be about 0.72 in dry conditions.

• The cross-sectional area size of the wear scar increased as the number of cycles increased.The growth rate of the cross-sectional area size increased according to imposed displacementamplitude up to 0.09 mm.

• The approximate wear volume on the cold rolled high strength steel specimen increased accordingto the number of cycles. A rapid increase in the wear rate occurred at imposed displacementamplitudes lower than 0.09 mm. The increase in the wear rate was found to transition fromrapid to gradual between displacement amplitudes of 0.09 mm and 0.2 mm. In other words, thetransition from fretting to reciprocal sliding regimes was identified between 0.09 mm and 0.2 mm.

The obtained values of the friction and the wear rate could be used for indicating tribologicalproperties of cold rolled high strength steel. In addition, the wear rate can be used to predict thelifetime of an automotive seat slide track. Further work needs to include the measurement of accuratewear volume after a series of tests with additional displacement amplitudes (between 0.09 mm and0.2 mm). In this study, only AISI52100 steel counterparts were considered. Thus, other counterpartssuch as ceramics and stainless steel balls need to be used to determine the wear rate of the cold rolledhigh strength steel.

Acknowledgments: This work was supported by the National Research Foundation of Korea (NRF) grant fundedby the Korea government (MSIP) (No. 2016R1C1B1008483).

Author Contributions: J.H. and K.K. conceived and designed the experiments; J.H. performed the experiments;J.H. and K.K. analyzed the data; J.H. and K.K. contributed reagents/materials/analysis tools; K.K. wrote the paper.

Conflicts of Interest: The authors declare no conflict of interest.

Metals 2017, 7, 90 10 of 11

Appendix A

The maximum contact pressure (p0) between a sphere and a plate is calculated from Hertz contacttheory [13]

p0 =

(6 · P · E∗2

π3 · R2

) 13

(A1)

1E∗ =

1 − ν21

E1+

1 − ν22

E2(A2)

where P denotes normal force, R is the radius of a sphere, E1 and E2 are elastic moduli of the sphere andof the plate, respectively, and ν1 and ν2 denote Poisson’s ratios of the sphere and the plate. The valuesfor the parameters were presented in Table 2.

Appendix B

Cross-sectional area size of a wear scar on a cold rolled high strength steel plate according to thenumber of cycles. R indicates the quality of curve fitting with linear regression.

Metals 2017, 7, 90 10 of 11

3

1

23

2

0

6

R

EPp

*

(A1)

2

22

1

21 111

EEE*

(A2)

where P denotes normal force, R is the radius of a sphere, 1E and 2E are elastic moduli of the

sphere and of the plate, respectively, and 1 and 2 denote Poisson’s ratios of the sphere and the

plate. The values for the parameters were presented in Table 2.

Appendix B

Cross-sectional area size of a wear scar on a cold rolled high strength steel plate according to the

number of cycles. R indicates the quality of curve fitting with linear regression.

Figure B1. Cross-sectional area size versus Number of cycles.

References

1. Hofmann, H.; Mattissen, D.; Schaumann, T.H. Advanced cold rolled steels for automotive applications.

Steel. Res. Int. 2009, 80, 22–28.

2. Kuziak, R.; Kawalla, R.; Waengler, S. Advanced high strength steels for automotive industry. Arch. Civ.

Mech. Eng. 2008, 8, 103–117.

3. Kim, K. A study of the frictional characteristics of metal and ceramic counterfaces against electro-deposited

coatings for use on automotive seat rails. Wear 2014, 320, 62–67.

4. He, X.; Deng, C.; Zhang, X. Fretting behavior of SPR joining dissimilar sheets of titanium and copper alloys.

Metals 2016, 6, doi:10.3390/met6120312.

5. Lavella, M. Contact properties and wear behavior of nickel based superalloy Rene 80. Metals 2016, 6,

doi:10.3390/met6070159.

6. Waterhouse, R.B. ASM Handbook, Friction, Lubrication and Wear Technology, 1st ed.; ASM International:

Materials Park, OH, USA, 1992; 18, pp. 242–256.

7. Bhushan, B. Introduction to Tribology, 1st ed.; John Wiley & Sons, Inc.: New York, NY, USA, 2002.

8. Vingsbo, O.; Soderberg, S. On fretting maps. Wear 1988, 126, 131–147.

9. Kim, K.; Korsunsky, A.M. Effect of imposed displacement and initial coating thickness on fretting behavior

of a thermally sprayed coating. Wear 2011, 271, 1080–1085.

10. Hur, J.W.; Baek, S.Y.; Kim, K. Effect of displacement on kinetic frictional behavior between electro-deposited

coating and AISI 52100 steel under fretting conditions. Proc. Inst. Mech. Eng. J J. Eng. Tribol. 2016, 230, 1172–1179.

11. Li, J.; Lu, Y.H. Effects of displacement amplitude on fretting wear behaviors and mechanism of Inconel 600

alloy. Wear 2013, 304, 223–230.

Number of cycles, N

Cro

ss-s

ecti

onal

are

a si

ze,

A(µ

m2)

0

2000

4000

6000

8000

10000

12000

14000

0 1000 2000 3000 4000 5000

0.05mm 0.07mm 0.09mm 0.2mm 0.3mm

980

11806680

.R

.N.A

980

52630800

.R

.N.A

990

41547511

.R

.N.A

960

92952412

.R

.N.A

980

62691462

.R

.N.A

For 0.2 mmFor 0.3 mm

Figure A1. Cross-sectional area size versus Number of cycles.

References

1. Hofmann, H.; Mattissen, D.; Schaumann, T.H. Advanced cold rolled steels for automotive applications.Steel. Res. Int. 2009, 80, 22–28. [CrossRef]

2. Kuziak, R.; Kawalla, R.; Waengler, S. Advanced high strength steels for automotive industry. Arch. Civ.Mech. Eng. 2008, 8, 103–117. [CrossRef]

3. Kim, K. A study of the frictional characteristics of metal and ceramic counterfaces against electro-depositedcoatings for use on automotive seat rails. Wear 2014, 320, 62–67. [CrossRef]

4. He, X.; Deng, C.; Zhang, X. Fretting behavior of SPR joining dissimilar sheets of titanium and copper alloys.Metals 2016, 6, 312. [CrossRef]

5. Lavella, M. Contact properties and wear behavior of nickel based superalloy Rene 80. Metals 2016, 6, 159.[CrossRef]

6. Waterhouse, R.B. ASM Handbook, Friction, Lubrication and Wear Technology, 1st ed.; ASM International:Materials Park, OH, USA, 1992; Volume 18, pp. 242–256.

7. Bhushan, B. Introduction to Tribology, 1st ed.; John Wiley & Sons, Inc.: New York, NY, USA, 2002.8. Vingsbo, O.; Soderberg, S. On fretting maps. Wear 1988, 126, 131–147. [CrossRef]9. Kim, K.; Korsunsky, A.M. Effect of imposed displacement and initial coating thickness on fretting behavior

of a thermally sprayed coating. Wear 2011, 271, 1080–1085. [CrossRef]

Metals 2017, 7, 90 11 of 11

10. Hur, J.W.; Baek, S.Y.; Kim, K. Effect of displacement on kinetic frictional behavior between electro-depositedcoating and AISI 52100 steel under fretting conditions. Proc. Inst. Mech. Eng. J J. Eng. Tribol. 2016, 230,1172–1179. [CrossRef]

11. Li, J.; Lu, Y.H. Effects of displacement amplitude on fretting wear behaviors and mechanism of Inconel600 alloy. Wear 2013, 304, 223–230. [CrossRef]

12. Landolt, D.; Mischler, S. Tribocorrosion of Passive Metals and Coatings, 1st ed.; Woodhead Publishing Limited:Cambridge, UK, 2011; pp. 406–407.

13. Sackfield, A.; Hills, D.A.; Nowell, D. Mechanics of Elastic Contacts, 1st ed.; Butterworth-Heinemann: Oxford,UK, 1993.

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