ORIGINAL PAPER

Bauschinger’s Effect and Dislocation Structure Under Frictionof LiF Single Crystals

E. Harea • I. Lapsker • A. Laikhtman •

L. Rapoport

Received: 28 May 2013 / Accepted: 13 August 2013 / Published online: 24 August 2013

� Springer Science+Business Media New York 2013

Abstract Friction and wear of LiF single crystals in

unidirectional and bidirectional motion have been studied.

The friction coefficient and wear are found to be higher

under unidirectional motion. The experimental evidence of

the dislocation structure around the wear track is presented.

Friction and wear of LiF single crystals are determined

both by the Bauschinger’s effect and by redistribution of

the contact spots due to plowing and adhesion of wear

particles to rubbing surface.

Keywords LiF single crystal � Friction � Wear �Dislocations

1 Introduction

Recently, the wear of Cu-40 % Zn alloy during unidirec-

tional and bidirectional abrasion processes was studied for

the first time [1, 2]. It was found that unidirectional abra-

sion caused more wear loss in a Cu-40 %Zn alloy than in

bidirectional abrasion. The strain-hardening effect

decreased under bidirectional sliding, suggesting that the

Baushinger’s effect (BE) plays an important role under

these worn conditions. Much stronger cracking also pre-

sented as a result of the Bauschinger’s effect.

It is well known that the strain hardening of a metal

depends on the loading path. For instance, if plastically

prestrained under compression, a metal may show decreased

yield strength when tested in tension. This softening is

known as the Bauschinger’s effect [3, 4]. At the microscopic

level, BE could be attributed to local reversible movement of

dislocations and annihilation of dislocations of opposite

signs when the applied stress is reversed (e.g., [5, 6]).

Annihilation of dislocations is accompanied by a decrease in

the rate of dislocation accumulation and, consequently, it

lowers the strain hardening. It was also shown that the BE

affects the fatigue life of materials [7]. Several authors

concluded that the BE is important for forming processes and

for other mechanical properties of formed components [8, 9].

It was reported that the BE is tied not only to plasticity of

metals but also to the damage state, as well [10]. Concerning

to the Bauschinger’s effect under friction of the Cu-40 %Zn

alloy, the macroscopic level parameter (hardness of surface

layers) was used for explanation. In this case, the analysis of

the dislocation patterns during friction in opposite directions

(at the microscopic scale) seems to be an interesting problem.

Single crystals are widely used for the analysis of the

dislocation motion. In particular, this research is based on

the study of LiF single crystals. A number of works on the

influence of the environment on surface layers were carried

out using alkali halides. LiF is a typical representative of

the alkali halides class. Friction and wear transition to

seizure and galling as well as the effect of a Vaseline oil on

friction and wear of the single crystals of LiF were studied

previously [11, 12]. The object of the present work is a

comparison of the friction and wear behavior of LiF single

crystals in unidirectional and bidirectional motions. We

also present the experimental evidence of the dislocations

around the wear tracks when the annihilation of disloca-

tions during bidirectional motion is observed. A damage of

the surface layers is determined both by the BE and by

redistribution of the applied stress due to the wear particles

adhered to the friction surface.

E. Harea

Institute of Applied Physics, Chishinau, Moldova

I. Lapsker � A. Laikhtman � L. Rapoport (&)

Holon Institute of Technology, 5810201 Holon, Israel

e-mail: rapoport@hit.ac.il

123

Tribol Lett (2013) 52:205–212

DOI 10.1007/s11249-013-0206-y

2 Experimental Procedure

Dry friction tests were conducted using a linear ball-on-flat

device at room temperature in air (relative humidity of

55 ± 5 %). The ball (2 mm in diameter), made of bearing-

type steel hardened to 60 HRc, was slid against a plate of LiF.

The concentration of impurities in LiF was less than 10-3

wt% of Ca and Mg while cationic and anionic impurities

comprised less than 10-4 wt%. The sliding velocity was

0.15 9 10-3 m s-1; the load was 0.1 N. For evaluation of

the BE, the unidirectional sliding was compared with the

bidirectional motion: for instance, a surface of the wear track

and the dislocations around the track after 2 passes in one

direction were compared with one cycle in the bidirectional

motion. The scheme of loading is shown in Fig. 1. Finally,

the results of the unidirectional motion after 10 passes were

compared with 5 cycles in the bidirectional motion. The

friction of the ball was measured in the [100] sliding direc-

tion and (001) cleavage of the LiF crystal. The dislocations

were revealed by a method of selective etching by an aqueous

solution of FeCl3 (1.5 9 10-4 M). The density of disloca-

tions was determined in the definite distance from the wear

tracks both in the unidirectional and bidirectional motion.

The Vickers hardness was measured at the load of 0.1 N. The

mean standard deviation of the hardness was calculated

based on the 20 measurements for each sample. To reveal the

effect of fresh dislocations associated by plastic deforma-

tion, the samples were etched before and after friction. The

surfaces after friction were analyzed using optical micros-

copy, scanning electron microscopy (SEM), and atomic

force microscopy (AFM).

3 Results

3.1 Friction and Wear in the Unidirectional

and Bidirectional Motions

A surface of the wear track after one pass is shown in

Fig. 2. Strong plowing and adhesion of the wear particles

appear on the rubbing surface. Much deeper grooves and

large aggregates of the wear particles are observed when

friction continued in the same direction (2 passes), as can

be observed from Fig. 3a. Entirely different picture is

obtained in Fig. 3b for a ball moved in the opposite

direction (one cycle).

As can be seen from the above images, the wear parti-

cles fill the plow grooves formed during the first pass, thus

decreasing the formation of the deep grooves and the

aggregates on the rubbing surface. The general picture of

the rubbing surfaces after unidirectional and bidirectional

motions is preserved with an increase in the number of

cycles/passes: much more aggregated particles and deep

grooves appear under the unidirectional motion.

Figure 4 depicts the wear tracks after the unidirectional

motion (4 passes) and the bidirectional motion (2 cycles).

Much smoother surface with a small number of deep

grooves and adhered aggregates of the wear particles is

observed under the bidirectional motion. Figure 5 demon-

strates high magnified SEM image of the wear track where

all stages of plastic deformation and fracture after friction

during 4 cycles are observed.

In the range (1), plastic deformation of surface layers

occurs. Severe plastic deformation leads to a breaking (2)

and fragmentation (3) of the structure in surface layers. The

cracks appear in the boundaries of the fragments. Then, a

crushing of the fragments occurs (range 4). A size of the

wear particles is 100–200 nm.

Atomic force microscopy topography measurements

were performed for better understanding of the effect of

sliding motion on the profile of the wear tracks. Figure 6

demonstrates the AFM image and the profile of the wear

track after friction in the unidirectional motion (2 passes).

It can be observed that a depth of the grooves is about

150 nm while the regions of aggregated and pressed wear

particles are quite smooth (lesser than 50 nm). Friction in

the opposite direction is characterized by the formation of

much smoother surface without deep grooves, as presented

in Fig. 7. A depth of the grooves is less than 50 nm.

Furthermore, the effect of sliding direction on the fric-

tion coefficient has been studied.

The dependence of the friction coefficient on the number

of passes/cycles is shown in Fig. 8.

It is shown that friction in the unidirectional motion is

higher than in the bidirectional motion. The effect of

sliding direction on the wear loss is similar to that observed

for the friction coefficient. The width of the wear track

after friction in the unidirectional motion is larger than

after the bidirectional motion, and this difference increases

with the number of cycles/passes, as depicted in Fig. 9.

3.2 Dislocation Structure, Hardening and BE

The dislocation structure around the wear track after one

pass is shown in Fig. 10a.

Fig. 1 Scheme of the wear tracks on the surface of the LiF single

crystal: one pass in the unidirectional motion, the bidirectional motion

(1 cycle), and the unidirectional motion (two passes) are shown by

arrows

206 Tribol Lett (2013) 52:205–212

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A width of the dislocation zone around the wear track is

about 235 lm. During the first pass, the edge components

of dislocations are more active in the direction of sliding.

In fact, two regions of the dislocations appear: a first one is

the region of the high dislocation density near the wear

track and a second one is the region where the dislocation

density decreases with a distance from the wear track. A

region of the high dislocation density is attributed to an

Fig. 2 SEM images of the wear tracks on the surface of LiF after the unidirectional motion (one pass). The magnified image of the track

indicates the plow grooves and adhered aggregates on the rubbing surface (b). Sliding direction is shown by arrow

Fig. 3 SEM images of the wear tracks after the unidirectional motion (2 passes) (a) and the bidirectional motion (1 cycle) (b). Sliding direction

is shown by arrow

Fig. 4 SEM images of the worn surfaces after the unidirectional motion (4 passes) (a) and the bidirectional motion (2 cycles) (b). Sliding

direction is shown by arrow

Tribol Lett (2013) 52:205–212 207

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intersection between the edge and the screw components of

dislocations. After two passes of the ball, an increase in the

size of the first region with the high dislocation density is

revealed, Fig. 11. This can be attributed to an increase in

the activity of the end and screw components of disloca-

tions. A size of the second dislocation zone is also

increased up to about 325 lm.

In comparison with the dislocation pattern in the uni-

directional motion, the density of dislocations around the

wear track decreased under friction in the bidirectional

motion, especially in the second region, as can be observed

from Fig. 12. For instance, the density of dislocations in

the distance of 40 lm from the wear track in the unidi-

rectional motion was 7 9 109 m-2 while this value was

more than two times lower in the bidirectional motion

(3 9 109 m-2). A general picture of the dislocation regions

is preserved with increasing the number of cycles/passes

(up to 5/10, respectively). A size of the dislocation regions

around the wear tracks does not changed—the saturated

state is obtained, although a width of the wear track is

increased with a number of the cycles/passes. After a study

of the dislocation patterns, the samples were cleaved per-

pendicular to the sliding motion. The dislocation patterns

of cross-sectional samples are shown in Fig. 13.

It can be seen that the length of screw components of

half-loops on {110}45 planes is shorter in the bidirectional

motion (Fig. 13a) in comparison with the unidirectional

motion, Fig. 13b. High density of dislocations in subsur-

face layers is determined by motion of edge and screw

components of half-loops of dislocations on {110}45

planes. The results of hardness measurements in the wear

tracks are depicted in Fig. 14. The hardness of surface

layers under friction in the bidirectional motion is smaller

than in the unidirectional motion. Moreover, the hardness

values are preserved with following cycling/passing—the

saturated hardness/strength is obtained similar to that

observed for the dislocation regions around the wear track.

It is important to note that etching, rinsing, and drying of

the LiF samples after friction led to removal of the wear

particles from the wear track. In this case, the accuracy of

hardness measurement was higher and the damage in the

wear track was revealed in a better way.

Fig. 5 SEM image of the wear track after friction during 4 cycles.

The numbers show the different stages of plastic deformation and

fracture: 1—a range of the plastic deformation; 2—breaking of the

grain structure; 3—cracking around the fragments; 4—crushing of the

fragments. Sliding direction is shown by arrow

Fig. 6 AFM image of the wear track after the unidirectional motion (2 passes) (a) and the profile of the wear track (b)

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4 Discussion

Friction and wear of LiF single crystals have been studied

during unidirectional and bidirectional motions. It has been

shown that both the friction coefficient and wear are

smaller under friction in the bidirectional motion. A

decrease in the values of the friction coefficient and wear

is attributed to the formation of a smooth film of adhered

and pressed wear particles under friction in an opposite

direction. Moreover, the formation of this film limits a

direct contact between the rubbing surfaces. In the unidi-

rectional motion, the process of plowing and the formation

of the aggregated wear particles are strengthened with a

following passing. This general relationship between the

formation of the wear track in the unidirectional and

bidirectional motions is preserved with an increase in the

number of passes/cycles. It seems to us reasonable to

assume that the improved friction and wear properties in

the bidirectional motion are associated not only to the

formation of much smoother surfaces but also to an

increase in plasticity of the surface layers due to the BE.

In order to evaluate the role of the BE on friction and

wear of LiF single crystals, the dislocation structures in

unidirectional and bidirectional motions have been ana-

lyzed. The dislocation pattern after one pass corresponds

mainly to the edge components of dislocation half-loops on

{110} planes at 90� to the surface, as shown in Fig. 10a.

The dislocations around the wear track can be presented as

a part of a series of the dislocation arms around the indent,

see Fig. 10b. During a second pass, the density of both the

edge components and the screw components {110}45 of

dislocations increased. When the ball moved in the oppo-

site direction, the edge components of opposite signs

annihilate thus decreasing the dislocation density and the

deformation hardening. A decrease in the deformation

hardening is confirmed by the analysis of hardness after

friction, see Fig. 14. Substantially, longer arms of the

screw components in subsurface layers during the unidi-

rectional motion also confirm an important role of the BE

on plastic deformation and fracture during friction of the

LiF single crystals.

To quantify the magnitude of the BE, a number of dif-

ferent definitions have been used. Abel [6] introduced the

parameter called the Bauschinger stress parameter (BSP).

BSP ¼rf

����� rrj jrf

����

Fig. 7 AFM image of the wear track after the bidirectional motion (1 cycle) (a) and the profile of the wear track (b)

Fig. 8 The dependence of the friction coefficient on the number of

passes/cycles

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where rf is the forward prestrain stress and rr is the

reversal stress. This parameter was calculated using the

saturated values of the hardness after friction in the uni-

directional (forward) and the bidirectional (reversal)

motion (r * H/3). In our case, the value of the BSP is

close to 0.1. It is clear that the BSP depends on the max-

imum forward prestrain. For instance, for the prestrain of

the aluminum alloy of 0.01, the BSP is 0.25 [10]. We have

not studied the effect of the prestrain magnitude in this

work.

Although the analysis of the dislocation structure and

the hardness measurements indicates an important role of

the BE, the friction and wear results are also attributed to

redistribution of the contact spots on the rubbing surface of

LiF. They are associated with adhesion of the aggregates of

wear particles and a plowing of surface layers. In other

words, the adhered wear particles and plowing grooves

affect the real contact pressure. A variation of the real

contact pressure (the applied stress) can also affect the

dislocation mobility. These two effects cannot be analyzed

separately. Generally, the formation of wear particles under

friction of the LiF single crystals is determined by brittle

fracture under friction at room temperature [11]. It is

expected that an increase in the plasticity due to annihila-

tion of the dislocations has to decrease the brittleness of the

process of wear particle formation. This tendency is

apparently observed during a friction in the bidirectional

motion. Based on these results, it can be concluded that

both the BE and the effect of redistribution of the contact

stress due to the adhered wear particles and plowing of

surface layers are responsible for the friction and wear

phenomena LiF single crystals.

0 1 2 3 4 5

30

35

40

45

50

55

60

65

70Number of passes

Wid

th o

f tr

ack,

µm

Number of cycles

2 4 6 8 10

Fig. 9 The effect of the direction of motion on the width of the wear

track

Fig. 10 The dislocation pattern around the wear track (unidirectional motion, one pass) (a). The dislocation pattern around the indent (b).

Orientation of indentation: d | | {100}. Sliding direction is shown by arrow

Fig. 11 The dislocation pattern around the wear track (unidirectional

motion, two passes). Sliding direction is shown by arrow

Fig. 12 The dislocation pattern around the wear track (bidirectional

motion, one cycle)

210 Tribol Lett (2013) 52:205–212

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It is clear that the friction and wear properties of the LiF

single crystals are mainly determined by the dislocation

structure in the wear track. SEM image of the dislocation

structure around the wear track is shown in Fig. 15. The

low magnified image indicates free dislocations in cellular

arrangement around the wear track, Fig. 15a. High density

of dislocations in the wear track is accompanied by for-

mation of cell structure, Fig. 15b. The formation of the cell

structure is apparently attributed to the intersection

between the edge and screw components of dislocations in

the wear track as it shown in Fig. 13. The size of the cells

varies from 100 to 500 nm.

It is expected that the size of single wear particles is

close to the size of the cells. This suggestion should be

confirmed in the future work.

5 Conclusions

Friction and wear of the LiF single crystals in unidirec-

tional and bidirectional motions have been studied. The

friction coefficient and wear are found to be higher under

the unidirectional motion. The dislocation structure and

hardness of surface layers were analyzed after friction. An

annihilation of the dislocations and a decrease in the den-

sity of dislocations and the hardness of surface layers under

bidirectional motion confirm the role of the BE under

friction. Friction and wear of the LiF single crystals are

Fig. 13 The dislocation patterns of subsurface layers after friction in the bidirectional (2 cycles, a) and the unidirectional motion (4 passes, b)

0 1 2 3 4 5

Har

dnes

s H

V, M

Pa

Number of cycles

Number of passes

2 4 6 8 10

700

800

900

1000

1100

Fig. 14 The effect of unidirectional and bidirectional motion on the

hardness of surface layers

Fig. 15 Dislocation configurations of {001} LiF single crystal after strong deformation and fracture during two passes of friction (a). High

magnified image of the dislocation structure indicates the formation of cells in surface layers of the wear track

Tribol Lett (2013) 52:205–212 211

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determined not only by the BE but also by redistribution of

the contact spots due to plowing and adhesion of wear

particles to the rubbing surface. This work demonstrates a

similarity in the behavior of LiF single crystals with the

metals and a possibility to simple analysis of the disloca-

tion interaction and damage development.

6 Highlights

• Friction and wear of LiF single crystals were studied.

• Unidirectional and bidirectional motions are compared.

• Dislocation structure is evaluated.

• Friction is associated to the Bauschinger’s effect.

• Adhesion of wear particles also affects the friction.

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