dislocation structure and stick–slip phenomenon

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Tribology Letters ISSN 1023-8883Volume 55Number 2 Tribol Lett (2014) 55:295-301DOI 10.1007/s11249-014-0358-4

Dislocation Structure and Stick–SlipPhenomenon

V. Perfilyev, A. Moshkovich, I. Lapsker,A. Laikhtman & L. Rapoport

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ORIGINAL PAPER

Dislocation Structure and Stick–Slip Phenomenon

V. Perfilyev • A. Moshkovich • I. Lapsker •

A. Laikhtman • L. Rapoport

Received: 24 March 2014 / Accepted: 4 June 2014 / Published online: 18 June 2014

� Springer Science+Business Media New York 2014

Abstract Friction is a complex process involving multi-

scale asperity contact and large plastic deformation asso-

ciated with the development of a dislocation structure.

Friction is closely associated with the stick–slip phenom-

enon. In spite of the large number of papers, dedicated to

stick–slip effects, little effort has been directed toward

elucidating the development of the dislocation structure

during stick–slip phenomena. Here, we report some new

systematic investigations into the dislocation nature of

stick–slips during low-velocity friction of a lithium fluoride

single crystal rubbed against a spherical diamond indenter.

It is shown that the average velocity of the indenter in the

stick phase is about 300 times lower than the maximal

velocity in the slip. This difference in velocities leads to

entirely different dislocation behavior and damage devel-

opment in the stick and slips phases. The stick phase is

mainly determined by time-dependent strain (creep)

wherein, as in metals and alloys, three stages of creep are

observed. Based on the analysis of the dislocation struc-

ture, a model of the dislocation distribution in the regions

of stick (creep) and slip is proposed.

Keywords Stick–slip � Friction � Lithium fluoride (LiF)

single crystal � Dislocations � Creep � Plastic deformation

1 Highlights

• The first experimental evidence showing the interaction

between stick–slips and the dislocation structure during

the low-velocity friction of lithium fluoride (LiF) single

crystals is presented.

• The velocity of the indenter during the slip phase was

about 300 times higher than in the stick phase.

Variation of the velocity of the indenter is accompanied

by a change of the dislocation mobility around the

stick–slip regions.

• A model of the dislocation distribution around the

stick–slip regions is proposed.

2 Introduction

Friction plays a crucial role in various systems from the

macro to the nanoscale [1–4]. Contact interaction during

low-velocity friction is usually characterized by stick–slip

phenomena. Stick–slips as a part of solid friction have been

observed over a wide range of length scales: from earth-

quakes to articular joints and nano-devices [5–7]. The

fundamental laws of stick–slip phenomena based on dry-

friction dynamics have been promulgated in the pioneering

experiments of Rabinovicz [8] and in the works of Ba-

umberger et al. [9–11]. Based on these experiments, it was

concluded [8, 9] that:

• The static friction, ls increases slowly with the duration

of stationary contact prior to dragging.

• It is no longer possible to speak of a truly motionless

‘‘stick state,’’ but rather, of stress-induced creep.

• The solid–solid contacts usually referred to as the

memory effect are characterized by length.

V. Perfilyev � A. Moshkovich � I. Lapsker � A. Laikhtman �L. Rapoport (&)

Department of Science, Holon Institute of Technology,

Golomb St. 52, P.O. Box 305, 5810201 Holon, Israel

e-mail: [email protected]

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Tribol Lett (2014) 55:295–301

DOI 10.1007/s11249-014-0358-4

Author's personal copy

These three basic concepts were then developed in the

analysis of low-velocity friction. Some classes of solids

were extensively studied, and it was shown that bulk

microscopic structure and plastic properties are necessary

conditions for a definite variation of friction threshold from

dynamic to static and the creep phenomenon.

Different models are used for the description of stick–

slip phenomenon. A spring-block model is widely used to

represent stick–slip of rubbed bodies [12]. During the

stick phase, the block is fixed and the spring elongates

with the storage of elastic energy. When the shear stress

in the system block counterface reaches the contact

strength, a sudden slip occurs. Recently, the stick–slip

phenomena have been analyzed by molecular dynamics

simulation [13, 14]. Atomic scale stick–slip was associ-

ated with dislocation nucleation and propagation [13]. It

is assumed that the stick phase is related to the elastic

deformation of the substrate atoms on the atomic scale

[13]. A model based on the cooperative formation and

rupture of the bonds between two plates has been

developed [15]. It was assumed that low-velocity friction

is accompanied by strong pinning in the interface leading

to an increase in the friction (static friction force).

Developing rate and state models of static friction, Muser

[16], Yang et al. [17] confirmed that the static friction

may not even be static and that creep-like motion can

take place before the rapid slip event. Models of the

dislocation structure activated by friction and based on

the fundamental theory of dislocations have been pro-

posed [18–21]. Hurtado and Kim [18, 19] proposed a

model of slip assisted by the nucleation and gliding of a

dislocation loop and then developed a model for multiple-

dislocation-cooperated slip. Analyzing dislocation plas-

ticity in static friction, Deshpande et al. [20] showed that

the shear stress needed to initiate sliding is a function of

contact size; for large contacts, sliding initiates at a value

approximately equal to the tensile yield strength, while

for small contacts, sliding initiates at the cohesive

strength. Considering briefly the model of work hardening

and stick–slip, Merkle and Marks [21] assumed that the

motion of dislocations due to surface steps and surface

impurities increases the density of dislocation and the

stress leading to a different path for sliding and stick–slip.

Later, M’ndange-Pfupfu and Marks [22] described a

model for the nanoscale processes of shear and plowing

friction. The authors showed that the interfacial shear

component can be modeled via dislocation drag at the

interface, and the plowing can be considered in terms of

power-law creep. For the description of plowing, the

semi-empirical high-temperature, power-law creep rela-

tionship was used.

At present, little is known about the interaction between

the dislocation structure of materials and stick–slips events

in low-velocity friction. It is therefore useful to study the

effect of the velocity of the slider on stick–slip events and

the dislocation structure during stick, creep, and slip.

Single crystals are widely used for the analysis of the

dislocation structure. For instance, the effect of friction on

the dislocation structure of LiF single crystals has been

previously studied [23, 24]. In the present work, we studied

the interaction between the parameters of scratching and

the dislocation structure developed during low-velocity

friction. For the first time, the mobility of the dislocation

during stick–slip regimes is described.

Scratching of a LiF single crystal by a diamond indenter

was selected due to its highly reproducible behavior in the

stick–slip regime and for the potential of analyzing the

dislocation structure.

3 Experimental Procedure

Scratching of LiF single crystals was conducted using a

diamond indenter (R = 0.2 mm). The lower (fixed) LiF

sample was glued onto the surface of a table. The main

experiments were performed at sliding velocities,

V = 1 lm s-1 and with a soft spring, k = 15 N m-1.

However, for the analysis of the effect of the driving

velocity on the dislocation structure, tests with a sliding

velocity, V = 1, 10 and 1,000 lm s-1 using a stiff spring,

k = 2,400 N m-1, were also carried out. To provide this

range of V’s, an M-110 compact microtranslation stage

(Physik Instrumente, PI, Germany) was used. Depending

on the range of V’s studied, track lengths of 2–6 mm were

used. The friction force and the displacement of the

indenter in relation to the LiF plate were measured during

one pass of the indenter. A constant load of 0.07 N was

applied. The scratching was measured in the 100h i sliding

Fig. 1 Typical curves of the friction force and displacement of

indenter versus time. Sliding velocity, V = 1 lm s-1. Load,

P = 0.07 N. Single stick–slip event is shown by arrows

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direction and {001} cleavage of the LiF crystal. Average

dislocation density was determined by counting the number

of pits in a series of optical and electron photomicrographs.

The density of dislocations was determined at a defined

distance from the scratching tracks. The virgin density of

dislocation was 8 9 108 m-2. To reveal the effect of fresh

dislocations associated with the plastic deformation, the

samples were etched before and after friction. The surfaces

after friction were analyzed using optical and scanning

electron microscopy (SEM) and atomic force microscopy

(AFM) techniques.

4 Results

Representative plots of the stick–slips and the displacement

of the indenter in relation to the LiF crystal are shown in

Fig. 1.

As can be seen, the friction force increases with the

duration of practically stationary contact prior to pinning.

The transition from stick to slip, marked by arrows in

Fig. 1, was analyzed in more detail in Fig. 2.

Clearly, the velocity of the indenter increased nonlin-

early at the time in the transition from stick to slip. The

maximum velocity of the indenter was obtained during a

rapid slip event, and it is occurred in the mid-part of the

slip phase, while the friction force continued to decrease.

This transition from rapid slip to stick was accompanied by

a remarkable decrease in the velocity of the indenter. It was

found that the average velocity of the indenter in the stick

phase was about 300 times lower than the maximum

velocity in the slip phase. So large a difference in the

velocities leads to a completely different dislocation

behavior observed in the stick–slip regimes. In fact, the

dislocation track length around the stick phase is much

larger than in the slip phase (Fig. 3).

The density of dislocations at a distance of 10 lm

around the scratch track in the stick and slip regions was

2.8 9 1011 and 1.5 9 1011 m-2, respectively. The forma-

tion of the dislocation structure around the stick phase

occurs similarly to that observed under static indentation of

LiF, when the compression and shearing are determined by

activity of the four planes within the {110}45 system [24].

After a study of the dislocation patterns, the samples were

cleaved perpendicular to sliding motion. The dislocation

pattern of cross-sectional samples is shown in Fig. 4. It can

be seen that the screw components of half-loops on {110}45

planes are more active in subsurface deformation. In order

to understand better the effect of sliding velocity on the

dislocation structure, the scratch tests were performed with

driving velocities of, V = 1, 10, and 1,000 lm s-1. To

Fig. 2 Velocity of indenter and the friction force versus time in the

transition from stick to slipFig. 3 Dislocation structure around the friction track on the surface

of LiF single crystal. The circles depict the places of sticks. The

sliding direction is shown by arrow

Fig. 4 Typical dislocation pattern of subsurface deformation after

friction in unidirectional motion

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avoid the sticks, a stiff spring, k = 2,400 N m-1, was used.

SEM images of the scratch and dislocation tracks after

scratching with sliding velocity, V = 1 lm s-1 (a) and

V = 1,000 lm s-1, are shown in Fig. 5.

A completely different behavior was observed along

low-velocity track in comparison with scratching with high

velocity. The width of the dislocation track increases

remarkably during sliding with low velocity in comparison

with high velocity (100 and 70 lm, respectively). More-

over, the width of the scratched track also increased (21

and 16 lm, respectively). Scratching with low driving

velocity is also accompanied by a plowing of surface layers

and a formation of wear particles, whereas a relatively

smooth surface appeared after scratching with high veloc-

ity. The AFM images confirmed the results obtained by

SEM analysis (Fig. 6). The depth of plowing under

scratching with low driving velocity is increased.

The length of dislocation arms around the wear track

and the width of the wear tracks are shown in Fig. 7.

A definite correlation is observed between the length of

dislocation arms and width of wear tracks. Our measure-

ments show that the dislocation behavior in the slip phase

is determined mainly by the velocity of the indenter, while

a time-dependent loading is responsible for dislocation

motion and plowing in the stick phase. The time-dependent

displacement of the indenter in the stick (creep) region was

analyzed in more detail. Typical creep curves for two slip

events are shown in Fig. 8.

The time of creep is *130 s, whereas the slip time is

*1 s. The creep curve exhibits three phases as is generally

observed for base metals and alloys [25]: The primary

creep regime after slip phase (1) followed by ‘‘full’’ stick in

steady state (2) and an accelerating tertiary creep regime in

the transition to slip (3). As can be seen, the displacement

of the indenter in the primary and tertiary phases of creep is

described by a power-law relationship. In the primary

creep, a growth of the dislocation motion and the plowing

raises the shear stress during the pinning phase. The dis-

location loops expanded during a long time in creep regime

jump at a long distance from the scratch track; the number

of contact bonds is increased. In the steady state (‘‘full’’

stick), the measured displacement of indenter was below

the detection limit of our equipment (B0.05 lm s-1).

Therefore, we cannot unambiguously draw conclusions

about the shearing in the ‘‘full’’ stick phase. A rupture of

the bonds (depinning effect) characterizes the tertiary creep

in the stick phase. The time of creep depinning is signifi-

cantly larger than the time of pinning (45 and 15 s,

respectively) (Fig. 2). Displacement of the indenter in the

primary creep is 1.5 lm, whereas in tertiary creep it is two

times larger, 3 lm.

5 Discussion

The stick–slip experiments showed that the static threshold,

ls, depends on the stick time, sstick. The time scales for

stick and slip processes are distinct (sstick � sslip). The

velocity of the indenter in the stick phase is 300 times

lower than in the slip phase. Major differences between the

velocity of the indenter in the stick and slip phases deter-

mine the dislocation modification of structure and plowing

in the scratch track. We have demonstrated for the first

time that the dislocations jump over much longer distances

than those that occur under low driving velocity. Low-

velocity friction is accompanied by deep plowing, while a

smooth surface of track is observed under scratching with

high velocity.

In accordance with Heslot et al. [9], the displacement

during creep can be considered as the average shearing

displacement necessary to break a typical contact, D0. We

define here two creep lengths: D1 = 1.5–2 lm as the dis-

placement of the indenter after slipping (pinning phase)

and D2 = 3–4 lm after creep but before slipping (depin-

ning phase). Following the works of Scholz [5] and

Fig. 5 SEM images of the scratch and dislocation tracks after friction

with sliding velocity, V = 1 lm s-1 (a) and V = 1,000 lm s-1 (b).

Stiff spring, k = 2,400 N m-1

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Rabinovicz [8], the parameter, D, can be considered as an

average ‘‘contact size.’’ In fact, the full creep distances

during scratching of LiF were *6–8 lm. These values are

close to the diameter of contact spots.

The experiments showed that the low-velocity scratch-

ing of LiF single crystals is strongly influenced by plastic

deformation and plowing leading to the evolution of the

contact area. As the creep proceeds, the dislocation track

length and the density of dislocations increase around the

scratched track. Scratching is accompanied by dislocation

generation and multiplication attributed mainly to motion

of the edge components of dislocation loops. Indeed, the

edge components of dislocation loops in LiF move about

50 times faster than the screw components [25]. During a

long period (*130 s), the intersection between the edge

and screw components of dislocations appeared in the stick

region, resembling the familiar ‘‘rosette’’ patterns on LiF.

Based on the analysis of the dislocation structure, the

scheme of the dislocation distribution around the scratch

track is depicted in Fig. 9. This scheme demonstrates mush

stronger activity of primary and secondary sliding systems

in the phase of creep in comparison with slip. A difference

in the activity can be explained by long time of creep stage

in comparison with slip one. These results indicate also the

definite similarity in the dislocation motion during the

processes of indentation and scratching.

Three stages of creep are revealed between two slip

events. The primary creep is associated with the formation

of bonds (pinning effect), whereas the tertiary creep is

characterized by the rupture of bonds (depinning effect).

During the second long-time steady state, the number of

bonds is apparently increased. Concerning a nature of

bonds, we can just speculate, especially when the bonds are

considered at different scale length. It may be the

Fig. 6 AFM images and

profiles of the tracks after

scratching with sliding

velocities, V = 1,000 lm s-1

(a, b) and V = 1 lm s-1 (c, d)

Fig. 7 Length of the dislocation arms around the wear tracks and the

width of the wear tracks

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dislocation interaction or molecular bonds in atomic scale

or adhesion bonds in macroscale. Here, for the sake of

simplicity, we assumed that the pinning (depinning) effects

to be the interaction (rupture) of the molecular or

mechanical bonds. The formation of bonds in the primary

creep is attributed to the plastic deformation and plowing

of surface layers. As a result, the shear stresses, rs, are

increased. The shear stress can be calculated as, rs = lH,

where l is the friction coefficient and H is the hardness

after deformation. The calculated value in the onset of

pinning for LiF is rs1 = 110 MPa. This value is high

enough in order to activate nonconservative slip of dislo-

cations in a LiF single crystal [25]. The plastic deformation

is accompanied by the penetration of the indenter into the

surface layers leading finally to an increase of the contact

area and retardation in the displacement of the indenter. At

the steady state, small shearing is possible. However, our

threshold of the observability of the indenter’s displace-

ment is limited. The steady state is attributed to the

dynamic equilibrium between the dislocation motion and

their annihilation. At this state, the number of bonds is

increased during a long period, *100 s. An increase in the

number of bonds leads to a rise in the shear stress needed

for the rupture (depinning) of these bonds. The calculated

value of the shear stress at the end of the steady state is

close to 160 MPa. The tertiary creep is associated with the

rupture of the typical contact bonds due to movement and

annihilation of dislocation and plowing. Plowing during

pinning and depinning results from the same physical

process, namely creep of the contact spots.

Creep of metals and alloys as well as creep in low-

velocity scratching is a thermally activated process [e.g. 9,

26]. The creep during stick event is defined using power-

law equations of steady state creep at high temperature. We

suggest that the creep and plowing of a complex nonlinear

dynamic friction system in low-velocity sliding cannot be

described by the power-law equations of steady state creep

only. Stick events in low-velocity friction are characterized

by creep, aging of contact, and memory length (the average

shearing displacement). For instance, an increase in aging

leads to an increasing the number of contact bonds and thus

raises the stress for depinning of bonds. On the other hand,

the aging depends on the stiffness of the dynamic friction

system.

6 Conclusion

The stick–slip phenomenon has been studied by scratching

LiF single crystals with a diamond indenter. The

Fig. 8 Real displacement of the

indenter during stick (creep)

events occurring between two

slips: 1 primary creep, 2 steady

state ‘‘stick,’’ 3 tertiary creep

Fig. 9 Schematic summary of the dislocation activity around the

scratch track during stick (creep) and slip events

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dislocation structure around the scratch track has been

analyzed. Maximum velocity of the indenter in the slip

phase is about 300 times larger than in the stick phase.

Large difference in the velocities of the indenter in stick

and slip leads to a totally different dislocation behavior:

The dislocation mobility around the stick phase is much

larger than in the slip phase. These results were confirmed

by a special experiment where the dislocation structure has

been studied after scratching with the velocity of machine,

V = 1, 10 and 1,000 l s-1, using a stiff spring. Time-

dependent deformation in the stick phase is considered as

three-staged creep: Primary creep regime (pinning) fol-

lowed by ‘‘full’’ stick in a steady state and an accelerating

tertiary creep regime (depinning). We have shown that the

analysis of the dislocation structure during stick–slip

events is of great significance for understanding the

mechanism of plastic deformation and damage develop-

ment during friction with stick–slips.

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