Wear 268 (2010) 59–66
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Wear
journal homepage: www.elsevier.com/locate/wear
Subsurface shear instability and nanostructuring of metals in sliding
S. Tarasov ∗ , V. Rubtsov, A. Kolubaev
Institute of Strength Physics & Materials Science SB RAS, Academicheskii, 2/4, Tomsk, Russia
a r t i c l e
i n f o
Article history:
Received 15 July 2008
Received in revised form 10 April 2009
Accepted 18 June 2009
Available online 26 June 2009
Keywords:
Sliding
Shear instability
Strain localization
Nanostructuring
Viscous flow
Numerical simulation
a b s t r a c t
Dry sliding wear conditions were used to obtain a 500 ␮m-thick layer of nanosize grains on copper
samples. As shown, this layer reveals a flow behavior pattern similar to that of a viscous non-Newtonian
fluid. Four structurally different zones were found in the longitudinal cross-sections of samples below
the worn surface. Upper two of them are nanocrystalline and consist of many ∼1 ␮m-thick sublayers,
which show either laminar or turbulent flow behavior. These sublayers demonstrate different levels of
elasticity as compared to each other and may be related to an interplay between work-hardening and
thermal softening. Lower two zones undergo usual plastic deformation and severe fragmentation without
viscous mass transfer. High level of Young’s modulus in the fragmentation zone is evidence of insufficient
thermal softening at that depth. We believe that viscous flow zones are the result of shear instability and
subsequent shear deformation developed in subsurface layers due to thermal softening. Numerical study
has been carried out to simulate friction-induced deformation and shear instability under conditions close
to the experiment. As shown, such a situation is possible when deformation-generated heat is taken into
account. Another interesting result relates to the sublayers’ strain rate distribution. It was found that
1 ␮m-thick sublayers may show either high strain rate gradient or zero strain rate as a function of depth
below the worn surface. The latter case means that a pack of layers may exist and behave like an elastic
body in ductile medium.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
One of the most interesting and intriguing problems in tribology is structural changes in materials in sliding contact. These
changes may be responsible for mild-to-catastrophic wear mechanism transition and is a very complex phenomenon while its main
contributing factors are plastic deformation and friction-generated
heat. When a ductile material slides against a harder one, the subsurface layers of the ductile material undergo plastic deformation
and may even form a thick layer of severely deformed and even
nanocrystalline metal. The depth of such a layer is determined both
by the contact stress and the temperature dependence of the material’s yield point. It is a problem to observe in situ the strain stages
in subsurface layers of metals in sliding since the deformation goes
through all the stages in a very fast manner and in most cases we
can observe only the final stage of this process without any intermediate states. Also these deformation stages do not necessarily
coincide with those found in stress–strain compression diagrams
of a corresponding metal.
Nanostructuring in sliding wear is a fundamental problem that
is receiving increased attention but no satisfying models have been
∗ Corresponding author. Tel.: +7 382 2 286815; fax: +7 382 2 492576.
E-mail address: [email protected] (S. Tarasov).
0043-1648/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.wear.2009.06.027
developed. The mechanism of deformation which serves to produce nanocrystalline grains under condition of sliding wear and
temperature gradients is not fully understood. Studies into such a
phenomenon would help to gain better understanding of the nanostructuring in deformation since the severity of deformation is a
function of depth below the worn surface.
Another problem is deformational behavior of the nanostructured layers in sliding together with its effect on the tribological
parameters such as coefficient of friction and wear rate. It is
reported elsewhere [1] that nanocrystalline materials obtained by
severe plastic deformation demonstrate high diffusivity for interstitial and impurity atoms, which may fully modify the tribology
behavior of the sample.
There are several mechanisms suitable for nanostructuring in
sliding [2–4], but one of the most plausible ones is a shear instability
mechanism [5,6]. This mechanism implies fast (almost adiabatic)
shear deformation under conditions of thermal softening. However, it neglects all previous deformation stages and one of the most
important ones is a stage of plastic strain localization. We do not
fully understand how and why the shear instability happens at the
microstructural scale.
This work has been devoted to both experimental and numerical
verification of shear instability mechanisms by studying structural
fragmentation, mechanisms for the formation of structurally fragmented layer, and its morphology and flow behavior during sliding
60
S. Tarasov et al. / Wear 268 (2010) 59–66
Table 1
Chemical composition of the tool steel disk.
G (MPa)
y (MPa)
Gpl (MPa)
◦
◦
◦
◦
◦
20 C
1000 C
20 C
1000 C
20 C
1000 C
41,500
29,300
4
2
70
3.5
in the absence of mechanical intermixing of metals at the worn
surface.
2. Experimental details
Samples in the form of Ø5 mm and 20 mm length pins were cutoff the Ø5 mm commercial copper rods using a lathe tool. Chemical
composition of copper was as follows—Cu: min 99.9%; Fe: 0.005
(wt.%); Ni: 0.002%; S: 0.004%; As: 0.002%; Pb: 0.005%; Zn: 0.004%;
Ag: 0.003%; O: 0.05%; Sb: 0.002%; Bi: 0.001%; Sn: <0.002%. The pins’
end surfaces were ground manually and gently to remove the lathe
grooves and then used in wear test. Vertical pin-on-disk sliding
tester 2169 UMT-1 (Tochpribor, Ivanovo) was used to test three
samples simultaneously against a counterface of Ø320 mm 64 HRc
tool steel disk (see Table 1). These samples were brought in the
unlubricated sliding contact and then loaded stepwise to achieve
nominal contact stress of 0.5 MPa. On finishing the test, the samples were mounted in Wood’s metal and sectioned using an abrasive
wheel rotating at 1000 rpm with water cooling in a diametric plane
parallel to the sliding direction, manually ground, polished with
corundum abrasive papers followed by diamonds pastes of grades
2 and 1.0 ␮m and etched in 10% NH4 OH for metallography.
Microstructure of the worn samples was characterized using
both an optical and a differential-interferential (DIC) contrast
microscope Axiovert 200 MAT (Carl Zeiss) as well as an AFM
instrument Solver Pro 47H (NT-MDT, Zelenograd) with atomic
force acoustic microscopy (AFAM). This technique allows mapping
the surfaces so that the brightness signal is proportional to the
Young’s modulus magnitudes as determined from the stiffness of
a probe/sample contact. The resolution of this method is higher
than that of the basic contact AFM mode. It is a very helpful, simple and reliable method to detect the nanosize grains by the local
difference in elasticity between the grain body and boundary. Also
both Young’s modulus and nanohardness numbers have been determined using a CSEM Nanohardness tester (Oliver & Pharr method
[7]).
(kg/m3 )
, W/(m K)
c, J/(kg K)
8900
395
386
◦
parallel to the sliding direction while zone II is a place of intense
structural fragmentation [8,9].
Morphological specificity of zones III and IV is that they both
consist of <1 ␮m-thick sublayers (Fig. 3). Such a stratification originates from their flow behavior under shear stress. The AFAM image
of zone IV material in Fig. 4a shows that those sublayers are composed mainly of <100 nm horizontally elongated grains but nearly
equiaxial >200 nm grains may be found too—Fig. 4b.
The AFAM image of the zone II/III interface in Fig. 5b shows that
the Young’s modulus magnitudes of zone II are higher those of zone
III. It is conceivable that since zone II material is rheologically immobile, heavily fragmented and accumulates elastic strain from high
dislocation density. Moreover, the sublayers of zone IV may flow at
different speeds and also be either softened or hardened. Nanoindentation experiments carried out according to the Oliver & Pharr
method [7] provide support to this point of view (Fig. 6).
Fig. 1. Time dependence of friction moment for two different sliding regimes: (1)
mild wear and (2) catastrophic wear (scuffing).
3. Results
Time dependencies of the friction coefficient are shown in Fig. 1
for two different wear modes. Dependence 1 corresponds to relatively stable sliding and mild wear, which resulted in no structural
changes other than subsurface metal grains rotated and elongated
with respect to the sliding direction. The result of sliding under conditions of regime 2 was a 300–500 ␮m-thick nanocrystalline layer
having a clear interface separating it from the underlying material
(Fig. 2). Structurally, this layer may be divided into four zones as
follows: plastic deformation and texturized grain zone I; intense
fragmentation zone II; “turbulent” flow zone III (may be absent)
and finally, “laminar” flow zone IV (Fig. 2). Let us note that we just
use these terms by drawing an analogy with the flow of very viscous
fluid. Zones I and II may be called also by usual deformation zones
whereas both III and IV are the viscous flow zones. One may see
that both strain and fragmentation gradually grow starting from
the deepest layers of zone I to the fragmentation zone II until an
interface between zones II and IV (III) is formed as a result of shear
instability. Zone I is characterized by crystallographic rotation of
the grains with respect to shear stress so that {1 1 1} planes become
Fig. 2. Optical micrograph of the plastic deformation zones in a longitudinal crosssection of copper sample worn against tool steel counterface (0.6 m s−1 , 0.5 MPa): (I)
plastic strain zone; (II) fragmentation zone; (III) turbulent flow zone; (IV) laminar
flow zone.
S. Tarasov et al. / Wear 268 (2010) 59–66
61
Fig. 3. Optical micrograph (differential-interferential contrast) micrographs of zone
III/II interface.
Fig. 5. AFM (a) and AFAM (b) images of zone IV/II interface. The brighter zones in
the AFAM image correspond to those of higher Young’s modulus.
Fig. 4. AFAM images of nanocrystalline layer: (a) elongated nanocrystalline grains
and (b) equiaxial grains.
Fig. 6. Nanohardness (1) and Young’s modulus (2) vs. depth below the worn surface.
(I) Plastic strain zone; (II) fragmentation zone; (III) turbulent flow zone; (IV) laminar
flow zone. Curves 1 and 2 are the least square approximation lines.
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S. Tarasov et al. / Wear 268 (2010) 59–66
Generally, the distribution of nanohardness numbers qualitatively coincides with that of the Young’s modulus except for zone III,
where the nanohardness peak has been found. The distribution of
the nanohardness numbers and Young modulus’ magnitudes across
zone IV show a peak, which may originate from a higher stress
level sublayer (Fig. 6). One may see that apart from the peaks, the
mean level of the Young’s modulus is the same for zones I and IV
whereas the nanohardness levels are different. According to the
Oliver & Pharr method, the Young’s modulus is determined from
the unloading portion of the indentation curve, therefore nanocrystalline material of zone III is deformed in a manner that allows
no far-range elastic stress accumulation. On the contrary, the fragmented structure of zone II material shows the highest level of
Young’s modulus of 140 GPa. An explanation may be given in terms
of an interplay between processes of hardening and softening in
different zones [10]. The hardening is considered as a process of
accumulating dislocations at the grain boundaries while softening
is provided by annihilation of dislocations at the grain boundaries
activated by the friction-generated heat. Deformation behavior of
nanocrystalline material in zone IV (III) dramatically differs from
that of zones I and II. Such a mass transfer mechanism looks like
flow of a very viscous non-Newtonian fluid. However, unlike the
fluid, this layer is really composed of smaller sublayers which may
flow at different rates with respect to each other. The most suitable
deformation mechanism may be grain-boundary slipping (GBS)
with the only specificity that slipping mainly occurs at the sublayer
interfaces. Taking into account the grain size in zone IV one may
suggest that deformation is controlled also by diffusion-assisted
grain-boundary processes.
Zone II material structure is composed of grains’ fragments having almost the same size as zone IV grains, however, no shear
instability is observed below the zone IV/II interface because of
insufficient thermal softening. It follows from the contrast of the
AFAM image in Fig. 5b that zone II shows high level of elasticity
that may be related to high level of far-range elastic inner stress
exerted by subgrain boundaries saturated with numerous defects
and strain localization bands [10]. The most intense fragmentation
occurs when two strain localization bands cross each other [11].
Such a crossing may serve as a place where first nanocrystalline
grains nucleate and provoke shear instability by activating grainboundary slipping mechanism. The result is generation of a shear
band in subsurface layers of the ductile sample [9].
4. Model description and numerical simulations
It seems that a reason for the layered structure formation is
macroscopic stress and strain distributions across the subsurface
layer of materials in sliding contact. Plastic flow in subsurface layers
of metal in sliding contact that may result in generation of layers parallel to the sliding direction can be simulated within the
framework of a dynamic one-dimensional sliding contact model
described elsewhere [6,12–13]. This model can be called a macroscopic one in the sense that it does not account distinctly for both
microstructure and deformation mechanism of the medium but
operates by its macroscopic characteristics only.
The model describes friction process occurring on a single contact spot, which is formed when a ductile micropin slides over
an absolutely rigid counterbody at the constant velocity Vc . The
micropin of height hsample is assembled of many uniform thickness
layers—Fig. 7.
The counterbody exerts both contact stress P and shear
stress from the friction force ␮P (where is the friction
coefficient) to the pin’s topmost layer. The bottom layer is
rigidly fixed on the base. All the layers are assumed to be
absolutely rigid and have equal lengths L and thicknesses
hlayer . The layer material is characterized by the density ,
heat conductivity , uniaxial yield point y , shear modulus
G and “plastic” shear modulus Gpl , which characterizes the
work-hardening susceptibility of the material. Additionally, each
layer is characterized by the coordinate x and travel velocity
V.
It is assumed in this model that the micropin may experience
the shear deformation when its composing layers displace with
respect to each other in the direction parallel to the worn surface. As
suggested, each layer may interact only with its closest neighbors.
Two neighboring layers are counted as a unit of shear deformation. We do not consider explicitly the compression of the sample
under normal stress P in this model assuming it to be constant over
the micropin’s height and equal to the normal stress in the contact
area. The normal stress level is considered in computing a plasticity
criterion.
To determine the shear stress level for a couple of layers, we use
an elastic–plastic response function which is described in detail
elsewhere [12]. As shown schematically in Fig. 8, this function
serves to establish a relation between the shear stress and the
shear strain in a couple of layers. Its parameters are as follows:
elastic and plastic moduli Gc and G cpl , maximal elastic strain el
and equilibrium shear eq . The magnitude of el is a maximum
shear strain at which the material still retains its elasticity, eq is
the total plastic shear strain accumulated from the deformation
onset. The line portion AB in Fig. 6 shows elastic deformation mode
while portions DA and BC denote plastic deformation with linear
hardening.
Also we use a deformational plasticity criterion with this model.
A cross-over from elastic to elastic–plastic deformation occurs for
a couple of layers when the strain magnitude becomes higher the
maximum elastic strain at the current temperature within this couple, i.e. > el . At the beginning of the computation procedure, the
layer couple’s properties are set to be the mean values of those
belonging to the layers. In further computations, the couple’s properties are changed so that both Gc and G cpl values are corrected
for the current temperature at each time step. In addition to the
temperature dependence, the values of eq and el depend also
on the previous deformation history of the given couple of layers.
The onset value of maximum elastic deformation 0el corresponds to the undeformed material and may be determined
according to Ref. [14] with the use of the von Mises criterion for
plain deformation. Such an approach allows us to take into consideration the fact that two types of stress are applied to the micropin
within the framework of the one-dimensional problem, namely,
normal and shear.
Before the simulations, we calculated the starting values of maximum elastic strain for each layer coupled within
√ the possible
temperature range as follows: 0el =
y 2 − P 2 / 3Gc .
A special procedure of the response function modification is
applied in this model to take into account all previous history
of both deformation and temperature changes. This modification
procedure allows consideration of two competing and concurrent
processes such as work-hardening and thermal softening as well
as thermal stress relieving and irreversible plastic deformation.
Details on the response function modification procedure are given
elsewhere [12].
To determine the temperature field in the micropin, we were
looking for a solution of the one-dimensional friction heat problem.
The calculation lattice nodes were placed at the layer interfaces. For simplicity, we assumed that both heat conductivity
and capacity did not depend on the temperature. When modeling the single contact, we considered that its life is rather short,
therefore, the depth of the heat propagation below the worn surface is not larger the micropin’s height and the temperature at
S. Tarasov et al. / Wear 268 (2010) 59–66
63
Fig. 7. Schematic of the modeling system.
Fig. 8. The response function shape.
the micropin/base interface is constant and equal to the starting.
It is assumed that the heat generated on the worn surface is
distributed in equal portions between the sample and counterbody, therefore, the heat release power transmitted to the sample
is determined as 0.5P␮Vc − V1 |, where 0.5 stands for the heat flux
distribution; |Vc − V1 | is an absolute value of sample/counterbody
sliding velocity; V1 is the sample’s top layer velocity.
Earlier [6,13] we used this model to show that subsurface plastic
shear strain as high as tens of percents and even higher may develop
during sliding for contact times being on the order of 1 × 10−4 s. It is
rather severe deformation and most of its energy is released in the
form of heat in the bulk of subsurface layer. This heat would change
greatly both the heat dissipation regime and materials’ deformation behavior. The drawback of the mentioned above model is that
it takes into account the heat generated only on the sliding surface.
In this work we improve the model by introducing the heat generated in the subsurface layer due to its plastic deformation. This
model implies that if a couple of layers experience shear deformation during some moment of time, it simultaneously generates
some quantity of heat.
We assume that the plastic deformation work fully transforms
into the heat, therefore the quantity of heat released in a couple of
layers per a time interval was made equal to the mechanical work
spent for plastic deformation of that couple.
During the simulation, we first determine the temperature fields
for all procedure steps. Then, the response function parameters of
each layer couple are modified in accordance with the temperature
and deformation prehistory. At the next stage, we integrate the system of classic motion equations applied to the micropin, determine
coordinates and velocities of each layer and, finally, obtain the shear
strain magnitudes. On doing so, we find the heat release power at
the worn surface as well as power of the internal (subsurface) heat
sources and use the results to calculate the temperature for the next
moment of time.
To estimate the lifetime tc of a contact spot of length L, let us
invoke a simple approximation tc = L/Vc . Changing the procedure
time tc , we can change the spot lifetime in the same way and carry
out simulation for contact spots of different sizes.
The simulation was carried out for the 500 ␮m contact spot and
typical sliding velocity 1 m s−1 , which gives us the contact duration
tc = 5 × 10−4 s. The friction coefficient was = 0.5 which is not an
unexpected value for unlubricated sliding test of metals.
It was shown experimentally in this work that the thickness of
plastically deformed layer (total thickness of zones I through IV)
may achieve 600–700 ␮m and thickness of zone IV (III) sublayers
is about 1 ␮m (Fig. 3). Taking it into account for simulations, we
assume the micropin’s height to be 1000 ␮m, and compose it of one
thousand 1 ␮m-thick layers. Thus, a zone of interest to us in which
the plastic shear is developed contains at least several hundreds of
layers. The thickness of the model micropin’s layers corresponds
to the minimal thickness of the experimentally found sublayer. We
believe it is an adequate assumption to describe the behavior of the
material within the framework of the proposed here macroscopic
approach.
The starting temperature for simulation was 20 ◦ C, normal contact stress 51.8 MPa (Table 2).
The objective was to observe the plastic shear strain development in the subsurface layers of the material and, therefore, the
shear stress magnitude was adjusted to produce only elastic strain
Table 2
Physical constants of model material.
G (MPa)
Gpl (MPa)
y (MPa)
20 ◦ C
1000 ◦ C
20 ◦ C
1000 ◦ C
20 ◦ C
1000 ◦ C
41,500
29,300
4
2
70
3.5
(kg/m3 )
, W/(m K)
c, J/(kg K)
8900
395
386
64
S. Tarasov et al. / Wear 268 (2010) 59–66
Fig. 9. Time dependence of ratio between current yield point and its onset value for
n different moments of time. 1–1 × 10−5 s; 2–3 × 10−5 s; 3–5 × 10−5 s; 4–1.5 × 10−4 s.
for the given friction coefficient and temperature during the very
first moment of time.
During the very first moment of time, the shear stress at the sliding surface is kept below the yield point so the sample will undergo
only elastic deformation. As time has passed, the subsurface layer
heats up and then starts reducing its yield point level. The ratio
between the current yield point and its onset value is shown in
Fig. 9 for different moments of time. As long as the stress magnitude is kept below the yield point, the maximum of temperature
and, therefore, the maximum of thermal softening are found at the
very surface of the sample (see curve 1, Fig. 9). However, when the
shear stress magnitude overcomes the yield point, there occurs a
local shear stress instability in the form of adiabatic plastic shear
(Fig. 9, curve 2).
This deformation act produces the heat that will further elevate
the local temperatures in already softened layer and thus enhance
the softening. At the same time, the yield point must grow due
to work-hardening. As shown by modeling, those two competing
processes result in keeping the yield point approximately constant
(Fig. 9). Curves 3 and 4 have their minimums in the form of plateaus,
which correspond to one and the same yield point level, being
approximately equal to the actual shear stress level. The plateau
describes behavior of heat softened and then plastically deformed
and work-hardened material. The curve portions on the right of the
plateau relate to only elastically deformed material, which, however, is softened to some of its depth. Heat generated on the worn
surface together with heat effect of deformation serves to elevate
the mean temperature in the subsurface layer, thermal softening
and plastic deformation of progressively deeper layers (curves 3
and 4, Fig. 9). The length of plateau at curves 3 and 4 (Fig. 9) coincides with the plasticized layer thickness for the given moment of
time.
Fig. 10 shows development of both shear strain (Fig. 10a) and
layer velocity (Fig. 10b) in the sample. It is clear (Fig. 10a) that
both the plasticized layer thickness and accumulated plastic strain
steadily grow with time. However, the layer velocity distribution
curves in Fig. 10b demonstrate that plastic deformation in subsurface layer is not a stationary process both in space and time.
With time, the plasticized layer thickness grows and the subsurface strain develops two types of layer velocity distributions. High
layer velocity gradient portions of the curves in Fig. 10b relate to
shear instability behavior and intense plastic deformation. Another
type of behavior is expected at the plateau portions, where layer
velocity gradient is zero and a whole pack of equal layer velocity
layers is formed and move in parallel to the sliding direction. As
shown in Fig. 11, these packs consist of five and more sublayers.
This pack is composed of layers capable of only elastic deformation
Fig. 10. Plastic shear strain (a) and layer velocity (b) as function of depth below
the worn surface for different moments of time. 1–8.18 × 10−5 s; 2–1.463 × 10−4 s;
3–2.9 × 10−4 s; 4–4.03 × 10−4 s; 5–4.874 × 10−4 s.
with respect to each other. Such a formation moves as an elastic
solid body through the plasticized medium. The number of zones
of both types may vary during the deformation; zones may change
their thickness, migrate down from the surface and then come back.
For instance, on passing 8.18 × 10−5 s since the beginning of the
sliding we can see at least three zones: two of them are the shear
instability zones and between them is the 5 ␮m-thick elastic pack
(Fig. 10b, curve 1). The next deformation stage shows already three
instability zones and two elastic packs (Fig. 10b, curve 2). Later we
Fig. 11. Plastic shear strain vs. time at fixed depth of 100 ␮m below the surface.
S. Tarasov et al. / Wear 268 (2010) 59–66
can see two shear instability zones separated by the elastic pack
(Fig. 10b, curve 3).
Generally, the number of both packs and plastic shear zones is
increased with the whole layer thickness as well as the elastic pack
mean thickness. Zones of both types never stop migrating, disappearing and appearing again during sliding (Fig. 10b, curves 4 and
5) and therefore the time-dependent accumulation of plastic shear
strain within the plasticized layer occurs non-uniformly. The time
dependence of shear strain at the 100 ␮m depth below the surface is shown in Fig. 11. Horizontal line portions E1, E2, E3, E4 and
E5 denote the time intervals within which only elastic packs are
migrating in material at his depth. The sloped line portions P1, P2,
P3, P4 and P5 correspond to the time intervals of intense plastic
deformation.
One may see from Fig. 11 that subsurface layer deformation is a
cyclic process when plastic shear time interval is followed by the
interval of no plastic deformation. The mean time period of such
a process is ≈5 × 10−6 s, which is five times longer of time needed
for the elastic shear wave to travel down from the surface to the
bottom and back. Also this period is two times longer as compared
to the period of the observed elastic oscillations of the whole sample. The strain rate in the plastic deformation intervals is as follows:
≈3.2 × 102 s−1 in P1 interval and up to ≈ 2.5 × 102 s−1 in P5 interval. Mean shear strain rate for the total time as shown in Fig. 11 is
≈2.2 × 102 s−1 .
It is important that alternating horizontal and sloped portions
of the strain curve are found not only for some specific depth. The
results of simulations show that such a behavior is typical for the
total plasticized layer thickness when elastic strain time intervals
alternate with plastic shear ones.
5. Discussion
Both the morphology of the nanocrystalline layer and specificity
of its flow at the interface enable a suggestion that the most feasible mechanism for formation of such a layer is a mechanism that
includes both formation and relative displacement of zone II fragments with respect to each other. Strain localization and structural
fragmentation of material in zones I and II may be considered a precursor stage of the shear instability which is necessary to provide a
degree of structural fragmentation suitable for launching the shear
instability mechanism.
Using the speckle decorrelation technique, we studied kinetics
of strain localization and shear instabilities in subsurface layers of
ductile metals in sliding [11]. It was shown that there are three
stages of strain development in subsurface layers of metal in sliding.
Fig. 10 shows a time-scan of strain zone development in a longitudinal cross-section of the sample. Stage 1 is characterized by the strain
zones travelling across the sample’s longitudinal cross-section at
the speed equal to the speed of sliding. At the stage 2 the zones
may slow down and even stop (localize) at some place in a sample. This stage is marked by the growing slope of initially vertical
areas in Fig. 10. Stage 2 is a stage when strain localization bands
are formed below the worn surface and intense fragmentation is
initiated in the sites where these bands cross each other [11]. One
may say this is a process of zone II nucleation and growth.
Finally, the strain zones may start travel again at the sliding
speed (stage 3), thus marking the moment of shear instability
(Fig. 12). The result of shear instability was nanostructuring in
thin subsurface layer and a sharp interface between the layer and
the base metal. It is our view that generation of such a nanocrystalline layer is similar to the generation of a shear band in severely
deformed metal under condition of thermal softening by friction
heat. Microstructurally this softening means that the grain fragments formed by severe deformation undergo recovery and even
65
Fig. 12. Development of plastic strain localization and shear instability in subsurface layers of copper–zinc alloy. Arrow shows a direction of strain localization
zone displacement. L is the sample’s longitudinal cross-section width. Sliding speed
5 mm/min.
recrystallization, thus reducing effect of work-hardening and forming the nanosize grains suitable for grain-boundary slipping (GBS).
The definitive role played both by kinetics of lattice and boundary dislocations in the deformation of nanocrystalline materials
has been demonstrated in Ref. [10]. It has been shown that dislocations may either accumulate in the grains or annihilate at the
grain boundaries thus reducing the effect of their accumulation.
In addition to the grain boundaries (Fig. 2), the sliding-induced
nanocrystalline material shows sublayer boundaries (Fig. 3). It was
shown earlier that friction-induced nanocrystalline material shows
self-affine geometry in some structure scales [15], which is believed
to originate from its layered structure. This self-affine geometry
suggests self-consistent mode of sublayer deformation similar to
that obtained in numerical simulation.
The sublayers (or a pack of sublayers) undergo shear deformation with respect to each other along the sublayer boundaries.
However, it was shown by numerical simulations that the sublayers demonstrate a wide range of strain rates. It was established
also that shear instability fronts may travel across the longitudinal cross-section of the sample thus creating conditions for the
lessened fragmentation of source structure and layered structure
formation. The results of numerical simulations provide support
for the earlier suggestion that shear stress and strain distribution
will determine the layered structure formation. It turned out that
these distributions are non-uniform both in time and depth below
the surface and really can be the reason for development of the
layered structure.
It is plausible that slow sublayers are more prone to accumulate dislocations. The faster sublayers generate more heat during
deformation, since the dislocations are expelled to the sublayer
boundaries and annihilate there. The slower sublayers play the role
of strain localization bands in the nanocrystalline material.
6. Summary
The microstructure and mechanical characteristics of frictiongenerated nanocrystalline copper layer were investigated. The
results of experiments were consistent with the results of numerical simulations carried out on the assumption that shear instability
is controlled by competing processes of thermal softening and
work-hardening. We develop a macroscopic numerical simulation
approach, which allows us to study a material response to severe
deformation under reasonable test conditions.
Strain-induced structural changes in subsurface layers of metal
have been examined and it is demonstrated that shear instability
develops in a severely deformed zone composed of fine grain fragments due to the thermal softening. This mechanism is responsible
for the generation of a 500 ␮m-thick nanocrystalline layer, which,
in its turn, consists of numerous <1 ␮m-thick sublayers having
66
S. Tarasov et al. / Wear 268 (2010) 59–66
different elasticity levels depending on their strain rate. Such a layered structure suggests a viscous flow mechanism of deformation
during sliding similar to that of non-Newtonian fluid or a granular
medium that has great influence on the mild-to-catastrophic wear
mechanism transition.
Acknowledgements
The present work has been carried out according to Project No.
3.6.1.2 of SB RAS basic research Program 3.6.2 and Project 3.6.2.1 of
SB RAS basic research Program 3.6.1 of as well as supported by the
Russian Fund for Basic Research (Grant No. 06-08-00200a).
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