2013 ME Graduate Student Conference
April 27, 2013
ANALYSIS OF CONTACT IN SMOOTH AND ROUGH SURFACES: CONTACT
CHARACTERISTICS AND TRIBO-DAMAGE
Ali Beheshti
Ph.D. Candidate
Faculty Advisor: Prof. Michael M. Khonsari
The current research investigates three of the most
observed contact degradation processes: adhesive wear in
unlubricated and lubricated components, rolling/sliding
contact fatigue and fretting fatigue [1-4]. In addition, the
effect of surface roughness on the behavior of contacting
bodies through both deterministic [3] and statistical [5]
approaches is studied. The results are further utilized to
evaluate the effect of roughness on different contact damage
processes [3,6].
Unlubricated and Lubricated Adhesive Wear
The wear coefficient can be interpreted as the inverse of
the number of events N required for formation of a wear
particle. This concept allows one to relate wear to the
fatigue properties: for a specific material and the loading
condition, given the number of cycles to fatigue failure N,
one can estimate the wear coefficient [1]. Of particular
interest is the treatment of damage using the
thermodynamically-based continuum damage mechanics
(CDM). Recently Bhattacharya and Ellingwood [7] treated
the “growth of damage” as an irreversible process that
obeys the laws of thermodynamics. For a uni-axial loading
case, the damage parameter, Di, at the ith cycle, is given by
[7]:
1  (1  Di 1) Fi
Di  
 Di 1
Fi 
; if  max  Se
; otherwise
(1  1/ M )1 oi11 / M   li1/ M  oi  Ci
(1  1/ M )1 mi11 / M   li1/ M  mi  Ci
(1)
where the symbols definition can be found in Ref. [1]. We
compute the parameter Di for each cycle recursively by Eq.
(1) until the damage reaches the specified critical value of
Dc, after N cycles. As an example, the numerical and
experimental results for Aluminum 6061 are plotted in Fig.
1 showing good agreement.
10
10
Wear Coefficient
ABSTRACT
The interactions between contact surfaces play an
important role on the tribological performance of
mechanical and bio-mechanical components ranging from
miniature bearings and gears to hard disk drives and
artificial hip and knee joints to large bearings and gears in
wind turbine systems. Therefore, understanding the contact
characteristics as well as the contact failure phenomena in
tribological components are of significant importance.
10
10
10
10
10
10
0
-1
Predicted
Experimental
-2
-3
-4
-5
-6
-7
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
Friction Coefficient
Fig. 1. Left: Experimental set up, Right: Predicted and experimental results for wear
coefficient of Aluminum 6061-T6 as a function of friction coefficient [1]
The approach is further extended to the lubricated
sliding wear in line-contact configuration (like gears and
roller bearings) [6]. In mixed lubrication, which is the focus
of the current study, part of the load is carried by the fluid
and part by the asperities [8]. Empirical formula developed
previously by the authors [5] is adopted here to estimate the
load-carrying shares between the asperities and the
lubricant. Using CDM approach in conjunction with the
fractional film defect approach and load sharing concept,
we predict steady state lubricated line-contact wear.
Rolling/Sliding Contact Fatigue
Contact fatigue wear is the prevailing failure mode in a
properly lubricated rolling/sliding element, which is a type
of material degradation commonly experienced in bearings,
gears, railways tracks and the like. Material degradation
occurs as a result of the accumulation of damage in the
material microstructure due to the repeated rolling and
sliding. We compute the stress level change due to the
unidirectional travel of Hertzian-type contact at the edge of
a semi-infinite domain and again utilize the CDM approach
to assess the state of damage.
Ground surface
3500
Current Model
Harris & Barnsby
Chen et al.
Bhattacharyya et al.
Dc=0.46
0.5
Honed surface
Damage
Pmax(MPa)
Contact Characteristics of the Rough Surfaces
This part of research applies different statistical asperity
micro-contact models to the deformation of rough line
contact and provides a comparison study among them. It
involves a simultaneous solution of the asperity interaction
with the elastic bulk deformation of the surface. It predicts
the apparent pressure distribution as well as the contact
width and the real area of contact for the line contact
configuration. Figure 4 shows the pressure distribution and
contact half width using current model in addition to the
classical Hertzian theory. It also shows the experimental
results for the contact half width. Good agreement between
current model and experimental results is observed.
0.6
4000
3000
z = 0.196mm(max)
0.4
z = 0.218mm
z = 0.158mm
0.3
z = 0.256mm
2500
0.2
2000
z = 0.0mm
0.1
1500
4
5
10
10
6
7
10
Number of Cycles
8
10
10
0.0
0
30
60
90
K Cycles
120
150
180
Fig. 2. Left: Number of cycles to failure for different maximum Hertzian
pressure; Right: Damage evolution at x=0 at different depth [2]
Figure 2 (left) shows the maximum pressure plotted as a
function of number of cycles for failure. As seen, there is a
good agreement between the current model and the
experimental data. Figure 2 (right) demonstrates the damage
evolution at the line of symmetry based on the maximum
shear stress criterion for 175,000 loading cycles.
W
-6
0.9
p
0.6
0.5
0.4
0.2
0.1
10
ZMC
KE
-3
240
Qc (N/mm)
-3
SWT
-3
5x10
-3
Hertzian
b0.01
1.
2.
5.
160
120
6.
80
2x10
0
-2.0
-1.5
-1.0
-0.5
0.0
X
0.5
1.0
1.5
2.0
0
-8
10
Numerical Simulations (Randomly generated surfaces)
Proudhon et al.
10
-7
10
2
10
3
10
4
10
W (N)
REFERENCES
-3
-3
1
10
ACKNOWLEDGMENTS
I would like to thank my supervisor Prof. Khonsari for
his continuous support and kind help through my research.
Also I want to thank my colleagues in CeRoM for their
support.
3x10
1x10
0
10
The results of extensive sets of simulations are used to
derive expressions for the prediction of the contact
characteristics including maximum contact pressure, contact
width and real area of contact.
200
40
-6
10
different loads based on Hertzian and elasto-plastic models [5]
4x10
-3
Kagami et al.
beff
Fig. 4. Left: Normalized pressure distribution; Right: Half of the contact width at
4.
6x10
beff(JG)
10
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
3.
7x10
beff(KE)
-5
JG
0.3
In this study, a deterministic approach to predict the
pressure and tangential distributions in a rough line contact
configuration is developed where surface separation and
load balance equations are solved simultaneously with an
iterative procedure instead of the sequential procedure.
Hence, it offers a fast convergence rate. In addition, the
calculation methodology for the deterministic tangential
traction distribution for cyclic loading condition in stick-slip
regime is obtained. Results given for the pressure,
tangential distribution and sub-surfaces stress field are
useful for the prediction of micro surface damage
phenomena. The proposed methodology can be
conveniently implemented on the computer. The surface
tractions obtained by means of the described technique are
used to evaluate the fretting fatigue crack initiation risk
(FFCIR) in rough line-contact configuration (Fig. 3).
Comparison of the numerical results with experimental
observation shows good accordance.
280
b0.01(KE)
b0.01(JG)
-4
GW
CEB
X
-3
10
0.7
Fretting Fatigue in Rough Surface Contact
Fretting fatigue crack initiation is another type of
surface degradation observed commonly in applications
where compressed components are subjected to vibration.
8x10
-2
10
10
-5
0.8
-3
10
10
-3
 =5x10
(rough)
 =8
Hertzian
-4
-5
10
1.0
b (m)
4500
-6
7.
Ra (m)
Fig. 3. Up-Left: FFCIR for the entire domain for a smooth surface, Up-Right:
Schematic of the contact of a rough surface with a smooth cylinder, BottomLeft: FFCIR at the surface for a rough surface, Bottom-Right: The critical
tangential force amplitudes for different mean roughness values [3]
8.
Beheshti A, Khonsari MM. A thermodynamic approach for prediction
of wear coefficient under unlubricated sliding condition. Tribology
Letters 2010; 38:347–54.
Beheshti A, Khonsari MM. On the prediction of fatigue crack
initiation in rolling/sliding contacts with provision for loading
sequence effect. Tribology International 2011; 44:1620–8.
Beheshti A., Aghdam A. B., Khonsari MM. Deterministic Surface
Tractions in Rough Contact under Stick-Slip Condition: Application
to Fretting Fatigue Crack Initiation. International Journal of Fatigue
2013; under review.
Aghdam AB, Beheshti A, Khonsari MM. On the fretting crack
nucleation with provision for size effect. Tribology International
2012; 47:32–43.
Beheshti A, Khonsari MM. Asperity Micro-Contact Models as
Applied to the Deformation of Rough Line Contact. Tribology
International 2012; 52: 61-74.
Beheshti A, Khonsari MM. An Engineering Approach for the
Prediction of Steady State Wear in Mixed-Lubricated Contacts, in
preparation, April 2013.
Bhattacharya B, Ellingwood B. Continuum damage mechanics
analysis of fatigue crack initiation. Int. J Fatigue 1998; 20:631–9.
Masjedi M, Khonsari MM. Film Thickness and Asperity Load
Formulas for Line-Contact EHL with Provision for Surface
Roughness. Journal of Tribology-Transactions of the ASME 2012;
134: 011503.