1

0.1

Fretting wear of low current electrical contacts:

quantification of electrical endurance

S. Fouvry1, J. Laporte

1, O. Perrinet

1, P. Jedrzejczyk

1,

O. Graton1

1 Ecole Centrale de Lyon, LTDS

Lyon, France

(siegfried.fouvry@ec-lyon.fr)

O. Alquier2, J. Sautel

3

2 PSA, Vélizy - France

3 Radiall,Voreppe, France

Abstract— In many industrial applications like automotive,

aeronautics, train but also nuclear energy connectors need to

maintain low stable electrical contact resistance. However, they

are subject to vibrations that cause severe fretting wear damage

which increases the electrical contact resistance and degrades

information transmission. Fretting wear damages can induce

dramatic increase of the direct current Electrical Contact

Resistance (ECR) inducing the connector failure. The purpose of

this paper is to expose a synthesis describing how fretting

loadings but also material properties of coatings can influence

the fretting DC-ECR behavior. The analysis first focuses on

“laboratory” fretting test specifications that must be as

representative as possible of the pin-clip interface and sufficiently

instrumented to measure fretting loading parameters such as

sliding amplitude, normal loading friction energy, and ambient

condition. To compare noble (Au, Ag) and non noble (Sn)

coatings, an ECR endurance variable is introduced so that

N(fretting cycle) = Nc when ∆R> ∆Rc = 4mΩ. This study first

investigates the effect of the sliding condition and the transition

from an infinite ECR endurance under partial slip condition to a

finite endurance above the gross slip transition.

Then focusing on the gross slip finite endurances, different

formulations are introduced to quantify the effect of fretting

sliding amplitude, normal force, material properties but also

coating thickness. Focusing on Ag/Ag interface, this research

demonstrates that the ECR endurance is controlled by the

fretting wear rate of the contact. This investigation also

underlines how the application of sequential large reciprocatings

can increase the fretting ECR endurance through a refilling

process of fretting scar with silver transferred from the outer

part of the lateral reciprocating track.

I. INTRODUCTION

In automotive applications and many other industrial

domains (energy,aviation, etc.), the number of electrical

devices has increased significantly in recent decades. The

safety of systems and people relies on the quality of electrical

connectors. These are, however, subject to vibrations (car

engine, thermal environment) which induce micro-

displacements in the contact. Those movements cause

interface wear and induce debris formation, which increase

electrical contact resistance and degrade information

transmission [1]. Extensive studies have been done to

determine the mechanisms of electrical contact damage. Many

researchers have worked on this issue [2-8]. Silver coatings

were the focus of thorough investigations by Kassman-

Rudolphi et al. [3] and Song et al. [9]. Park et al. performed

[10] extensive researches on the influence of environmental

loads on the electrical resistance. Ren et al. investigated the

influence of temperature [11] and fretting corrosion on contact

resistance. Silver-plated electrical contacts were extensively

studied in [3, 12-16]. The influence of corrosive atmosphere

was addressed by Chudowsky et al. [13] whereas Imrell [14]

addressed the influence of coating thickness. Most of these

researches focused on material or tribo-chemical aspects of the

problem. The purpose of this paper is to synthesize the

tribological approach developed at LTDS describing the ECR

evolution using a friction energy approach to quantify the

fretting wear of electrical contacts.

Fig. 1. Illustration of the fretting damages and related increase of electrical

contact resistance in a pin-clip contact of connector subjected to vibrations.

2

II. EXPERIMENTAL STATEGY

Low current connectors are usually qualified using

normative vibration tests. Due to inertial effects, oscillating

displacements (i.e. fretting) are occurring between pin and clip

contacts promoting fretting wear and potentially electrical

contact resistance (ECR) failures. The larger the acceleration,

the larger the relative displacement, the faster the surface wear

and finally the shorter the ECR endurance. This technical

approach is however limited in many aspects. For instance,

due to accessibility aspects, the real sliding conditions

operating between the pin and clip remain unknown whereas

the normal force is only estimated from elastic computations

of the clip bending shape.

To better investigate the effects of fretting damages,

alternative laboratory “fretting” test systems were designed to

be representative of low current pin-clip interfaces and

sufficiently instrumented to measure fretting loadings such as

sliding amplitude, normal force, friction energy, and ambient

conditions (relative humidity & temperature).

A. Contact configuration

The most common laboratory contact configuration is the

sphere/plane geometry, firstly because it approximates well

the pin-clip contact and secondly because it avoids

experimental dispersions induced by contact misalignments.

The sphere/plane geometry is presently established using a

crossed cylinder configuration with a cylinder radius r = 2.3

mm (i.e. equivalent to a r =2.3 mm radius sphere/plane

contact) (Fig. 2) [15]. The cylindrical shape of specimens was

obtained by a stamping process of CuSn4 or CuZn37 thin

rectangular plates. Then a electrodepositing process was

applied to coat the Cu alloy substrate with a 2µm nickel

interlayer to limit copper diffusion. Then various Ag, Au or Sn

top layers were deposited using an equivalent

electrodepositing process.

It is interesting to note that by translating the two

cylindrical specimens, more than 20 fretting tests could be

performed on a single specimen pair. Hence less than 8

specimens are required to investigate a given contact

configuration. This reduces the experimental cost and above

all the coating discrepancy. Except specific cases, the given

investigation focuses on homogeneous interfaces which

implies the application of similar specimens.

B. Fretting Test

As illustrated in Fig. 2, the low current LTDS electrical

fretting test involves a crossed cylinder contact configuration.

Fig. 2 : Illustration of LTDS fretting test and crossed cylinders contact

configuration

One specimen holder is fixed on the bottom frame and the

other adapted on the top moving harm connected to the

fretting actuator. For high frequencies and small

displacements electromagnetic shaker are usually preferred.

For larger reciprocating slidings, linear electromagnetic

actuators can be considered. Recent systems associate these

two actuator technologies [16]. The test system needs to be

instrumented to measure the relative displacement (δ) between

the specimens (laser sensor), and to measure the tangential

force (Q) induced by the contact sliding. The normal load is

applied using a dead mass. Note that flexure stripes are

usually adopted to guarantee that the normal load is well

transmitted via the contact and not supported by the fretting

frame. Most of this research work was undertaken keeping

constant the normal load P=3 N. This normal load was

optimized in relationship with the cylinder radius (r = 2.3 mm)

to reproduce the contact configuration of a standard pin-clip

automotive contact configuration. Assuming Hertzian

hypothesis, it leads to a maximum pressure pmax,H = 780 MPa

and a contact radius aH=43 µm. Tests were performed in a

close chamber to control relative humidity and temperature.

The present synthesis focuses on mechanical aspects and

therefore all the experiments were done in dry conditions

(RH= 10%) and at ambient temperature (T=25°C).

3

Fig. 3 : Illustration of the fretting loop, definition of quantitative variables,

plotting of fretting loops versus N (log scale) leads to the Fretting Log

representation.

A key aspect to investigate fretting wear damages is the

plotting of the so-called “fretting loop” related to the evolution

of the tangential force versus the applied displacement (Fig.

3). From the fretting loop, the tangential force amplitude (Q*),

the displacement amplitude (δ*), the friction energy (Ed) (i.e.

area of the fretting loop) but also the residual displacement

(δ0) measured on the δ axis when the tangential force is zero

are extracted [17]. The coefficient of friction is then given by:

*µ Q P=

(1)

If the forces parameters (P & Q) are effectively applied in the

contact, the real displacement operating inside the contact is

more difficult to establish. In fact, a significant part of the

measured displacement is accommodated by the tangential

deformation of the frame. The measured displacement (δ) can

be defined as the sum of the real contact displacement (δC) and

the apparatus accommodation components (δA). Assuming an

elastic response of the test system, δA can be expressed as the

product of the operating tangential force by the test apparatus

compliance (CA) [17]:

( ) ( ) ( ) ( ) ( )C A C At t t t C Q tδ δ δ δ= + = + ×

(2)

Hence for a given displacement amplitude δ*, different contact

slidings are occurring depending on the fretting setup used.

This explains why it is so difficult to compare experimental

fretting data in literature. To palliate such discrepancy, one

solution consists in considering the residual displacement

measured when Q=0.

0 ,0 ( 0)C Qδ δ δ= = =

(3)

Indeed when the tangential force is zero, there is no more

signature of the test. Any test performed imposing a given δ0 is

comparable regardless the test apparatus. Besides δ0 provides

a rather fine estimation of the real sliding amplitude operating

inside the interface [17]. Indeed δ0 can be expressed as the

sum of the effective interfacial sliding amplitude (δS) and a

plastic shear amplitude occurring inside the interface (δp) [18].

Plastic accommodation can be approximated by multiplying

the cyclic shear strain amplitude (γp) by the plastic coating

thickness (e).

0p

S p S eδ δ δ δ γ= + = + ×

(4)

Most of the studied coatings are very thin (less few microns).

Hence, plastic shear accommodation can be neglected and the

effective contact sliding amplitude ( Sδ ) approximated by the

residual displacement [17, 19]:

0Sδ δ≈

(5)

Depending on the scientific objectives, the present

experimental investigation was performed monitoring either δ*

for the sliding condition analysis and δ0 for the gross slip

fretting wear rate investigation.

C. DC electrical contact resistance measurements

To measure the electrical contact resistance during the test, a

four wire method was applied [17] (Fig. 2). A current source

applies I= 0.005A with a 10V voltage compliance, whereas a

µvoltmeter system measures the contact voltage with a 0.01µV

resolution. This system enables electrical resistance from 10-6

to 103

to be measured. The lifetime of the contact was

assumed equal to the number of sliding cycles to reach the

threshold value of the electrical resistance, ∆Rc=0.004 (Fig.

1&4).

III. PLAIN FRETTING SLIDING

A. Influence of partial and gross slip sliding conditions

As illustrated in figure 4a, the ECR resistance highly depends

on the applied displacement amplitude. Former investigations

demonstrated that as long as the fretting contact is running

under small partial slip condition, inducing closed fretting

loop, low and stable ECR are maintained, inducing an infinite

ECR endurance. Partial slip condition maintains an inner

undamaged stick zone providing direct metal/metal

interactions and a good electrical conduction [8].

4

(a)

(b)

Fig. 4. (a) Displacement amplitude and sliding condition on ECR

evolutions; (b) evolution of the ECR as a function of the displacement

amplitude at 10 000 fretting cycles (Sn/Sn (e= 1.3 µm); P= 3N, f= 30 Hz,

RH=10%, T=25°C).

However, when the displacement amplitude overpasses the

gross slip transition (δt), a full sliding is operating over the

whole fretted interface inducing a quadratic fretting loop

shape. This promotes a generalized surface wear, the

formation of nonconductive oxide debris and finally a decay

of ECR (Fig. 4b). As developed by Hannel et al, the fretting

sliding transition can be considered as a mechanical criterion

discriminating finite and infinite electrical contact endurance

[8]:

*

*

Nc infinite

Nc finite

t

t

δ δδ δ

< ⇒ →≥ ⇒ →

(6)

B. ECR endurance chart

The larger the sliding amplitude the faster the surface wear,

the faster the ECR rising and therefore the shorter the ECR

endurance (Fig. 5). To quantify the ECR endurance,

endurance charts have been introduced plotting the evolution

of Nc versus the applied displacement amplitude. Asymptotic

evolutions were observed and formalized using a simple

power law function [15]:

*( )=

− nt

NcNc δ

δ δ

(7)

With Ncδ the ECR endurance when δ*-δt = 1µm and n the

absolute value of the ln(Nc)-ln(δ*-δt) decreasing slope.

Fig. 5. Endurance curves of Sn/Sn, Ag/Ag and Au/Au fretting interfaces

(e=1.3 µm, P= 3N, f= 30 Hz, RH=10%, T=25°C). Comparison between

experiments and power law function.

The ECR endurance relationship is simplified using the

residual displacement variable according [15, 20]:

* 0 * then t tif δ δ δ δ δ> = −

(8)

and therefore :

0( )=

n

NcNc δ

δ

(9)

Fig. 5 suggests that this power law function is able to describe

the ECR endurance whatever the nature of the coating. Non-

noble Sn coating promotes a very fast formation of

nonconductive oxide debris and consequently very short ECR

endurances. In contrast, noble coatings like Au or Ag require

first to eliminate the noble material from the fretted interface

before generating oxide debris from fretting wear of non noble

Ni sub-layer and Cu alloy substrate. This surface wear delay

provides longer ECR endurances.

C. ECR endurance ratio chart

To quantify the comparison between surface treatments (i.e.

coating X versus Y), an endurance ratio KX/Y= Nc(X)/Nc(Y) is

considered and plotted versus the applied displacement

amplitude [15].

5

Fig. 6. Comparison of electrical coating endurance performances (Ag versus

Sn) as a function of the applied displacement amplitude.

Fig. 6 shows that for small partial slip conditions the ratio is

equal to 1 according that the two contacts are running under

partial slip condition en therefore the ECR endurance is

infinite whatever the nature of the coating. When the two

interfaces reach the gross slip condition (δ*> δt(Sn)= δt(Ag)),

the higher endurance of silver coating induces a very high

value of KAg/Sn . However the endurance ratio decreases

asymptotically with the increase of the sliding amplitude.

Indeed the larger the sliding amplitude, the faster the surface

wear and finally the smaller the endurance difference between

the two tribo-systems.

D. ECR response of heterogeneous interfaces

Heterogeneous interfaces can be observed in industrial

applications. Experimental investigations suggest that if the

nature of materials is similar (i.e. noble/noble or non-

noble/noble) the ECR endurance of heterogeneous contact

corresponds to the averaged value of the corresponding

homogeneous interfaces (i.e. NcAu/Ag ≈ (NcAu/Au + NcAg/Ag.)/2).

In contrast noble/non noble interfaces display a very different

response (Fig. 7) [21]. For instance the ECR endurance of a

Ag/Sn interface is 10 times larger than the corresponding

Sn/Sn contact but more than 30 times smaller than the Ag/Ag

interface. Deeper investigations demonstrate that the

heterogeneous contact still obeys a noble/noble fretting wear

response: the ECR failure is reached when most of the

available noble material is worn out from the fretting

interface. However, it demonstrates that the presence of a Sn

layer by forming very abrasive Sn oxides sharply increases the

fretting wear rate of the silver layer and in return drastically

reduces the ECR endurance.

Fig. 7. Evolution of ECR endurance (e = 2µm, Nc :∆R>∆Rth= 4mΩ, I =5

mA, δg = +/- 9 µm, RH=10%, P=3N, T=25 °C, f=30Hz) as a function of

residual displacement amplitude (i.e sliding amplitude): comparison between

Sn/Sn, Ag/Ag homogeneous interfaces and heterogeneous Ag/Sn interface

[21].

E. ECR response & interface chemical composition

SEM and EDS analysis of Ag/Ag fretting scars at Nc display

a typical “U-shape” distribution of silver concentration (Fig;

8) [12, 15].

Fig. 8. Ag, O, Ni and Cu concentration (At.%) profiles in the fretting scar of a

lower sample (Ag/Ag, e=2µm, P=3N, f=30Hz, T=25°C, RH=10%, δg=±9µm,

Nc=97,500 cycles).

6

If on lateral sides the Ag concentration is still high, the silver

concentration remaining in the inner part is very poor. A

reverse distribution is observed for the oxygen concentration

which is maximal in the inner part of the fretting scar. This

observation implies that the ECR-failure may be related to the

chemical composition of the central part of the fretted area

where the maximum contact pressures inducing electrical

junctions are operating. Hence a chemical concentration

criteria consisting in computing the averaged atomic

composition in an inner square area with a diagonal equal to

20% of the final fretting scar diameter (ϕf) is introduced (Fig.

9). Interrupted tests clearly underline that the rising of ECR

corresponds to a progressive elimination of silver material and

an increase of oxide debris. The analysis of various coating

thicknesses and fretting sliding conditions showed that the

ECR failure could be related to a chemical composition

threshold [12, 15]:

N= Nc if [Ag]at%< 5% and [O]at% > 45% (10)

Fig. 9. O and Ag concentrations (At.%) in the fretting scar at ECR failure

(Ag/Ag, e=2µm, P=3N, f=30Hz, T=25°C, RH=10%, δ0=±4µm to ±16.75µm).

F. Friction energy wear approach

ECR Fretting response of noble coatings is controlled by a

progressive wear process. Many investigations demonstrated

that the fretting wear rate can be formalized using a friction

energy description [22]. The main assumption of this theory is

that the increment of wear depth (h) per fretting fretting cycle

may be related to the local friction energy density imputed in

the fretted interface per fretting cycle (φ). Assuming that worn

interfaces promote flat pressure and therefore flat friction

energy profiles, it justifies a mean friction energy density

approximation:

f

f

Ed

Aϕ = (11)

With Ed the friction energy dissipated during a fretting cycle

and Af the final contact area measured at the contact opening.

Fig. 10a compares the ECR evolution obtained for different

sliding amplitudes and various normal loads. The single

sliding amplitude description displays a rather large

discrepancy. For each normal load a given set of Ncδ and n

parameters needs to be applied to predict the ECR endurance.

In contrast, the friction energy formulation leads to a single

endurance master curve [12]. This confirms a posteriori the

potential interest of predicting the fretting ECR-endurance

using the more general friction energy density approach.

Again the ECR endurance can be formalized using a power

law function:

( )=

f

NcNc

ϕβϕ

(12)

With Ncφ the ECR endurance when φf=1 J/m² and β the

absolute value of the decreasing slope of ln(Nc)-ln(φf) curve.

(a)

(b)

Fig. 10. (a) evolution of ECR endurance versus sliding amplitude (i.e.

residual displacement δ0 for 6 different normal forces (1N to 6N) (Ag/Ag,

e=2µm, f=30Hz, T=25°C, RH=10%) with Ncδ(6N)=24.105 cycles, n(6N) =2.22,

Ncδ(1N)=14.107 cycles and n(1N) =2.58; (b) related evolution of ECR

endurance versus mean friction energy density (identification of a single

master curve).

The integration of fretting loop to compute the friction energy

is long and fastidious. Friction energy can be extrapolated

from fretting sliding parameters according to [17] :

04Ed Pµ δ= × × × (13)

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Alternatively the contact area extension is well described

using a power law function of normal force [12]:

0m

fA A P= ×

(14)

Combining equations (12), (13) and (14), a basic explicit

expression of fretting ECR endurance is derived [12]:

0

(1 )0

1

4 −

= × × × ×

m

ANc Nc

P

β

ϕ βδ µ

(15)

Although a very large spectrum of normal loads and sliding

amplitudes was investigated, Fig. 11 confirms the stability of

the proposal to formalize the studied Ag/Ag ECR fretting

endurance [12].

Fig. 11. Comparison between experimental and predicted ECR endurances as

a function of sliding amplitude (δ0), normal force (P) and coating thickness (e)

(Ag/Ag, f=30Hz, T=25°C, RH=10%) (eref= 2 µm, Ncφ=8.1012 cycles, β=

2.583, A0=72,575 µm² and m=0.256).

The few parameters required by the model (A0, β and m) can

be easily extracted from a limited number of fretting tests. Of

course these variables will depend on the contact geometry

and material properties and need to be related to the studied

interface.

G. Influence of coating thickness

The noble coating ECR response is controlled by surface wear

processes. This suggests that the thicker the coating layer, the

longer the ECR endurance [12,20,23,24]. Different

investigations performed on gold and silver coatings confirm

this tendency and showed that the increase of Nc versus

coating thickness (e) is not linear but fits a power law function

with exponent values between 2.5 and 3 [12]. Hence for the

studied Ag/Ag interface (P= 3N, f= 30 Hz, δ0 = ±9 µm) it was

found:

w

ref ref

Nc e

Nc e

=

(16)

with w= 2.85 and Ncref= 97,5000 cycles the ECR endurance

when eref =2 µm.

Fig. 12. Evolution of ECR endurance versus silver coating thickness (Ag/Ag,

f=30Hz, T=25°C, RH=10%, P =3N, δ0 = 9µm), eref =2 µm,

Ncref(e=eref)=97,500 cycles.

Several hypotheses can be considered to explain the rather

high value of w exponent. First it may be stated that the ECR

failure (Nc) is occurring for a fretting wear volume threshold

(Vc) which itself is proportional to the available silver volume

in the fretted interface(V[Ag]). This implies the following

relationships:

2[ ]∝ ∝ ×Ag fVc V e a

(17)

Where af is the contact radius at the ECR failure.

The thicker the coating layer, the larger the wear volume

required to reach the ECR failure and therefore the larger

contact radius af . Fig. 13 confirms a significant increase of af

with the coating thickness.

Fig. 13. Evolution of final contact radius at ECR failure as a function of

coating thickness (Ag/Ag, f=30Hz, T=25°C, RH=10%, P =3N, δ0 = 9µm).

A power law function can be considered so that :

,1= × hf f µma a e

(18)

8

with af,1µm= 125µm (i.e. the extrapolated contact radius when

e= 1µm) and h = 0.43.

This implies

(1 2 ) 1.86[ ] =

+∝ hAgVc e e

(19)

The predicted value of w exponent (1.86) is smaller than the

experimental one (w=2.85). A residual contribution needs to

be considered so that:

(1 2 ) = − + ×w hκ

(20)

Which is found around 1≈κ .

This residual contribution can be related to the plastic shear

accommodation of the interface. Indeed, thicker silver

coatings increase the plastic accommodation of pδ and

consequently decrease the effective sliding amplitude δS

providing that δ0 is kept constant (equation (4)) [19]. A

reduction of the effective sliding amplitude by reducing the

friction dissipation decreases the wear rate and therefore

increases the ECR endurance. Deeper FEM investigations

involving elastoplastic analyses are expected to quantify this

plastic strain description of the interface. Such investigation

will require accurate estimation of cyclic silver plastic

hardening which unfortunately is still not available.

This coating thickness description can be re-injected in the

friction energy description to predict the ECR failure coupling

equation (15) and (16) [12].

0

(1 )0

1

4 −

= × × × × ×

w

mref

A eNc Nc

eP

β

ϕ βδ µ

(21)

Again, Fig.11 confirms the stability of this approach. Many

improvements could be considered to take into account the

effect of ambient condition, material properties, contact

geometry, etc. However this investigation suggests that in

using a simple friction energy density description, the ECR

fretting endurance can be predicted or at least formalized.

IV. COMPLEX FRETTING-RECIPROCATING SLIDING

Real connectors undergo fretting but also macro sliding

induced by intermittent plug-in and un-plug-in procedures.

Hence, there is a key interest to evaluate how the combined

application of fretting and macro sliding can influence the

ECR endurance [16, 25]. To investigate this aspect a constant

fretting sliding condition (P= 3N, f= 30 Hz, δ0 = ±9µm, T=

25°C, RH=10%) was considered and the effect of intermittent

macro sliding applied every Nf fretting cycle, with a total

stroke D from 250 µm to 1500 µm at a constant vR=8.3µm/s

reciprocating sliding speed was investigated. The analysis

demonstrated that the periodic application of macro sliding

sharply increases the ECR endurance (Fig. 14). Surface

analysis suggests that this increase of ECR lifetime is induced

by a transfer process of silver material from the outer

reciprocating track toward the fretting scar. ECR failure is

observed when fretting but also outer reciprocating tracks are

becoming very poor in silver material:

Nc when in fretting scar: [Ag]at%<5% and [O]at%>45%

& in reciprocating track [Ag]at%<5% (22)

Fig. 14. Evolution of ECR as a function of fretting cycles (P=3N, RH=10%,

δ0,ref = ±9µm, T=25°C): comparison between plain fretting and fretting +

reciprocating sliding (D=1mm, Nf =10,000 fretting cycles), related SEM

observations of upper fretting scar at ECR failure.

On the other hand, fretting ECR failure occurs when no more

additional silver can be transferred from the reciprocating

track. Fretting endurance under combined fretting-

reciprocating slidings depends on the reciprocating stroke (D)

but also on the number of fretting cycle (Nf) applied between

macro sliding. Indeed, if Nf period is too long, the ECR failure

can be reached before the successive macro sliding refills the

fretting scar with transferred silver material. This tendency

was illustrated by a stair case decreasing evolution of Nc

versus Nf [16].

For D=1mm the transition was established at Nf,tr = 4.3 104

cycles. This stair case evolution can be expressed using a

sigmoid function [16]:

9

( )max (0)

(0)

,1 /f f tr

Nc NcNc Nc

N Nα

− = + +

(23)

Fig. 15. Evolution of Nc fretting ECR endurance related to the complex

fretting-reciprocating sliding sequence (Ag/Ag, e=2µm, P=3N, RH=10%,

T=25°C, f=30Hz, δ0= ±9µm and D =1mm at v=8.3µm/s) as a function of

fretting cycles per block (Nf).

With Nc(0) the minimum endurance related to the plain fretting

condition (NR=0), Ncmax the maximum endurance related to a

full silver transfer condition. For the studied Ag/Ag interface

it was found Nc(0)=105 cycles and Ncmax= 2.10

5 cycles,

whereas the best fitting of Nc evolution was found for α =

3.53. The full silver transfer condition inducing the highest

Ncmax endurance plateau was observed for the shortest fretting

period so that Nf < Nf_ft ≈ 2.104 cycles. It corresponds to a

limited number of reciprocating sliding NR_ft =10 above which

all the silver material present in the reciprocating track is

effectively transferred in the fretting scar before the ECR

failure. Focusing on a full transfer condition (Nf = 104 cycles <

Nf,ft , so NR> NR,ft) we investigate the evolution of the fretting

endurance Nc (total number of fretting cycle before ECR

failure) as a function the the reciprocating stroke D. An

unexpected non monotonic evolution is observed (Fig. 16).

The ECR endurance decreases from the plain fretting

condition (D=0) Nc(0) down to the minimum value Nc(ϕf)

observed when the reciprocating stroke is equivalent to the

diameter of the fretting scar (i.e. D= fφ ). Then a quasi linear

increase is observed. Such typical evolution can be formalized

expressing the ECR endurance as the ratio between the silver

worn volume (Vc) at ECR failure divided by the fretting wear

volume rate per fretting cycle ( fV& ):

VcNc

V=

&

(24)

To formulate the ECR endurance prediction both Vc and fV&

must be explicited.

Fig. 16. Evolution of fretting ECR endurance (Nc = total fretting cycles before

ECR failure ∆R> ∆Rth=4mΩ) (P=3N, RH=10%, T=25°C, f=30Hz, δ*g,ref = ±

9µm and Nf =10,000 cycles) as a function of reciprocating sliding stroke

(250µm ⩽ D ⩽ 1500µm at v=8.3µm/s), comparison between experiment and

silver wear rate modeling.

The silver worn volume at ECR failure can be expressed as a k

proportion of the available silver volume in fretting and

reciprocating fretted interfaces (V [Ag] ) (Fig. 17) [16]:

[ ]2

f

Ag fVc k V k e Dπ φ

φ×

= × = × × × +

(25)

Where fφ

is the diameter of the fretting scar measured at the

ECR failure.

Fig. 17. Illustration of the estimation of available silver volume involved in

the fretting-reciprocating domains.

The experimental analysis gives k≈ 0.94 which infers that

most of the available sliver volume is worn out at the ECR

failure.

Alternatively, the silver wear rate can be approximated with:

VcV

Nc=&

(25)

10

The non-monotonous evolution of Nc in Fig. 16 suggests that

the fretting wear rate is not constant but depends on the

reciprocating stroke (Fig. 18).

To illustrate such an evolution the fretting wear rates obtained

for 3 key reciprocating strokes are computed :

Plain fretting (D=0) : (0)

(0)(0)

=&Vc

VNc

Maximum wear rate (D= fφ ) : ( )

( )

( )

=& f

f

f

VcV

Nc

φφ

φ

Large stroke (D=Dref=1000µm) : ( )

( )( )

=& ref

refref

VcV

Nc (26)

Using experimental results we found (0)V& = 4 µm3/cycle ,

( )fV φ& = 26 µm

3/cycle and ( )refV& = 7 µm

3/cycle.

Hence two fretting wear regimes can be observed depending

on the reciprocating stroke (Fig. 18):

D< fφ : (0) ( ) (0)( ) ( / ) SD

f

nfV V V V Dφ φ= + − ×& & & &

D> fφ : ( ) ( ) ( )( ) ( / ) LD

f

nref ref fV V V V Dφ φ= + − ×& & & &

(27)

With nSD and nLD respectively the small and large stroke

exponents driving the effect of D regarding fretting wear rate.

Fig. 18. Evolution of the mean fretting wear rate at ECR failure versus the

applied reciprocating stroke D ((P=3N, RH=10%, T=25°C, f=30Hz, δ0,ref = ±

9µm and Nf =10,000 cycles).

Combining Eq. 24 and 26, the ECR endurance can then be

expressed by :

D< fφ :

(0) ( ) (0)2( ) ( / )

× × × = × +

+ − × & & & SD

f

f f

nf

k eNc D

V V V Dφ

φ π φφ

D> fφ :

( ) ( ) ( )2( ) ( / )

× × × = × +

+ − × & & & LD

f

f f

nref ref f

k eNc D

V V V Dφ

φ π φφ

(28)

The best fitting regarding ECR endurance was found with nSD

=2 and nLD=-3. Fig. 16 confirms a very good correlation with

the experiments. This confirms the interest of the proposed

wear rate description. ECR endurance predictions however

depend on the silver wear rate which is characterized by a

non-monotonous evolution (Fig. 18). The wear rate rising

during the first domain D< fφ may be explained by the third

body theory: the sequential introduction of macro sliding by

ejecting wear debris outside the fretting scar increases the

silver fretting wear rate. However, above fφ , a constant wear

rate should be expected providing that all the reciprocating

slidings were performed at a constant reciprocating sliding

speed (vR=8.3µm/s). The asymptotic decrease above fφ is

still unclear. Again, considering third body theory, it may be

considered that because the worn fretting area is becoming

larger when D is increased due to longer Nc endurance, wear

debris remain longer in the fretting interface inducing thicker

third body layer. The fretting wear rate is therefore decreasing

according that a larger proportion of the friction energy is

consumed by the third body layer rather than to be involved in

the degradation of silver coating. Deeper investigations need

to be undertaken to quantify this aspect thus to provide a

physical demonstration of discontinuous fretting wear rate

evolution versus the reciprocating stroke.

V. CONLUSION

This synthesis displayed a thorough analysis of fretting wear

effects on ECR and ECR endurance response. The following

points have been underlined.

- The ECR endurance (Nc) depends on the displacement

amplitude (δ*).

If the contact is running under partial slip (δ*< δt), Nc is

infinite.

If the contact is running under part gross slip (δ*> δt), Nc is

finite whatever the nature of the material.

Focusing on gross slip condition it was concluded:

Plain fretting condition:

- The ECR endurance is better formalised using the so-called

“residual displacement” (δ0) parameter to consider the

effective sliding amplitude imposed in the interface.

- Non noble coatings display very short ECR endurance due to

the immediate formation of oxide debris. The ECR endurance

of noble coatings is longer due to the delay required to fully

eliminate the presence of noble material like Au or Ag from

the fretting interface.

- Heterogeneous noble/non noble ECR interfaces display

rather short ECR endurances according that non noble

materials like Sn generate abrasive oxides which accelerate

the wear rate of noble coating.

- ECR failure is occurring when most of the noble material is

worn out from the contact and replaced by an oxide debris

induced by the fretting wear of non noble sublayers. A

11

chemical composition criterion of inner fretting scars was

established: Nc when [Ag]at%<5% and [O]at%>45%.

- Noble coating ECR endurance which is fretting wear rate

dependent can be rationalised as an inverse power law

function of friction energy density (i.e. 1∝ fNc βϕ ). For the

particular case of constant normal force condition, this general

formulation can be simplified to a simple inverse evolution of

sliding amplitude (i.e. 01∝ nNc δ ).

- Noble coating ECR endurance displays an exponential

increase versus coating thickness (i.e. ∝ wNc e with w>2.5).

The large w exponent may be explained by the lateral

extension of fretting scar (i.e. available silver volume 1.9

[ ] ∝AgVc e ) and an increase of the plastic accommodation

within the interface which tends to decrease the effective

sliding.

- Simple explicit formulations are introduced to quantify the

ECR endurance using a limited number of parameters which

can be identified using a restricted number of experimental

fretting test.

Complex Fretting & Reciprocating sliding condition:

- The application of intermittent macro reciprocating slidings

increases the global ECR fretting endurance. This increase of

the ECR endurance was explained by a transfer process of

silver from the outer reciprocating track toward the fretting

scar. Taking into account the fact that the fretting wear rate

depends on the reciprocating stroke, a simple model was

introduced to predict the fretting ECR endurance under

complex fretting-reciprocating slidings.

The synthesis demonstrates that the ECR of low current noble

fretting contacts can be quantified using very basic

formulation taking into account the friction energy dissipated

in the interface. Future developments are now required to

better integrate the material properties and contact geometry.

References

[1] R. S. Timsit, “High Speed Electronic connectors: A Review of Electrical

Contact Properties”, IEICE Transactions on Electronics 88 (8), (2005), pp.

1532-1545

[2] M. Antler, “Electrical effects of fretting materials: a review,” Wear 106,

(1985), pp. 5–33.

[3] A. Kassman Rudolphi, S. Jacobson, “Stationary loading, fretting and

sliding of silver coated copper contacts — influence of corrosion films and

corrosive atmosphere,” Tribol. Int. 30 (3), (1997), pp. 165–175.

[4] R. D. Malucci, “Accelerated testing of tin-plated copper alloy contacts,”

IEEE Trans. Components Packag. Technol. 22 (1), (1999), pp. 53–60.

[5] N. Benjemaa and J. Swingler, “Correlation between Wear and Electrical

behaviour of contact interfaces during Fretting vibration,” Proc. 23rd ICEC

Conf., (2006), pp. 215–219.

[6] S. Noël, N. Lécaudé, S. Correia, P. Gendre, and A. Grosjean, “Electrical

and tribological properties of tin plated copper alloy for electrical contacts in

relation to intermetallic growth,” Proc. 52nd IEEE Holm, (2006), pp. 1–10.

[7] W. Ren, L. Cui, J. Chen, X. Ma, and X. Zhang, “Fretting Behavior of Au

Plated Copper Contacts Induced by High Frequency Vibration,” Proc. 58th

IEEE Holm, pp. 204–210, 2012.

[8] S. Hannel, S. Fouvry, P. Kapsa, and L. Vincent, “The fretting sliding

transition as a criterion for electrical contact performance,” Wear 249(9),

2001, pp. 761–770,.

[9] J. Song, V Schinow, “Correlation between friction and wear properties and

electrical performance of silver coated electrical connectors”, Wear 330–331,

(2015), pp 400–405.

[10] Y.W. Park, T.S.N. Sankara Narayanan, K. Y. Lee, Fretting corrosion of

tin-plated contacts Tribology International 41(7),(2008)pp 616-628.

[11] W. Ren, P. Wang, Y. Fu, C. Pan, J. Song, Effects of temperature on

fretting corrosion behaviors of gold-plated copper alloy electrical contacts

Tribology International 83,(2015), pp 1-11.

[12] J. Laporte, O. Perrinet, and S. Fouvry, “Prediction of the electrical

contact resistance endurance of silver-plated coatings subject to fretting wear,

using a friction energy density approach,” Wear 330–331, (2015), pp. 170–

181.

[13] B. H. Chudnovsky, “Degradation of Power Contacts in Industrial

Atmosphere : Silver Corrosion and Whiskers,” Proc. 48th IEEE Holm, (2002),

pp. 140–150.

[14] T. Imrell, “The importance of the thickness of silver coating in the

corrosion behaviour of copper contacts,” Proc. 37th IEEE Holm (1991).

[15] S. Fouvry, P. Jedrzejczyk, and P. Chalandon, “Introduction of an

exponential formulation to quantify the electrical endurance of micro-contacts

enduring fretting wear: Application to Sn, Ag and Au coatings,” Wear 271 (9–

10), (2011), pp. 1524–1534, 2011.

[16] J. Laporte, S. Fouvry, O. Alquier, “Prediction of electrical contact

resistance failure of Ag/Ag plated contact subjected to complex fretting-

reciprocating sliding”, Wear (2017),in

press(http://dx.doi.org/10.1016/j.wear.2016.12.033).

[17] S. Fouvry, P. Kapsa, and L. Vincent, “Quantification of fretting damage,”

Wear 200, (1996), pp. 186–205.

[18] A. Kassmann Rudolphi and S. Jacobson, “Gross plastic fretting

mechanical deterioration of silver coated electrical contacts,” Wear 201,

(1996), pp. 244–254.

[19] P. Jedrzejczyk, S. Fouvry, and O. Alquier, “Quantification of the

electrical contact endurance of thin platted silver coatings subjected to fretting

wear: influence of coating thickness”, in Proc. of the 26th International

Conference on Electrical Contacts (ICEC 2012), (2012), pp. 205-212.

[20] S. Fouvry, P. Jedrzejczyk, and O. Perrinet, “Introduction of a modified

Archard wear law to predict the electrical contact endurance of thin plated

silver coatings subjected to fretting wear,” in Proc. of the 58th IEEE Holm,

(2012), pp. 23–26.

[21] O. Perrinet, J. Laporte, S. Fouvry, O. Alquier, “The electrical contact

resistance endurance of heterogeneous Ag/Sn interfaces subjected to fretting

wear”, in Proc. Of the 27th International Conference on Electrical Contacts

(ICEC 2014), (2014),pp. 114-119.

[22] Fouvry, C. Paulin, T. Liskiewicz, “Application of an energy wear

approach to quantify fretting contact durability: Introduction of a wear energy

capacity concept”, Tribology International, 40(10-12), (2007), pp. 1428-1440.

[23] M. Esteves A. Ramalho F. Ramos, “A Synergetic Model to Predict the

Wear in Electric Contacts”, Tribol. Lett., (2016), 64: 21.

[24] T. Dyck, A. Bund, An adaption of the Archard equation for electrical

contacts with thin coatings, wear 102, (2016), pp 1–9.

[25] J. Laporte, S. Fouvry, O. Perrinet, and G. Blondy, “Influence of large

periodic sliding sequences on the electronical endurance of contacts subjected

to fretting wear,” in Proc. of the 59th IEEE Holm, (2013), pp. 40–48.