# Wear Data: What can be Made of it? Simulation Tuning

Yves Berthier, Marie-Christine Baietto, Maurice Godet, Léo Vincent

## ► To cite this version:

Yves Berthier, Marie-Christine Baietto, Maurice Godet, Léo Vincent. Wear Data: What can be Made of it? Simulation Tuning. 18th Leeds-Lyon Symposium on Tribology, Sep 1991, Lyon, France. pp.161-172, 10.1016/S0167-8922(08)70521-2. hal-01951917

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# Wear Data: What Can be Made of It? Simulation Tuning

Y. Berthier, M.-C. Dubourg, M. Godet and L. Vincent

Damage, be it breakage, deformation or wear is initiated by **overstraining** or **overstressing**. Full modelling of both these causes is not possible today and one resorts to "simulation" to produce the data needed by design engineers to predict function loss. The question then is: how reliable is the data furnished by simulation ? The answer is brought by the analysis of data produced in fretting tests which show that even very small variations in running conditions, in this case in amplitude, can change the nature of the damage. Simulation tests have to be undertaken with the utmost care.

## 1. INTRODUCTION

Basic research has naturally dominated the wear scientific scene. Recently, questions coming from the engineering world have oriented research efforts towards more practical problems. Emphasis on reliability, security, comfort, component life predictions, invites tribologists to consider surface performance [1]. The change was expected as the performance of machine components subjected to wear governs machine life. Such changes in outlook, however necessary, are long in coming and early results show that data alone on wear is not enough to answer the questions coming from the engineering world. Indeed, today:

- wear data is common,

- wear maps are plenty,

- wear laws flourish,

- some governing parameters are identified,

- modelling is discussed extensively,

- experimental or simulation programs are initiated,

but the problem is to find out what can be done with these new tools from a practical point of view and how can design engineers introduce them in their models.

## 2. MODELLING

Design engineers use models [2]. Some models rest on sound scientific foundations others on empirical laws. Both are used indifferently as long as they work. This is standard practice and design engineers, who are rarely trained in this subject, react towards wear as they do towards other subjects as wear is just one headache amongst others.

They don't see why such a fuss is made by tribologists over it. They do not understand the formidable differences in wear rates that we publish. The 3 orders of magnitude spread that we commonly report does not make sense to either a brake specialist who sees at most a difference of 50 % in life between two brake pads or to a tyre specialist who notes a variation of 30 % between two different tyre lives.
Tribologists and designers approach the problem differently. The first seek refuge behind their pin and disc machines and applaud at the low wear rates they measure for a given material combination. The second foam at the mouth as they wear out their machines in no time with the same material combination. Both produce figures which supposedly can feed models, unfortunately they do not correlate. The tribologists' experiments, or models, must give results closer to practice. This might entail retiring most of the pin and disc machines, used for this purpose, or at least changing their running conditions. The question is: what should they be replaced by?

## 3. WHAT REALLY SHOULD BE MODELLED ?

From an engineering point of view, models should bring answers to 2 questions:

- will the machine work?

- will it last?

### 3.1 Will the machine work?

Clear answers are given in fully lubricated (thick film) mechanisms as sound physical models exist [3]. Semi or fully empirical guides are common elsewhere [4]. The range of application of these guides is not always known. Interpolation is possible, when interpolation parameters are identified, which is not always the case. Extrapolation is dangerous [5]. In most instances, design engineers rely on experience to make machines work.

### 3.2 Will it last ?

Life of fully lubricated systems is (theoretically) infinite. Life of machine parts is limited by loss of function.

Tribologists are usually called when the machine works but when it does not last, that is when it loses function too rapidly.

## 4. FUNCTION LOSS

The pin of a pin and disc machine has no engineering function. It can go on wearing even when the pin holder also starts rubbing against the disc. The machine will go on working. A machine component loses function if:

- it breaks: through crack initiation and propagation (usually with very little debris or none). Part failure through breakage initiated in contacts is common in hertzian contacts and in fretting, or when subjected to fatigue.

- if it loses guidance and/or kinematic compatibility: through deformation and/or wear (usually with a significant amount of debris). Some parts wear without loss of function. Brake pads for instance can lose up to 3/4 of their original thickness and still give perfect service. Kinematic compatibility is maintained. In others, small localised wear cannot be tolerated. A small change in the cam nose profile, for instance, can strongly
impair engine performance. Guidance is lost.

Hence, from an engineering point of view, function loss through contact damage must be traced rather than wear which gives only one side of the story. Further events which lead to function loss, either through crack initiation and propagation or deformation and wear are encountered simultaneously in contacts which operate under widely different running conditions. As an example, both cracks and wear are found in gears and fretting assemblies. It is therefore necessary to look at the parameters which govern these types of damages.

## 5. GOVERNING PARAMETERS

Paragraph 4 suggests that performance prediction, or function loss prediction is centred around parameters which favour either crack behaviour, or deformation and wear which have to be identified. These can be grouped under three headings [6]:

- imposed running conditions

- material (first-body) properties and limits

- induced running conditions

which are discussed below.

### 5.1 Imposed running conditions

The imposed running conditions (table 1) are those generated in the machine (gears, brakes ...)

Loads are sometimes expressed in terms of pressure (Pa). The contact load acts within the contact, the external load takes in all other loads, seen by the structure. This distinction

is necessary because contact stresses do not act alone in many applications. Kinematics are important; continuous unidirectional rolling or sliding operations (ball and slider bearings), non-continuous unidirectional (gears) and alternating contacts (fretting) generate different conditions at the interface which control the velocity accommodation mechanisms (i.e. how the velocity is accommodated across the interface) which have been shown to govern wear [7]. The role of temperature and environment on material (first and third bodies) properties and changes are obvious and will not be discussed here.

### 5.2 Material properties and limits

Material properties orient the test towards one form of damage (cracks) or an other (deformation or wear), (table 2). The stress intensity factor thresholds ($K_{ith}$ ($i=1,2$)) which define the conditions for crack propagation, and the % elongation to fracture which is a measure of the "strain reserve" before material rupture are added to the familiar yield stresses and strains and rupture strength.

The Wöhler fatigue limit $\sigma_D$ is discussed in § 8.1.

### 5.3 Induced running conditions

The induced running conditions (table 3) are quantities which characterise the condition of the loaded material. While all elements of the stress and strain tensors should appear under the induced running condition heading, special notice must be given to the internal skin stress and strain $\sigma_{xx}$ and
<table><caption>Table 1 - Imposed running conditions</caption><thead><tr><th>Parameters</th><th>Units</th><th>Observations</th></tr></thead><tbody><tr><td>Loads</td><td>Newton</td><td>Contact and external</td></tr><tr><td>Kinematics</td><td>m/s</td><td>frequency, amplitude</td></tr><tr><td>Temperature</td><td>°C</td><td></td></tr><tr><td>Environment</td><td>Composition</td><td></td></tr></tbody></table>

<table><caption>Table 2 - Material properties and limits</caption><thead><tr><th>Parameters</th><th>Units</th><th>Observations</th></tr></thead><tbody><tr><td>K<sub>ith</sub> (i=1,2)</td><td>Pa/m</td><td>S.I.F. threshold</td></tr><tr><td>A<sup>§</sup></td><td>Non d.</td><td>% elongation to fracture</td></tr><tr><td>σ<sub>D</sub></td><td>Pa</td><td>Wölher fatigue limit</td></tr><tr><td>σ<sub>R</sub></td><td>Pa</td><td>Rupture strength</td></tr><tr><td>σ<sub>y</sub></td><td>Pa</td><td>Yield stress</td></tr><tr><td>ε<sub>y</sub></td><td>Non d.</td><td>Yield strain</td></tr></tbody></table>

<table><caption>Table 3 - Induced properties and limits</caption><thead><tr><th>Parameters</th><th>Units</th><th>Observations</th></tr></thead><tbody><tr><td>σ<sub>xx</sub></td><td>Pa</td><td>skin stress</td></tr><tr><td>ε<sub>xx</sub></td><td>Non d.</td><td>deformation</td></tr><tr><td>K<sub>i</sub> (i=1,2)</td><td>Pa/m</td><td>stress intensity factors</td></tr></tbody></table>

<figure><img src="image_2.png" /><figcaption>Figure 1 : Schematic representation of fracture toughness as a function of yield stress of plastics, ceramics, and metallic alloys (ref. 8).</figcaption></figure>
$\epsilon_{xx}$, $\sigma_{xx}$ is the internal surface stress which in a hertzian contact for instance is strongly dependent on maximum normal pressure $p_o$, on the coefficient of friction $f$ and on the location within the contact as shown in the equation below:

$$ \sigma_{xx} = - p_o \left\{ (1 - x^2/a^2)^{\frac{1}{2}} + 2fx/a \right\} $$

where $a$ is the hertzian half-width and $x$ the abscissa of the point considered.

## 6. OVERSTRESSING AND OVERSTRAINING

Materials fail through overstressing and overstraining. Over-stressing leads to crack formation or rupture either instantaneously or after fatigue. Material transformation is noted only in the immediate crack lip vicinity. Particle detachment or debris formation is a secondary effect. Overstressing is noted for instance when, under very high friction, low toughness materials fail by rupture; they crack, rather than slide with respect to one another. Overstraining leads to toughness loss and particle detachment. Crack initiation or crack propagation are secondary effects. Overstraining is observed for instance when, under moderate friction, high toughness materials slide with respect to one another and deform (plastically). The relation between overstressing and overstraining when damage is present is not limited to classical stress strain laws.

Overstressing and overstraining are governed by both imposed and induced running conditions, but also by material properties and limits. Toughness is the first material

factor which comes to mind when overstressing and overstraining are discussed.

## 7. TOUGHNESS

The relation between toughness and hardness or yield stress is illustrated in a graph (fig.1) taken from Zum Gahr [8]. If, as shown in the figure, the difference in toughness between different "as received" materials is great, it drops considerably following work hardening. In other words the difference in toughness between work hardened materials is significantly smaller.

Under rubbing conditions, in initially low toughness materials, such as some ceramics and glasses:

- if friction (and thus $\sigma_{xx}$) is high, cracks form rapidly as first-bodies have little residual plasticity, their percent elongation to rupture $A\%$ is low.

- if friction (and thus $\sigma_{xx}$) is low, cracks are avoided, sliding takes place; as the material cannot overstrain, small localised overstressed particles are detached from the bulk.

Low toughness materials fail essentially through overstressing. Depending on the global stress level either cracks or debris can be generated.

Also under rubbing conditions, in initially high toughness materials, such as metals or metal alloys, with high $A\%$, crack initiation or debris production is not instantaneous. High toughness materials gradually over-
strain, lose toughness and
generate debris as above. High
toughness materials are first
transformed through <u>over-
straining</u> and fail later
through <u>overstressing</u>.

Function loss thus depends on
the cause of the damage, be it
overstressing and overstrain-
ing, and on its intensity.
This is exemplified in the
practical case of fretting as-
semblies. The running condi-
tions which lead to either
form of damage are discussed.

8. OVERSTRESSING AND OVER-
STRAINING IN FRETTING

Fretting results illustrate
the effects of overstressing
and overstraining. It takes
little change in running con-
ditions to go from overstress-
ing to overstraining yet the
damage observed is sig-
nificantly different. This ex-
plains the contradictions and
the difficulties met in the
interpretation of fretting
results.

In fretting, cracks initiate
at contact edges through over-
stressing, and the transformed
zones which result from over-
straining are found in the
contact zone. Depending on im-
posed conditions, and par-
ticularly on load and
amplitude, either edges are
overstressed, or contact
centres overstrained. Contact
conditions are different in
both places and material
properties differ after only a
few cycles. Mixed conditions
can of course be encountered.

8.1 Crack initiation and
propagation

Crack initiation is predict-
able as it is governed by
overstressing. The maximum in-
ternal tensile stress σ<sub>XX</sub>, is
compared to the tensile

fatigue limit stress σ<sub>D</sub>
produced in classical material
tests. If σ<sub>XX</sub> < σ<sub>D</sub>, initia-
tion is avoided. If σ<sub>XX</sub> > σ<sub>D</sub>,
cracks are expected and the
incubation time, taken here as
the sum of the initiation and
propagation times, depends on
the difference between σ<sub>XX</sub> and
σ<sub>D</sub> and on the sensitivity of
the materials to cyclic strain
hardening.

In most laboratory fretting
fatigue studies, initiation
often leads to failure as the
entire test specimen is
stressed. Each new crack
decreases the specimen effec-
tive section, thus weakening
the specimen, and crack in-
ition normally leads to
propagation and failure. In
many industrial contacts,
stresses are high in the con-
tact vicinity but drop rapidly
away from that zone causing
propagation to stop [9].
Laboratory conditions are of-
ten more severe than those
found in practice. Full frac-
ture mechanics analyses are
therefore needed to predict
failures initiated by over-
stressing alone. Experimental
values, listed in the material
properties and limits table
($5.2$), are needed to conduct
such studies.

8.2 Debris

In metals, debris emerge from
a very hard modified structure
made out of very stable phases
[10]. Modifications start
during the first passes of the
wear test and rapidly the lo-
cally consolidated surface can
no longer accommodate the
deformation imposed by the
contact load and it cracks
[11]. Debris spring from the
fragile transformed layer.
Damage is initiated by over-
straining and ends through
overstressing. Modelling of
the debris formation process
is not within reach today. The
rate of change of structure
under well defined contact
conditions is needed before
any modelling can be con-
sidered. This is a study in
itself. Note further that par-
ticle detachment is only the
first step in the production
of a wear particle and that a
global wear model would have
to model particle progress
from its detachment to its
elimination from the contact
and wear track [2].

9. SIMULATION

Paragraphs 8.1 and 8.2 show
that in spite of the con-
siderable progress in under-
standing surface damage and of
the identification of the
phenomena which govern at
least some of its different
forms, it is not yet possible
to predict surface performance
(or function loss) under fret-
ting and other running condi-
tions. This progress is
nevertheless useful in setting
up experimental programs which
will bring the necessary in-
dications to the design en-
gineers, and in interpreting
fretting results.

9.1 Friction loops and friction logs

In fretting individual
force/displacement (FD)
cycles, or friction loops,
take on different shapes
during a fretting test
(fig.2).

- a closed (cc) conserva-
tive FD cycle, as-
sociated with elastic
accommodations. Tangen-
tial contact stiffness
is given by the slope
of the FD line.

- an elliptic (ec)
slightly dissipative FD
cycle, found in con-
tacts which exhibit

either partial slip or
interfacial crack fric-
tion or both.

- a trapezoidal (tc)
cycle, characteristic
of gross slip, the
near horizontal seg-
ments are dissipative,
the near vertical seg-
ments are conservative.

Friction loops can be drawn
for each cycle of a given
test. These loops, when posi-
tioned on a 3D friction
coefficient/displacement/cycle
number plot, form a friction
log (fig.3). Depending on
materials and conditions,
that log can exhibit the 3 in-
dividual loops illustrated
above. Experience showed that
plotting force and displace-
ment versus the log of the
cycle numbers gives the best
test description.

Plots can be drawn for dif-
ferent loads, amplitudes,
frequency and of course
material combinations. They
are therefore capable of
measuring the sensitivity of
the contact to changes in any
one of these parameters. The
different friction logs shown
in figure 3 were all obtained
with the same load, frequency,
the same materials but for
different amplitudes. Com-
pletely different damage types
were obtained in figure 3 when
the amplitude varied from 15
to 50 micrometers.

9.2 Fretting maps

Crack initiation and propaga-
tion, and debris formation
seen in fretting, have dif-
ferent origins even if they
occur within the same contact
and with the same original
material combination. Fretting
maps originated by Vingsbo
[12] were further developed in
this study (fig.4). The first,
the running condition fretting
<figure><img src="image_3.png" /><figcaption>Fig. 2 : 3D friction logs obtained for different amplitudes with 7075 aluminium alloys (ref. 13)</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>DOMAIN 1
Closed cycle (c.c)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>DOMAIN 2
Elliptical cycle (e.c)</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>DOMAIN 3
Trapezoidal cycle (t.c)</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Running Condition Fretting Maps (L : Load, a : Amplitude)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Material Response Fretting Maps (S : Stress, a : Amplitude)</figcaption></figure>

<caption>Figure 4 : Running conditions and material response fretting maps</caption>
FRETTING CHART

<figure><img src="image_9.png" /></figure>

N.B.: C.I. crack initiation, P.D. particle detachment, T.B. third-body, t : time, T.T.Z. tribological transformed zone

Fig. 5 Fretting chart: crack initiation and propagation, high and low wear
map (RCFM) identify the contact kinematic conditions: **full adhesion**, **partial slip**, **gross slip**. They can be drawn directly from the friction logs as the three kinematic conditions correspond respectively to the closed, elliptical, and trapezoidal cycles of figure 2. In RCFMs, load is plotted versus amplitude. The second, the material response fretting map (MRFM) identify damage forms: **no degradation**, **cracks**, and **particle detachment**. In MRFMs, skin stress is plotted versus amplitude, and damage areas are identified after surface examination. The positions of the lines which delimit the kinematic conditions and the damage areas can vary during the test. The curves presented in figure 4 are representative of many tests, run with different materials and different loads. They illustrate the effect of load on the kinematic conditions and on the type of damage encountered. Similar fretting maps can be drawn for different parameters.

## 10. FRETTING CHARTS

The examination of many different **friction logs** led us to set up **fretting charts** (fig.5) which show how combinations of imposed and induced conditions and material properties interact. A ball on flat geometry is chosen. Materials and running conditions, except amplitude are fixed. Two critical nominal amplitudes (different from actual slip) $a_{c1}$ and $a_{c2}$, where $a_{c2} > a_{c1}$, are identified which define 3 domains:

Domain 1: $a < a_{c1}$ (no slip)

Domain 2: $a_{c1} < a < a_{c2}$
(partial slip)

Domain 3: $a > a_{c2}$
(gross slip)

Thus the critical amplitude $a_{c1}$ (a machine parameter), is set opposite the yield strain $\epsilon_y$ (a material parameter), even though the deformation $\epsilon$ is not constant along the contact.

In domain 1 (fig.5), both $\sigma_{xx}$ and $\epsilon_{xx}$ are small at start. Friction increases rapidly as the surfaces are in close contact, $\sigma_{xx}$ rises, cracks are initiated and depending on the stress intensity factors, they will either stop (crack arrest) or propagate (propagation failure). In domain 3 (fig.5), $\sigma_{xx}$ is low and $\epsilon_{xx}$ is high. Friction rises moderately as sliding is observed. If the % elongation to fracture $A\%$ of the material is small ($A\% < A\%_c$), the contact zone breaks up and debris is produced quasi-instantly; if it is large ($A\% > A\%_c$) the material strainhardens, is transformed (tribologically transformed zone, T.T.Z) and only then will produce debris [10]. In both cases the debris is either trapped in or eliminated out of the contact. Domain 2 is a combination of domain 1 and 3 and can, depending on whether crack initiation precedes or follows particle detachment, go towards crack propagation or wear as also seen in figure 5.

## CONCLUSION

This paper has tried to answer the question "Wear data: what can be made of it?". It was first shown that wear data is not really what the design engineers need. They want to know when a given component loses function, that is when it breaks or when it loses kinematic compatibility through either deformation or wear. The next answer is then to find out what parameters govern either breakage or
deformation and wear? Three sets of tables are presented: the first lists the running conditions imposed to the contact, the second the material properties and limits, the third the conditions induced by the running conditions on the materials.

Damage, be it breakage, deformation or wear is initiated by **overstraining** or **overstressing**. Full modelling of both these causes is not possible today and "simulation" is needed to produce the data required by design engineers to predict function loss. The question then is: how reliable is the data furnished by simulation ? The answer is brought by the analysis of data produced in fretting tests which show that even very small variations in running conditions, in this case in amplitude, can change the nature of the damage. Simulation tests have to be undertaken with the utmost care.

References

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2) M. Godet, Y. Berthier, J. Lancaster and L. Vincent "Wear modelling: using fundamental understanding or practical experience ?" (to be published in WEAR 1991).

3) J. Frêne, D. Nicolas, B. Degueurce, D. Berthe, M. Godet "Lubrification hydrodynamique: paliers et butées" Editions Eyrolles, 61 Bd Saint-Germain, Paris 5ème, 1990.

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5) M. Godet "Extrapolation in tribology" WEAR, 77, (1982) 29-44.

6) L. Vincent, Y. Berthier, M.C. Dubourg and M. Godet "Mechanics and materials in fretting" (to be published in WEAR 1991)

7) Y. Berthier, L. Vincent and M. Godet "Velocity accommodation in fretting" Wear, 125, (1988) 25-38

8) K. H. Zum Gahr "Microstructure and wear of materials" Elsevier Tribology Series, 10, 1987.

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11) S. Fayeulle, P. Blanchard and L. Vincent "Fretting wear behaviour of several titanium alloys" presented at STLE annual meeting, Montreal May 1990, to be published in STLE transactions.

12) O. Vingsbo and D. Soderberg "On fretting maps", Wear, vol. 126, 1988, pp. 131-147.

13) V. Pellerin "Etude du comportement en usure induite sous petits débattements d'alliages d'aluminium et de titane" Thèse, Ecole Centrale de Lyon, Lyon, France, Jan. 1990.