Wear mechanisms of silicon nitride bearing materials under contact fatigue stresses


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Wear mechanisms of silicon nitride bearing materials under contact fatigue stresses
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vi, 214 leaves : ill. ; 29 cm.
Chen, Zheng
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Thesis (Ph. D.)--University of Florida, 1995.
Includes bibliographical references (leaves 203-213).
Statement of Responsibility:
by Zheng Chen.
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University of Florida
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I would like to especially thank my advisor, Dr. John J. Mecholsky,

Jr., for his constant guidance, support, and inspiration throughout the course

of this work. I also wish to thank Dr. J. H. Adair, Dr. B. V. Sankar, Dr. R.

K. Singh, and Dr. E. D. Whitney for advising throughout the research and

for serving as committee members. I am very grateful for support by the Air

Force Office of Scientific Research on the URI program.

I would like to extend my thanks to my colleagues, Mr. J. Cuneo, Mr.

T. Joseph, and Dr. S. Hu for help in AFM analysis and FEA analysis.

Special mention must be given to my officemates, Mr. L. P. Hehn and Dr. Y.

Tsai, for the many discussions and suggestions (technical and otherwise)

which helped keep everything in perspective.

I would like to express sincerest thanks to my parents for their love

and encouragement throughout my entire life, and to my wife, Rongrong Jia,

for her love, patience, and understanding, and for helping me to keep my

sanity during the most difficult times.



ACKNOWLEDGMENTS ................................................................ ii

ABSTRACT ...... ........... ................. ....................................... ........... v


1. INTRODUCTION..................................................................... 1

2. LITERATURE SURVEY.................................................................. 11

2.1 Theoretical Background........................................................ 11
2.2 M echanisms of W ear.......................................................... ... 18
2.2.1 Wear by Plastic Deformation................................... 19
2.2.2 Wear by Brittle Fracture............................. ......... 20
2.3 Wear by Tribochemical Reaction........................................ 23
2.4 Wear Mechanisms in Si3N4................................. ......... 24
2.5 Apparent Study in Si3N4 Wear.......................................... 25
2.6 H ertzian Stress.................................................................... 30

3. EXPERIMENTAL PROCEDURES........................................... 34

3.1 Silicon nitride Materials................................................. 34
3.2 Microstructural Analysis................................................ 36
3.3 Influence of Crack Size
on Si3N4 Strength and Toughness.......................... ......... 37
3.4 Ball on Disc Contact Fatigue Test.................................... 39
3.5 Diametral Compressive Fatigue Test................................... 44
3.6 Characterization of Surface Geometry
Using Fractal Dimension................................................ 48

4. RESULTS AND DISCUSSION................................................. 54

4.1 Microstructure of Si3N4 Bearing Materials........................... 54
4.2 Fracture Behavior of Si3N4................................................... .. 62
4.2.1 R-Curve Behavior................................................ 62
4.2.2 Crack Initiation............................................................... 78
4.3 Contact Fatigue Test..................................................... 88
4.3.1 Stage I Wear-Roughening on the Contact Surface......... 92
4.3.2 Stage Wear II Wear
-Cone Crack Initiation and Propagation...................... 104
4.3.3 Stage Ill Wear-Material Removal
from Outside the Contact Area...................................... 111
4.3.4 The Effect of Surface Finish
on Si3N4 Wear Behavior............................................... 123
4.3.5 Subsurface Damage....................................................... 133
4.3.6 Effect of Microstructure on Wear Behavior................. 137
4.4 Diametral Compression Fatigue Test
under Different Environments............................................... 141
4.5 The Geometry of Wear and Fracture Surface......................... 157
4.6 XPS Surface Analysis............................................................ 175

5. CON CLU SION S.......................................................................... 178

FINITE ELEMENT ANALYSIS.................................... 188

PREDICTION OF CRACK PATH................................ 197

REFERENCES.................................................................................... 203

BIOGRAPHICAL SKETCH............................................................. 214

Abstract of Dissertation Presented to the Graduate School of the University
of Florida in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy



Zheng Chen

May 1995

Chairman: Dr. John J. Mecholsky, Jr.
Major Department: Materials Science and Engineering

The objective of this research was to investigate wear mechanisms of

silicon nitride as bearing elements. The study is focused on two questions:

(1) How does Si3N4 wear initiate and develop in the hybrid ball bearing

system? (2) What materials and mechanical factors control wear initiation

and development? The properties and fracture behavior of advanced silicon

nitride bearing material, such as toughness, crack initiation and propagation,

R-curve behavior, cyclic fatigue resistance, subcritical crack growth, and

fractography, have been studied. The ball-on-disc cyclic-fatigue testing

method has been successfully designed and applied to simulate loading

conditions in a hybrid ball-bearing operation. The diametral compression

test has been used to study crack growth mechanisms and environmental

influence on crack growth. The AFM, SEM, and XPS are the primary

techniques that were used to study the topography and chemistry of the

fracture and wear surfaces. From this research, wear mechanism models for

Si3N4 bearing materials have been established. The causes of the wear have

been determined to be directly related to a mode I brittle fracture process.

The results of this research will lead to improvement in silicon nitride wear

resistance by adjustment of the microstructure.


High quality silicon nitride (Si3N4) ceramics have low densities, low

friction coefficients, low thermal expansions, high strengths, and high

temperature and chemical stability, and are non magnetic. The combination

of these properties makes silicon nitride an attractive material for rolling

element bearing applications to withstand higher loads, severe environments,

and high speeds [1]. The low density of the silicon nitride material presents

particular advantages as the rolling elements of high-speed air turbine

bearings. The centrifugal forces and gyroscopic moments induced during

high speed, which are major contributors to the contact stresses generated in

the bearings, are significantly reduced. Another advantage in using Si3N4 is

that, because silicon nitride has high temperature and chemical stability, is

an electrical insulator, and is non-magnetic, silicon nitride rolling-element

bearings can be used at elevated temperatures, corrosive environments, and

in magnetic fields in which conventional bearing steels are limited. In order

to successfully use silicon nitride as rolling elements, the material must have

reasonable hardness, high toughness, and a high Weibull modulus which

indicates a narrow distribution of defects in the material.

In the early 1960s, material scientists started to think that silicon

nitride could be a potential rolling-bearing material [2]. Since that time,

many investigators have devoted their time to processing and evaluating of

silicon nitride bearing materials [3-10]. Since silicon nitride has a covalently

bonded structure (hexagonal crystalline structure), difficulty in sintering

became a major barrier to its manufacturing. Machining was also extremely

difficult because of the high hardness of silicon nitride. All these reasons

resulted in the fact that it was impossible to limit all defects, such as

porosity, large inclusions, surface damage, and sintering flaws, in silicon

nitride products. The various types of defects resulted in an uncertainty in

the silicon nitride failure mode for many products. Even though many

investigators explored wear mechanisms in Si3N4 and have documented their

attempts in the literature [11-15], the wear mechanisms of silicon nitride in

hybrid ball-bearing systems have not been precisely explained. This is

because most of the failures resulted from random, external factors (such as

defects caused by manufacturing and machining or improper preparation and

improper selection of test) rather than from the aspects of material structure.

In the past two decades, the material manufacturing processes have

been continuously improved, from porous silicon nitride materials with poor

surface finish to dense materials with fine surface finish (up to 0.01 pm).

Therefore, failure origins also changed from surface defects and/or large

internal pores to small interior inclusions. Silicon nitride fracture and

mechanical properties, e.g., strength, creep, toughness, and dynamic fatigue,

have been reported by numerous authors [16-20] and show significant


In the study of silicon nitride wear mechanisms, numerous

investigators have described Si3N4 wear mechanisms as cracking, spelling,

subsurface damage, and tribochemical reaction mechanisms [20-25].

Another investigator suggested that plastic deformation was also involved

[26]. The basic experiments currently used are rolling contact fatigue (three

balls with one rod, or four-or five-ball contact rolling) [22,23,24,26,27], pin

on disc [12], and rolling and sliding contact fatigue [11,13]. These

experiments had success in evaluating quantitative volume loss with loading

time. However, these experiments lack control of the wear process and, as a

result, are unable to monitor the different stages in wear initiation and

development. Notably, a large surface area was tested in these experiments


and it is unavoidable that random defects due to specimen preparation could

involve the tests. The defects will enhance the material degradation during

the tests and may result in a change in the wear mechanism. Therefore, the

artificial factors due to specimen preparation could confuse the final results.

With increasing demand for Si3N4 hybrid bearing applications, a

mechanism which can precisely describe the Si3N4 wear initiation and

development in hybrid ball bearing is needed. The understanding of aspects

of material structure (not random defects) which causes Si3N4 wear could be

difficult to gauge by existing experiments, i.e., rolling contact fatigue

experiments. Noticeably, previous studies used an excessive wear condition,

which is a diamond rider sliding on a silicon nitride disc [26]. This resulted

in plastic deformation and phase transformation occurring in Si3N4. Plastic

deformation and phase transformations rarely happen in hybrid ball-bearing

operations. So, these factors need to be considered in the design of a

research schemes.

The understanding of the process of material failure initiation and

development can be gauged by considering the following two parameters:

first, the primary factor which results in silicon nitride rolling element

degradation or wear in bearing systems; second, a well-defined stress field

which is similar to the stress field in the bearing systems. The well-defined

stress can lead to a more precise description of wear i.e., wear initiation and

wear development.

Figure 1 shows a typical bearing ball wear pattern from a recent

bearing test which was conducted by Torrington Co. Based on this wear

pattern, we presume that this failure was caused by brittle fracture due to

contact stress fatigue.

In order to verify this, a research scheme was developed. The

assumptions of the research scheme are as follows.

1. There is no significant external tangential traction force existing

between the silicon nitride ball and M50 steel race because of very low

friction between the M50 steel and the Si3N4 ball when liquid lubricant is

applied. Therefore, the external tangential force can be ignored and Hertzian

contact force is the only force which was considered in the designed


2. There is no three-body abrasive wear; the lubricant with which we

start is free of particles.

Figure 1 SEM photo shows a typical bearing ball wear pattern
from a recently bearing test. The pattern indicates the
wear due to multiple Hertzian contact stress fatigue.

3. The surface of the specimens has the same or better surface finish

than commercial balls. So, there is no additional wear caused by surface


4. Wear is caused by contact fatigue stress.

The objectives of this study are to investigate the mechanisms of wear

initiation and development in an Si3N4 hybrid bearing system and to

determine what material factors and mechanical factors cause Si3N4 wear.

The results from the experiments should lead to improvement in Si3N4 wear

resistance by adjustment of the microstructure. The work presented in this

dissertation consists of four major aspects.

1. Characterization of mechanical properties for advanced silicon

nitride material (TSN-03H). Toughness and strength of silicon nitride

bearing material were evaluated as functions of initial crack size. The

results demonstrated the material's sensitivity to crack size. In the study of

failure initiation, Si3N4 specimens were fractured under the rotating

cantilever beam test, and failure origins were identified using fracture

surface analysis and chemical analysis. Based on the first stage of the

study, an overview of the material properties and the material weaknesses

under mechanical loading were established.

2. The models for Si3N4 wear initiation and development under

contact fatigue stress were established by designing a wear testing method to

simulate the loading condition in the hybrid ball-bearing system.

Considering the general Si3N4 ball failure pattern during the hybrid bearing

operation, a well-defined contact fatigue Hertzian stress field was applied to

the silicon nitride disc-shaped specimen using a hard ball (WC). Exxon

turbo oil 2380 was used as a lubricant during all the tests. By using different

loading levels, cycling numbers, and frequencies, three wear stages were

observed from the experiment. The mechanisms for silicon nitride wear

initiation and development were determined in this investigation. Two types

of advanced silicon nitride bearing materials have been used in order to

study the influence of microstructure on the wear process. In this section of

the dissertation, I will demonstrate the models of wear initiation and

development in silicon nitride bearing materials under contact fatigue

loading and explain on what they are based.

3. Investigation of crack growth in silicon nitride bearing materials

under mode I stress. The fatigue crack growth rate is a key factor in

determining wear development in brittle materials. The modified diametral

compression testing method was employed in this part of the study. Static


and cyclic fatigue loading was used to study the mechanisms for crack

growth. The tests were conducted under different environments and stress

levels. The effectiveness of microstructure and environments on crack

growth were evaluated

4. The failure mode was verified through surface geometric analysis.

Fractal dimension techniques were applied to study the link between surface

geometry and fracture and wear surfaces. Instead of using qualitative words

such as smooth or rough surfaces to describe different surface appearances,

the fractal dimension, a quantitative number to describe the surface

geometry, was used. The fractal dimensions of wear and fracture surfaces

were measured and the relationship between the wear surface and fracture

surface was established. A wear failure mode was verified from this


The results from this study demonstrate the following. (1) Si3N4 wear

in the hybrid ball bearing is a brittle fracture process under mode I stress.

From wear initiation to large volume loss in the materials, the wear process

follows a typical brittle fracture process. (2) Three different wear stages in

Si3N4 bearing materials were observed. These are grain pull-out, cone-crack

initiation and propagation, and large-volume material removal due to the

propagating crack curving up to the free surface. (3) Heterogeneity in the

material's structure is the cause of wear initiation. (4) Cyclic fatigue crack

growth contributes to major Si3N4 volume loss. (5) Different stress states

created by contact loading can be used to study different types of failure. (6)

Fractal geometry may be used to identify the material failure mode. (7) A

high strength grain boundary phase and uniform microstructure can improve

the wear resistance of Si3N4 bearing materials.


2.1 Theoretical Background

The strength, a, of most ceramics depends on the crack size, c, and

toughness and can be obtained using fracture mechanics [28]:

C= (2.1)

where Y is a well-documented parameter of crack and specimen geometry,

KjI is the critical stress intensity factor, i.e., a measure of the toughness of

the material, and c=(ab)12 where a is the depth and 2b is the width of a semi-

elliptical crack. When an applied stress on a material in which a crack has

length c results in a stress intensity factor KI at the crack tip larger than Ki,

the material will fracture instantly. The crack can propagate continuously

from the initial crack or defect, c, until the entire material is fractured, only if

the stress intensity K, is larger than KI.. However, when loading in terms of

stress intensity factor (KO) applies to the crack tip in a wave form, which is

called cyclic fatigue loading, the crack can grow under global loading, K, <


Kic [29,30]. Consider a structure under a global stress intensity factor K,

much smaller than the material KjI in which a crack propagates.

Due to cyclic loading or due to a combination of loading and

environmental attack, such as molecular water and corrosive chemicals, the

crack will propagate with time [31-37]. When the crack grows, the crack

length c increases with time. The crack growth rate can be generally

described as a simple power law [38]:

dc = C(AK)" (2.2)

dc/dN is the crack growth rate per cycle, AK is the stress intensity factor

range, and C and n are material and environmental constants. The strength

of the material decreases as loading time increases. The strength eventually

will reach a time at which the material fractures. It is very important to be

aware of the crack growth rate of materials under a particular mechanical or

chemical attack during their applications. However, equation 2.2 does not

fully represent reality. Actual data of crack growth rate vs. stress intensity

factor fall on an S-shaped curve, or a line with variable slope when you plot

a double logarithmic plot of dc/dN versus AK [39,40]. At low AK values

crack propagation is extremely slow. Conceivably there is a threshold value

of AK below which crack growth can be ignored. Experimental verification

of the existence of this threshold is difficult. A growing crack of some

length has to be arrested by gradually decreasing AK until below the


In reality, the mechanisms of crack growth is more complicated.

Using a single interpretation for the crack growth mechanism in all materials

is obviously awkward, at best. Since many more parameters are involved

than AK and another material constant such as Young's modulus, it is

reasonable to assume that the mechanisms for crack growth in ductile

(metals or metal alloys) materials are totally different from the mechanisms

for crack growth in ceramics.

The crack growth in ductile materials is initiated by local plastic

deformation [41, 42]. During the rising-load part of the cycle, slip occurs on

favorably oriented slip planes resulting in crack growth. The crack growth is

then inhibited by strain hardening. During subsequent cycles, the crack will

continue growing in a slip plane in which slip can take place. Therefore,

fatigue crack growth in the ductile material always leaves beach-marks on

the fracture surface. These beach marks are formed due to crack growth in

different slip planes created under different loading cycles.

The crack growth in ceramics has different mechanisms. The covalent

or ionic bond structure limits crack growth through dislocation slipping. The

crack growth mechanisms in ceramics are not as clear as in ductile materials.

One mechanism describes the crack growth due to molecular water attack of

molecular bonds in ceramics such as the O-Si-O bond in silica or the O-A1-O

bond in alumina when these bonds are stretched by a tensile stress [43,44].

In recent years, the cyclic fatigue behavior of ceramics has been actively

investigated [45-55]. It has been shown that crack growth occurs under

cyclic loading conditions in non-oxide ceramics. This crack growth in non-

oxide ceramics is inexplicable by the cracking mechanism due to molecular

water attack alone. In particular, with silicon nitride, the effects of cyclic

loading on crack growth have been confirmed experimentally [56]. So far,

there are two mechanisms to rationalize the cyclic fatigue phenomenon

experimentally observed and both of them are very dependent on

microstructure and composition of materials. These are: (1) microscale-

crack branching and (2) crack-path deflection [57].

In the case of microscale-crack branching, during tensile loading, the

growing crack 0 (K0 > Kij) branches off after growing a Aat distance, being

followed by crack arrest (Ki=K2=K3=K4

(1) Tensile loading (1) Tensile loading


Where Ko>KIc and KI, K2, K3, and K4

Asperity contact
(2) Unloading K3>KIc (2) Unloading Aserit contact

4 Asperity contact a


(3) Tensile loading K3>KIc (3) Tensile loading



(a) (b)

Figure 2 The fatigue mechanisms in material were characterized by
microscale-crack branching in (a), and crack path deflection
in (b). Aa, and Aa, are crack increments during tensile loading
and unloading, respectively.

be aware that the stress intensity factor referred here is the local stress

intensity factor. Note that such branching occurs along grain boundaries

only in intergranular-fracture type materials, such as polycrystalline silicon

nitride and alumina. During unloading, some of the branched cracks might

grow a Aau distance, if there are some asperities or loose particles on the

crack faces caused by the crack propagation. The advancement is most

pronounced in crack 3 where the extent of asperity/particle-induced damage

due to "wedge effect" is the highest. During the subsequent tensile loading,

only crack 3 can grow because of only K3>KI, at this moment. Then crack

branching occurs again to arrest the cracks. Such a sequence is repeated

during cyclic loading and results in cyclic crack growth.

In the case of crack-path deflection (Figure 2b), a propagating crack is

deflected due to some obstacle in the front of the crack path during tensile

loading. The crack is then arrested because the deflected crack is at an angle

to the microscopic crack direction, consequently lowering the stress intensity

factor below Kic. During unloading, in the area behind the crack tip where

particle-contact was produced during the crack growth, the crack may grow

due to a local tensile load to open the crack by a "wedge effect" through the

particle-contact point [57]. In this case, the crack growth occurs during the

unloading rather than loading.

Previous research found little enhancement of fatigue crack growth by

environmentally assisted crack growth at room temperature [58, 59].

However, the microstructural features, preexisting defect shapes, and

composition of sintering aids can also affect crack growth mechanisms.

Most previous experiments were conducted using bending specimens with a

crack induced using a Vickers' indenter. The crack then grew from a

indentation crack under a cyclic bending load.

Regardless of which crack growth mechanism is active for crack

growth, the result of crack growth will eventually cause either material

fracture or material loss. The material loss usually occurs in a localized

region in which most likely a highly concentrated stress exists.

From an atomic scale view point, fracture or crack growth in materials

is an atomic bond breaking process under stress [60-62]. The choices

include a plastic-type bond break, i.e., dislocation movement, or a brittle-

type bond break, i.e., mode I stress fracture, depending on material

properties and bond structures, and the stress states in materials.

2.2 Mechanisms of Wear

Wear is defined as "damage to a solid surface, generally involving

progressive loss of material, due to relative motion between that surface and

a contacting substance or substances [63]." The mechanisms of wear can be

divided into three categories. One is adhesive wear, in which two contact

surfaces bonded by diffusion due to high pressure, are fractured by the

motion of one substance on another substance [64]. Adhesive wear is not

considered to be the case for wear in silicon nitride hybrid ball bearings

because liquid lubricant is used to separate the two surfaces and hinder

diffusion. Another is abrasive wear [65]. The last one is tribochemical


Abrasive wear can be further divided into two types: one is two-body

abrasion, in which rough surface contact results in wear; another is three-

body abrasion, in which foreign particles are trapped between two solid

surfaces. In principle, abrasive wear is caused by hard protuberances among

the surfaces that slide over the surfaces and move material from these.

There are two types of mechanisms involved in abrasive wear: wear by

plastic deformation and wear by brittle fracture.

2.2.1 Wear by Plastic Deformation

A simple model can be explained for abrasive wear involving material

removal by plastic deformation [66,67]. A hard protuberance, idealized as a

cone of semi-angle, ac, is plowed across the surface of a ductile material

which plastically deforms under an indentation pressure, P. A scratch is

formed in the material after the protuberance slides on the surface, and wear

is assumed to occur by the removal of some portion of the material from the

scratch. The normal load, w, carried by the protuberance, which causes a

pressure P to act over the area of contact between the protuberance and the

surface [68],

w = Pttan c (2.3)

And the wear rate, Q, (volume per unit sliding distance) can be described:

-Kw (2.4)

where H is the hardness of material, and K a constant dependent on the

friction of the materials and the geometry of the protuberance.

2.2.2 Wear by Brittle Fracture

When a hard angular particle is pressed against the surface of a brittle

material, local plastic deformation can occur at the point of contact, followed

by the formation of cracks which can lead to the detachment of material, and

hence, to wear [69-77]. Cracks form in a brittle solid subjected to a point

load. At the point of initial contact, very high stresses occur. Indeed, if the

tip of the indenter were perfectly sharp and there was no plastic deformation

in the material around the tip, there would be a stress singularity at this

point. However, the intense stresses (shear and hydrostatic compression) are

usually relieved by local plastic flow or densification around the tip of the

indenter; the zone of deformed material is indicated by the letter D in Figure

3. When the load on the indenter increases to a critical value, tensile

stresses across the vertical mid-plane initiate a median crack, indicated by M

in Figure 3. Further increase in load is accompanied by progressive

extension of the median crack. On reducing the load the median crack

closes. Further unloading is accompanied by the formation and growth of

lateral cracks (labeled L). The formation of the lateral cracks is driven by

residual stresses, caused by the relaxation of mismatched deformation(elastic

and plastic) around the region of the contact. As unloading is completed, the


d e f

Figure 3 Diagram showing crack formation in a brittle material due to
point indentation as the normal load is progressively increased
from a to c and then reduced from d to f.


lateral cracks curve upwards and terminate at the free surface. The median

cracks propagate down into the bulk of the solid with increasing loads on the

indenter, and do not grow further during unloading. They are not associated

with the removal of material. Lateral cracks, in contrast, can lead directly to


Lateral cracks form only when the normal load on the indenter has

exceeded a critical value, w*. The value of w* depends on the fracture

toughness of the material Kic and its hardness, H [68].

w*= (--)'K (2.5)

The ratio of H/Kji for a material provides a useful measure of its brittleness:

a low value of this brittleness index corresponds to a high value of w*, and

therefore indicates a material which is reluctant to fracture by indentation.

This mechanism for the abrasive wear of brittle materials is based on the

removal of material by lateral cracking. It is assumed that material is

removed as chips from the region bounded by the lateral cracks and the free

surface, and the volume wear rate, Q, is then estimated from the volume of

this region [77];

Q=a2N( K4H1 ) (2.6)
iKc H

where a2 and N are a geometric constant and number of particles,

respectively. In order to create this type of wear, the w here has to be equal

to or larger than w*. In other words, wear by fracture will occur only when

a critical load (yield strength) on each abrasive particle is exceeded.

2.3 Wear by Tribochemical Reaction

It is well known that friction and wear can cause chemical reaction to

proceed much faster than they would otherwise. A number of mechanisms

can be responsible for the kinetics of these tribochemical reaction [78-81]:

(1) local or general temperature can be increased due to the dissipation of

frictional energy; (2) the reaction products are removed periodically; (3) the

diffusion of reactants increases because of injection of lattice defects by

deformation and breaking of chemical bonds. The formation of the film and

dissolution of matter in the chemical liquids under friction are tribochemical

oxidation and hydrolysis reactions which occur only in the wear tracks. The

tribochemical reaction rate is as a function of the friction coefficient of

materials, traction force, and contacting velocity.

Tribochemical reaction can cause different results for different

materials: for A1203 in water vapor, the wear increases due to tribochemical

reaction; while for Si3N4 in high humidity environment, the wear decreases

due to the tribochemical reaction [82-84]. The tribochemical wear is not

primary wear in Si3N4 hybrid bearing system. The precise mechanism of

tribochemical wear is still not substantially understood.

2.4 Wear Mechanisms in Si3N

Although the theoretical treatments of wear mechanisms discussed

above are successful in explaining several aspects of observed behavior, they

have many limitations. In some cases, this is because the theory is

insufficiently developed and can not provide an accurate model for the

mechanism of wear which occurs. In other cases, the mechanism itself

differs significantly from that assumed in the model. In the case of Si3N4

wear in hybrid ball bearing applications, the observations of the wear

pattern on Si3N4 ball surfaces (Figure 1) are different from those described

with the above mechanisms for several reasons. First, the race in hybrid

bearings is made of M50 steel which has a much lower hardness about {8

GPa (DHP)} than silicon nitride hardness which is about 16 GPa. The ratio

of the hardness between Si3N4 and M50, HM5o/ Hsi3N4 is well below the

critical value, which could result in abrasive wear by plastic deformation.

Therefore, the wear mechanism by plastic deformation is not a contribution,

or at least not a major one, in silicon nitride wear. Second, the maximum

stress in the silicon nitride ball (compression/tension) in the hybrid ball

bearing operation is well below the yield stress. So, the mechanism for

abrasive wear of brittle materials, which is based on removal of material by

lateral cracking, is also unable to explain the wear in silicon nitride. Many

authors have described one of silicon nitride wear mechanisms as rolling

contact fatigue [13,15,24,86-88]. However, there are few documents which

explain in detail how and why the fatigue failure occurs in Si3N4 material.

So far, few precise models for silicon nitride wear in hybrid ball bearing

system have been developed, and the mechanisms of material removal in

this case remain unclear.

2.5 Apparent Study in Si3NA Wear

Interest in using silicon nitride as rolling bearing elements began two

decades ago. Baumgartner, Dalal and Chiu began to evaluate the wear

resistance of hot-pressed silicon nitride as a rolling bearing material in the

early 70's [89,90]. Since then, several investigators, promoted by the

increasing applications of silicon nitride in bearing systems, have explored

the wear, friction, tribochemical reaction, and fatigue behavior in Si3N4

bearing materials. Bhushan, Sibley, and Lucek [24,91] in their studies

indicated that the wear is a contact fatigue mechanism. High tensile stress in

the region just outside the contact area initiates a crack and then causes a

localized failure. Morrison and Pirvics [92,93] also found that spelling was

initiated from microporosity and foreign inclusions. Braza and Cheng [13]

in their investigation used a rolling sliding contact test and found that the

friction coefficient is governed by the type of contact rather than by the type

of material. Grain pull-out contributes to a high wear rate. Galbato and

Harris [15] conducted a silicon nitride wear investigation using two different

testing methods: one was the five ball rolling contact test, another was the

V-groove/ball rolling contact test. They also found silicon nitride failure

outside the race tracks which they called spelling failure and Fischer et al

[12,21] showed that a dramatic heat load could be created during high speed

and high stress rolling and sliding contact. These accumulated high

temperatures not only promote tribochemical reaction but also cause plastic

deformation in the silicon nitride. Fischer, Tomizawa, and Akazawa [12]

from their pin-on-disc experiment found that the tribochemical reaction was

involved in wear mechanisms when the environmental moisture increases.

Frictional deformation was observed in Adewoye's conical riders sliding on

a flat silicon nitride substrate test [22].

Considering spallation as a failure mechanism, the silicon nitride

bearing lifetime was estimated using the Lundberg-Palmgren formulation

based on statistical data [94,95]:

N2 =Ps, v4 \-3(E SiN4stee )-6.3 (2.6)
1N Psteel E'steel/steel

where N2, is the fatigue life-time of silicon nitride with steel bearings and

steel with steel bearings, respectively. E' is a reduced modulus which is

2/[(1-v,2)/El+(l-V22)/E2, E1,2 a Young's modulus of bodies 1 and 2,

respectively, and p is the material density. From this experimental equation,

the higher modulus leads to higher contact stress and thus lower fatigue life,

but the difference in density leads to even greater increases in fatigue life

(N2/N1j5) at high operating speeds where centrifugal loading is

predominant. These experiments indicated silicon nitride materials have

very good wear performance in high speed bearing applications, longer

fatigue lifetime and higher loading capacity.

However, the lifetime of silicon nitride bearing elements is much

shorter than the prediction due to the variation of defects. Spallation is

considered as one of many failure patterns in the bearing elements. Hadfield

and Stolarski found that artificially induced defects in the silicon nitride balls

can significantly reduce the ball lifetime [87]. In reality, the failure could be

initiated from random surface defects, such as pores, scratches, cracks, and

inclusions. The random defects result in the measured fatigue lifetime

values being scattered. It is obvious that the wear mechanisms obtained

from previous experiments were also greatly influenced by wear testing

methods, material defects and surface condition. Evaluation of a testing

method is dependent on whether the selected wear testing method can

represent the predominantly loading condition in bearing applications and

can result in a similar wear pattern to these observed in bearing applications.

Bhushan and Sibley [91] published silicon nitride sliding friction

coefficient data for various contacting materials and environments in 1981.

The friction coefficient between M50 and silicon nitride in different

lubricants range between 0.11 and 0.36. The low friction values indicate

that the tangential traction force on the contact surfaces in the systems is

very small and can be ignored without change in its primary loading



Most of Si3N4 failure in the hybrid ball bearing systems were

classified as local surface failure. The predominant failure appearances in

the surface are fracture patterns under cyclic contact fatigue. However, the

failure region is localized, not catastrophic. No evidence of plastic

deformation was observed [15, 21,24]. The wear is attributed to material

removal by fracture. Since most of the studies were based on rolling contact

fatigue and pin on disk experiments, the contact areas are not well defined

due to multiple contact paths on the rolling specimen surface. Stress states

could also overlap each other. All these factors make the study of the wear

initiation and development difficult. In addition, the high speed friction in

limited contact areas could create a significant localized temperature rise in

the contact area. Therefore, the wear process and failure appearances from

these tests may not precisely represent the failure patterns observed in the

silicon nitride hybrid bearing systems.

Recently, the incidence of failure related to microstructure defects and

surface finishing conditions has been substantially reduced by development

of more uniform, defect-free, dense silicon nitride materials and more

sophisticated surface finishing techniques. More substantial study of the

wear mechanisms in these advanced materials is needed in order to more

fully understand the performance of these materials in the bearing operation

based on their structural behavior aspects rather than their material defect

aspects. Far fewer investigations have evaluated the problems, such as

silicon nitride wear initiation and development, the influence of

microstructures on wear behavior, and wear surface topography, in hybrid

ball bearing systems.

2.6 Hertzian Stress

In rolling element bearing systems, the silicon nitride materials are

under a cyclic contact stress field during the bearing operations. This type of

stress state can be created in a plate by simply pressing a rigid hard ball on a

large flat brittle plate. The stress field was proposed by Hertz [96] and well

described by others [97]. The axisymmetric stress field is shown in Figure 4

under the following assumptions: (1) there is no traction force on the contact

surface (this is a reasonable assumption for the conditions of very low

friction coefficient between silicon nitride and M50 steel under liquid

lubricant) and (2) there is no plastic deformation in the materials under the

applied load. Therefore, the tensile stress field outside the contact area

creates a condition for crack initiation and propagation.







o (




0 0

C )C

: -5
0: | .


r- (M

Several investigators have studied the wear mechanisms of silicon

nitride materials under high contact stress [99-103]. Therefore, severe

plastic zones are initiated underneath the contact surface. These

investigators found that plastic deformation induces slip regions and creates

lateral cracks that then induce wear by removal of materials from these

damaged regions. Other investigators described the subsurface damage due

to a shear fault loop underneath the contact surface. It is difficult to

understand that a brittle structure will fracture under a shear stress within a

hydrostatic compression region. Obviously, the local plastic deformation

created using a indenter at high local pressure could result in structural

failure either on the surface or subsurface. .However, the stress field is

beyond the Hertzian stress field definition once plastic deformation occurs in

the contact region. Therefore, it is awkward using this mechanism to explain

wear in bearing systems which always operate under Hertzian stress field.

Other investigators observed that an unstable cone crack forms at a

characteristic load (KI>KIc) [98]. However, few investigators have studied

the stable cone crack initiation and growth in silicon nitride bearing

materials under Hertzian cyclic contact loading.


A mixed stress state created by Hertzian contact provides an

opportunity to investigate the failure mode for different materials. Many

material structures are operated under Hertzian type loading such as various

types of bearing operations.

Brittleness of the materials is an obvious factor which causes material

wear. However, the precise mechanisms of wear under contact fatigue stress

are not clearly determined. Several subjects need clarification and

examination: (1) wear initiation and development in silicon nitride bearing

materials under cyclic Hertzian contact stress; (2) the influence of material

structural aspects on wear; and (3) the relationship between the wear surface

and fracture surface.


3.1 Silicon Nitride Materials

Two types of silicon nitride bearing materials which are currently

widely used in bearing industries were selected as the test materials. One is

manufactured by Toshiba Co. and whose brand name is TSN-03H. It was

designated as type A. Another material is from Cerbec with a brand name

NBD-200. This material was designated as type B in this research. The

physical and mechanical data of these materials which were provided by the

manufactures are listed in Table 1. The geometric configuration of these

materials as supplied include about 10 mm diameter cylinders and 16x12x6

mm rectangular plates. The study focused more on type A materials rather

than type B because more type A material was available. Type B was used

for comparison purposes. The composition of type A is silicon nitride with

primarily Y203 and A1203 as sintering aids. The type B is silicon nitride

with primarily MgO as the sintering aid.


c o u




X o






a 0
.2 *-
0 t

c 5
(S ^i


r- o

0 0

m m


0, 0i

3.2 Microstructural Analysis

Specimens 10 mm in diameter and 3- mm in thickness were cut from

type A and type B silicon nitride rods, respectively. The specimens then

were ground using a 30 pmn and then a 15 pm metal bonded-diamond

polishing plates to remove any visible scratches or pits on the surfaces. An

automatic polishing machine then polished these samples until the samples

showed mirror-like surface. The measured surface roughness of all the

specimens was less than 6 nm.

Surface roughness is calculated from a surface image using the

compute software which comes with from NanoScape Ml. The Surface

roughness value, RMS, is the standard deviation of the Z values with the

given area and calculated using the following expression:

RMS = 2 (3.1)

where Zave is the average of the Z values within the given area, Zi is the

current Z value, and N is the number of points within the given area.

Two techniques were used to study the microstructure of the

materials. One of these techniques is plasma etching, that is, using corrosive

gases activated by plasma arc to react with the grain boundary phase. The

grain morphological image is created due to the grain boundary phase

removed by chemical reaction. This plasma etching was conducted by Pratt

and Whitney (West Palm Beach, FL). Scanning electron micrographs of the

resulting silicon nitride microstructure of etched samples were imaged by

JOEL 6400 SEM.

Another technique which was employed used the atomic force

microscope (AFM). The polished samples were directly analyzed using the

AFM. We take advantage of AFM's high 3-D resolution feature to identify

the different heights between boundaries and grains on the polished surface.

This tiny difference in the heights is due to the grain boundary phase and the

fact that the grains have different wear resistance during the polishing

process. The computer digital images of the resulting silicon nitride

microstructures were created using Digital's Nanoscope I.

3.3 Influence of Crack Size on Si.3N Strength and Toughness

The indentation-strength technique was applied to type A silicon

nitride. The geometry of the specimens used was 16 mm long, 12 mm wide

and 6 mm thick. The surface finish roughness was 1 pm. The initial flaws

were introduced using a Vickers diamond pyramid. Indentation loads were


0.1, 0.2, 0.5, 1, 2, 5, 7, 24 kg, respectively. Larger initial flaws in the

surface of specimens were created by applying multiple indentations. A

seven kilogram indentation load was used to make 5, 7, 9, 12, 15, and 25

impressions in different specimens, respectively, along the middle line of the

tensile surface perpendicular to the tensile stress direction. The distance

between each crack tip was kept within 10 pm. Indented samples were then

mounted in a 3 point fixture whose span distance was 10 mm. Cyclic

loading in a form of a half sine wave was applied to the samples. The cyclic

tensile stress range from 100 MPa to 0 MPa on the indented surface. Each

indented specimen experienced 300 loading cycles at 1 Hz frequency. The

purpose of this pre-cyclic loading is to release residual stress around the

crack tip, which was induced during indentation, and to link multiple indent

cracks into a large single crack. Afterwards, the specimens were fractured

using a three point-bend test fixture in an Instron test machine. The span

distance used was 12 mm and the displacement rate was 0.02 mm/sec. The

fracture strength a was calculated using:

3 = 2 (3.2)
w/ 2


where L is the span distance, P the load, and t and w the thickness and the

width, respectively. The critical flaw size, c, and mirror size r were

measured directly from the fracture surface under optical microscope. In

Figure 5, a schematic shows how to measure c and r. The mirror size r was

a larger value from r, and rr, where r1 is measured at the left side of mirror

boundary and rr is measured at the right side mirror boundary. The

toughness of type A material was measured using the following equation:

K, = 1.24a0 (3.3)

The reason to choose 1.24 as the crack geometry constant is because the

indentation residual stress has been released during cyclic loading.

3.4 Ball on Disc Contact Fatigue Test

Disc-shaped specimens of type A and B silicon nitride materials were

cut from 10 mm diameter rods in about 3-5 mm in thick. The specimens

then were ground down to 15 pm using diamond polishing plates in order to

remove any visible scratches or pits. An automatic polishing machine

further polished these samples until the surface roughness was less than 6

nm. A 4.76 mm (3/16") hard ball (WC) with surface roughness = 10 nm was

used as a rigid indenter. The ball was used to create a Hertzian stress in

Figure 5 Schematic showing a fracture surface. The initial flaw size c is
calculated using c = fab. r represents a mirror size which is a
larger value from ri and rr.

Si3N4 discs. Cyclic loading in the form of a half sine wave was used in the

experiment. The number of cycles which varied from 1 cycle to 5 million

cycles was chosen to examine the wear initiation and development in Si3N4

materials. A frequency range (5, 7, and 10 Hz) was used to investigate the

frequency effectiveness on fatigue lifetime of the materials. The maximum

contact stress was calculated using the following expression [97]:

6PE *2
ma=[ ( 3R2 )1/3 (3.4)


1 1_-v2 I V2
S + 2 (3.5)
E E, E2

and P is the applied load, R the radius of the indenter, El,2 and vi,2 the

Young's modulus and Poisson ratio of the disc and the indenter,

respectively. The different maximum compressive stresses (3.2, 7, 10, 15,

17, and 20 GPa) were applied to the specimens, respectively.

The strain in the Si3N4 due to contact loading is within the elastic

range. This was verified using the following experiment. A fine surface

finished silicon nitride disc was coated with about 50 nm thick Au-Pd. The

specimens then were loaded at different contact stresses. The Au-Pd coating

recorded the contact area corresponded to each loading level. The measured

radius a' of the contact areas was plotted with the calculated radius a of the

contact areas in Figure 6. The calculated radius a is given by an elastic

equation [97]:

a=( )1/3 (3.6)

When a load starts to cause the measured area deviation from the calculated

area, the load is a transition load. Loading above this value will result in

plastic strain occurring in the Si3N4. All the loads which were used in the

contact fatigue experiment were below the transition load. Considering the

advantage in test time, higher contact stresses than the stresses used in

bearing operations were used most of time in this experiment. The Hertzian

stress distributions within the Si3N4 material were calculated using the finite

element analysis method. This calculation was performed in collaboration

with Wright-Patterson Air Force Laboratory. The detail of this analysis is

described in Appendix A.

The contact fatigue test was designed to simulate the loading

condition in the Si3N4 hybrid ball bearing system under the assumption that

there is no external tangential traction force on the contact surface. This is

because very low friction between silicon nitride and M50 steel was

Figure 6 The plot shows measured radius a' of the contact area vs.
calculated radius a. Some inelastic deformation occurred in the
contact area after the contact stress exceeded 20 GPa (labeled
with solid triangles).

observed [91]. Hertzian contact stresses are applied to the silicon nitride

specimens using the WC ball. The tests were conducted in an MTS machine

using a load control mode. Exxon turbo oil. 2380 was used at the contact

surfaces as a lubricant. A schematic of the test method is shown in Figure 7.

From this test, two interesting regions were investigated. One was the

contact area where initial wear occurred. The whole wear process in this

area was able to be examined. Another was the tensile region which was

outside the contact area. From this region, the cone crack initiation,

propagation and its path were examined afterwards. This test method

provides total control in stress level, cyclic frequency and the number of

cycles. The stress state in the contact region is also well defined. Therefore,

the damage process (or wear process) under the contact stress region has be

closely monitored.

3.5 Diametral Compressive Fatigue Test

The diametral compression test was introduced by Carniero and

Barcellos in 1953 [104]. This test is primarily used to test the strength of

brittle materials because of the ease of simple preparation and simple

loading. The specimens fracture from interior (rather than at a free surface),

- Ball Holder

Exxon Turbo Oil
Si3N4 Disc

WC Ball
S Container

Figure 7 A schematic which exhibits the ball on disc contact
fatigue test.


and biaxial stress is produced within the test specimen (along the plane AB

in Figure 8). The biaxial stress state, which is similar to the stress state near

the contact area of rolling elements in the bearing systems, can be used to

study crack propagation. The configuration of the specimen is also ideal for

measurement of crack propagation in the materials. Moreover, the test can

also be used for in-situ monitoring crack growth under cyclic tensile and

compressive stresses simultaneously, when a pre-crack is induced in the

middle surface of the specimen using an indentation technique. If the

specimen is acted on by a pair of concentrated loads, the tensile stress ax

can be calculated based on classical plane elasticity [105, 106]:

o= (3.7)

where P is the applied concentrated load per unit length along the thickness

of the specimen, and R the radius of the sample. In reality, the load applied

on the specimen is distributed on a finite width instead of a line (Figure 9).

The tensile stress under a distributed load was calculated based on the

equation [107]:

P 1 2b +4(R-y)2 4(R-y)
S+ ) (3.8)
x 7(R b 2 (b2 +(R -y))2 ) b2 (3.8

where b is the half-width of the distributed load (Figure 9), and y the

Figure 8 Schematic showing a diametral compression test. A
biaxial stress state exists along plane AB which is
parallel to the loading direction.

distance from the center of the specimen along the radius parallel to the

loading direction. Therefore, the stress calculated from equation 3.7 is a

more accurate description of the stress state encountered by the specimen

than equation 3.6.

Different environments were employed in this experiment to study the

influence of environment on crack growth rate. A schematic of the testing

system is shown in Figure 10. Crack growth was monitored by a traveling

microscope. Precise measurement was conducted using an optical

microscope when the samples were removed from the testing machine after

experiencing a number of loading cycles. The specimens used in this

experiment were 10 mm in diameter and 2.5 mm in thickness. Both Type A

and B were used in this test for the purpose of comparison. The surfaces of

the specimens were polished and the surface roughness was less than 6 nm.

3.6 Characterization of Surface Geometry Using the Fractal Dimension

Two different techniques were used to experimentally measure the

fractal dimension. One technique used dental impression material to create a

negative replica of the fracture surface. After the replica dries, a positive of

the fracture surface is made by filling the cavity formed in the impression

Concentrated Loading

Distributed '

Figure 9 When an applied load is distributed on a width 2b, the
tensile stress cxx along plane AB shows that it is different
than the stress caused by the concentrated loading.

material with epoxy. After the epoxy is cured, the positive impression is

coated with an electroless nickel plating. The coated sample is then covered

by epoxy. The replica is now treated in the usual manner to produce slit

island contours by polishing approximately parallel to the fracture surface

(Figure 11). The detail of this process was described by Plaia[108]. The

second technique uses the atomic force microscope (AFM) [TopoMetrix,

Santa Clara, CA 95054]. The basic components of an AFM are shown in

Figure 12. The cantilever beam keeps a constant distance between the tip

and fracture surface by control of the beam angle. The distance between the

tip and the surface is determined by the atomic force between these two

materials. When the sample moves in the x-y plane, the change of the

surface profile is measured using PSPD (photo sensitive position

displacement) by detecting the angle change of the reflected laser beam from

the cantilever beam. The AFM creates a 3-D image directly from the

fracture surface. Packaged software then sections the 3-D fracture surface

image parallel to the fracture surface. This sectioning forms slit islands from

which the fractal dimension is obtained. Monotonic fracture surfaces,

fatigue fracture surfaces, and wear surfaces were used in this experiment to

investigate the link between the fracture surface and the wear surface.

Water or
Exxon Turbo Oil
Si3N4 Cylinder

- Disc Holder

Ij-j.Growing Crack
: 4 Container

A diametral compression fatigue test used to study
the influence of environment on crack growth.

Figure 10




S 0..

&I I

. I I -

I 0
cY L~~ I ~e 0


4.1 Microstructure of Si3N4 Bearing Materials

The mechanical properties of silicon nitride are greatly influenced by

its microstructure. SEM photomicrographs of Type A and B silicon nitride

after plasma etching are shown in Figure 13. These two specimens were

carefully prepared, to show the complete structure in 3-dimensions. In both

pictures, the p phase grains showed a rod-like grain structure. Type B has

some amount of very fine (0.1 pim or less) grain structure. The finer grains

generally are distributed among the intersections of large rod-like grains.

Type B also has some larger size rod-like grains, i.e., over 10 pm long and 2

pm wide. The shapes of all grains in Type B are irregular and nonuniform.

Type A shows more uniform grain structure and has very few large sized

grains. The cross-sections of all the rod-like grains have a hexagonal

geometry. Most of the grains in Type A are less than 2.5 pm long and about

0.5 pmn wide. Their aspect ratio is about 5. Closer examination of the

second sinteringg) phase distribution in the microstructure under high


SEM photos show the microstructures of Si3N4 bearing
materials in both 2 and 3-dimensions. (a) type A
material and (b) type B material.

Figure 13


magnification shows that most of the sintering phase material in Type A is

located at the triple-point of the grains (Figure 14 a). Only a very small

amount of sintering phase was found to exist along the grain boundaries in

Type A. In contrast, the sintering phase in the Type B microstructure is

uniformly distributed along the grain boundaries and has a much thicker

grain boundary phase than the grain boundary phase in Type A

microstructure (Figure 14 b).

Even though the plasma etching technique can give a clear picture of

the grain structure, the process is time consuming and expensive. Another

purpose of the characterization study was to try to find a new way to

characterize the microstructure in an easy and more cost effective way.

Observation of the wear process showed that material removal was easier

with softer and less wear resistant materials during the polishing process

than with harder and high wear resistant materials. After a certain amount of

polishing, differences in heights between the grain boundaries and grains

appear. The scanning electron microscope (SEM) has high resolution in the

lateral direction, but poor resolution in the vertical direction. The SEM can

not resolve height differences between grains and grain boundaries less than

20 nm. The atomic force microscope(AFM) uses a small tip, generally


Figure 14 High magnification pictures display that the sintering
phase is distributed in the triple-points (a) rather than
along the grain boundaries (b). (a) Shows Type A
material and (b) Type B material.

5-10 nm, to generate a profile of the surface. The AFM is non-destructive;

the tip uses van der Waals forces on the order of a 10 pN-1 pN to generate an

image. The basic components of an AFM were shown schematically in

Figure 12. The AFM has been widely used for the study of surface

topography and roughness on many types of materials, in part, because it is

non-destructive to the surface and requires little or no sample preparation.

Because of the differential hardness of Si3N4 grain boundaries, a Si3N4

surface polishes preferentially at the grain boundaries, revealing the grain

structure. Due to its high vertical resolution, the AFM is able to display

contrast between the grains and grain boundaries. The 2-D images created

by the AFM for both Type A and B are shown in Figure 15. The resulting

images of the grain structure are as accurate as those using plasma etching.

The AFM is also able to image 3-D microstructures. The 3-D images of

both materials are displayed in Figure 16. From 3-D images, it was found

that Si3N4 grains polish preferentially on the plane parallel to the c-axis of

the hexagonal crystal. Therefore, the polished surface shows that the faces

of these vertically oriented rod-like grains have higher altitude (with light

color in Figure 16). The information from 3-D images implies that

heterogeneous mechanical properties exist in the grain structure. In other


5.0 7.5

75.0 nM

37.5 nM

0.0 nn







4U.U nn

20.0 nn

0.0 nm



AFM images of Type A Si3N4 microstructure. In (a)
Type A microstructure, in (b) Type B microstructure.
The resulting images of the grain structure are as accurate
as those using plasma etching.

0 2.5

Figure 15

X 2.000 pn/div
2 75.000 nn/div

'i. 2^ 4

X 2.000 pM/div
2 40.000 nn/div

Figure 16 3-D AFM images, (a) Type A material and (b) Type B
material. Preferential polishing in the plane parallel to
the base plane of Si3N4 hexagonal structure indicates the
heterogeneous nature of the crystals.

words, the wear resistance on different crystalline planes of Si3N4 would be

expected to be different.

From the study of the microstructure, several conclusions can be

drawn and are described in this paragraph. Both microstructures of Type A

and B consist of rod-like grain structures. Type A microstructure shows that

it has more uniform grain size and structure than Type B. Type B has a

number of large size grains which disrupt the uniformity and could result in

localized residual stress. The sintering phase in Type B is distributed more

uniformly in the microstructure than Type A, but Type B also shows that it

has a thicker sintering phase along the grain boundaries than Type A. The

sintering phase in Type A preferentially concentrates at the triple-points of

the grains. The AFM's 3-D microstructural images indicate that different

Si3N4 crystalline planes have different mechanical properties. The basal

plane of hexagonal Si3N4 shows a higher wear resistance. The results further

imply the heterogeneous Si3N4 structures resulting in heterogeneous

mechanical properties. The heterogeneity of the grain structure could

enhance the mechanical damage due to the mechanical property mismatch

when the structure is under a large load. The AFM could provide an

additional tool in analysis of material microstructure with a more simple,

quick, and less-expensive way. The AFM microstructural analysis method

can be mostly automated and, as such, can rapidly obtain results. 3-D

images can be further employed to determine material heterogeneity.

4.2 Fracture Behavior of Si3N4

4.2.1 R-Curve Behavior

The fracture strength of Type A silicon nitride was measured as a

function of critical crack sizes. The strength data, critical crack sizes, and

fracture toughness values are listed in Table 2. In Figure 17 the strength is

plotted as a function of critical crack size c. Notably, the function (solid

line) shown in Figure 17 does not agree with the function described by

equation 2.1. The critical crack size, c, ranged from 6 pm to 800 pm. In

Figure 18, optical microscope photos of fracture surfaces with different

critical crack sizes are shown. The fracture strength shows a decrease with

increase in c. Type A Si3N4 exhibits strength sensitivity to crack size. The

fracture toughness of Type A was measured with different critical crack

sizes. Equation 3.2 was used for the toughness calculation. For Type A, KI,

increases with the critical crack size and displayed the so called "R" curve

behavior (Figure 19). The K1i was found to increase from 5.8 to 10 MPam1/2

Table 2 Fracture strength of, toughness KIc and c/r ratio of Type
A material are dependent on the critical crack size c.

c (pm) r (pml) af(MPa) Ki (MPaamz) c/r ratio
6.1 / 1887 5.8 /
9.8 / 1489 5.8 /
13.1 187.8 1229 5.5 0.40
16.3 202.3 1117 5.6 0.41
29.5 328.7 856 5.8 0.30
24.0 273.7 968 5.9 0.33
94.4 730.5 611 7.4 0.35
129.2 661.0 574 8.0 0.32
209.9 1001.8 479 8.7 0.34
227.1 1021.8 485 9.0 0.23
298.1 1249.6 466 9.6 0.20
292.8 1247.8 450 9.9 0.21
335.9 1478.3 455 10.3 0.16
336.9 1580.5 456 10.4 0.09
337.5 1352.2 433 9.8 0.09
392.6 1853.5 421 10.2 0.08
387.4 1748.7 413 10.3 0.07
825.4 / 296 10.5 /
817.0 / 283 10.0 /

* r is the mirror size of the fracture surface.

0 100 200 300 400 500 600 700 800 900

c (Qm)

The fracture strength of type A Si3N4 is a function of
critical crack size, c. However, the function does not
follow (the fracture mechanics) equation 2.1. The solid
line is a best fit to the data.





Figure 17




The fracture surfaces of Type A Si3N4 show different
appearances when the critical crack size increases from
small (a) to medium (b) to large (c).

Figure 18


S10 .

^ 6



0 100 200 300 400 500 600 700 800 900

c (Urm)

Figure 19 The toughness of type A Si3N4 displays "R" curve




with increasing crack size. This result indicates that the resistance to crack

growth increases with increase in initial crack length.

Several studies have proposed possible mechanisms responsible for R-

curve behavior in brittle materials [109-112]. Phase transformation, crack-

opening microstructural residual stress, elastic grain-bridging, and frictional

grain-pullout have been proposed as possible mechanisms for rising crack

resistance. From our microstructural study, the silicon nitride bearing

material consists of rod-like or "whisker-shaped" grains. These grains grow

in randomly oriented directions and are interwoven with one another. This

interweaving results in an additional mechanical interlock force causing

them to remain in close contact. Since silicon nitride has a very strong

covalent bond structure, most of the fracture in silicon nitride is through the

grain boundaries. When the cracks start to propagate through the grain

boundaries, the crack immediately faces an interlock force among the grains

which resists in the grains pulling apart during crack opening. This resistant

force is also called a crack bridging force. In Figure 20 a photo of grain

bridging in Type A material is shown. Some of the grains are seen to be

pulled-out and others fractured during the bridging process.

In order for bridging to occur, a growing crack has to be deflected

Grain-bridging toughening was found in type A

Figure 20

locally by grains into the grain boundaries. The bridging changes the strain

energy release rate AG by exerting a closure (bridging) stress on the crack

surfaces. The change in strain energy release rate can be expressed by the

following equation [113]:

AG = 2JP[u(x)Vu (4.1)

where P[u(x)] is the bridging stress 2u is the total crack surface opening at

a distance x from the crack tip, and u=u* at x=c. If grain bridging occurs in

the elastic range, AG can be expressed in the following form [113]:

AG = 2Pmax*(u*/um)()n
AGnl (4.2)

where Pmax is the maximum bridging stress, and umax is the maximum crack-

opening displacement that can be supported by the bridging grain at x=Db

(bridging zone size). The value for the constant n can be either 0.5 or 1

depending on whether elastic grain bridging deformation is restricted by

grain boundary friction, or elastic grain bridging deformation is continuous

until grain fracture or pull-out, respectively. The present experimental

observations that elastic grain bridging deformation is restricted by grain

boundary friction (n=0.5) is the most common case for Type A and Type B

silicon nitride bearing materials. In terms of a relationship between the

critical stress intensity factor Kic and AG, the expression can be written:

E' AG *2 1.5 E/2
K, = K(1+ k2 = Ko(1+4 +. (4.3)
o )3K~O

For maximum rising KIc, Ki, max, at c=Db and u*=umax, we have:

PmaxUmax E') 1/2
KIcma, = Ko (1+ (4.4)

where Ko is the material's intrinsic toughness (Ko = 5.8 MPam1/2 at the

smallest initial crack size), E' = E/(1-v2), E is the elastic modulus of the

material, and v is Poisson's ratio. From this equation, part of the rising Kig

is dependent on the grain boundary strength and grain boundary mechanical

interlock force which, in turn, is dependent on the shape of the grains. When

the crack length, c, is very small and u* is close to zero, the Kic is equal to

the intrinsic toughness Ko. With increasing crack size, c, the bridging force

starts to play a role in suppressing the crack opening and results in a rising

Ki. When the crack c = Db, and u*=umx, KIc reaches its maximum. High

grain boundary strength and longer interwoven grains produce a high crack

bridging force Pmax Longer grains and higher frictional forces along the

boundary increase the maximum crack opening displacement umax. Both

Pmax and uax help increase Kic when the crack size increases. From Table 2


and Figure 19, we see that K1i stays at about 5.8 MPam'/2 for a crack size of

c=6 pm until the crack gets larger than about 30 pm. For c=30 pm to 335

pm, the KIo rises at a very steep rate to reach a value of about 10 MPam1/2

From then on, K10 stays at about 10 MPam/2 for a wide range of c. The R-

curve behavior also indicates that the grain bridging zone size is about 335

pm. This is because when the crack is less than 30 prm, less than 10% of the

grain bridging effective zone acts as a closure stress on the crack surface and

no significant bridging occurs to increase KIc. After the crack increases to

greater than 335 pm which is the maximum bridging zone size, K, reaches

its maximum. Further increase in the crack size does not result in an

increase in bridging force and hence there is also no increase in KIc.

In figure 21, rf vs. c is again plotted and compared with crf obtained

from equation 2.1 (assuming no toughening by bridging), where KI, = 5.8

MPami2 (intrinsic toughness) and Y = 1.24. From Figure 21 when c is

larger than 335 tpm the difference between the two curve is constant

(Aacf155 MPa). At this point, Aof is an estimate of the maximum bridging

stress. This value reasonably agrees with the value of 105 MPa calculated

by Li [114].

Fracture surface analysis can be used to study the relationship

S1200- Measured af

600 f=Kc/[1.24 (c)], K =5.8 MPam"n

0 200 400 600 800 1000
0 200 400 600 800 1000

c lm

The maximum grain bridging stress can be measured
from the difference between experimentally measured
af and calculated of (from equation 2.1).

Figure 21


between crack size, crack branching size, and fracture energy. In this study,

we found that the ratio of the critical crack size c and mirror boundary size,

r, increases with an increase in c (Figure 22). The mirror boundary is where

the crack front at some locations starts to deviate from its original crack

plane and create more than one crack path [113]. Many criteria were

developed to explain the cause of crack branching [115-118]: (1) a velocity

criterion in which branching occurs when the crack velocity reaches a

maximum value (close to the sound velocity); (2) a critical stress intensity

factor criterion in which branching occurs when the stress intensity factor

reaches a critical value; (3) a strain intensity criterion requiring that the

strain energy available at the crack tip must be sufficient to form two cracks;

and (4) a energy criterion [61]. All these criteria have different explanations

but indicate crack branching needs a critical energy. However, the study

indicates that the c/r ratio is a material constant dependent on material

brittleness [117]. This is because Kic is a constant for glasses and most

monolithic ceramics. The present results show that the c/r ratio varies as a

function of the crack size. Previously, it was shown that there is an elastic

grain bridging stress on the crack surfaces when a crack propagates in

silicon nitride. This bridging stress balances part of the applied stress at the


The ratio of critical crack size c over mirror size r shows
a function of c in (a) and a function of r in (b).

*.4 0.4 -
1 0.3
" 0.2--

0 100 200 300 400 500
c (9m)

*" 0.35 -
5 0.15.
-0.05 500 1000 1500 2000 2500

r (im)

Figure 22

crack tip. Extra stress is needed to reach the critical stress intensity factor

Ki., at which crack starts propagation. Therefore, a longer crack has a

higher bridging force in suppressing crack opening and hence a higher

critical strain energy is needed to drive crack propagation. The grain

bridging, therefore, results in KI, as a function of the initial crack size c:

K, (c) = Yf Jr (4.5)

The stress intensity criterion Kg for crack branching is

KB = Yyf (4.6)

where failure stress af is the stress that causes the initial crack propagation,

and r is the mirror size. The branching starts at the maximum strain energy

release rate or at the maximum crack velocity [119]. Since the stress wave

velocity is a constant for an identical material, the crack velocity in the

material is dependent on the material and the stress level. Therefore, KB

should be a material constant based on equation 4.6. The curve of

normalized Kg (KI/K ) versus mirror size r is plotted in Figure 23. Ki is

one of 15 crack branching stress intensity constant measurements obtained

from 15 different fracture surfaces, where the superscript j is equal to 1, 2,

etc. up to 15. K, is one of the KL measured from a pair of of1 and r1 values

(equation 4.6). The curve in Figure 23 shows a straight line with slope zero



S0.8 -

04 Standard deviation is 0.056
4 0.4

0 500 1000 1500 2000 2500 3000 3500 4000
2r (tLm)

Figure 23

The normalized Kg (K /K ) value is independent of
the mirror size r. This indicates that Kg is a material
constant. The standard deviation for the average of
normalized Kg is 0.06.


and with a small standard deviation of 0.06. The result indicates that Kiis a

material constant regardless of the initial crack size. From equation 4.5 and

4.6, we have

K2 Yac
Y,- 2 YcK (4.7)

where Yrc=Y/Yc is a constant (Yr is about 1.24 when r is measured along the

tensile surface). Since Kg is a constant for the material, the ratio of c over r

increases with c. The c/r ratio totally depends on Kic, which is a function of

the initial crack size, c.

Material with a rod-like grain structure can increase the material's

capability to resist crack growth. The results of the present experiment

demonstrated that Type A material has a rising resistance to the crack

growth (R-curve behavior). Its rod-like grain structure acts as a grain

bridging stress on the crack faces to suppress the crack opening. However,

the R-curve behavior only has effect when the crack length, c, is greater than

30 pm. For small cracks which are usually found in bearing elements, the

R-curve behavior has little effect. In fact, localized residual stress could be

induced due to material and structural heterogeneity (rod-like grains). In

addition, thermal expansion anisotropy around rod-like grains has much

more influence on crack propagation at small size ranges (on the order of a

few grains). Therefore, a high aspect ratio of rod-like grain structure may

result in a decrease in material strength when small defects or flaws are

present in the material. The present research questions whether it is

recommended to develop material with R-curve behavior to be used in

bearing applications as a trade-off for material homogeneity. This design

decision should be considered in the future.

4.2.2 Crack Initiation

High quality silicon nitride is now being manufactured in which large

pores and inclusions are nearly eliminated. The question is: "what major

factors (if not large defects) cause material failure under fatigue loading?"

Fracture mechanics provides a theoretical basis for fracture analysis in brittle

materials. However, without fractographic analysis, the theory and failure

analysis will be handicapped, especially for materials which fracture

catastrophically after a number of loading cycles. In this case, the use of

fracture mechanics alone to conduct failure analysis is difficult. The

following experiment was the result of a collaboration with Torrington Co.

which performed the rotating cantilever beam preparation and rotating

cantilever beam fatigue tests. Two types of materials, Type A and Type B,

were tested. Failure origins were found in ten out of 30 samples. Failure

origins were difficult to identify in the rest of the samples because of

material loss during fracture. All of the 10 failures initiated internally from

regions rich in sintering phase material. No specimens were found in which

failure was initiated by surface defects. Figure 24a shows a typical Type A

failure origin. EDS identified that the Type A failure origin is rich in Y, Al,

and O (Figure 24b). For Type B samples, most of the origins were difficult

to identify due to material loss. This is because the Type B microstructure

consists of irregular-shaped grain with a wide range of sizes. The

microstructure seems to lack the mechanical interlock forces among the

grains and evidently results in surface grain pullout after fracture. This

phenomenon is surmised because of missing grains on the fracture surface.

In Figure 25, the photo of the Type B fracture surface shows some fracture

debris and loose grains on the surface. From some fracture surfaces, the

region from which the crack started was identified as a Mg and O rich


From the failure analysis, all the failures initiated in a glassy

sinteringg) phase rich region. This observation indicated that slow crack

C.r"or: O 000I.v 0 ROI '1) 0 00: 0 300C




A typical failure origin of Type A materials (a), EDS
spectrum displaying the composition in the failure
origin (b).

Figure 24

SEM photo showing a typical failure origin of Type B
Si3N4 rich in Mg and O.

Figure 25


growth may have occurred in the glassy phase rich region under fatigue

loading. The crack growth rate in the glassy phase region is dependent on

the stress level at its location and the amount of moisture (H20 molecules)

around it. The OH- ions or H20 molecules may exist in the material or

diffuse into the material from the outside surface. The crack growth rate, v,

can also be described as a function of stress intensity factor, K,i by the

following equation [120]:

v= ot'exp(- )K" (4.8)

where ca' is a constant, AH is the activation enthalpy of the reaction between

the glassy phase and water molecules, T is the temperature, R is

Boltzmann's constant, and n is a material constant which determines the

material sensitivity for slow crack growth. AH is generally found to be

temperature independent. For most of the oxide ceramics, n is a value in the

range of 10 to 20, e.g., n=16 [120] for alumina.

Crack growth rate depends not only on the stress intensity factor but

also on environmental factors such as the amount of moisture. Under a load,

crack growth in the material starts very slow at low KI because of the small

initial flaw size. The crack growth rate for pure A1203 in 50% humidity air

is less than 1011 m/sec under a 800 MPa stress. We assume that the initial

flaw size, c, from which the crack growth starts is plm, or about half the

grain size. The crack growth increases with KI due to an increase in flaw

size. After the crack grows to a critical size, which depends on the local

toughness, catastrophic fracture occurs. From one of the fatigue fracture

surfaces (Figure 26a), the fracture appearance is similar to a monotonic

fracture surface (Figure 26b). The resulting failure analysis indicates that

fatigue fracture in silicon nitride materials is a process which consists of a

slow crack growth for a small distance in the glassy phase and then

monotonic fracture when the stress intensity factor reaches a local critical

stress intensity factor.

Since most of the critical flaw sizes are very small (<18 pm), it is

difficult, if not impossible to measure them under an optical microscope due

to the limitation of the depth of field. The mirror boundary on the fractured

specimens appears clearly when visible white side light is properly directed

to the surface. The critical flaw size, c, was obtained from the c/r ratio using

the measured mirror radius, r. The c/r ratio is a function of r as shown in

Figure 22b. Using this method, the critical flaw size, c, of each fracture

surface was determined. The failure stress was calculated based on the

(a) A fatigue fracture surface is similar to (b) a
monotonically loaded fracture surface.

Figure 26

failure origin location y (distance between the origin and tensile surface)

using the equation:

M(R y)
S=,- 1 (4.9)

where M is the bending moment, I the moment of inertia of the specimen,

and R the radius of the cantilever beam at the fracture location (equal to 2.4

mm). The local critical stress intensity was calculated using the formula for

an embedded initial crack[121]:

K,C = a (4.10)

where Q is the flaw shape parameter (equal to 1.35 when the ratio of a/2b is

0.3). Equation 4.10 can then be expressed as:

K,, = 1.18r.o c (4.11)

The fracture surface analysis data are given in Table 3. The local

critical stress intensity was found to be about 3.4 MPam12 which is much

smaller than the toughness (about 5.8 MPam12) measured using indentation.

The results indicate that the materials prefer to fail from the lower local

critical stress intensity (Kic) region. The region with the lowest local KIo in

the material is the region rich with a glassy phase. Both the low toughness

of the glassy phase and the local residual stress due to heterogeneous

kr) 9t C CNC4 r4 c 11 CcI f-

rn 00 c?) r r; e;M e

...... .- .
C.) CCO ~i d-y)

C-00 C14tt
'n 00 1-- n 00

0\ \ID00 \O t
, r- ---4 C14 -q

C)Oo ON I-
00 00 00 t-- 00

1O 0W)00 kn O
tn W) OC 00

C) C4 11 Nt r- t t 10 k) 1,


~ 00 00c f


.. . . .. .. . .

I'D c0sC) C00
00 ItoOo=It
IC 00 00 o 00

00 00 00 00




cd 0


C) a)




C~~co 0
a) al)

ci~ a)0- a


bo o~

** +d i

m O N 00 CN


C> (O,\
"D o I' "

mechanical behavior may contribute to material failure at low stress intensity


This experiment clearly demonstrates that the local toughness of the

material determines the failure stress under cyclic loading. The fracture

surface analysis explained why materials always appear to fail at low stress

during fatigue loading.

The failure origins for both materials were identified using SEM and

fracture surface analysis. The crack initiated through a slow crack growth

process in the region rich in glassy phase. Catastrophic fracture occurred

when the stress intensity of the growing crack under cyclic fatigue loading

exceeds the local KI,. The location of the failure origin is dependent on the

size of glassy phase and the stress level in this region. No fatigue fracture

marks were found on the fracture surfaces in this experiment. Slow crack

growth was limited to a small region and then monotonic fracture takes over

the fatigue crack growth. The critical crack size and local fracture toughness

in the failure origin region can be determined using fracture surface analysis

by measuring the crack branching radii.

4.3 Contact Fatigue

In Figure 27b, an SEM photo shows the Si3N4 wear pattern that was

caused by the ball on disc fatigue test. A typical silicon nitride bearing ball

wear pattern caused by a bearing test is shown in Figure 27a. The wear

pattern in Figure 27a was caused by multiple contact fatigue damage, the

wear pattern in Figure 27b was caused by single contact fatigue damage.

Regions 1, 2, and 3 in Figure 27a exhibit a similarity to Hertzian cone type

fracture that is shown in region 4 of Figure 27b. It is concluded, then, that

the ball on disc contact fatigue testing method is appropriate for use in

studying silicon nitride material wear mechanisms in hybrid bearing


The ball on disc contact fatigue test data are listed in Table 4. The

wear process observed in these tests basically consisted of three different

stages (Figure 28): roughening of the contact surface (Stage I), cone crack

initiation and propagation (Stage II), and large volume of material removal

from outside the contact area (Stage mII). In the following sections, each

stage of wear will be discussed and the mechanisms of wear will be


Damage caused by bearing test after

30.6 IMcycles at ,,, = 3.58 GPa

Damage caused by ball on plate tes

after 1.7 Mcydes a a.., 17.0 GI

(a) A type hybrid bearing ball failure pattern and (b) a
Hertzain contact failure pattern from the ball on disc
contact fatigue test. Both of them show some similarity
in the egions labeled with the numbers such as 1, 2, 3,
and 4.

Figure 27


o o

0 0

o a t

0 o




0 0

o 0

0 0

oa :,

<^ oo S3

C. 0

- o
t0" 0 0 0000 0000
So oooo ro o0o o
ootN^ o O p0o
0 0 )
4-o C)

--4 -4 1 r--4 r--

.. . . .. . . .. . .


Q u
0 U

c c
0 0
0 0

o o

- -

&, &.
ic cn
ri CO



n m., (N m ooooO
..O oo;
In r0 0. 0 o,- "
o .-: t-0 t-~- 00
r^^ ^ o'- ^ o r r m.
C, n 0C>(q 1

Stame I Stage II Stage III

(a) (b) (c)

Figure 28 Wear due to the ball on disc contact fatigue test consists
of three different stages: (a) wear at Stage I, (b) wear at
Stage II, and (c) wear at Stage III.


4.3.1 Stage I Wear-Roughening on the Contact Surface

The Type A specimen was tested under a 3.2 GPa maximum stress at

10 Hz frequency. Figure 29a is the wear pattern after 5 million loading

cycles. The plot of roughness vs. its corresponding location on the contact

surface is shown in Figure 29b. Each location is represented by a letter A,

B, C, or D, respectively, corresponding to the location shown in Figure 29a.

An increase in the contact surface roughness indicates that wear has

occurred. For convenience in later discussion, the middle of the contact

surface (labeled with a letter A in Figure 29a) was designated as the central

region. The roughest area just outside the middle contact area was called the

outside central region (labeled with a letter B). The contact area was

examined under high magnification SEM. In the central region (Figure 30a),

most of the grain boundaries were damaged and a few grains were pulled out

from the surface. Away from the central region, many more grains were

lifted up in the outside central region shown in Figure 30b.

For theoretically dense brittle materials with covalent or ionic bonds,

it is difficult to fracture under a hydrostatic compression. This is because

none of three fracture modes in fracture mechanics can explain fracture

under hydrostatic compression. The questions raised here are: why



;) 75



0 25 50 75 100 125



I 20

a 10



(a) is AFM image resulting from a wear surface. (b) is a
plot of surface roughness vs. different locations on the
contact surface which is corresponding to the location
labeled in (a).

Figure 29

Wear surface topography, the picture in (a) shows wear at
the central region and the picture (b) wear at the outside
central region.

Figure 30