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FRACTURE AND DEFORMATION OF LiF BICRYSTALS
UNDER IMPACT EROSION AND QUASI-STATIC INDENTATION

by

Jong Yeon Lee

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of
DOCTOR OF PHILOSOPHY
Department of Metallurgy, Mechanics, and Materials Science

1985

ABSTRACT

FRACTURE AND DEFORMATION OF LiF BICRYSTALS
UNDER IMPACT EROSION AND QUASI-STATIC INDENTATION
by
JONG YEON LEE

LiF bicrystals were eroded by particle impact so as to understand
the role of grain boundary on fracture and deformation during impact
erosion. LiF bicrystals with grain boundaries possessing only tilt
character were eroded with blunt 0.5 mm quartz sand particles under normal
impact at room temperature. The damage patterns produced by impact of

1 were studied by

particles whose velocities ranged from 2.5 to 20 ms'
optical and scanning electron microscopy.
Experimental results of crack propagation caused by particle impact
are discussed and compared with the predictions by a model of mode I
crack propagation based on the normal stress law for brittle fracture.
Such an analysis implies that the crack propagation direction in crystals
with strong cleavage tendencies is mainly governed by the anisotropy of
surface energy, regardless of the method of the crack initiation. The
mechanism of material removal in LiF bicrystals under particle impact is
the interaction of lateral fractures with other lateral fractures or
grain boundaries. Fine slip occurs as a result of particle impact, and
such fine slip is usually blocked by the tilt boundary. Slip propagation

through the grain boundary was rarely observed under such conditions.

Damage caused by quasi-static indentation is compared with that due

 

 

to particle impact. Lateral fractures are not produced by quasi-static
indentation of the LiF bicrystals. Indentation loading produces wide
slip bands whose interaction with tilt boundary results in propagation

of slip through the boundary. The main factors influencing the slip
propagation through tilt boundaries under indentation loading are the
indentation distance from the grain boundary, relative crystallographic
orientation, and the magnitude of indentation load. The critical
indentation distance for slip propagation decreases as the misorientation
angle increases. In a semibrittle material like LiF, deformation and
fracture caused by quasi-static indentation are not representative of

damage resulting from particle impact.

ACKNOWLEDGEMENTS

The author wishes to express his deepest appreciation to his
advisor, Dr. Karatholuvu N. Subramanian, for his guidance and help
during the course of this study. He sincerely thanks also to his
graduate committee, Dr. R. Summitt, Dr. N. Altiero, Dr. C. Foiles,
and Dr. P. Schroeder, for their review and discussion. The entire
faculty and staff of the Department of Metallurgy, Mechanics, and
Materials Science are thanked for their assistance and helpful
discussion.

He is grateful to his fellow graduate students for their help
and friendship.

Finally, to his wife and two sons, the author expresses his

deep gratitude for their patience and encouragement.

ii

TABLE OF CONTENTS

Page
LIST OF TABLES ................................................. v
LIST OF FIGURES ................................................ vi
Chapter
I. INTRODUCTION .......................................... 1
1.1 Materials Selection ............................. 2
1.2 Crystallography of LiF .......................... 2
1.3 Objectives of This Research ..................... 3
II. THEORETICAL STUDIES AND HISTORICAL BACKGROUND ......... 7
2.1 Fracture and Deformation of Materials by
Impact Erosion .................................. 7
2.2 Fracture and Deformation of Materials by
Indentation ..................................... 13
2.3 Single Crystal Studies .......................... 19
2.3.1 Impact Erosion of Single Crystals ....... 19
2.3.2 Indentation of Single Crystals .......... 21
2.4 Role of Grain Boundaries on the Fracture and
Deformation of Materials ........................ 28
III. EXPERIMENTAL PROCEDURE ................................ 34
3.1 Bicrystal Growth and Specimen Preparation ....... 34
3.2 Impact Erosion Test ............................. 38
3.3 Indentation Test ................................ 41
3.4 Microscopic Studies ............................. 42

Page
IV. RESULTS AND DISCUSSION ..................................... 43
4.1 Damage Produced by Normal Particle Impact of Blunt
Projectiles .......................................... 43
4.1.1 Damage Produced by Normal Particle Impact on

the Cleavage Planes in the Region away from

the Grain Boundary ........................... 44
4.1.1.1 Crack Initiation and Propagation... 44
4.1.1.2 Slip Propagation ................... 57

4.1.2 Damage Produced by Normal Particle Impact on
the Cleavage Planes near the Grain Boundary.. 57
4.1.2.1 Crack Initiation and Propagation... 57

4.1.2.2 Mechanism of Material Removal under

Particle Impact .................... 69

4.1.2.3 Direction of Crack Propagation ..... 73

4.1.2.4 Slip Propagation ................... 89

4.2 Damage Produced by Quasi-static Indentation .......... 92

V. CONCLUSIONS ................................................. 108
BIBLIOGRAPHY ..................................................... 111

iv

LIST OF TABLES

TABLE Page
1 Chemical composition of LiF powder ........................ 36
2 Calculated values of fracture stress of LiF crystal ....... 8O

FIGURE

LIST OF FIGURES

Crystal structure of lithium fluoride .......................
Projection of {110} slip planes onto (001) surface of LiF
crystal ....................................................
Co-ordinate system for indentation stress field ............
(A). Displacement of material in the <110> directions
forming rows of edge dislocations by indentation on the
(001) surface of LiF crystal.

(8). Dislocation pattern for a indentation on the (001)
surface of MgO crystal ....................................
Arrangement of edge dislocations on

(A). indented, and

(B). cleaved surfaces

of M90 crystal ............................................
Slip planes and dislocation half-loops in indented MgO
crystal.

(A). {1101450 planes : (101), (101), (011), (011).

(B). {1101900 planes : (110), (110) .....................
Schematic drawing of indentation damage on (001) surface

of MgO crystal involving {101} <101> slip and <110> surface

cracking ..................................................

vi

Page

16

22

24

25

27

10
11

12

13
14

15

16

17

Page

(A). Co-ordinate axes in two adjacent grains.

(B). Relationship between the two systems of co-ordinates.. 3O
Passage of a dislocation from one crystal into the other ..... 31
Czochralski furnace used for growing LiF crystals ............ 35
Seed setting used for bicrystal growth.

(A). Schematic drawing.

(B). Top view .............................................. 37
Standard Ottawa quartz sand grains used as projectiles for
impact erosion (Average diameter : 0.5 mm) ................... 39
Schematic drawing of the erosion test setup .................. 40
Schematic drawings of the impacted damage on the (001) surface
of LiF crystal.

(A). Top view.

(B). Sectioned view ........................ - ................ 45

A typical crater and lateral fractures formed on the (001)

surface of LiF crystal by particle impact (p = 20°, V = 11 ms'l)
.............................................................. 46
Plot of the diameter of circle of contact as a function of
the velocity of projectile ................................... 47
Plot of the length of lateral fracture as a function of the
velocity of projectiles ...................................... 49

vii

18

19

20

21

22

Page

Schematic drawing of crack initiation mechanism by the
interaction of dislocations.

(A). Stroh’s model.

(B). Hashburn’s model.

(C). Keh’s model .......................................... 50
Craters and lateral fractures formed due to the particle

impact on the (001) surface of LiF crystal.

20 ms‘l.

(A). a = 20° v
(B). a = 30° v = 16 ms“ ............................... 54
Lateral fractures propagating along {100} planes as well as

along {110} planes due to particle impact on the (001)

° 1) ..............

surface of LiF crystal ( p = 20 , V = 5.5 ms' 55
Crater and lateral fractures in LiF single crystals due to
particle impact on the (001) surface. Continuation of
lateral fractures along non-cleavage surfaces as well as
along the cleavage planes, due to the compromise between the
Hertzian stress field and crystallographic nature of the
Specimen can be observed in this figure ( d = 20°, V = 20

ms'l) ....................................................... 56

Slip on {110} planes due to the particle impact on the (001)

1) .............

surface of LiF bicrystal ( d = 20°, v = 20 ms' 58

viii

23

24

25

26

27

28

Page

Slip lines formed along {110}450 slip planes as well as

along {llolgoo planes by particle impact on the (001)

1) ..........

surface of LiF bicrystal ( a = 6°, v = 2.5 ms' 59

Lateral fractures due to the particle impact blocked by

30°,v = 11 ms'1

the grain boundary ( d ) ................. 61
Interaction of lateral fractures caused by particle impact
with grain boundary. Lateral fractures that are blocked

by the grain boundary as well as those that propagate
through the grain boundary can be seen in these micrographs.

5.5 ms'l.

(A). a = 15° v
(b). D

Lateral fractures due to the particle impact in a region

II
N
O
S
in

1

30° v

very close to grain boundary. In this case, the lateral
fractures propagated across the grain boundary ( D = 45°,
V = 11 ms'l) ............................................... 63
Cracks initiated along the {100} primary cleavage planes

in addition to the {110} cleavage cracks ( d = 30°, V = 20
ms-1) ...................................................... 65
Intercrystalline and transcrystalline crack propagation

under particle impact.

(A). a = 20° v = 20 ms‘1

(B). Magnified view of (A) ............................... 66

ix

29

3O

31

32

33

34

Page

Crack branching in a specimen eroded by particle impact on
(001) plane.

(A). a = 30° v = 11 ms‘l.
(B). Magnified view of (A) ................................ 67
Discontinuous multiple cracks initiated in adjacent grain

from the grain boundary under the particle impact ( p = 20°,
v = 20 ms‘l) ................................................ 68
Lateral fractures and microfractures formed by particle

impact on the grain boundary.

(A). a = 30° v = 11 ms‘l.

(B). a = 15° v = 11 ms'1 .............................. 70
Severely curved lateral fractures formed by particle impact

near the grain boundary.

(A). d = 300 V = 16 ms'l. ’

(B). a = 30° v = 11 ms'1 .............................. 71
Lateral fractures intersecting with grain boundary causing
material removal. The segment (marked '*') in these figures

are the examples for such a mechanism of material loss.

(A). a = 1° v = 11 ms'l.

(B). a = 15° v = 16 ms‘1 ................................ 72
Intersection of lateral fractures with cleavage cracks along

the {110} 450 cleavage plane resulting in material removal
indicated by '*' ( a = 1°, v = 11 ms‘l) ...................... 74

35

36

37

38

39

40

Schematic drawing of Specimen surface illustrating
potential crack propagation directions for the case

of {100} crack interaction with grain boundary.

Specimen surface is (001) in both grains ................

Crack propagation mode for various 0 and s when (100)
crack in grain I intersects with a tilt boundary. ( d

is tilt angle and e is the angle between crack path in

grain I and grain boundary) .............................

Schematic drawing of specimen surface illustrating
potential crack propagation directions for the case of

(110) crack interaction with grain boundary. Specimen

surface is (001) in both grain ..........................

Crack propagation mode for various 0 and a when (110)
crack in grain I interacts with a tilt boundary. (0 is

tilt angle and e is the angle between crack path in

grain I and grain boundary) .............................

Blockage of slip lines (formed by particle impact) by

a tilt boundary ( d = 6°, V = 20 ms'l) ..................

Propagation of slip due to particle impact (near the
grain boundary) through the grain boundary in regions

marked 'X' and 'Y'.

5.5 ms-l.

11 ms'l.

(A). t = 5° v
(8). ¢

20° v

xi

Page

77

83

85

87

‘ 41

42

43

44

45

46

47

48

Page

Rosette patterns formed by particle impact on the
grain boundary.

(A). d
(B). ¢=2o° v

20° V

II
N
In
5‘.

ll
H
05
3
M

Typical dislocation rosette pattern produced by the
indentation in the grain boundary region ( d = 6°, P =
0.245 N) .............................................. 95
The relation between indentation load and the diagonal
length of indentation ................................. 99
Plot of diagonal length of indentation versus the

distance of travel of leading edge dislocation ........ 100
Dislocation pile-up and slip propagation through tilt
boundary under indentation loading.

(A). 16-
(3). a = 10° p

I
0‘
O
.0
ll

0.245 N.
0.490 N ......................... 102

Plot of distance between the grain boundary and

indentation site versus slip line length in adjacent

grain (grain II) ...................................... 103
Plot of misorientation angle versus critical

indentation distance for slip propagation ............. 105
Plot of indentation load versus the critical

indentation distance for slip propagation ............. 106

xii

I. INTRODUCTION

Mechanical damage introduced in materials by the impact of small
particles is of considerable academic and practical importance.
Materials can be eroded by the abrasive actions of solid particles
present in flowing liquids or compressed gases. Such erosion by
particle impact is a very common and important phenomenon since it can
cause significant material loss and mechanical degradation of the
material.

There are many examples illustrating the significance of erosion
by particle impact in engineering practice. Performance restrictions
on the useful life of gas turbine blades, coal conversion plants, rocket
nozzles, and helicopters operating in sandy region are based on such
erosion. On the other hand, the destructive aspects of the erosion
process are utilized in drilling, rock cutting, and sand blasting
operations.

Erosion of materials by particle impact is a complex process
involving fracture nucleation, growth, and interaction which leads to
removal of material from the exposed surface. Such complex erosion
behavior is affected by various factors such as fluid pressure,
temperature, particle velocity, particle shape and hardness, impingement
angle, and surface conditions and micro-structure of the target material.
There have been several investigations dealing with such environmental
factorsl'ls. However, most of those investigations have dealt with

macroscopic erosion behaviors of amorphous materials or fairly

complicated industrial materials containing a large number of grains and

8'15 As a result, obtaining a basic understanding of the

multiple phases.
mechanism of erosion under particle impact has been difficult. Studies
on simple model systems are essential to obtain a basic understanding of

erosion mechanism.

1.1 Material Selection

A simple model material is desirable for the investigation of
fundamental mechanisms of erosion by particle impact. A target material
which has well-defined slip systems and cleavage planes, and exhibits
both elastic and limited plastic contact behavior (semi-brittle) would
be appropriate for such a study concerned with microscopic aspects of
impact erosion. LiF bicrystal is an ideal model system for such
studies, since it will satisfy all of the above requirements. In addition,
LiF bicrystal possess only one grain boundary.

Some of the other advantages in using LiF for the present study are
the following: LiF is moderately plastic at room temperature and very
resistant to atmospheric corrosion. Grain boundaries and slip lines can
be observed clearly using etch pit techniques. Due to its low solubility
in water, the damage introduced by the particle impact can be preserved
during washing and etching process. Its optical transparency is also
helpful in determining the extent of damage caused by particle impact by

conventional optical microscopy.

1.2 Crystallography of LiF

 

Lithium fluoride is a transparent ionic crystal possessing rock-salt

structure which is actually an fcc lattice with a cation and an anion as

16

a basis. This structure is a nearly perfect example of ionic bonding

with alternate lattice sites occupied by cations (Li+) and anions (F') as

3

shown in figure 1. The unit cell is composed of two interpenetrating face
centered cubic structures, one of Li+ ions and one of F' ions, displaced
relative to each other by a distance of half the lattice parameter along
one of the three <100> directions.

The slip systems in LiF are simple ones. The primary slip planes are
the {110} type planes and the secondary slip planes are the {001} type.
The slip directions are <110> in both cases. There is only one <110>
direction in each {110} slip plane. The projection of the six {110} planes
onto the (001) plane is shown in figure 2. There is only one kind of mobile
dislocation in each active slip plane and hence the complication of
dislocations with different Burgers vectors to be found in the same slip
plane can be avoided. Since no two primary slip planes have the same slip
direction, cross-slip at room temperature is improbable. At room
temperature, the primary cleavage planes are {001} type planes and the

secondary cleavage planes are {110} type planes.

1.3 Objectives of This Research

The main objective of this study is to gain a better understanding of
the basic mechanism of erosion by particle impact. For this study, the
roles of microsc0pic deformation and fracture on erosion mechanism are
investigated experimentally by analyzing the mechanisms of the slip
propagation and material removal. The mechanisms of crack initiation and
propagation are also analyzed by comparing the experimental results with
the predictions of a model for mode I crack propagation based on normal
stress law for brittle fracture. Besides, the roles of relative
crystallographic orientation, grain boundary orientation, and particle
velocity is investigated experimentally since they affect the erosion

behavior of LiF bicrystals. A study of the damage introduced by quasi-static

Figure 1. Crystal structure of lithium fluoride.

Figure 2. Projection of {110} slip planes onto (001) surface
of LiF crystal (Ref. 17).

(101)[101]

 

(011)[011]

 

 

 

 

[100]

> [010]

 

 

indentation is also carried out in order to investigate the slip
propagation conditions in LiF bicrystals. By comparing the damage
produced by particle impact with that produced by indentation, the effect

of loading rate on the deformation and fracture is discussed.

II. THEORETICAL STUDIES AND HISTORICAL BACKGROUND

2.1 Fracture and Deformation of Materials by Impact Erosion

Hhen particles impact on the surface of material, they leave either

plastic impressions or small chipped regions at the region of impact.
The plastic impressions are formed when the stresses at the impact site
do not exceed the threshold value for fracture. In the elastic region,
the maximum tensile stresses are radial, and in the elastic/plastic
region, the maximum tensile stresses are tangential. 0n the other hand,
in the sub-surface, the maximum tensile stresses are approximately
parallel to the surface.18
Considering the directions of the maximum tensile stresses introduced
by particle impact, the radial cracks propagate from the contact zone on
planes normal to the surface, and the lateral cracks propagate outward
from the base of contact zone on planes nearly parallel to the surface.
The radial cracks are the main source of strength degradation of the
target material while the lateral cracks are responsible for material
removal by particle impact.19
Most theories of erosion of brittle materials are based on Hertz's

analysis of the stresses generated when an isotropic, linear elastic

surface is subjected to normal loading by a smooth spherical projectile.

The radius of circular elastic contact is given as20
a3=ikPR , (1)
4
where a is radius of the circular elastic contact,

P is applied normal load,

R is radius of spherical projectile,

 

 

v1 is Poisson's ratio of specimen,
02 is Poisson‘s ratio of projectile,
E1 is Young's modulus of specimen, and

E2 is Young's modulus of projectile.

The distance of mutual approach (Z) between the specimen surface
and the impacting particle is20
2

Z “3“ (2)

These two equations specify the loading conditions for particle impact.
The relationship between the applied normal load (P) and the

velocity of projectile (V) can be obtained by equating the kinetic

energy of the impacting particle to the strain energy at the time of

maximum impression:

.1 2 -.1
2 mV - 2 (

col-b

upR3IV2 = Igmax P(Z)dZ , (3)

where m is mass of the projectile, and

p is density of the projectile.

21

According to the solution by Timoshenko and Goodier , the maximum

contact load (Pm) is

l
15 35 s

P = 1.14 { m V R
m I?” (c1 + C2)2 1} . (4)

 

2
l'vl
where, C =
1 “E1 ’
and
1.-sz
C —
2 ["52

By relating equation (4) with the mass of the projectile and the
projectile density,
6 3

2
Pm=1.52R[ "V 9 2
(C1 + C2)

h—J
UflH‘

 

(5)

Thus, the maximum normal load can be related to the impact velocity and

radius of the particle:

01

,_ 25
Pm-CR . (5)

where C is a constant.

22

Rickerby et al modelled the impact process by assuming that all of

the kinetic energy of the particle is used in permanently deforming the
target, i.e.
2

-1
Pch - 2 mV , (7)

where pC is pressure over the contact area (dynamic hardness),
vc is crater volume, and
V is the velocity of projectile.

This equation can be rewritten as

10

P = . (8)
2nd2 ( d )
Where d is crater depth. Thus, the crater depth can be calculated by

this equation when the dynamic hardness value is known since other

parameters can be obtained experimentally. The dynamic hardness is the
resistance of a material to indentation under dynamic load, and can be

defined by using the equation given by Tabor.23

3 2
i "8 vr )

where, Hd is dynamic hardness,
m is the mass of the projectile,

V1 is the incident velocity of projectile,
V is the rebound velocity of projectile, and
v is the volume of the indentation.

From equation (9), dynamic hardness can be determined experimentally

by measuring the incident and rebound velocities of the projectile and
the size of the residual indentation.27

The crucial contact parameters in determining the mode and the

extent of the damage caused by particle impact are the pressure, the
contact radius, and the contact time. The pressure determines whether
the target response will be elastic or plastic, the contact radius
relates the pressure to the effective applied force, and the contact

time determines the force history. The pressure and contact radius can

be changed by changing the size and material of projectiles, and

11

the projectile velocity.

18, the

According to the investigations of Evans and Nilshaw
contact time of WC particles (400 um diameter) on ZnS target was found
to be 2.2 usec at the velocity of 520 m/sec. From the results of impact
erosion in Pyrex and soda-lime glasses impacted by small steel spheres

(800-1000 um), Knight et al 20

concluded that the reflected stress pulse
does not play a crucial role in the initiation of impact damage as
evidenced by the shorter contact time ( 51 usec),which is far less than
the time for the reflected wave to return to the contact zone ( > 2 u-
sec). Length of the contact time measured by Knight et al is very
similar to that obtained by Evans and Nilshaw.

24 studied the effect of material parameters

Hiederhorn and Hockey
on the erosion resistance of brittle materials by using SiC particles as
projectiles. The erosion rate of the brittle target materials was found
to decrease as the toughness of the target material increases. At 500
and 1000°C, the erosion rate of silicon and hot-pressed silicon nitride
increased slightly, whereas the erosion rate of glass, saphire, and
sintered aluminum oxide was reduced. By examining the morphology of
eroded surfaces they observed that as the toughness of the material
increased, the relative number of impacts that result in chipping is
reduced regardless of impact velocity.

In addition to the contact parameters, the ductility of the target
material is another important factor in determining the erosion mode. The
ductile erosion mode, which is typical in most metallic targets, is
characterized by maximum erosion occurring at an impact angle of about

25

30 degree. 0n the other hand, in ceramics and glasses, the brittle

erosion mode where maximum erosion occurs by normal impact is typical.

12
In brittle materials, Hoff et al 26 observed a critical velocity below
which there is no erosion and above which ceramics and glasses fail
rapidly due to severe crack propagation.
According to the investigations of Chaudhri et al27, most of
the energy of the impacting particle is dissipated in the plastic
deformation of the target material. The energy loss can be classified
as follows,
(i) the energy dissipated by the plastic flow of the target
material (major loss),
(ii) the energy of the elastic waves generated by impact (less than
10%)”.
(iii) surface energy of the cracks formed (less than 5%), and

(iv) kinetic energy of detached fragments (negligibly small).

Ashford29 recorded a fivefold reduction in the strength of silicon
carbide rods impacted by small steel spheres indicating that the
mechanical damage associated with particle impact can be severe although
the damage may be barely detectable by visual inspection. Hiederhorn and

Lawn30

studied the nature and extent of strength degradation in soda-lime
glass by impacting with spheres of steel and tungsten carbide.
Examination of the sections of impacted specimens revealed well-defined
cone cracks at low impact velocities. The threshold velocity for cone

formation was typically 10 to 20 ms'l.

At intermediate velocities median
cracks were initiated, and when the projectile velocity was high (50 to
100 ms'l), the median cracks provided the main source of degradation since
they extend deeper into the specimen. Also, at this stage, rapid
unloading caused the Hertzian cracks to bend back abruptly towards the

surface.

13

Knight et al 20

studied impact erosion in Pyrex and soda-lime
glasses impacted by small steel spheres. In Pyrex glass, well developed

cone cracks were observed outside the contact zone with semi-apex angle

of ~50° at the crack velocities of 1400 to 1500 ms'l. These cone cracks

turned up toward the surface during the unloading procedure. In soda-lime
glass, a large number of fine splinter cracks were initiated beneath the
impact site and propagated along the trajectories of maximum tensile
stress. Fracturing beneath the impact site was found to be completed
within 4 to 5 micro-seconds, and the maximum magnitude of the cone crack
angle was 630 in Pyrex glass. The impact damage observed by Evans and

Hilshaw18

under fully plastic contact conditions in ZnS has been shown to
be identical in form to that obtained by indentation, consisting of

radial, lateral and median cracks outside a plastic contact zone.

2.2 Fracture and Deformation of Materials by Indentation

The indentation test is probably the simplest method for obtaining a
measure of the strength of materials. It has two unique advantages:
(i) it can be applied to very small specimens which are in the general
form during development of materials on a laboratory scale, and (ii) it
is capable of measuring the fracture toughness of a material of small

31 The

size not suitable for conventional fracture toughness testing.
major disadvantage of this method is the detrimental effects of residual
stresses associated with the indentation on the over-all properties of
finished material.

The indentation is usually made by slowly pressing the indenter into
the solid and maintaining the load for several seconds. The representa-

27

tive strain rate is of the order 5 x 10'2/sec. Stress and strain

distributions due to several types of indentations in isotropic

14

continuous medium have been analyzed by using the continuum theory.

Those results can not be applied directly to single crystals having well-
defined slip systems and cleavage planes due to their anisotropic
character. This situation is also true when the size of the projectile
is smaller than individual grains in a polycrystalline solid.

In order to establish the nature of the indentation damage and
indentation stress field, it is necessary to specify the parameters such
as contact geometry, loading conditions, temperature, and mechanical
properties of the specimen in details as evidenced by the results
obtained by several investigators.32"40

The shape of the indenter is an important factor in detennining the
nature of contact geometry and the stress field. Indenters are
classified into two types: "blunt" indenters (shperes), characterized
by the formation of a Hertzian cone crack; and "sharp” indenters (pyramids,
cones), with a plastic contact resulting in the formation of median and
lateral cracks. When a pyramid indenter is used, the contact pressure is
independent of indent size, and thus a pyramid indenter is ideal for
indentation test.41

A Boussinesq stress field is developed when an isotropic, linear
elastic half-space is subjected to normal loading by a sharp indenter

such as pyramid indenter used in the Vickers hardness test. From the

contact geometry, the mean contact pressure can be expressed as

P0 = P2 , (10)

01rd

where Po is mean contact pressure,

P is applied load

a is
The Boussinesq

follows in the

13'

where P is

15

constant depending on the geometry of indenter (C = 1
for symmetric indenter), and

radius of contact area.

stress field due to sharp indenter can be written as

curvilinear coordinate system shown in figure 3:

 

applied load

radial distance from the point of contact, and

independent angular function.

42
In this coordinate system, the stress components can be written as

Q
ll

 

2 [{(‘lig! ) sec2‘§-- g-cos¢ si02¢ ] , (12)

°96 =T7-[(l§-g-‘i)(cos¢-%sec2g)l , (13)

022 =7";— (--23-COS3 ¢) 9 (14)
3 2 . )

°rz = -;r§- (- E-cos ¢ Sin ¢ , and (15)

a . Caz = 0 o (16)

16

Figure 3. Co-ordinate system for indentation stress field.

16(a)

 

 

 

 

17

The high stress concentration in the Boussinesq stress field can be

relieved by non-linear and inelastic deformation, and the stress field
becomes complicated due to the inelastic deformation. The stress field
through which the cracks must ultimately propagate is relatively ill-
defined, and tends to result in a more complex fracture pattern than in
the Hertzian stress field caused by spherical indenter.41

Hagan and Swain43 suggested that the deformation flow lines in the
subsurface region are responsible for the median, radial, and lateral
cracks that develop around indentations and ultimately lead to strength
degradation of brittle materials. The formation of the median cracks to
accommodate strains at the intersection of flow lines is just like crack
nucleation from dislocations on two intersecting slip planes.44’ 45
However, the lateral cracks are initiated at nuclei at the elastic/plastic
boundary or along the flow lines, and they are propagated by the unloading
residual stresses.

46

Lawn and Evans have obtained critical conditions for the

initiation of the sub-surface flaws by indentation. The minimum load

(Pc) to propagate the critical flaws is

K 3
PC = 2.2 x 104 ( ___|1{c ) K (17)

IC
where KIc is critical stress intensity factor and H is hardness. The

size of the corresponding critical flaw (C ) is given by

min

K
= __I.§_ 2
Cmin 44.2 ( H ) . (18)

. 41
By indentation of carbides with a Vickers indenter, PalmqVist found

that the load increased linearly with the crack length. By extending

18

48

Palmqvist's method, Dawihl and Altmeyer noticed that the dependence

of the crack length on the load was influenced by the character of the

surface, and eliminated this problem by carefully polishing the specimen

141, 42, 49

surface. Lawn et a established indentation as a technique for

the determination of the toughness of brittle materials by investigating
the indentation fracture. Lawn and Fuller carried out indentation tests on

soda-lime glass and discovered that crack length increased with load P as

49
P2/3. Crack length was observed to depend on the profile of the indenter

as well as on the friction coefficient between the specimen and indenter.

50

Evans observed radial cracks in $13N4 under pyramid indentation, but

they were not observed in relatively coarse grained materials ( :20 um
grain size).

51

Petrovic and Mendiratta investigated indentation - produced cracks

in hot-pressed silicon nitride by using diamond pyramid and Knoop
indenters. 0n the specimen surface, sharp cracks radiated from the
corners of the diamond pyramid indentation, while for the Knoop indentation

a sharp crack was observed along the long diagonal only under 25.5 N load.

These cracks correspond to the "median vents" described by Lawn et al41

52

By 50 N load indentation in fused silica glass, Hagan observed

median and lateral cracks around the impression in sectioned specimen.

He found that the dominant cracks in fused silica are cone cracks which
do not form in soda-lime glass of similar surface finish. Median cracks
were produced by the expansion of the compacted zone boundary beneath the
indentation, while the mismatch of strain at this boundary lead to lateral

crack formation during unloading.52

19

2.3 Single Crystal Studies

 

2.3.1 Impact erosion of single crystals

53'57 have studied the erosion behavior of single

Some investigators
crystals by particle impact in order to gain a better understanding of
the fundamental mechanism of erosion since single crystals are ideal
models due to their well-defined crystal structure. Although the impact
damage superficially resembles a Hertzian type fracture, the lateral
fractures do not completely follow the path predicted by the Hertzian
stress field; some compromise between the tendency for cracks to follow
stress trajectories and cleavage planes occurs in single crystals.

22 studied the influence of particle properties on

Rickerby et al
impact damage on mechanically polished {100} surfaces of LiF single
crystals by using steel and NC spheres at velocities ranging from 50 to
350 m sec'l. The typical damage which was observed by SEM consisted of a
central crater formed by a combination of {110} <110> slip and modes II
and III cleavage crack propagation, and a surrounding region from which
material loss occurred through intersection of {100} and {110} cleavage
cracks.22

Single crystals of NaCl, MgO and LiF were deformed by impacting with
glass and HC particles of diameter in the range of 0.4 - 1.0 mm, and
their deformation and fracture behavior was analyzed by Chaudhri et al.27
The dynamic hardness of these materials were determined and found to be
several times the quasi-static hardness. At high strain rates the
crystals were observed to behave in a brittle manner and the dynamic
hardness increased linearly as the strain rates increased.

The dislocation rosette size around the impact sites also increased

as the dynamic load increased. The material loss was found to occur both

20

during the loading and unloading parts of the impact.

Subramanian and Schuon55’ 57

investigated the microstructural
aspects of impact erosion in single crystals of LiF, NaCl, KCl, and

CaF2 by using glass beads (0.25 mm diameter) and standard Ottawa quartz
sand (0.5 mm diameter) as blunt projectiles. Some complete ring
fractures were observed at the impact site and lateral fractures spreaded

out from the contact zone. In NaCl and KCl, fractures on the (010)

planes were found to develop as a result of dislocation reaction:

(%)[011](01'1') + (%)[0111(011) + a[010](010) . (19)

In LiF, lateral fractures were formed through the dislocation reaction

(_%)[10'1'](101) + (%)[0111(011) + (gmioimz) . (20)

At 200 and 400°C, deformation was accommodated more easily in LiF
crystal since secondary slip system {100}<011> also became active.
Lateral fractures were not observed in specimens eroded at 400°C.
At normal impact, the length of the lateral fractures was found to
be proportional tthhe diameter of contact zone. In LiF, the observed
values of contact zone size were larger than the calculated values
according to Hertz's analysis by a factor of about 10. This difference was
attributed to the fact that plastic deformation is neglected in Hertz's
analysis.57
The critical velocity was found to be much lower in CaF2 than in more

ductile materials such as LiF, NaCl, and KCl indicating that the critical

velocity increases as the ductility of the material increases.

21

Micromachining was found to be a dominant mode of erosion in oblique
impact as proposed by Finnie58 when the impact angle is greater than 300

from the normal to the surface in LiF, NaCl, and KCl.

2.3.2 Indentation of Single Crystals

In order to establish the nature of the stress field introduced by
indentation, the mechanical anisotropy of the material is a critical
factor to be considered. For the investigations on the effect of
anisotropy of specimens during indentation, single crystals are ideal
models because they exhibit strong anisotropic character due to their
crystallographic nature. Some attempts have been made to study the
deformation mechanism associated with indentation in single crystals.60’ 61

By pyramid indentation of NaCl single crystal, Aerts et al.59 found
that the hardness depended somewhat on the orientation of the diagonals of
the indentation figures with respect to the crystallographic axes of the
lattice. Higher hardness values were obtained when one diagonal of the
indenter was parallel to [100] as compared to a situation when it was
parallel to [110]. This variation is attributed to the alteration in
shape of the indentation figure as a result of the crystallographic
anisotropy.60 By using the dislocation etch pit technique, Vaughan and
Davisson61 studied dislocation behavior in LiF single crystals by indenting
on (001) planes. They observed that the dislocation patterns consisted of
edge dislocations extended along the <110> directions, and those of screw
dislocations extended along the <100> directions. The insertion of the
indenter into a (001) plane of LiF displaces planes of material along the
<110> slip directions forming two rows of edge dislocations as shown in
figure 4(A).61

Keh60 studied dislocation rosette patterns produced by pyramidal and

Figure 4.

(A).

22

Displacement of material in the <110> directions
forming rows of edge dislocations by indentation
on the (001) surface of LiF crystal (Ref. 60).
Dislocation pattern for a indentation on the (001)

surface of MgO crystal (Ref. 60).

22(a)

IQ y ~( )~
«/\ 7’ Q /\
V <
3’
(A)
A———> [0101
( {110}450 {1101900

 

screw edge

 

23

spherical indenters on the cleaved surfaces of MgO single crystals,which
also have rock-salt structure. Etch pit studies of two-dimensional and
three-dimensional dislocation structures,as shown in figure 4(8) and 5.
revealed that all dislocation lines formed by indentation lie in the
{110} primary slip planes. Two of the slip planes are perpendicular to
(001) plane and can be referred to as {110}900 planes. Four other slip
planes are inclined at 450 to the (001) plane and can be referred to as
{110}450 planes. From the crystal structure of MgO and etch pit patterns,
the dislocation loops formed on the {110} type planes by indentation on
(001) planes can be sketched as shown in figure 6. In this figure the
etch pits in the <110> directions correspond to edge components since the
dislocation segments are perpendicular to the Burgers vector. Those in
the <100> direction are screw components because the dislocation segments
are parallel to the Burgers vector. By measuring the distances (0) of
travel of leading dislocations of the edge (e) and screw (s)

dislocations on the (110)450 and {110}900 planes, the following relations

were found by Keh.60
DS {110}450 ; 1.4 0e {110}900 , (21)
Ds {110}450 ; De {110}450 , and (22)
De {1101900 ; 20S (110)900 . (23)

During the process of indentation the material is pushed away from
the indenter and dislocations are formed along the slip planes. Thus, the
dislocations formed on the two sides of each wing are of opposite sign as

60

shown in figure 5. Keh observed that the dislocations with the same

sign as the applied shear stress moved out along their slip planes.

24

Figure 5. Arrangement of edge dislocations on
(A). indented, and
(B). cleaved surfaces

of MgO crystal (Ref. 60).

24(a)

/\

[110] [110]

T,»

5: 9%

51“?— plane of cleavage
M/g/K “are, SE}
//‘ \\<:(‘ ”C
Mr "T

(A)

/\

m1 [011] indented surface

“‘32 I", /
@‘o f} 6’»;
“3““ ’6" \$’>

C ‘eaifyy ‘V’v 9x5 C

V
T

C\

(B)

C:compression
T:tension

25

Figure 6. Slip planes and dislocation half-loops in indented
MgO crystal (Ref. 60).
(A). {1101450 planes: (101), (101), (011). (011)
(B). {11o}goo planes: (110), (110)

25(a)

   
 

’ .......
I

,’,’ (101) ,”

 

 

 

 

 

e : edge component

5 : screw component

26

Johnston found that in M90 the linear velocity of the edge component of a
dislocation half-loop is approximately 200 times that of a screw component

of another loop under the same applied shear stress in a homogeneous stress

60 observed that the dis-

field.60 However, by the indentation method, Keh
tance of travel of the edge component of the leading dislocation is approxi-
mately the same as that of the screw component indicating that the stress
field around an indentation is not homogeneous. Pyramid indentation on a
cleaved (001) surface of a MgO crystal with small loads of a few grams caused

60 With high indentation loads about 5 N

cracking in the <110> directions.
and above, irregular cracking was observed. Chemical polishing revealed
that these cracks were lying along the <110> direction and were present in
the {100}900 planes.

By indenting LiF single crystals at an indenter load of 10 N, Hagan62
observed shear cracks in the subsurface region. These shear cracks are
formed by the interaction of dislocations on intersecting (110)900 and

63 also studied plastic deformation zones

(101)450 planes. Armstrong and Wu
surrounding pyramid indentation in M90 single crystals. The total plastic
deformation seems to be accounted for by slip on the six {110} <110> slip
systems as shown in the figure 7. It was proposed that the edge
dislocations on adjacent slip systems interact and generate a sessile

dislocation which forms a nucleus for cracking on the (110) plane.63

G%)[1011(101) + (%)(0111(011) +- (§)11101(112) . (24)

The reacted (%)[110] edge dislocation with its line vector parallel to
07%r)[111] is sessile because it is contained in the (112) plane which is

not a slip plane in M90. According to their observation, four {110}

cracks spread outward from indentations on the (001) cleavage plane of MgO

27

Figure 7. Schematic drawing of indentation damage on (001)
surface of M90 crystal involvingilOl} <101> slip
and <110> surface cracking (Ref. 63).

 

27(a)

[001]

010

 

[100 V/ /‘ i,

am” :2
757/ i
é m

”WA 3

w
./ / [A

17‘

 

 

 

28

at 1 to 5 N load at room temperature.

2.4 Role of Grain Boundaries on Fracture and Deformation of Materials

Grain boundaries are the most important barrier to dislocation
motion during the early stages of plastic deformation of polycrystalline
solids. The influence of grain boundaries on the mechanical properties
of materials has long been recognized, and various theories and models
have been proposed for the structure of the boundary region between
adjacent crystals.

Dislocations pile-up on slip planes at grain boundaries during plastic
deformation. When the pile-up contains many dislocations, stress concentra-
tion of the order of the threshold shear stress can develop. However,
because of the difficulties in forcing a dislocation from one grain into

another, it is to be expected that slip will spread from one grain into its
neighbor by the process of introducing sources of dislocations in the
adjacent grain to become active.64

When the slip planes on either side of the grain boundary are almost
coplanar (small misorientation), the shear stress concentration ahead of
the dislocation pile-up results in slip propagation into the adjacent
grain and relaxes the stress concentration without forming cracks.

65 with MgO bicrystals

According to the investigations of Johnston et al
under compression, when a single slip band impinged upon the small tilt
boundary (0-50), both edge and screw type slip bands propagated across
the boundary without crack nucleation.

Sadananda and Marcinkowski66 analyzed the deformation of grain

boundaries geometrically by using the slip systems as reference co-

ordinate axes to describe the orientation of the two grains. As pointed

29

out Lange67, for a complete mathematical description of a boundary

separating two crystals, five parameters are necessary since such a
b0undary has five degrees of freedom. Figure 8 shows how the grain.
coundary is specified with respect to the two slip systems in adjacent
grains. 91 and 92 are the Burgers vectors and 31 and 32 are vectors
normal to the slip plane in grain I and II respectively. _r_i_I is the
outward normal to the boundary before deformation. The relation between
the two systems of coordinates is shown in figure 8(8). As illustrated
in figure 9, for the passage of a dislocation from grain I to grain II,
the magnitude of the Burgers vector and the interplanar distances need
not be the same in both the grains.66
The continuity of slip planes across the grain boundary is

66 A disturbance is

established by the presence of boundary dislocations.
left at the boundary when a dislocation passes from one grain to the
other due to the misorientation and the difference in magnitudes of the
slip vectors. Such a disturbance is characterized by an effective Burgers

vector (91) given by

.QI 3 (91 ' 992) a (25)
where 'a' is the directional cosine between primed and unprimed
co-ordinates axes as shown in figure 8(8).66 As a result of shear,
the boundary itself undergoes shape and orientation changes that can be
determined from the geometrical properties of the dislocations responsible

for the shear.65

Johnston et al 65

concluded that the probability of crack
nucleation by dislocation pile-up increases with increasing misorientation

across the grain boundary. They observed that edge bands({110}900)were

30

Figure 8. (A). Coordinate axes in two adjacent grains.
(8). Relationship between the two systems of

coordinates (Ref. 66).

30(a)

 

 

 

 

 

Grain 1 Grain Grain II
boundary
§2//nl
n
-I
X1//§
(A)
(nx'
-2 x
05 13
cos-la
12
1‘1
-1
cos all
’53
x

(B)

31

Figure 9. Passage of a dislocation from one crystal into the

other (Ref. 66).

31(a)

 

1:3

 

 

Grain II

 

Grain I Grain boundary

A: Magnitude of the Burgers vector

a: Interplanar distance

32

associated with transcrystalline cracks and screw bands({110}450)either
terminated at, or passed through, the boundary without forming cracks for

65 For a

a medium tilt plus medium twist boundary in M90 bicrystals.
large tilt plus large twist boundary, edge bands were associated with
intercrystalline cracks according to the classical Zener model.

Westwood68 proposed from the observations on MgO bicrystals that
cracks may be nucleated at a low angle grain boundary only through the
superposition of the tensile stress fields of two dislocation pile-ups
generated on both sides of the boundary.

69 showed that in silver chloride, the mode of slip

Carnahan et al
controls the role of grain boundaries on mechanical behavior. When
plastic deformation occurs by pencil glide, grain boundary has only a
minor effect on the flow stress. But, at temperatures where plastic
deformation is confined essentially to planar slip, they exert a strong
influence on the flow stress and fracture behavior. According to the

70, KCl single crystal can be extended by as

studies by Johnston et al
much as 40% at room temperature, while a KCl polycrystal fractures with
very limited macroscopic deformation, indicating the strong influence of
grain boundaries on deformation and fracture.

71 investigated the role of relative

Lee and Subramanian
crystallographic orientation and grain boundary orientation relative to
the crack front on crack propagation in LiF bicrystals. The anisotropy
in surface energy governs the direction of crack propagation due to the
strong cleavage tendency of LiF crystal. This was evidenced by the
observations that the crack paths change at the grain boundary according
to the crystallographic orientation of the adjacent grain, and grain

boundary orientation relative to the crack front. In the specimens

33

having small misorientation angles, transcrystalline crack propagation
along the primary cleavage planes was the dominant fracture mode. For
specific relative crystallographic misorientation and grain boundary
orientation, primary and secondary cleavage cracks were initiated
simultaneously at the grain boundary resulting in crack branching.
Intercrystalline fracture was also observed when the grain boundary
orientation angie is smaller than the critical angle at which inter-
crystalline fracture and transcrystalline cleavage occur simultaneously.
These results were consistent with a model based on surface energy

considerations.

III. EXPERIMENTAL PROCEDURE

 

3.1 Bicrystal Growth and Specimen Preparation

 

Lithium fluoride single crystals were grown by Czochralski method
(figure 10), using LiF single crystal seed. LiF melt was obtained by
heating LiF powder obtained from Kawecki Chemical Company in a graphite
crucible. The chemical composition of LiF stock is given in the table 1.
Details of the Czochralski furnace used and the condition employed
during crystal growth are the following: The heating element and
crucible were made of high density graphite (AUC), and the furnace was
water-cooled. Two chromel-alumel thermocouples were placed at
diametrically opposite points, and a potential-divider circuit was used
to find the average thermo-emf. Argon gas was used to provide an inert
furnace atmosphere. The crucible and the seed were rotated in opposite
directions at the rate of approximately one to two revolutions per minute
to obtain a homogeneous melt and a planar solid-liquid interface. The
crystals were grown at the rate of 6 to 12 mm per hour.

The single crystals were cleaved and used as seeds to grow LiF
bicrystals by the Czochralski method. The procedures for growing the
bicrystals by the Czochralski method were the same as those employed for
growing single crystals. In order to grow bicrystals having simple tilt
character, two seeds were held by two seed rods fixed parallel to each
other as shown in figure 11. The relative crystallographic orientation of
the two grains in the bicrysta1 was controlled by the setting of the two
seeds.

Bicrystal specimens having single tilt character were cleaved by

using chisel and hamner since (001) planes in both grains matched as a

34

35

Figure 10. Czochralski furnace used for growing LiF crystals.

35(a)

 

0.0....

3..
D u
.e:

 

36

Table 1. Chemical composition of LiF powder

(weight percent)

 

 

LiF 99.200 %
H20 0.700 %
SO4 0.050 %
Acidity as HF < 0.040 %
Fe203 < 0.020 %
Na < 0.005 %

 

 

 

37

Figure 11. Seed setting used for bicrystal growth.
(A). Schematic drawing.

(B). Top view.

 

 

(001)

f---_-_..---_-_-_-

 

(100)

 

37(a)

(A)

(B)

 

 

 

(010)

b ~— - - -

 

 

 

 

II

(001)

 

(100)

 

 

38

plane. The cleaved specimens were stored in a desiccator in order to
minimize degradation from moisture and mechanical damages. The specimens

used for the study were thin discs (3 mm thick, and 15 mm in diameter).

3.2 Impact Erosion Test

Standard Ottawa quartz sand was used as blunt projectiles. The
surface of the projectile is highly weathered and rounded as shown in
figure 12. To achieve a uniform particle size for the present
investigation, all particles were sieved with screens before being used
as projectiles. The average diameter of the sand particles was 0.5 mm
with a standard deviation of 0.02 mm. The quartz sand has a hardness of
approximately 7 on the Mohs' scale whereas the hardness of LiF is 3.

A schematic drawing of the test equipment used is shown in figure 13.
The setup was designed to feed sand particles into a stream of nitrogen
gas. Compressed nitrogen gas was used as the carrier medium accelerating
the projectiles to the desired velocity as they passed along a nozzle.
The projectile velocity was controlled by the pressure of the nitrogen
gas. The particle-nitrogen gas mixture was passed through a tube in order
to obtain a relatively uniform beam of projectiles. The projectile
velocities were measured by using double-flash exposure technique
controlled by a time delay controller. The range of time gap between two
flashes used in the present experiment was 0.1 - 10 m sec. Such a
technique is considered to be more accurate than the rotating disc method
developed by Ruff and Ives72 for measuring projectile velocities. The
specimens were held on an aluminum block at a distance of 2 cm below the
exit end of the nozzle to allow clearance for the timing disc to pass
between the nozzle and the specimen. The projectiles impacted at

approximately normal incidence at a velocity in the range of 2.5 to 20 ms'

1

39

Figure 12. Standard Ottawa quartz sand grains used as projectiles for
impact erosion.

(Average diameter: 0.5 mm)

33333

 

 

40

Figure 13. Schematic drawing of the erosion test setup.

 

 

 

 

 

 

 

 

 

 

110700 .4":

a
.l
v .
o I.
a . .
' I
I

 

 

   

 

41

onto the cleaved (001) surfaces of the specimens. Exposure time for
eroding was controlled by a timing disc with a 200 wedge. It was

rotated at a constant angular velocity of 11 RPM by using a motor. The

range of the total exposure time was from 1 to 3 seconds. After eroding,
the specimens were etched with a very dilute solution of ferric chloride
in distilled water (10'4 molal solution) in order to reveal the
dislocation etch pit patterns. These specimens were gold coated (about
100 A) in a sputtering unit to make LiF specimens electrically conductive
for SEM study. A slight pressure of argon gas was maintained in the

chamber in order to improve the quality of gold coating.

3.3 Indentation Test

 

In order to compare the damage patterns due to particle impact with
those produced by quasi-static indentation, indentation tests were also

18 in ZnS

carried out. The impact damage observed by Evans and Wilshaw
has been shown to be identical in form to that produced by quasi-static
indentation, consisting of radial, lateral, and median cracks outside a
plastic contact zone. A series of indentations, spaced 25 um apart, were
formed on (001) planes in the grain boundary region by means of 1360
Vickers diamond indenter using a micro-hardness tester. In one series,
the indentations were made with one of the diagonals of the indenter
parallel to the primary cleavage direction of the grain being indented.
Three different loads (0.245, 0.735, 1.225 N) were used for the
indentation. In another series, the diagonals of the indenter and
primary cleavage directions made 45° each other. After the size of the

indentations had been measured, the specimens were etched and gold

coated for SEM studies. The loading time used was about 10 seconds.

42

3.4 Microscopic Studies

 

By the etching procedure (15 to 20 seconds), grain boundaries and
slip lines were revealed clear enough to be observed by optical and
scanning electron microscopes. In addition to being a dislocation
etchant, the etchant used preferentially dissolved material at fracture
surfaces. This was helpful in revealing cracks that may be tightly
sealed and be invisible during optical microscopy prior to etching.

This characteristic of the etchant was helpful to reveal the very fine
fracture patterns around the impact site.

Optical and scanning electron microscopic studies were helpful in
determining fracture origins, estimation of the size and shape of the
damages, and in observation of fracture paths. Enhanced depth of focus
of SEM was helpful in studying the details of the damage in the impacted
region. These details could not be resolved by optical microscopy.

In the following chapters, grain I refers to the grain in which
impact or indentation occurred. Grain II refers to the grain adjacent to

the grain I.

IV. RESULTS AND DISCUSSION

 

4.1 Damage Produced By Normal Impact Of Blunt Projectiles

 

Several interesting aspects of the deformation and fracture behavior
of LiF bicrystals at high strain-rates produced by blunt particle impact
have emerged from the present investigations. A blunt projectile would
be expected to produce a Hertzian stress field which has been proposed

2 Such an

as a starting point for the analysis of impact erosion damage.
analysis is related to the classical Griffith theory of fracture for
elastic-brittle solids. Only normal impact method was used during this
research since normal impact causes maximum erosion in a semi-brittle
material as observed by Sheldonzs.

During the initial stages of the impact the target deforms
elastically, and as the impact pressure continues to increase beyond the

27 When

flow pressure of the target, the material deforms plastically.
the impact occurs on the (001) surface, slip takes place on {1101450 and
{110}900 planes which are inclined to the impacted surface at 45° and

90° respectively. According to Keh's model, {110} cracks are produced by
the interactions of dislocations gliding on {110} planes. Such a fracture

27

has been observed by Chaudhri et al also. Low-velocity impacts on (001)

surface of LiF produces only {110} cracks and (001) subsurface cleavage

27

cracks. As the impact velocity increases, (100) and (010) cleavage cracks

are also initiated and the initiation point of these cracks is about

50-100 um below the surface of the impact crater.27
Under the impact of a blunt projectile, very localized radial tensile

stresses are generate in the contact zone, and these tensile stresses

generate Hertzian cone cracks and give rise to the formation of (001)

43

44

cleavage cracks. By these stresses, some material is thrown upwards,
normal to the specimen surface, at the same velocity as that of the
rebounding projectiles.27 So, very high projectile impact velocities cause
material around the impact site to be detached from the crystal surface
in the form of small fragments.

Diagrammatic representations of the top and sectional views of the

major features of impact damage are shown in figure 14.

4.1.1 Damage_produced by Normal Particle Impact on the Cleavage Planes

 

in the Region away from the Grain Boundary

 

4.1.1.1 Crack Initiation and Pr0pagation

 

The micrographs taken in a region away from the grain boundary
represent the behavior of LiF single crystals under particle impact.
The contact zone for a blunt projectile is characterized by massive
plastic flow. Above the critical impact velocity, the damage is
characterized by a contact zone from which a set of lateral fractures
spread out. A typical crater and lateral fractures formed on (001)
surface at impact velocities above 2.5 m/sec is shown in figure 15. Four
main lateral fractures pr0pagated along the crystallographic cleavage
planes from the contact zone as evidenced by the linear shape and
perpendicular angular relation between them. Although severe plastic
flow and numerous microfractures occur inside the contact zone, usually
four major lateral fractures along the {110} cleavage planes are
developed outside the contact zone at low impact velocities. At normal
impact in the region away from the grain boundary, the diameter of the
contact zone increases linearly with increasing impact velocity as shown
in figure 16. These results are very similar to those obtained by Schuon

57

and Subramanian. They found that the experimentally measured values of

45

Figure 14. Schematic drawings of the impacted damage on the
(001) surface of LiF crystal (Ref. 27).
(A). Top view.

(B). Sectioned view.

45(a)

100) cleavage crack

  
 
 
   
   
 

(110) crack

residual 010) cleavage crack
indentation
region of

intense damage
subsidiary (100)

and (010) cracks

ubsurface (001) crack

(A)

region of
intense damage

  
 
 
   

 

 

subsurface (001) subsidiary cracks

cleavage crack

(010) cleavage crack (100) cleavage crack

(8)

46

Figure 15. A typical crater and lateral fractures formed
on the (001) surface of LiF crystal by particle

impact.

¢ = 20° v = 11 ms‘1

46(a)

 

47

Figure 16. Plot of the diameter of circle of contact as a

function of the velocity of projectile.

47(a)

22

 

 

20

16

14

12

10

r6

 

 

7O

60 7

0
5

q q u
nv nu nu
4 3 2

.E:. «umpcou .o mpugwo mgu mo cmpwEmwa

10 ‘

Velocity of the projectile (ms'l)

48

contact zone diameter are larger than the calculated values by a factor
of about 10. These calculations were carried out by using Hertz's
analysis. This discrepancy between theoretical and experimental values has
been suggested by them to stem from the neglect of plastic deformation in
the Hertz's analysis.

The length of lateral fractures also increases with increasing impact

velocity as shown in figure 17 at velocities below 20 ms'l.

55, 57

Schuon and
Subramanian also found same tendency in single crystals of NaCl,
KCl, and Can under particle impact. At higher velocities ranging from

1

50 to 200 ms" , Chaudhri et al found a tendency for the length of (110)

lateral cracks to approach limiting value in LiF single crystals.27
In LiF crystals, three types of cleavage cracks could be nucleated

73 is based on

by the interaction of slip dislocations. Stroh's model
the coalescence of piled-up dislocation. In this model, a crack forms
when the leading dislocations in a pile—up are forced to within a

distance 'b' (magnitude of Burgers vector) of one another. Washburn's

74 44, is associated with

model , which is a modification of Cottrell's model
the interaction of dislocations contained in the slip planes intersecting
perpendicularly each other. Keh's model45 is associated with the
interaction of dislocations contained in the slip planes intersecting
each other with an angle of 120°. The schematic illustrations of

these three models are drawn in figure 18.

The Washburn's model can be represented by the following equation:
a ' a '- _ '
E-[Olll + 51011] - a[010] . (26)

This reaction does not result in a change of elastic energy;

i.e., b +02 = b32 , (27)

49

Figure 17. Plot of the length of lateral fracture as a

function of the velocity of projectiles.

49(a)

 

 

 

 

7O

60..

50

u
d d

0 0 0
4 3 2

.s;. mssuomsm .msmuup mo space;

10

22

20

18

16

14

12

10

-1)

Velocity of the projectile (ms

Figure 18.

50

Schematic drawing of crack initiation mechanism
by the interaction of dislocations.

(A). Stroh's model (Ref. 73)

(B). Washburn's model (Ref. 74)

(C). Keh's model (Ref. 45)

50(a)

OBSTACLE

 

—>

 

(11°) ‘ .1. .1. 1.11

(A)

)
B
(

 

(C)

51

a -

where, b1 = E-[Oll] ,
- g '-

and £3 = aioio]

Washburn's model can be applied for the interaction of dislocations
contained in the {110} slip planes intersecting perpendicularly each
other, such as (001) plane with (011) plane,and (101) plane with (101)
plane. As can be seen in figure 18(8), cracks are initiated on {100}
type primary cleavage planes in Washburn's model.

Similarly, Keh's model can be represented by the following equation.

34011] + %[101] = gifio] . (28)

In this reaction, half of the elastic energy is released by the

dislocation interaction, i.e., 012 + 022 = 2632 , (29)

where g =§[011] ,

1
122 = %[1011 .
and b = 2{110]
3-3 2 '

Therefore, reaction (28) is more favorable than reaction (26). Keh's
model can be applied in the interaction of dislocations contained in the
{110} slip planes intersecting each other with an angle of 120° such
as (011) plane with (101) plane, (011) plane with (101) plane, (011)

52

plane with (101) plane, and (011) plane with (101) plane. By considering

the edge and screw components of the individual dislocations, reaction

(28) can be rewritten as following:74
a ' a " - a ‘ a"
71011] + 24101] - (61211]edge + 3[111]screw)
a -- a 7
+ (61121]edge + 311111screw )
_ a ' e --
- (6[211]edge + 6[121]edge )
a " a -
+ (31111]screw + 311111screw)
- a T
- i-[llO] + O . (30)

Thus, the two screw components cancel each other and the two edge
components combine together. Therefore the elastic energy due to the
coalescence of the screw components is released. The resultant

74 This

dislocation line vector %-a[110] lies on the (112) plane.
dislocation is immobile since (112) plane is not a slip plane in LiF
crystal due to its higher Peierls-Nabarro force than that of {110} planes.
Therefore, the dislocations generated on the two intersecting slip planes
(011) and (101) pile up against this immobile dislocation and initiate a
crack in the (110) plane as shown in figure 18(0). The intersections of

these cracks with the (001) surface are along <110> directions, as

53

evidenced by the four lateral fractures propagated along <110> directions
as indicated in figure 19. These four lateral fractures which are formed
along the <110> directions are associated with Keh's model. Since LiF has
cubic symmetry, there are four {110} planes of symmetry for blunt projectiles
impacting in the [001] direction onto the (001) surface. As can be
observed in the micrographs presented in figure 19, this type of lateral
fractures along the <110> directions are the dominant feature of crack
propagation caused by the particle impact on (001) surfaces. Moreover, the
directions of these dominant lateral fractures coincide with those of the
leading edge dislocation etch pits which are formed along <110> directions
on the {110}900 slip planes. The fact that these lateral fractures lie in
the {110}900 planes can be also confirmed easily by chemically polishing
down the specimen surface and examining the cracks underneath.
Occasionally, lateral fractures along the <100> directions were also
observed, indicating that crack nucleation according to Washburn's model,

74 This feature can

along {100} primary cleavage planes was also Operative.
be observed in figure 20. Primary {1001 cleavage planes made 45° with
secondary {110} cleavage planes. Such a lateral fracture along {100} can
be also formed by the mode I crack mechanism due to the crack opening
tensile stress caused by the particle impact and crater formation process.
In crystals with strong cleavage tendencies, there is some
compromise between the tendencies for cracks to follow stress trajectories
and to follow cleavage planes. Crystallographic nature of cleavage and the
presence of Hertzian stress field results in a compromise in crack
propagation; fracture occurs along the non-cleavage surfaces as well as

along the cleavage planes due to this compromise, as can be observed in

figure 21. Such non-cleavage cracks were never observed in LiF bicrystals

54

Figure 19. Craters and lateral fractures formed due to
the particle impact on the (001) surface of
LiF crystal.
(A). a = 20° v
(8). ¢ = 30° v

20 ms"1

16 ms'1

54(a)

 

M-I -_- " '-

55

Figure 20. Lateral fractures propagating along {100}
planes as well as along {110} planes due to
particle impact on the (001) surface of LiF
crystal.

6 = 20° v = 5.5 ms'1

55(a)

 

Figure 21.

56

Crater and lateral fractures in LiF single crystals
due to particle impact on the (001) surface.
Continuation of lateral fractures along non-cleavage
surfaces as well as along the cleavage planes, due
to the compromise between the Hertzian stress field
and crystallographic nature of the specimen can be

observed in this figure.

¢ = 200 V = 20 ms'1

56(a)

 

57

under mode I crack propagation due to its strong anisotropic character as

analyzed by Lee and Subramanian.71

4.1.1.2 Slip Propagation
60

 

According to Keh , all dislocation lines formed by indentation on
(001) surface of MgO single crystal lie in the {110} primary slip planes,
and the leading edge dislocations propagate along <110> directions on the
{llolgoo slip planes under such conditions.

In case of particle impact on (001) surface of LiF bicrystal, etch
pit patterns similar to those obtained by Keh were observed as shown in
figure 22, since LiF and MgO have the same crystal structure.
Specifically, these two planes are (110) and (110) planes. The fact that
the leading edge dislocations propagate along <110> directions can be
easily confirmed by measuring the angles between slip lines and the {100}
primary cleavage planes formed by cleaving with chisel and hammer.

In addition to the two {110}9oo slip planes, four {110}450 slip
planes are also activated due to the shear stress caused by particle
impact as can be observed in figure 23. The presence of all these slip
systems produces a characteristic “rosette" pattern as presented in
figure 23. In this micrograph, the rosette pattern is symmetric since

the direction of impact site is normal to the surface and the grain

boundary is far from the impact site.

4.1.2 Damage produced by normal particle impact on the cleavage planes
near the_grain boundary
4.1.2.1 Crack Initiation and Prgpagation
When the plastic deformation is confined essentially to planar slip,

grain boundaries exert a strong influence on the flow stress and the

58

Figure 22. Slip on {110} planes due to the particle impact

on the (001) surface of LiF bicrystal.

a = 20° v = 20 ms’1

58(a)

 

59

Figure 23. Slip lines fOrmed along {1101450 slip planes as
well as along {1101900 planes by particle impact
on the (001) surface of LiF bicrystal.

¢ = 6° v = 2.5 ms‘1

59(a)

 

60

fracture behavior.65 Westwood68 concluded from the observations on MgO
bicrystals that cracks may be nucleated at a low angle grain boundary
through the superposition of the tensile stress field of two dislocation
pile-ups generated on both sides of the boundary.

In this present study, impact load is applied only on one grain since
the particle size is much smaller than the size of each grain. Due to
the existence of grain boundary near the impact site and the Hertzian
stress field introduced by the particle impact near the grain boundary,
the shapes of craters and lateral fractures are more complicated as
compared to those formed by particle impact in a region away from the
grain boundary.

As can be seen in figure 24, some lateral fractures are blocked by
the grain boundary indicating the strong influence of the crystallographic
misorientation on crack prOpagation. In bicrystal specimens having small
tilt angle, such blockage was observed less frequently than in the case
of the specimens having large tilt angle, implying that the resistance of
grain boundary against the crack prOpagation increases as the magnitude
of tilt angle increases.

When the impact occurred in a region close enough to the grain
boundary, transcrystalline crack propagation was also observed in
addition to the blockage of lateral fractures as can be observed in
figure 25. In figure 25, one crack which was initiated along the (110)
cleavage plane in grain I propagated across the grain boundary into the
grain 11 along the (100) primary cleavage plane. As can be seen in
figure 26, most of the lateral fractures prOpagated across the grain
boundary when the particle impact occurred in a region very close to the

grain boundary.

61

Figure 24. Lateral fractures due to the particle impact

blocked by the grain boundary.

0 = 30° v = 11 ms'1

61(a)

 

Figure 25.

62

Interaction of lateral fractures caused by particle
impact with grain boundary. Lateral fractures
that are blocked by the grain boundary as well as
those that propagate through the grain boundary can
be seen in these micrographs.

(A). ¢ = 15° v = 5.5 ms'1

(8). p = 30° v = 20 ms'1

62(a)

 

 

 

63

Figure 26. Lateral fractures due to the particle impact
in a region very close to grain boundary.

In this case, the lateral fractures propagated

across the grain boundary.

a = 45° v = 11 ms’1

7i
63(a) ‘

 

 

64

In some cases, as shown in figure 27, cracks also initiated along
the (100) primary cleavage plane in addition to the (110) cleavage in
grain I and propagated along the (100) plane in grain II implying that
direction of crack propagation is based on which cleavage plane the
resolved normal stress first reaches the fracture stress of that plane.

Under particle impact, intercrystalline crack prOpagation was also
observed in addition to the transcrystalline crack propagation, as can be
observed in figure 28. In this case, the resolved normal stress on grain
boundary should have first reached the fracture stress of grain boundary
surface. Although LiF shows very strong cleavage tendencies at room
temperature, intercrystalline crack prOpagation is also possible due to
the dynamic loading conditions and stress concentration at the grain
boundary.

In some cases, crack branching was also observed as can be seen in
figure 29. Due to the existence of grain boundary near the impact site,
one non-cleavage crack (marked '*') was initiated in grain I and
propagated toward the grain boundary. This non-cleavage crack made two
branches along the (110) and (100) cleavage planes. The direction of
(110) cleavage crack coincides with the [110] primary slip direction, and
the two branched lateral fractures make 45°.

Multiple cracks were also initiated in the adjacent grain from the
grain boundary under the particle impact as can be observed in figure 30.
By recognizing that these multiple cracks are not in contact with cracks
formed by particle impact, one can conclude that these mu.tiple cracks are
formed by the tensile stress components in the Hertzian stress field
introduced by particle impact.

Occasionally, when particle impact occurred exactly on the grain

65

Figure 27. Cracks initiated along the {100} primary cleavage

planes in addition to the {110} cleavage cracks.

¢ = 30° v = 20 ms'1

65(a)

 

66

Figure 28. Intercrystalline and transcrystalline crack
propagation under particle impact.
(A). a = 20° v = 20 ms'1

(8). Magnified view of (A).

66(a)

 

 

67

Figure 29. Crack branching in a specimen eroded by particle
impact on (001) plane.
(A). a = 30° v = 11 ms‘1
(8). Magnified view of (A).

67(a)

 

68

Figure 30. Discontinuous multiple cracks initiated in
adjacent grain from the grain boundary under
the particle impact.

d = 200 V = 20 ms-1

68(a)

 

 

69

boundary as can be observed in figure 31, two sets of lateral fractures
along the {110} planes were observed in each grain. Microfracture within
the region of contact is extensive as can be observed in figure 31(8).
These microfractures departed from cleavage planes and produced numerous
microcrystals. During plastic flow, these microcrystals may become

reoriented and possibly form curved boundaries.

4.1.2.2 Mechanism of Material Removal under Particle Impact

The main mechanism of material removal under impact erosion is the
intersection of lateral fracture with another lateral fracture or grain
boundary.

Lateral fractures propagate radially outward from the impact site
without any intersections between them. Therefore, material loss was
seldom observed during single impact by blunt projectiles on LiF single
crystals. Material removal under such cases usually occurs by multiple

57 On the other hand, even one single impact on LiF bicrystals

impact.
can produce material loss as can be observed in figures 32-34. In the
case of the impact damage shown in figure 32, severely curved lateral
fractures aid material removal process. Such lateral fractures form due
to the presence of grain boundary near the impact site and stress
distribution caused by dynamic loading near the grain boundary. Such a
feature has never been observed in a region away from the grain boundary
during the course of this investigation.

In the case of the impact damage shown in figure 33, lateral
fractures intersected with grain boundary resulting in material removal.
Such a feature emphasizes the important role of grain boundaries on

material removal during particle impact. The segment in figure 33(8)

(marked '*') is an example for such a mechanism of material loss.

70

Figure 31. Lateral fractures and microfractures formed by
particle impact on the grain boundary.
(A). p = 30° v 1
(8). d = 15° v

11 ms'
1

11 ms-

70(a)

 

 

.324: vs '
57 a; vglé: 1!.-

I.-

, as
‘3 47‘

  

 

Figure 32.

Severely
particle
(A). 95

71

curved lateral fractures formed by

impact near the grain boundary.

= 30° v = 16 ms'1

(8). ¢ = 30° v = 11 ms‘1

 

 

71(a)

 

 

Figure 33.

72

Lateral fractures intersecting with grain boundary
causing material removal. The segment (marked '*')

in these figures are the examples for such a mechanism

of material loss.
(A). p = 1° v
(8). ¢ = 15° v

11 ms‘1

1

16 ms-

72(a)

 

 

 

73

Intersection of lateral fractures with cleavage cracks along the
{110}450 plane is also another possible mechanism for the material removal
as can be identified in figure 34. Such a mechanism can also occur in a
region away from the grain boundary.

Material loss occurs both during the loading and unloading parts of
the impact.27 During loading, material flows plastically along (1101450
slip planes. At high velocities the inertia of this deformed material

causes material removal during the rebound of projectiles.

4.1.2.3 Direction of Crack PrOpagation

The condition which determines the extension of a crack can be

expressed in terms of the total energy for a quasi-static system.41
U=('NL+UE)+US a (31)

where WL is the work of the applied forces,
UE is the elastic strain energy in the cracked body, and

US is the total surface energy.

Since ( -WL + UE ) decreases while US increases with crack extension, an
energy interchange occurs between them. The variation of the energy terms

becomes as following with respect to crack area (C).

du - d (-WL + UE) + dUS

dc dc dc ’

 

‘6 T 2'Y 9 (32)

where G is the mechanical energy release-rate and y is the fracture

74

Figure 34. Intersection of lateral fractures with cleavage
cracks along the {110}450 cleavage plane resulting
in material removal (indicated by '*').

¢ = 1° v = 11 ms'1

74(a)

’7 3'
a“

9

I

.

'*_ ”site-é;

Azfé

 

75

surface energy.
Cracks tend to propagate along trajectories of lesser principal
stresses, thereby maintaining near-orthogonality to a major component of

75 For an ideally brittle solid, the relative orientation of an

tension.
incremental extension dc is that which maximizes the quantity (G-2y). For
anisotrOpic solids, it is necessary to take into account the orientation
dependence of both elastic constants and surface energy in determining
maxima in (G-Zy). Clearly, in crystals with strong cleavage tendencies
the anisotropy in y will govern the direction of crack prOpagation.41
However, some compromise occurs between the tendencies for cracks to
follow stress trajectories and cleavage planes.

7° normal stress law for the brittle

According to the Sohncke's
fracture, the cleavage of a single crystal occurs when the resolved normal
stress on the cleavage plane reaches a critical value. Such feature
of brittle fracture was fully identified in a model established

71 using LiF bicrystals. In that

experimentally by Lee and Subramanian
study, mode I loading method was used for the initiation of cleavage crack.
This method is extended in this investigation in order to analyze the
crack prOpagation mechanism under impact loading since the specimens are
very similar although the damage patterns produced by particle impact are
much more complicated than those obtained by mode I loading method.

By particle impact, let primary or secondary cleavage cracks be
initiated and propagated in grain I. When these cracks reach the grain
boundary, the mode of fracture in the adjacent grain, grain II, will
depend on which plane the resolved normal stress for fracture is reached
first.

Based on the crystal structure of LiF and seed setting, grain II

76

has two potential primary cleavage planes, (100) and (010), and two potential
secondary cleavage planes, (110) and (110), along which the (100) cracks
initiated in grain I could propagate as illustrated in figure 35. Cracks
can also propagate along the grain boundary surface as well as cleavage
planes depending upon the misorientation angles and the orientatiOn of

grain boundary with respect to the approaching crack path. Thus, crack
propagation direction is decided depending on which fracture plane (or
boundary) the resolved normal stress first reaches the fracture stress of
the plane (or boundary).

8y assuming that tensile stress a is developed at grain boundary

9
when the crack tip approaches the grain boundary along (100) plane in
grain I in which impact occurred, the resolved normal stresses of 09 on
cleavage planes and grain boundary are obtained. When this resolved
normal stress reaches the critical normal (fracture) stress of one of the
above planes, crack will propagate along that plane.

Equations for the homogeneous continuum can be assumed to be

applicable in this region because grain boundary has weak anisotropic

character and its thickness is extremely small (320 A).
C(loo) = Cg COS ¢ 9 (33)
6 cos2 (90° - p) . (34)

Gr(010) = g

6(110) = 09 cos2 (45° - p) , (35)

77

Figure 35. Schematic drawing of specimen surface illustrating
potential crack propagation directions for the case
of {100} crack interaction with grain boundary.

Specimen surface is (001) in both grains.

77(a)

 

mo.)
m
a.
O
. . . . .. W H
. . . 9 0L.c
:8. . ‘ 4

 

II

 

 

78

_ _ 2 o
0(110) - Cg cos (45 + p) ,

°gb = °g cos 0 , (37)

and
where 0(110), 0(010), 0(110), and 0(110) are the fracture stresses of the

corresponding cleavage planes and o is the fracture stress of the grain

gb
boundary.

According to the crystal structure and seed setting, the range of
misorientation angle is 0°<¢§45°. Thus, as can be seen clearly in

figure 35, in this range
A <9o° - A . (38)

and

cos2 p > cos2 (900 - p) . (39)
Therefore, the transcrystalline crack prOpagation along the primary
cleavage plane occurs only along the (100) plane in grain 11 because the
resolved normal stress on (100) plane is larger than that for (010) plane

under such conditions.

Similarly, for the case of secondary cleavage,
45°-p<45°+¢ , (40)
and

cos2 (45o - d) > cos2 (450 + A) . (41)

79

Therefore, the resolved normal stress on (110) plane is larger than that
for (110) plane. Consequently, the transcrystalline crack propagation along
the secondary cleavage plane occurs only along the (110) plane.

As a result, (100) cleavage crack initiated in grain I can prOpagate
by one of the following three modes: transcrystalline fracture along the
(100) primary cleavage plane in grain II, transcrystalline fracture along
the (110) secondary cleavage plane in grain II, or intercrystalline
fracture. When the critical normal stress exceeds the fracture stress of
that plane, crack propagates along that plane. Fracture stress of each
plane can be calculated by using surface energies of these planes or
grain boundary energy.

From Hooke's law, the equation relating the fracture stress and

surface energy can be written as folloWing.

where, of is fracture stress,
E is Young's modulus,
y is surface energy, and
a0 is lattice constant.

11

By substituting the constants of LiF (E = 10.2 x 10 dyne/cmz,

8 cm) and the surface energy values71 of LiF (y{100} =

ao= 4.027 x 10'
2 2 2

520 ergs/cm , 7(110} = 2,000 ergs/cm , ng = 940 ergs/cm ) into the

equation (42), the fracture stress needed for separation is calculated

and the values are listed in table 2.

From the values shown in table 2,

80

Table 2. Calculated values of fracture stress
of LiF crystal (Ref. 71)
unit : N/m2

 

 

Primary cleavage plane 1.15 x 1010
Secondary cleavage plane 2.25 x 1010
Grain boundary 1.54 x 1010

 

 

 

 

81

0(100) = 0.746 ng , (43)
0(110) = 1.461 ogb , and (44)
°(100) = °°°11 °(110) . (45)

f=rom the equations (33), (37), and (43) the condition for transcrystalline
(:rack propagation along the primary cleavage plane (instead of

‘intercrystalline fracture) is

cos2 p < 0.746 cos2 8 , (46)

and the condition for intercrystalline fracture is

cos2 p > 0.746 cos2 8 . (47)

Likewise, from the equations (35), (37), and (43) the condition for
transcrystalline crack propagation along the secondary cleavage plane

"Instead of intercrystalline fracture is

cos2 (45o - p) < 1.461 cos2 9 . (48)

“Id the condition for intercrystalline fracture is

cos2 (45 - p) > 1.461 cos2 0 . (49)

The orientation of grain boundary with respect to the approaching crack

path does not have any effect on the determination of crack prOpagation

82

along the primary or secondary cleavage planes in grain II. Therefore, from
the equations (33), (35), and (45), the condition for crack prOpagation
along the (100) cleavage plane, instead of (110) cleavage, is

2 (

cos2 p < 0.511 cos 45° - p) . (50)

Similarly for secondary cleavage, instead of primary (100) cleavage,

cos2 p > 0.511 cos2 (45O - d) . (51)

These six conditions for the determination of crack path were drawn and
superimposed in figure 36. In this figure, TR. I, TR. II, and INT.
indicate the zones for the transcrystalline cleavage along the primary
cleavage plane, transcrystalline cleavage along the secondary cleavage
plane, and intercrystalline fracture, respectively.

The three curves of figure 36 represent the various combinations of
critical angles ( 9 and p ) for which two different modes of crack
prOpagation can occur simultaneously. The critical value of p is 44.40
at which transcrystalline cleavage could occur along the primary cleavage
plane or secondary cleavage plane. When the tilt angle (0) is smaller
than 30.30, only primary cleavage fracture occurs regardless of the value
of the angle of relative grain boundary orientation (9). For the values
of 8 ranging from 34.20 to 90°. primary cleavage always occurs provided p
is smaller than 44.40. For the values of 0 ranging 0° to 34.2°, primary
cleavage occurs provided 0 is smaller than the corresponding critical
angles, ranging from 30.30 to 44.40. As can be seen in figure 36, the
dominant crack propagation mode, when (100) crack interacts with a grain

boundary is transcrystalline crack propagation along the (100) cleavage

Figure 36.

83

Crack propagation mode for various 0 and 6 when
(100) crack in grain I interacts with a tilt
boundary. (6 is tilt angle and 6 is the angle

between crack path in grain I and grain boundary)

0 : Transcrystalline crack propagation
along promary cleavage plane,
II : Transcrystalline crack propagation
along secondary cleavage plane,
A : Intercrystalline crack propagation,
IN.: Intercrystalline crack propagation zone,
TR.I.: Transcrystalline(primary) crack propagation
zone, and
TR.II.: Transcrystalline(secondary) crack propagation

zone .

83(a)

/.TR.II.

34.2

 

 

 

   

TR.I.

 

 

44.4 - ------------

40

30.3 -

10

9O

80

70

60

50

40

3O

20

10

84

plane in grain 11.

Experimental results are incorporated in this figure by placing
different markers in order to indicate various fracture modes as a
function of the misorientation angles 8 and p. As can be seen from the
figure 36, the experimental observations fully conform with the
predictions of the model. However, the number of results illustrating
the propagation of (100) crack was quite a few because (100) crack
initiation was very rare in the projectile velocity range (2.5 to 20 ms'l)
used in this research.

When the secondary cleavage crack is initiated and prOpagated in
grain I along (110) plane, crack propagation conditions similar to those

for the case of primary cleavage crack interaction with grain boundary

exist as shown in figure 37. Under such conditions

6(100) = 09 cos2 (45° - 0) , (52)
_ 2
= 0 cos2 0 . (54)

°9b 9

From the equations (52), (54), and (43) the condition for
transcrystalline crack propagation along the (010) cleavage plane

instead of intercrystalline fracture is

cos2 (45o - p) < 0.746 cos2 9 , (55)

and the condition for intercrystalline fracture is

85

Figure 37. Schematic drawing of specimen surface illustrating
potential crack propagation directions for the case
of (110) crack interaction with grain boundary.

Specimen surface is (001) in both grain.

85(a)

 

 

II

 

 

86

cos2 (45° — d) > 0.746 cos2 9 . (56)
Likewise, from the equations (53), (54), and (44), the condition
for transcrystalline crack propagation along the (110) cleavage plane

instead of intercrystalline fracture is

cos d < 1.461 cos2 9 . (57)
From the equations (52), (53), and (45), the condition for crack
prOpagation along the (010) cleavage plane instead of (110) cleavage in

grain II is

2

cos2 (45o - p) < 0.511 cos p , (58)

and the condition for intercrystalline fracture is

cos2 (45o - p) > 0.511 cos2 p . (59)

These six conditions for the determination of crack path were drawn
and superimposed in figure 38.

The three curves of figure 38 represent the various combinations of
critical angles ( O and p ) that control the mode of crack propagation.
The critical value of p for the transcrystalline cleavage along the (010)
or (110) planes is 0.60 since the surface energy of (010) plane is much
smaller than that of (110) plane. When the tilt angle (p) is larger than
14.70. only primary cleavage fracture occurs regardless of the value of 0.
For the values of 0 ranging from 34.2° to 90°, primary cleavage always
occurs provided p is larger than 0.6°. For the values of 9 ranging from

0° to 34.2°, primary cleavage occurs provided p is larger than the

87

Figure 38. Crack propagation mode for various p and 0 when
(110) crack in grain I interacts with a tilt
boundary ( p is tilt angle and 6 is the angle
between crack path in grain I and grain boundary).

0 : Transcrystalline crack propagation
along promary cleavage plane,
I. : Transcrystalline crack propagation
along secondary cleavage plane,
A : Intercrystalline crack propagation,
IN.: Intercrystalline crack propagation zone,
TR.I.: Transcrystalline(primary) crack propagation
zone, and
TR.II.: Transcrystalline(secondary) crack propagation

ZONE .

45

4O

30

20

14.7

10

0.61

87(a)

 

 

TR.I.

 

 

88

corresponding critical angles, ranging from 0.60 to 14.70. For the case
of (110) crack initiation, the domonant crack prOpagation mode is also
transcrystalline crack propagation along the (010) primary cleavage plane
in grain 11 because of the lower value of surface energy of (010) primary
cleavage plane than that of the (110) secondary cleavage plane.
Experimental results are also incorporated in the figure 38. As

can be seen in this figure, most of the experimental results conform with
the prediction of the model. Such a good agreement is the same tendency

71 This may imply

as the case of mode I loading in the previous research.
that the direction of brittle crack propagation is mainly governed by the
anisotropy of surface energy in crystals with strong cleavage tendencies
regardless the crack initiation mechanism. Another possible reason for
such a good agreement may be the similar magnitudes of the crack velocity.
The velocity of cracks produced by particle impact in the present study
is comparable with that obtained by mode I loading method since the range
of projectile velocity used was very low (2.5 to 20 ms'l).
However, four results do not match with the prediction of the model.
For the case of two specimens (15° and 200 tilt), intercrystalline
fractures and a secondary cleavage were observed in the zone which
illustrates the angular conditions of the specimens for transcrystalline
crack prOpagation along the primary cleavage plane in grain II. This
mismatch may be due to the compromise between the crack prOpagation
tendencies along the stress trajectory and cleavage planes. The stress
distribution produced by dynamic loading near the grain boundary mav be the
another cause for such a mismatch between the experimental results and the
prediction of the model. These experimental points that do not agree with
the predictions of the model were observed to occur mainly when the point

of impact was too close to the boundary. The complicated stress state

89

that will develop in the boundary region in such cases may be responsible

for the inconsistencies observed.

4.1.2.4 Slip Propagation

The highly localized shear strain associated with slip in one grain
of a LiF bicrystal introduces elastic or plastic distortion in the
adjacent grain. One possible result is the generation of a crack when a
slip band intercepts the grain boundaries having mixed characters.

However, when the grain boundary has only pure tilt character, slip
propagation can occur across the boundary if the dislocation pile-up
stress reaches a critical value.

As can be seen in figure 39, usually very fine slip lines were formed
under particle impact and they were usually blocked by the grain boundaries.
This general tendency of the blockage of slip lines by grain boundaries
implies that even the tilt boundaries are extremely effective barriers to
the propagation of fine slip caused by particle impact. However, cracks
caused by dislocation pile-up at the grain boundary have never been
observed during this investigation. This implies that pile-up stresses
are not high enough to cause crack nucleation based on the Stroh’s
model.

In some cases (figure 40), it was also observed that slip lines are
continuous across the grain boundary showing slip prOpagation to the adjacent
grains. Such slip prOpagation was also observed by Johnston et al65 in
M90 bicrystals having small tilt boundaries under compression. Furthermore,
additional slip systems may also be found to be activated in adjacent
grains as proposed by Cottrell64 due to the stress concentration introduced
by dislocation pile-up. These features are presented in figure 40., The

continuity of slip across the boundary may imply that glide dislocations can

90

Figure 39. Blockage of slip lines (formed by particle

impact) by a tilt boundary.

0 = 6° v = 20 ms’1

90(a)

 

 

Figure 40.

91

Propagation of slip due to particle impact
(near the grain boundary) through the

grain boundary in regions marked 'X' and 'Y'.
(A). ¢=6° v 1
(B). p = 20° v

5.5 ms-
1

11 ms-

91(a)

 

92

6°, and

pass through the boundary as proposed by Marcincowski and Sadananda
that the boundary itself may undergo deformation because of this passage.
The results explaining such passage of dislocations were not obtained in
this research since TEM could not be used for LiF due to its
low melting point. The ease with which the boundary undergoes
deformation should control the ease with which slip can prOpagate from
one grain to the other. The slip propagation under particle impact
occurred only when the misorientation angle is less than 20°. This implies
that the relative crystallographic orientation is an important factor that
controls slip propagation through a grain boundary. The distance from the
impact spot to the grain boundary is another important factor that
determines when slip can propagate through a grain boundary. When the
distance is less than the critical distance, most of the slip lines are
blocked by the grain boundary as shown in figure 39.

When the particle impact occurred on the grain boundary, two sets of
rosette patterns consisting of slip lines are observed in both grains as
shown in figure 41. As can be seen in this figure, primary and secondary

slip lines are formed in both grains independently due to the particle

impact on the grain boundary.

4.2 Damage Produced by,9gasi-static Indentation

As discussed in previous section 4.1.2.4, most of the fine slip lines
formed by particle impact are blocked by the grain boundaries. 0n the
(Ither hand, indentation loading produces wide slip bands as shown in
f“igure 42. The formation of such wide slip bands under indentation is
“mainly due to the much longer duration of loading time (about 10 seconds)
Compared with the very short loading time (few micro-seconds)20 under

Particle impact. Under indentation, the rate. of loading is also much slower

93

Figure 41. Rosette patterns formed by particle impact on
the grain boundary.
(A). d = 20° v
(8). d = 20° v

2.5 ms.1

1

16 ms'

93(a)

 

94

than the case of particle impact. Therefore, extensive plastic flow
occurs with the formation of wide slip bands on the (001) surface of
specimens under indentation.

Such wide slip bands are similar to the slip bands observed by
Subramanian et al77'79 in single crystals of rock-salt structure under
compression or cyclic loading conditions. These wide slip bands
propagate through the grain boundary easily when indentation is produced
near the grain boundary as illustrated in figure 42 since the wide slip
bands cause very effective pile-up stress on the boundary. This pile-up
stress cause slip propagation instead of crack nucleation since boundary

6° concluded that the

has tilt character only. Even though Johnston et al
probability of crack nucleation by dislocation pile-up increases with
increasing misorientation, no such cracks were Observed in the LiF
specimens having maximum tilt angle (45°) during this investigation.

Due to the sharp tip of the pyramid indenter, the stress field
produced by indentation corresponds to the Boussinesq type stress field.
However, the equations describing Boussinesq stress field can not be used
directly to the calculation of indentation stress in LiF bicrystals. As
can be seen in equations (derived by Lawn and Swain42) which describe the
stress components for the point loading in the range of elastic deformation,
°er= °re= 0. This stress component, °er’ is the shear stress which causes
slip along <110> directions. The crystal anisotropy also plays a very
significant role as evidenced by the dislocation rosette pattern.
Moreover, the specimens have strong anisotropic character possessing
primary and secondary cleavage planes as well as primary and secondary

slip systems just beneath the indentation site. In addition the indenter

used was pyramidal, not conical.

95

Figure 42. Typical dislocation rosette pattern produced by

the indentation in the grain boundary region.

0

¢ = 6 P = 0.245 N

95(a)

II .sUQ.‘H\V. . 1

Fr...
. c. ..

.0
.

 

96

The typical dislocation rosette pattern produced by indentation in
the grain boundary region is shown in figure 42. Each etch pit
corresponds to the intersection of a segment of a dislocation loop with
the surface. Due to the cubic symmetry of LiF crystal, the rosette pattern
consists of eight wings with lines of etch pits either in the <100>
direction or in the <110> direction. This rosette pattern is very similar

63

to that obtained by Armstrong and Wu in M90 single crystals with pyramid

indentation method as shown in figure 7. And the etch pit patterns observed
in indentation test are very similar to those produced by particle impact
in LiF bicrystals, although the extent of deformation and width of the slip

bands differed in both cases. Such similarity was also observed by Evans

18

and Wilshaw in ZnS under fully plastic contact conditions.

When the indenter elastically contacts the LiF crystal, resolved shear

stresses are developed on the {110}450 planes but not on the {1101900

60

planes. These stresses on the {1101450 planes nucleate new dislocations

and cause slip. After the indenter penetrates into the crystal, shear

6O

stresses develop on the {1101900 planes also. The insertion of the

pyramidal indenter into a (001) surface of LiF crystal displaces material
along the <110> slip directions forming two rows of edge dislocations.61
The dislocation lOOps formed on {110}450 and {1101900 planes are shown
schematically in figure 6. Etch pits due to edge dislocations extend
along the <110> directions while those due to screw dislocations extend along

the <100> directions as observed by Keh°°

and Vaughan et al,61 The
dislocations formed on the two sides of each wing are of Opposite sign
because they are formed by a shear stress which is introduced by the
indentation process, during which the material is pushed away by the

indenter.°°

97

Dislocations pile-up on slip planes at barriers such as grain
boundaries, second phases, or sessile dislocations. Most pile-ups are
made up of dislocations with an edge component since screw dislocations
can cross—slip out of the slip plane. In the present study, edge dislocation
pile-ups at grain boundaries are observed and analyzed according to the
nature of specimens and loading conditions. The distribution of dislocations
in a pile-up has been calculated by Eshelby et al°°. The number of edge
dislocations (N) along a slip plane between the indentation and grain

boundary i580

(1-v) Dts
N = . (60)
Gb

 

where, D is distance of indentation from the grain boundary,
Ts is average resolved shear stress in the slip plane,

G is shear modulus of specimen, and

b is magnitude of Burgers vector.
The leading edge dislocation in the pile-up is acted on by the interaction
force with other dislocations as well as the applied shear stress
which induce a high stress concentration on the leading dislocation in the
pile-up. The magnitude of this pile-up stress is proportional to the
applied shear stress, and this shear stress in the boundary region
decreases as the indentation distance from the grain boundary increases.
When the pile-up contains many dislocations, the large stresses that
develop can either nucleate a crack at the boundary, or initiate slip in the

16

adjacent grain. Pile-ups form until the force on the leading dislocations

is sufficient to make them break through the grain boundary.

98

According to Stroh's model73, crack froms when the leading
dislocations in a pile-up are forced to within a distance 'b' of one

another. Stokes et al81

observed such cracks in a MgO single crystals
under compression. In the LiF bicrystals with pure tilt character, there
are two potential slip planes in grain II, and these two planes have the
same zone axis as the slip plane containing dislocation pile-ups in grain
1. Under such conditions, the slip lines can propagate easily to the
adjacent grain without forming any Stroh type crack. The magnitude of
the stress level needed for slip propagation is less than that needed for
crack initiation in LiF bicrystals.

The dislocation rosette patterns produced by indentation loading are
analyzed in terms of indentation load, misorientation angle, and the
indentation distance from the grain boundary. According to the definition
of Vickers hardness (Hv), indentation load (P) is related to the diagonal

length of indentation (DC) by the following equation.82

2P sin 136°/2
D 2 .
c

Hv =

 

(61)

This parabolic relation between the indentation load and the diagonal
length of indentation is shown in figure 43.

The size of rosette pattern can be determined by the average
distance over which the leading edge dislocations extend. The distance of
travel of leading edge dislocations increases as the diagonal length of
indentation increases, as illustrated in figure 44. Such tendency between

41

indentation load and crack length was also observed by Palmqvist in

carbides.

99

Figure 43. The relation between indentation load and the

diagonal length of indentation.

99(a)

 

mNN.H

owm.o

.z. nae. eoPBaueoeeH

mmn.o

L

om¢.o

b

me~.o

. cm

i oe

- on

..om

 

 

co.

(md) uotqetuaput go uqfiual leuofieta

100

Figure 44. Plot of diagonal length of indentation versus

the distance of travel of leading edge dislocation.

100(a)

 

 

 

 

600

500 ‘

400 —

.

0
0
3

200 -

.21. mco.pmuo—m.u move
mcpumw. mo pm>mep .o wucmum.o

100

20 30 40 50 6O 70 80 90 100

10

Diagonal length of indentation (pm)

101

The distance between the grain boundary and the indentation site is
an important factor in slip propagation mechanism since the stress
concentration at grain boundary due to indentation decreases as this
distance increases. As can be seen in figure 45(A), dislocations pile-up
at grain boundary when the distance between indentation and grain boundary
is shorter than the distance of travel of leading edge dislocation. The
maximum number of piled-up dislocations are observed when indentation
distance equals the critical distance at which slip prOpagation to the
adjacent grain just initiates. 0n the other hand, dislocations
resulting from indentation at a distance shorter than the critical
distance propagate across tilt boundaries as shown in figure 45 (A) and
(B). After propagating across the tilt boundary, slip lines bend to comply
with the misorientation between the adjacent grains as can be seen in figure
45(8). These slip bands are very wide compared with the fine slip lines
produced by particle impact, and as a result are capable of producing
higher stress concentration at the boundary.

The relation between the indentation distance and the length of slip
lines in the adjacent grain is plotted in figure 46. As can be seen in
this graph, the length of propagated slip lines decreases as the
indentation distance increases. The intersecting points of each curve
with abscissa (corresponding to zero prOpagation length of slip line in
adjacent grain) gives the corresponding critical indentation distances for
the three misorientation angles. The prOpagated slip line length also
desreases as the misorientation angle increases.

Relative crystallographic misorientation also has a strong influence
on the slip propagation mechanism. Misorientation angle of each bicrystal

was determined by measuring the misfit angle between two slip lines formed

102

Figure 45. Dislocation pile-up and slip propagation through
tilt boundary under indentation loading.
(A). 0 = 6° P = 0.245 N
(8). ¢ = 10° P = 0.490 N

 

102(a)

 

 

 

103

Figure 46. Plot of distance between the grain boundary and
indentation site versus slip line length in

adjacent grain (grain II).

Slip line length in adjacent grain (pm)

103(a)

 

 

 

 

140
C) : 10o tilt,
A : 20° tilt,and
120‘
[:1 : 45° tilt.
(indentation load : 0.245 N)
100 ‘
8O ‘
60 d
40 4
20 -
0 l I—J G—I V! l
0 20 40 60 80 100

Distance between grain boundary and

indentation site (pm)

 

104

along the primary slip directions of both grains. The slip propagation
through grain boundary has been usually observed when 90° slip bands in
grain I interact with the boundary. This may be due to effective pile-Up
of stress that can develop when edge dislocations are blocked by the
boundary. In the case of 45° slip band intersecting with the boundary,
screw dislocations present in such slip bands may cross-slip to relieve
pile-up stress. The relation between the misorientation angle and the
corresponding critical indentation distance is shown in figure 47. Due

to the geometrical relationship between two primary slip planes of grain I
and II, resolved shear stress on the primary slip plane of grain 11
decreases as the misorientation angle increases. This may be due to the
fact that the resolved shear stress in a given slip plane of grain II
depends on the misorientation angle. Therefore, the critical distance for
slip propagation decreases as the misorientation angle increases as can be
seen in figure 47.

Indentation load is also an important factor in the slip propagation
mechanism. In the stress field produced by pyramid indenter, the stress
concentration at grain boundary increases as the indentation load is
increased. This tendency can be seen in the plot provided in figure 48,
for a specimen with 15° tilt boundary.

8y superimposing the tendencies revealed in the two figures 47 and
48 illustrating the change of critical indentation distance on the
different values of tilt angle and indentation load, the conditions for
the propagation of slip lines in LiF bicrystals possessing pure tilt
character is essentially established.

When pyramid indentations were made on a cleaved surfaces of a LiF

bicrystals using loads ranging from 0.245 to 5.145 N, cracks on the

105

Figure 47. Plot of misorientation angle versus critical

indentation distance for slip propagation.

105(a)

 

 

 

 

100

. . _
0 0 0
m 6 4 2

.51. :oPHammnoca a._m com magnum.u .mu.».co

6O

40

20

Tilt angle (degree)

106

Figure 48. Plot of indentation load versus the critical

indentation distance for slip propagation.

Critical indentation distance (pm)

140

106(a)

 

120 -

100 ‘

80 7

60 ‘

4o-i

20 ‘

 

15° tilt

 

 

 

0.245

0.490

I

0.735

Indentation load (N)

0.980

1.225

107

specimen surface were never observed due to the slow loading rate and

ductility of LiF under such conditions. Petrovic and Mendiratta55

observed sharp cracks initiated from the corners of the pyramid indentation.
In the case of indentation on MgO single crystals with few grams load,
cracks were formed in the <110> direction due to its lower ductility as

6° 8y chemical polishing method, Keh found that those

60

compared with LiF.
cracks lay in the (110)900 planes. Keh et al observed the same type
cracks in LiF single crystals when the indentation was carried out at a
sub-zero temperature. Hagan62 has observed only sub-surface cracks beneath
the indented surface under similar loading conditions to those used in the
present research. The direction of such cracks is exactly same as the
crack directions observed in the LiF specimens under impact erosion.

As discussed in the previous sections 4.1.1.1 and 4.1.2.1, lateral
fractures are the main features of the surface damage under impact erosion
in LiF crystals. Such lateral fractures were also observed even at
very low projectile velocities (about 2.5 ms'l). However, under
indentation test of LiF crystals carried out at room temperature, lateral
fractures were never observed. Such observations imply that the loading
rate and ductility of material are the main contributing factors for

material removal mechanism since the main source of material removal under

impact erosion is the intersection of lateral fracture with another lateral
fracture or grain boundaries. Observations of such a fine slip due to
particle impact, and formation of wide slip bands under indentation loading,
also emphasize the importance of rate of loading in deformation of semi-

brittle materials.

V.

CONCLUSIONS

 

The fracture and deformation of bicrystals of LiF, a semi-brittle

material, under particle impact erosion and quasi-static indentation

were investigated experimentally. The main conclusions obtained during

this investigation are as follows:

1.

In crystals with strong cleavage tendencies, like LiF, there is
some compromise between the tendencies for cracks to follow stress

trajectories and cleavage planes.

Particle impact of LiF crystal causes (110) cracks initiated
predominantly according to Keh's model. Under indentation loading

at room temperature, using loads ranging from 0.245 to 5.145 N,

lateral fractures were never observed, whereas they were the main
features of surface damage under impact erosion in LiF crystals. This
implies that the loading rate and ductility of materials play significant

roles in material removal mechanism in impact erosion.

When the cracks due to the particle impact reach the grain boundary
present in a bicrystal, they initiate intercrystalline or trans-
crystalline cracks provided they are not blocked by the grain
boundaries due to large crystallographic misorientations between
the adjacent grains or due to a weak driving force for crack
propagation resulting from large distances of impact from the

boundary.

Experimental results on crack propagation in the grain boundary

region under particle impact are in good agreement with the

108

 

109

predictions of a model for mode I crack propagation based on
the normal stress law for brittle fracture. This implies that the
crack propagation direction in crystals with s:rong cleavage
tendencies is mainly governed by the anisotrOpy of surface energy

even under impact loading conditions.

The main cause of material removal in LiF single crystals under
particle impact using blunt projectiles is the interaction of lateral
fracture. However, under this condition, material removal from
bicrystals occurs by interaction of lateral fractures with other

lateral fractures or grain boundaries.

Fine slip occurs as a result of particle impact, and such fine slip

is usually blocked by the grain boundary. Slip propagation through
the grain boundary was rarely observed under such conditions. 0n

the other hand, under indentation loading, wide slip bands are formed.
When such wide slip bands interact with tilt boundary, slip prOpaga-
tion through the boundary usually occurs. This may be due to more
effective stress concentration that may arise when wide slip band is
blocked by the boundary. However, presence of applied load for
sufficient lengths of time during indentation may also aid this

process.

The main factors having strong influence on the slip prOpagation
mechanism under indentation loading are indentation distance from the
grain boundary, relative crystallographic misorientation, and magnitude
of indentation load. The critical indentation distance for slip
propagation decreases as the relative crystallographic misorientation

angle between the grains increases.

8.

110

Dislocation pile-ups at pure tilt boundaries in LiF bicrystals do not
cause enough stress cencentrations to initiate crack. Crack nucleation
caused by the blockage of slip at tilt boundaries was not observed,

either under particle impact or under indentation loading. The

observations of slip propagation to the adjacent grain during quasi-
static indentations imply that the magnitude of stress concentration
needed for crack initiation is larger than that needed for slip

propagation through simple tilt boundaries of LiF bicrystals.

In a semi-brittle material like LiF, deformation and fracture caused
by quasi-static indentation produced by Vickers hardness test are not
representative of damage resulting from low velocity (up to 20 ms'l)

particle impact.

10.

11.

Bibliography

F.8. Langitan and B.R. Lawn, "Hertzian Fracture Experiments on
Abraded Glass Surfaces as Definitive Evidence for an Energy Balance
Explanation of Auerbach's Law," J. Appl. Physics, 49, 4009 (1969).

F.B. Langitan and B.R. Lawn, "Effect of a Reactive Environment on
the Hertzian Strength of Brittle Solids," J. Appl. Physics, 42,
5540 (1971).

G.P. Tilly, "A Two Stage Mechanism of Ductile Erosion," Wear, 23,
87 (1973).

S.M. Wiederhorn and D.E. Roberts, "A Technique to Investigate High
Temperature Erosion of Refractories," Am. Ceram. Soc. Bull., 55,
185 (1976).

S.M. Wiederhorn and B.R. Lawn, "Strength Degradation of Glass
Impacted with Sharp Particles: I, Annealed Surfaces," J. Am. Ceram.
Soc., 62, 66 (1979).

B.R. Lawn and 0.8. Marshall, "Strength Degradation of Glass Impacted
with Sharp Particles: II, Tempered Surfaces," J. Am. Ceram. Soc.,
.gg, 71 (1979).

0.8. Marshall and A.G. Evans, "Measurement of Dynamic Hardness by
Controlled Sharp-Projectile Impact," J. Am. Ceram. Soc., §§, 580
(1983).

I. Finnie, "Erosion of Surfaces by Solid Particles," Wear, 3, 87
(1960). ‘

A.G. Evans, "Strength Degradation by Projectile Impacts," J. Am.
Ceram. Soc., gg, 405 (1973).

R.E. Winter and I.M. Hutcnings, "Similarities and Differences in the
Erosion Behavior of Materials," Wear, 25, 141 (1975).

S.M. Wiederhorn and B.R. Lawn, "Strength Degradation of Glass
Resulting from Impact with Spheres," J. Am. Ceram. Soc., 60, 451
(1977).

111

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

112

F.F. Lange and A.G. Evans, "Erosive Damage Depth in Ceramics: A
study on Metastable, Tetragonal Zircornia," J. Am. Ceram. Soc., 4g,
62 (1979).

C.E. Smeltzer, M.E. Gulden, and W.A. Compton, "Mechanisms of Metal
Removal by Impacting Dust Particles," J. Basic Eng., Trans. ASME,
2gp, 639 (1970).

M.E. Gulden, "Effect of Number of Impacts on Erosion of Poly-
crystalline Mng in the Elastic-Plastic Response Regime," J. Am.
Ceram. Soc., 6}, 121 (1980).

J.R. Lewis, ”Erosion Characteristics of Materials for Centrifugal
Coal Slurry Pumps, Presentation TMS-AIME Meeting (1984), Abstract
in J. of Metals, p. 55, July (1984).

J.P. Hirth and J. Lothe, Theory of Dislocations, P. 377, McGraw-Hill
Book Co., New York, 1968.

 

J. Washburn, G.W. Groves, A. Kelly, and G.K. Williamson, "Electron
Microscope Observations of Deformed Magnesium Oxide," Phil. Mag.,
g, 991 (1960).

A.G. Evans and T.R. Wilshaw, "Dynamic Solid Particle Damage in
Brittle Materials," J. Mater. Sci., 12, 97 (1977).

J.E. Ritter, P. Strzepa, K. Jakus, L. Rosenfeld, and K.J. Buckman,
"Erosion Damage in Glass and Alumina," J. Am. Ceram. Soc., 41, 769
(1984).

C.G. knight, M.V. Swain, and M.M. Chaudhri, "Impact of Small Steel
Spheres on Glass Surfaces," J. Mater. Sci., lg, 1573 (1977).

S. Timoshenko and J.N. Goodier, Theory of Elasticity, p. 383,
McGraw-Hill Book Co., New York, 1951.

 

D.G. Rickerby, B.N. Pramilabai, and N.H. Macmillan, "The Influence of
Particle Properties on Impact Damage in LiF," J. Mater. Sci., 44,
3006 (1979).

D. Tabor, The Hardness of Metals, p. 120, Clarendon Press, Oxford,
1951.

 

S.M. Wiederhorn and 8.J. Hockey, "Effect of Material Parameters on

 

25.

26._

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

113

the Erosion Resistance of Brittle Materials," J. Mater. Sci., 15,
305 (1983).

G.L. Sheldon, "Similarities and Differences in the Erosion Behavior
of Materials," J. Basic Eng., Trans. ASME, 525, 619 (1970).

G. Hoff, W. Herbert, and H. Rieger, "Rain and Sand Erosion, Phenomena
of Material Destruction Caused by Repeated Loads," Characterization

 

and Determination of Erosion Resistance, ASTM Spec. Tech. Publ.,
No. 474, p. 353 (1970).

 

M.M. Chaudhri, J.K. Wells, and A. Stephens, ”Dynamic Hardness,
Deformation and Fracture of Simple Ionic Crystals at Very High
Rates of Strain," Phil. Mag., 45, 643 (1981).

I.M. Hutchings, "Energy Absorbed by Elastic Waves during Plastic
Impact," J. Phys. 0., Appl. Phys. lg, 1819 (1979).

J.P. Ashford, Special Ceramics 4, Published by British Ceramic
Research Association, pp. 173-189 (1969).

 

M.M. Chaudhri and P.A. Brophy, "Single Particle Impact Damage of
Fused Silica," J. Mater. Sci., 45, 345 (1980).

R.H. Marion, "Use of Indentation Fracture to Determine Fracture
Toughness," Fracture Mechanics Applied to Brittle Materials, ASTM
Spec. Tech. Publ., No. 678, p. 103 (1978).

 

J.J. Gilman, "Hardness of Pure Alkali Halides," J. Appl. Phys.,
44, 982 (1973).

D.R. Pande and T.S. Murty, "Mechanism for the Formation of {100}
Slip Lines around a Dynamical Indentation on 100 Faces of
Sodium Chloride Single Crystals," J. Phys. 0., Z, 403 (1974).

B.R. Lawn, S.M. Wiederhorn, and H.H. Johnson, "Strength Degradation
of Brittle Surfaces: Blunt Indenters," J. Am. Ceram. Soc., 55,
428 (1975).

B.R. Lawn, E.R. Fuller, and S.M. Wiederhorn, "Strength Degradation of
Brittle Surfaces: Sharp Indenters," J. Am. Ceram. Soc., 55, 193
(1976).

B.R. Lawn and 0.8. Marshall, "Hardness, Toughness, and Brittleness:

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

114

An Indentation Analysis,” J. Ceram. Soc., 55, 347 (1979).

J.T. Hagan, "Shear Deformation under Pyramidal Indentations in Soda-
lime Glass," J. Mater. Sci., 45, 1417 (1980).

J.C. Conway, Jr. and H.P. Kirchner, "The Mechanics of Crack
Initiation and Propagation beneath a Moving Sharp Indenter,"
J. Mater. Sci., 45, 2879 (1980).

B.R. Lawn, T.P. Dabbs, and C.J. Fairbanks, "Kinetics of Shear-
Activated Indentation Crack Initiation in Soda-lime Glass," J.
Mater. Sci., 18, 2785 (1983).

0.8. Marshall, "Geometrical Effects in Elastic/Plastic Indentation,"
J. Am. Ceram. Soc., 54, 57 (1984).

B.R. Lawn and R. Wilshaw, "Review, Indentation Fracture: Principles
and Applications," J. Mater. Sci., 49, 1049 (1975).

B.R. Lawn and M.V. Swain, "Microfracture beneath Point Indentations
in Brittle Solids," J. Mater. Sci., 49, 113 (1975).

J.T. Hagan and M.V. Swain, "The Origin of Median and Lateral Cracks
around Plastic Indents in Brittle Materials," J. Phys. D. Appl.
Phys. 44, 2091 (1978).

A.H. Cottrell, "Theory of Brittle Fracture in Steel and Similar
Metals," Trans. Met. Soc. AIME 544, 192 (1958).

A.S. Keh, J.C.M. Li, and Y.T. Chou, "Cracks due to the Pilling-up of
Dislocations on Two Intersecting Slip Planes in M90 Crystals," Acta
Metall., 4, 694 (1959).

B.R. Lawn and A.G. Evans, "A Model for Crack Initiation in Elastic/
Plastic Indentation Fields," J. Mater. Sci., 44, 2195 (1977).

S. Palmqvist, Archiv Eisenhfittenwesen, 45, 629 (1962), as cited in
Fracture Mechanics Applied to Brittle Materials, ASTM Spec. Tech.
Bubl., No. 678, p. 112 (1978).

V.W. Dawihl and G. Altmeyer, Zeitschrift.f0r Metallkunde, 55, 231
(1964), as cited in Fracture Mechanics Applied to Brittle Materials,
ASTM Spec. Tech. Publ., No. 678, p. 114 (1978).

B.R. Lawn and E.R. Fuller, "Equilibrium Penny-like Cracks in

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

115

Indentation Fracture," J. Mater. Sci., 49, 2016 (1975).

A.G. Evans, "Fracture Toughness: The Role of Indentation Techniques,"
Fracture Mechanics Applied to Brittle Materials, ASTM Spec. Tech.

 

Publ., No. 678, p. 113 (1978).

J.J. Petrovic and M.G. Mendiratta, "Fracture from Controlled Surface
Flaws," Fracture Mechanics Applied to Brittle Materials, ASTM Spec.
Tech. Publ., No. 678, p. 83 (1978).

 

J.T. Hagan, ”Cone Cracks around Vickers Indentations in Fused Silica
Glass," J. Mater. Sci., 44, 462 (1979).

B.R. Lawn, "Hertzian Fracture in Single Crystals with the Diamond
Structure," J. Appl. Physics, 55, 4828 (1968).

J.L. Routbort, R.O. Scattergood, and E.W. Kay, "Erosion of Silicon
Single Crystals," J. Am. Ceram. Soc., 55, 635 (1980).

S.R. Schuon, "Microstructural Aspects of Impact Erosion in Lif, NaCl,
KCl, and CaF2 Single Crystals," Ph.D. Thesis, Michigan State
University, East Lansing, Mi, 1980.

S.R. Schuon and K.N. Subramanian, "Impact Erosion of Single
Crystals of LiF and Can by Sharp Projectiles," Wear, 54, 357 (1982).

S.R. Schuon and K.N. Subramanian, "Microstructural Aspects of Impact
Erosion in Single Crystals of Lif, NaCl, KCl and Can by Blunt
Projectiles," J. Mater. Sci., 45, 732 (1983).

I. Finnie, "Some Observations on the Erosion of Ductile Metals,"
Wear, 45, 81 (1972).

E. Aerts, S. Amelinckx, and W. Dekeyser, "The Surface Hardening of
X-ray Irradiated NaCl," Acta Metall., Z, 29 (1959).

A.S. Keh, "Dislocations in Indented Magnesium Oxide Crystals," J.
Appl. Physics, 54, 1538 (1960).

W.H. Vaughan and J.W. Davisson, "Dislocation Motion Associated with
Indentations," Acta Metall., 5, 554 (1958).

J.T. Hagan, "Micromechanics of Crack Nucleation during Indentations,"
J. Mater. Sci. 44, 2975 (1979).
R.W. Armstrong and C.C.M. Wu, "Lattice Misorientation and Displaced

64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

76.

116

Volume for Microhardness Indentations in M90 Crystals," J. Am.
Ceram. Soc., 54, 102 (1978).

A.H. Cottrell, Dislocation and Plastic Flow in Crystals, p. 107,
Clarendon Press, Oxford, 1953.

 

T.L. Johnston, R.J. Stokes, and C.H. Li “Crack Nucleation in
Magnesium Oxide Bicrystals under Compression," Phil. Mag., 4, 23
(1962).

K. Sadananda and M.J. Marcinkowski, "Deformation of Internal
Boundaries," J. Mater. Sci., 5, 245 (1974).

F.F. Lange, "Mathematical Characterization of a General Bicrystal,”
Acta Metall., 45, 311 (1967).

A.R.C. Westwood, "On the Fracture Behavior of Magnesium Oxide
Bicrystals," Phil. Mag., 5, 195 (1961).

R.D. Carnahan, T.L. Johnston, R.J. Stokes. and C.H. Li, "Effect of
Grain Size on the Deformation of Polycrystalline Silver Chloride at
Various Temperatures," Trans. AIME, 554, 45 (1961).

T.L. Johnston, C.H. Li, and R.J. Stokes, "The Strength of Ionic
Solids," Strengthening Mechanisms in Solids, p. 341, ASM, Metals
Park, OH (1962).

 

J.Y. Lee and K.N. Subramanian, "Fracture of LiF Bicrystals," J.
Mater. Sci., 45, 1765 (1983).

A.H. Ruff and L.K. Ives, "Measurement of Solid Particle Velocity in
Erosive Wear," Wear, 55, 195 (1975).

A.N. Stroh, "The Formation of Cracks in Plastic Flow. II," Proc.
Roy. Soc. London, A 232, 548 (1955).

J. Washburn, A.E. Gorum, and E.R. Parker, "Cause of Cleavage Fractures
in Ductile Materials," Trans. AIME, 545, 230 (1959).

F.C. Frank and B.R. Lawn, "On the Theory of Hertzian Fracture,"
Proc. Roy. Soc. London, A 299, 291 (1967).

L. Sohncke, Poggendorfs Ann., 454, 177 (1869), as cited in E. Schmid
and I.W. Boas, Plasticity of Crystals, p. 169, p. 241, Chapman and
Hall, London, 1950.

77.

78.

79.

80.

81.

82.

117

K.N. Subramanian and J. Washburn, "Fatigue Deformation of Magnesium
Oxide," J. Appl. Physics, 54, 3394 (1963).

K.N. Subramanian, "Work Hardening and Deformation Structure in
Lithium Fluoride Single Crystals," Ph.D Thesis, Michigan State
University, East Lansing, MI, 1966.

K.N. Subramanian, "Cyclic Stressing in Crystals of Rock-Salt
Structure," Phys. Stat. Sol., 55, 9 (1968).

J.D. Eshelby, F.C. Frank, and F.R.N. Nabarro, "The Equilibrium of
Linear Arrays of Dislocations," Phil. Mag., 45, 351 (1951).

R.J. Stokes, T.L. Johnston, and C.H. Li, "The Relationship between
Plastic Flow and the Fracture Mechanism in Magnesium Oxide Single
Crystals," Phil. Mag., 4, 920 (1959).

K. Tanaka, Y. Kitahara, Y. Ichinose, and T. Iimura, "Fracture
Analysis of Single Crystal Maganese Zinc Ferrites Using Indentation
Flaws," Acta Metall., 55, 1719 (1984).