311?... 93...;
I26... v. at... ti
.1 D shift? I.
.33.... .

 

Eat. .ZLEnLu. . . , ...
.\ V” 1...,‘..5__m._§mé;. . _ _ A . ‘

2.3:. .27.

 

V-fiai: :3.

fit)

lHllIHIIHHIIIIllIIHHIHIililllillillllllhUlillllllllhl

3 1293 01037 3664

This is to certify that the

dissertation entitled

Optimization of Metal-Ceramic Bonding to Enhance
Mechanical Properties of Ceramic
Matrix Composite

presented by

Taekoo Lee

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Materials Science

2

 

 

 

 

Major professor

Date 9-29-93

 

MS U i: an Affirmative Action/Equal Opportunity Institution 0- 12771

 

LIBRARY
Michigan State
University

 

 

 

PLACE IN 38111th BOX to remove this checkout from your record.

TO AVOID FINES Mum on at bdoro dd. duo.

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Optimization of Metal-Ceramic Bonding to Enhance

Mechanical Properties of Ceramic Matrix Composite
by

Taekoo Lee

A DISSERTATION

submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Materials Science and Mechanics
1993

K. N. Subramanian, Advisor

Abstract

Optimization of Metal-Ceramic Bonding to Enhance Mechanical
Properties of Ceramic Matrix Composite
by

Taekoo Lee

The role of interface on the fracture toughness of ceramic glass reinforced
with metallic ribbon was investigated. A strong interfacial bonding
strength is essential for the load transfer between the matrix and ribbon,
and for the utilization of the ductility of the reinforcement. However, weak
interfacial bonding is considered to be important so that ribbon pull-out
can improve the toughness of brittle ceramic matrix composites. The main
aim of the present study is to carry out interface design to optimize
mechanical properties of brittle ceramic matrix composites reinforced with

ductile metallic ribbons.

Acknowledgment

The author wishes to express his sincere gratitude to his major thesis advi-
sor Dr. K.N. Subramanian for his generous assistance and guidance which

ultimately led to the completion of the work reported in this dissertation.

The author is also grateful to the members of his doctoral committee, Dr.
David S. Grumman, Dr. Dashin Liu and Dr. Carl Foiles, who with their
helpful and understanding attitude greatly encouraged him in the course

of his research.

Thanks are also extended to the Composite Materials and Structures Cen-
ter at Michigan State University for financial support during the doctoral

program.

Finally, and above all, I wish to express my deepest thanks to my parents,
my lovely wife, Suekyung, and son, Kwangmin, for their consistent sup-
port, encouragement and understanding, throughout the course of this

study.

ii

Contents

LIST OF TABLES
LIST OF FIGURES

1. Introduction

 

 

 

2. Literature Survey
2-1. Evaluation of Interfacial Bonding Strength in Ceramic
Matrix Composite
2-1-1. Interface Test Methods
2-1-2. Theoretical Analyses of Interfacial Debonding and
Fiber Pull-out during Interface Tests ------------

 

2-2. Fracture Toughness Measurements in Ceramic Matrix

 

Composites
2-3. Strength Analyses in Ceramic Matrix Composites -----
3. Experimental Procedure

3-1. Materials

 

 

3-2. Composite Fabrication

3-3. Interface Modification
3-3-1. Thermal Cycling Technique
3-3-2. Acid Etching Technique

3-4. Mechanical Testing

 

 

 

 

3-5. Micrographic Observation
4. Results and Discussion
4-1. Theoretical and Experimental Analysis of Debonding Pro-
cess of Ductile Ribbon Embedded in Brittle Matrix
4-1-1. Theoretical Modelling

 

iii

H

11

17
21

24
25

29
32
32
36

37

4-1-1-1. Load Required to Initiate Debonding -------
4-1-1-2. Load Required for Continuation of Debond-

 

ing
4-1-2. Experimental Analysis
4-2. Interface Modifications
4-2-1. Thermal Cycling Technique
4-2-1—1. Effects of Thermal Cycling on The Interfa-
cial Bonding Strength and Frictional Shear

 

 

 

Stress
4-2-1-2. Effects of Thermal Cycling on The Com-
plete Debonding Stress

 

4-2-2. Acid Etching of The Ribbon

 

4-3. Fracture 'lbughness Behavior
4-3-1. Effect of Fracture Toughness(K1c) on Interfacial

 

Bonding
4-3-2. Tensile Behavior of Pre-cracked Composite -----
4-3-3. Toughness due to Crack Bridging(AGc) -------

 

5. Conclusions

 

6. References

iv

38

40
44

56

67
73

87
92
94
100
103

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

List of Tables

Physical and mechanical properties of constituents of

 

the composite.
Measured interfacial properties of 650-TC specimens
after various numbers of thermal cycles. -----------
Measured interfacial properties of thermal cycled speci-
mens up to various maximum temperatures after 5 ther-
mal cycles.

Fracture toughness (ch) of soda-lime glass matrix rein-

 

forced Nichrome ribbon with various bonding conditions.

Effect of interfacial bonding on the displacement at the

 

ribbon fracture.

Fracture toughness due to crack bridging (AGc) in vari-

 

ous bonding conditions.
Critical embedded length (19) for the maximum fracture

toughness due to crack bridging in various bonding con-

 

ditions.

27

62

63

88

93

95

98

Fig.

Fig.

Fig.

Fig.

8

List of Figures

A schematic illustrating mechanisms of toughening in
ceramic matrix reinforced with ceramic fibers. -------
A schematic illustrating mechanisms of toughening in
ceramic matrix reinforced with metallic fibers. --------
Schematic diagrams of indentation techniques:

(a) with microhardness indenter(thick specimen), -----
(b) with spherical indenter(thick specimen) ----------
(c) push-through specimen (thin slice of the composite).
Schematic diagram of the fiber push-through and push-

 

back apparatus.

(a) Variation in average interfacial shear stress with

 

embedded fiber length.

(b) Variation in maximum pull-out load with embedded

 

fiber length.
Variation of maximum pull-out load:
(a) as a function of embedded fiber length, --------

(b) as a function of fiber displacement, for various friction

 

conditions.
Dugdale-Barenblatt crack model:

(a) Cohesive zone at crack tip with restraining stress

 

dependent on separation distance.

(b) Force-displacement relation for atomic attraction in

 

elastic brittle fracture.

Typical stress-strain curve of the Nichrome ribbon

10

13

13

14

14

2O

20

 

 

Fig. 9

Fig.

Fig.

.10

11

.12

.14

.16

.17

18

obtained from tensile test.

 

The schematics of sandwiching of a series of aligned rib-

bons between the glass slides:

 

a) general set-up

b) composite from which pull-out test samples were cut

 

out

c) composite from which fracture toughness test samples

 

were cut out
The schematic Of typical pull-out specimen. ............
The schematics of typical fracture toughness test speci-
mens:

a) single notched specimen for flexure test ..............

 

b) pre-cracked specimens for tensile test.

Schematics of experimental details of the tensile test:

 

a) general set-up

 

b) self-aligning fixture.
Shear stresses due to tensile loading at edge of the

 

embedded area.
Load (P) required for continuation of debonding. --------
Static frictional force at the debonded interface. ----------
Typical load-displacement curve obtained in pull-out

tests of Nichrome ribbon embedded in soda lime glass

 

matrix.
SEM micrograph of the partially debonded interface

between the Nichrome ribbon and the soda lime glass

 

matrix.

Mechanical keying of debonded surfaces produced by

vii

26

28

28

28

30

31

31

33
33

39
41
43

45

47

 

 

Fig.

Fig.

Fig.

Fig.

Fig.

19

20

21

22

.23

.24

.25

.26

27

roughness of debonded surfaces, transverse contraction,
and longitudinal plastic extension of the ribbon due to
tensile loading after debonding.

 

SEM micrograph of the interface between the Nichrome

ribbon and soda lime glass matrix after debonding

 

progresses to some degree.
Interfacial shear stresses for debonding various embed-

ded lengths of the Nichrome ribbon.

 

Loads required to continue debonding as a function of

 

debonded length.
Effect of embedded length on the normal stress on the
ribbon when debonding starts (6,), and normal stress
when debonding is completed (Cf) in soda lime slide glass

reinforced with Nichrome ribbon.

 

Typical stress-displacement curves of as-fabricated, and

650-TC specimens after various numbers of thermal

 

cycles.

SEM micrographs at interfaces of:

 

(a) as-fabricated specimens,
(b) 650-TC specimen after 3 thermal cycles,
(c) 650-TC specimen after 5 thermal cycles.

 

 

Stress-displacement curves of specimens that have

undergone 5 thermal cycles with various maximum tem-

 

peratures.

Interfacial bonding strengths of 650-TC specimens after

 

various numbers of thermal cycles.

The effect of maximum cyclic temperature on the interfa-

49

50

51

52

55

57

58

59

60

61

65

Fig. 28

Fig. 29

Fig. 31

Ifig. 32

cial bonding strength after 5 thermal cycles. ------------
The complete debonding stresses as a function of the

embedded ribbon length after various numbers of ther-

 

mal cycles of 650-TC specimens.
SEM micrographs at debonded interface:

 

(a) due to thermal stress,
(b) due to shear stress during pull-out tests. ---------

The effect of maximum cyclic temperature on the com-

 

plete debonding stress.
Ribbon surfaces roughened by acid etching of:

 

a) as-received,

 

b) pre-oxidized ribbons for 90 seconds

The effect of ribbon surface treatment on stress-displace-

_ ment curves obtained from pull-out tests. .............

Fig. 33

Fig. 34

Fig. 35

Debonded surface in which debonding crack has propa-

gated along the interface between metal and oxide layer.

SEM micrographs of the ribbon and the matrix surfaces

after ribbon is completely pulled-out from the matrix for

the composite with:

a) the ribbon roughened by acid etching for 60 seconds,
(ribbon)
(martix)

 

 

b) the pre-oxidized ribbon roughened by acid etching for
60 seconds. (ribbon)
(matrix)

 

 

Schematic profile of the interface after ribbon surface

treatment, composite fabrication, and during pull-out

66

68

69
7O

72

74
75

76

77

79
8O

81
82

Fig. 36

Fig. 37

Fig. 38

Fig. 39

test for the composite with:

a) as-received ribbon roughened by etching, --------
b) pre-oxidized ribbon roughened by etching. --------
Pull-out stress of ribbons that have undergone various
treatments for an embedded length of 1.7 mm. -------
Fractographic observation of the crack shielding by the
ribbon. Interference fringes represent the path of the

 

crack.
Typical stress-displacement curves obtained from the
tensile loading of the pre-cracked composite specimens
with various interfacial bonding conditions. --------
Stress-displacement curves showing the efl'ect of the

embedded ribbon length on toughness (AGO) of NT com-

 

posite specimens.

83

84

86

9O

91

97

1. Introduction

Ceramics are a promising class of structural materials for applications
where high strength, high stiffness, low thermal expansion, low density
and high temperature stability are desirable attributes. However, the brit-
tleness of ceramics which catastrophically fail is always a problem in use of
conventional ceramics as a structural materials. Ceramic matrix compos-
ites may achieve the marked improvements in mechanical properties, espe-
cially in fracture toughness, by reinforcements. The main goal of ceramic
matrix composites is to reduce the brittleness of ceramics while retaining
most of the strength of the ceramic matrix, for structural applications.

Various studies on fracture toughness and interfacial bonding in
ceramic matrix reinforced with ceramic fibers have shown that high frac-
ture toughness can be obtained in ceramic matrix composites that possess
weak interfacial bonding (1-15). A major mechanism of enhancement of
fracture toughness in such a composite system is the bridging of crack sur-
faces by intact fibers (Fig. 1). This involves the frictional sliding of fibers
against the matrix following interfacial debonding and failure of the fibers.
It requires weak interfacial bonding between the reinforcements and
matrix. On the other hand, ceramic matrix composites containing metallic
reinforcements strongly bonded to the matrix have exhibited profoundly
high fracture toughness. The work done during plastic deformation of the
metallic reinforcements between the crack surfaces in the bridging zone
contributes to the overall toughness of these composites (16-28) (Fig. 2).
Therefore, if both plastic deformation of the reinforcement and frictional

sliding between the components can be utilized in the same composite, the

 

 

 

 

MATRIX

 

crack front

 

 

 

 

 

 

 

Fig.1 A schematic illustrating mechanisms of toughening in
ceramic matrix reinforced with ceramic fibers.

frictional sliding

 

 

  
 

   
 

 

plas c deform ti“-

 

'd bondi g'

 

 

 

 

Fig. 2 A schematic illustrating mechanisms of toughening in
ceramic matrix reinforced with metallic fibers.

fracture toughness of the ceramic matrix composite with metallic reinforce-
ment may be significantly improved. Since such contributions are con-
trolled by the interfacial bonding strength between the matrix and the
reinforcement, the maximum fracture toughness can be achieved by modi-
fication of interfacial characteristics.

Several investigations of interfacial shear stress on fiber pull-out in
ceramic matrix composites have been reported (29-36). However, the plas-
tic behavior of the metallic fibers in brittle ceramic matrix composites has
not been taken into account in analyses of fiber pull-out reported in litera-
ture. Slip due to plastic defamation of the metallic fiber may affect the
distribution of shear stress at the bonded interfacial area. Moreover, the
radial plastic contraction of the metallic fiber at tensile stresses beyond
yield stress may take its surface out of contact with the matrix resulting in

significantly reduced residual gripping pressure.

Coating of the reinforcements is the most widely used technique to mod
ify the interfacial characteristics in ceramic matrix composites (37-40).
Modification of the interface between the reinforcement and matrix by
means of thermal cycling is also a possibility when the thermal expansion
mismatch between the components is relatively large. Radial and tangen-
tial stresses are generated at the interface of the composite during cooling
after composite fabrication due to the mismatch of thermal expansion coef-
ficients between the reinforcement and matrix. These residual thermal
stresses may cause microcracking at the interface or in the matrix, depend-
ing on the interfacial bonding strength and matrix strength of the compos-
ite. In glass matrix composites, microcracks present in the matrix can heal
by viscous flow during heating portion of thermal cycling (41). However,

microcracks in the interface layer can not be expected to self-heal. Instead,

 

 

with continued thermal cycling, such interfacial microcracks will link
together, resulting in weaker interfacial bonding.

Interface modification can also be achieved by surface treatments such
as chemical etching of the metallic reinforcements in as-received or pre-
oxidized condition prior to the composite fabrication. Moore and Kunz (42)
showed that in glass matrix composites containing metal particles, acid
etching of pre-oxidized metal particles generates extensive, uniform sur-
face roughness and that the cracks proceed along the roughened contour of
the particles during the composite fracture. As a result, fracture tough-
ness in this composite considerably improved with such a surface treat-
ment of metal particles.

The principal aim of present study is to elucidate interfacial effects on
mechanical properties of brittle matrix with ductile reinforcement, and
finally to control the interfacial bonding strength in order to obtain opti-
mum mechanical properties in the composite. Ribbon geometry of the rein-
forcement was selected in this study to facilitate ease of fabrication and
theoretical modelling of the composite. First of all, a method to evaluate
the interfacial bonding strength of this composite, single ribbon pull-out
test was adopted in the present study to investigate the interfacial effects
in this composite. Secondly, the interfacial characteristics between the rib-
bon and matrix were modified to obtain the optimum interfacial bonding in
this composite by means of thermal cycling and acid etching techniques.
Finally using the specimens with various interfacial bonding conditions
achieved, increment in fracture toughness of the composite due to crack
bridging was evaluated and consequently, optimum interfacial bonding
strength for maximum fracture toughness in this composite was deter-

mined.

 

 

2. Literature Survey

2-1. Evaluation of Interfacial bonding strength in Ceramic Matrix

Composite
2-1-1. Interface Test Methods

Due to importance of the interfacial properties in composites, numerous
studies have focussed on controlling interfacial bonding strength by means
of modifying interfacial characteristics to achieve desirable composite
properties. Therefore, there is considerable interest in developing simple
experimental techniques and adequate model for assessing interfacial 1
properties. It may be possible to observe debonding initiation in trans-
verse tension and calculate the bonding strength from micromechanics in
some metal matrix composites (43). However, for most composites, this
technique is not adequate because composite fracture precedes interfacial
debonding (44).

The single fiber pull-out test has been widely used to assess interfacial
properties of composites (29-36, 45-53). The pull-out test can determine
the interfacial bonding strength from not only the stress conditions when
debonding initiates, but also the frictional sliding resistance as the deb-
onded fiber is pulled out from the matrix. However, this technique has dif-
ficulty in fabrication of the pull-out test specimens in ceramic matrix
composites, and also the interface in specially prepared pull-out specimens
may not be representative of the actual composites.

To avoid the difficulties associated with the pull-out tests in ceramic

 

matrix composite, Marshall has used microindentation method [Fig. 3(a)],
which is referred to as push-out (or push-down) tests (54,55), to measure
interfacial properties of glass ceramic composites reinforced with SiC
fibers. This technique involves application of a force to the end of a fiber
embedded in a matrix using a microhardness indenter. Interfacial shear
stresses can be evaluated from the applied load and the displacement of
the fiber. Grande et al. (44) have used a spherical indenter [Fig 3(b)]
instead of conventional Vickers microhardness indenter in order to get rid
of the problem arising from sharp indenter; at high load, cracks may be
introduced into the fibers that can influence the measurements. Since
such indentation techniques use real composites, the problems involved in
single fiber pull-out tests do not arise in these techniques. However, the
identification of the debonding event involves a somewhat inaccurate pro-
cedure. Laughner et al. (56) have used thin slices of the composite speci-
mens instead of thick specimens as a variation of the above techniques,
which is sometimes referred to as a push-through method [Fig. 3(c)]. The
thin slice is advantageous for frictional measurements for known debonded
length; however, sufficiently thin slices are difficult to prepare properly
and test, for small-diameter fiber systems. Recently an improved fiber
push-through test has been designed by Warren et al. (57) in metal and
glass matrix composites reinforced with SiC fibers (Fig. 4). This technique
involves push-back procedure following push-through test, which can give
additional information about frictional sliding characteristics of interface
in such composites.

Since indentation techniques are not suitable for this study due to the
geometry of the ribbon reinforcement, the single ribbon pull-out test was

used in this study to evaluate interfacial behavior.

Load

   

lndenter

(8)
Matrix
Fiber
S herical
0’) lanenter

 

 

Fig. 3 Schematic diagrams of indentation techniques (a) with
microhardness indenter (thick specimen), (b) with spherical
indenter (thick specimen), and (c) push-through specimen

(thin slice of the composite).

 

i-

->
<-

Hf

 

 

I
2. L i '2
Fiber //A

(C)

Fig. 3 (continued)

Matrix

A Base

10

Cylindrical Push Rod

Fiber

Matrix

 

 

 

 

 

Piston Support Base

 

 

 

 

 

 

Fig. 4 Schematic diagram of the fiber push-through and push-back
apparatus.

 

11

2-1-2. Theoretical Analyses of Interfacial Debonding and Fiber Pull-out
during Interface Tests

A number of investigations of interfacial shear stress on fiber pull-out in
composites have reported so as to evaluate the bonding strength between
fiber and matrix, using above interface test methods (29-36). Kelly and
Tyson (45) have assumed that shear stress at the interface is distributed
uniformly along the fiber embedded into metal matrix. The stress in the
fiber required to pull-out the fiber from metal matrix is given by

of = 218; (Eq. 1)
where I, is the shear stress at the fiber/matrix interface, a: is a distance
from the end of the fiber, and r is the radius of the fiber. Since this
assumption is based on the idea of metal-matrix yielding under high shear
stress, it can not be applied to ceramic matrix composite in which the shear
stresses at the interface are not alleviated by matrix yielding.

A general relationship between fiber/matrix interfacial shear stress and
embedded fiber length in a pull-out specimen has been developed by
Greszczuk (29), using the assumptions of shear-lag theory (58). The equi-
librium of forces acting on an element of the fiber in a model pull-out spec-
imen and the corresponding boundary conditions are considered. As a
result, he has derived the maximum shear stress along the interface occur-

ring at the point where the fiber enters the matrix, which is given by

Tmax

 

= ale cothale (Eq. 2)

av

12

where can is the average shear stress along the interface, I, is embedded
length of the fiber, and a is a shear-lag parameter dependent on elastic
properties of the constituents and their dimensions (58). If the maximum
shear stress exceeds the interfacial shear strength of the composite, imme-
diate catastrophic debonding between the fiber and the matrix occurs.

Lawrence (30) has developed a theory taking partial debonding and the
effect of frictional forces acting over the debonded portion of the interface
into account. The interfacial frictional force along the debonded interface
results from the existence of residual gripping pressure. The applied load
should overcome this static frictional force along the debonded interface in
addition to the force required for debonding the bonded regions of the
interface. Using the same geometry of the model and the results as
Greszczuk’s, he discussed the maximum load (Pflax) on the fiber required
to achieve complete debonding and initiate pull-out from the matrix. He
concluded that whether debonding continues at this load or an increase in
load is necessary depends on the embedded length of the fiber (1,) and the
ratio of the interfacial shear strength (1;) to the frictional shear stress after
debonding (17). In comparison with Greszczuk’s results (Fig. 5), his conclu-
sion is illustrated in Fig. 6.

Lawrence assumed that the interfacial frictional shear stress(1:f) is con-
stant over the debonded region. However, Takaku and Arridge (31) have
pointed out that due to the Poisson’s effect, the fiber contracts in the lat-
eral direction under tensile stress. This contraction reduces the compres-
sive stress from the matrix, and consequently the interfacial frictional
force decreases. Although they have noticed such behavior of interfacial
frictional stress, they, like Greszczuk, did not take the contribution of fric-

tional shear stress along the debonded interface to their maximum load

13

 

 

 

 

 

 

 

1iav
Tmax
p
'e
(a)
meax‘
- n n
// rav— co sta t
‘\ two.)
>
'9
(b)

Fig. 5 (a) Variation in average interfacial shear stress with embed-
ded fiber length. (b) Variation in maximum pull-out load
with embedded fiber length [from Greszczuk (29)].

 

14

pma
f ’X ,r'lv'i/Tf=1
/ /l1<Ti/Tf<°°

 

 

 

 

 

 

 

 

 

 

 

 

M—
Ti/Tr=°°
>
ocle
(a)
Pf‘ Ti/‘Cf=1 Pf‘ 1<Ti/Tf<°° Pf? Tiltf=oo
> p >
6 5 8

(b)

Fig. 6 Variation. of maximum pull-out load (a) as a function of
embedded fiber length, and (b) as a function of fiber displace-
ment, for various friction conditions [from Lawrence (30)].

15

required to debond into consideration, and assumed that the debonding
process is catastrophic as soon as the maximum shear stress exceeds the
interfacial bonding strength. Instead they have derived the pull-out stress
after complete debonding has occurred, in consideration of the decrease of
the frictional stress due to Poisson contraction of the fiber under tensile

stress. The initial pull-out stress is given by
oi = A (1 — exp (-Bxe)) (Eq. 3)

where x, is the embedded length of the fiber, A is a function of the normal
compressive stress exerted by the matrix on the fiber across the interface
and the elastic properties of the fiber and the matrix, and B is a function of
the coefficient of friction between the fiber and matrix at the interface, and
their elastic properties.

Bowling and Groves (59) have developed a model for the debonding and
pull-out of a ductile fiber embedded in a brittle matrix. They followed a
theoretical treatment of the debonding stress proposed by Outwater and
Murphy (60), based on an energy balance argument:

 

ad = (8:77] + .2151? (Eq. 4)
f f
where Ef is the Young’s modulus of the fiber, rfis its radius, If is the fric-
tional shear stress in the debonded region, 7 is the fiber-matrix interfacial
energy and Id is debonded length of the fiber. According to their model, at
a sufficiently large value of Id, the debonding stress exceeds the yield

stress of the fiber and the relatively large plastic radial contraction of the

16

fiber reduces the frictional shear stress in the debonded region to zero.
Therefore, they have concluded that debonding stress is independent of the
embedded length and is determined by the yield stress and work-harden-
ing rate of the fiber and roughness of debonded surfaces.

A graphical interpretation and analysis of pull-out test results for duc-
tile fibers embedded in a brittle matrix was proposed by Bartos (32), and
Lawrence’s theory was extended to calculate the load-displacement curve
during pull-out, the crack spacing and strength of aligned short fiber com-
posites by Laws (46). Recently Hsueh (35) has provided rigorous solutions
for stresses required to debond the fiber/matrix interface and to pull-out a
fiber in a manner similar to shear-lag analysis incorporating shear defor-
mation in the matrix.

Several approaches have been used to analyze the interfacial shear
stresses in push-out configurations (44,55,57,61-69), since the development
of an indentation method for measuring frictional stresses at interface in
ceramic matrix composite by Marshall. In Marshall’s calculations of slid-
ing frictional stresses at the interfaces based on an energy balance analy-
sis (55), it was assumed that the interfacial shear stress over the embedded
length is uniform, and consequently the influence of Poisson expansion of
the fiber on the frictional shear stresses at interfaces was neglected.
Grande et al. (44) have analyzed the fully bonded fibers in push-out tests
using finite-element method, providing a more accurate modelling of the
localized point loading at the free fiber. A modified shear-lag analysis for
the push-out tests has been proposed by Shetty (61). The Poisson expan-
sion of the fibers under the compressive loads and the consequent increase
of the normal stress aeross the interface leads to a nonlinear variation of

the frictional shear stress along the embedded fiber length. Weihs et al.

17

(64,65) have attempted to incorporate Marshall’s energy balance analysis
with Shetty’s consideration of Poisson expansion of the fiber.

In addition, the importance of roughness of debonded surfaces to the
frictional shear stress at the interface was considered by several research-
ers (53,70,71) who have modelled its effect as an addition to the clamping
pressure causing interfacial frictional shear stress. A detailed analysis of
asperity interactions was presented by Carter et al. (70). Roughness is
modelled as Hertzian contacts, leading to a sinusoidal modulation of the
sliding pressure. Kerans et al. (53) included asperity pressure due to
roughness of the interface in their treatment of clamping pressure, and
have provided a discussion of abrasion during fiber sliding. Most recently
Mackin et al. (71) developed a model considering an elastic asperity mis-
match at the interface resulting in an asperity pressure at the interface

and incorporating fractal models of interface roughness.

2-2. Fracture Toughness Measurements in Ceramic Matrix Compos-

ites

Ceramic matrix composites exhibit dramatic improvement in toughness
compared with monolithic ceramics. Nevertheless, due to the difficulty in
defining representative and universal characteristics of crack propagation
arising from crack front deflection, crack wake delamination and crack
bridging, it is hard to provide a meaningful technique to measure mechani-
cal properties of fiber-reinforced ceramic matrix composite. A number of
researchers have proposed various techniques of fracture toughness mea-
surements in ceramic matrix composites (1-28,72-76).

Single notched beam loaded in three point or four point bending is com-

18

monly used for fracture toughness measurement of ceramic matrix compos-
ites (2-4,18,19). Such measurements are based on the linear elastic
fracture mechanics, which assumes the same mechanical behavior over the
whole sample and the occurrence of a very small process zone in the vicin-
ity of the crack tip. The critical stress intensity factor (fracture toughness)
for single notched beam in three point bending is given by (77)

K, = Y—lnfl— (Eq. 5)

where M max is applied bending moment at peak load, B is the thickness of
the specimen, W is the width of the specimen, a is initial crack length, and
Yis a geometry factor which is a function of a / W. However, as observed by
Marshall et al. (78), debonding along the interface is accompanied with
crack propagation normal to the fibers during failure of the ceramic matrix
composites unidirectionally reinforced with fibers. Therefore, measure-
ment of fracture toughness by flexural tests on the linear elastic fracture
mechanics basis becomes invalid (78,79). In addition to this, the pull-out
effect is not included in this analysis because the behavior after peak load
is neglected. However, this technique may be applicable to ceramic matrix
composites reinforced with particles, assuming isotropic behavior of the
material due to uniform dispersion of small size particles.

Several recent studies have dealt with J -integral method for analyzing
the toughening due to crack bridging in ceramic matrix composites (5-8,10-
13,21-25,73,74). J-integral method developed by Rice (80) provides a solu-
tion for considerable mathematical difficulties encountered in determina-

tion of concentrated strain fields near crack tip in nonlinear elastic

l9

materials. Path independent J -integral is defined by
J = I(wdy— (T. 93)“) (Eq. 6)
r Bx

where F is a curve surrounding the crack tip, (0 is the strain-energy den-
sity, T is the traction vector defined according to the outward normal along
F, E is the displacement vector and ds is an element of arc length along 1".
J is equal to the strain energy release rate as calculated from the usual
continuum solution for small-scale yielding. Employing path independent
J -integral in Dugdale-Barenblatt crack model (81) shown in Fig. 7, with
dy=0 on F, Eq.6 can be written as

J = jg‘o(8)d5 (Eq. 7)

where 5, is the separation distance at the crack tip. Some researchers
evaluated the fracture toughness due to crack bridging by intact fibers in
ceramic matrix composites using J -integral method with same concept as

Dugdale-Barenblatt crack model (Eq. 7) and obtained
AGc = Jc .-.- ijg‘orumu. (Eq. 8)

where AGc is the critical strain energy release rate, Vf is the area-fraction
of reinforcement intercepted by the crack, o( u) is the normal stress acting
on the reinforcement, and u" is the crack opening at the point where rein-
forcement fails. However, if the crack opening distance in the crack bridg-

ing zone is relatively large due to weak bonding, then dy in Eq. 6 can not be

20

in

 

5: SEPARATION DISTANCE
gr
{‘I I I I I I I I l Ezra-—

v “II

31
t 0(5): RESTRAINING STRESS
X

(a)

 

 

 

 

‘—
‘—
<—

l

 

6.

 

(b)

Fig. 7 Dugdale-Barenblatt crack model (81). (a) Cohesive zone at
crack tip with restraining stress dependent on separation
distance; (b) force-displacement relation for atomic attraction
in elastic brittle fracture.

21

considered as zero, and consequently Eq. 7 can not be obtained in this case.
Therefore, J -integral method does not seem to be an appropriate method to
evaluate the fracture toughness of ceramic matrix composite, especially
with metallic fiber-reinforcement. However, taking only the result of this
approach into account, Eq. 8 represents the strain energy release rate due

to crack bridging by intact reinforcements.

2-3. Strength Analyses in Ceramic Matrix Composites

Many ceramic matrix composites in which the failure strain of the
matrix is less than that of the fiber experience cracking of the matrix when
subjected to a uniform stress in the fiber direction. A critical stress at
which the composite displays first evidence of the matrix cracking is called
first matrix cracking stress. The first matrix cracking can cause damage to
mechanical behavior of the composites. First of all, matrix cracking
reduces the elastic modulus of the composite. Moreover, the intact fibers
are exposed to oxidizing environment due to such cracks resulting in
strength deterioration of the composite at elevated temperatures. There-
fore, the first matrix cracking stress can be considered as a design stress in
many applications of the composites at elevated temperatures. A number
of micromechanics] models which relate the first matrix cracking stress to
composite parameters have been developed (82-88).

Aveston, Cooper and Kelly (ACK) (82) have analyzed the mechanism of
matrix fracture in fiber-reinforced brittle matrix composites with friction-
ally coupled interface. Their approach was based on an energy balance cri-
terion under steady state cracking. According to this analysis, the matrix

failure strain of the composite, smuc, will be enhanced only when

22

 

2 1/3
(Vi ) E’ (E 9)
emu< 12mm 717; (E61531) q.

where emu is the normal failure strain of the monolithic matrix, 1: is the
fiber/matrix interface shear strength, 7m is the matrix fracture energy, r is
the fiber radius, and Ef, EC and Em are the Young’s moduli of the fiber, com-
posite and matrix, respectively. As long as the condition in Eq.9 is satis-
fied, emuc increases with variation in composite parameters. On the other
hand, as mentioned by Davidge (84), when the inequality in Eq. 9 is not
obeyed, the matrix failure strain in the composite will be equal to the fail-
ure strain of the monolithic matrix, i.e. emu=emuc. Further increase in
strain results in matrix cracks normal to the fibers.

Budianski, Hutchinson and Evans (BHE) (83) have treated both fric-
tionally and adhesively coupled interfaces and studied the matrix cracking
stress in a more rigorous fashion. They concluded that in the Coulomb
friction-operative case, the larger strain mismatch would not lead to the
higher matrix cracking stress, despite the larger frictional resistance avail-
able. This is due to the fact that the same strain mismatches also lead to
axial tensile stresses in the matrix which act to reduce the matrix cracking
stress. Therefore, optimal strain mismatches exist for maximizing the
matrix cracking strength. On the other hand, in the case of initially
bonded fibers, the matrix cracking stress would increase with interface
bonding toughness. More recently, Sutcu and Hillig (SH) model (86) also
included the effect of both the adhesion and friction on the first matrix
cracking stress, considering axial tensile stress to cause debonding. Each
of these models assumed a steady-state matrix cracking and predicted

dependence of the first matrix cracking stress on the interfacial shear

23

strength in brittle matrix composite.

Singh (87) has recently compared the theoretical predictions of these
models with experimentally observed values of matrix cracking stress in
ceramic matrix composite. According to his experimental results, the
matrix cracking is controlled by the critical strain for matrix cracking
rather than the interfacial properties. He concluded that his results did
not agree with the prediction of energy-based models such as ACK, BHE
and SH models, but appeared to be in good agreement with a strain-based
model suggested by Davidge (84).

In addition to the first matrix cracking stress, the ultimate load-carry-
ing capacity of the composite is of interest as well. Schwietert et al. (88)
have presented a theory for computing the ultimate tensile strength of
fiber-reinforced composites with multiple matrix cracking, considering the
distribution of fiber breaks and their contribution to the diminished load-
carrying capacity of the composite. They concluded that the strength of the
composite depends sensitively on the interfacial shear stresses and on the

fiber strength variability.

3. Experimental Procedure

The composite specimens were fabricated by sandwiching technique (89)
using as-received or acid-etched ribbons. The ribbon geometry for rein-
forcement was selected to facilitate the ease of fabrication and theoretical
modelling of the composite. Acid etching of the ribbon, in as-received or
pre-oxidized conditions, was performed in order to medify the interfacial
characteristics of the composite (42). Interface modification was also car-
ried out by thermal cycling the composite specimens reinforced with as-
received ribbon for various numbers of thermal cycles (41); the maximum
temperature of the thermal cycles was also changed to achieve different
thermal stress conditions. Pull-out tests of the specimens in various bond-
ing conditions were carried out to evaluate the interfacial bonding
strength. The fracture toughness of the composites was measured by three
point bending test using single notched beam specimens, and by tensile

testing pre-cracked specimens (22).

3-1. Materials

The matrix material used in this study was soda-lime slide glass (73
wt% Si02 - 15 wt% Na20 - 4 wt% MgO - 7 wt% CaO - 1 wt% A1203 ). The
dimensions of this slide glass was 76.2mm x 25.4mm x 1.1mm. Nichrome
ribbon (80 wt% Ni - 20 wt% Cr) was chosen as the reinforcement. The
Nichrome ribbons were 1.5 ~1.8mm wide and 80 um thick. Tensile proper-
ties of a Nichrome ribbon with same heat treatment conditions as involved

in the composite fabrication (450°C for 1 hour, and then 710°C for 3 hours)

24

 

25

was determined by Instron testing machine. The tensile stress-strain
curve of the Nichrome ribbon used is shown in Fig. 8. The mechanical and
physical properties of the matrix and ribbon used in current study are

shown in Table 1.

 

3-2. Composite Fabrication

Specimens were fabricated by sandwiching a series of aligned ribbons

between the glass slides (89), as shown in Fig. 9. Prior to sandwiching the

 

ribbons, the glass slides and Nichrome ribbons were cleaned with acetone
and rinsed in distilled water. To avoid misalignment of the glass slides and
ribbons during loading of the specimen into the furnace, a small amount of
epoxy glue was applied to the corners of the glass slides. A pair of stainless
steel plates (100mm x 40mm x 1.5mm), one as the base plate on which the
specimen is placed inside the furnace, the other as cover plate on which the
weight is applied, were utilized. A stainless steel block (100mm x 35mm x
10mm) (0.75 lbs) was used as a weight to achieve good contact between the
matrix and the ribbon. The stainless steel plates were coated with BN
spray in order to avoid sticking to the samples and to prevent their oxida-
tion during fabrication.

The composite fabrication involved two steps of heating: 450°C for 1
hour and 710°C for 3 hours. The low temperature step avoided gas trap-
ping at the interface regions of the composites resulting from outgassing of
the epoxy glue during fabrication. The high temperature step, which used
a temperature of 10°C higher than the softening temperature of soda lime
glass, allowed the glass to flow and cause adherence to the reinforcements.

The weight (stainless steel block), and the top stainless steel plate were

STRESS (MPa)

 

26

 

 

 

 

 

 

 

 

 

 

 

unit: mm
R:6.4
\ i
5 10
s
‘*—'127'—*fi
700—
600-
500-
400-
300-
200-
100-
0 l I I l I I I l T j
01) 01 ()2 0&3 OA- ()5

STRAIN (mm/mm)

fig. 8 Typical stress-strain curve of the Nichrome ribbon obtained

from tensile test.

27

Table 1: Physical and mechanical properties of constituents of the composite

 

 

 

 

 

 

 

 

Matrix Ribbon
soda lime
Material slide glass Nichrome
Thermal Expansion Coeffi- 9.2 14.3
cient
(10'6/°C) , (25 °C ~ 500 °C)
Young’s Modulus (GPa) 72 213
Yield Strength (MPa) 305
Tensile Strength (MPa) 700
Softening 'Ibmperature (°C) 700

 

 

 

 

 

28

 

 

 

 

 

 

 

 

I
::':11211;222:2335:2:2;2;2;t~:°:~:-:°:'Rot-:0}:-:-:tot-9:40:09??? ‘ WBIth
.,_. A_.,l,-.; .' ‘ .
r. ICU"; .4.- ‘-I-‘.’-1a;~ . utvn :5. ~.. -' ‘7‘ Sta|nless Steel p'ate
.-:::_I.""TT"““TT'Tmimff'” ”tr-"mm- ~ nah-er - l~" ‘ ”W!- “W _ BN t. g
. l. ~1- r W coa 'n
Sllde glass——
_ — ——--N' h 'bb
IC rome II on
.M'IJJ M...“ ”:5“ ;‘i u “M ‘7‘!—
(a)

 

 

 

 

 

 

Fig. 9 The schematics illustrating sandwiching of a series of
aligned ribbons between the glass slides: a) general set-up, b)
composite from which pull-out test samples were cut out, and
c) composite from which fracture toughness test samples

were cut out.

 

29

removed after cooling to 500°C. The composites were annealed at 500°C
for 2 hours, then cooled to room temperature in the furnace. Entire com-
posite fabrication was carried out in ambient atmosphere.

Pull-out specimens (4mm x 10mm x 15mm) and fracture toughness test
specimens (5mm wide and 6mm thick) were cut out from the fabricated
composite stocks using a low speed diamond saw. The schematics of typical
pull-out and pre-cracked tensile specimens are shown in Figs. 10 and 11
respectively. The composite specimens cut to proper dimensions were
mechanically polished with a series of abrasive grit papers ranging from

240 grit to 600 grit.

3-3. Interface Modification

3-3-1. Thermal Cycling Technique

Thermal cycling method used in this study involved placing the specimens
on a platform in the center of a standard laboratory furnace (Lindberg) at
various temperatures for 3 hours, followed by cooling in still air and hold-
ing at room temperature for 3 hours. The maximum temperatures used for
thermal cycling were 500, 550, 600, and 650°C. These temperatures lie
between the strain temperature (480°C) and softening temperature
(700°C) of soda lime glass. These thermally cycled specimens are referred
to as 500-TC, 550-TC, 600-TC, and 650-TC specimens in this study. The
number of thermal cycles chosen in this study were 3, 5, and 7 cycles for

each maximum cyclic temperature.

 

 

30

Y (transverse)

j—v X (longitudinal)

Z (lateral)

 

MATRIX

 

 

 

 

 

f
l

RIBBONI

 

 

 

 

 

 

Fig. 10 The schematic of typical pull-out

specimen.

 

 

31

 

 

 

 

a =1 ~1.2mm

Id—B——> (a) B = 6.0mm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

W=5.0mm
w = 1.8mm
t = 80 um
i)
I ‘ I6 is variable.
nbbon
' w - le
pro-crack -‘ ' f ,_ =7 y
mTjr I
(b)

Fig. 11 The schematic of typical fracture toughness test specimens:
a) single notched specimen for flexure test, and b) pre-

cracked specimens for tensile test.

32

3-3-2. Acid Etching Technique

Prior to the composite fabrication, the surfaces of Nichrome ribbons
were etched in order to modify the interfacial characteristics of the com-
posites. The ribbons in both as-received and pre-oxidized conditions were
acid etched. Pro-oxidizing of the ribbon involved holding the Nichrome rib-
bons (cleaned with acetone and rinsed with the distilled water) at 650°C
for 1 hour. The oxide layer produced by such a step reduced the intensity
of acid etching on the ribbon surfaces. The Nichrome ribbons, in both con-
ditions, were etched with a solution of 20% HNO3 and 80% HCl for various
lengths of time: 5, 15, 30, 60 and 90 seconds.

3-4. Mechanical 'lbsting

Pull-out tests were carried out on the composite specimens with various
interfacial bonding conditions to evaluate the interfacial bonding charac-
teristics. These tests were conducted on a computer controlled Instron
testing machine (model#4206), with a specially designed self-aligned fix-
ture. The crosshead speed used was 0.5mm/min. For effective tensile grip-
ping, the glass part of the specimen was held by glass-fiber reinforced
epoxy tabs which was glued to the fixture (90). The glass fiber-reinforced
epoxy tabs were used to prevent the cracking of glass matrix during tight-
ening of the sample to the fixture. In addition, a dab of glue was also
applied to the glass part of the specimen, before putting it on the fixture, to
avoid slippage during pull-out test. The schematic of the experimental set-

up for the tensile test is shown in Fig. 12.

33

 

crosshead
> load cell

 

 

 

 

 

U 33"}?

 

3——> upper grip

\J

 

UUV

self-aligning fixture

lower grip

 

4
.I
I
I'
4
.I
.I
.I
I
l
.I
.I
.I
.I
I
I'
4
.I
.I
.l
I
I’
a
.I
I
I

 

 

 

 

 

 

 

 

(a)

Fig. 12 A schematic of the experimental set-up for the tensile test:
a) general set-up, b) self-aligning fixture. The aligning rails
were removed after positioning the specimen in the testing

machine.

Inside of fixture
covers

 

 

 
 
 

glass reinforced
epoxy

 

supporting 1

rod

Fig. 12 (continued)

 

 

 

 

 

 

+ screw hole

--> pull-out sample

—> aligning rail

 

 

 

 

i—r screw

 

 

i

35

Fracture toughness behavior of the composite was evaluated by both

 

flexure and tension tests on the same specimen. The tension tests were
carried out on pre-cracked specimens resulting from the flexure tests. The
length of the specimens was varied from 20mm to 30mm. For flexure test,
the composite specimens (5mm wide and 6mm thick) were initially notched
by a slow speed diamond saw at the center of the specimen. Since diamond

saw provides a blunt notch, a razor blade was used to produce a sharper i

notch at the base of the blunt notch. The resulting depths of the notches

 

were measured after tension tests. Those values ranged between 1mm- I
1.2mm. These single notched specimens were loaded on a three point
bending fixture with a 18mm span in an Instron testing machine. The
crosshead speed was 0.2mm/min. Bending of the composite specimen was
continued until the matrix cracked, as indicated by a drop in load. Due to
such a procedure, the specimen contained a continuous matrix crack
around the Nichrome ribbon. A sketch of a pre-cracked specimen is shown
in Fig. 11. Using values of the peak load obtained from three point bending
tests, ch was calculated using linear elastic fracture mechanics (7 7). Ten-
sion tests were carried out with these pre-cracked specimens, in order to
study the effect of crack bridging on the fracture toughness of the compos-
ite (22). A tensile testing machine (Instron) was used in these tests with a
specially designed self-aligning fixture (Fig.12). The crosshead speed was
0.5mm/min. The pre-cracked specimens were placed in the self-aligning
fixture. The ends of the specimens (to be gripped) were held by glass-fiber
reinforced epoxy tabs which were already glued to the fixture. In addition,
a dab of glue was also applied to the ends of the specimen (to be gripped)

before putting it on the fixture. The stress-displacement curves were

36

obtained using the Instron testing machine at a crosshead speed of 0.2mm/
min. The areas under the curves were measured, and the values of the

fracture toughness due to crack bridging were calculated by using Eq. 8.

3-5. Micrographic Observation

For the interfacial studies using SEM, the specimens were cut perpen-
dicular or parallel to the specimen length with a low speed diamond saw.
The cut samples were mounted in lucite and mechanically polished with a
series of abrasive grit papers ranging from 240 grit to 600 grit followed by
polishing on cloth using 5pm to 0.3um size alumina powder abrasives. The
polished specimens were etched with a solution of 20% HNO3 and 80% HCl
for 20 seconds. Fractographic observations were made on the specimens
fractured during tensile loading, using the Olympus stereo optical micro-
scope equipped with two fiber-optic transmitted light sources. The direc-
tions of light sources were changed until a interference fringe pattern

representing the crack path could be observed.

 

4. Results and Discussion

4-1. Theoretical and Experimental Analysis of Debonding Process
of Ductile Ribbon Embedded in Brittle Matrix

4-1-1. Theoretical Modelling

Several analytical models of debonding process during fiber pull-out in
fiber-reinforced ceramic matrix composites have been developed (29-36).
Among these, the model suggested by Lawrence (30) was adopted in this
study for elastic behavior of the sample shown in Fig. 8. The ribbon geom-
etry of the reinforcement was used in this study so as to simplify the mod-
elling and to achieve easy fabrication of composites. The distribution of
shear stress (1:) along the interface at a point with a distance x from the

embedded end of the ribbon due to applied load (P) is given by (30)

 

(Eq. 10)

1: _ Pa coshax
' 2(w+t) (Sinhale)

where w and t are width and thickness of the ribbon respectively, I, is

embedded length of the ribbon, and a is a shear-lag parameter dependent
on elastic properties of the matrix and the ribbon and on their dimensions
(31). The maximum shear (“rm”) which is obtained at the boundary where

the ribbon enters the matrix is

Pa

Tmax = 2(w+t)

cothale (Eq. 11)

37

 

38

Since the values of coth (11,, approach unity for larger values of le, tmax can

be considered to be independent of I, for large values of le.
4-1-1-1. Load Required to Initiate Debonding

In ceramic matrix composite reinforced with metallic ribbon, the bound-
ary where the ribbon enters the matrix is affected by plastic deformation of
the unembedded region of the ribbon. Therefore, the shear stress due to
plastic deformation of the ribbon as well as the shear stress due to shear-
lag analysis acts at the interface along the boundary between free and
embedded areas of the ribbon. These shear stresses are shown in Fig. 13.
For simplification of this modelling, this can be considered as a 2-dimen-
sional model because the thickness of the ribbon is negligible compared to
its width and length. Accordingly, the sketches in Fig. 13 illustrate long
transverse faces of the specimens. The amount of shear stress that can
contribute to debonding (1:8) equals to the resolved shear stress available in
excess to that required to initiate plastic deformation, and Is is assumed to
act along a direction at 45° to the pull-out direction. This assumption can
be explained by Hall-Patch model for deformation of polycrystals (91).

o P-wtoo

= —— (Eq. 12)

1-1 -1: -O—°
- -2 .2— 2wt

8 rss yrss
where 1,8, is resolved shear stress due to applied normal stress, 1:3,,“ is
resolved shear stress required for yielding of the reinforcement, o is
applied normal stress, and do is yield stress. 18 is combined with In,” to
obtain the resultant shear stress (It) at the interface along the boundary

between free and embedded areas of the ribbon, so that

 

39

 

 

 

 

 

 

Fig.13 Shear stresses due to tensile loading at edge of the embedded
area Irma, : shear stress obtained by modified shear lag
model (30), t, : resolved shear stress available in excess to
that required to initiate plastic deformation of the ribbon by
slip, and 1. : resultant shear stress due to 1m” and 1,] Note:
1, is at 45° to the direction of P.

40

 

1:t = «ltrznax + Jz-tmaxts + If (Eq' 13)
When resultant shear stress along the boundary between free and embed-
ded areas of the ribbon (1,) exceeds the interfacial shear strength of the
composite (ti), interfacial debonding initiates. Therefore, the interfacial

shear strength of the composite can be written as

 

ri=frxd )2+J§(rd

max max

) (13H (1,852 (Eq. 14)

where superscript ‘d’ corresponds to debonding condition. Accordingly,

Pd-wto

Pdor a
max = WcOthale and I: = W (Eq. 15)
where Pd is the load required to initiate interfacial debonding of the com-

posite.
4-1-1-2. Load Required for Continuation of Debonding

After initiation of interfacial debonding, static frictional force (Pf)
arises at the debonded interface due to residual gripping stress (on). This
residual gripping stress is due to thermal expansion coefficient mismatch
between the ribbon and the matrix (31). Therefore, in order to continue to
debond, the applied load (PI) should overwhelm this static frictional force
as well as the load required to debond at the bonded/debonded boundary
(Fig. 14).

 

41

 

 

 

 

 

Fig. 14 Load(P Jrequired for continuation of debonding:
P > P, + P,f where P,d 18 force required to debonding, and

P, x" 18 the frictional force between debonded region (shaded
area) of ribbon with the matrix.

42

The load required to continue debonding at the bonded/debonded boundary
(P,d) can be determined from (Eqs. 14 and 15) under the assumption that
interfacial shear strength (12,-) is uniform through the whole interface of the
composite. At the location marked Q in Fig. 14, the debonded length is (l,-
x), and the interfacial shear strength is

 

2 2
r, = Jeff) + Jé (cf) (1?...) + (1?...) (Eq. 16)

where

Pda P? -wto

= x d = ____° .
x 2 (w+t) cothorx, and 1: ’ (Eq 17)
The static frictional force (P,f) at the debonded interface can be determined
in the following manner. Assuming coefficient of friction (u) to be a con-
stant throughout the debonded interface, frictional force change (dP,f)
with infinitesimal change in distance (dx) at Q (Fig. 15) is

dPJft = 2 (w+t)uondx (Eq. 18)

However, under external tensile loading, contraction of thickness of the
ribbon due to elastic and plastic deformation reduces the gripping stress
from the matrix, resulting in decreased frictional force. Reductions in the
gripping stress from the matrix result from Poisson’s effect due to elastic
deformation by he, (31) and from slip due to plastic deformation by as,
where k is a constant depending on the elastic properties of the constitu-
ents of the composite, a, is normal stress at Q in the direction of the ribbon

pull-out, and a, is a component of r, mentioned in previous section in the

43

 

 

 

W//////////////%

 

Fig.15 Static frictional force at the debonded interface : contraction
of thickness of the ribbon due to elastic and plastic defama-
tion reduces the gripping stress from the matrix.

 

 

44

thickness direction of the ribbon. Under such conditions Eq. 18 can be

rewritten as
de = 2(w+t)u(on-kor—os)dx (Eq. 19)

a, in this equation can be replaced by 0'0 since the ribbon would have
yielded under these conditions. The static frictional force at Q (P,f) can be
obtained by substitution of o, and o", and by integration of Eq. 19 from I,
through 1::

x (w'I't) 1:
pl; =2(w+t)uL.(on-koo)dx- J2wt u ,(PZ—wtcowx (19,20)

 

In order to continue debonding, the applied load (P1) should become
19,310;l +P§ (Eq. 21)

Further plastic deformation of the ribbon after debonding is neglected in

this analysis.
4-1-2. Experimental Analysis

A typical load-displacement curve obtained in pull-out test of the
Nichrome ribbon embedded in soda-lime glass matrix is given in Fig. 16.
In this test, the load linearly increases up to the point ‘A’, corresponding to
the yield point of the ribbon. The free (unconstrained) area of the ribbon
starts to deform plastically at point ‘A’, and work hardens on further defor-

mation. This smooth work hardening curve is interrupted by small load

 

STRESS(MPa)

45

 

 

700-
. C Pull—out. starts
600- _
Debonding
. starts
500-
400- .
- A 33:338. 2.1.2::
300-
soc-JI
100-
0 r I I I I I I l I I I [ fi
0 1 2 3 44 5 6 '7
DISPLACEMENT(mm)

Fig.16 Typical stress-displacement curve obtained in pull-out tests
of Nichrome ribbon embedded in soda lime glass matrix.

46

drops, and the first load drop ‘B’ is associated with initial debonding at the
ribbon-matrix interface. As speculated by Morten et al. (90), the debonding
front actually propagates in small jumps rather than continuously, accom-
panied by the small load drops on the load-displacement curve. After ini-
tial debonding, the load continuously increases as debonding progresses
until the load reaches a peak point ‘C’. At point ‘0’, complete debonding
occurs along the full embedded length, and at the same time the ribbon
pull-out initiates. The sudden load drop at this initiation of pull-out of the
ribbon was not observed in this experiment. The explanation for this fact
will be discussed in detail later. After initiation of pull-out, the load con-
tinuously decreases to zero until the ribbon is completely pulled out from
the matrix.

SEM micrographs of the ribbon/matrix interface are shown in Fig. 17. A
relatively thin oxide layer that can be seen at the interface facilitates
chemical bonding between glass matrix and ribbon. The interface of this
composite contains partially debonded regions due to the considerable mis-
match in thermal expansion coefficients of the ribbon and the matrix. The
crack was observed along the weak interface between the oxide layer and
the Nichrome-metal. In this composite, the ribbon experiences tensile '
stresses in the lateral, longitudinal, and transverse directions due to the
larger thermal expansion coefficient of the ribbon than that of the matrix.
Therefore, once debonding occurs, the ribbon contracts not only in the lat-
eral direction but also in both longitudinal and transverse directions. Con-
sidering dimensions of the ribbon, displacements due to longitudinal and
transverse contraction of the ribbon are much larger than that due to lat-
eral contraction. On the other hand, tensile loading during pull-out test

gives rise to longitudinal plastic extension of the ribbon. As a result, longi-

47

MATRIX

 

Fig.17 SEM micrograph of the partially debonded interface between
the Nichrome ribbon and the soda lime glass matrix

48

tudinal contraction of the ribbon due to release of the residual tensile
stress by debonding vanishes and only plastic extension of the ribbon
exists in the longitudinal direction. ' Consequently, transverse contraction
and longitudinal plastic extension of the ribbon, coupled with the micro-
scale roughness of the debonded surfaces, result in the mechanical keying
of the debonded surfaces providing compressive stresses at the interface,
as schematically shown in Fig. 18. The SEM micrograph of the interface
between the ribbon and the matrix after debonding progresses to some
degree is given in Fig. 19. To confirm progress of the debonding process,
loading had been interrupted just before the ribbon can pull out from the
matrix. The shear failure at the interface can be observed at the deep
embedded location (M). It could have resulted from the plastic contraction
in width of the ribbon as well as from the distribution of the shear stresses
along the interface due to tensile loading. Although further plastic defor-
mation of the ribbon after debonding was not considered in this analysis,
this behavior was also indicated by increased crack opening of initially
debonded location (N) in this figure.

The interfacial shear strength (1:5) of this composite as a function of
embedded ribbon length is shown in Fig. 20. These values of the interfa-
cial shear strength of this composite were obtained by equations (14) and
(15), using the results of load-displacement curves obtained experimen-
tally. The interfacial shear strength of this composite was evaluated to be
97.9 :l: 15.0 MPa. Plot of loads required to continue debonding as a function
of debonded length, obtained on the basis of section 4-1-1-2, is given in Fig.
21. The load required for continuation of debonding (P,) is the sum of the
load required to debond at the bonded/debonded boundary (P,d) and static
frictional force (Pf). P,d gradually decreases with increasing debonded

 

49

 

MATRIX >

SURFACES \/\/\/\/

<-—- RIBBON

00
W
\ \ \

Fig.18 Mechanical keying of debonded surfaces produced by rough-
ness of debonded surfaces, transverse contraction, and longi-
tudinal plastic extension of the ribbon due to tensile loading
after debonding.

50

MATRIX RIBBON

 

RIBBON MATRIX

 

 

 

 

 

 

 

Fig.19 SEM micrograph of the interface between the Nichrome rib-
bon and soda lime glass matrix after debonding progresses to
some degree

51

 

 

 

,\ 200-
‘U ..
Q.
E q
:3 .
S a
z 150‘
a: .
01 ..
9*
U) ' 0
U " ' AV. : 97.9MPa
E 100- . .
Q - o
5 ~ - -
a] .
2] .
E3 50-
< 1
E4 .
D:
m a:
5‘ .
E
O I l I l I
2 3 4

EMBEDDED LENGTH (mm)

Fig.20 Interfacial shear stresses for debonding various embedded
lengths of the Nichrome ribbon

52

 

 

 

 

 

DEBONDED LENGTH (mm)

Fig.21 Loads required to continue debonding as a function of deb-
onded length : P, = 1D," + P,’

 

53

length (le-x) at a very low rate in the beginning. However, when the
bonded length(x) remains very short, P,d rapidly drops. This phenomena
is attributable to the behavior of function coth our in the expression for t,d,
and the contribution of plastic deformation of the ribbon (1:8,,d) (Eq. 17 ).
Especially, at short bonded length, since P,d is not large enough to yield
the ribbon, the contribution of plastic deformation of the ribbon does not
affect the plot of P,d. P,d eventually becomes zero when complete debond-
ing is accomplished. On the other hand, the static frictional force (P,f)
monotonically increases with debonded length (le-x), with a rapid increase
at small :5 due to the absence of plastic deformation of the ribbon. Since
the plastic deformation of debonded ribbon is neglected in this analysis,
the values of P,f obtained will be overestimations. Therefore, the sum of
the above two components which represents loads required for continua-
tion of debonding (P,) must also be overestimated in this analysis,
although the difference of maximum peak loads between this analysis
(94.5N) and actual result (92.0N) was not remarkable. As shown in Fig.
21, loads required for continuation of debonding (P,) steadily increases to a
maximum and then drops. Therefore, the debonding process in this case is
catastrophic at the maximum required debond load. In general, it is said
that if catastrophic debonding occurs, the load suddenly drops in load-dis-
placement curve (34). However, this sudden load drop was not observed in
load-displacement curve in this experiment. It can be explained by the
roughness of the debonding surfaces of the composite which influences the
sliding frictional force during the pull-out of the ribbon from the matrix.
The roughness of the debonded surfaces that exist in this composite (Fig.
19) may contribute to this behavior.

The effects of embedded length on the normal stress acting on the rib-

| .1 ' LI
-3'
I :L

54

bon when debonding starts (6;), and normal stress when debonding is com-
pleted (Of) are shown in Fig. 22. These stresses were obtained by dividing
the corresponding loads by the ribbon cross-sectional area. The experi-
mental results indicate that bath a,- and of remain constant for embedded
lengths in excess of a critical length. The result of o,- agrees well with the
theoretical analysis by Hseuh (35), which dealt with elastic fiber/elastic
matrix system. This good agreement may be due to the fact that the term
accounting for plastic deformation of ribbon (Eq. 12) is independent of the
embedded ribbon length. On the other hand, contraction in thickness due
to further plastic deformation of the ribbon after debonding gives clearance
to debonded interface, resulting in no static frictional farce. Therefore, no
matter how long the embedded length may be, only certain newly debonded
length undergoes static frictional farce. Since ofis mainly affected by ini-
tial debonding stress (6;) and static frictional force at the debonded inter-
face as illustrated in Fig. 21, it reaches a constant value for embedded

length in excess of a critical value.

55

700!

 

03

O

O
l

J

 

0‘

O

O
l

 

4:.

O

O
l

NORMAL STRESS (MPa)

 

 

O l I I l I I I I I
0 1 2 3 4

EMBEDDED LENGTH(mm)

(”J

Fig.22 Effect of embedded length on the normal stress on the ribbon
when debonding starts (6;), and normal stress when debond-

ing is completed (6,) in soda lime slide glass reinforced with
Nichrome ribbon.

56

4-2. Interface Modifications

4-2-1. Thermal Cycling Technique

Typical stress-displacement curves of as-fabricated, and 650-TC speci-
mens that have undergone 3, 5 and 7 cycles given in Fig. 23 illustrate that
these thermal cycles significantly affect the mechanical behavior of the
composite. However, stress-displacement curves of 500-TC specimens are
about the same as that of the as-fabricated specimens. This behavior indi-
cates that the thermal stresses developed in 500-TC specimens might not
be high enough to cause microcracks at the interface after 5 thermal cycles.
As shown in Fig. 24, in 650-TC specimens microcracks are generated at the
interface after 3 thermal cycles and they link to form an almost completely
connected crack after 5 thermal cycles. These SEM findings account for
the observed stress-displacement behavior of the composite due to thermal
cycling. In addition, a variation in stress-displacement curves for TC spec-
imen, with various maximum cyclic temperatures, is apparent in Fig. 25.
These curves were obtained after 5 thermal cycles up to each maximum
cyclic temperature. Although a maximum temperature of 500°C does not
cause microcracks at the interface after 5 thermal cycles, microcracks do
accumulate at the interface after 5 thermal cycles with increasing maxi-
mum cyclic temperatures. The experimentally measured values of interfa-
cial bonding strength and frictional shear stress are summarized in Tables

2and3.

57

     

 

 

 

 

 

 

 

7001
600-
”a?
0.. 500-
5
Cf) .l
E3 400- 3 cycles
0:.
E. d
U)
._‘1 300-
<2
E c-
E ..
O 200
Z .
100
0I ' I ' H—Fx I I I T I
1 2 3 4 5 6 '7
DISPLACEMENT(rnm)

Fig.23 Typical stress-displacement curves of as-fabricated, and 650-
TC specimens after various numbers of thermal cycles.

58

 

(a)

Fig.24 SEM micrographs at interfaces of (a) as-fabricated speci-
mens, (b) 650-TC specimen after 3 cycles, and (c) 650-TC
specimen after 5 cycles.

59

 

(b)

Fig.24 (continued)

 

60

 

 

(c)

Fig.24 (continued)

61

. AS-FAB
500°C

0"

O

O
l

A

O

O
l

 

 

NOMINAL STRESS(MPa)

 

 

 

-
C
_
I
-

 

INSPLACEMENThnnfl

Fig.25 Stress-displacement curves of specimens that have under-
gone 5 thermal cycles with variaus maximum temperatures.

 

62

ous numbers of thermal cycles

Table 2: Measured interfacial properties of 650-TC specimens after vari-

 

thermal cycling conditions

 

 

 

 

interfacial
properties

as-fab 3 cycles 5 cycles - 7 cycles
interfacial
bonding 97.9 74,9 20.7 7.61
strength 1218.2 110.2
(MPa) i156
frictional
shear 9.24 3,33 2.62 1.05
stress 1 2.16 fl 13 $1.07 :l:0.44
(MPa) '

 

 

 

 

 

 

63

Table 3: Measured interfacial properties of thermal cycled specimens up

to various maximum temperatures after 5 thermal cycles

 

thermal cycling conditions

 

 

 

 

interfacial
properties

as-fab 500°C 550°C 600°C 650°C
interfacial
bonding 97.9 98.1 83.7 45.2 20.7
strength i182 :l:7.8 :84 110.2
(MPa)
frictional
shear 9.24 10.26 5.05 4.90 2.62
stress :l:2.16 i248 i218 $1.07

(MPa)

 

 

 

 

 

 

 

 

64

4-2-1-1. Effects of thermal Cycling on The Interfacial Bonding Strength

and Frictional Shear Stress

The interfacial bonding strengths of 650-TC specimens that underwent
various numbers of thermal cycles are given in Fig. 26. These were
obtained from modified shear-lag analysis, taking plastic behavior of the
metallic ribbon into account as mentioned in sec. 4-1-1 (Eqs. 14 and 15).
The interfacial bonding strength decreases with increasing number of
cycles and drops significantly between 3 cycles and 5 cycles. As mentioned
earlier in 650-TC specimens, microcracks were generated after 3 cycles,
and most of them linked together after 5 cycles, and resulted in a com-
pletely connected crack at the interface after 7 cycles. As a matter of fact,
most of the specimens that have undergone 7 thermal cycles showed com-
pletely debonded interfaces. The value of the interfacial bonding strength
for this condition shown in Fig. 26 was obtained from only one specimen
that contained some bonded interface. The effect of maximum cyclic tem-
perature on the interfacial bonding strength after 5 thermal cycles is pre-
sented in Fig. 27. Rapid decrease in interfacial bonding strength occurs
between 500°C and 600°C.

In addition, the frictional shear stresses on the debonded surfaces of
650-TC specimens after various numbers of thermal cycles, and after 5
thermal cycles at various maximum temperatures are presented in Tables
2 and 3 respectively. These values of the frictional shear stress were calcu-
lated under the assumption that frictional shear stress is constant over the
debonded region, and were obtained from dividing the initial pull-out load
by total embedded area. As can be noticed from Tables 2 and 3, the fric-

65

 

 

 

A 140-

(U

m d

E 120

:1: " __

5‘ ..

E

0.1

E“ q

U)

U 80- —

E .

O

z 60-

O

m I

j 40-

8 I

E

Q: 20" 1

E13

2 ‘ o
0 I I

l l l I l I I
0 1 2 3 4 5 6 7 8

NUMBER OF CYCLES

Fig. 26 Interfacial bonding strengths of 650-TC specimens after vari-
ous numbers of thermal cycles.

66

 

 

 

A 140-
(D
[L .
5 120
E . ‘i’
LzD
as
Eq -
m I
0 so- ——
g .
a
z 60-
o
m I
O
:3 4a-
5 .
<2
fi 20- I
m ,
E“ III
E
O I I I I I I I l I l I I I I
a 100 200 300 400 500 600 700

MAXIMUM CYCLIC TEMPERATURE( C)

Fig. 27 The effect of maximum cyclic temperature on the interfacial
bonding strength after 5 thermal cycles.

67

tional shear stress on the debonded surfaces decreases with increasing
number of thermal cycles, and with increasing maximum cyclic tempera-
ture. It is believed that continual rubbing between the debonded surfaces
with continued thermal cycling, or higher mismatch strain due to differ-
ence in thermal expansion coefficients with increasing maximum cyclic
temperature, causes smoothening of the debonded surfaces. As a result,
the frictional shear stress becomes lower due to less mechanical keying

effect of debonded surfaces.

4-2-1-2. Effects of Thermal Cycling on The Complete Debonding Stress

The complete debonding stress is defined as the normal stress on the
ribbon required to completely debond along the matrix-ribbon interface
and is given by the maximum stress in the stress-displacement curves
obtained in pull-out tests. The complete debonding stresses as a function
of the embedded ribbon length in 650-TC specimens after various numbers
of cycles is given in Fig. 28. The results illustrate that the complete deb-
onding stress decreases with increasing number of thermal cycles in 650-
TC specimens. After initiation of debonding, the frictional shear stress,
which must be overcome to continue to debond, exists at the debonded
interface due to roughness of the debonded surfaces and also due to ther-
mal expansion mismatch between components. Therefore, the difference
between the values of the complete debonding stress and the initial deb-
onding stress, which represents the normal stress on the ribbon when deb-
onding starts, can be considered to be such a frictional shear stress. The
magnitude of frictional shear stress can be accounted for by the roughness

of the debonded surfaces. As shown in Fig. 29, debonding due to thermal

COMPLETE DEBONDING STRESS(MPa)

68

AS—F‘AB. (o)

\1

O

O
I

  

600- ‘
fi>3 CYCLES (o)

a:
500_ ' 5 CYCLES (2x)

400-
300- x x ,/*”
200-

100-
. ' . 7 CYCLES (v)

 

 

O l I I I I l I l I l
O l 2 3 4 5

EMBEDDED LENGTH(mm)

Fig. 28 The complete debonding stresses as a function of the embed-
ded ribbon length after various numbers of thermal cycles of

650-TC specimens.

69

          

\z »' ~ 2* .‘ ' y “"3 * . - jf'?I\E¢-.
I. :1 .>*“‘ 5"{W , [-5 ‘Y . u
k | @L.fr.tx’~7:

‘ ’ w ..
~e"r kn-H: ‘L‘r’q-m

(a)

Fig. 29 SEM micrographs at debonded interface (a) due to ther-
mal stress, and (b) due to shear stress during pull-out
tests.

 

70

 

(b)

Fig.29 (continued)

71

stress generates smooth surfaces [Fig 29(a)], while debonding due to shear
stress realized in pull-out tests of embedded ribbons generate rough deb-
onded surfaces [Fig. 29(b)]. Smoother debonded surfaces result in lower
frictional shear stress, as mentioned in the previous section. In the case of
as-fabricated specimens, after debonding initiates, stresses required for
continuation of debonding steadily increase up to complete debonding
stress due to higher frictional shear stress at the debonded interface
resulting from rough interfacial cracking. However, in 650-TC specimens
that have undergone 3 and 5 cycles, the frictional shear stress at the deb-
onded interface is too low to contribute to stresses required for continua-
tion of debonding. As a result, catastrophic debonding was observed in
stress-displacement curves of these specimens. In brief, the complete deb-
onding stress has two contributors; one is the initial debondingstress, the
other is the frictional shear stress. Since both contributors decrease with
increasing number of cycles, the complete debonding stress decreases with
increasing number of thermal cycles. The effect of temperature on the
complete debonding stress can be seen in Fig. 30. The complete debonding
stresses of 650-TC specimens after 5 cycles are considerably lower, com-
pared to those of as-fabricated ones, because both initial debonding stress
and frictional shear stress decrease with increasing maximum cyclic tem-
perature. However, 5 cycles of 500-TC do not affect the complete debonding
stress or the stress-displacement curve and the interfacial bonding strength of

the as-fabricated composite.

COMPLETE DEBONDING STRESS(MPa)

 

72

 

 

700— D500°C (0)

. AS-FAB.(0)
600- 550°C (7)
500- 650°C (x)
400-

300- x x
2004 *

.. 3K
100-

0 l I I l I I I l I 1

o 1 2 3 4 5

EMBEDDED LENGTH(mm)

Fig. 30 The effect of maximum cyclic temperature on the complete

debonding stress

73

4-2-2. Acid Etching of The Ribbon

The surfaces of the as-received and pre-oxidized ribbons after acid etching
for a given time are shown in Fig. 31. The shapes of the dimples formed by
acid etching the as-received and pre-oxidized ribbons are significantly dif-
ferent from each other. Since the oxide layer protects the metallic ribbon p
from severe attack by acid in the case of etching the pre-oxidized ribbon,
the resultant density and size of dimples formed on the metallic ribbon

surface were significantly reduced as compared to those in the case of etch-

 

ing the as-received ribbons, as can be observed later in the micrographs of
metallic ribbon surfaces after ribbon pull-out.

The effect of ribbon surface treatment on stress-displacement curves
obtained from pull-out tests of the N ichrome ribbon embedded soda-lime
glass matrix sample is illustrated in Fig. 32. The pull-out stress, defined
as the normal stress on the ribbon required to initiate ribbon pull-out from
the matrix, significantly changed with ribbon surface treatment. Preoxida-
tion at 650°C for 1hr did not affect the debonding and pull-out processes in
this composite. This was due to the fact that the oxide layer was also cre-
ated on the as-received ribbon during composite fabrication and the deb-
onding crack predominantly propagates along the interface between metal
and oxide layer in the pull—out test as can be observed in Fig. 33. On the
other hand, acid etching of the Nichrome ribbon for 60 seconds led to a
large improvement in the pull-out stress of the composite. Acid etching for
the same time after pre-oxidization of the ribbon at 650°C for 1 hour, how-
ever, showed only a moderate improvement in the pull-out stress.

SEM micrographs of the ribbon and the matrix surfaces after ribbon is

74

 

(a)

Fig. 31 Ribbon surfaces roughened by acid etching of (a) as-received
and (b) pro-oxidized ribbons for 90 seconds

75

 

(b)

Fig. 31 (continued)

 

76

 

 

 

 

700- C
. A: as—received
600- D A B: pre—oxidized
. M C: etching of as—received
’5 // ribbon for GOsecs.
0.. 500- , D: etching of pre-oxidized
E , B ribbon for 60secs.
m .
g 400- /
D:
E. .
m
.4 300- ‘
<2
E q
2 .1
C) 200
Z .
100-
0 ' I E I T I ' I '— I I I ' I ' I
O 1 2 3 4 5 -6 7 8
DISPLACEMENT(mm)

Fig. 32 The effect of ribbon surface treatment on stress-displacement
curves obtained from pull-out tests.

77

 

Fig. 33 Debonded surface in which debonding crack has propagated
along the interface between metal and oxide layer. Oxide
layer shown is stuck to the matrix after complete debonding.
(A:matrix, Bzoxide layer)

78

completely pulled-out from the matrix for each case of surface roughening
treatment are shown in Fig. 34. The abrasion process of the jagged inter-
face of the composite with the as-received ribbon roughened by acid etching
for 60 seconds is illustrated in Fig. 34(a). In the composite with the preox-
idized ribbon roughened by acid etching for 60 seconds, the portions of
glass which fill the dimples on the ribbon at the jagged interface failed by
shear and stuck to the ribbon during ribbon pull-out as can be seen in Fig.
34(b). Fig. 35 provides schematic illustrations of the mechanisms of ribbon
pull-out processes of the composites for the different ribbon surface treat-
ments. During composite fabrication in air, an oxide layer is formed on the
riben surface already roughened by acid etching [Fig. 35(a)]. Dimples
formed on the ribbon surface by etching, are filled up with the glass
matrix. During loading, debonding crack front propagates under shear in
the same manner as mentioned earlier. When debonding along the inter-
face is complete, the ribbon is not pulled-out right away because of
mechanical interlocking at the jagged interface. However, once the higher
stress required to overcome the interlocking at the interface is attained,
the jagged interface starts to move. This moving interface scratches the
metallic ribbon surface until the interface wears out, and flattens. This
mechanically interlocked interface, which exhibits features of the abrasion
process of the jagged interface, results in considerable increase in the pull-
out stress as compared to that of the composite reinforced with the as-
received ribbon. On the other hand, for the case of pre-oxidized ribbons,
after a thin oxide layer has been created on the smooth as-received ribbon
surface, the ribbon is roughened by acid etching. Since the oxide layer
alleviates acid attack on the metallic ribbon surface, the effect of mechani-
cal interlocking at the jagged interface is considerably reduced under the

79

 

RIBBON

(a)

Fig. 34 SEM micrographs of the ribbon and the matrix surfaces after
ribbon is completely pulled-out from the matrix for the com-
posite with: a) the ribbon roughened by acid etching for 60
seconds, and b) the pre-oxidized ribbon roughened by acid
etching for 60 seconds. Note that the abrasive process has
left striations in both the matrix and ribbon in a), and por-
tions of glass stuck to the ribbon appear as bright specks in
b).

80

 

MATRIX

Fig. 34 (continued)

81

 

RIBBON

(b)

Fig. 34 (continued)

82

 

MATRIX

Fig. 34 (continued)

83

After acid etching,

‘—\./ v v
flbbon

 

 

 

 

 

 

After composite fabrication,

 

 

 

 

During pull-out test,

 

 

 

 

 

-—-\,—-\7 1m? , arr——
debonding crack

 

 

 

During ribbon pull-out,

l malrIX ~ _>

 

 

 

(a)

Fig. 35 Schematic profile of the interface after ribbon surface treat-
ment, composite fabrication, and during pull-out test for the
composite with: a) as-received ribbon roughened by etching,
b) pre-oxidized ribbon roughened by etching.These schemat-
ics explain the mechanisms involved for processes that can
cause features observed in Fig. 34.

 

 

 

84

After pre-oxidized, oxide layer

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\‘.s\\\\\

fibbon

   

    
    

 

After acid etching,

W

After composite fabrication,

 

   

matrix

 
 
 

 

  

fibbon

 

oxide layer

During pull-out test.

 

 

 

 

 

 

(b)

Fig. 35 (continued)

85

shearing action during the pull-out tests. In addition, due to the relatively
low ratio of the width to the depth of jagged areas at the interface, the fail-
ure at the glass portion which fills the dimple on the ribbon surface can be
expected before ribbon starts pulling-out. As a result, with this ribbon sur-
face treatment, the pull-out stress can be obtained in a range between
those of the composites reinforced with the as-received ribbon, and with
the ribbon roughened by etching. Hence, this oxide layer helps in control-
ling more precisely the density, size and depth of the dimples, as compared
to those obtainable by etching of the as-received ribbon.

Pull-out stresses of the composites containing ribbons with various sur-
face treatments (for 1.7 mm-embedded ribbon length ) are given in Fig. 36.
Etching of as-received ribbon for 60 seconds resulted in 100 MPa increase
in pull-out stress, as compared to that for as-received or pre-oxidized rib-
bons. Moreover, acid etching for 90 seconds resulted in matrix failure at
the end of the embedded ribbon before ribbon starts to pull out due to high
degree of interlocking at the interface. Slight increments in pull-out
stresses (approximately 30 MPa) were obtained by etching the pre-oxidized
ribbon for 60 seconds (as compared to as-received, and pre-oxidized rib-
bons).

In composites with as-received ribbon reinforcements, small load drops
in stress-displacement curve representing that debonding front propagates
in small jumps rather than continuously have been observed. Such a fea-
ture was not found to be significant in this study since randomly spread
out jagged edges of the interface cause delayed propagation of the debond-
ing front with etched reinforcements. This results in continuous propaga-

tion of the debonding front.

86

 

 

 

 

 

 

 

 

 

 

 

700 ._ 66—61:}110 5941122
A 600: 562i17.3 545:2” Q
g 500: §
:5 300: \
2:... §

only (60 secs.) (60 secs.)
only after oxidized

Ribbon Treatments

Fig. 36 Pull-out stress of ribbons that have undergone various treat-
ments for an embedded length of 1.7 mm.

87

4-3. Fracture Toughness Behavior

4-3-1. Effect of Fracture Toughness (ch) on Interfacial Bonding

The calculated fracture toughness (K10) values of soda-lime glass matrix
composites reinforced with Nichrome ribbons in various interfacial bond-
ing conditions are given in Table 4. The interfacial bonding conditions uti-
lized were as follows: 1) The specimens which were subjected to thermal
cycling have weak interfacial bonding conditions. Moreover, it is impor-
tant to note that as the number of thermal cycles increased, the interfacial
bonding strength decreased. 2) The composite specimens reinforced with
acid etched Nichrome ribbon showed strong interfacial bonding due to
mechanical interlocking along the interface. This mechanical interlocking
effect was lower in the composite with ribbons that were preoxidized prior
to acid etching.

Regardless of the interfacial bonding condition, an increase of up to 20%
in fracture toughness was achieved for composites with 0.5 vol% reinforce-
ment. Prestressing of the matrix due to the thermal expansion coefficient
mismatch between the matrix and ribbon and crack shielding by the rib-
bons may be attributed to the enhancement in fracture toughness (ch) of
the present composite system. Since the thermal expansion coeflicient of
the ribbon is larger than that of the glass matrix, the matrix is in compres-
sion along the direction parallel to the length of the ribbon, thus providing
a compressive zone which increases the level of applied stress required to
open the crack (9,93,94). Crack shielding by the ribbon impedes the crack
propagation and also changes crack front configuration (93,95,96). Fracto-

 

88

Table 4. Fracture toughness (ch) of soda-lime glass matrix reinforced
Nichrome ribbon with various bonding conditions.

 

 

 

 

 

 

Bonding Conditions vol% K1,,(MPa 5:)
Matrix 0 0.98 i005
NT 0.8 1.16 $0.09
TC-3 0.5 1.22 10.11
TC-7 0.5 1.17 i016
AE-60 0.5 1.11 $0.04
FAB-60 0.5 1.17 i009

 

 

 

 

 

89

graphic evidence of the crack shielding by the ribbon is shown in Fig. 37.
The interference fringes represent the path of the crack. Fig. 37 clearly
shows that the ribbon impedes the motion of the crack as it crosses the rib-
bon. As described by Green (95), the crack is pinned at both the edges of
the ribbon, resulting in crack bowing. Following crack bowing, the second-
ary crack initiates behind the ribbon and propagates fast to catch up with
the primary crack.

However, the interfacial debonding process which has been reported as
a major mechanism of fracture toughness enhancement in fiber reinforced
ceramic matrix composites was not observed during matrix cracking in the
case of the present system. Catastrophic matrix failure, due to consider-
ably low volume fraction of the ribbon in the composites, leads to negligible

interfacial debonding during flexural loading.

4-3-2. Tensile Behavior of Pre-cracked Composite

Typical stress-displacement curves (with nominal stress referring to
load per unit ribbon cross-sectional area) obtained from the tensile tests on
the pre-cracked composite specimens with various interfacial bonding con-
ditions are given in Fig. 38. The results given in Fig. 38 are for composites
reinforced with a ribbon of 12 mm embedded length (19, defined in Fig. 11).
In this study, the composite specimens that have undergone 3 and 7 ther-
mal cycles between room temperature and 650°C are referred to as TC-3,
and TC-7 respectively. AE-60 and AE-9O are used to refer to 60 and 90 sec-
ond acid etched ribbons in as-received conditions, and PAE refers to 60 sec-
and acid etching of ribbons in preoxidized condition. NT is used for

composites with ribbons in as-received condition. In the AE specimen (the

90

Crack Direction
—————>

 

Fig. 37 Fractographic observation of the crack shielding by the rib-
bon. Interference fringes represent the path of the crack.
Note: A: primary crack plane, B: ribbon, C: secondary crack
plane. Crack direction refers to direction of crack movement.

91

A:AE
BzNT
CzTC—3
DzTC-7

 

NOMINAL STRESS(MPa)

 

 

 

 

 

 

O ' ' I ' I ' I ' I I ' I ' F 1
O 2 4 6 8 10 12 14 16
DISPLACEMENT(rnm)

Fig. 38 Typical stress-displacement curves obtained from the tensile
loading of the pre-cracked composite specimens with various
interfacial bonding conditions.

92

strongest bonding condition) the ribbon fractured at a considerably small
displacement (curve ‘A’). As the bonding becomes weaker, the ribbon frac-
tured at larger displacements as seen in curve ‘B’ for the non-treated com-
posite specimen. The “gauge length” of the ribbon is confined to the
debonded length along the embedded ribbon. Also, the debonded length
decreases with an increase in interfacial bonding strength of the composite
for a given applied stress. As a result, a general trend, in spite of some
inconsistencies, indicating that the displacement at the point where the
ribbon fractured decreased with an increase in the interfacial bonding
strength can be noted in the data provided in Table 5. On the other hand,
the ribbon pull-out from the matrix after complete debonding was observed
in TC-3 and TC-7 specimens (curves ‘0’ and ‘D’, respectively). However,
there was noticeable difference between these two cases. For TC-3 speci-
mens, the interfacial bonding was strong enough to prevent complete deb-
onding of the ribbon during initial stages of the test. As a result, the
effective length of the bonded portion of the ribbon was large enough to
sustain considerable plastic deformation, before complete debonding
occurred. On the other hand, in the TC-7 specimens containing mostly
inter-connected microcracks, the interfacial bonding was so weak that the
debonding crack propagated more easily along the interface as compared to
the TC-3 specimen. In addition to this, the low static frictional shear
stress at the debonded interface (in TC-7) was not effective enough to hold
the debonded portion of the ribbon. Therefore, complete debonding
occurred at a much lower stress than that of the TC-3 specimen. Hence,
the extent of plastic deformation was very low in the case of the TC-7 spec-
imens. However, the displacement at a given stress level was considerably

large when compared to that of the TC-3 specimen because of the differ-

93

Table 5. Effect of interfacial bonding on the displacement at the ribbon

 

 

 

fracture.
Bonding
Condition TC'7
=
Displacement at
Ribbon Fracture 0.67 0.85 1.02 1.64 1.63 1.48
0.05 0.28 0.50 0.58 0.24

(mm)

 

 

 

 

 

 

 

 

 

94

ence in the debonded length (“gauge length”) of the ribbon between both
cases.

The heavy shaded portion observed in the case of TC-3 specimen (Fig.
38) indicates the “stick-slip” friction phenomenon. In this portion of the
curve, each load drop was accompanied by an audible “click”. The mecha-
nism of this phenomenon has been explained by Griffin et al. (50) and
Deshmukh et al. (49). According to Griffin et al., the Poisson contraction
and expansion of the fiber in combination with a difference between static
and dynamic friction leads to stick-slip friction. In contrast, Deshmukh et
al. pointed out that the release of excess strain energy stored in the free
length of the fiber when the fiber reloads contributes to the above phenom-
enon. As illustrated in curve ‘C’, the stress amplitude and wavelength of
the stick-slip behavior decreases as the ribbon is progressively pulled out.
This can be explained by the smoothening effect of the debonded interface
during ribbon pull-out, since such a behavior predominantly depends on
the asperities of the debonded surfaces at the interface. The stick-slip
behavior was not observed in the TC-7 specimens due to the smooth fea-

ture of the debonded interface, resulting in low frictional shear stress.
4-3-3. Toughness due to Crack Bridging (AG0)

Fracture toughness due to crack bridging (AGO) in the composite under
various bonding conditions was evaluated using Eq. 8 and the area under
the stress-displacement curves. The results are given in Table 6.
Enhancement in fracture toughness resulting from thermal cycling (curve
‘C’) of the composite [as compared to that of as-received ribbon (curve ‘B’),

or acid-etched ribbon (curve ‘A’)] can be observed in Fig. 38. Plastic defor-

95

Table 6. Fracture toughness due to crack bridging (AGc) in various bond-
ing conditions.
AGc = Vf x area under the stress-displacement curve in Fig. 38.

 

AG, (KJ/mz)

 

    

Frictional
sliding

Plastic
deformation

   

Total

    
 

 

 

 

NT 6.08 0 6.08
AE-60 2.87 0 2.87
TC-3 7.03 13.48 20.51
TC-7 3.25 7.67 10.92

 

 

 

 

 

 

96

mation and frictional sliding play important roles in the enhancement of
fracture toughness due to thermal cycling (curve ‘C’). For as-received or
acid-etched ribbons, the lower fracture toughness realized can be attrib-
uted to the ribbon fracture prior to the onset of any extensive plastic defor-
mation. It is evident from curves ‘A’ and ‘B’ that stronger the interfacial
bonding the smaller is the area under the curve, due to the small displace-
ment at ribbon fracture. Even though both the curves ‘C’ and ‘D’ are com-
prised of plastic deformation and frictional sliding stages, the total area
under curve ‘D’ is much smaller than that of the curve ‘0’, because of the
low plastic deformation and low frictional shear stress involved in curve
‘D’. From these observations, it can be inferred that TC-3 specimen with
11mm-embedded length of the ribbon shows the maximum fracture tough-
ness due to crack bridging (AGc). In addition, the effect of the embedded
ribbon length on toughness of non-treated composite specimens is shown in
Fig. 39. The ribbon fractured in the composite with over 12mm-embedded
ribbon length, while ribbon pull-out occurred after plastic deformation of
the debonded ribbon in the composite with less than 11mm-embedded rib-
bon length. As a result, the maximum fracture toughness due to crack
bridging (AGO) in the non-treated composite was achieved at 11mm-embed-
ded ribbon length. Therefore, it can be defined as “critical embedded
length (1a)” for the maximum fracture toughness due to crack bridging in a
given bonding condition (and for the given ribbon thickness) since the rib-
bon with this length effectively undergoes both plastic deformation and
frictional sliding phenomena. The critical embedded length in various
bonding conditions is shown in Table 7. Due to the wide variation in data,
the results were presented as a range, instead of a single value. Neverthe-

less, it can be concluded from the results of this study that the maximum

 

800—
1 =12mm

l
(D

700-

600-

 

500

400

300-

200-

NOMINAL STRESS(MPa)

100-

 

 

 

. I '

III

97

le=11mm

 

III II

. IIIII IIIIIIIIII I l‘

IMI

"'II'III I'll” III 1'! IIIII

II

II I

 

O I I I l
O 2 4

I I I

T'I‘I'I
6 8101214

DISPLACEMENT(mm)

Fig. 39 Stress-displacement curves showing the effect of the embed-
ded ribbon length on toughness (AGc) of NT composite speci-

mens.

98

Table 7. Critical embedded length (18) for the maximum fracture tough-
ness due to crack bridging in various bonding conditions.

 

 

B°nfiing NT AE-60 PAE-60 TC-3 TC-7
Condltlons
Critical Embedded 10~ 12 less less 10» 13 15~ 17

Length (mm) than 3 than 3

 

 

99

fracture toughness due to crack bridging can be achieved by using discon-
tinuous metallic reinforcements with a length less than or equal to the crit-

ical embedded length in the ceramic matrix composites.

 

 

5. Conclusions

Metallic ribbons embedded in a ceramic matrix may debond from the

matrix due to the combined effects of plastic behavior of the metallic ribbon

 

and the distribution of shear stress along the embedded ribbon (shear lag
model). Hence, the plastic behavior of the metallic ribbon was taken into
account in analyses of ribbon pull-out in present study. The interfaces

between Nichrome ribbon and soda lime glass matrix were modified by

 

means of various numbers of thermal cycles, and various maximum tem-
peratures used in thermal cycles. The interfacial bonding strength, com-
plete debonding stress and frictional shear stress were measured by pull-
out tests on thermally cycled specimens. Also, the interface of this compos-
ite was modified by acid etching of as-received or oxidized ribbon surface.
Finally, on the basis of above interface modifications, interfacial effects on
mechanical properties of brittle matrix with ductile reinforcement were

evaluated. The important observations are summarized below:

1) Plastic deformation of ductile ribbon provides significant contribution to
the resultant interfacial shear stress (rt) at the interface in ductile ribbon

reinforced brittle matrix composites.
2) Although the debonding process in this composite is catastrophic at the
maximum required debond load, mechanical keying due to the roughness

of the debonded surfaces may prevent a sudden load drop.

3) The applied tensile stresses required to initiate and complete debonding

100

101

(oi and Cf respectively) are independent of the embedded length in excess

of a critical value.

4) Microcracks at the interface of 650-TC specimens are generated after 3
thermal cycles, they link together after 5 cycles, and make a completely
connected crack after 7 cycles. A 500-TC treatment might not create
enough thermal stresses to generate microcracking at the interface after 5

cycles.

6) The interfacial bonding strength decreases with increasing number of

thermal cycles and drops significantly after 5 cycles of 650-TC.

7) Frictional shear stress on the debonded surfaces decreases with increas-
ing number of thermal cycles due to smoothening effect which results from
continual rubbing between the debonded surfaces during continued ther-

mal cycling.

8) The complete debonding stress decreases with increasing number of
thermal cycles because both contributors, initial debonding stress and fric-

tional shear stress, decrease with increasing number of cycles.

9) The results of this study suggest that optimum interfacial bonding
strength of soda-lime glass/Nichrome ribbon composite can be achieved by

thermal cycling.

10) Acid etching of the ribbon gives rise to considerable improvement in

pull-out stress of the composite. However, it is very difficult to control the

102

pull-out stress because ribbon is severely attacked by the acid even in very

short time period.

11) A pre-oxidation treatment of the ribbon surface before etching can pro-
tect the metallic ribbon from severe attack by acid so as to provide a better

control of the ribbon pull-out behavior in the composite.

12) In composites with etched ribbons, randomly spread-out jagged inter-
face causes delayed propagation of debonding front, and consequently deb-
onding front propagates continuously rather than in small jumps, a feature

exhibited by the composites reinforced with smooth ribbons.

13) Increases of fracture toughness (ch) of these composites up to 20%
were achieved due to “prestressing of the matrix” and “crack shielding by

the ribbon”.

14) Introduction of even a very low volume fraction of metallic ribbon pro-
vides significant improvement in fracture toughness due to crack bridging

(AGc) of the brittle glass matrix.

15) To obtain maximum toughness in this composite, it is essential to

retain the optimum bonding strength.

16) The results of this study suggest that enhancement in toughness may
be achieved by using discontinuous metallic ribbon reinforcement in the

brittle. ceramic matrix (16 S lcr).

References

1) DC. Phillips, J. Mater. Sci., 9 (1974) 1847
2) KM. Prewo and J .J . Brennen, J. Mater. Sci., 15 (1980) 463
3) J. Brennen and K. Prewo, J. Mater. Sci., 17 (1982) 2371
4) KM. Prewo and J .J . Brennen, J. Mater. Sci., 17 (1982) 1201
5) A.G. Evans and RM. McMeeking, Acta metall., 34 (1986) 2435
6) MD. Thouless and A.G. Evans, Acta metall., 36 (1988) 517
7) L.S. Sigl and HE Fischmeister, Acta metall., 36 (1988) 887
8) B. Budiansky, J .C. Amazigo and A.G. Evans, J. Mech. Phys. Solids, 36
(1988) 167
9) A.G.Evans and DB. Marshall, Acta metall., 37 (1989) 2567
10) A.G. Evans, Mater. Sci. Eng., A107 (1989) 227
11) L.S. Sigl and A.G. Evans, Mech. Mater., 8 (1989) 1
12) E. Bischofi', O. Sbaizero, M. Riihle, and A.G. Evans, J. Am. Ceram. Soc.,
72 ( 1989) 741
13) A.G. Evans, J. Am. Ceram. Soc., 73 (1990) 187
14) S.V. Nair, J. Am. Ceram. Soc., 73 ( 1990) 2839
15) G.H. Campbell, B.J. Dalgleish, M. Riihle and A.G. Evans, J. Am.
Ceram. Soc., 73 (1990) 521
16) GA. Cooper and A. Kelly, J. Mech. Phys. Solids, 15 (1967) 279
17 ) P. Hing and G.W. Groves, J. Mater. Sci.,7 (1972) 427
18) VD. Krstic, P.S. Nicholson and R.G. Hoagland, J. Am. Ceram. Soc., 64
(1981) 499
19) VD. Krstic, Philos. Mag. A48 (1983) 695

103

104

20) MS. Newkirk, A.W. Urqhart and HR. Zwicker, J. Mater. Res. 1 (1986)
81

21) L.S. Sigl, P.A. Mataga, B.J. Dalgeish, R.M. McMeeking and A.G. Evans,
Acta metall., 36 (1988) 945

22) M.F. Ashby, F.J. Blunt and M. Bannister, Acta metall., 37 (1989) 1847

23) H.C. Cao, B.J. Dalgleish, H.E. Déve, C.K. Elliot, A.G. Evans, R. Mehra-
bian and G.R. Odette, Acta metall., 37 (1989) 2969

24) B. Flinn, M. Riihle and A.G. Evans, Acta metall., 37 (1989) 2969

25) H.E. Déve, A.G. Evans, G.R. Odette, R. Mehrabian, M.L. Emiliani and
R.J. Hecht., Acta metall. mater., 38 (1990) 1491

26) G. Baran, M. Degrange, C.Roques-Carmes and D. Wehbi, J. Mater.
Sci., 25 (1990) 4211

27) KS. Ravichadran, Acta metall. mater., 40 (1992) 1009

28) FE. Heredia, M.Y. He, G. E. Lucas, A.G. Evans, H.E. Déve
and D. Konitzer, Acta metall. mater., 41 (1993) 505

29) LB. Greszczuk, in " WW", ASTM STP 452 (Ameri-
can Society for Testing and Materials,1969) p. 42.

30) P. Lawrence, J. Mater. Sci. 7 (1972) 1.

31) A. Takaku and R.G.C. Arridge, J. Phys. D: Appl. Phys. 6 (1973) 2038.

32) P. Bartos, J. Mater. Sci. 15 ( 1980) 3122.

33) C.W. Griffin, S.Y. Limaye, D.W. Richerson and D.K. Shetty, Ceram.
Eng. Sci. Proc. 9 ( 1988) 671.

34) R.W. Goettler and KT. Faber, Ceram. Eng. Sci. Proc. 9 (1988) 861.

35) Chun-Hway Hsueh, Mater. Sci. and Eng. A123 (1990) 1.

36) V.M. Karbhari and D.J. Wilkins, Scrip. Metall. Mater. 24 (1990) 1197.

37) R.W. Rice, J .R. Spann, D. Lewis and W. Coblenz, Ceram. Eng. Sci.
Proc., 5 (1984) 614

 

105

38) B. Bender, D. Shadwell, C Bulik, L. Invorvati and D. Lewisill, Am.
Ceram. Soc. Bull., 65 (1986) 363

39) RA. Lowden and DP Stinton, Ceram. Eng. Sci. Proc., 9 (1988) 705

40) RN. Singh, Ceram. Eng. Sci. Proc., 10 (1989) 883

41) L.P.Zawada and R.C.Wetherhold, J. Mater. Sci., 26 (1991) 648

42) RH. Moore and SC. Kunz, Ceram. Eng. Sci. Proc., 8 (1987) 839

43) M.J. Klein, in "WW", 1: Interfaces in Metal Matrix
Composites, edited by A.G. Metcalf, L.J. Broutman and RH. Krock
(Academic, New York, 1974) 169

44) DH. Grande, J .F. Mandell and K.C.C. Hong, J. Mater. Sci. 23 ( 1988)
311

45) A. Kelly and W.R. Tyson, J. Mech. Phys. Solids, 13 (1965) 329

46) V. Laws, Composites, 13 (1982) 145

47) R.J. Gray, J. Mater. Sci., 19 (1984) 861

48) M.R. Piggott, Comp. Sci. Tech., 30 ( 1987) 295

49) U.V. Deshmukh and T.W. Coyle, Ceram. Eng. Sci. Proc., 9 (1988) 627

50) CW. Griffin, S.Y. Limaye, D.W. Richerson and D.K. Shetty, Ceram.
Eng. Sci. Proc., 9 (1988) 671

51) Chun-Hway Hseuh, J. Mater. Sci. Letters, 7 (1988) 497

52) J. Kim, C. Baillie and Y. Mai, Scripta metall. mater., 25 (1991) 315

53) J. Kerans and T.A. Parthasarathy, J. Am. Ceram. Soc., 74 (1991) 1585

54) D.B. Marshall, J. Am. Ceram. Soc., 67 (1984) C-259

55) D.B. Marshall and W.C. Oliver, J. Am. Ceram. Soc.,70 (1987) 542

56) J .W. Laughner, N.J. Shaw, R.T. Bhatt and J .A. Dicarlo, presented at
10th Annual Conference on Composites and Advanced Ceramic Materi-
als, American Ceramic Society, Coco Beach, FL, 1986

106

57) RD. Warren, T.J. Mackin and A.G. Evans, Acta metall. mater., 40
(1992) 1243

58) H.L. Cox, Brit. J. Appl. Phys. 3 (1952) 72

59) J. Bowling and G.W. Groves, J. Mater. Sci., 14 (1979) 431

60) J .D. Outwater and M.C. Murphy, in W

.0 . O 0
[-g. :_ 01"¢'0 9“... ‘0 :f : once: ‘:.‘:cq

The Society of the Plastics Industry, Inc. Washington DC. 1969, p. 11-c

61) D.K. Shetty, J. Am. Ceram. Soc., 71 (1988) C-107

62) J .D. Bright, D.K. Shetty, C.W. Griffin and S.Y. Limaye, J. Am. Ceram.
Soc.,72 (1989) 1891

63) J .D. Bright, S. Danchaivijit and D.K. Shetty, J. Am. Ceram. Soc., 74
(1991) 115

64) T.P. Weihs and W.D. Nix, J. Am. Ceram. Soc., 74 (1991) 524

65) T.P. Weihs, O. Sbaizero, E.Y. Luh and W.D. Nix, J. Am. Ceram. Soc., 74
(1991) 535

66) C-H Hsueh, J .D. Bright and D.K. Shetty, J. Mater. Sci. Letters, 10
(1991) 135

67) R.J. Kerans and T.A. Parthasarathy, J. Am. Ceram. Soc., 74 (1991)
1585

68) D.B. Marshall, M.C. Shaw and W.L. Morris, Acta. metall.mater.,40
( 1992) 443

69) D.B. Marshall, Acta. metall. mater. 40 (1992)427

70) W.C. Carter, E.P. Butler and E.R. Fuller, Scripta metall.mater. 25
( 1991) 579

71) T.J. Mackin, P.D. Warren and A.G. Evans, Acta. metall. mater. 40
(1992) 1251

107

72) S. Small, R.P. Vozzola and LP. Zawada, J. Am. Ceram. Soc. 72 (1989)
1175

73) D.B. Marchall and B.N. Cox, Mech. Mech,Mater., 7 (1988)127

74) MD. Thouless, Acta. metall., 37 (1989) 2297

75) M. R’Mili, D. Rouby, G. Fantozzi and P. Lamicq, Comp. Sci. Tech., 37
(1990) 207

76) M. Bouquet, J .M. Birbis and J .M. Quenisset, Comp. Sci. Tech., 37
(1990) 223

77) W.F. Brown, Jr. and J .E. Slawley, W

W ASTM STP 410 (American Society
for Testing and Materials, 1966)

78) D.B. Marshall and A.G. Evans, J. Am. Ceram. Soc., 68 (1985) 225

79) M.F. Ashby, Acta metall. mater., 41 (1993) 1313

80) J .R. Rice, J. Appl. Mech., 35 (1968) 379

81) G.I. Barenblatt, Advances in Applied Mechanics, 7 Academic Press,
1962

82) J. Aveston, G.A. Cooper and A. Kelly, in W

BMW, National Physical Laboratory, Tedding-
ton, UK 1971 (IPC Science and Technology Press, Guildford, 1971) pp

15-24

83) D.B. Marshall, B.N. Cox and A.G. Evans, Acta. metall., 33 ( 1985) 2013

84) R.W. Davidge, Composites, 18 (1987) 92

85) B. Budiansky, J .W. Hutchinson and A.G. Evans, J. Mech. Phys. Solids,
34 (1986) 167

86) M. Sutcu and W.B. Hillig, Acta metall. 38 (1990) 2653

87) RN. Singh, J. Am. Ceram.‘Soc., 73 (1990) 2930

88) H.R. Schwietert and RS. Steif, J. Mech.Phys. Solids, 38 (1990) 325

108

 

89) G.W. Sherer and SM. Rekhson, J. Am. Ceram. Soc., 65 (1982) 399
90) KM. Prewo, J. Mater. Sci., 17 (1982) 3549
91) H. Mecking, in W

WWW. Aachen. August 1979. edited by P-
Haasen, V. Gerold and G. Kostorz (Pergamon Press,1979) 1573

92) J. Morton and G.W. Groves, J. Mater. Sci., 11 (1976) 617

93) R.W. Rice, Cer. Eng. Sci. Proc., 2 (1981) 661

94) R.L. Lehman and GA. Doughan, Comp. Sci. Tech., 37 (1990) 149

95) D.J. Green, P.S. Nicholson and J .D. Embury, J. Mater. Sci., 14
(1979)1413

96) R.U. Vaidya and K.N. Subramanian, J. Mater. Sci., 25 (1990) 3291