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Fragmentation study of interfacial shear strength of single SiC fiberreinforced Al after fatigue

Yongning Liu a,1,1, Wei Kang a, Jiawen He a, Zuming Zhub

a State Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, Peoples Republic of Chinab State Key Laboratory for Fatigue and Fracture of Materials, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, Peoples

Republic of China

Received 4 January 2002; received in revised form 17 May 2002

Abstract

The interfacial shear strength of SiC fiber reinforced aluminum composite has been studied by the fragmentation test of single

fiber reinforced model specimens after a number of fatigue cycles. The result shows that apparent stiffness of the testing machine is

influenced by cyclic loading, which will affect the calculation of fiber strength by Cloughs model. An extracting test in which

fragmented fiber was extracted out by dissolving the matrix material in NaOH water solution indicated that the fiber strength did

not lose via vacuum hot press treatment. This result contradicts the Cloughs model. The experimental result showed that the critical

length of the fiber increases a little after a few cycles of fatigue loading and thus, the interfacial shear strength decreases. The reason

for this is that the thermal residual stress around the fiber developed during fabrication decreases in cyclic loading.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Fragmentation; Composite materials; Fracture; Fatigue

1. Introduction

The fiber reinforced metal matrix composites (MMC)

have been subjected to intensive researches for their

good merits such as high stiffness, high strength, high

damping and high fatigue crack propagation resistance.

The interface between fibers and matrix plays a very

important role in transferring load and turn out to be a

key factor in the mechanical properties of MMC [1/3].

There are several ways to measure the interfacial

strength such as push out, pull out and fragmenta-tion for single fiber reinforced model specimen. Each

method is characterized with its way of measurement

and the results are different. [4/6]. For MMC, push

out and fragmentation are two methods used often [6/

10]. In the fragmentation test, both fiber strength and

interfacial shear strength can be obtained [9/11].

Clough [11] developed a model which can calculate the

fiber strength in the fragmentation test. However, the

calculated results are much smaller than that of the

intrinsic strength of the fiber [11]. As a result a few

papers still followed the way to do the experiments and

released the data [12,13]. According to Clough way, it

seems that the fibers were damaged in the fabrication

process. However, some published data [6,7] did not

agree with the results. The thermal exposure test of a

SiC reinforced aluminum [6] indicated that the fiber

strength did not reduce even at 6008

C for 700 h. This isa problem which needs to be clarified. Further more,

many research efforts have been aimed at the study of

the interfacial shear strength via different fabrication

technologies [5/7,14,15], little work has been done to

examine the fatigue effects on the interfacial shear

strength of fiber reinforced MMC [16,17]. Research

showed that the interfacial shear friction stress between

SiC fiber and titanium alloy matrix measured by the

push out method decreased after fatigue loading [18].

The reason was explained as (1) asperity wear of the

SCS coating layer, and (2) relaxation of radial residual

thermal stress in the matrix. There are two interesting

1 Corresponding author. Tel.: '/86-29-266-9071; fax: '/86-29-266-

3453

E-mail address: [email protected] (Y. Liu).1 Now as a visiting scholar in Institute of Composite Materials,

Shanghai Jiaotong University.

Materials Science and Engineering A343 (2003) 243/250

www.elsevier.com/locate/msea

0921-5093/02/$ - see front matter# 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 9 2 1 - 5 0 9 3 ( 0 2 ) 0 0 3 6 3 - 5

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questions: (1) whether this phenomenon will occur also

in SiC reinforced aluminum matrix, (2) whether this

phenomenon can be repeated by fragmentation test

because there is no asperity wear effect in the test. This

work is going to study these problems by fragmentation

testing single fiber reinforced aluminum matrix model

specimens.

2. Experimental procedure

The model specimens were prepared by vacuum hot

press. The fiber is SiC with diameter 90 mm and provided

by the Institute of Metals, Sinica Academy. The fiber is

a pure SiC with no any surface treatment. The matrix is

pure aluminum plate of thickness of 1 mm. The hot

press process is conducted at temperature of 600 8C

with constant pressure of 40 MPa for 2 h. The platespecimen was cut into a size of 5 mm in width, 1.8 mm in

thickness and 20 mm in gage length. The tensile and

fatigue tests were conducted in a computer controlled

screw driving testing machine with capacity 10 kN. In

order to study the effect of cyclic loading on interfacial

strength, the fatigue test was performed using the

pulsating method at a stress ratio of smin/smax0/0.

The maximum stress is about 0.8 to /0.9 of the yield

stress of the material. All force and displacement signals

were recorded and processed by a computer. In this test

the fiber will break during tensile process. There is a

critical length of fiber, beyond it the fiber will not breakanymore. An important result is to obtain the critical

length. So an acoustic emission detector AE-02 was used

to monitor the fiber fracture during the tensile test [11].

To obtain the number of fiber fractures after the tensile

test, the fractured fibers were extracted out by dissol ving

the matrix material in NaOH water solution. So the

critical fiber length can be obtained. The critical length

was obtained by a statistical result given by Kelly and

Tyson [20]

lc01

0:75Lc (1)

where lc is critical length, Lc is fragmentation length and

can be obtained by an average of the fiber length in gage

span divided by the number of the fractures.

To examine the fiber strength calculated by Clough

equation and measurement, the fiber was tested by

gluing the fiber onto two steel plates at two sides of the

fiber. The steel plates were clamped by grips of the

testing machine. The stress and strain were recorded and

process by a computer system.

The fracture strength of the fiber can be calculated by

the Clough equation in term of load drop and number of

fractures [11].

sf0NDsuLA

2s

AfkLDN(2)

where Ds0DP=As; DP is the magnitude of the loaddrop, As is the cross section area of the specimen, Af is

the cross section area of the fiber, uL is the macro work

hardening rate at the gage length L , k is the stiffness ofthe test machine, N is the total number of the fibers

fractured, DN is the number of repeated fracture in one

drop, which can be obtained by

DN$DP

DP(3)

where DP is the average of all load drops, DP is one

load drop. Calculated DN is 2 for Figs. 1 and 2.

The stiffness of the test machine can be calculated by

the following equation [13,19]

k0 v

(dP=dt)max(

l

AsEs(1

(4)

where v is the crosshead velocity of the machine, (dP/

dt )max is the maximum slope of the load versus time

curve at the elastic part. l, As and Es are gage length,

cross-section area and Youngs modulus of the speci-

men, respectively. The interfacial shear strength can be

calculated by the Kelly and Tyson [20] approach when

the critical length and fracture strength of fiber are

known

ti0sfd

2lc(5)

where ti is the interfacial shear strength, d is the

diameter of fibers. Putting Eq. (1) into Eq. (5), it yields

[21/23]

ti03

8sf

d

Lc(6)

3. Experimental result

Figs. 1 and 2 are a set of tensile and acoustic emissionsignal curves. Fig. 1 shows the result of virgin specimen

and Fig. 2 is after ten cycles fatigue loading. In order to

show the load drops during tensile test, the part of the

curves with a number of load drop peaks has been

magnified as in Figs. 1b and 2b. Each load drop is

corresponding to the acoustic emission signal in Figs. 1c

and 2c. The signals at the beginning of the acoustic

emission are produced by tightening between the speci-

men and grips, which are basically in the non-linear

region at the initial part of the tensile curves of Figs. 1a

and 2a. The fiber fracture usually occurs after the bulk

yielding of the specimen and results in a load drop, yet

Y. Liu et al. / Materials Science and Engineering A343 (2003) 243 /250244

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Fig. 1. The tensile curves and corresponding acoustic emission signals

of specimen without fatigue. (a) Load and time curve of tensile test. (b)

Local high magnification of A. (c) Acoustic emission signals.

Fig. 2. Tensile curve after 10 cycle fatigue loading and corresponding

acoustic emission signals. (a) Tensile curve. (b) Local high magnifica-

tion of A. (c) Acoustic emission signals.

Y. Liu et al. / Materials Science and Engineering A343 (2003) 243 /250 245

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the duration time and load drop magnitude are differ-

ent. This fact indicates that more than one fracture

could be involved in one load drop and this was

confirmed by the extraction test. For instance, the

specimen of Fig. 1 showed eight fractures according to

the accounts of acoustic emission signal and load/time

curve, however, the extraction test exhibited 13 times offracture. For the specimen in Fig. 2, the accounting

number by acoustic emission and tensile curve was 10,

however, the extraction result was 15. In order to make

a precise measurement of the number of fractures and

the critical length in this study, we are based on the

counted using the extraction test.

From Figs. 1 and 2, it is obvious that there is a great

difference in dP/dt in the elastic regions for the speci-

men before and after fatigue. Because the geometry of

the specimen is the same, from Eq. (4) the stiffness will

deviate according to the difference in dP/dt . The

measurement of (dP/dt )max and the calculations ofstiffness are shown in Table 1.

The values in Table 1 indicate that (dP/dt)max is the

main factor in determination of k. The geometry of the

specimen and the Youngs modulus in the second term

of Eq. (4) would not change much, thus, one order

magnitude difference in (dP/dt )max before and after

fatigue will lead to the same order of difference in the

calculated stiffness. Putting different stiffnesses in Eq.

(2), the calculated fiber strengths are shown in Fig. 3.

The remarkable difference in fiber strength is by no

means due to the specimen being fatigued 10/100 cycles.

The strength of the fibers should be determined by the

manufacturing technology, the composite process andthe chemical reaction at the interface. It should not

depend so strongly on the process of physical loading.

4. Discussion

4.1. Stiffness

The stiffness k is a very important parameter and will

affect the calculation of fiber strength sf with Eq. (2).

Table 1 shows that the difference in k before and afterfatigue is great. This difference real does not come from

machine stiffness while comes from slippage between

specimens and grips of testing machine. Suppose the

displacement between two crossheads could be written

U0Um'Us'Uo (7)

where Um is the displacement caused by machine such as

elastic deformation of machine columns, gaps betweenthe screw threads. Us is the displacement caused by

deformation of the specimen. Uo is the displacement

arisen from slippage.

Differentiating above equation

dU

dt0

dUm

dt'

dUs

dt'

dUo

dt(8)

where dU/dt is the crosshead velocity of the test

machine and can be expressed by v and dUo/dt is

slippage rate and is simplified as vo. dUm/dt is the elastic

deformation rate of the test machine and can be

expressed by omLm and dUs/dt is the deformation rateof the specimen and can be expressed by osl: om and osare the strain rates of the test machine and specimen. Lmand l are the rod lengths of the columns between the

crossheads of the test machine and the gage length of the

specimen respectively. Then,

v0 omLm' osl'vo (9)

The elastic deformation is calculated by Hookes law

o01

EA

dP

dt(10)

Putting Eq. (10) into Eq. (9)

v0

Lm

EmAm'

l

EsAs

dP

dt'v0 (11)

then

dP

dt0

v( v0Lm

EmAm'

l

EsAs

(12)

This equation indicates that the slippage v0 in tensile

test will decrease dP/dt . In the first loading as shown in

Fig. 1, there is slippage effect. After several cycles of

Table 1

Stiffness k and (dP/dt )max with and without cyclic treatments

No cycle 10 cycles 100 cycles

(dP/dt )max (N min(1) 256.0 3180.8 3064.8

k (kN m(1) 257.8 3480.6 3340.3

Fig. 3. Fiber fracture strength calculated by Cloughs relationship

with cycle loading number.


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fatigue loading, the specimens had been tighten and the

slippage had been diminished. Clough [11] did not

mention this effect in the stiffness measurement. How-

ever, It had been recommended by international stan-

dard IOS 2573 [24], that one should first apply and

remove a force at least as great as the maximum load

used in the determination of the compliance of the testsystem.

4.2. Fiber strength

The calculation of fiber strength using Eq. (1)

indicates that there is a great difference using the

stiffness measured before and after fatigue. The calcu-

lated sf seem to be a reasonable, around 2300 MPa, if

the stiffness before fatigue is used. Otherwise, sf is quite

small, around 150 MPa, if we use the stiffness after the

fatigue, which would be much approaching the correct

stiffness, see Fig. 3. It is questionable if the fiber strengthis so low, how can it reinforce the matrix materials?

Some published data showed similar magnitude values

of fiber strength by using Clough model, paper [12]

reported that sf0/494 MPa for fiber SiC, sf0/715 MPa

for SiO/2 treated SiC, and sf0/567 MPa for carbon

treated SiC. Paper [11] reported sf0/798 to /340 MPa

for carbon treated SiC. All these strength values are

around the strengths of aluminum alloys or medium

carbon steels and there would have been a great loss of

the fiber strength in comparison with the original

strength, 3500 MPa [7,25], during hot press process. If

so great a loss of the fiber strength is true, it would be

impossible to use the fiber reinforced composites. In

order to clarify this problem, several specimens which

were subjected to the same hot press technology and

fatigue pre-loading were dissolved in NaOH water

solution. The fibers were taken out and the strengths

were measured again. The result is shown in Fig. 4. In

this figure, 1 presents as received state, 2 presents the hot

pressed state and 3 presents the hot pressed and fatigued

state. There is no substantial loss of the fiber strength

after the hot pressing and fatigue pre-treatment.

This result agrees with many published results

[6,17,26] but disagrees with Cloughs [11,13] data. If

we make a close look at Eq. (2), Clough adopted an

assumption that the crosshead displacement was much

smaller than that of the specimen in a load drop, that is

vdt&/dus, see Appendix A in Ref. [11]. So vdt could be

omitted. Since no data had been shown in his publica-tion to prove this assumption, we did the measurements

in this test.

In Table 2, six load drops have been measured for two

specimens on the tensile curves. The sketch of this

measurement is shown in Fig. 5. For one load drop, the

starting point marked 1 and the end point 2, the

displacement, x , time, t and load, p , at different sites

can be obtained by computer acquisition. Because the

velocity of the crosshead is a constant, the crosshead

displacement can be obtained by vdt0/v (t2(/t1). Con-

cerning the specimen displacement, for a tensile system,

the displacement of the crosshead should be

x0

1

km'

1

ks

P (13)

where km is the stiffness of the testing machine and ks is

the stiffness of the specimen. Because the stiffness of test

machine is a constant, when a fiber breaks, the stiffness

of the specimen will be changed by Dks, then

x2(x10

1

km'

1

ks ' Dks

P(

1

km'

1

ks

P

0 1ks ' Dks

(1

ks

P (14)

This means the displacement between crosshead is

mainly caused by fiber breaking and can be treated as

the specimen displacement. Thus,

Us0x2(x1 (15)

The results in Table 2 indicate that the specimen

displacements Us and the crosshead displacement are in

Fig. 4. Fiber strength after dissolving the matrix aluminum.

Fig. 5. A high magnification of a local region of the tensile curve to

show the load drop and the values which can be measured on this

drop.


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the same order and no rule of vdt&/dus was exhibited.

Even more, there are some values ofvdt larger than that

of specimens. The measurements indicate that the

presumption in Cloughs theory is not true.

4.3. Interfacial shear stress and its changes with fatigue

If the strength of the fibers does not change remark-ably after hot pressure, the critical length of the fibers

can be obtained by dissolving aluminum after tensile

test. The result is shown in Fig. 6. The critical length

increases as the number of fatigue loads increase.

Taking these results into Eq. (6), the interfacial shear

strength can be calculated and the result is shown in Fig.

7. Contrary to the change of the critical length, the

interfacial strength decreases as the number of fatigue

loading increases. The result is in agreement with a push

out experiments of SiC fiber-reinforced titanium alloy

[18].

Guo and Kagawa [18] ascribed the effect of fatigue onthe interfacial shear strength to asperity wear and

residual stress. In fragmentation test, there is no asperity

wear influence. Concerning the residual stress effect,

there is an experimental fitting equation [18]

sTr (N)0sTr (0)exp((b

T11N) (N5100) (16a)

sTr (N)00:65sTr (0)exp((b

T12N) (N]100) (16b)

where sTr (0) is the initial residual thermal compressive

stress of the composite and bT11 and bT12 are the numerical

coefficients and larger than zero. This equation indicates

that the residual stress will decrease with the increase of

the number of fatigue loads. The initial radial thermal

stress sTr (0) is approximately given by [26]

sTr (0)0b1 gDT

0

(af(am)dT (17)

and

b10rEmEf

Em(1( nf)' Ef(1' nm)(18)

where Ef, Em, nf and nm are Youngs modulus and

Poissons ratio of the fiber and matrix, respectively, afand am are thermal expansion coefficient of the fiber

and the matrix in the radial direction, respectively, DT is

the temperature difference over which the residualthermal stress develops in the composite, and r is an

adjustment factor for the effect of fiber volume fraction.

r is equal to unity for an infinite single composite and is

less than unity in usual case [26]. Here, in calculation of

sTr (0); the fiber volume fraction can be neglected and r/0/1 [18], the calculated sTr (0)/0/(/890 MPa. The con-

stants used in the calculation are shown in Table 3.

In the push out test, the interfacial shear frictional

stress, t; is written as [18]

t0(msr (srB0) (19)

where m is friction coefficient and sr is the average

Table 2

The measurements of the displacements of crosshead and specimens in load drops

Specimen 1 1 2 3 4 5 6

Us (mm) 0.0153 0.0089 0.0093 0.0004 0.0045 0.0110

Vdt (mm) 0.0137 0.0063 0.0085 0.0076 0.0069 0.0029

Specimen 2 1 2 3 4 5 6

Us (mm) 0.0084 0.0123 0.0054 0.0046 0.0073 0.0083

vdt (mm) 0.0140 0.0090 0.0050 0.0090 0.0076 0.0140

Fig. 6. Fiber critical length vs cyclic loading number.

Fig. 7. Interfacial shear strength vs cyclic loading number.


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compressive stress acting on perpendicular to the sliding

interface. The friction coefficient m can be calculated by

[18]

m0P(0)

2phRfsr(0)(20)

where P(0) is the maximum load in push out test at

initiation state, h is the thickness of the push out slice, Rfis the radius of the fiber and sr/(0) is the compressive

stress perpendicular to the sliding interface. A push out

test of SiC fiber reinforced aluminum composite was

carried out by Yang [27] and the results were P(0)0/0.65

N, h0/0.17 mm, Rf0/4.57 mm. Putting these values and

the compressive stress calculated above into Eq. (20),

the calculated friction coefficient m0/0.149, which is a

little smaller than that of titanium alloy [18]. Then, from

Eq. (19), the calculated the interfacial shear friction

stress is 132.6 MPa. Comparing the values in Fig. 7 at

pristine case, which is around 75 MPa, the agreement in

the order of magnitude is reasonable. The differencemainly comes from two different measurement systems

as mentioned at the beginning of the paper and in

fabrication technology of samples making. The sample

used by Yang [27] is made by casting while here is made

by vacuum hot press of aluminum plates. Anther factor

is that there is asperity wear effect in push out test. If

putting Eq. (16a) into Eq. (19), we get

ti0(msTr (0)exp((b

T11N) (21)

It is clear that the interfacial shear stress decrease with

increasing of fatigue loading number. Thermal residual

compression stress around the fiber decreases duringfatigue. This makes the interfacial shear strength

decreases also. The Fig. 6 indicates that the fiber critical

length increases with fatigue loading. This phenomenon

related to the interfacial shear stress, from Eq. (5), when

interfacial shear stress decreases, the critical length will

increase.

5. Conclusions

When Cloughs model is used in the fragmentation

test of single fiber reinforced specimen, the stiffness of

the test machine will influence greatly the calculation of

the fiber strength. There is significant slippage between

the grips and plate specimen at the first tensile loading.

One to two times pre-loading is required before the

formal measurement of stiffness.

By dissolving the matrix aluminum and testing the

remaining SiC fiber, it is found that the fiber strength isnot changed after the hot pressure at 600 8C in vacuum

furnace for 2 h. This fact against to the Cloughs data

remarkably.

The measurements of the displacements of the cross-

head and the specimen during load drops on load vs

time curves of tensile test did not prove the Cloughs

assumption that the crosshead motion is much smaller

than that of specimen during fiber breaking in the

fragmentation test.

After 10/100 cycles fatigue loading, the fiber critical

length increases a little and the interfacial shear strength

decreases with fatigue loading.That the interfacial shear stress of SiC fiber reinforced

composite decrease with fatigue cyclic number is mainly

due to the thermal residual stress between the fiber and

the matrix, which decrease with fatigue cyclic loading.

Acknowledgements

This research is a part work of NSFC project:

evaluation of the interfacial properties of aluminum

matrix lamella composite and its relationship with

fatigue (no: 59731020). Authors are also grateful for

the support by Visiting Program of Chinese Education

Ministry as a visiting scholar in State Key Lab. Of

Composite Materials, Shanghai Jiaotong University.

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The constants of fiber and aluminum matrix

Aluminum matrix constants

Youngs modulus, Em 80 GPa

Poissons ratio nm 0.3

Thermal expansion coefficient, am 23.6)10(6 K(1

Fiber constants

Youngs modulus, Ef 400 GPa

Poissons ratio nf 0.17

Radial thermal expansion coefficient,af 2.6)10(6 K(1


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