Fatigue damage evolution in SiC fiber-reinforced Ti-15-3 alloy matrix composite

MATERIALS SCIENCE & ENGINEERING

l

ELSEVIER

Materials Science and Engineering A220 (1996) 57-68

Fatigue damage evolution in SiC fiber-reinforced Ti-15-3 alloy matrix composite S.Q. Guo a, Y. Kagawa a,*, J.-L. Bobet b, C. Masuda ° ~Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo I06, Japan bInstitute of Solid State Chemistry of Bordeaux, Avenue du Dr A. Schweitzer, 33600 Pessac, France ~National Research Institute for Metals, Sengen, Tsukuba, Ibaraki 305, Japan

Received 18 April 1996; revised 17 June 1996

Abstract Tension-tension fatigue damage behavior of an unnotched SiC (SCS-6) fiber-reinforced Ti-15-3 alloy matrix composite at room temperature was examined, applying maximum stresses of 450, 670 and 880 MPa with R = 0.1. The change in stress-strain hysteresis curves was measured. Fiber fracture behavior and matrix cracking behavior were observed in situ and the results were compared with the change of unloading modulus obtained from the hysteresis curves. The fiber fracture behavior inside the specimen was also determined by dissolving the Ti alloy matrix. The results showed abrupt reductions in the unloading modulus of the composite at stresses of 450, 670 and 880 MPa; the normalized unloading modulus decreased by 8%, 12% and 17%, respectively, in the initial stage (N~< 10 cycles). This reduction was caused by the multiple fiber fragmentation. Thereafter, the unloading modulus maintained a nearly constant valueand non-propagating matrix cracks were initiated adjacent to the end of fractured fiber. The propagation of the matrix crack again led to a rapid reduction of the unloading modulus, and the composite then failed. With higher applied stress, the fatigue life was reduced. The fracture behavior of the composite was discussed with special attention to the fiber fracture behavior and its effect on the modulus of the composite. Keywords: Fatigue; Crack; Unloading modulus; SiC/Ti-15-3 composite; Fiber fracture; Thermal residual stress

1. Introduction Titanium alloys reinforced with SiC fibers have m a n y potential applications as structural materials because of their light weight with high stiffness and strength. The composites are often expected to subject a cyclic loading, thus strong fatigue resistance of composites is necessary. The fatigue properties of various types of SiC fiber-reinforced titanium matrix composite were studied [1-6] and results indicated that the composite possesses better fatigue resistance than that of unreinforced Ti alloy matrix. The mechanism predominantly responsible is reported to be the shielding effect of matrix crack tip stress intensity by the fiber bridging which operates behind the advancing crack tip [1-4]. Very little information is, however, available

* Corresponding author. Tel.: + 81 3 34026231 (ext. 2436); fax: + 8I 3 34026350. 0921-5093/96/$15.00 © 1996- Elsevier Science S.A. All rights reserved PII S0921-5093(96) 10438-X

concerning the details of fatigue growth crack behavior of an unnotched Ti matrix composite reinforced with continuous SiC fiber [7]. The authors reported [7] that the fatigue life of the composite was controlled by an early stage fiber fracture and matrix crack initiation/ propagation behavior from the edge of the broken fiber by stress concentration. Such micro-fatigue damage evolution seems to play a very important role in the change in mechanical properties of the composite, although there are no reports o f the effects of this process on the properties. This work studied the change in the mechanical behavior and its origin in SiC fiber-reinforced Ti-t5-3 alloy matrix composite during a fatigue test on an unnotched specimen. The effects of relaxation of the residual stress on the fiber fracture and the influence of fiber fragment length on the modulus were discussed on the basis of the experimental results.

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S.Q. Cruo et at. / Materials Science and Engineer#~g A220 (I996) 57-68

2. Experimental procedure

(a)

2.1. Composite material SiC fiber (SCS-6, Textron, Lowell, MA) reinforced Ti-15-3 alloy matrix composite was used in this study (hereafter SiC/Ti-15-3) (Table 1). The chemical composition of the Ti-15-3 alloy was: V, 15.22 wt.%; Cr, 3.26 wt.%; At, 3.12 wt.%; Sn, 2.94 wt.%; and the remainder Ti. Unidirectional reinforced Ti-15-3 alloy matrix composite panels containing four plies of the fiber layer were fabricated by a hot isostatic pressing (HIP) process. The composite panel had an approximately 210 gm fiber free matrix region in both surfaces of the panel. Details of the processing were reported elsewhere [8]. The composite panels were supplied by Mitsubishi Heavy Industries, Tokyo, Japan. A typical example of the polished transverse section of the composite is shown in Fig. 1. The nominal volume fraction of fiber, f, was 0.32 beside the fiber free matrix region in both surfaces of the panel.

?

i:

2.2. Fatigue test Fatigue testing at room temperature (298 K) was done in a tension-tension mode, using a specially designed axial fatigue test facility [9]. Equipment was operated by a servo-controlled closed-loop hydraulic system in a toad-controlled mode with an in situ observation system. The polished surface was observed with a scanning laser optical microscope (LM-21, Laser Tech., Tokyo, Japan) attached to the fatigue test machine. Beam specimens with dimensions of approxiTable I Properties of fiber, matrix, reaction layer and composite Fiber properties: Young's modulus of fiber Tensile strength of fiber Thermal expansion coefficient Radius of fiber Matrix properties: Young's modulus of matrix Yield stress of matrix Thermal expansion coefficient Tensile strength of matrix Reaction layer properties: Young's modulus of reaction layer Thermal expansion coefficient Tensile strength of reaction layer Composite properties: Tensile strength of composite Volume fraction of fiber

Er ~rf~ ~f Rf

400 GPa 3000 MPa 4.5 x 10.6 K -1 140 gm

[24] [8] [15] [24]

Em

115 GPa

~r~ 9 x 10 .6 K -1 Crmu 950 MPa

[14] [14] [15] [14]

ER

466 OPa

[16]

¢R 7.5x 10 .6 K -~ crr~ 1400 MPa

[16] [22]

~r~ t725 MPa f 0.32

[8] --

0"my 750 MPa

5 ~tm

Fig. 1. Opticat photograph of a typical transverse section of the composite: (a) fiber distribution, (b) details of reaction layer (F, fiber; M, matrix; RL, reaction layer).

mately 15 x 2 x 1 mm were cut from the composite panels with the longest dimension parallel to the fibers, using a diamond wafering blade. Specimen surfaces were polished with diamond pastes of progressively increasing fineness up to 1 gm size to ensure against possible surface damage during the grinding and rough polishing stages. Commercially pure aluminum end tabs were affixed to the gripped area of the composite specimen, using epoxy base adhesive. All the fatigue testing was conducted at 2 Hz in a load-controlled mode with R = 0.1 (R = minimum applied stress/maximum applied stress). The maximum applied stress, ~ra was 450, 670 and 880 MPa, respectively. The strain of a specimen was measured with resistance type strain gages with a base area of 4.0 by 0.7 mm affixed to the opposite sides of the specimen. The stress-strain response during the fatigue loading cycle was digitized and continuously recorded by a digital memory scope (ORM 1200, Yokogawa Electric, Tokyo, Japan). The

S.Q. Guo et al. / Materials Science and Engineering A220 (1996) 57-68

] ~r~*

3. Experimental results

................................ ----~ ,//'

~2*°S rain 0

Sa

8amax

8a

--

Strain Fig. 2. Definition of strains and unloading modulus for hysteresis curve,

accuracy of stress (o-) and strain (e) measurements were ~r +0.9 MPa, e___0.0005%, o-+ 1.4 MPa, e___ 0.0007% and o- _+ 1.7 MPa, s + 0.001% MPa, for maximum applied stress of 450, 670 and 880 MPa, respectively. Fig. 2 shows definition of unloading modulus at Nth number of cycles (E~(N)), maximum strain (e max) and minimum strain ( e ~ ) , for closed loading-unloading hysteresis curves and permanent strain, Asp. " An optical microscope (BUH-2, Olympus, Tokyo, Japan) and a scanning laser microscope (LM-21, Lasertech, Tokyo, Japan) were utilized to determine the distribution of fiber fracture length in the fatigued specimens. Morphology of the fiber extracted from the gage section of the fatigue-tested specimen was observed by scanning electron microscopy (SEM) after dissolving the matrix with Krolt's solution at room temperature. Kroll's solution has been found to have no influence on the morphologies of the extracted fibers [7]. 800

Typical examples of loading-unloading hysteresis curves for oa = 450 and 880 MPa with applied number of cycles, N, are shown in Fig. 3. The curves were obtained from strain gage data and measured loads. The first loading curve was linear at low loads but nonlinear at high loads. After one cycle, a permanent strain, Asp, appeared and was 0.002%, 0.006% and 0.012% for applied stresses of 450, 670 and 880 MPa, respectively. The maximum loop width, 6, and the permanent strain, Acv, tended to increase with the increase of applied stress. For the same maximum applied stress, the shape of hysteresis curves after the first few cycles was nearly the same until strain gage failure due to matrix crack propagation. However, the maximum strain, s2% and the minimum strain, e~'m, changed with the number of applied cycles. Fig. 4(a) and (b) shows the change of e y = and ep ax with the number of applied cycles for N>i27 000 cycles, respectively; both strains tended to increase with the number of cycles, N. The increase rate of em=x and e~ n (defined as dem~/dN and de~=/dN, respectively) was in good contrast with the change of Ec(N) with N. Most abrupt increases of e~ = were recognized within five cycles (1 , with the number of fatigue cycles, N, for the three applied stresses used. The normalized unloading modulus, , was defined as 1200

(a)

(b)

Maximum Applied Stress

6OO

59

1000 Number of Cycles

% = 4 5 0 MPa

Maximum Applied Stress ~a=880 MPa

Number of Cycles 1

2

~ " 800

g

1

2

N>2

13_

"g 03

400

600

400

2OO 200

Strain

Strain

Fig. 3. Examples of stress-strain recording of a specimen during fatigue test: (a) G~ = 450 MPa; (b) ~ = 880 MPa.

N>2

60

S.Q. Guo et al. / Materials Science and Engineering A220 (1996) 57-68

0.14

0o7

MaximumAppliedStress 0.12

a []

(a)

f

~a=450 MPa {Ja=670 M P a

x

. . . . . . . .

i

. . . . . . . .

,

. . . . . . . .

i

. . . .

0.5

E E = E

,

MaximumAppliedStress ~ ea=450MPa [] ~a=670MPa o {~a=880MPa

0.6

~,~ 0.10

co

........

0.08 E 0.4 0.06

~

E "~ :~ 0.3

r-

0.04

0.02

. . . . . . . .

i

10

........

J

. . . . . . . .

J

. . . . . . . .

102 10a Number of Cycles, N

f

.

,

.

q3--~--~'o

0.2

,,,,,

104

.

105

10

102 t03 Number of Cycles, N

104

10`5

0.60

~ ~, 0.50 x I

~

(c)

MaximumAppliedStress z~ •a=450 MPa [] {Ja=670MPa o ~a=880MPa

0.55

0.45

~o

0.40 • "

r-

O

-

-

o

_

_

O

~

~

'

O

-

-

O

o.35 0.30 c .

~ ~ . . _ _ ~ - - - - ~ 4 3 q 3 - .

c;--cb..~-'=

C3 0.25 ¢-

0.20 0.15

.......................................... 10 102 103 104 105 Number of Cycles, N Fig, 4. Strain vs. number of applied cycles during fatigue test as above. (a) Maximum strain, 8mi~; (b) minimum strain, em~×; (c) strain difference,

1

-- ~a

)"

Eo(N)

(Ec)= £o

(1)

where E ° and E~(N) are the unloading modulus at the first and Nth number of cycles, respectively. (Eo} reduced rapidly with the increase of the number of applied cycles for the maximum applied stresses when N<~ 3-5 cycles. With further increase of the number of applied cycles, (Eo} reduced slowly up to N ~ 10 cycles. This behavior originates from the early stage of fiber fracture, especially N~<3-5 cycles [7]. After N ~ 10 cycles, the normalized unloading modulus decreased approximately 8%, 12% and 17% from E ° for the maximum applied stresses of 450, 670 and 880 MPa, respectively. This was viewed as stage I. Then, the (Eo}--~ N relations were nearly constant (stage II). After stage II, (Eo} decreased rapidly with the increase of N (stage III). These three stages were observed for all the applied maximum stresses, i.e., the three stages independent of the applied maximum stress, o-~. The number of applied cycles for the transition from stage I to stage II was independent of the applied stress; how-

ever, the transition from stage II to stage III was dependent on the maximum applied stress. Higher maximum applied stress yielded fewer transition cycles from stage II to stage III. A typical example of the evolution of the fiber fracture behavior observed at the surface of the composite is shown in Fig. 6. Random fiber fracture behavior, which means the fiber fracture location occurred randomly within or outside of the same fiber, was seen at an early stage. In addition, transverse cracking of the fiber and formation of small wedge-like pieces of fractured fiber, were noted between two adjacent fiber fracture surfaces (indicated by arrows); the pieces were typically less than about 40 gm in length. The number of the fiber fractures increased at an early stage of the fatigue test (N~< 10 cycles); after N > 10 cycles, almost no new fractures appeared. This was independent of the applied maximum stress level. Some examples of extracted fibers from the specimens subjected to N = 10000 cycles at 450, 670 and 880 MPa are shown in Fig. 7. The photographs demonstrate that random fiber

S.Q. Guo et at. / Materials Science and Engineering A220 (1996) 57-68 oo

1.2

........ ,

........

i

........

Maximum Applied Stress

:7

1.1 J.0

o

450 MPa

[]

670 MPa

a

880 MPa

Stage I Stage II

./

r--

~ o e-

0.9

i

o.8 ©

~

oo

OoooO~.

_

rl

u

o

A

h

AA

/, []

uu=..~

Z~ A

~

_~om,,' ~

A

///'

............................

:7 0.7 10

10 2

10 s

9 e !!l 10 4

10 5

N u m b e r of Cycles, N

Fig. 5. Unloading modulus vs. number of cycles showing fatigue damage evolution during fatigue. fracture also occurred inside the specimen. The fracture appearance of the fiber was completely different from that usually observed in tensile multiple fiber fracture behavior [11,12], with irregularly shaped pieces of fiber, longitudinal splitting, and separation of SiC from the carbon core. Fig. 7 also shows that the appearance of fiber fractures was the same for the three different maximum applied stresses. This suggests that the random fiber fracture behavior was independent of maximum applied stress. The distribution of fragmented fiber length measured within the gage length of the specimen surface for N = 10 and 10 000 cycles at different applied stresses is shown in Fig. 8; distribution differed with the stress applied and the number of

Loading Direction

61

cycles, and tended to decrease with the increase in applied stress. The effect of cycle number on length of the fractured fibers, however, was considerably less than that of the maximum applied stress. Fig. 9 shows typical examples of the surface of a specimen observed at stage IIt (o-~= 450 MPa, N = 40 000 cycles). The traces of plastic deformation are found near the broken fiber tip (Fig. 9(a)) and crack initiations are in the matrix (typical example is indicated by arrows in Fig. 9(b)). With the increase in number of applied cycles, many matrix cracks 'were initiated on both sides of the broken fibers, although only one or two pairs of cracks were extended with further cyclic loading. Most of the matrix cracks initiated showed a non-propagating behavior, which means that their growth rate was considerably slower than that of the primary crack (propagating crack). The fracture of fiber ahead of a matrix crack occurred when the matrix crack tip reached the fiber. After the matrix crack propagated with three or four fiber fractures, the crack extended rapidly. Note that this fiber fracture behavior was different from the random fiber fracture which occurred at stage I (N ~< 10 cycles). This behavior was in every way the same as previously reported by the authors [7]. Fig. 10 shows plots of applied stress, o-~, versus the number of applied cycles, N, causing initiation of matrix cracking and failure of composite. The number of cycles for both events decreased with the increase in maxhnum applied stress, as did differences in the number of cycles between the initiation of matrix crack and fracture of the composite. This means that the fatigue life of the composite strongly depended on the initiation of the matrix crack and its growth process.

4. Discussion

4.1. Change of hysteresis loop during fatigue

Fig. 6. Fiber fracture behavior in specimen showing random fiber fracture and small wedge-likepieces of fractured fiber between two adjacent fractured fibers during fatigue test (~a = 450 MPa, N = 100 cycles).

The stress-strain hysteresis loops of the composite changed within a few cycles and then showed a similar curve until strain gage failure due to rapid matrix crack propagation during fatigue (Fig. 3). The loading part of the stress-strain hysteresis loop bent gradually after the initial linear response near the origin. The stress-strain relation at the beginning of the unloading was linear, but with further reduction in stress, the curve bent toward the origin and the slope lessened. This loop characteristic is due to dissimilar deformation behavior of the matrix and the fiber during unloading. The titanium alloy matrix deform plastically, while the fibers only deform elastically until fracture. During the unloading process, the stiff fibers return to their original position, bringing the matrix with them. This produces compressive plastic deformation in the matrix,

62

S.Q. Guo et al. / Materials Science and Engineering A220 (I996) 57-68

a=450 MPa, N=10000 Cycles

Ga=670 MPa, N=10000 Cycles

•a=880 MPa, N=10000 Cycles

Fig. 7. SEM photographs of extracted fibers from a fatigued specimen showing irregular fiber fracture ((a), (c) and (e)), and splitting of fiber (Co), (d) and (f)) ( N = 10000 cycles; (a) and (b) G~=450 MPa; (c) and (d) o-a 670 MPa; (e) and (f) ~r~= 880 MPa). =

resulting in non-linearity in the unloading part of the stress-strain curve (here, the Bauschinger effect is neglected). Thus, at R = 0.1, after only one cycle, both tensile and compressive plastic deformation occur in the matrix, while only tensile elastic deformation occurs in the fibers. This change of the stress condition in the fiber and the matrix results in the production of residual strain after a single cycle. The larger the applied stress, the larger the permanent strain introduced. Fig. 11 is a schematic drawing of the effect of residual stress on the stress-strain response of the corn-

posite, fiber and matrix during the fatigue test. During the test, tensile stress raises the matrix axial stress, because the stress starts from a positive initial stress level due to thermal residual stress; thus, yielding of the matrix occurs at a lower strain value than it would have for the initially stress-free stage. As the tensile load and strain continue to increase, the fraction of the load carried by the matrix diminishes when its stress-strain curve bends from the point of matrix yielding. The fibers must therefore carry this extra load and, being elastic, will strain commensurately. As the tensile load

63

S.Q. Guo et at. / Materials Science and Engineering A220 (1996) 57-68

10

20 ~ 18

8

16

i

.< 14 u_ 12 -~ 10

g

L~ .o

Fiber Fragment Length, k~(ram)

i ~ 14

~ 12 -Q iT_. 10

--Q

E 0

1 Fiber Fragment Length, Lf (mm)

2

0

0

1 Fiber Fragment Length, Lf (ram)

2

Fig. 8. Distribution of fiber fracture length on fatigued specimen. (a) #a = 450 MPa; (b) ¢a = 670 MPa; (c) G~= 880 MPa, N = I0 cycles; (d) era = 880 MPa, N= I0000 cycles. is removed and reduced to approximately zero, i.e., 0.1 o-, in this experiment, the matrix will be driven into compression and a small amount of reverse yielding will result [13]. Thus, at the lower load after only single cycle, the thermal residual stresses of the fibers and matrix switch their signs. After the first cycle, fiber is stretched and brought closer to maximum tensile strength. As this cycle continues, two cyclic stressstrain responses can occur in the matrix: cyclic relaxation of the mean stress to zero (i.e., the matrix stress tends toward a completely reversed response) and cyclic tensile ratcheting, as schematically shown in Fig. 11. This is evidence of the behavior that the minimum strain of the composite obviously increased with the cyclic loading at an early stage o f fatigue (.N < 10 cycles), as in Fig. 4(a). Thus, when the composite undergoes N-times cyclic loading ( N < 10 cycles), the maximum tensile stress in fibers apparently adds to extra tensile stresses, which were produced by increasing residual stress in the fiber and both cyclic relaxation and ratcheting of the matrix. Thereafter, the stressstrain responses of the composite were nearly constant, i.e., the hysteresis loop of the composite continues to

repeat itself with further increase in the number of applied cyclic loadings. 4.2. Fiber f r a c t u r e behavior at early stage

In situ observation results demonstrated that the reaction layer cracking and fiber fracture occurred within the first few cycles of the fatigue test (mostly at N~< 10 cycles). During the test, the maximum tensile stress in the reaction tayer t is given by

where o-~ax is the maximum longitudinal tensile stress of the TiC layer, ER and E~( = E r f q - E r a ( 1 - f ) ) are Young's modulus of the TiC layer and the composite, respectively, o-~ is the maximum applied stress, and o-~ is the longitudinal thermal residual stress introduced 1 As reported in [14,16], the main reaction product between SiC fiber and Ti-15-3 is TiC, since the fiber outer surface consists of a carbon-rich phase; other reaction products include various titanium silicides.

S.Q. Guo et al. / Materials Science and Engineerh~g A220 (t996) 57-68

64

Loading Direction y

Fig. 9. A typical example of (a) the matrix plastic deformation (slip bands (sb) originated from fractured fiber and grain boundaries (gb)) and (b) crack initiations and propagation behavior of the composite at stage III (arrows indicate matrix cracks). ( ~ = 450 MPa, N = 40 000 cycles). during the fabrication process by the thermal expansion m i s m a t c h between the fiber and matrix. In the composite system used, the thermal expansion coefficient of the matrix is ~m = 9 x 10 - 6 K - t [15], and this value is larger than that of the fiber for longitudinal direction, c~f=4.5 x 10 . 6 K - t [15]. Consequently, on cooling f r o m the processing temperature, the matrix experiences an axial tensile stress, cry, whereas the fiber experiences an axial compressive stress, - o - f (positive sign m e a n s tension and negative sign m e a n s compression). The thermal expansion coefficient of the T i C layer is ~.p. = 7.5 x 10 - 6 K - z [16] and is very close to that of the titanium alloy matrix. Therefore, the reaction layer also experiences an axial tensile stress, ~ . , and this stress level can be assumed to be nearly the same as o-~.

2000 "

.

.

.

.

.

.

.

Ot~

TensileFractureStress " Matrix • Composite r~ MatrixCracking • Fatigue Failure

160 "~ 12001-

\

I •4,o< ~_ 80

"

<

:a~.

E "'2

400

i

0

t

I:113

~ --

¢

~"

i

" 'AA A

f(1

-,

i

10000 20000 30000 40000 50000 60000 Number of Cycles

Fig. 10. Plots of applied maximum stress, a~, vs. number of applied cycles, N, for initiation of the matrix crack and the composite failure.

E l \)Ems r 4- -~c

o-~ =

(3a)

1 +(1 -2v)~ and 1 o-~ -

El\ ~°/

I + (1 -

r ,

(3b)

E~

respectively, where s T is the thermal misfit strain, and v is Poisson's ratio, assumed to be the same for fiber and matrix (v = vr = vm = 0.25). A s s u m i n g that the thermal expansion coefficients are t e m p e r a t u r e independent and the volume expansion associated with the/1--* c~ transf o r m a t i o n is neglected 2, the thermal misfit strain, e T, is written as er=

"-A A• "'~1:3

0

.

Neglecting the relaxation effects due to matrix creep and/or plasticity, the thermal residual stresses of the matrix and fiber are [17]

(~m -- ~f) d T

(3c)

where A T is the t e m p e r a t u r e difference between fabrication t e m p e r a t u r e and r o o m temperature ( A T = 860 K). F r o m Eqs. (3a), (3b) and (3c), the estimated thermal residual stresses in the matrix and fiber are equal to am--r _ 342 M P a and o-~ = - 727 M P a , respectively. The calculated thermal stresses are lower than the tensile 2 The change of volume expansion by the ,8 --*~ transformation in Ti-6A1-4V alloy is reported to be approximately 2.2% [18]; however, it is not clear for the present composite, thus the phase transformation strain is not considered here.

S.Q. Guo el al. / Materials Science and Engineering A220 (I996) 5 7 - 6 8

Stress.

m~,~,. D~.,-,,-,,-,se

rna) Oa

r Grr

atrix esponse

Gamil

0

l,g

-oI

Fig. 11. Schematic drawing showing the effect of thermal residuaI stress on the stress-strainresponses of the composite,fiber and matrix during fatigue process. yield stress of the matrix (Gray = 750 MPa [14]) and the values roughly agree with the reported values [19]. Thermal residual stress in the reaction layer is also estimated to be 342 MPa, i.e., o-[~~ o -~~--3 4 2 MPa. The maximum tensile stress in the reaction layer for the first cycle is 1390, 1903 and 2392 MPa for the maximum applied stresses of 450, 670 and 880 MPa, respectively. Although the residual stress of the matrix and the fiber switch signs after only the first cycle, the sign of the residual stress of the TiC layer does not change but still maintains tension because of the fully elastic behavior of this layer. After the first cycle, the tensile stress of the reaction layer changes with the number of applied cycles, N. Fig. 12 shows plots of normalized reaction layer stress versus number of applied cycles for o-~ = 450, 670 and 880 MPa, respectively. The calculation was done using Zarka's method [20] modified by Bobet et al. [21]; details of the calculation procedure are reported in reference [21]. The figure indicates that the maximum tensile stress in the reaction layer reached N ~ 3 cycles and then decreased with the increase in number of applied cycles, N. At more than N ~ 10 cycles, the tensile axial stress in the reaction

65

layer did not greatly decrease. When the number of cycles was approximately N ~ 3, the maximum tensile stresses in the reaction layer approached approximately 105%, 110% and 120% of the initial thermal residual stress for the applied stresses of 450, 670 and 880 MPa, respectively. In this experiment, in situ observation showed the reaction layer cracking at N,~ 2 and the cracking was also observed on the extracted fiber surface (iV ~ 2 cycles [7]). The fracture stress of the TiC is reported to be approximately 1400 MPa [22]. The estimated longitudinal tensile stress at the reaction layer exceeded or was equal to this (o-~--450 MPa) level. Thus, the reaction layer cracking occurred due to increase of the thermal axial residual stress in the reaction layer. Once the reaction layer cracking occurred, the interface between the reaction layer and coating layer, and/ or coating layer and fiber debonded because the interface shear debond energy release rate of the composite, Gi, ( , ~ 4 J m -2) [23], is smaller than the critical value ( ~ G f / 4 = 11 J m - z) for onset of the crack deflection along the interface [24]. Thus, the interface debonding is preferable to the fiber fracture due to stress concentration by the reaction layer cracking. The fiber strength lessens after the onset of the interface debonding. The reduction in fiber strength after the debonding of interface between the coating layer and fiber is reported to exceed about 50% of the coated one ( ~ 1500 MPa) [25]. Neglecting the stress at the TiC layer because of low volume fraction, the maximum stress of the fiber is given by [17] =

:7

1.4 ,

~-~+ cry.

..................................................... Maximum Applied Stress

1.2

~r~"~ E ~Oob~u'~ o 1.01 "--~ bk~\

rr

0.8

(4)

\

o ~ ,',

Ga=450MPa ~a-=670MPa %=880 MPa

co

°

0.6

<'~

0.4

---- 0.2 E O z

!

................................................... 10 102 103 1 04 1 05

10 e

N u m b e r of Cycles

Fig. 12. Change of axial stress in the reaction layer (TiC layer) as a function of the number of cycles, N, for three different applied maximum loads.

66

S.Q. Guo et al. / Materials Science and Engineering A220 (1996) 57-68

After the first cycle, the maximum stress is equal to approximately 1627, 2067 and 2487 MPa, for the maximum applied stress, o-a, of 450, 670 and 880 MPa, respectively. Thus, it is natural that fiber stress, after the interface debonding, exceeds its fracture strength, and fiber fracture occurs at the location of interface debonding. At this time, the interface is not perfectly debonded along the entire gage length and thus the multiple fiber fracture at random locations is possible, which is independent of a critical stress transfer length [26]. The in situ observation showed that the interface reaction layer (TiC layer) cracking occurs randomly and, at the location of interface debonding, fiber fracture follows near the crack of reaction layer. After N > 10 cycles, the thermal residual stress relaxation in the matrix causes reduction in tensile stress of the fiber [27], while interface debonding and sliding proceed because the interface shear sliding causes degradation of shear stress transfer potential by wear of the interface [28]. If fiber fracture occurs, the load carried by the fiber is transferred to the matrix, and the stress concentration in the matrix causes plastic deformation [29]. At the same time, the stress concentration near the broken fiber [30] also causes a high probability of fracture of the nearest fiber. In Fig. 6, the fiber fracture tends to occur within _+ 100 gm of the adjacent fiber fracture as a result of the stress concentration due to the fracture. After random fiber fracture, almost all the interface debonds and slides. Fiber fracture also occurs at this stage, but the location is limited to approximately Lo/2 from the first fiber fracture because the entire interface at the gage section is debonded at this stage, and fiber stress increase requires the critical stress transfer length, L¢. Lo is given by Lo -

O'f~Rr T

,

(5)

where v is the interfacial shear stress, R e is the fiber radius and Cr~uis the fiber strength. In the SiC fiber-reinforced Ti-15-3 composite, interface shear sliding stress, v, for the pristine composite by push-out experiment is about 140 MPa [23], lower than that of shear yielding stress of the matrix ( ~ O-my/x/~~ 433 MPa [31]). We consider the shear stress at the interface which is governed by the shear yield strength of the matrix during the fatigue test. The mean fiber strength, ofu, is obtained by extracting fibers from the matrix of the fabricated composite, and the value is approximately 3000 MPa [8]. Thus, the estimated minimum critical length is Lo ~ 390 gm. Longer fiber fracture length measured at an early stage roughly agrees with this. It should be noted that this multiple fiber fracture behavior is different from that observed in composites with a fiber volume fraction smaller than the critical value, because the critical fiber volume fraction, refit, is approximately 0.06 for SiC/Ti-15-3 [32].

4.3. Modulus loss during fatigue

In stage I, the unloading modulus decreased rapidly within about 5 cycles, then continued to decrease gradually. After about 10 cycles, the unloading modulus remained nearly constant and was equal to about 92%, 88% and 83% of the original one in the case of maximum applied stresses of 450, 670 and 880 MPa, respectively. This reduction in the modulus was very similar to that reported by Johnson [33] with the same type of composite. Assuming that the decrease of the unloading modulus at stage I depends on the number of fiber fractures, the unloading modulus of the composite Eo(N) is approximately given by Eo(N) ~ (1 - c~)EoL +

~E,,

(6)

where E~ is the unloading modulus of a discontinuous fiber-reinforced composite with the same volume fraction, respectively, and ~ is the fraction of broken fiber to the total number of fibers contained. If all the fibers in the gage section are fractured at length, L~, i.e., ~ is equal to one and the interfacial shear stress between fiber and matrix is constant along the sliding interface, Eq. (6) reduces to Eo(N) ,~ ~E~.

(7)

The unloading modulus calculated from Eq. (7) means that Young's modulus of the discontinuous fiber composite has the same fiber length, Lf. For a uniaxially aligned discontinuous fiber composite, the longitudinal modulus, Eg is given by [34] Eg =

1 - 2--~-fv)/~}J + E~(1 - f ) .

(8)

The experimental results demonstrated that the fiber fracture length in the specimen is nearly constant and depends on the maximum applied stress (Fig. 8). At the end of stage I, nearly all the fibers are fractured with a mean length Lf 3, and Lf is equal to 440, 380 and 315 gm for the maximum applied stresses of 450, 670 and 880 MPa at N--10 cycles, respectively. Substituting the experimentally obtained average fiber fracture length Lf into Eq. (8), the unloading moduli of the composite after fiber fracture are obtained and are equal to 150, 141 and 129 GPa for maximum applied stresses of 450, 670 and 880 MPa, respectively, in steady stage (N> 10 cycles), i.e., in stage II. The calculated result from Eq. (8) is shown in Fig. 13 as a function of average fracture fiber length, and the experimentally obtained result Eo(N) from the end of stage I is also plotted in this figure. The agreement between experiment and calculation of the unloading modulus also indicates that the 3 The meanfiber lengthLfisshorter than the gagelength,thus, one fiber broke into 2-5 pieces.

S.Q. Cmo et al. / Materials Science and Engh~eerhTg A220 (1996) 57-68 24O (3_ Measured Value

220 z,%

uJ

200

5. Conclusions

F-4

180 03 "~ 03

160

-o O

140

(33

0

-~

with an increase in the number of cycles applied. At the end of stage III, the composite fails catastrophically with rapid major matrix crack growth.

............ Calculated Value

03

._

67

~a=670MPa

120

%=450 MPa

~a=880MPa i i I i r i r , i 100 280 300 320 340 360 380 400 420 440 460 480

Mean Fiber Fracture Length, Lf (/am)

Fig. I3. Plot of the unloading modulus vs. average fracture fiber length for the fatigued composite in stage II. abrupt decrease of the unloading modulus originated from a decrease in fiber efficiency due to the multiple fiber fracture. The increase of the strains, em~ and e~ n (fatigue creep), with the number of applied cycles is also due to fiber fracture, because the local strain concentration near the fracture contributes to the increase in local deformation of the matrix and this, in turn, contributes to the increase in unrecovered permanent strains in the matrix. At stage II, only a slight increase in the number of fiber fractures is recognized and E o ( N ) does not decrease at this stage, i.e., it is nearly constant throughout this stage. Notice that each specimen approaches a stabilized value of Eo(N) or E o ( N ) / E ° (Fig. 5). The fatigue creep of the composite is also still visible and the rate is remarkable at higher applied stress, although the effect of creep on E:(N) is quite small. The beginning of stage II is well contrasted with the end of fiber fracture behavior and the number of applied cycles at the end of stage II agree with the matrix crack initiation behavior (Figs. 5 and 10). The authors previously reported on the micro-damage evolution process in the same composite [7] and showed that the matrix cracking initiates from beside a fiber fracture; the matrix crack initiates when the matrix micro-hardness ahead of a fracture fiber ( ~ 10 gm from the fiber) reaches a critical hardness ( ~ 6 GPa). Slight decrease of E o ( N ) through this stage is due to additional fiber fractures. Initiation of non-propagating cracks contributes to the decrease of E°(N), although the effect is negligible. Stage IIt follows the initiation of matrix cracking at stage II beside broken fiber. The decrease of the unloading modulus, E o ( N ) at this stage is due to the increase of e~ ~. That is, large plastic deformation is introduced to the composite at this stage and the propagating crack growth in the matrix is accelerated

A tension-tension cyctic fatigue test on SiC/Ti-15-3 composite was carried out with the following results: (1) The longitudinal unloading modulus of the composite decreased with the increase in the applied number of cycles, N. The decrease fell into three characteristic stages which were strongly related to the number of multiple fiber fractures and length of the fractured fibers. (2) The modulus decreased rapidly within N ~ 5 (stage I), at a rate which increases with the increase of maximum applied stress. After this rapid decrease, the modulus remained nearly constant (stage II) until matrix crack growth and propagation (stage III). (3) The early stage random fiber fracture at stage I is strongly related to the thermal residual stress at the reaction layer because cracking of this layer acts to trigger fiber fracture. (4) The change of the modulus is explained by the multiple fiber fracture behavior and the measured unloading modulus agrees well with the prediction of simple rule-of-mixtures for discontinuous fiber-reinforced composite.

Acknowledgements The authors would like to thank Dr K. Honda for help in experimental work and discussions. They also thank A. Fukushima and C. Fujiwara for helpful discussions and assistance with the composite materials. This work was supported in part by the Ministry of Education and the Agency of Science and Culture, Japan.

References

[1] D.P. Walls, G. Bao and F. Zok, Scr. MetaIL Mater., 25 (1991) 911-916. [2] D.P. Walls, G. Bao and F.W. Zok, Aeta Metall. Mater., 41 (1993) 2061-207I. [3] J.R. Jira and LM. Larsen, Metall. Trans. A, 25 (1994) 14131424. [4] S.M. Jeng, P. Aiassoeur and J.M. Yang, Mater. Sei. Eng., AI54 (1992) 11-t9. [5] K.S. Chan and D.L. Davidson, Metall. Trans. A, 2I (1990) I603-1612. [6l P.K. Liaw, E.S. Diaz, K.T. Chiang and D.H. Lob, MetalL Mater. Trans. A, 26 (1995) 3225-3247. [7] S.Q. Guo, Y. Kagawa and K. Honda, Metall. Mater. Trans., On press).

68

S.Q. Guo et al. / Materials Science and Eng#~eering A220 (1996) 57-68

[8] A. Fukushima, C. Fujiwara, S. Kiyoto, Y. Kagawa and C. Masuda, Proc. 94, Annu. Meet. JIME/MMO, Oct. 13-I4, 1994, Vol. B, Japan Society for Mechanical Engineers, Tokushima, Japan, pp. 140-141. [9] Y. Kagawa and K. Honda, Seisan Kenkyu (Rep. Inst. Ind. Sci., Univ. Tokyo), 46 (1994) 465-468. [10] E. Jinen, J. Mater. Sei., 2I (1986) 435-443. [11] P.K. Brindley, S.L. Draper, J.I. Eldridge, M.V. Nathal and S.M. Arnold, Metall. Trans. A, 23 (t992) 2527-2540. [12] S.M. Jeng, J.-M. Yang and C.J. Yang, Mater. Sci. Eng., A138 (1991) 169-180. [13] B. Lerch and G. Halford, Mater. Sci. Eng., A200 (1995) 47-54. [14] S. Jansson, H.E. Deve and A.G. Evans, lVletalI. Trans. A, 22 (1991) 2975-2984. [15] B.S. Majumdar and G.M. Newaz, Philos. Mag. A, 66 (I992) 187-212. [16] S.H. Thomin, P.A. Noel and D.C. Dunand, Metall. Mater. Trans. A, 26 (1995) 883-895. [17] B. Budiansky, J.W. Hutchinson and A.G. Evans, J. Mech. Phys. Solids, 34 (1986) 164-189. [18] C. Barrett and T.B. Massalski, Structure of Metals, 3rd edn., Pergamon Press, Oxford, 1980, p. 361. [19] R.T. Bhatt and H.H. Grimes, in Fatigue of Fibrous Composite Materials, ASTM STP 723, American Society for Testing and Materials, Philadelphia, PA, 1981, pp. 274-290. [20] J. Zarka and J. Casier, Mech. Today, 5 (1979) 93-I98. [21] J.-L. Bobet, C. Masuda and Y. Kagawa, 9". Mater. Sei., in press. [22] G.V. Samsnov, Hand Book of High Temperature Materials, No. 2, Plenum Press, New York, 1964. [23] Y. Kagawa, C. Masuda, C. Fujiwara and A. Fukushima, in W.S.

Johnson, J.M. Larsen, and B.N. Cox (Eds.), Life Prediction Methodology for Titanium Matrix Composites, ASTM STP 1253, American Society for Testing and Materials, Philadephia, PA, 1996, 26-42. [24] K.S. Chan, Metall. Trans. A, 24 (1993) 153t-1542. [25] C. Masuda, Study of characteristics of metal matrix composite, Rep. Natl. Res. Inst. Met. Jpn, (1995). [26] Y. Kagawa and H. Hatta, Tailoring Ceramic Composite, AguneShofu Press, Tokyo, 1990, pp. 69-84. [27] J.-L, Bobet, C. Masuda and Y. Kagawa, Composites '95: recent advances in Japan and the United States, Proe. dapan-U.S., CCM-VII, Kyoto, Japan, t995, pp. 417-424. [28] D.P. Walls and F.W. Zok, Acta Metall. Mater., 42 (1994) 2675-2681. [29] I. Leddet and A.R. Bunsell, in S.W. Tsai (Ed.), Composite Materials: Testing and Design (Fifth Conf.), ASTM STP 674, American Society for Testing and Materials, Philadelphia, MA, 1979, pp. 581-596. [30] A. Kelly and G.J. Davies, Metall. Rev., 10 (1965) 1-77. [31] Y.L. KAipfel, M.Y. He, R.M. McMeeking, A.G. Evans and R. Mehrabian, Aeta Metatt. Mater., 38 (1990) 1063-1074. [32] A. Kelly and N.H. Macmillan, Strong Solids, 3rd edn., Oxford Science Publications, Oxford, 1986. [33] W.S. Johnson, in W.S. Johnson (Ed.), Metal Matrix Composites: Testing, Analysis, and Failure Modes, ASTM STP 1032, American Society for Testing and Materials, Philadelphia, PA, 1989, p. 194. [34] C. Zweben, in C. Zweben, H. Thomas Hahn and Tsu-Wei Chou (Eds.), Mechanical Behavior and Properties of Composite Materials, Vol. 1, Press, Weston, t989, pp. 39-43.