An investigation of the effects of microstructure on fatigue damage in a symmetric [090 ]2s silicon carbide (SCS6) fiber-reinforced titanium matrix composite

ELSEVIER

Materials Scienceand Engineering A200 (1995) 89-102

A

An investigation of the effects of microstructure on fatigue damage in a symmetric [ 0 / 9 0 1 2 s silicon carbide (SCS6) fiber-reinforced titanium matrix composite W.O. Soboyejo", B.M. Rabeeh b ~Department o]' Materials Science and Engineering, The Ohio State University, I16 West 19th Avenue, Columbus, OH 43210, USA bDepartment of Industrial, Welding and Systems Engineering, The Ohio State University, 190 West 19th Avenue, Columbus. OH 43210, USA

Abstract

The results of a systematic study of the effects of microstructure on the mechanisms of fatigue damage in a symmetric eight ply [0/9012s Ti-15A1 3Cr-3A1-3Sn/SiC (SCS6) composite are presented. Damage mechanisms are elucidated using optical/scanning electron microscopy and acoustic emission techniques. Damage initiation under cyclic loading is shown to occur early in life, and is dominated by longitudinal and transverse interfacial cracking. Subsequent damage occurs by matrix and fiber cracking, slip band formation and crack coalescence prior to the onset of catastrophic failure. However, the sequence of the damage is sensitive to changes in the metastable fl matrix and interracial microstructure. Based on the experimental evidence, a micromechanics model is developed for the prediction of fatigue life. This model involves the use of crack-tip shielding concepts in the assessment of crack bridging phenomena during fatigue crack growth. Keywords: Microstructure; Fatigue; SiC/Ti composites

1. Introduction

Titanium matrix composites with various architectures are currently being considered for high temperature structural aerospace applications due to their attractive combinations of high strength and creep resistance [1,2]. The interest in potential aerospace applications of these composites has stimulated a number of focused research efforts aimed at improving our limited understanding of fatigue [3 14] and fracture [15 17] mechanisms. Most of the studies have revealed that a complex sequence of damage is associated with failure under monotonic and cyclic loading. The layered interface that forms between the SCS6 fiber and the Ti-15-3 matrix has also been shown to have a highly complex structure in recent high resolution transmission electron microscopy studies [18,19]. However, there have been very few efforts to study the effects of composite microstructure on fatigue damage mechanisms [19]. There is also a strong need for micromechanics-based models for the prediction of the fatigue lives of structures fabricated from titanium matrix composites. The results of a systematic study of the effects of 0921-5093/95/$09.50 ,~:; 1995 ElsevierScience S.A. All rights reserved S S D I 0921-5093(95)07017-6

microstructure on the micromechanisms of fatigue damage in a T i - 1 5 V 3Cr-3A1 3Sn/SiC (SCS6) composite are reported in this paper. This includes an assessment of matrix, fiber and interfacial damage at room temperature. The observed crack-tip shielding mechanisms (crack bridging and fiber pull-out) are modeled using fracture mechanics models. The effects of crack-tip shielding are also assessed in the estimation of the effective driving force required for the growth of the dominant cracks identified during progressive cyclic loading to failure. The current article is divided into six sections. The materials and microstructures are presented in Section 2, prior to a detailed description of the experimental procedures in Section 3. Fatigue damage mechanisms are then discussed in Section 4, prior to a presentation of micromechanics models for the estimation of fatigue life in Section 5. Salient conclusions arising from this work are summarized in Section 6.

2. Material and microstructures

The symmetric model eight ply composite material

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Fig. 1. Effects of annealing in the matrix :~ + fl phase field on composite microstructure: (a) as-received (included for comparison); (b) 540 °C/10 h/AC; (c) 540 °C/50 h/AC; and (d) 540 °C/100 h/AC.

that was used in this study was fabricated by Textron Specialty Metals, Lowell, MA. It was p r o d u c e d by the foil/fiber/foil technique via hot pressing. The resulting composite microstructure is shown in Fig. l(a). These show the side view o f a typical hot pressed composite. A uniform distribution o f SiC fibers was observed in the [0/9012s lay-up that was used. Large ( ~ 500 /tm average diameter) metastable fl grains are also observed in the as-received composite. The layered interface has a highly complex microstructure [18,19] which consists p r e d o m i n a n t l y o f titanium carbides (TiC and TizC ). phase was also stabilized by the M o wire that was used to hold the SCS6 fibers in place during composite fabrication. T w o sets o f heat treatments were used to control the composite microstructure. The first set o f heat treatments involved annealing for different durations (10 h, 50 h and 100 h) below the fl solvus (approx. 800 °C for Ti 1 5 V - 3 C r - 3 A 1 - 3 S n in Ref. [20]). This heat treatment resulted in a refined Widmanstfitten colony micro-

structure with small acicular ~ grains in a matrix o f fl (Fig. l ( b - d ) ) . The changes in the matrix microstructure also occurred without significant coarsening o f the interfacial structure (Fig. l ( a - d ) and Table 1). N o t e that the e grains shown in Fig. l ( b - d ) are the light Table l Summary of interracial dimensions and tensile properties Condition/ heat treatment

Titanium carbide thickness (~m)

Carbon coating thickness (lam)

Ultimate tensile stress (MPa)

Strain to failure x 10 ~

AR 540 °C/10 h/AC 540 °C/50 h/AC 540 °C/100 h/AC 815 °C/10 h/AC 815 °C/50 h/AC 815 °C/100 h/AC

2.9 2.6 2.3 3.1 3.2 3.2 2.9

2.6 2.6 2.4 2.8 3.0 3.0 2.8

856 1028 1028 1000 867 891 881

ll.1

12.5 11.9 12.3 10.5 11.4 9.5

AR, as-received; UTS, ultimate tensile strength; AC, air cooled.

W.O. Soboye]o, B.M. Rabeeh / Materials Science and Engineering A 200 (1995) 89-102

91

(white) phase, while the fl phase is the dark (gray) matrix background in Fig. l(b d). Some slip bands were also observed in the Widmanst/itten matrix microstructure of the material annealed at 540 °C for 50 h. It is presumed that these were induced as a result of yielding due to residual stresses in the composite. The second set of heat treatments were carried out at 815 °C. Heat treatment durations of 10, 50 and 100 h were employed. These heat treatments were designed to promote significant coarsening of the interfacial microstructure (Table 1 and Fig. 2) without significant alteration of the matrix microstructure. However, unlike the four-ply unidirectional Ti-15-3/SiC (SCS9) composite examined in previous studies [14], the degree of interfacial microstructure evolution was limited in the eight-ply [0/9012s Ti-15-3/SiC (SCS6) composite that was used in this study. Typical scanning electron microscopy (SEM) photomicrographs of the Ti-15-3/SiC (SCS6) composite annealed at 815 °C are presented in Fig. 2(a-c). Further details on the complex structure of the layered interfacial region are provided in Ref. [19]. The coarse grained (500 /~m average grain size) as-received microstructure is retained after annealing in the fl phase field. The average room-temperature tensile properties obtained for the as-received and heat treated composites are summarized in Table 1. All the composites failed before a plastic strain of 0.2% was reached. Typical ultimate tensile strength values were between 1000 and 1030 MPa in material annealed at 540 °C. These strength levels are higher than typical strength values between 800 and 900 MPa obtained in the as-received condition or after annealing at 815 °C. The higher strengths in the composites annealed at 540 °C may be due to the higher strength levels associated with the Widmanstfitten matrix microstructures that were produced after such heat treatment. No clear effect of heat treatment on Young's modulus was observed in the composites that were examined. Average values of initial (tangential) Young's modulus obtained from stress-strain plots were between 97 and 166 GPa. Inelastic behavior was also observed to initiate at relatively low stresses between 50 and 300 MPa.

3. Experimental procedures Triplicate stress-controlled low-cycle/high-cycle ( L C F / H C F ) tests were performed at room temperature on smooth rectangular specimens (1.2 m m x 12.7 mm x 152.4 mm) which were fabricated by water jet cutting. A servohydraulic test machine was employed in the fatigue tests. The tests were carried out at stress ranges, Ao-= O'max -- O'min, corresponding to 0.5 UTS, 0.6 UTS and 0.7 UTS (UTS is the average ultimate tensile stress determined from duplicate tensile tests).

Fig. 2. Effects of annealing in the matrix fl phase field on composite microstructure: (a) 815 °C/10 h/AC; (b) 815 °C/50 h/AC; and (c) 540 °C/100 h/AC.

The applied stress ranges are above the 500 MPa endurance limit which has been reported for Ti-15-3/ SiC composites in previous studies [9]. The tests were

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W.O. Soboyejo, B.M. Rabeeh / Materials Science and Engineering A200 (1995) 89 102

carried out at a cyclic frequency of 10 Hz and a stress ratio, R = amin/Oof 0.1. Changes in strain were monitored across the gauge location with a contact extensometer (25.4 mm gauge length). The specimens were loaded continuously to failure to obtain initial estimates of the number of cycles to failure, Nf, in the first set of tests. Deformation and cracking phenomena were monitored with an acoustic emission unit in the second set of tests. The acoustic emission unit consisted of two piezoelectric sensors which were located at either end of the gauge section. These were used to locate the sources of acoustic emission data, and to ensure that only signals from the gauge sections of the specimens were processed in subsequent analysis. Relevant acoustic emission data such as amplitude, energy, number of counts/ hits, rise time and duration were obtained form the acoustic emission unit. Further details on the use of acoustic emission techniques in the detection of damage in Ti-15-3/SiC composites can be obtained from Ref. [14]. In addition to the use of acoustic emission techniques, ex-situ optical and scanning electron microscopy techniques were used to study the initiation and evolution of damage in the third set of tests. The sides of the specimens were polished to a mirror finish with 1 /lm diamond paste to facilitate microscopic examination. Microscopic examination was carried out before loading, and after incremental cyclic loading stages that correspond to one tenth of the total number of cycles to failure, Nr, obtained from the first set of tests in which the specimens were loaded continuously to failure. Microscopic examination was thus carried out at 0.1Nf, 0.2Nf, 0.3Nf ... until catastrophic failure occurred. Modulus estimates were obtained, after each incremental loading stage, from hysterisis stress-strain plots that were generated by loading and unloading to the mean cyclic stresses. These tangent modulus values were used as qualitative measures of damage. Fracture mechanisms were studied by scanning electron microscopy (SEM) in all the fatigue specimens that were loaded continuously, or in incremental steps, to failure. The deformation and cracking phenomena associated with specimens loaded to different fractions of Nf (not to failure) were also studied. The fractions of Nf in these cases were selected to correspond to characteristic signals in the acoustic emission data. The signals, which will be discussed later, correspond to damage initiation and evolution phenomena identified during subsequent microstructural (SEM and optical microscopy) analysis of the polished sides of the specimens. Further details on the correlation of acoustic emission data with observed damage phenomena are provided in Section 4.1.

4. R e s u l t s and d i s c u s s i o n

....

4. I. Fatigue

behavior

The plots of stress range, Aa = O-max --O'min, versus the number of cycles to failure, Nf, are presented in Fig. 3(a,b). These so-called S - N curves are comparable to those reported by other research groups [3-14] for as-received composites. However, this is the first report of the effects of interfaces (815 °C heat treatments) and matrix microstructure (540 °C heat treatments) on the fatigue behavior of [0/9012s Ti-15-3/SiC (SCS6) composites. Unlike the 540 °C heat treatmenta, which do not appear to have a clear effect on fatigue life (Fig. 3(a)), the effects of the 815 °C heat treatments are relatively easy to interpret. Fatigue life in the 815 °C specimens decreases with increasing annealing duration. It is interesting to note here that the 540 °C/50 h heat treatment results in the lowest fatigue life, presumably as a result of the effects of residual stresses which may be responsible for the slip bands that were observed in this heat treatment condition prior to fatigue deformation (Fig. l(c)). 6o0

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W.O. Soboyejo, B.M. Rabeeh / Materials Science and Eng&eering A200 (1995) 89-102

93

Table 2 Number of cycles to matrix cracking (Ni + Np) and total number of cycles to composite failure (N 0 Material

Stressrange(ffactionof~uTs) 0.5

As-received 540/10/AC 540/50/AC 540/100/AC 815/10/AC 815/50/AC 815/100/AC

0.6

0.7

Ni

Np

Nr

Ni

Np

Nf

NI

Np

Nf

4410 3669 1558 2651 8250 4821 3293

10290 8561 4212 7609 14850 11249 9877

14700 12230 5770 9720 23100 16070 13170

2460 1896 2192 3048 3543 2146 2097

5740 2844 3288 4572 8267 3984 3893

8200 4740 5480 7620 11810 6130 5990

1055 878 1416 828 1282 2020 819

3165 2632 3304 552 4488 3030 1911

4220 3510 4720 1380 5770 5050 2730

The fatigue initiation and propagation components associated with the different material/heat treatment conditions are summarized in Table 2. The number of fatigue initiation cycles, Ni, is defined arbitrarily in this Table 2 as the number of cycles required for the initiation of matrix cracking. The number of propagation cycles is therefore equal to the difference between Nr and Np. Table 2 shows that both Ni and Np generally decrease with increasing annealing duration and stress range. Consequently Nf also tends to decrease with increasing annealing duration and stress range. The 815 °C heat treatments result in the longest fatigue lives in the stress range that was examined. The differences in fatigue behavior are attributed to changes in microstructure [14,19] and residual stresses [21,22] which may be induced during heat treatment. Further discussion on the effects of heat treatment on fatigue requires a detailed analysis of the damage initiation and evolution, which is presented below. The stages of deformation associated with damage initiation and propagation under cyclic loading are summarized in Figs. 4 and 5. Damage initiation is defined arbitrarily in this study to consist of all deformation stages prior to matrix cracking. Damage propagation is therefore assumed to involve matrix cracking and all subsequent stages of damage. As in previous studies on unidirectional Ti-15-3/SiC composites [14], interfacial damage was observed to initiate during the first fatigue cycle. The initial damage involved interfacial decohesion along the 90 ° fibers (Fig. 4(a)). The initial partial debond extended progressively with increased cycling across the fiber length. This occurred presumably as a result of the relatively high shear stress in the off-axis plies and plane stress conditions at the specimen surfaces. Interracial decohesion in the 90° plies was followed by debonding in the 0 ° plies (Fig. 4b). The decohesion, which typically occurred first at the interface between the carbon coating on the SiC fiber and the predominantly TiC interface, is attributed to the significant degradation in interfacial fracture strength which has been shown to occur in these composites under cyclic

loading [13]. Previous studies have shown that the interfacial/friction stress drops from 150-200 MPa to 34-50 MPa during fatigue loading. The drop in interfacial stresses may also be further exacerbated by the very low cleavage fracture strength of the TiC/TizC carbide interface [8]. The early nucleation of fatigue damage in the Ti-15-3/SiC (SCS6) composites is therefore attributed to the brittle nature of the interfacial phases. This suggests the need for protective fiber coatings to prevent the formation of TiC or Ti2C during composite processing or high temperature exposure. Such approaches are being explored by other researchers [25] who are using Ag-Ta interlayers to limit or prevent the reaction between Ti and C. After interfacial decohesion, damage occurs by fiber fracture (Fig. 4(c)). The initial damage spreads gradually from the outer plies, where it is concentrated initially, to the inner plies (Fig. 4(d)). The initial concentration of damage in the outer plies is important since it indicates that the outer plies are more susceptible to damage, presumably as a result of surface oxidation or mechanical damage that can occur during hot pressing. This observation is important since most micromechanics models are based on simple ply theories in which the properties of the individual plies with similar lay-ups are assumed to be the same, i.e., all zero plies are assumed to have equivalent properties, just as all the 90 ° plies are assumed to have identical properties. The observation of damage progression from the outer to the inner plies is also important for the modeling of the general direction damage, as discussed in the next section. Subsequent damage involved slip band formation in the titanium matrix of the materials subjected to annealing for 540 °C for 10 h (Fig. 4(e,f)). Slip band initiation was observed after cycling for approximately 0.7 Nf in the specimen subjected to a stress range of 0.7 O'VTs. Note that Air is the number of cycles to failure obtained from the first set of tests, and crtn-s is the ultimate tensile stress. The slip band orientations were similar within individual colonies in the Widmanst/itten microstructure. However, no crystallographic analysis has been done to study the orientation relationships.

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Nevertheless, it is clear from the microscopic observations that some of the matrix cracks were nucleated by the broadening of slip bands and the extension of interfacial cracks into the matrix, as shown in Fig. 4(f). Upon matrix crack initiation, damage propagated from the outer plies to the inner plies, and multiple

Fig. 4 (a) (f).

matrix cracks extended and coalesced to form longer single cracks (Fig. 4(g)) prior to catastrophic failure (Fig. 4(h)). Some transgranular cracking was also observed in the Mo cross-weave that was used to hold the fibers in place during composite fabrication. However, failure did not always initiate from the Mo cross-weave,

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95

Fig, 4. Damage mechanisms in fatigue specimen annealed at 540 °C/10 h/AC and deformed at Aa = 0.7 trvTS: (a) Debonding in 90 ° plies at 0.1Nf; (b) debonding in 0 ° plies at 0.2Nf; (c) initiation of fiber fracture at 0.5N6 (d) damage propagation in outer at 0.5N 6 (e) slip band formation in Widmanst~itten structure at 0.7N6 (f) matrix crack nucleation from interface at 0.7 Nr; (g) crack coalescence and fiber fracture at 1.2N6 and (h) typical fracture surface at 1.4Nf.

and crack coalescence typically involved the linkage of matrix and fiber cracks that were in the Mode I direction (Fig. 4(g)). Matrix fracture typically occurred by ductile dimpled fracture, while fiber and interface fracture occurred by cleavage (Fig. 4(h)). Similar damage initiation and evolution phenomena were observed in the other heat treatment/testing conditions (Fig. 5(ah)). However, cyclic deformation-induced slip band formation was only observed after annealing at 540 °C for 10 h. Fatigue striations (Fig. 5(h)) and deformation-induced matrix subgrain formation (Fig. 5(d)) were also observed in the metastable fl matrices of the composites annealed at 815 °C. 4.2. Acoustic emission

An understanding of bulk damage levels can be developed by analysis of the acoustic emission data that were obtained [26,27]. Events with amplitudes less than 60 dB were filtered out to eliminate extraneous noise from the acoustic emission signals. This filtration level is somewhat higher than the arbitrary 40 dB threshold level that was used in previous studies on unidirectional Ti-15-3/SIC composites [14]. Typical plots of number of hits versus time, number of counts versus time, duration versus time, amplitude versus time, energy versus time, and rise time versus amplitude are presented in Fig. 6(a-f), respectively. Consistent with the visual observations, these plots show that damage initiated early in the fatigue life. The number of hits (acoustic events) also increased with time, presumably as a result of the overall contributions from the damage phenomena discussed above. Correlations were established for the different types of damage initiation and propagation phenomena iden-

tiffed during incremental cyclic loading to failure (Table 3). Since these correlations were established for composites with an equiaxed fl and Widmanstatten matrix microstructures (Figs. 1 and 2), the current results suggest that the general guidelines provided in Table 3 may be independent of composite microstructure. Further work is needed to verify this speculation. The guideline/correlations for damage initiation and evolution are discussed below. Damage initiation by debonding at the fiber-matrix interface was found to be associated with a moderate number of hits/events when all the other acoustic emission parameters were low. Persistent slip band (PSB) and subgrain formation, i.e., dislocation reactions, were correlated with a high number of counts and low number of events when all the other acoustic emission parameters remained moderate. Damage propagation by matrix cracking resulted in a moderate number of events when all the other acoustic emission parameters were high. Fiber cracking was associated with a high number of hits/events with high amplitude, when all the other acoustic emission parameters were low, and crack coalescence prior to catastrophic failure was correlated with high or very high acoustic emission parameters. The above definitions of the signal ranges corresponding to high, moderate and low acoustic emission parameters are somewhat arbitrary (Table 3). Nevertheless, such simple arbitrary guidelines and correlations may be useful to those involved in the non-destructive evaluation of structures/components fabricated from titanium matrix composites. More work is clearly needed to develop rigorous wave mechanics-based models for the prediction of the acoustic emission parameters shown in Fig. 6 and Table 3.

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4.3. M a t r i x hardness and elastic modulus

Matrix hardening occurs in the composites during cyclic loading to failure. This was confirmed by the results of microhardness measurements that were obtained after incremental fatigue loading (Fig. 7(a-d)).

Fig. 5. (a)-(f).

The matrix microhardness exhibits an approximately symmetric variation across the plies of the composites, with the most significant hardening occurring in the inner plies (Fig. 7(a,b)), presumably as a result of complex reversed plasticity effects across the laminated composite structure. The matrix hardness also increases

W.O. Soboyejo, B.M. Rabeeh / Materials Science and Engineering A200 (1995) 89-- 102

97

Fig. 5(continued). Damage mechanisms in fatigue specimen annealed at 815 °C/10 h/AC and deformed at 0.7 auws: (a) debonding in 90° plies at 0.2Nf; (b) debonding in 0 ° plies at 0.2N6 (c) extension of interfacial crack into matrix in outer ply at 0.6N~,; (d) formation of subgrains due to fatigue loading at 0.8N(, (e) cracking of inner ply after outer ply damage at 0.8N6 (f) fiber fracture at 0.9 Nf: (g) crack coalescence at 1.6Nr: and (h) fracture surface at 1.6Nf.

during the first 30 percent of life prior to saturation during the next 30-40 percent of life. The saturation stage is then followed by a final phase during which matrix hardening occurs until failure (Fig. 7(c,d)). Similar trends were observed in the composites annealed at 540 °C and those annealed at 815 °C. However, the measured hardness values were greater in the composites annealed at 540 °C, consistent with the UTS data (Table 1). Composite modulus will therefore depend on the combined effects of matrix hardening (modulus enhancement) and the cracking phenomena (modulus reduction) discussed above. Hence, the composite modulus will increase when hardening effects dominate, or decrease when cracking phenomena dominate. The modulus may also remain constant when the modulus increase due to matrix hardening is balanced by the modulus decrease due to cracking. Such combined effects of matrix plasticity and cracking phenomena were revealed by the trends in modulus values (Fig. 8) obtained using strain data from contact extensometers. The initial increase in modulus (Fig. 8) was associated with the dominant role of matrix hardening (over initial debonding) due to reversed plasticity (Fig. 8(c,d)). A subsequent drop in the modulus was also observed as the initial debonds extended across the fiber-matrix interfaces. This drop was followed by a matrix crack initiation phase (Figs. 4(f) and 5(c)) during which elastic modulus and matrix hardness remained almost constant. Slip band and sub-grain formation (Figs. 4(e) and 5(c)) occurred in this regime of constant hardness and modulus. Subsequent matrix hardening and modulus increase was then observed during the final stages of damage prior to failure (Figs. 4 and 5).

The simultaneous changes in matrix hardness and composite modulus have some important practical implications. First, they suggest that modulus alone cannot be used as a measure of bulk or local damage since the effective changes in modulus are due to the combined effects of hardening and cracking phenomena. Second, they indicate the sensitivity of strain-based modulus measurements to matrix hardening phenomena. It is also important to note here that similar fatigue behavior was observed in the samples heat treated at different temperatures (540 and 815 °C), regardless of the duration of heat treatment and the fatigue stress levels. Thus, the above discussion should apply to Ti-15-3/SiC composites with similar microstructures.

5. Micromechanical modeling The complex sequence of interfacial, matrix and fiber cracking described above is difficult to model exactly. The interactions between the multiple configurations of cracks are also extremely difficult to model within a conventional fracture mechanics framework [28,29]. However, a simple idealization of the damage sequence can be obtained by recognizing that the damage generally initiates in the outer plies prior to propagation into the inner plies. This can be represented by the initiation of a center crack (with initial length equal to the fiber diameter) from a 90° fiber in the outer ply. Note that symmetry is assumed across the boundary between the fourth and fifth plies in the schematic idealizations shown in Fig. 9. The initial center crack is assumed to have a total length that is equal to the fiber diameter at the start of

98

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3oo-!::

~~

I:

:---::l

}

!

~

e-,

.... -:

....

i ....

! ....

: . . . . . . . . .

! ..................

! ....

: . . . . . . . . .

:-

~ ....

~...:~

I: il

Q

40

152

263,

376

(e)

488

Time

I

.

il . ~i

....

600

: ll..t

~,

II

i:-q i

lOO-~,---t[ . . . . ::. . . . "'I

;

~ ~-.

~ : i

200-I:: . . . . . . . . . . . . . . . . . . . . . . . . . . . .

:: g

zuUU-l

~ .... i .........

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

-li ...............................

I~

60"

(see)

I:

i.-. : : ....

264

"

Time

!

8000-I . . . . . . . . . . . . . . . . . . . . ::. . . . ::. . . . i . . . . i . . . . ::. . . . 4' . . . . ! . . . . i . . . . ~ . . . . ~ . . . . ::. . . . i . . . . i . . . . ::. . . . ::. . . .

' ~ 5 2

(e)

(see)

Time

-!

74]0

600

I

:, . . . .

~-t-, . . . .

ddl,

.:.~I I I II i

i:

II:

i . . . . .

....

i.~,..

.-~-i~~-~~--~,~ ;1111

|l ~1:11:::

g~-i-i--ii.ii.~,-~:~

I t I | I h I | I|.II

llllllll:l

"

:I

(t)

(see)

....

....

Time

(see)

Fig. 6. Typical acoustic e m i s s i o n d a t a obtained under cyclic loading for specimen a n n e a l e d at 540 °C/10 h / A C and d e f o r m e d at A~r = 0.7 auTs: (a) hits versus time; (b) c o u n t s versus time; (c) d u r a t i o n versus time; (d) a m p l i t u d e versus time; (e) energy versus time; and (f) rise time versus amplitude.

cycling

(Fig.

propagate extends then

9(a)).

The

center

crack

as a through-thickness completely

recharacterized

through

is a l s o a s s u m e d

center

t h e first p l y .

as an edge

crack

The

(Fig.

allowed

to

to extend

as an unbridged

until

it

t h e first r o w

crack

is

c r a c k is t h e n a s s u m e d

crack

9(b))

second

and

of 0 ° fibers

to be bridged

p l y u n t i l it r e a c h e s

c r a c k u n t i l it r e a c h e s

in t h e s e c o n d

ply. The

t h e 0 ° f i b e r s in t h e f o u r t h

Table 3 Correlation o f acoustic emission activities and visual o b s e r v a t i o n s in 0o/90 ° c o m p o s i t e s Damage mechanism

A c o u s t i c emission activity Hits (events)

Counts

Amplitude (dB)

Duration (~s)

Energy (J)

Rise time (~s)

Debonding

20-25

150-200

80-90

250-300

600-800

80-100

PSBs a or subgrain f o r m a t i o n

18 50

80-100

70-80

250-300

400-600

30-60

Matrix cracking Outer ply Inner ply

2 0 - 30 40-80

200 - 300 400-600

80 - 90 90 100

3 0 0 - 500 500-1000

1000 - 1500 200-2500

250-300 250-350

Fiber c r a c k i n g

20-30

1600-1800

100

5500-6500

7800-8600

Crack coalescence

40-50

1400

100

5000

7000

aPBSs, persistent slip bands.

edge

b y t h e f i b e r s in t h e

50-80 200 250

ply

W.O. Soboyejo, B.M. Rabeeh / Materials Science and Engineering A200 (1995) 89 102

99

3OO

500 •

~ 2s°I

A R Matrix H v 540110h/0.0Nf Matrix Hv 5 4 0 / 1 0 h / 0 . 4 Nf Matrix H v 5 4 0 / 1 0 h / 1 . 0 Nf Matrix H v

~

f

"~k

200

400

2 ~

3oo

=

150

815/100h/0.0 Nf matrixHardness 8151100h/0.4Nf Matrix Hardness 815-10Oh/t .0Nf Hardness 815/100h/1.6Nf[Mat fix)

" ~ 20C 100

1oc

I

(a)

I

I

I

4

6

8

lo

i

I

I

I

2

4

6

8

(C)

Ply

Number

Ply Number

280

400

S

300

/

240

220

-

2OO

540•50 Outer Ply [Hv]

I.

540150 I n n e r

Ply [Hv]

~ ,11,

% (b)

0

i

I 0

N/Nf

(J0

05

(d)

815/100hl Matrix Hv (Ouler Ply) 8151100111Matrix Hv (Inner Ply)

'

'

10

1.5

N/N[

Fig. 7. Variation of matrix micro-hardness (Hv) with number of cycles and ply number: (a) micro-hardness versus ply number for AR and 540 °C samples; (b) micro-hardness versus ply number for AR and 815 °C samples; (c) micro-hardness versus N / N r for AR and 540 °C samples; and (d) micro-hardness versus N/N¢ for AR and 815 °C samples.

(Fig. 9(c)). The configuration shown in Fig. 9(c) is then maintained until the crack reaches the boundary between the fourth and fifth plies (Fig. 9(d)). A number of simplifying assumptions were also made in the crack growth analysis. First, matrix fracture toughness values were not used to determine critical fracture conditions since such data are not available for the different heat treatment conditions. Also, only fibers in the 0 ° plies were assumed to bridge the crack, and the possible effects of crack opening displacement on fiber fracture and bridging characteristics were neglected, i.e., the bridge lengths were equated to the lengths of the cracks. It was also assumed that the fibers in the 90 ° plies did not have a significant effect on the Mode I crack path, although it is quite clear that such fibers may promote crack deflection (Fig. 5(g)) since the modulus of the SCS6 fiber is higher than that of the matrix [30,31]. Finally, the possible effects of residual stress [21,22] were neglected in the analysis, and the calculations were carried out for the as-received composite, since the matrix and fiber mechanical property data were only available for material in this condition.

The shielding due to the crack bridging was modeled using the analysis techniques reported in Refs. [32-34]. A simplified case of constant friction (bridging tractions) was used in the assessment of crack bridging. This yields the following expression for the stress intensity factor at the crack tip, Ktip: Kt~,,=K,,,,,,-X/~j

°- ," r,... k--D-- ,)

.,,. ,.,~.

(1)

where Kapp is the applied stress intensity factor, L is the length of the bridging zone which is equated to the crack length since fiber fracture was not observed until just before failure, Vr is the volume fraction of fiber, C is a constraint/hardening parameter, D is the fiber diameter, v is the interfacial friction stress after fatigue damage, and x is the distance from the crack-tip. Eq. 1 can be solved analytically to give [32] 1 L2/ZTC--~. ~_ 2 Ktip ----~ [ d b ~ --~4c - b]

(2)

where b and c are given by mathematical expressions in Ref. 32. The above analysis applies strictly to the bridging of stationary cracks under monotonic loading.

W.O. Soboyejo, B.M. Rabeeh / Materials Science and Engineering A200 (1995) 89 102

100 160

AKfip = |

~

,4o F

A

[ 1201-

y

\\

Z

\\

815/10h/0.5 U T S ~,

815/10h/0.7UTS

4,

815/100h/O.5UTS

+

540/lOh/O.ZUTS

,oot

.

/

s O,lOOh,OSO

0

/,-'m

6O

4O

20

,

I 0.2

, 0.4

0.6

0.8

1.0

I 14

1.2

,

Fraction of Number of Cycles to

I 1.6

Failure

Fig. 8. Plots of the measured elastic constants (obtained at the mean stress using compliance techniques) versus number of cycles to failure (540 and 815 °C samples).

EdOe c~ack

:

(a)

[

1 00 ¢~ber

(b)

La~d d,,ec:lon

® I

o~Oondmg

,n oo ~ber

Stage 3

(c)

t.(bdeg,ng) N ~3

Outer D;ie~

Inner! p~,~s

Outer p',e~

/

2Ktip(Ao'/2)

(3)

where Ktip(Ao/2) is the near-tip stress intensity factor for a bridged crack subjected a maximum stress of under monotonic loading. A stress ratio, R = Kmi,/ Km,x = 0, is assumed in the analysis of McMeeking and Evans [33]. Nevertheless, this analysis was used in the current study in which a stress ratio of 0.1 was employed. The fatigue life of the composite can now be predicted by separation of variables and integration of the following Paris law expression which was obtained by curve-fitting of data presented in Ref. [13]. da - 2 . 9 3 x I0 l°(AKCfr)3.38 m/cycle dN

(4)

where AK~fr is the effective stress intensity factor range in MPa m 1/2. This is approximately equal to AKtip if closure effects are small, as reported in Ref. [13]. The fatigue lives of the as-fabricated composite specimens can thus be estimated by combining Eqs. 3 and 4, and substituting appropriate material property data into the resulting expression. Constant interfacial friction stresses of 35, 50 and 200 MPa were employed in the calculations. These values correspond to data reported for as-fabricated Ti-15-3/SiC composites before (approx. 200 MPa) and after (35-50 MPa) fatigue damage [23,24]. The predicted fatigue lives are presented in Fig. 10. The predicted S - N curves obtained using an interfacial shear stress of 200 MPa are in close agreement with the S - N curves obtained from experiments on material in the as-received condition. This suggests that the degradation of interfacial shear strength may not be very significant in the un-notched specimen examined in this study. Notched specimens have been shown to have lower interfacial shear strengths after being subjected to fatigue damage [34]. However, similar interfacial friction strength losses have not been reported for smooth specimens deformed under cyclic loading. Differences between the degree of degradation of interfacial shear strength in smooth and notched specimens may be due to the higher crack opening displacements in notched

®}

® ,

) Actual.(Tau=2OOMPa) Theoreficol (Tau = 2OOMPo} Thgoreticol (Tou = 50 MPo) Theoretical (Tou = 35 MPo) - -

Fig. 9. Schematic illustration of idealized crack growth and crack bridging configurations used in the modeling of damage under cyclic loading: (a) center crack initiation from outer (90°) plies; (b) edge crack propagation from outer plies; (c) edge crack propagation into inner plies; and (d) crack coalescence at the center of inner plies.

500

400

However, it can be extended to the assessment of bridging under cyclic loading. This can be done using the analysis by McMeeking and Evans [33] which yields:

300

,

,

10000

,

20000 Number

of

30000 Cycles

40000

50000

Fig. 10. Comparison of predicted and measured S - N curves.

W.O. Soboyejo, B.M. Rabeeh / Materials Science and Engineering A200 (1995) 89-102

specimens. However, further research is needed to verify this speculation. The lower bound estimates of the interfacial friction strength employed interfacial shear strength values of 35 and 50 MPa to account for the effects of fatigue damage on the interfacial properties. The fatigue lives predicted using both 35 and 50 MPa are lower than the measured values. The proposed model therefore appears to provide the best estimates of fatigue life when the fatigue degradation of interfacial shear strength observed typically in notched specimens (these undergo larger crack opening displacements and hence greater interfacial damage) is neglected. The apparent accuracy of the proposed fracture mechanics model is somewhat surprising given the simplicity of its formulation. Nevertheless, the current results do show the potential for the development of accurate fatigue life prediction methodologies for structures and components fabricated from titanium matrix composites. Above all, however, the current paper illustrates the importance of simplified composite modeling based on actual experimental observations of composite damage.

6. Conclusions 1. Fatigue damage in [0/9012 s Ti-15-3/SCS6 composites occurs initially by debonding of the 90 ° fibers. This is followed by debonding of the 0 ° fibers prior to matrix deformation and matrix crack initiation after 0.5 N~-. Subsequent fatigue damage involves matrix crack growth and coalescence, and fiber pull-out and fracture. 2. Slip band formation may occur owing to residual stresses that are induced after heat treatment at 540 °C for 50 h, or as a result of the reversed plasticity during cyclic deformation of samples that are heat treated at 540 °C for 10 h. Sub-grain formation is also observed during cyclic deformation of the composites annealed at 815 °C. Matrix deformation may therefore occur by slip band formation, sub-grain formation or conventional slip. 3. Cyclic deformation occurs by a combination of matrix plasticity and cracking processes which control the effective composite moduli. Correlations have been established between the matrix deformation/composite cracking phenomena and acoustic emission parameters such as number of hits, number of counts, amplitude, duration of events and energy. These correlations can be used to detect the onset of debonding, slip band or sub-grain formation, matrix cracking, fiber cracking and crack coalescence prior to failure. 4. A simple fracture mechanics model has been developed for the prediction of the fatigue life of [0/9012s Ti-15-3/SCS6 composites. This model uses center and edge crack idealizations to simplify the fatigue and

101

crack bridging analysis. The best predictions of fatigue life are obtained when the fatigue degradation of interfacial shear strength is neglected in the crack bridging analysis.

Acknowledgments The authors are grateful to Mr. David Harmon of McDonnell Douglas for supplying the composite material. The research is supported by a grant from The National Science Foundation (Grant No. MSS 9309520) with Dr. Oscar Dillon and Dr. William Spitzig as Program Monitors. Appreciation is also extended to Dr. Bhaskar Majumdar and Dr. Brad Lerch for useful discussions.

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[7] [8] [9]

[10]

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[18]

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102

W.O. Soboyejo, B.M. Rabeeh / Materials Science and Engineering A200 (1995) 89-102

[19] J. Shyue, W.O. Soboyejo and H.L. Fraser, Scr. Met. Mater., submitted for publication. [20] H.W. Rosenberg, J. Metals, 35 (1983) 30-34. [21] K. Kendig, W.O. Soboyejo and D.B. Miracle, Scr. Met. Mater. (1994) in press. [22] S.M. Pickard, D.B. Miracle, B. Majumdar, K. Kendig, L. Rothenflue and D. Coker, Acta Metall. Mater. (1994) in press. [23] M.C. Watson and T.W. Klein, Acta Metall., 40 (1992) 141-148. [24] P. Kantzos, J.1. Eldridge, D. Koss and L.J. Ghosn, Proc. H1TEMP Conference, 1991, NASA Conference Publication No. 10082, NASA-Lewis Research Center, OH, 36-1 to 36-11. [25] H.-P. Chiu, J. Yang and J. Graves, J. Mater. Res., 9 (1994) 198-206. [26] W.O. Soboyejo, P. Ramasundaram and B. Rabeeh, An investigation of the effects of matrix microstructure and interfacial properties on the fatigue and fracture behavior of a metastable titanium matrix composite, in S.I. Rokhlin, S.K. Datta and Y.D.S, Rajapakse (eds.) ,Proc. Symp. on Ultrasonic' Characterization and Mechanics of Interfaces, ASME Book No. H00875,

[27]

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American Society of Mechanical Engineers, New York, 1993, pp. 33-44. W.O. Soboyejo, On the evolution of matrix microstructure and damage in titanium matrix composite, in M.N. Gungor, E.J. Lavernia and S.G. Fishman (eds.), Proc. Syrup. on Advanced Metal Matrix Composites for Elevated Temperatures, ASM International, Metals Park, OH, 1991, pp. 141-155. W.O. Soboyejo, J.F. Knott, M.J. Walsh and K.R. Cropper, Eng. Fract. Mech., 37 (1990) 323-340. W.O. Soboyejo, K. Kishimoto, R.A. Smith and J.F. Knott, Fatigue Fract. Eng. Mater. Struct., 12 (1989) 167-174. W.O. Soboyejo, K.T. Venkateswara Rao, S.M.L. Sastry and R. O. Ritchie, Metall. Trans. A, 24 (1993) 585-600. K,T. Venkateswara Rao, W.O. Soboyejo and R.O. Ritchie, Metall. Trans. A, 23 (1992) 2249-2257. J.W. Hutchinson and H.M. Jensen, Mech. Mater., 9 (1990) 139-163. R.M. McMeeking and A.G. Evans, Mech. Mater., 9 (1990) 217. K.S. Chan, Acta Metall. Mater., 41 (1993) 761-768.