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Ductile phase toughening mechanisms in a TiAlTiNb laminate composite
Acta metall, mater. Vol. 40, No. 9, pp. 2381-2389, 1992 Printed in Great Britain. All rights reserved
0956-7151/92 $5.00 + 0.00 Copyright © 1992 Pergamon Press Ltd
DUCTILE PHASE T O U G H E N I N G MECHANISMS IN A TiA1-TiNb LAMINATE COMPOSITE G. R. ODETTE, B. L. CHAO, J. W. SHECKHERD and G. E. LUCAS Materials Department, University of California, Santa Barbara, CA 93106, U.S.A.
(Received 8 November 1991) Al~traet--Toughening mechanisms in a laminate composite composed of alternating layers of brittle ),-TiA1 and ductile TiNb reinforcements were studied. The TiNb phase comprising about 20% of the composite volume, contributed to toughening by both crack renucleation and bridging mechanisms, yielding a steep resistance curve and effective toughness more than ten times higher than the matrix value. In part, the extraordinary toughening is derived from large scale bridging effects, which occur when the size of the bridging zone is not small compared to the crack and specimen dimensions. Large scale bridging model predictions based on independent evaluations of the fundamental composite properties, including the reinforcement stress~lisplacement function, were in good agreement with the experimental observations. We demonstrate how the models can be used to optimize the composite properties for specific applications. R6sum~4)n 6tudie les mrcanismes de trnacit6 dans un composite feuillet6 compos6 de couches alternres de renforts de TiAI-~ fragile et de TiNb ductile. La phase TiNb, qui occupe environ 20% du volume du composite, contribue fi la trnacit6 fi la fois par la regermination de tissues et par des mrcanismes de pontage, fournissant une courbe de rrsistance abrupte et une trnacit6 plus de dix fois plus 61evre que celle de la matrice. La trnacit6 exceptionnelle drcoule partiellement des effets de pontage fi grande 6chelle qui se produisent lorsque la taille de la zone de pontage n'est pas petite devant les dimensions de la fissure et de l'rchantillon. Des prrvisions du modrle de pontage ~. grande 6chelle basres sur des 6valuations indrpendantes des proprirtrs fondamentales des composites, y compris la fonction contraintedrplacement du renfort, sont en bon accord avec les observations exprrimentales. On montre comment les modrles peuvent &re utilisrs pour optimiser les propri&rs d'un composite pour des applications sprcifiques. Zusammenfassung--Die Mechanismen der Z/ihigkeitsverbesserung werden in einem LaminatVerbundwerkstoff, bestehend aus abwechselnden Schichten aus spr6dem ),-TiA1 und duktiler TiNbVerstbirkung, untersucht. Die TiNb-Phase, die etwa 20% des Volumens umfaBt, tr/igt zur Z/ihigkeitssteigerung sowohl durch RiB-Neubildungs- und -Oberbriickungsmechanismen bei. Dadurch ergibt sich eine steile Widerstandskurve und eine effektive Z/ihigkeit, die zehnmal gr6Ber ist als die der Matrix. Teilweise ergibt sich die auBergew6hnliche Z/ihigkeitsverbesserung aus dem EinfluB der ausgedehnten t3berbriickungen, die auftreten, wenn die Gr6Be der Oberbrfickungszone nicht klein ist im Vergleich zu RiB und Probengeometrie. Die Voraussagen des Modells der ausgedehnten l~berbr/ickung, die auf unabh~ingigen Auswertungen der grundlegenden Eigenschaften des Verbundes aufbauen, einschlieBlich der Spannungs-Dehnungs-Funktion des Verstiirkungsmaterials, stimmen mit exp6rimentellen Ergebnissen gut fiberein. Wir zeigen, wie mit den Modellen die Eigenschaften des Verbundmaterials fiir bestimmte Anwendungen optimiert werden kfnnen.
INTRODUCTION The concept of increasing the fracture toughness of brittle materials by adding ductile phases has been discussed theoretically [1-3] and experimentally demonstrated for a number of ceramic and intermetallic matrices containing metal reinforcements [4-13]. The dominant toughening mechanism is partial shielding of the stress intensity factor at the crack tip by the tractions from the bridging zone of unbroken ductile reinforcements in the crack wake. G r o w t h of the bridging zone with extension of an initially unbridged crack yields a resistance curve of increasing toughness with increasing crack length.
The fundamental composite properties mediating ductile phase toughening are the (plane strain) elastic modulus, E ' [ = E / ( 1 - v 2 ) ] , where E is Young's modulus and v is Poisson's ratio; the critical tip stress intensity required for crack extension, Kt; and the reinforcement stress-displacement function, tr(u), where u is the crack opening. The a(u) function generally does not correspond to the simple tensile behavior of an isolated reinforcement. Rather it is mediated by constraint imposed by the matrix, evolution of constraint associated with debonding, the basic constitutive properties of the reinforcement, and large geometry changes due to processes such as shear band formation. Most
2381
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ODETTE et al.: PHASE TOUGHENING IN TiA1-TiNb
often, K t has been assumed to be directly controlled by the brittle matrix toughness, Kt ~ Kin. When the size of the bridging zone is sufficiently small compared to both the crack length and specimen dimensionst, small scale bridging (SSB) theories are applicable. For SSB the effective toughness saturates at a maximum level corresponding to a steady-state bridge length as illustrated in Fig. 1. The SSB steady-state toughness can be determined from the work-of-rupture or J-integral of the reinforcement, Jr, as Jr = f~" cr(u) du
KF~ooo~KSSB Kt [ - 4 Depends On ~(u) Shape
da b
(1)
where u* is the crack opening at fracture of the ductile phase. The corresponding steady-state toughness, K,,b, is K,sb = ~/K~ + f E'Jb = ~/K~ + E'faytZ.
(2)
Here Z is the dimensionless work-of-rupture of the reinforcement, or the area under the normalized stress--displacement function, a(u/t)/ay (see Fig. 1), f is the area fraction of the reinforcement on the crack face, Cry is the uniaxial yield stress and t is a characteristic reinforcement dimension. Thus, for a given X, ductile phase toughening would be expected to increase with increasing reinforcement size, volume fraction and yield stress. For normal strain hardening reinforcements, X also increases with the increasing debond length [8], since the strains in the ductile phase are spread over a longer effective gauge length. Debonding also lowers the triaxility of the stress state which may also increase the fracture strain. Hence, for a given reinforcement, composite designs which promote debonding might be expected to be optimal. However, debonding and loss of triaxiality also lower the peak reinforcement stress, which can have a detrimental effect on toughening in many cases. Indeed, the simple work-of-rupture model of ductile phase toughening is inadequate for a number of reasons including: • Extrinsic effects of size and geometry on bridge zone toughening when the size of the bridging zone is not sufficiently "small" with respect to the crack and specimen dimensions, or large scale bridging (LSB) conditions. • Increases in the critical crack tip stress intensity, Kt, by the reinforcements due to the tTypical size requirements are that the dimensions exceed both: about 40 times the computed bridge length for a Dugdale type (constant) stress-displacement function with the same work-of-rupture as the actual reinforcement; and about 8000 times the critical reinforcement displacement, u*. ~:The composite was produced by Ed Aigeltinger of the Pratt and Whitney Corporation.
u
u/t
u*/t
Fig. 1. Ductile phase toughening under small scale bridging (SSB) conditions illustrating: (a) resistance curve behavior and steady-state toughness; (b) a steady-state bridge zone; and (c) a normalized stress
The laminate composites were fabricated by hot pressing and forging a nominally uniformly spaced array of TiNb foils which were infiltrated with - 8 0 mesh RSR y-TiAl powder (Ti-31 wt% A1 plus small concentrations of Nb, Ta, C and O) at about 1050°C for about 3 hJ;. This yielded approximately 150+ 15/~m layers of TiNb separated by about 530 + 80/~m of consolidated ~-matrix plus an ~2 reaction layer 1 0 _ 3 #m thick. Thus, the average
O D E T T E et al.:
PHASE T O U G H E N I N G IN TiA1-TiNb
a
-L
-R
ot
J / Ductile Reinforcement. Precrack
~
~
/ Fig. 2. Specimens used in this study, including: (a) laminate bend specimens in two orientations; and (b) a sandwich tensile test specimen. TiNb volume fraction was approximately 22%. Chevron-notched three point bend specimens with widths of 1.5cm were cut in both the C - R t or edge and C-L or face orientations as illustrated in Fig. 2. Due to limitations in the available material, only 1 edge and 2 face specimens were fabricated. Note that the TiNb layers were not precisely parallel and evenly spaced; and in the edge specimen one intersected the specimen surface at a/w less than about 0.6. The specimens were precracked and the chevron removed by grinding to within about 50 #m of the crack front. Resistance curve, Kr(da), tests were carried out under displacement control in a servohydraulic test frame. The cracks were regrown in small increments. Toughness was characterized using standard stress intensity formulas [14] based on the reinitiation loads and the nominal crack lengths which were monitored by a high resolution optical video system. The a(u) function was independently measured under appropriate conditions of constrained deformation using sandwich specimens shown in Fig. 2 as described in more detail elsewhere [8]. The sandwich specimens were produced by hot pressing the TiNb foils between thick ( ~ 1500/~m) lapped ?-TiA1 plates "fin the C-L orientation the crack intersected the face of the reinforcement foils, while in the C-R orientations the intersections were with the foil edge. Hereafter, we will use face and edge to designate the specimen orientation.
2383
at 1066°C at 10 MPa for 4 h and precracked prior to tensile testing. An elastic modulus of 172 GPa was obtained for a similar TiA1 matrix composite containing 20% Nb particles using a resonance technique. Poisson's ratio was taken as 0.33 yielding a nominal estimate for E ' of 193 GPa. Load and bend bar deflection displacements at the notch face were also recorded during the tests. Careful calibration measurements of the loading system displacements (both reversible and irreversible for both loading and unloading cycles) were made to permit correction of the measured displacements to actual specimen deflections. These corrections could be made to within about + 5 #m; the residual scatter was due to random specimen-tospecimen load train set-up variations. Since, on average, the initial displacements were consistent with predictions of standard compliance equations and nominal modulus, the deflections for the individual tests were adjusted slightly to conform to the elastic calculations, thereby removing most of the random scatter. Corollary studies included characterization of: the crack paths; crack-reinforcement interaction processes; and reinforcement deformation and fracture mechanisms. The as-fabricated and post-deformation microstructures and microchemistries of the matrix, reaction layer and ductile phases have also been characterized in a similar system containing TiNb pancake shaped particles [6]. MODELING Rigorous modeling of bridging mechanics was carried out by calculating self-consistent solutions for the crack opening profile, and the crack face stress distribution for a specified set of tr(u), E ' and Kt composite properties using a model developed by Odette and Chao [15]. The calculational procedure is outlined in Appendix A. For load controlled failure conditions, the critical fracture load and crack extension P*(da*) can be determined directly from the extrinsic resistance curve calculations. However, under more general conditions failure is mediated by the compliance of the load point. In this case, the applied load (P)-load line displacement (6) crack growth (da) function P(6)-da is needed to specify failure conditions--P*, 6" and da*. A model to compute the extrinsic P(b)-da functions for specific geometries and fundamental composite properties has also been developed by Odette and Chao [16] and is outlined in Appendix A. RESULTS
Crack-reinforcement interactions and TiNb deformation and fracture The basic microstructural characteristics of the TiA1-TiNb system have been reported [6]. High
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ODETTE et al.: PHASE TOUGHENING IN TiAI-TiNb
temperature processing produced an approximately 10#m thick ct2 reaction layer between the y-TiAl matrix. The ~2 phase deformed by planar slip of super-dislocation pairs; limited deformation was observed in the y by both slip and twinning. The TiNb reinforcements did not readily debond from the matrix in either the laminate composites or sandwiches. However, limited debond cracking in the matrix or at the 7--~2 interface was sometimes observed and was extensive in one instancet. Even in this case, however, the primary mode I crack continued to propagate. The TiNb reinforcements deformed by forming extensive planar arrays of dislocations and did not strain harden [8]. Macroscopically, slip occurred in coarse bands shown in Fig. 3(a). The macroscopic fracture paths were mediated by localized necking or by the dominant member of a set of intense intersecting shear bands as illustrated in Fig. 3(b, c). This behavior suggests that at small u, a(u) is likely to be increased significantly by constraint effects. The overall cracking patterns also appeared to be strongly influenced by the coarse localized slip in the TiNb and ~2 phases: cracks often branched as a result of multiple renucleation at points of strain concentration on the back sides of the TiNb foils as illustrated in Fig. 3(d, e). Crack renucleation took place at small crack openings and it is not clear if the strain concentrations caused renucleation or vice versa. Crack renucleation may be locally assisted by dislocation pile-ups in the ~2, as well as by intersections of y twin ledges at the matrix-reaction layer boundary [6]. However, renucleation behind TiNb reinforcements required stress/strain concentrations such that Kt was considerably greater than Kin. Sandwich tests Typical results of the sandwich tests reported previously [8] are shown in Fig: 4. Peak stresses, ap, were about 9 0 0 _ 90 MPa and maximum displacements, u*, about 110 _+ 20 #m. Standard tensile tests of the TiNb foil shown as the dashed~zlotted line gave yield stress values of about 430 + 30 MPa; the tensile foils did not strain harden and failed by local necking at displacements similar to those observed in the sandwich specimens (independent of the specimen gauge length). ~This debond is considered an anomaly since it occurred between two TiNb foils which were unusually closely spaced ( < 100-200 #m). The longer of the debond cracks initially ran on the back of the first foil, but subsequently jumped to the front of the second foil. The shorter debond crack did the opposite and actually jumped back and forth between the foils. A secondary mode I crack was observed on one side, propagating through the matrix segment beyond the second foil. The local debond
crack path was near the ct2-~/interface, displaying an interesting quasi-periodic pattern of deflections into the ct2 with arrests at the TiNb. The main debond cracks were bridged on the surface by short sections of intact ~t2-), regions.
V
Direction of Crack Propagation
Fig. 3. The deformation, fracture and crack propagation behavior of TiNb: (a) intense shear bands emanating from a blunted crack tip; (b) initiation of crack extension in an intense shear band; (c) final fracture in one of the two pairs of shear bands; (d) and (e) crack renucleation, branching and opening at regions of intense shear band strain on the back of the foil. The characteristic sawtooth a(u) function can be understood in terms of significant constraint (~2.1 ___0.2) effects which occur at small values of u with the stress falling off rapidly at large displacements due to the decrease in the load bearing cross section coupled with a loss of constraint. For purposes of modeling the a(u) function can be represented simply by a sawtooth function shown as the dashed line in Fig. 4 and characterized by the peak stress ap, the displacements at the peak stress, up, and the fracture displacement u*.
10001 800 ~ =
v
I
I
I i Sandwich Test
\
400 . ~ ' ' ' . - . . . . . ~ L S B | 200 t 0 Up
r
t
Model Form
_
~ . " * , .~¢ ~. Foil ~'~', Test
-
75 U(txm)
U
150
Fig. 4. Results of tensile test of TiA1-TiNb sandwich specimens (solid line) and TiNb foils (dashed-dotted line). The dashed line is a parameterized stress~lisplacement function used in the model calculations.
ODETTE et al.: PHASE TOUGHENING IN TiAI-TiNb
125
i
i
about 3 m. Hence, analysis of the data requires the application of LSB models.
i
LE1""~,~
100
/
o
LSB ANALYSIS OF TOUGHENING
t
I,.~ 75
Resistance curves
13.
~
50
Kssb@>42mm ~,,,,-
2s
~.~:~. . . . .
0.000
¢
.s" .s
ssB . . . . . . . . . K
,
0.002 0.004 0.006 0.008 da (m)
Fig. 5. Resistance curve data for edge (LE1) and face (LF2) specimens. The behavior predicted for the SSB regime is shown as the dashed~totted line and the matrix toughness as the dashed line. Resistance
and
2385
load-displacement-crack
growth
curves
The toughness data for both face and edge orientations are shown in Fig. 5f. Significant resistance curves were observed in all cases; after about 6-8 mm of crack extension the toughness was a factor of ten or more than the matrix values. The data show no indication of leveling off, as is characteristic of small steady-state scale bridging (SSB) conditions. Three significant differences in crack growth behavior in the two orientations were observed. First, due to the necessity for complete crack renucleation, the initiation toughness in the face orientation was significantly higher than the matrix toughness. In contrast the initiation toughness in the edge orientation was found to be comparable to the matrix toughness of about 8 MPa~/m; this is expected since the edge cracks do not need to renucleate. Second, the crack in the edge orientation grew continuously in a stable fashion while the cracks in the face orientation grew unstably between the TiNb layers. Third, while the toughness in the edge orientation started out below that in the face orientation, its resistance curve was steeper and a crossover occurred at large a/w. Figure 5 shows the initial portion of the resistance curve predicted for SSB conditions assuming a nominal sawtooth stress displacement curve illustrated in Fig. 4 with Uo= 4 #m, u * = 110 # m O'max = 200 MPa (for f = 0.22) and Km = 8 MPa~/m. The predicted SSB steady-state toughness is reached after about 4.2 cm of crack growth (the full SSB bridge length) at a level of 46.7 MPa~/m. Hence, the 1.5 cm width of the experimental bend specimen is clearly far below that required for SSB. Indeed, based on detailed evaluation of size effects [15], the specimen width required for SSB in this composite is estimated to be ?The behavior of the LF I specimen (not shown for clarity) was similar to LF2.
The LSB model calculations reflected differences between the two orientations. First, the Kt was taken as 20 and 8 MPa~/m for the face and edge orientations respectively. The estimate for the face orientation was based on correcting the apparent initiation toughness for the shielding effect of the first reinforcement. Second, unlike composites toughened with a nominally uniform distribution of ductile particles, the reinforcement and corresponding tractions in the face orientation were highly localized. The effect of this was modeled using different stress-displacement functions for the two orientations. For the face orientation the a(u) parameters measured in the sandwich test were used (ap = 9 0 0 _ 90 MPa and the nominal average of u* = 110), but the stresses along the crack face ~r(x) (where x is the distance from the crack tip) were only permitted to act in regions nominally occupied by the TiNb foils; the calculations also assumed the TiNb foils were parallel and uniformly spaced. Bridging in the edge orientation is continuous, hence, the reinforcement stresses were averaged over the crack face based on the nominal volume fraction ( f ~ 0.22) of the TiNb phase. The face and edge or(x) functions are schematically illustrated in Fig. 6. Note that the most significant irregularities in the foil locations were in the edge orientation (see Experimental); this reduced the effective volume fraction and strength of the reinforcement at a/w less than about 0.65 by an unknown amount. Therefore, in this case large relative uncertainties were assigned with ¢rp = 200 MPa 4- 40 MPa. The predictions of the model are shown in Fig. 7. The shaded region reflects the uncertainties in ap (note, variations in u* would also widen the band). The predicted resistance curves in the face orientation were serrated with decreases in Kr occurring between the reinforcements, consistent with observations of unstable crack growth. The deviations between the nominal prediction and data are larger for the edge orientation, but the trends are qualitatively
~.-..-¢ Localize d
X Fig. 6. Localized vs continuous traction models used for the face and edge specimen orientations respectively.
ODETTE et al.: PHASE TOUGHENING IN TiA1-TiNb
2386
120 100
.
I
,
I
line. Finally, it may be notable that the measured toughness of the LF2 specimens starts to fall above the nominal prediction at the point where the extensive debond forms; however, some of these deviations may be due to irregularities in the TiNb layer locations and the overall effect of debonding on the toughness appears to be modest.
'
LEI
80 ~ 60 ~
40 20
Load-displacement-crack growth curves
.=.,.,.,.I,,°,.==.=..°°,..,,,,.,.°,..,,
I
120
i
I
i
l
I
i
i
As noted previously P(6)-da curves can also be modeled using the fundamental composite properties. Figure 9 compares predicted P(6)-da curves (line and solid points) to measured values (open circles). The curves have been normalized to the elastic fracture loads and displacements of an unreinforced specimen with the same initial a/w (e.g. P and 6 at
I
LF1
100
80 g_ 60 4o
20 .....
°°..,°,=m.,,°,=,.°
i
I
120
i
.............
-°,
I
i
i
I
Km
4 LE1
LF2
100
~
i
3
0
0
80
~. 60 ~Z
Q.
40
v
1
2O ,.°..,.=
8 ,00
.....
I
,..=°.°..,,..,,.,..,,
I
I
I
,,°°,
'
Km
I
0.002 0.004 0.006 0.008 da (m)
10
(~/~m
Fig. 7. Predicted vs measured resistance curves. consistent with the irregularities in the reinforcement locations. Figure 8 shows that the model also correctly predicts the higher toughness in the edge orientation at large a/w. This is primarily due to differences in Kt and to a lesser extent the initial crack depth in the two specimens. Figure 8 also shows that the toughness resulting from the localized bridges was, on average, slightly higher than the corresponding value predicted for continuous bridging shown as the dashed
4
|
LFI 3 n Q.
2
v
O0
i
I
~ / " ' ' ' "
3 50
I
I0 61~m
%LF2
4
~. 100
20
20
i
iii'
Continuous -"-,~,,f~.~,"~ , ---~,*_,~L,I:::dge
Ma,r
--'- .............--" h%o " . . . . . . . . .
0 0.000
I
I
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.002
I
I
I
0.004 da (m)
I
0.006
I
I
0
0.008
Fig. 8. Comparisons of the predicted resistance curves for the edge and face orientations predicting a crossover at a/w ~ 0.5. The effect of continuous vs localized reinforcement tractions is illustrated for the face orientation.
0 =
0
i
I
10
i
20
~lSm Fig. 9. Predicted vs measured normalized P(6)-da curves.
ODETTE et al.: PHASE TOUGHENING IN TiAI-TiNb
are significantly larger for the edge specimen; however, the deviation trends are again consistent with the irregular TiNb foil locations which was not explicitly modeled.
Kapp = Km = 8 MPax/m and no bridge). Following initiation, indicated by the asterisk, the predicted and measured points are paired in equal increments of crack extension up to a/w = 0.85. In the face orientation the reinforcements increased the composites' strength by a factor of about 3.5 _+0.25 and its deflection capacity by a factor of about 16 -I- 3. The data generally fall somewhat above the nominal predictions. The reason for this discrepancy is not known; however, it may be significant in the case of the LF2 specimen the deviations initiate at the point that an extensive debond crack is formed. In the face orientation, crack growth primarily occurs beyond the maximum loads. A similar increase in the deflection capacity is observed in the edge orientation, but the composite is strengthened by a somewhat smaller factor of about 2.5. A significant amount of crack growth takes place prior to maximum load in the edge orientation. These effects of orientation are primarily due to the differences in the critical crack tip stress intensity factor, Kt, which is increased in the face orientation by the renucleation mechanism. The discrepancies between the predictions and experiment 400
•
,
2387
DISCUSSION The results of this study clearly demonstrate that LSB models can be used to predict the extrinsic toughness behavior of ductile phase reinforced composites, based on independent measurements of the stress-displacement function, tr(u) and the other fundamental composite properties (Kt and E'). Thus the models can be used to quantitatively evaluate the effects of various composite design parameters for specific applications. For example, as noted previously, small scale bridging models suggest that debonding enhances ductile phase toughening by increasing the work of rupture. However, for large LSB conditions increases in X do not necessarily translate into increases in the effective toughness. This is clearly shown in Fig. 10 where Kr(da) and P(&)-da curves are plotted for three or(u) functions and for both LSB (W = 0.015 m) and •
,
•
,
•
300 L
~" 100 . . . ~ . ~ b ......
....
°o ",oo
oo"
,oo
u (pm)
200
LSB: W = 0.015m, ao/w = 0.5 , , ,
SSB: W = 9m, ao/w = 0.5 200
|
i
i
I~EIO 0
~oo
..... ,°.,.°°- .........
,°.o 2
4
'
6
da (ram)
7.5
7.5
10
'
i
I
100 da (mm)
i
I
150
i
200
i
5.0
5.0 E
E (3_
2.5
2.5
I
s
6/6m Fig. I0. LSB model predictions of Kr(da) and P(6)-da curves for various or(u) functions. 616 m
2388
ODETTE et al.: PHASE TOUGHENING IN TiA1-TiNb
SSB ( W = 9 m) conditions; the initial crack depth was taken as ao/W = 0.5 in both cases. The solid line represents the nominal tr(u) for TiNb found in this study; the dotted lines are for ap decreased by a factor of 2 and u* increased by a factor of 3 (i.e. a Z which is 50% higher than the base case), representing the typical effect of debonding; and the dashed line is for trp increased by 50% and u* decreased by a factor of 2 (i.e. a Z of 75% of the base case), representing a stronger (or higher constraint) but less ductile reinforcement. For SSB the effective toughness as measured by both Kr(da) and P (5)-da increase with increasing X as expected. However, for the LSB the opposite is observed: the relative load capacity increases with higher values of trp, in spite of the corresponding decreases in Z. The different a(u) and sizes have modest effects on the relative deflection capacity of the composite. The increases in the relative load capacity due to the ductile phase are larger for SSB, in spite of the fact that values of Kr(da) are less. The amount of crack growth required to reach K,,b is very large (note the difference in the crack growth scales for the LSB and SSB plots). This behavior can be qualitatively understood based on standard crack stability concepts which have been discussed [17] and are schematically illustrated in Fig. 1 l(a, b) for load controlled fracture. For SSB large crack lengths result in the instability point occurring at crack extensions near the maximum toughness, Kssb. However, for LSB the smaller widths and crack lengths result in crack growth instability near the crack initiation point. In this case the initiation toughness and initial slope of the resistance curve mediates fracture. Figure 11 (c) shows that the initial slope is largely controlled by trp, and is also larger for SSB vs LSB conditions. Note that shorter cracks would also be controlled by the initial part of the resistance curve even in the case of SSB. While it is inappropriate to generalize these results, they clearly demonstrate that debonding may not always be beneficial for typical applications in which LSB prevails. In particular, the LSB models provide a quantitative basis for optimizing microstructural designs. CONCLUDING REMARKS
In summarizing the results for a TiNb reinforced ~-TiAi matrix laminate, there are several general conclusions relevant to toughening of brittle matrix composites with ductile phases that can be drawn: • Toughening may be induced by multiple mechanisms, including shielding due to bridging and increases in the critical crack tip stress intensity due to crack renucleation mechanisms. • Crack deflection, branching and microcracking-which can contribute to toughening in some syst e m s - h a d a relatively minor role in this case.
Kr2
SSB
p* ~s
~s
s S
at)
0
da
da*
K LSB
/
/ =, da
It a0 ~a* 0 200
,
,
,
W=0.~
z
..-t"....:'?Oq
S.S.B
I
I
I
I
2
4
6
8
10
da (mm)
Fig. 11. A schematic illustration of SSB (a) vs LSB (b) on stable crack growth under load controlled conditions; and (c) a comparison of the initial slopes of the resistance curves for SSB and LSB conditions and the a(u) functions shown in Fig. 10. • Simple steady-state SSB work-of-rupture models have limited applications for either analyzing or applying test data for the TiAI-TiNb laminate composite. • LSB conditions will often be encountered in practice. However, LSB toughening can be modeled based on proper characterization of the fundamental composite properties, namely tr(u), Kt and E'. • Extensive ductile phase toughening was observed without debonding of the TiNb reinforcements. • Microstructural designs which optimize steady state toughness performance in the SSB regime, K~sb, may be suboptimal for LSB conditions, where crack instability occurs in the region of increasing toughness. Specifically, debonding of reinforcements may be detrimental to engineering performance measured in terms of the composite P(5)-da capacity. • Techniques are available to model P(5)-da using fundamental composite properties and can be applied to alloy design assessments.
Acknowledgements--This work was supported by the Defense Advanced Projects Agency under Contract No. URI-N00014-86-K0753. Helpful discussions with A. G.
ODETTE et al.: PHASE TOUGHENING IN TiAI-TiNb Evans and R. M. McMeeking are gratefully acknowledged. Thanks are also due to Ed Aigeltinger and Pratt and Whitney for providing the material. • REFERENCES
1. L. R. Rose, J. Mech. Phys. Solids 34-6, 609 (1986). 2. A. G. Evans and R. M. McMeeking, Acta metall. 34, 2435 (1986). 3. B. Budiansky, J. C. Amazigo and A. G. Evans, J. Mech. Phys. Solids 36, 167 (1988). 4. M. F. Ashby, F. J. Blunt and M. Bannister, Acta metall. 37, 1847 (1989). 5. C. K. Elliott, G. R. Odette, G. E. Lucas and J. W. Sheckherd, High-Temperature~High-Performance Composites (edited by F. D. Lemkey, A. G. Evans, S. G. Fishman and J. R. Strife), MRS Syrup. Proc., Vol. 120, p. 95 (1988). 6. G. R. Odette, H. E. Deve, C. K. Elliott, A. Hasegawa and G. E. Lucas, Interfaces in Ceramic Metal Composites (edited by R. J. Arsenault, R. Y. Lin, G. P. Martins and S. G. Fishman), p. 443. TMS-AIME, Warrendale, Pa (1990). 7. H. C. Cao, B. J. Dalgleish, H. E. Deve, C. Elliott, A. G. Evans, R. Mehrabian and G. R. Odette, Acta metall. 37, 2969 (1989). 8. H. E. Deve, A. G. Evans, G. R. Odette, R. Mehrabian, M. L. Emiliani and R. J. Hecht, Acta metall, mater. 38, 1491 (1990). 9. L. S. Sigl, A. G. Evans, P. Mataga, R. M. McMeeking and B. J. Dalgleish, Acta metall. 36, 946 (1988). 10. B. D. Flinn, M. Rhule and A. G. Evans, Acta metall. 37, 3001 (1989). 11. V. D. Krstic, Phil Mag. A 48, 695 (1983). 12. T. C. Lu, A. G. Evans, R. J. Hecht and R. Mehrabian, Acta metall, mater. 39, 1853 (1991). 13. K.T. Rao, G. R. Odette and R. O. Ritchie, Aeta metall. mater. 40, 353 (1992). 14. H. Tada, P. C. Paris and G. R. Irwin, The Stress Analysis of Cracks Handbook. Del Research Corp., St Louis, Miss. (1985). 15. G. R. Odette and B. L. Chao, to be published. 16. G. R. Odette and B. L. Chao, to be published. 17. M. Bannister, H. Shercliff, F. Zok, G. Rao and M. F. Ashby, Acta metall, mater. 40, 1531 (1992).
APPENDIX A Rigorous modeling of bridging mechanics was carried out by calculating self-consistent solutions for the crack opening profile u(x), the crack face stress distribution a(x), where x is the distance from the crack tip, for a specified set of a(u), E' and Kt composite properties using a procedure developed by Odette and Chao [15]. The calculational procedure for the resistance Kr(da) curve is as follows: • A trial cr'(x) function is used to calculate: (a) a trial reduction in crack tip stress intensity (shielding) AK~, from the bridging zone; and (b) by applying Castigliano's theorem, the corresponding trial crack face closure displacements u'b(x). The requisite point load stress intensity functions (in this case for the single edge cracked specimen) are taken from Tada [14]. The resulting integrals are
•
•
•
2389
numerically evaluated except for very near the crack tip where an analytical asymptotic solution is used. The total trial applied stress intensity is taken as K'p(da) = Kt + AK~,. A numerical integration, again based on Castigliano's theorem, is used to compute the trial crack opening Up(X) due to the trial three point bending load (P') corresponding to K'p(da). A net trial crack opening is computed as u'(x) = u'p(x) - U'b(X) and used to compute a trial ~r'(u) from the trial ~'(x) and u'(x). The difference between the specified and trial stress~lisplacement functions is evaluated, e,(u)= a ( u ) - tr'(u). A solution is achieved when e(u) is less than a specified convergence criteria. If convergence is not achieved the trial ~'(x) is recomputed based on the trial u'(x) and the specified a(u) and the process repeated until convergence is achieved, usually in a few iterations.
The uncertainties in the calculations are contolled by: (a) the numerical procedure, which introduces < 1% error; (b) the accuracy of stess intensity factor formulas; and (c) the validity of the assumptions in the model--mode I cracks, all plasticity is treated in terms of the crack face tractions and the specimen itself is taken to be linear elastic, and the crack propagates at precisely Ktip = K,. The cr(x) and P(Kr ,a) from the converged Kr(da) solution can also be used to calculate the load-load point displacements P(8) curves at each computed point in the crack extension based on application of Castigliano's theorem to displacements at the load point using the procedure developed by Odette and Chao [16]: • The elastic displacements of the load point at the external load P for cracked (6c) and uncracked (6no) specimens without a bridge are computed using standard analytical formulas given in the Tada [14]. • The corresponding elastic deflection at the loading point due to the bridge a(x) distribution (fib) is computed by numerical integration again using of Castigliano's theorem. • The net displacement is taken as 6n = ~c + 6n~ + 6b" The major additional assumption in the load displacement model is that the bridge tractions prevent unstable elastic fracture. This is clearly consistent with the results of our experiments. Indeed, we have found that for the "stiff" MTS system and small specimens used in this work we are able to stably grow cracks even in unreinforced brittle TiA1 which, of course, does not have a resistance curve. It is also noted that in the case of localized tractions (for the face oriented laminate) the deflections decrease for crack extension between the reinforcements, corresponding to predictions of decreased loads during unstable growth. For purposes of clarity, the P(6)-da shown in Fig. 9 represent the maximum load~lisplacement envelope. Finally we note that the differences between the P(6)-da calculations and experiment can be expected to be larger than the corresponding differences in predicted vs observed K~(da) curves. For the load~:tisplacement calculations none of the dependent variables (P, 6 or da) are directly fixed at the point of observation; however, in the case of the resistance curves, the Kr values are compared at the same amount of crack extension, da.
0956-7151/92 $5.00 + 0.00 Copyright © 1992 Pergamon Press Ltd
DUCTILE PHASE T O U G H E N I N G MECHANISMS IN A TiA1-TiNb LAMINATE COMPOSITE G. R. ODETTE, B. L. CHAO, J. W. SHECKHERD and G. E. LUCAS Materials Department, University of California, Santa Barbara, CA 93106, U.S.A.
(Received 8 November 1991) Al~traet--Toughening mechanisms in a laminate composite composed of alternating layers of brittle ),-TiA1 and ductile TiNb reinforcements were studied. The TiNb phase comprising about 20% of the composite volume, contributed to toughening by both crack renucleation and bridging mechanisms, yielding a steep resistance curve and effective toughness more than ten times higher than the matrix value. In part, the extraordinary toughening is derived from large scale bridging effects, which occur when the size of the bridging zone is not small compared to the crack and specimen dimensions. Large scale bridging model predictions based on independent evaluations of the fundamental composite properties, including the reinforcement stress~lisplacement function, were in good agreement with the experimental observations. We demonstrate how the models can be used to optimize the composite properties for specific applications. R6sum~4)n 6tudie les mrcanismes de trnacit6 dans un composite feuillet6 compos6 de couches alternres de renforts de TiAI-~ fragile et de TiNb ductile. La phase TiNb, qui occupe environ 20% du volume du composite, contribue fi la trnacit6 fi la fois par la regermination de tissues et par des mrcanismes de pontage, fournissant une courbe de rrsistance abrupte et une trnacit6 plus de dix fois plus 61evre que celle de la matrice. La trnacit6 exceptionnelle drcoule partiellement des effets de pontage fi grande 6chelle qui se produisent lorsque la taille de la zone de pontage n'est pas petite devant les dimensions de la fissure et de l'rchantillon. Des prrvisions du modrle de pontage ~. grande 6chelle basres sur des 6valuations indrpendantes des proprirtrs fondamentales des composites, y compris la fonction contraintedrplacement du renfort, sont en bon accord avec les observations exprrimentales. On montre comment les modrles peuvent &re utilisrs pour optimiser les propri&rs d'un composite pour des applications sprcifiques. Zusammenfassung--Die Mechanismen der Z/ihigkeitsverbesserung werden in einem LaminatVerbundwerkstoff, bestehend aus abwechselnden Schichten aus spr6dem ),-TiA1 und duktiler TiNbVerstbirkung, untersucht. Die TiNb-Phase, die etwa 20% des Volumens umfaBt, tr/igt zur Z/ihigkeitssteigerung sowohl durch RiB-Neubildungs- und -Oberbriickungsmechanismen bei. Dadurch ergibt sich eine steile Widerstandskurve und eine effektive Z/ihigkeit, die zehnmal gr6Ber ist als die der Matrix. Teilweise ergibt sich die auBergew6hnliche Z/ihigkeitsverbesserung aus dem EinfluB der ausgedehnten t3berbriickungen, die auftreten, wenn die Gr6Be der Oberbrfickungszone nicht klein ist im Vergleich zu RiB und Probengeometrie. Die Voraussagen des Modells der ausgedehnten l~berbr/ickung, die auf unabh~ingigen Auswertungen der grundlegenden Eigenschaften des Verbundes aufbauen, einschlieBlich der Spannungs-Dehnungs-Funktion des Verstiirkungsmaterials, stimmen mit exp6rimentellen Ergebnissen gut fiberein. Wir zeigen, wie mit den Modellen die Eigenschaften des Verbundmaterials fiir bestimmte Anwendungen optimiert werden kfnnen.
INTRODUCTION The concept of increasing the fracture toughness of brittle materials by adding ductile phases has been discussed theoretically [1-3] and experimentally demonstrated for a number of ceramic and intermetallic matrices containing metal reinforcements [4-13]. The dominant toughening mechanism is partial shielding of the stress intensity factor at the crack tip by the tractions from the bridging zone of unbroken ductile reinforcements in the crack wake. G r o w t h of the bridging zone with extension of an initially unbridged crack yields a resistance curve of increasing toughness with increasing crack length.
The fundamental composite properties mediating ductile phase toughening are the (plane strain) elastic modulus, E ' [ = E / ( 1 - v 2 ) ] , where E is Young's modulus and v is Poisson's ratio; the critical tip stress intensity required for crack extension, Kt; and the reinforcement stress-displacement function, tr(u), where u is the crack opening. The a(u) function generally does not correspond to the simple tensile behavior of an isolated reinforcement. Rather it is mediated by constraint imposed by the matrix, evolution of constraint associated with debonding, the basic constitutive properties of the reinforcement, and large geometry changes due to processes such as shear band formation. Most
2381
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ODETTE et al.: PHASE TOUGHENING IN TiA1-TiNb
often, K t has been assumed to be directly controlled by the brittle matrix toughness, Kt ~ Kin. When the size of the bridging zone is sufficiently small compared to both the crack length and specimen dimensionst, small scale bridging (SSB) theories are applicable. For SSB the effective toughness saturates at a maximum level corresponding to a steady-state bridge length as illustrated in Fig. 1. The SSB steady-state toughness can be determined from the work-of-rupture or J-integral of the reinforcement, Jr, as Jr = f~" cr(u) du
KF~ooo~KSSB Kt [ - 4 Depends On ~(u) Shape
da b
(1)
where u* is the crack opening at fracture of the ductile phase. The corresponding steady-state toughness, K,,b, is K,sb = ~/K~ + f E'Jb = ~/K~ + E'faytZ.
(2)
Here Z is the dimensionless work-of-rupture of the reinforcement, or the area under the normalized stress--displacement function, a(u/t)/ay (see Fig. 1), f is the area fraction of the reinforcement on the crack face, Cry is the uniaxial yield stress and t is a characteristic reinforcement dimension. Thus, for a given X, ductile phase toughening would be expected to increase with increasing reinforcement size, volume fraction and yield stress. For normal strain hardening reinforcements, X also increases with the increasing debond length [8], since the strains in the ductile phase are spread over a longer effective gauge length. Debonding also lowers the triaxility of the stress state which may also increase the fracture strain. Hence, for a given reinforcement, composite designs which promote debonding might be expected to be optimal. However, debonding and loss of triaxiality also lower the peak reinforcement stress, which can have a detrimental effect on toughening in many cases. Indeed, the simple work-of-rupture model of ductile phase toughening is inadequate for a number of reasons including: • Extrinsic effects of size and geometry on bridge zone toughening when the size of the bridging zone is not sufficiently "small" with respect to the crack and specimen dimensions, or large scale bridging (LSB) conditions. • Increases in the critical crack tip stress intensity, Kt, by the reinforcements due to the tTypical size requirements are that the dimensions exceed both: about 40 times the computed bridge length for a Dugdale type (constant) stress-displacement function with the same work-of-rupture as the actual reinforcement; and about 8000 times the critical reinforcement displacement, u*. ~:The composite was produced by Ed Aigeltinger of the Pratt and Whitney Corporation.
u
u/t
u*/t
Fig. 1. Ductile phase toughening under small scale bridging (SSB) conditions illustrating: (a) resistance curve behavior and steady-state toughness; (b) a steady-state bridge zone; and (c) a normalized stress
The laminate composites were fabricated by hot pressing and forging a nominally uniformly spaced array of TiNb foils which were infiltrated with - 8 0 mesh RSR y-TiAl powder (Ti-31 wt% A1 plus small concentrations of Nb, Ta, C and O) at about 1050°C for about 3 hJ;. This yielded approximately 150+ 15/~m layers of TiNb separated by about 530 + 80/~m of consolidated ~-matrix plus an ~2 reaction layer 1 0 _ 3 #m thick. Thus, the average
O D E T T E et al.:
PHASE T O U G H E N I N G IN TiA1-TiNb
a
-L
-R
ot
J / Ductile Reinforcement. Precrack
~
~
/ Fig. 2. Specimens used in this study, including: (a) laminate bend specimens in two orientations; and (b) a sandwich tensile test specimen. TiNb volume fraction was approximately 22%. Chevron-notched three point bend specimens with widths of 1.5cm were cut in both the C - R t or edge and C-L or face orientations as illustrated in Fig. 2. Due to limitations in the available material, only 1 edge and 2 face specimens were fabricated. Note that the TiNb layers were not precisely parallel and evenly spaced; and in the edge specimen one intersected the specimen surface at a/w less than about 0.6. The specimens were precracked and the chevron removed by grinding to within about 50 #m of the crack front. Resistance curve, Kr(da), tests were carried out under displacement control in a servohydraulic test frame. The cracks were regrown in small increments. Toughness was characterized using standard stress intensity formulas [14] based on the reinitiation loads and the nominal crack lengths which were monitored by a high resolution optical video system. The a(u) function was independently measured under appropriate conditions of constrained deformation using sandwich specimens shown in Fig. 2 as described in more detail elsewhere [8]. The sandwich specimens were produced by hot pressing the TiNb foils between thick ( ~ 1500/~m) lapped ?-TiA1 plates "fin the C-L orientation the crack intersected the face of the reinforcement foils, while in the C-R orientations the intersections were with the foil edge. Hereafter, we will use face and edge to designate the specimen orientation.
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at 1066°C at 10 MPa for 4 h and precracked prior to tensile testing. An elastic modulus of 172 GPa was obtained for a similar TiA1 matrix composite containing 20% Nb particles using a resonance technique. Poisson's ratio was taken as 0.33 yielding a nominal estimate for E ' of 193 GPa. Load and bend bar deflection displacements at the notch face were also recorded during the tests. Careful calibration measurements of the loading system displacements (both reversible and irreversible for both loading and unloading cycles) were made to permit correction of the measured displacements to actual specimen deflections. These corrections could be made to within about + 5 #m; the residual scatter was due to random specimen-tospecimen load train set-up variations. Since, on average, the initial displacements were consistent with predictions of standard compliance equations and nominal modulus, the deflections for the individual tests were adjusted slightly to conform to the elastic calculations, thereby removing most of the random scatter. Corollary studies included characterization of: the crack paths; crack-reinforcement interaction processes; and reinforcement deformation and fracture mechanisms. The as-fabricated and post-deformation microstructures and microchemistries of the matrix, reaction layer and ductile phases have also been characterized in a similar system containing TiNb pancake shaped particles [6]. MODELING Rigorous modeling of bridging mechanics was carried out by calculating self-consistent solutions for the crack opening profile, and the crack face stress distribution for a specified set of tr(u), E ' and Kt composite properties using a model developed by Odette and Chao [15]. The calculational procedure is outlined in Appendix A. For load controlled failure conditions, the critical fracture load and crack extension P*(da*) can be determined directly from the extrinsic resistance curve calculations. However, under more general conditions failure is mediated by the compliance of the load point. In this case, the applied load (P)-load line displacement (6) crack growth (da) function P(6)-da is needed to specify failure conditions--P*, 6" and da*. A model to compute the extrinsic P(b)-da functions for specific geometries and fundamental composite properties has also been developed by Odette and Chao [16] and is outlined in Appendix A. RESULTS
Crack-reinforcement interactions and TiNb deformation and fracture The basic microstructural characteristics of the TiA1-TiNb system have been reported [6]. High
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ODETTE et al.: PHASE TOUGHENING IN TiAI-TiNb
temperature processing produced an approximately 10#m thick ct2 reaction layer between the y-TiAl matrix. The ~2 phase deformed by planar slip of super-dislocation pairs; limited deformation was observed in the y by both slip and twinning. The TiNb reinforcements did not readily debond from the matrix in either the laminate composites or sandwiches. However, limited debond cracking in the matrix or at the 7--~2 interface was sometimes observed and was extensive in one instancet. Even in this case, however, the primary mode I crack continued to propagate. The TiNb reinforcements deformed by forming extensive planar arrays of dislocations and did not strain harden [8]. Macroscopically, slip occurred in coarse bands shown in Fig. 3(a). The macroscopic fracture paths were mediated by localized necking or by the dominant member of a set of intense intersecting shear bands as illustrated in Fig. 3(b, c). This behavior suggests that at small u, a(u) is likely to be increased significantly by constraint effects. The overall cracking patterns also appeared to be strongly influenced by the coarse localized slip in the TiNb and ~2 phases: cracks often branched as a result of multiple renucleation at points of strain concentration on the back sides of the TiNb foils as illustrated in Fig. 3(d, e). Crack renucleation took place at small crack openings and it is not clear if the strain concentrations caused renucleation or vice versa. Crack renucleation may be locally assisted by dislocation pile-ups in the ~2, as well as by intersections of y twin ledges at the matrix-reaction layer boundary [6]. However, renucleation behind TiNb reinforcements required stress/strain concentrations such that Kt was considerably greater than Kin. Sandwich tests Typical results of the sandwich tests reported previously [8] are shown in Fig: 4. Peak stresses, ap, were about 9 0 0 _ 90 MPa and maximum displacements, u*, about 110 _+ 20 #m. Standard tensile tests of the TiNb foil shown as the dashed~zlotted line gave yield stress values of about 430 + 30 MPa; the tensile foils did not strain harden and failed by local necking at displacements similar to those observed in the sandwich specimens (independent of the specimen gauge length). ~This debond is considered an anomaly since it occurred between two TiNb foils which were unusually closely spaced ( < 100-200 #m). The longer of the debond cracks initially ran on the back of the first foil, but subsequently jumped to the front of the second foil. The shorter debond crack did the opposite and actually jumped back and forth between the foils. A secondary mode I crack was observed on one side, propagating through the matrix segment beyond the second foil. The local debond
crack path was near the ct2-~/interface, displaying an interesting quasi-periodic pattern of deflections into the ct2 with arrests at the TiNb. The main debond cracks were bridged on the surface by short sections of intact ~t2-), regions.
V
Direction of Crack Propagation
Fig. 3. The deformation, fracture and crack propagation behavior of TiNb: (a) intense shear bands emanating from a blunted crack tip; (b) initiation of crack extension in an intense shear band; (c) final fracture in one of the two pairs of shear bands; (d) and (e) crack renucleation, branching and opening at regions of intense shear band strain on the back of the foil. The characteristic sawtooth a(u) function can be understood in terms of significant constraint (~2.1 ___0.2) effects which occur at small values of u with the stress falling off rapidly at large displacements due to the decrease in the load bearing cross section coupled with a loss of constraint. For purposes of modeling the a(u) function can be represented simply by a sawtooth function shown as the dashed line in Fig. 4 and characterized by the peak stress ap, the displacements at the peak stress, up, and the fracture displacement u*.
10001 800 ~ =
v
I
I
I i Sandwich Test
\
400 . ~ ' ' ' . - . . . . . ~ L S B | 200 t 0 Up
r
t
Model Form
_
~ . " * , .~¢ ~. Foil ~'~', Test
-
75 U(txm)
U
150
Fig. 4. Results of tensile test of TiA1-TiNb sandwich specimens (solid line) and TiNb foils (dashed-dotted line). The dashed line is a parameterized stress~lisplacement function used in the model calculations.
ODETTE et al.: PHASE TOUGHENING IN TiAI-TiNb
125
i
i
about 3 m. Hence, analysis of the data requires the application of LSB models.
i
LE1""~,~
100
/
o
LSB ANALYSIS OF TOUGHENING
t
I,.~ 75
Resistance curves
13.
~
50
Kssb@>42mm ~,,,,-
2s
~.~:~. . . . .
0.000
¢
.s" .s
ssB . . . . . . . . . K
,
0.002 0.004 0.006 0.008 da (m)
Fig. 5. Resistance curve data for edge (LE1) and face (LF2) specimens. The behavior predicted for the SSB regime is shown as the dashed~totted line and the matrix toughness as the dashed line. Resistance
and
2385
load-displacement-crack
growth
curves
The toughness data for both face and edge orientations are shown in Fig. 5f. Significant resistance curves were observed in all cases; after about 6-8 mm of crack extension the toughness was a factor of ten or more than the matrix values. The data show no indication of leveling off, as is characteristic of small steady-state scale bridging (SSB) conditions. Three significant differences in crack growth behavior in the two orientations were observed. First, due to the necessity for complete crack renucleation, the initiation toughness in the face orientation was significantly higher than the matrix toughness. In contrast the initiation toughness in the edge orientation was found to be comparable to the matrix toughness of about 8 MPa~/m; this is expected since the edge cracks do not need to renucleate. Second, the crack in the edge orientation grew continuously in a stable fashion while the cracks in the face orientation grew unstably between the TiNb layers. Third, while the toughness in the edge orientation started out below that in the face orientation, its resistance curve was steeper and a crossover occurred at large a/w. Figure 5 shows the initial portion of the resistance curve predicted for SSB conditions assuming a nominal sawtooth stress displacement curve illustrated in Fig. 4 with Uo= 4 #m, u * = 110 # m O'max = 200 MPa (for f = 0.22) and Km = 8 MPa~/m. The predicted SSB steady-state toughness is reached after about 4.2 cm of crack growth (the full SSB bridge length) at a level of 46.7 MPa~/m. Hence, the 1.5 cm width of the experimental bend specimen is clearly far below that required for SSB. Indeed, based on detailed evaluation of size effects [15], the specimen width required for SSB in this composite is estimated to be ?The behavior of the LF I specimen (not shown for clarity) was similar to LF2.
The LSB model calculations reflected differences between the two orientations. First, the Kt was taken as 20 and 8 MPa~/m for the face and edge orientations respectively. The estimate for the face orientation was based on correcting the apparent initiation toughness for the shielding effect of the first reinforcement. Second, unlike composites toughened with a nominally uniform distribution of ductile particles, the reinforcement and corresponding tractions in the face orientation were highly localized. The effect of this was modeled using different stress-displacement functions for the two orientations. For the face orientation the a(u) parameters measured in the sandwich test were used (ap = 9 0 0 _ 90 MPa and the nominal average of u* = 110), but the stresses along the crack face ~r(x) (where x is the distance from the crack tip) were only permitted to act in regions nominally occupied by the TiNb foils; the calculations also assumed the TiNb foils were parallel and uniformly spaced. Bridging in the edge orientation is continuous, hence, the reinforcement stresses were averaged over the crack face based on the nominal volume fraction ( f ~ 0.22) of the TiNb phase. The face and edge or(x) functions are schematically illustrated in Fig. 6. Note that the most significant irregularities in the foil locations were in the edge orientation (see Experimental); this reduced the effective volume fraction and strength of the reinforcement at a/w less than about 0.65 by an unknown amount. Therefore, in this case large relative uncertainties were assigned with ¢rp = 200 MPa 4- 40 MPa. The predictions of the model are shown in Fig. 7. The shaded region reflects the uncertainties in ap (note, variations in u* would also widen the band). The predicted resistance curves in the face orientation were serrated with decreases in Kr occurring between the reinforcements, consistent with observations of unstable crack growth. The deviations between the nominal prediction and data are larger for the edge orientation, but the trends are qualitatively
~.-..-¢ Localize d
X Fig. 6. Localized vs continuous traction models used for the face and edge specimen orientations respectively.
ODETTE et al.: PHASE TOUGHENING IN TiA1-TiNb
2386
120 100
.
I
,
I
line. Finally, it may be notable that the measured toughness of the LF2 specimens starts to fall above the nominal prediction at the point where the extensive debond forms; however, some of these deviations may be due to irregularities in the TiNb layer locations and the overall effect of debonding on the toughness appears to be modest.
'
LEI
80 ~ 60 ~
40 20
Load-displacement-crack growth curves
.=.,.,.,.I,,°,.==.=..°°,..,,,,.,.°,..,,
I
120
i
I
i
l
I
i
i
As noted previously P(6)-da curves can also be modeled using the fundamental composite properties. Figure 9 compares predicted P(6)-da curves (line and solid points) to measured values (open circles). The curves have been normalized to the elastic fracture loads and displacements of an unreinforced specimen with the same initial a/w (e.g. P and 6 at
I
LF1
100
80 g_ 60 4o
20 .....
°°..,°,=m.,,°,=,.°
i
I
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i
.............
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LF2
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i
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,..=°.°..,,..,,.,..,,
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I
I
,,°°,
'
Km
I
0.002 0.004 0.006 0.008 da (m)
10
(~/~m
Fig. 7. Predicted vs measured resistance curves. consistent with the irregularities in the reinforcement locations. Figure 8 shows that the model also correctly predicts the higher toughness in the edge orientation at large a/w. This is primarily due to differences in Kt and to a lesser extent the initial crack depth in the two specimens. Figure 8 also shows that the toughness resulting from the localized bridges was, on average, slightly higher than the corresponding value predicted for continuous bridging shown as the dashed
4
|
LFI 3 n Q.
2
v
O0
i
I
~ / " ' ' ' "
3 50
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I0 61~m
%LF2
4
~. 100
20
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i
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Continuous -"-,~,,f~.~,"~ , ---~,*_,~L,I:::dge
Ma,r
--'- .............--" h%o " . . . . . . . . .
0 0.000
I
I
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.002
I
I
I
0.004 da (m)
I
0.006
I
I
0
0.008
Fig. 8. Comparisons of the predicted resistance curves for the edge and face orientations predicting a crossover at a/w ~ 0.5. The effect of continuous vs localized reinforcement tractions is illustrated for the face orientation.
0 =
0
i
I
10
i
20
~lSm Fig. 9. Predicted vs measured normalized P(6)-da curves.
ODETTE et al.: PHASE TOUGHENING IN TiAI-TiNb
are significantly larger for the edge specimen; however, the deviation trends are again consistent with the irregular TiNb foil locations which was not explicitly modeled.
Kapp = Km = 8 MPax/m and no bridge). Following initiation, indicated by the asterisk, the predicted and measured points are paired in equal increments of crack extension up to a/w = 0.85. In the face orientation the reinforcements increased the composites' strength by a factor of about 3.5 _+0.25 and its deflection capacity by a factor of about 16 -I- 3. The data generally fall somewhat above the nominal predictions. The reason for this discrepancy is not known; however, it may be significant in the case of the LF2 specimen the deviations initiate at the point that an extensive debond crack is formed. In the face orientation, crack growth primarily occurs beyond the maximum loads. A similar increase in the deflection capacity is observed in the edge orientation, but the composite is strengthened by a somewhat smaller factor of about 2.5. A significant amount of crack growth takes place prior to maximum load in the edge orientation. These effects of orientation are primarily due to the differences in the critical crack tip stress intensity factor, Kt, which is increased in the face orientation by the renucleation mechanism. The discrepancies between the predictions and experiment 400
•
,
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DISCUSSION The results of this study clearly demonstrate that LSB models can be used to predict the extrinsic toughness behavior of ductile phase reinforced composites, based on independent measurements of the stress-displacement function, tr(u) and the other fundamental composite properties (Kt and E'). Thus the models can be used to quantitatively evaluate the effects of various composite design parameters for specific applications. For example, as noted previously, small scale bridging models suggest that debonding enhances ductile phase toughening by increasing the work of rupture. However, for large LSB conditions increases in X do not necessarily translate into increases in the effective toughness. This is clearly shown in Fig. 10 where Kr(da) and P(&)-da curves are plotted for three or(u) functions and for both LSB (W = 0.015 m) and •
,
•
,
•
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SSB: W = 9m, ao/w = 0.5 200
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150
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2388
ODETTE et al.: PHASE TOUGHENING IN TiA1-TiNb
SSB ( W = 9 m) conditions; the initial crack depth was taken as ao/W = 0.5 in both cases. The solid line represents the nominal tr(u) for TiNb found in this study; the dotted lines are for ap decreased by a factor of 2 and u* increased by a factor of 3 (i.e. a Z which is 50% higher than the base case), representing the typical effect of debonding; and the dashed line is for trp increased by 50% and u* decreased by a factor of 2 (i.e. a Z of 75% of the base case), representing a stronger (or higher constraint) but less ductile reinforcement. For SSB the effective toughness as measured by both Kr(da) and P (5)-da increase with increasing X as expected. However, for the LSB the opposite is observed: the relative load capacity increases with higher values of trp, in spite of the corresponding decreases in Z. The different a(u) and sizes have modest effects on the relative deflection capacity of the composite. The increases in the relative load capacity due to the ductile phase are larger for SSB, in spite of the fact that values of Kr(da) are less. The amount of crack growth required to reach K,,b is very large (note the difference in the crack growth scales for the LSB and SSB plots). This behavior can be qualitatively understood based on standard crack stability concepts which have been discussed [17] and are schematically illustrated in Fig. 1 l(a, b) for load controlled fracture. For SSB large crack lengths result in the instability point occurring at crack extensions near the maximum toughness, Kssb. However, for LSB the smaller widths and crack lengths result in crack growth instability near the crack initiation point. In this case the initiation toughness and initial slope of the resistance curve mediates fracture. Figure 11 (c) shows that the initial slope is largely controlled by trp, and is also larger for SSB vs LSB conditions. Note that shorter cracks would also be controlled by the initial part of the resistance curve even in the case of SSB. While it is inappropriate to generalize these results, they clearly demonstrate that debonding may not always be beneficial for typical applications in which LSB prevails. In particular, the LSB models provide a quantitative basis for optimizing microstructural designs. CONCLUDING REMARKS
In summarizing the results for a TiNb reinforced ~-TiAi matrix laminate, there are several general conclusions relevant to toughening of brittle matrix composites with ductile phases that can be drawn: • Toughening may be induced by multiple mechanisms, including shielding due to bridging and increases in the critical crack tip stress intensity due to crack renucleation mechanisms. • Crack deflection, branching and microcracking-which can contribute to toughening in some syst e m s - h a d a relatively minor role in this case.
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Fig. 11. A schematic illustration of SSB (a) vs LSB (b) on stable crack growth under load controlled conditions; and (c) a comparison of the initial slopes of the resistance curves for SSB and LSB conditions and the a(u) functions shown in Fig. 10. • Simple steady-state SSB work-of-rupture models have limited applications for either analyzing or applying test data for the TiAI-TiNb laminate composite. • LSB conditions will often be encountered in practice. However, LSB toughening can be modeled based on proper characterization of the fundamental composite properties, namely tr(u), Kt and E'. • Extensive ductile phase toughening was observed without debonding of the TiNb reinforcements. • Microstructural designs which optimize steady state toughness performance in the SSB regime, K~sb, may be suboptimal for LSB conditions, where crack instability occurs in the region of increasing toughness. Specifically, debonding of reinforcements may be detrimental to engineering performance measured in terms of the composite P(5)-da capacity. • Techniques are available to model P(5)-da using fundamental composite properties and can be applied to alloy design assessments.
Acknowledgements--This work was supported by the Defense Advanced Projects Agency under Contract No. URI-N00014-86-K0753. Helpful discussions with A. G.
ODETTE et al.: PHASE TOUGHENING IN TiAI-TiNb Evans and R. M. McMeeking are gratefully acknowledged. Thanks are also due to Ed Aigeltinger and Pratt and Whitney for providing the material. • REFERENCES
1. L. R. Rose, J. Mech. Phys. Solids 34-6, 609 (1986). 2. A. G. Evans and R. M. McMeeking, Acta metall. 34, 2435 (1986). 3. B. Budiansky, J. C. Amazigo and A. G. Evans, J. Mech. Phys. Solids 36, 167 (1988). 4. M. F. Ashby, F. J. Blunt and M. Bannister, Acta metall. 37, 1847 (1989). 5. C. K. Elliott, G. R. Odette, G. E. Lucas and J. W. Sheckherd, High-Temperature~High-Performance Composites (edited by F. D. Lemkey, A. G. Evans, S. G. Fishman and J. R. Strife), MRS Syrup. Proc., Vol. 120, p. 95 (1988). 6. G. R. Odette, H. E. Deve, C. K. Elliott, A. Hasegawa and G. E. Lucas, Interfaces in Ceramic Metal Composites (edited by R. J. Arsenault, R. Y. Lin, G. P. Martins and S. G. Fishman), p. 443. TMS-AIME, Warrendale, Pa (1990). 7. H. C. Cao, B. J. Dalgleish, H. E. Deve, C. Elliott, A. G. Evans, R. Mehrabian and G. R. Odette, Acta metall. 37, 2969 (1989). 8. H. E. Deve, A. G. Evans, G. R. Odette, R. Mehrabian, M. L. Emiliani and R. J. Hecht, Acta metall, mater. 38, 1491 (1990). 9. L. S. Sigl, A. G. Evans, P. Mataga, R. M. McMeeking and B. J. Dalgleish, Acta metall. 36, 946 (1988). 10. B. D. Flinn, M. Rhule and A. G. Evans, Acta metall. 37, 3001 (1989). 11. V. D. Krstic, Phil Mag. A 48, 695 (1983). 12. T. C. Lu, A. G. Evans, R. J. Hecht and R. Mehrabian, Acta metall, mater. 39, 1853 (1991). 13. K.T. Rao, G. R. Odette and R. O. Ritchie, Aeta metall. mater. 40, 353 (1992). 14. H. Tada, P. C. Paris and G. R. Irwin, The Stress Analysis of Cracks Handbook. Del Research Corp., St Louis, Miss. (1985). 15. G. R. Odette and B. L. Chao, to be published. 16. G. R. Odette and B. L. Chao, to be published. 17. M. Bannister, H. Shercliff, F. Zok, G. Rao and M. F. Ashby, Acta metall, mater. 40, 1531 (1992).
APPENDIX A Rigorous modeling of bridging mechanics was carried out by calculating self-consistent solutions for the crack opening profile u(x), the crack face stress distribution a(x), where x is the distance from the crack tip, for a specified set of a(u), E' and Kt composite properties using a procedure developed by Odette and Chao [15]. The calculational procedure for the resistance Kr(da) curve is as follows: • A trial cr'(x) function is used to calculate: (a) a trial reduction in crack tip stress intensity (shielding) AK~, from the bridging zone; and (b) by applying Castigliano's theorem, the corresponding trial crack face closure displacements u'b(x). The requisite point load stress intensity functions (in this case for the single edge cracked specimen) are taken from Tada [14]. The resulting integrals are
•
•
•
2389
numerically evaluated except for very near the crack tip where an analytical asymptotic solution is used. The total trial applied stress intensity is taken as K'p(da) = Kt + AK~,. A numerical integration, again based on Castigliano's theorem, is used to compute the trial crack opening Up(X) due to the trial three point bending load (P') corresponding to K'p(da). A net trial crack opening is computed as u'(x) = u'p(x) - U'b(X) and used to compute a trial ~r'(u) from the trial ~'(x) and u'(x). The difference between the specified and trial stress~lisplacement functions is evaluated, e,(u)= a ( u ) - tr'(u). A solution is achieved when e(u) is less than a specified convergence criteria. If convergence is not achieved the trial ~'(x) is recomputed based on the trial u'(x) and the specified a(u) and the process repeated until convergence is achieved, usually in a few iterations.
The uncertainties in the calculations are contolled by: (a) the numerical procedure, which introduces < 1% error; (b) the accuracy of stess intensity factor formulas; and (c) the validity of the assumptions in the model--mode I cracks, all plasticity is treated in terms of the crack face tractions and the specimen itself is taken to be linear elastic, and the crack propagates at precisely Ktip = K,. The cr(x) and P(Kr ,a) from the converged Kr(da) solution can also be used to calculate the load-load point displacements P(8) curves at each computed point in the crack extension based on application of Castigliano's theorem to displacements at the load point using the procedure developed by Odette and Chao [16]: • The elastic displacements of the load point at the external load P for cracked (6c) and uncracked (6no) specimens without a bridge are computed using standard analytical formulas given in the Tada [14]. • The corresponding elastic deflection at the loading point due to the bridge a(x) distribution (fib) is computed by numerical integration again using of Castigliano's theorem. • The net displacement is taken as 6n = ~c + 6n~ + 6b" The major additional assumption in the load displacement model is that the bridge tractions prevent unstable elastic fracture. This is clearly consistent with the results of our experiments. Indeed, we have found that for the "stiff" MTS system and small specimens used in this work we are able to stably grow cracks even in unreinforced brittle TiA1 which, of course, does not have a resistance curve. It is also noted that in the case of localized tractions (for the face oriented laminate) the deflections decrease for crack extension between the reinforcements, corresponding to predictions of decreased loads during unstable growth. For purposes of clarity, the P(6)-da shown in Fig. 9 represent the maximum load~lisplacement envelope. Finally we note that the differences between the P(6)-da calculations and experiment can be expected to be larger than the corresponding differences in predicted vs observed K~(da) curves. For the load~:tisplacement calculations none of the dependent variables (P, 6 or da) are directly fixed at the point of observation; however, in the case of the resistance curves, the Kr values are compared at the same amount of crack extension, da.