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Effects of alloying on crack-tip deformation and shielding in gamma-based titanium aluminides
Pergamon PII: S1359-6454(96)00239-X
Acta mater. Vol. 45, No. 3, pp. 961-971, 1997 Copyright 0 1997Acta MetallurgicaInc. Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359-6454197 $17.00+ 0.00
EFFECTS OF ALLOYING ON CRACK-TIP DEFORMATION AND SHIELDING IN GAMMA-BASED TITANIUM ALUMINIDES C. MERCER and W. 0. SOBOYEJO Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210-l 179, U.S.A. (Received 1 April 1996; accepted 27 June 1996)
Abstract-The effects of ternary alloying of Ti-48Al (with 1-3 at.% Mn, Cr and V), and micro-alloying with 0.2% W, on crack-tip deformation and shielding mechanisms are discussed in this paper, for failure under cyclic (fatigue) loading. Crack-tip deformation mechanisms are elucidated by crack-tip transmission electron microscopy examination. Twin process zone dimensions and the degree of deformation-induced twinning are also determined via optical interference and transmission electron microscopy techniques, respectively. A micromechanics-based mode1 is proposed for the estimation of twin toughening ratios under monotonic or cyclic loading. The model, which is based on non-linear fracture mechanics concepts, assumes an average ‘smeared’ plastic stress distribution across the twin process zone. Differences in the resistance to crack growth in the ternary alloys are related to intrinsic microstructural features and crack-tip shielding phenomena. Copyright 0 1997 Acta Metallurgica Inc.
2.
1. INTRODUCTION Alloys based on gamma titanium aluminide (TiAl) are being considered as structural materials in a number of aerospace and automotive applications [ 11. Recent studies of the fracture and fatigue behavior of these materials have given some insight into the failure mechanisms in gamma alloys [2-191. However, further research is required to develop a more comprehensive understanding of the deformation mechanisms associated with fracture under monotonic or cyclic (fatigue) loading conditions. Detailed work performed by the authors on binary Ti-48Al alloys is reported in Refs [3, 13, 141. This work revealed the micromechanisms of crack-tip deformation that are associated with fatigue crack propagation. The purpose of this paper is to present an extension of this work to a number of ternary gamma alloys. More specifically, we study the effects of ternary additions of manganese, chromium, vanadium and tungsten on crack-tip deformation and shielding mechanisms. A micro-mechanical model is proposed to assess the contributions of crack-tip shielding via twin toughening in each alloy. The kinematic irreversibility associated with cyclic deformation-induced twinning and conventional slip is also elucidated. The overall crack growth rates are shown to depend largely on the overall levels of kinematic irreversibility and twin toughening.
tQuestarTM is a trademark of the Questar Corporation New Hope, PA.
of
EXPERIMENTAL PROCEDURE
The ternary alloys used in this investigation were all extruded at 1343°C from ingot material that was procured from Duriron, Inc., Dayton, OH. The ingots were canned in Ti-6Al-4V and extruded at the Wright Laboratories of the Wright Patterson Air Force Base, Dayton, OH. The composition and processing conditions of each alloy are given in Table 1, along with information on the binary alloys investigated previously. A number of square crosssection single-edged notched (SEN) specimens were fabricated from the extrusions by electro-discharge machining. These were used for subsequent fatigue crack growth tests. To ensure consistency and a stable microstructure, the specimens were all heat treated to the following schedule: 982”C/4 h/AC + 704”C/8 h/FC + 815”C/24 h/AC. This heat treatment schedule, which has become known as HTC [lo], has been found empirically to give a good balance of mechanical properties in a wide range of gamma alloys [lo]. Following heat treatment, the sides of the specimens were mechanically polished to a 1 pm diamond surface finish, before final polishing with colloidal silica. The polished SEN specimens were then pre-cracked under far-field compression loading [ 1, 71. Room temperature, constant amplitude, threepoint bend fatigue tests were conducted on each of the specimens at a frequency of 10 Hz. Fatigue crack propagation was monitored using a Questar QM lTMt telescope system with a resolution of approximately 2.5 pm. The initial cyclic load ranges were below, but
961
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MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION Table 1. (a) Processing histories and actual compositions of alloys studied Processing conditions Alloy Binary Ti-48AI Ternary Ti-48Al-2Mn Ternarv Ti-48Al- 1SCr Ternary Ti-48AL3V Ternary Ti-48Al-0.2W
Production route
Hot working route
Reduction ratio
P/M I/M I/M I/M I/M
Isothermally forged at 1065°C Extruded at 1343°C Extruded at 1343°C Extruded at 1343°C Extruded at 1343°C
8:l 14:l 14:l 14:l 14:l
I/M = ingot metallurgy; P/M = power metallurgy. Table 1. (b) Actual compositions (atomic %) of gamma-based titanium aluminides Allov composition
Ti
Al
C
0
Binary Ti-48Al Ternary Ti-48AL2Mn Ternary Ti-48Al-1.5Cr Ternary Ti-48Al-3V Ternary Ti-48Al-0.2W
Bal Bal Bal Bal Bal
49.4 48.2 49.1 48.4 49.5
0.034 0.041 0.034 0.057 0.019
0.157 0.099 0.104 0.085 0.111
Constituent elements H N Mn 0.134 0.086 0.011 0.011 0.011
0.037 0.075 0.075 0.075 0.075
1.98 -
V
W
Cr
Nb
S
2.79 -
~
~ 1.79
-
0.010 0.011
-
1
0.20
Bal = balance of composition.
close to the fatigue threshold, and the stress intensity range, AK, was increased in 0.5 MPaJm increments, until discernible crack growth was observed within 100 000 cycles. This was considered to be the approximate fatigue threshold. The tests were continued well into the steady-state crack growth (Paris) regime, but were halted prior to failure to enable subsequent transmission electron microscopy (TEM) examination of the crack-tip region. This was done to identify possible crack-tip deformation mechanisms. The TEM specimen preparation was rather difficult and time consuming. It involved taking thin foils from wafers of material cut perpendicular to the crack front, such that the tip of the crack was located within one plastic zone from the center of the foil. Dimpling and ion milling were then performed until the area around the crack-tip was sufficiently thin to allow TEM examination. Foils were also taken from undeformed material away from the crack and prepared using the same techniques, to give a reliable comparison of the deformed and undeformed material.
Fig. 1. Optical
interference
micrograph
showing
In order to allow the micro-mechanical model to be applied, to assess the effect of twin toughening, optical interference microscopy was used to determine the size/width of the plastic or twin process zone around the crack. This involved imaging of the crack in the interference microscope using a monochromatic light source. The width of the process zone was then determined by measuring the distance from the crack face to points where the interference fringe patterns deviated from linearity, as shown in Fig. 1. Finally, the remaining portions of the specimens were then fractured under monotonic loading. Scanning electron microscopy (SEM) examination of the fatigue fracture surface was then carried out to identify the failure mode under cyclic loading. 3. RESULTS 3.1. Fatigue crack growth rates and thresholds The fatigue crack growth rate data (da/dN vs AK) obtained for the four ternary alloys are presented in Fig. 2. The fatigue data obtained for a typical binary alloy are also included for comparison. The binary
deviation
of interference
fringes
around
crack.
963
MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION 1
10-3
??
??
+ ??
??
,L’ ,?g 9+ Q 0% 8 L
?? ??
B
ii-48AI-2Mn Tii48AL1.5Cr
W Ti-48AI-3V +s Typical Binary % Ti-48AC0.2W i
10-8
100
10
1
AK&Pa drn Fig. 2. Comparison of fatigue crack growth rates for each alloy studied in this investigation.
alloy exhibits stable fatigue crack growth behavior at stress intensity factor ranges below the fatigue thresholds of the ternary alloys (Fig. 2). Also, the near-threshold fatigue crack growth rates were similar in the different ternary alloys that were examined in this study. However, significant differences were observed between the fatigue crack growth rates in the gamma alloys at higher stress intensity factor ranges (in the Paris regime) where noticeably slower fatigue crack growth rates were obtained in the Cr, V and W containing alloys. These alloys had much lower Paris slopes than the binary and manganese containing alloys. Typical Paris exponents obtained for the different alloys are summarized in Table 2. The Paris exponents of the gamma alloys tested in this study are higher than those reported for metals which have typical Paris exponents between 2 and 4 [20,21]. However, with the exception of the Ti-48Al-2Mn alloy with a Paris exponent of approx. 84.7, the Paris exponents were generally below the values reported
Table 2. Summary
Alloy Ti-48Ai (Binary) Ti-48Al-2Mn Ti-48Al- I.50 Ti-48Al-3V Ti-48AL0.2W
previously for ceramic materials which have typical Paris exponents between 15 and 50 [21-251. The Paris exponents obtained for the gamma alloys also decrease with increasing fracture toughness, as shown in Table 2 in which the toughest alloy (Ti-48Al-1.5Cr extruded with a reduction ratio of 14:l) has the lowest Paris exponent of 6.7. The highest Paris exponent of 84.7 was obtained from the alloy with the lowest fracture toughness, i.e. Ti-48Al-2Mn. The fatigue thresholds obtained from the experiments are summarized in Table 2. The results indicate that the fatigue thresholds, AK,,,, obtained for all the four ternary alloys are significantly higher (around 7 MPaJm), than those obtained for the binary alloys tested in earlier studies [13]. The latter exhibit fatigue thresholds on the order of 5 MPa,/m. The fatigue crack growth thresholds in all the ternary alloys were between 6.7 and 7.0 MPaJm (Table 2). The differences between the fatigue thresholds obtained for the ternary alloys are within the limits of possible experimental error. In any case, the
of experimental
Twin processing zone height h (rm)
Volume fraction of deformation twins v,
Twinning energy release rate AG, (Jm-*)
83 400 700 290 250
0.8 0.8 0.8 0.3 0.8
19.5 299.9 1612 211.2 400.1
and theoretical Twin toughening ratio I, 1.10 1.32 2.14 1.12 1.44
fatigue data
Fatigue threshold AKLh (MPa,/m) 5.0 6.7 6.8 7.0 7.0
Fracture toughness KS, (MPa&) 1.5 8.3 13.0 11.2 25.0
Paris exponents 1.5 84.7 6.7 13.4 9.2
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MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION
Fig. 3. Typical fatigue fracture modes and crack/microstructure profiles: (a) Ti-48Al-2Mn fracture mode; (b) Ti-48Al-1SCr fracture mode; (c) Ti48Al-3Cr fracture mode, and (d) (b) Ti48Al crack profile.
fundamental reasons for the observed fatigue threshold levels are not well understood at present, and further work is needed to determine the intrinsic and extrinsic factors that can contribute to the fatigue threshold behavior of gamma titanium aluminides. 3.2. Fracture modes Typical fatigue fracture modes are shown in Fig. 3(a)-(c) for the Mn-, Cr- and V-containing alloys, respectively. The mode of fracture under cyclic loading was found to be predominantly intergranular across the equiaxed gamma grains and crystallographic ‘step’ fracture across lamellae in TiAl alloyed with Mn and Cr. However, the alloy containing V exhibited a brittle, transgranular, cleavage-like fracture mode with ‘river’ lines that are characteristic
of this failure mode. It is important to note here that the fracture surfaces were relatively flat in all the alloys that were examined, i.e. only very small levels of crack deflection were observed. Also, no evidence of toughening via crack bridging by shear ligaments [17, 181 was observed during fatigue crack growth in any of the specimens that were tested. This is illustrated in Fig. 3(d) in which a montage of a typical fatigue crack is presented. The reasons for the differences in the fracture modes of the different alloys are unclear at present. However, it is important to note here that recent work has shown that intergranular fracture may be induced by the segregation of sulphur and manganese to grain boundaries during processing or heat treatment [ 161. The occurrence of intergranular
MERCER
and SOBOYEJO:
CYCLIC
fracture may, therefore, be associated with segregation phenomena. It is also interesting to note that the alloys containing Mn and V have a similar grain size but quite different fracture modes under fatigue loading, whereas the Cr and Mn alloys show a common intergranular fracture mode despite the considerably smaller equiaxed y grains in the material alloyed with chromium. 3.3. Crack-tip deformation The undeformed substructures of the ternary alloys are shown in Fig. 4. In all cases except for the W-containing alloy, a typical undeformed and heat treated two-phase microstructure, consisting of lamellae and equiaxed y grains, was observed. The moderate to low dislocation density is indicative of the recovered microstructure that would be expected following the HTC heat treatment schedule, which is
Fig. 4. Transmission
CRACK-TIP
DEFORMATION
965
essentially a sub-critical annealing process [lo]. The alloy containing 0.2% tungsten, exhibited a fully lamellar undeformed microstructure with fairly extensive micro-twinning, i.e. across individual lamellae (Fig. 4(e)). Transmission electron micrographs of the crack-tip regions are presented in Fig. 5(a)-(g). For comparison, a crack-tip TEM micrograph a binary alloy studied previously is presented in Fig. 5(h). The binary alloy was tested at room temperature under the same conditions that were employed in the testing of the ternary alloys. The binary alloy exhibited a mixed crack-tip deformation mode which involved predominantly deformation-induced twinning with some evidence of conventional slip. The crack-tip region of the alloy containing Mn exhibited a very heavily deformed structure containing deformation twins across y grains (macro-twins)
electron micrographs showing undeformed microstructure for: (a) Ti48Al-2Mn, (b) Ti48Al&l.SCr, (c) Ti+8AlG3V, and (d) Ti_48Alk4)).2W.
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MERCER and SOBOYEJO:
CYCLIC CRACK-TIP DEFORMATION
and a very high dislocation density (Fig. 5(a),(b)). Bands of complex dislocation tangles were observed with channels of lower dislocation density between them. Deformation twins were also observed running across this banded dislocation substructure, as shown in Fig. 5(a),(b). The material alloyed with Cr also exhibited a combination of conventional slip and deformation-induced twinning in the deformed crack-tip region (Fig. 5(c),(d)). However, the dislocation and twin densities were lower than those observed in the Mn-containing alloy. Nevertheless, there was still strong evidence of macro-twinning across y grains and conventional slip across glide planes intersecting the twin planes, as shown in Fig. 5(c),(d). TEM examination of the V-containing alloy however, indicated a different crack-tip deformation mechanism. The amount of deformation-induced twinning was observed to be low in this material.
Instead, the deformation was in the form of extensive dislocation tangles which appeared to form a loose cell structure, as shown in Fig. 5(e),(f). This high dislocation density showed quite clearly that the crack-tip deformation in this material occurred predominantly by conventional slip. In the case of the material micro-alloyed with W, the substructure of the crack-tip region was not unlike that of the undeformed material. This is due to the fully lamellar nature of the microstructure in this alloy and also the high incidence of micro-twinning observed in the undeformed material. The only discernible difference was that the lamellae in the crack-tip specimen appeared to exhibit a fairly large number of stacking faults that were aligned in the same orientation as the micro-twins which were present in both the deformed and undeformed materials (Fig. 5(g)). The presence of these stacking faults may indicate that the mechanism of crack-tip
Fig. 5 (a-d).
MERCER and SOBOYEJO:
CYCLIC CRACK-TIP DEFORMATION
967
Fig. 5. Transmission electron micrographs showing crack-tip regions in: (a, b) Ti&48Alp2Mn; (c, d) Ti_48Al-1.5Cr; (e, f) Tii18Alp3V; and (g) Ti48Al-0.2W; (h) Ti--ISAl.
deformation under cyclic loading in this alloy involves the movement of the l/6(112) Shockley partial dislocations along the { 11 1} slip/twin planes. 4. DISCUSSION 4.1. Crack-tip deformation The TEM results presented above suggest that crack-tip deformation under cyclic loading in gamma-based alloys occurs by a combination of twinning and/or conventional slip. The results also suggest that ternary alloy additions play a role in determining which of these mechanisms becomes dominant, i.e. Mn and Cr additions seem to promote a mixed mode of twinning and slip, whereas small additions of V tend to suppress the extent of deformation-induced twinning and promote conventional slip. The formation of stacking faults in the fully lamellar W-containing alloy suggests that slip may also be the dominant deformation mechanism in this material.
The crack-tip TEM results obtained from the current study suggest that there is a correlation between fatigue crack growth rate and crack-tip deformation mechanisms. The fast crack growth rates observed in the binary and manganese containing alloys are associated with heavy deformation and a fairly high fraction of deformation-induced twinning activity. Conversely, the smaller level of deformation in material alloyed with Cr, V and W, and particularly the reduced level of twinning observed in the vanadium-containing alloy, are associated with slower crack growth rates. The irreversibility of the deformation-induced twinning process is thought to be the main cause of the above effects of crack-tip deformation on fatigue crack growth rates [14]. Since deformation-induced twinning is irreversible, a higher incidence of deformation twinning will result in almost complete irreversibility of crack growth under cyclic loading,
968
MERCER and SOBOYEJO:
CYCLIC CRACK-TIP DEFORMATION
(a)
Cd)
Paulal reversibility due to conventional slip Fig. 6. Schematic illustration showing crack extension under cyclic loading as a result of a mixed deformation mode of irreversible twinning and partially reversible slip: (a, b) crack opens during loading part of fatigue cycle, (c) crack-tip deformation due to deformation-induced twinning and conventional slip, (d) permanent crack extension upon unloading due to irreversibility of deformation-induced twinning.
i.e. greater crack extensions per cycle and hence faster fatigue crack growth rates. In contrast, the partial reversibility associated with conventional slip results in a smaller crack extension per cycle and hence, slower crack growth rates will be expected, as illustrated schematically in Fig. 6. The mechanism outlined above suggests that deformation-induced twinning may be undesirable as a crack-tip deformation mechanism during fatigue since it results in faster crack growth rates. However, the presence of a twin process zone around a crack may lead to a re-distribution of stresses over this zone, which may cause a beneficial crack-tip shielding effect in the form of a reduced stress intensity at the crack-tip. This effect is referred to as twin toughening [17-191. 4.2. Analysis of twin toughening In order
to assess whether
twin toughening
was
providing any contribution to crack-tip shielding, a micro-mechanical model was employed, which is essentially a modified version of the model proposed originally by Deve and Evans [19], uses non-linear elastic fracture mechanics techniques developed originally by Budiansky, Hutchinson and Lambro-
poulus [26]. Deve and Evans [19] have shown that the twin toughening ratio can be derived by considering the energy dissipation, AG,,, within the twin process zone (TPZ) of width h. However, this model assumes a cut-off value, ho, within the process zone. This is done to avoid the problems associated with AG,, -+ - co as h + 0, where h is the height of the process zone. The choice of ha is therefore somewhat arbitrary, and can be equated to the crack-tip opening displacement, (6 = K2/2Ecr,), as in a recent paper by Soboyejo and Mercer [14]. In order to eliminate the problem of a cut-off value, a modified analysis is presented here, which assumes that the average/smeared stress distribution across the process zone is comparable to the uni-axial yield sets measured in a simple tensile test. One consequence of this assumption is that the strain energy density, U, is no longer a function of the distance from the crack-face, y. The previous model by Dbve and Evans [ 191 yielded:
s h
AG,, = 2
0
WY) dv.
(1)
MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION But this can now be written as: AG,,=2
equation (10) by K. gives the following expression for 1, the twin toughening ratio:
hUdy s0
(2)
since U is assumed to be constant across the process zone around the crack. If U is equated to the area under the uni-axial stress-strain curve, equation (3) becomes: AG,, = 2 h oh s0
dy
(3)
Now, assuming piece wise linear elastic and linear strain hardening behavior in the TPZ, equation (4) can be written as: AG,, = 2
h {[(a + a,)/21(t - cv) + arty} dy s0
(4)
considering both the elastic and plastic portions of the stress-strain curve. Substituting for the strain terms in equation (5) gives: A& = 0h((0 + a,)[(~ - a,)lHl + (a:lE)} dv (5) j where H is the strain-hardening coefficient and E is the Young’s modulus. Re-arranging equation (6) yields: AG,, =
* [(d/H) - o;(l/H s0
- l/E)] dy.
(6)
However, the average/smeared stress in the plastic wake around the crack is assumed to be comparable to the yield stress, 0 = c(cr,, where c( is a stress-state parameter which will be discussed later. Substitution for 0 into equation (6) therefore gives: AG,, = Integration
’ [(c&:/H) - $(1/H I0
- l/E)] dy.
(7)
of equation (7) yields:
AG,, = {u’c+H - o;(l/H
- l/E)}h.
(8)
Now J, the total strain energy release rate, is given by: J = Pm/E = g/E
969
+ AG,,
(9)
where Km is the steady-state toughness and K. is the intrinsic ‘matrix’ toughness with no twinning present (which was assumed to be lowest matrix initiation toughness value measured experimentally). So, re-arranging and solving for K, yields: K, = J
(10)
where the parameter V, has been included, which is the average volume fraction of grains containing deformation-induced twins within the TPZ. Dividing
1= K,IKo = J(l
+ V,EAG,,/z).
(11)
The above equations were used to assess the role of crack-tip shielding under cyclic loading. Note that K and K. can be replaced respectively by AK and AK,, under cyclic loading. Also, the values of h that were employed were those determined by careful analysis of optical interference micrographs. The volume fraction of grains containing deformation-induced grains, V,, was determined from TEM observation of the crack-tip regions. Calculations of AG,, and 1, were performed for all of the binary and ternary gamma alloys examined in this study. These values are presented in Table 2 along with the corresponding values of fracture toughness, Kr,, and fatigue thresholds, AK,,,, for each alloy. Values of the volume fraction of twinned grains, V, and the TPZ width, h, are also included in Table 2. The values obtained for 1, show that the contribution to crack-tip shielding from twin toughening varies quite considerably between these alloys. The forged binary alloy had a very low twin toughening ratio of 1.10, thus implying that although the crack-tip deformation occurs primarily by twinning, i.e. a high volume fraction of twinned grains were observed in the TEM (Table 2), only a small twin toughening effect is observed in this alloy. It is due largely to the small twin process zone width that was observed in this alloy. The i, values are somewhat higher for the extruded binary, manganese-containing and tungsten-containing alloys (1.66, 1.32 and 1.44, respectively), which suggests a higher crack-tip shielding effect due to twinning. Higher values of TPZ width, h, and also large V, values are considered to be the major contributory factors to the higher i, values. However, the alloy containing 1.5% Cr gave the greatest crack-tip shielding effect, with a twin toughening ratio of 2.14. It would appear that the relatively high fracture toughness of this alloy is partly due to a fairly high twin toughening effect, giving a 50% reduction in crack-tip stress intensity. This large twin toughening effect is considered to be mainly due to a very high TPZ width (when compared to the other alloys studied in this investigation), and also a high yield strength. The high strength observed in this alloy is typical of Cr-containing gamma-based alloys [9, 151. The twin toughening ratio obtained for the material alloyed with V was only 1.12. Although the fracture toughness of this alloy was relatively high when compared to the other alloys discussed in this paper (around 12 MPaJm), the twin toughening contribution was quite small. This is considered to be due to the fact that deformation-induced twinning plays only a limited role in crack-tip deformation, deduced from the small volume fraction of twinned
970
MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION
grains observed in the TEM. Cyclic fracture in this alloy also appears to occur as a result of dislocation interactions which promote greater levels of crack-tip reversibility and possible dislocation shielding effects.
4.3. Implications It is important to discuss the implications of the combined effects of twin toughening and crack-tip deformation phenomena on fatigue crack growth. This is because the fatigue crack growth rates will depend largely on the degree of crack-tip reversibility associated with deformation-induced twinning/slip, and the reduction in the crack driving force due to twin toughening. With the exception of Ti48Al1SCr, however, the effects of kinematic irreversibility (due to increasing deformation-induced crack-tip twinning components) appear to be generally more important than the shielding effects associated with twin toughening. The fatigue crack growth rates are, therefore, slowest in the Ti-48Al-3V and Ti48A1-0.2W alloys in which crack-tip deformation occurred largely by partially reversible slip mechanisms (Fig. S(et(g)). Conversely, the fastest near-threshold crack growth rates are observed in the binary Ti48Al alloy in which crack-tip deformation occurred mainly by deformation-induced twinning (Fig. 5(h)). However, slow crack growth rates in the Ti+Al-1.5Cr alloy are attributed to the very high level of twin toughening (A, - 2.14) in this alloy (Fig. 2). The current results therefore suggest that the fatigue crack growth resistance of gamma alloys can be improved by alloying to promote crack-tip deformation by reversed plasticity. This can be achieved by ternary alloying with V or W. Under such circumstances, the fatigue crack growth rates appear to be slower due to the higher levels of slip reversibility. Improved fatigue crack growth resistance can also be obtained by alloying with Cr to promote crack-tip deformation by slip and twinning, and extremely high levels of twin toughening. Nevertheless, it is important to note that the fatigue crack growth rates in gamma alloys are typically very fast, when compared to those in existing structural alloys. This is true even when the crack growth-rates in the gamma alloys are reduced by ternary alloying with V, W or Cr. It may, therefore, be necessary to base future fatigue life assessment procedures on fatigue threshold levels (Table 2). Microstructural control to obtain nearly/ fully lamellar structures may also be used to improve the fatigue thresholds and crack growth resistance, as shown in recent studies by Rao et al. [12]. However, fatigue threshold-based designs may impose severe penalties on the (potential) use of gamma alloys, and alternative probabilistic mechanics techniques may be required to determine the levels of risk that can be tolerated in specific applications.
5. CONCLUSIONS (1) Small ternary additions of Mn, Cr, V and W have a noticeable effect on the fatigue behavior of TiAl-based alloys. Cr, V and W additions appear to promote slower crack growth rates, and all four alloying elements are associated with higher fatigue thresholds than those of the binary gamma Ti48Al alloys. (2) Crack-tip deformation in Ti48Al-2Mn occurs by a combination of twinning and slip. This leads to faster fatigue crack growth rates due to the kinematic irreversibility associated with deformation-induced twinning. A mixed crack-tip deformation mode, involving deformation-induced twinning and slip, is also observed in the Ti48Al-1SCr alloy. In contrast, small additions of V result in crack-tip deformation predominantly by conventional slip mechanisms, while micro-alloying with tungsten appears to promote stacking fault formation during cyclic deformation by slip of Shockley partial dislocations. (3) In general, gamma-based alloys that exhibit higher levels of deformation-induced twinning and low/moderate levels of twin toughening during cyclic deformation will have faster fatigue crack growth rates due to the kinematic irreversibility of the twinning process. Conversely, a crack-tip deformation mode that involves partially reversible slip, will result in slower fatigue crack growth rates. High levels of deformation-induced twinning and twin toughening are also associated with slower crack growth rates. (4) The twin toughening/crack-tip shielding contributions for the alloys studied ranged between 1.10 and 2.14. Alloying with chromium was found to give the greatest crack-tip shielding effect. The modified twin toughening model presented in this paper shows that high twin toughening ratios are dependent on parameters such as a large twin process zone size, high strength and a high volume fraction of grains exhibiting deformation-induced twinning in the crack-tip region. Acknowledgements-The
authors are grateful to The Ohio State University and The Division of Materials Research of The National Science Foundation (NSF) for financial support. Appreciation is also extended to Dr Bruce MacDonald, the Program Monitor at NSF, for his encouragement and support of the research. The authors are grateful to MS Yingfang Ni for assistance with the preparation of the manuscript. REFERENCES 1. Y.-W. Kim and D. M. Dimiduk, J. Metal 43,40 (1991). 2. T. S. Srivatsan, W. 0. Soboyejo and M. Strangwood, EFM 52, 107 (1995). 3. W. 0. Soboyejo, J. E. Deffeyes and P. B. Aswath, Muter. Sci. Engng A138, 95 (1991). 4. G. Henaff, B. Bittar, C. Mabru, J. Petit and P. Bowen, Mater. Sci. Engng A (submitted). 5. A. W.‘James and P. Bowen, In Proc. 7th World Conf. on Titanium, San Diego, CA (1992) The Minerals, Metals and Materials Society.
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and SOBOYEJO:
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6. D. L. Davidson and J. B. Campbell, Metall. Trans. 24A, 1555 (1993). K. T. Vekateswara-Rao, S. M. L. 7. W. 0. Soboyejo. Sastry and R. 0. Ritchie, Metall. Trans. 24A, 585 (1993). Y. Mutoh, K. Hayashi 8. R. Gnanamoorthy, and Y. Mizuhara, Scripta metall. mater. 33, 907 (1995). 9. W. 0. Soboyejo, Proc. 7th World Conf: on Titanium, San Diego, CA (1992) The Minerals, Metals and Materials Society. 10. W. 0. Soboyejo, D. S. Schwartz and S. M. L. Sastry, Metall. Trans. 23A, 2039 (1992). 11. K. S. Chan and Y.-W. Kim, Metall. Trans. 23A, 1663 (1992). 12. K. T. V. Rao and R. 0. Ritchie, Mater. Sci. Engng A153, 479 (1992). 13. C. Mercer and W. 0. Soboyejo, Symp. Fatigue and Fracture of Ordered Intermetallics (edited by W. 0. Soboyejo, T. S. Srivatsan and D. L. Davidson). TMS, Warrendale, PA (1993). 14. W. 0. Soboyejo and C. Mercer, Scripta metall. mater. 30, 1515 (1994).
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15. W. 0. Soboyejo and C. Mercer, Symp. Fatigue and Fracture of Ordered Intermetallics (edited by W. 0. Soboyejo, T. S. Srivatsan and D. L. Davidson). TMS, Warrendale, PA (1993). 16. W. 0. Soboyejo, K. Lou and M. McConnell. Scripta metall. mater. 31, 63 (1994). 17. K. S. Chan, J. Metal. 44, 30 (1992). 18. K. S. Chan, Metall. Trans. 24A, 569 (1993). 19. H. Deve and A. G. Evans, Acta metall. mater. 39, 1171 (1991). 20. R. 0. Ritchie, Int. Met. Reo. 20, 205 (1979). 21. S. Suresh, Fatigue of Materials. 2nd edn. Cambridge University Press (1995). 22. R. H. Dauskardt and R. 0. Ritchie. Closed Loop 27, 7 (1989). 23. R. H. Dauskardt, D. B. Marshall and R. 0. Ritchie, J. Am. Ceram. Sot. 73, 783 (1990). 24. L. X. Han and S. Suresh, J. Am. Ceram. Sot. 72, 1233 (1989). 25. M. J. Reece, F. Guiu and M. F. Sammur, J. Am. Ceram. Sot. 72, 348 (1989). Int. 26. B. Budiansky, J. Hutchinson and J. Lambropoulus, J. So1id.s Struct. 19, 337 (1983).
Acta mater. Vol. 45, No. 3, pp. 961-971, 1997 Copyright 0 1997Acta MetallurgicaInc. Published by Elsevier Science Ltd Printed in Great Britain. All rights reserved 1359-6454197 $17.00+ 0.00
EFFECTS OF ALLOYING ON CRACK-TIP DEFORMATION AND SHIELDING IN GAMMA-BASED TITANIUM ALUMINIDES C. MERCER and W. 0. SOBOYEJO Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210-l 179, U.S.A. (Received 1 April 1996; accepted 27 June 1996)
Abstract-The effects of ternary alloying of Ti-48Al (with 1-3 at.% Mn, Cr and V), and micro-alloying with 0.2% W, on crack-tip deformation and shielding mechanisms are discussed in this paper, for failure under cyclic (fatigue) loading. Crack-tip deformation mechanisms are elucidated by crack-tip transmission electron microscopy examination. Twin process zone dimensions and the degree of deformation-induced twinning are also determined via optical interference and transmission electron microscopy techniques, respectively. A micromechanics-based mode1 is proposed for the estimation of twin toughening ratios under monotonic or cyclic loading. The model, which is based on non-linear fracture mechanics concepts, assumes an average ‘smeared’ plastic stress distribution across the twin process zone. Differences in the resistance to crack growth in the ternary alloys are related to intrinsic microstructural features and crack-tip shielding phenomena. Copyright 0 1997 Acta Metallurgica Inc.
2.
1. INTRODUCTION Alloys based on gamma titanium aluminide (TiAl) are being considered as structural materials in a number of aerospace and automotive applications [ 11. Recent studies of the fracture and fatigue behavior of these materials have given some insight into the failure mechanisms in gamma alloys [2-191. However, further research is required to develop a more comprehensive understanding of the deformation mechanisms associated with fracture under monotonic or cyclic (fatigue) loading conditions. Detailed work performed by the authors on binary Ti-48Al alloys is reported in Refs [3, 13, 141. This work revealed the micromechanisms of crack-tip deformation that are associated with fatigue crack propagation. The purpose of this paper is to present an extension of this work to a number of ternary gamma alloys. More specifically, we study the effects of ternary additions of manganese, chromium, vanadium and tungsten on crack-tip deformation and shielding mechanisms. A micro-mechanical model is proposed to assess the contributions of crack-tip shielding via twin toughening in each alloy. The kinematic irreversibility associated with cyclic deformation-induced twinning and conventional slip is also elucidated. The overall crack growth rates are shown to depend largely on the overall levels of kinematic irreversibility and twin toughening.
tQuestarTM is a trademark of the Questar Corporation New Hope, PA.
of
EXPERIMENTAL PROCEDURE
The ternary alloys used in this investigation were all extruded at 1343°C from ingot material that was procured from Duriron, Inc., Dayton, OH. The ingots were canned in Ti-6Al-4V and extruded at the Wright Laboratories of the Wright Patterson Air Force Base, Dayton, OH. The composition and processing conditions of each alloy are given in Table 1, along with information on the binary alloys investigated previously. A number of square crosssection single-edged notched (SEN) specimens were fabricated from the extrusions by electro-discharge machining. These were used for subsequent fatigue crack growth tests. To ensure consistency and a stable microstructure, the specimens were all heat treated to the following schedule: 982”C/4 h/AC + 704”C/8 h/FC + 815”C/24 h/AC. This heat treatment schedule, which has become known as HTC [lo], has been found empirically to give a good balance of mechanical properties in a wide range of gamma alloys [lo]. Following heat treatment, the sides of the specimens were mechanically polished to a 1 pm diamond surface finish, before final polishing with colloidal silica. The polished SEN specimens were then pre-cracked under far-field compression loading [ 1, 71. Room temperature, constant amplitude, threepoint bend fatigue tests were conducted on each of the specimens at a frequency of 10 Hz. Fatigue crack propagation was monitored using a Questar QM lTMt telescope system with a resolution of approximately 2.5 pm. The initial cyclic load ranges were below, but
961
962
MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION Table 1. (a) Processing histories and actual compositions of alloys studied Processing conditions Alloy Binary Ti-48AI Ternary Ti-48Al-2Mn Ternarv Ti-48Al- 1SCr Ternary Ti-48AL3V Ternary Ti-48Al-0.2W
Production route
Hot working route
Reduction ratio
P/M I/M I/M I/M I/M
Isothermally forged at 1065°C Extruded at 1343°C Extruded at 1343°C Extruded at 1343°C Extruded at 1343°C
8:l 14:l 14:l 14:l 14:l
I/M = ingot metallurgy; P/M = power metallurgy. Table 1. (b) Actual compositions (atomic %) of gamma-based titanium aluminides Allov composition
Ti
Al
C
0
Binary Ti-48Al Ternary Ti-48AL2Mn Ternary Ti-48Al-1.5Cr Ternary Ti-48Al-3V Ternary Ti-48Al-0.2W
Bal Bal Bal Bal Bal
49.4 48.2 49.1 48.4 49.5
0.034 0.041 0.034 0.057 0.019
0.157 0.099 0.104 0.085 0.111
Constituent elements H N Mn 0.134 0.086 0.011 0.011 0.011
0.037 0.075 0.075 0.075 0.075
1.98 -
V
W
Cr
Nb
S
2.79 -
~
~ 1.79
-
0.010 0.011
-
1
0.20
Bal = balance of composition.
close to the fatigue threshold, and the stress intensity range, AK, was increased in 0.5 MPaJm increments, until discernible crack growth was observed within 100 000 cycles. This was considered to be the approximate fatigue threshold. The tests were continued well into the steady-state crack growth (Paris) regime, but were halted prior to failure to enable subsequent transmission electron microscopy (TEM) examination of the crack-tip region. This was done to identify possible crack-tip deformation mechanisms. The TEM specimen preparation was rather difficult and time consuming. It involved taking thin foils from wafers of material cut perpendicular to the crack front, such that the tip of the crack was located within one plastic zone from the center of the foil. Dimpling and ion milling were then performed until the area around the crack-tip was sufficiently thin to allow TEM examination. Foils were also taken from undeformed material away from the crack and prepared using the same techniques, to give a reliable comparison of the deformed and undeformed material.
Fig. 1. Optical
interference
micrograph
showing
In order to allow the micro-mechanical model to be applied, to assess the effect of twin toughening, optical interference microscopy was used to determine the size/width of the plastic or twin process zone around the crack. This involved imaging of the crack in the interference microscope using a monochromatic light source. The width of the process zone was then determined by measuring the distance from the crack face to points where the interference fringe patterns deviated from linearity, as shown in Fig. 1. Finally, the remaining portions of the specimens were then fractured under monotonic loading. Scanning electron microscopy (SEM) examination of the fatigue fracture surface was then carried out to identify the failure mode under cyclic loading. 3. RESULTS 3.1. Fatigue crack growth rates and thresholds The fatigue crack growth rate data (da/dN vs AK) obtained for the four ternary alloys are presented in Fig. 2. The fatigue data obtained for a typical binary alloy are also included for comparison. The binary
deviation
of interference
fringes
around
crack.
963
MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION 1
10-3
??
??
+ ??
??
,L’ ,?g 9+ Q 0% 8 L
?? ??
B
ii-48AI-2Mn Tii48AL1.5Cr
W Ti-48AI-3V +s Typical Binary % Ti-48AC0.2W i
10-8
100
10
1
AK&Pa drn Fig. 2. Comparison of fatigue crack growth rates for each alloy studied in this investigation.
alloy exhibits stable fatigue crack growth behavior at stress intensity factor ranges below the fatigue thresholds of the ternary alloys (Fig. 2). Also, the near-threshold fatigue crack growth rates were similar in the different ternary alloys that were examined in this study. However, significant differences were observed between the fatigue crack growth rates in the gamma alloys at higher stress intensity factor ranges (in the Paris regime) where noticeably slower fatigue crack growth rates were obtained in the Cr, V and W containing alloys. These alloys had much lower Paris slopes than the binary and manganese containing alloys. Typical Paris exponents obtained for the different alloys are summarized in Table 2. The Paris exponents of the gamma alloys tested in this study are higher than those reported for metals which have typical Paris exponents between 2 and 4 [20,21]. However, with the exception of the Ti-48Al-2Mn alloy with a Paris exponent of approx. 84.7, the Paris exponents were generally below the values reported
Table 2. Summary
Alloy Ti-48Ai (Binary) Ti-48Al-2Mn Ti-48Al- I.50 Ti-48Al-3V Ti-48AL0.2W
previously for ceramic materials which have typical Paris exponents between 15 and 50 [21-251. The Paris exponents obtained for the gamma alloys also decrease with increasing fracture toughness, as shown in Table 2 in which the toughest alloy (Ti-48Al-1.5Cr extruded with a reduction ratio of 14:l) has the lowest Paris exponent of 6.7. The highest Paris exponent of 84.7 was obtained from the alloy with the lowest fracture toughness, i.e. Ti-48Al-2Mn. The fatigue thresholds obtained from the experiments are summarized in Table 2. The results indicate that the fatigue thresholds, AK,,,, obtained for all the four ternary alloys are significantly higher (around 7 MPaJm), than those obtained for the binary alloys tested in earlier studies [13]. The latter exhibit fatigue thresholds on the order of 5 MPa,/m. The fatigue crack growth thresholds in all the ternary alloys were between 6.7 and 7.0 MPaJm (Table 2). The differences between the fatigue thresholds obtained for the ternary alloys are within the limits of possible experimental error. In any case, the
of experimental
Twin processing zone height h (rm)
Volume fraction of deformation twins v,
Twinning energy release rate AG, (Jm-*)
83 400 700 290 250
0.8 0.8 0.8 0.3 0.8
19.5 299.9 1612 211.2 400.1
and theoretical Twin toughening ratio I, 1.10 1.32 2.14 1.12 1.44
fatigue data
Fatigue threshold AKLh (MPa,/m) 5.0 6.7 6.8 7.0 7.0
Fracture toughness KS, (MPa&) 1.5 8.3 13.0 11.2 25.0
Paris exponents 1.5 84.7 6.7 13.4 9.2
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MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION
Fig. 3. Typical fatigue fracture modes and crack/microstructure profiles: (a) Ti-48Al-2Mn fracture mode; (b) Ti-48Al-1SCr fracture mode; (c) Ti48Al-3Cr fracture mode, and (d) (b) Ti48Al crack profile.
fundamental reasons for the observed fatigue threshold levels are not well understood at present, and further work is needed to determine the intrinsic and extrinsic factors that can contribute to the fatigue threshold behavior of gamma titanium aluminides. 3.2. Fracture modes Typical fatigue fracture modes are shown in Fig. 3(a)-(c) for the Mn-, Cr- and V-containing alloys, respectively. The mode of fracture under cyclic loading was found to be predominantly intergranular across the equiaxed gamma grains and crystallographic ‘step’ fracture across lamellae in TiAl alloyed with Mn and Cr. However, the alloy containing V exhibited a brittle, transgranular, cleavage-like fracture mode with ‘river’ lines that are characteristic
of this failure mode. It is important to note here that the fracture surfaces were relatively flat in all the alloys that were examined, i.e. only very small levels of crack deflection were observed. Also, no evidence of toughening via crack bridging by shear ligaments [17, 181 was observed during fatigue crack growth in any of the specimens that were tested. This is illustrated in Fig. 3(d) in which a montage of a typical fatigue crack is presented. The reasons for the differences in the fracture modes of the different alloys are unclear at present. However, it is important to note here that recent work has shown that intergranular fracture may be induced by the segregation of sulphur and manganese to grain boundaries during processing or heat treatment [ 161. The occurrence of intergranular
MERCER
and SOBOYEJO:
CYCLIC
fracture may, therefore, be associated with segregation phenomena. It is also interesting to note that the alloys containing Mn and V have a similar grain size but quite different fracture modes under fatigue loading, whereas the Cr and Mn alloys show a common intergranular fracture mode despite the considerably smaller equiaxed y grains in the material alloyed with chromium. 3.3. Crack-tip deformation The undeformed substructures of the ternary alloys are shown in Fig. 4. In all cases except for the W-containing alloy, a typical undeformed and heat treated two-phase microstructure, consisting of lamellae and equiaxed y grains, was observed. The moderate to low dislocation density is indicative of the recovered microstructure that would be expected following the HTC heat treatment schedule, which is
Fig. 4. Transmission
CRACK-TIP
DEFORMATION
965
essentially a sub-critical annealing process [lo]. The alloy containing 0.2% tungsten, exhibited a fully lamellar undeformed microstructure with fairly extensive micro-twinning, i.e. across individual lamellae (Fig. 4(e)). Transmission electron micrographs of the crack-tip regions are presented in Fig. 5(a)-(g). For comparison, a crack-tip TEM micrograph a binary alloy studied previously is presented in Fig. 5(h). The binary alloy was tested at room temperature under the same conditions that were employed in the testing of the ternary alloys. The binary alloy exhibited a mixed crack-tip deformation mode which involved predominantly deformation-induced twinning with some evidence of conventional slip. The crack-tip region of the alloy containing Mn exhibited a very heavily deformed structure containing deformation twins across y grains (macro-twins)
electron micrographs showing undeformed microstructure for: (a) Ti48Al-2Mn, (b) Ti48Al&l.SCr, (c) Ti+8AlG3V, and (d) Ti_48Alk4)).2W.
966
MERCER and SOBOYEJO:
CYCLIC CRACK-TIP DEFORMATION
and a very high dislocation density (Fig. 5(a),(b)). Bands of complex dislocation tangles were observed with channels of lower dislocation density between them. Deformation twins were also observed running across this banded dislocation substructure, as shown in Fig. 5(a),(b). The material alloyed with Cr also exhibited a combination of conventional slip and deformation-induced twinning in the deformed crack-tip region (Fig. 5(c),(d)). However, the dislocation and twin densities were lower than those observed in the Mn-containing alloy. Nevertheless, there was still strong evidence of macro-twinning across y grains and conventional slip across glide planes intersecting the twin planes, as shown in Fig. 5(c),(d). TEM examination of the V-containing alloy however, indicated a different crack-tip deformation mechanism. The amount of deformation-induced twinning was observed to be low in this material.
Instead, the deformation was in the form of extensive dislocation tangles which appeared to form a loose cell structure, as shown in Fig. 5(e),(f). This high dislocation density showed quite clearly that the crack-tip deformation in this material occurred predominantly by conventional slip. In the case of the material micro-alloyed with W, the substructure of the crack-tip region was not unlike that of the undeformed material. This is due to the fully lamellar nature of the microstructure in this alloy and also the high incidence of micro-twinning observed in the undeformed material. The only discernible difference was that the lamellae in the crack-tip specimen appeared to exhibit a fairly large number of stacking faults that were aligned in the same orientation as the micro-twins which were present in both the deformed and undeformed materials (Fig. 5(g)). The presence of these stacking faults may indicate that the mechanism of crack-tip
Fig. 5 (a-d).
MERCER and SOBOYEJO:
CYCLIC CRACK-TIP DEFORMATION
967
Fig. 5. Transmission electron micrographs showing crack-tip regions in: (a, b) Ti&48Alp2Mn; (c, d) Ti_48Al-1.5Cr; (e, f) Tii18Alp3V; and (g) Ti48Al-0.2W; (h) Ti--ISAl.
deformation under cyclic loading in this alloy involves the movement of the l/6(112) Shockley partial dislocations along the { 11 1} slip/twin planes. 4. DISCUSSION 4.1. Crack-tip deformation The TEM results presented above suggest that crack-tip deformation under cyclic loading in gamma-based alloys occurs by a combination of twinning and/or conventional slip. The results also suggest that ternary alloy additions play a role in determining which of these mechanisms becomes dominant, i.e. Mn and Cr additions seem to promote a mixed mode of twinning and slip, whereas small additions of V tend to suppress the extent of deformation-induced twinning and promote conventional slip. The formation of stacking faults in the fully lamellar W-containing alloy suggests that slip may also be the dominant deformation mechanism in this material.
The crack-tip TEM results obtained from the current study suggest that there is a correlation between fatigue crack growth rate and crack-tip deformation mechanisms. The fast crack growth rates observed in the binary and manganese containing alloys are associated with heavy deformation and a fairly high fraction of deformation-induced twinning activity. Conversely, the smaller level of deformation in material alloyed with Cr, V and W, and particularly the reduced level of twinning observed in the vanadium-containing alloy, are associated with slower crack growth rates. The irreversibility of the deformation-induced twinning process is thought to be the main cause of the above effects of crack-tip deformation on fatigue crack growth rates [14]. Since deformation-induced twinning is irreversible, a higher incidence of deformation twinning will result in almost complete irreversibility of crack growth under cyclic loading,
968
MERCER and SOBOYEJO:
CYCLIC CRACK-TIP DEFORMATION
(a)
Cd)
Paulal reversibility due to conventional slip Fig. 6. Schematic illustration showing crack extension under cyclic loading as a result of a mixed deformation mode of irreversible twinning and partially reversible slip: (a, b) crack opens during loading part of fatigue cycle, (c) crack-tip deformation due to deformation-induced twinning and conventional slip, (d) permanent crack extension upon unloading due to irreversibility of deformation-induced twinning.
i.e. greater crack extensions per cycle and hence faster fatigue crack growth rates. In contrast, the partial reversibility associated with conventional slip results in a smaller crack extension per cycle and hence, slower crack growth rates will be expected, as illustrated schematically in Fig. 6. The mechanism outlined above suggests that deformation-induced twinning may be undesirable as a crack-tip deformation mechanism during fatigue since it results in faster crack growth rates. However, the presence of a twin process zone around a crack may lead to a re-distribution of stresses over this zone, which may cause a beneficial crack-tip shielding effect in the form of a reduced stress intensity at the crack-tip. This effect is referred to as twin toughening [17-191. 4.2. Analysis of twin toughening In order
to assess whether
twin toughening
was
providing any contribution to crack-tip shielding, a micro-mechanical model was employed, which is essentially a modified version of the model proposed originally by Deve and Evans [19], uses non-linear elastic fracture mechanics techniques developed originally by Budiansky, Hutchinson and Lambro-
poulus [26]. Deve and Evans [19] have shown that the twin toughening ratio can be derived by considering the energy dissipation, AG,,, within the twin process zone (TPZ) of width h. However, this model assumes a cut-off value, ho, within the process zone. This is done to avoid the problems associated with AG,, -+ - co as h + 0, where h is the height of the process zone. The choice of ha is therefore somewhat arbitrary, and can be equated to the crack-tip opening displacement, (6 = K2/2Ecr,), as in a recent paper by Soboyejo and Mercer [14]. In order to eliminate the problem of a cut-off value, a modified analysis is presented here, which assumes that the average/smeared stress distribution across the process zone is comparable to the uni-axial yield sets measured in a simple tensile test. One consequence of this assumption is that the strain energy density, U, is no longer a function of the distance from the crack-face, y. The previous model by Dbve and Evans [ 191 yielded:
s h
AG,, = 2
0
WY) dv.
(1)
MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION But this can now be written as: AG,,=2
equation (10) by K. gives the following expression for 1, the twin toughening ratio:
hUdy s0
(2)
since U is assumed to be constant across the process zone around the crack. If U is equated to the area under the uni-axial stress-strain curve, equation (3) becomes: AG,, = 2 h oh s0
dy
(3)
Now, assuming piece wise linear elastic and linear strain hardening behavior in the TPZ, equation (4) can be written as: AG,, = 2
h {[(a + a,)/21(t - cv) + arty} dy s0
(4)
considering both the elastic and plastic portions of the stress-strain curve. Substituting for the strain terms in equation (5) gives: A& = 0h((0 + a,)[(~ - a,)lHl + (a:lE)} dv (5) j where H is the strain-hardening coefficient and E is the Young’s modulus. Re-arranging equation (6) yields: AG,, =
* [(d/H) - o;(l/H s0
- l/E)] dy.
(6)
However, the average/smeared stress in the plastic wake around the crack is assumed to be comparable to the yield stress, 0 = c(cr,, where c( is a stress-state parameter which will be discussed later. Substitution for 0 into equation (6) therefore gives: AG,, = Integration
’ [(c&:/H) - $(1/H I0
- l/E)] dy.
(7)
of equation (7) yields:
AG,, = {u’c+H - o;(l/H
- l/E)}h.
(8)
Now J, the total strain energy release rate, is given by: J = Pm/E = g/E
969
+ AG,,
(9)
where Km is the steady-state toughness and K. is the intrinsic ‘matrix’ toughness with no twinning present (which was assumed to be lowest matrix initiation toughness value measured experimentally). So, re-arranging and solving for K, yields: K, = J
(10)
where the parameter V, has been included, which is the average volume fraction of grains containing deformation-induced twins within the TPZ. Dividing
1= K,IKo = J(l
+ V,EAG,,/z).
(11)
The above equations were used to assess the role of crack-tip shielding under cyclic loading. Note that K and K. can be replaced respectively by AK and AK,, under cyclic loading. Also, the values of h that were employed were those determined by careful analysis of optical interference micrographs. The volume fraction of grains containing deformation-induced grains, V,, was determined from TEM observation of the crack-tip regions. Calculations of AG,, and 1, were performed for all of the binary and ternary gamma alloys examined in this study. These values are presented in Table 2 along with the corresponding values of fracture toughness, Kr,, and fatigue thresholds, AK,,,, for each alloy. Values of the volume fraction of twinned grains, V, and the TPZ width, h, are also included in Table 2. The values obtained for 1, show that the contribution to crack-tip shielding from twin toughening varies quite considerably between these alloys. The forged binary alloy had a very low twin toughening ratio of 1.10, thus implying that although the crack-tip deformation occurs primarily by twinning, i.e. a high volume fraction of twinned grains were observed in the TEM (Table 2), only a small twin toughening effect is observed in this alloy. It is due largely to the small twin process zone width that was observed in this alloy. The i, values are somewhat higher for the extruded binary, manganese-containing and tungsten-containing alloys (1.66, 1.32 and 1.44, respectively), which suggests a higher crack-tip shielding effect due to twinning. Higher values of TPZ width, h, and also large V, values are considered to be the major contributory factors to the higher i, values. However, the alloy containing 1.5% Cr gave the greatest crack-tip shielding effect, with a twin toughening ratio of 2.14. It would appear that the relatively high fracture toughness of this alloy is partly due to a fairly high twin toughening effect, giving a 50% reduction in crack-tip stress intensity. This large twin toughening effect is considered to be mainly due to a very high TPZ width (when compared to the other alloys studied in this investigation), and also a high yield strength. The high strength observed in this alloy is typical of Cr-containing gamma-based alloys [9, 151. The twin toughening ratio obtained for the material alloyed with V was only 1.12. Although the fracture toughness of this alloy was relatively high when compared to the other alloys discussed in this paper (around 12 MPaJm), the twin toughening contribution was quite small. This is considered to be due to the fact that deformation-induced twinning plays only a limited role in crack-tip deformation, deduced from the small volume fraction of twinned
970
MERCER and SOBOYEJO: CYCLIC CRACK-TIP DEFORMATION
grains observed in the TEM. Cyclic fracture in this alloy also appears to occur as a result of dislocation interactions which promote greater levels of crack-tip reversibility and possible dislocation shielding effects.
4.3. Implications It is important to discuss the implications of the combined effects of twin toughening and crack-tip deformation phenomena on fatigue crack growth. This is because the fatigue crack growth rates will depend largely on the degree of crack-tip reversibility associated with deformation-induced twinning/slip, and the reduction in the crack driving force due to twin toughening. With the exception of Ti48Al1SCr, however, the effects of kinematic irreversibility (due to increasing deformation-induced crack-tip twinning components) appear to be generally more important than the shielding effects associated with twin toughening. The fatigue crack growth rates are, therefore, slowest in the Ti-48Al-3V and Ti48A1-0.2W alloys in which crack-tip deformation occurred largely by partially reversible slip mechanisms (Fig. S(et(g)). Conversely, the fastest near-threshold crack growth rates are observed in the binary Ti48Al alloy in which crack-tip deformation occurred mainly by deformation-induced twinning (Fig. 5(h)). However, slow crack growth rates in the Ti+Al-1.5Cr alloy are attributed to the very high level of twin toughening (A, - 2.14) in this alloy (Fig. 2). The current results therefore suggest that the fatigue crack growth resistance of gamma alloys can be improved by alloying to promote crack-tip deformation by reversed plasticity. This can be achieved by ternary alloying with V or W. Under such circumstances, the fatigue crack growth rates appear to be slower due to the higher levels of slip reversibility. Improved fatigue crack growth resistance can also be obtained by alloying with Cr to promote crack-tip deformation by slip and twinning, and extremely high levels of twin toughening. Nevertheless, it is important to note that the fatigue crack growth rates in gamma alloys are typically very fast, when compared to those in existing structural alloys. This is true even when the crack growth-rates in the gamma alloys are reduced by ternary alloying with V, W or Cr. It may, therefore, be necessary to base future fatigue life assessment procedures on fatigue threshold levels (Table 2). Microstructural control to obtain nearly/ fully lamellar structures may also be used to improve the fatigue thresholds and crack growth resistance, as shown in recent studies by Rao et al. [12]. However, fatigue threshold-based designs may impose severe penalties on the (potential) use of gamma alloys, and alternative probabilistic mechanics techniques may be required to determine the levels of risk that can be tolerated in specific applications.
5. CONCLUSIONS (1) Small ternary additions of Mn, Cr, V and W have a noticeable effect on the fatigue behavior of TiAl-based alloys. Cr, V and W additions appear to promote slower crack growth rates, and all four alloying elements are associated with higher fatigue thresholds than those of the binary gamma Ti48Al alloys. (2) Crack-tip deformation in Ti48Al-2Mn occurs by a combination of twinning and slip. This leads to faster fatigue crack growth rates due to the kinematic irreversibility associated with deformation-induced twinning. A mixed crack-tip deformation mode, involving deformation-induced twinning and slip, is also observed in the Ti48Al-1SCr alloy. In contrast, small additions of V result in crack-tip deformation predominantly by conventional slip mechanisms, while micro-alloying with tungsten appears to promote stacking fault formation during cyclic deformation by slip of Shockley partial dislocations. (3) In general, gamma-based alloys that exhibit higher levels of deformation-induced twinning and low/moderate levels of twin toughening during cyclic deformation will have faster fatigue crack growth rates due to the kinematic irreversibility of the twinning process. Conversely, a crack-tip deformation mode that involves partially reversible slip, will result in slower fatigue crack growth rates. High levels of deformation-induced twinning and twin toughening are also associated with slower crack growth rates. (4) The twin toughening/crack-tip shielding contributions for the alloys studied ranged between 1.10 and 2.14. Alloying with chromium was found to give the greatest crack-tip shielding effect. The modified twin toughening model presented in this paper shows that high twin toughening ratios are dependent on parameters such as a large twin process zone size, high strength and a high volume fraction of grains exhibiting deformation-induced twinning in the crack-tip region. Acknowledgements-The
authors are grateful to The Ohio State University and The Division of Materials Research of The National Science Foundation (NSF) for financial support. Appreciation is also extended to Dr Bruce MacDonald, the Program Monitor at NSF, for his encouragement and support of the research. The authors are grateful to MS Yingfang Ni for assistance with the preparation of the manuscript. REFERENCES 1. Y.-W. Kim and D. M. Dimiduk, J. Metal 43,40 (1991). 2. T. S. Srivatsan, W. 0. Soboyejo and M. Strangwood, EFM 52, 107 (1995). 3. W. 0. Soboyejo, J. E. Deffeyes and P. B. Aswath, Muter. Sci. Engng A138, 95 (1991). 4. G. Henaff, B. Bittar, C. Mabru, J. Petit and P. Bowen, Mater. Sci. Engng A (submitted). 5. A. W.‘James and P. Bowen, In Proc. 7th World Conf. on Titanium, San Diego, CA (1992) The Minerals, Metals and Materials Society.
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and SOBOYEJO:
CYCLIC
6. D. L. Davidson and J. B. Campbell, Metall. Trans. 24A, 1555 (1993). K. T. Vekateswara-Rao, S. M. L. 7. W. 0. Soboyejo. Sastry and R. 0. Ritchie, Metall. Trans. 24A, 585 (1993). Y. Mutoh, K. Hayashi 8. R. Gnanamoorthy, and Y. Mizuhara, Scripta metall. mater. 33, 907 (1995). 9. W. 0. Soboyejo, Proc. 7th World Conf: on Titanium, San Diego, CA (1992) The Minerals, Metals and Materials Society. 10. W. 0. Soboyejo, D. S. Schwartz and S. M. L. Sastry, Metall. Trans. 23A, 2039 (1992). 11. K. S. Chan and Y.-W. Kim, Metall. Trans. 23A, 1663 (1992). 12. K. T. V. Rao and R. 0. Ritchie, Mater. Sci. Engng A153, 479 (1992). 13. C. Mercer and W. 0. Soboyejo, Symp. Fatigue and Fracture of Ordered Intermetallics (edited by W. 0. Soboyejo, T. S. Srivatsan and D. L. Davidson). TMS, Warrendale, PA (1993). 14. W. 0. Soboyejo and C. Mercer, Scripta metall. mater. 30, 1515 (1994).
CRACK-TIP
DEFORMATION
971
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