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Fatigue threshold and crack propagation in γ-TiAl sheets
Intermetallics 9 (2001) 89±96
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Fatigue threshold and crack propagation in g-TiAl sheets R. Pippan a,*, P. Hageneder b, W. Knabl c, H. Clemens d, T. Hebesberger a, B. Tabernig a a
Erich Schmid Institut fuÈr Materialwissenschaft der OÈsterreichischen Akademie der Wissenschaften, 8700 Leoben, Austria b Institut fuÈr Metallphysik, MontanuniversitaÈt Leoben, Austria c Plansee AG, Reutte, Austria d Institut fuÈr Metallkunde, UniversitaÈt Stuttgart, Germany Received 2 May 2000; received in revised form 24 August 2000; accepted 24 August 2000
Abstract The fatigue crack propagation behaviour of two dierent microstructures Ð a coarse-grained designed fully lamellar (DFL), and a ®ne-grained near g (FG) Ð of a Ti±46.5 at.% Al±4 at.% (Cr, Nb, Ta, B) alloy was studied. Both the threshold of stress intensity range and standard long crack growth behavior were determined. A special technique was applied to separate the dierent mechanisms Ð intrinsic and extrinsic eects Ð and their changes with crack length. The fatigue crack propagation rate of long cracks is much smaller in the DFL microstructure than in the FG microstructure at the same stress intensity range. The eective p threshold of stress intensity range of both microstructures is about 1.7 MPa m. The threshold of stress intensity range shows a strong R-curve behavior. In other words the propagation±non-propagation conditions of cracks are signi®cantly in¯uenced by the crack extension. The long crack thresholds of stress intensity range at the stress ratio 0.1 are relatively large; they are about 4.5 and p 8 MPa m in the DFL and the FG microstructure, respectively. The dierences in the crack growth behavior between the two microstructures are mainly induced by extrinsic resistance mechanisms. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Titanium aluminides based on TiAl; B. Fatigue resistance and crack growth
1. Introduction Titanium aluminide alloys based on g-TiAl are of considerable interest as advanced high temperature structural materials. Their structural applications demand a certain reliability and damage tolerance. In recent years the fatigue and fracture behavior of g-TiAl alloys have been studied extensively (see, for example [1±10]). The fracture toughness and the fatigue crack propagation behavior of long cracks are well established. However, there are many problems in the case of short cracks and in the transition from short to the long crack behavior for both static and fatigue loading. Therefore, useful data and design tools for a damage tolerant description in these regimes are required. In this study a new technique is applied to determine the threshold of stress intensity range for extrinsically * Corresponding author. Tel.: +43-3842-455-110; fax: +43-3842455-1216. E-mail address: [email protected] (R. Pippan).
short cracks. Two microstructures, a coarse-grained fully lamellar and a ®ne-grained near g-microstructure, have been investigated. The reason for the dierent behavior and the consequences for the application of data are discussed. 2. Material The nominal composition for the studied sheet material is Ti±46.5 at.% Al±4 at.% (Cr, Nb, Ta, B). Two dierent heat treatments were performed to obtain a ®ne-grained primary annealed (FG) and a designed fully lamellar microstructure (DFL). The FG microstructure shown in Fig. 1a predominantly consists of equiaxed g grains with a small amount of a2 phases at the grain boundaries and the triple points. The average grain size varies between 15 and 20 mm. The DFL microstructure (Fig. 1b) consists of colonies of parallel g-TiAl and a2-Ti3Al laths with a colony size of about 200 mm. More details about the fabrication of the sheets, the
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Fig. 1. Scanning electron micrographs of the ®ne-grained near g (FG) (a) and the designed fully lamellar microstructure (DFL) (b) of the sheet surfaces, the rolling direction is vertical, (c) and (d) are the micrographs from the corresponding cross-section.
microstructure and the creep and fatigue properties are given in [11±13] and [14], respectively. 3. General remarks At ®rst, it is appropriate to de®ne few terms regarding crack propagation resistance and short crack problems. 3.1. Extrinsic and intrinsic fatigue resistance Microstructures, temperature and environment signi®cantly aect the fatigue crack propagation behavior, especially near the threshold of stress intensity range. A vast amount of mechanisms are responsible for this eect. It is very helpful to divide the dierent mechanisms into classes. Here we will follow the classi®cation of Ritchie [15], which is schematically depicted in Fig. 2a. The ®rst class is that of the intrinsic mechanisms, which determine the inherent resistance of a material against fatigue crack propagation. In ductile metals the plastic blunting of the crack tip during loading (where a certain amount of cracking can be involved) which produces the new fracture surfaces and the resharpening of the crack tip during unloading is the intrinsic growth mechanism. In ceramics, fatigue crack propagation is caused predominately by a degradation of crack tip shielding [16±18], whereas the intrinsic mechanism is a
cleavage process. In g-TiAl the intrinsic mechanism may be induced by plastic blunting and re-sharpening in combination with a cleavage crack propagation process. The second class is that of the extrinsic mechanisms which cause a local reduction in the crack driving force at the crack tip. For this reason they are often called shielding mechanisms. The most important extrinsic mechanisms in the case of fatigue crack property which may play a signi®cant role in intermetallics are: geometrical shielding (crack de¯ection and crack branching), contact shielding (plasticity, roughness and corrosion debris induced closure, and crack bridging) and zone shielding (microcracks, and eects which are induced from the mismatch of the dierent phases). 3.2. The short crack behavior The basic problem with the short crack behavior is that the similitude concept of fracture mechanics Ð cracks with the same stress intensity range, K, will propagate with the same rate Ð does not hold. They grow at K-values below that of the threshold of stress intensity range determined in a standard crack growth test in this case called the threshold of long cracks, and they grow at the same K faster than long cracks (da=dN vs. K curve determined in a standard test). Hence, the estimation of the fatigue limit or the prediction
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Fig. 2. Representation of the dierent mechanisms which contribute to the fatigue crack growth resistance (i.e. the necessary K to cause a certain crack propagation rate, da=dN). In the case of da=dN 0, it corresponds to the threshold of stress intensity range and the dierent contribution to threshold (a) and the change of the dierent contributions of the resistance as a function of the crack extension (b).
of life time of components which contain a small ¯aw based on long crack data is non-conservative. In order to classify the observations and to identify the applicability of concepts it is helpful to divide the dierent types of short cracks into groups: microstructurally, mechanically, chemically and extrinsically short cracks [17,18]. Microstructurally short cracks are smaller than the characteristic length scale of the microstructure. In the ®ne-grained microstructure the characteristic length corresponds to the grain size; and in the designed fully lamellar microstructure it depends on the propagation mode. In the case of a ``interlamellar'' propagation (i.e. transcrystalline mode within a certain lamellae or intercrystalline mode at the phase or domain boundary of a lamellae) the characteristic length is the colony size and in the case of a translamellar fracture mode it is the lamellar spacing. At mechanically short cracks the plastic zone is no longer within the K dominated stress ®eld. Therefore, the linear elastic fracture mechanics relation between stress intensity factor and the plastic deformation of the crack tip breaks down. Most extrinsic mechanisms act in the wake of the crack tip. Cracks smaller than a certain value cannot build up the full shielding. They are called extrinsically small cracks (often designated as physically small cracks [17,18]). Such build-up of crack tip shielding induces an increase of the crack propagation resistance (usually called R-curve behavior). Ligament bridging is one of the best known mechanisms in TiAl alloys which induces such an R-curve behavior of toughness (see, for example [1,6,8]). In fatigue, this build-up of shielding should cause a behavior of the propagation resistance as schematically depicted in Fig. 2b.
4. Experimental method The basic idea of the applied technique is, to start the fatigue crack growth experiment on precracked specimens with a minimum contribution of crack tip shielding. The loading procedure, the resulting crack extension and the obtained data are schematically shown in Fig. 3 and a typical result is depicted in Fig. 4. The standard fracture mechanics specimen is pre-cracked in cyclic compression. The advantage of pre-cracking specimens in cyclic compression is that the crack closure load at the beginning of the real crack growth test is below zero (i.e. the crack closes only under a certain amount of compression load). Since the pre-crack is not perfectly plane, a certain amount of crack tip shielding induced by crack de¯ection or crack bridging cannot be avoided. In order to minimize this eect and to diminish the eects of prefatigue, we used very short pre-cracks (lengths between 10±50 mm) produced by small load amplitudes on specimens with very sharp notches (root radius about 10 mm) which were machined by a razor blade polishing technique [19]. An example of a typical notch and precrack is depicted in Fig. 5. In order to determine the threshold of stress intensity range and the long crack propagation behavior, the experiment is performed at constant load ratio by increasing the load amplitude in steps until the threshold value for a long crack is reached. If the load amplitude corresponds to a stress intensity range, K, which is smaller than a certain critical value, the crack will not propagate. In the case of the FG sheet material depicted p in Fig. 4 this occurred for K < 1:6 MPa m. If crack tip shielding of the pre-crack can be ignored, this procedure allows to determine an upper and a lower limit
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Fig. 3. Schematic illustration of the stepwise increasing load amplitude test [(a) and (b), load and crack extension vs. number of load cycles, respectively] and the resulting data [(c) crack growth curve and (d) R-curve for the threshold].
for the intrinsic threshold, Ki th. If only crack closure at the beginning of the test can be ignored and other shielding contributions are not changed during further crack extension, this permits to determine the eective threshold of stress intensity range Keff th. As long as the load amplitude corresponds to a K smaller than the long crack threshold of stress intensity range, Ki th, the crack starts to propagate and stops after a certain extension. The reduction of the growth rate until the crack stops propagation is caused by the increase of the eect of crack tip shielding. Finally, there is a step where the crack does not stop. From there on the test can be continued to measure the conventional da=dN vs K curve. The stress intensity factor range where the crack stops for the last time and the K value where the crack does not stop growing, provides an upper and lower bound for the long crack threshold of stress intensity range. In the depicted case of Fig. 4 of thepFG microstructure, Kth lies between 4.3 and 4.7 MPa m. In addition, a plot of the extension of the crack where it stops growing versus the corresponding K gives the Rcurve for the threshold of stress intensity range, which under certain circumstances can be used as the R-curve for static loading [20±23]. The fatigue crack growth experiments were performed on single edge notch tension (SENT)-specimens in LT and TL orientation with a width of 20 mm, thickness 1 mm, notch depth of about 5 mm, at room temperature and in laboratory air. The test frequency was about 100 Hz and the stress ratio R Kmin =Kmax 0:1. In the DFL-microstructure an additional test was also performed at R 0:5. The crack length was monitored by a DC-potential drop-technique. The accuracy to measure a change in crack length was about 1 mm.
Fig. 4. Typical measured crack extension with the potential drop technique in a stepwise increasing load amplitude test of a FG microstructure at K values below the long crack threshold stress intensity range.
Fig. 5. Optical micrograph of typical used notch and pre-crack.
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5. Results Figs. 6 and 7 summarize the measured R-curves for the threshold of stress intensity range Ð i.e. the stress intensity factor range where the crack stops propagation versus the corresponding crack extension Ð and the long crack growth behavior, respectively. Specimens machined from both directions Ð loading axis in the rolling direction (LT) and perpendicular to the rolling direction (TL), were investigated. The results indicate:
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. no signi®cant in¯uence of the loading direction was observed, . the threshold of both microstructures exhibit a strong R-curve eect, . the long crack threshold as well as the growth behavior of the long cracks is signi®cantly in¯uenced by the microstructure, Kth is about 4.5 and p 8 MPa m in the FG and the DFL microstructure, respectively, . in both microstructures the stress intensity range where the ®rst propagation of the p crack is observed, is very similar, about 1. 7 MPa m, . the stress ratio in¯uences signi®cantly both Kth and the da=dN vs K curve. 6. Discussion
Fig. 6. Stress intensity range vs. crack extension where the crack stops the propagation for both microstructures, (a) FG and (b) DFL microstructure in LT and TL orientation. These curves can be denoted as R-curve for the threshold of stress intensity range.
Fig. 7. Summary of the measured crack growth rates vs. K for both microstructures, FG and DFL, in the LT and TL direction. The arrow marks the last K level where a stopping of the crack was observed.
Fig. 8 shows the scanning electron microscope (SEM) image of the fracture surface of the pre-crack and the fracture surface produced during the ®rst few steps of the fatigue crack growth experiment with increasing load amplitude. The crack morphology of the pre-crack induced by cyclic compression and those produced in tension is very similar. Only in few regions along the crack front one can distinguish between the two fracture surfaces. The typical crack de¯ection angle on the microscale of the pre-crack and the ensuing fracture surface is comparable. Only the mean deviations from the macroscopic crack plane increases with the extension of crack. Hence, in the stepwise increasing load amplitude experiment the shielding induced by crack de¯ection should not signi®cantly change with crack extension. Since the length of the pre-crack was typically about 20 mm, the shielding contribution induced by crack bridging should be relatively small. The ®rst propagation of the crack should take place when the stress intensity range is larger than the intrinsic threshold plus a certain contribution of crack tip shielding induced by crack de¯ection. Therefore, it should be a measure for the eective threshold. In all fatigue crack propagation experiments, no extension of the p crack was observed at K values smaller than 1.4 MPa m. Or more exactly, if any crack extension occurred, it was below the detection limit of 1 mm. The ®rst extension of 2 or 3 mm was p measured at K values between 1.5±1.9 MPa m. This value is not signi®cantly in¯uenced by the microstructure, the loading direction and the stress ratio. Only two exceptions in the DFL microstructure were observed, where pthe ®rst propagation was determined at about 2.3 MPa m. (If we look to the more detailed plot in Fig. 10 it seems that this is only a problem of the detection limit.) The scatter of the extension of the crack where it stops the propagation is relatively large at K values p smaller than 3 MPa m. No signi®cant eect of the
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microstructure orp the loading direction can be observed. At K 3 MPa m, the crack stops the propagation after an extension between 5 and 20 mm. This is larger than the lamellar spacing and about equal to the grain size in the FG microstructure. In principle, it may be possible that the crack propagates only in few grains or few lamellae along the crack front. Since the pre-crack is relatively straight this may be the case at very short crack extensions of 1 or 2 mm. At larger extensions the crack should propagate along the whole crack front (not necessary over the same distance) because the typical structural features on the fracture surfaces are in the order of 1 or 2 microns. Despite the scatter in the stress intensity necessary for the ®rst propagation, the scatter p of the crack extension at K smaller than 3 MPa m, the possible variation of the crack extension along the
crack front (variation of propagation±non-propagation condition along the crack front) and some uncertainties which extrinsic mechanism acts at the beginning of the stepwise increasing load amplitude test, the trend in Fig. 9 suggests an eective threshold of about 1.7 for both microstructures. p At K larger than 3 MPa m or the crack extensions larger than 20 mm the behavior changes. The microstructure signi®cantly in¯uences both the R-curve for the threshold and the long crack fatigue crack propagation behavior. In the stepwise increasing load amplitude experiment in the DFL microstructure, the crack propagation stops after a certain extension till K reaches the long crack threshold value of about 8 and 4.5 p MPa m at R=0.1 and 0.5, respectively. The long crack threshold is reached after an extension of about 0.4 mm
Fig. 9. Stress intensity range vs. crack extension where the crack stops the propagation in the FG and DFL microstructure for K smaller p than 3 MPa m (detail of Fig. 6).
Fig. 8. SEM-fractographs of the fatigue fracture surface in the vicinity of the notch root. Material with the DFL (a) and in the FG microstructure (b).
Fig. 10. Change of crack length measured with a potential drop technique during the change of the load amplitude in a stepwise increasing load amplitude test (detail of Fig. 4). The crack length has been measured in intervals of about 40.000 cycles.
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at R=0.1 and at somewhat smaller values at R=0.5. The maximum stress intensity factor at the long crack threshold in the DFL microstructure is somewhat larger than the initiation fracture toughness, i.e. starting value of the R-curve for the fracture toughness (see, for p example, [23]), which is typically about 7 MPa m in both microstructures. In the FG microstructure, the opposite behavior is observed; the maximum stress intensity factor at the long crack threshold is somewhat smaller than the initiation fracture toughness. The rising of the R-curve for the threshold is much smaller in the FG microstructure than in the DFL microstructure, and the extension of the crack where the long crack threshold is reached in the FG microstructure is somewhat smaller than in the DFL microstructure. Why p is the eect of microstructure small below K 3 MPa p m and large above? At K smaller than 3 MPa m, the crack propagates only over a distance of about 10 mm, which is about 10 times the lamellar spacing and about equal to the grain size of the FG microstructure. A comparison of the topography of the fracture surface on the level of few micrometers (see Fig. 8) shows that the characteristic length of the fracture facets is in the order of 1 mm for both microstructures. However, on a level of few hundred micrometers, the fracture surfaces exhibit signi®cant dierences between the two microstructures which may be responsible for this eect. This is similar to the R-curve for the fracture toughness, where the initial toughness and the R-curve in the ®rst few microns is very similar. Possible mechanisms for the explanation of the steep rising R-curve of the threshold at the beginning are: . building up of a plasticity induced crack closure, . building up of roughness induced crack closure by ``nano roughness on the fracture facets' and contacts on dierent facets, . formation of a cloud of nanocracks in the vicinity of the main crack, or the formation of nanobridges as observed in dierent in situ transmission electron microscope studies [13,24]. At crack extensions larger than 10 mm, the increase of the eect of crack closure, crack bridging and a (possible) small amount of crack shielding induced by de¯ection and crack branching is then signi®cantly in¯uenced by the dierence in the microstructure. In the FG microstructure, this additional shielding contribution at the long crack threshold Ð which is reached after an extensionpof about 0.2 mm Ð is relatively small about p 1.5 MPa m compared to 5 MPa m in the DFL microstructure. The question whether a certain mechanism is responsible for the dierence in the crack propagation behavior at larger crack extension, can not be solved with this experiment, because it is only possible to measure the change of crack growth resistance, but not the change of each contribution to the resistance.
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From the change of the crack extension in Fig. 4, one would suggest that a simple static fracture process takes place after the increasing of the load amplitude. A more detailed plot of the crack extension versus the number of cycles in Fig. 10 shows that the crack propagation is really a fatigue process; only the growth rate is relatively large after the increase of the load amplitude. Furthermore, one can see that the large growth rate drops very quickly to zero. The comparison of R=0.1 and 0.5 crack growth results shows a further interesting behavior. One can see that Kmax at the threshold is about equal. This may be explained by a Kmax controlled crack growth mechanism or a very large crack closure stress intensity range which is not in¯uenced by Kmax. However, the crack propagation curves da=dN vs. Kmax do not coincide (see Fig. 11), which indicates that it is not a (pure) Kmax controlled crack growth process. In order to test the applicability of the R-curve concept, a fatigue test on a through thickness short crack was performed in the DFL microstructure. The pre-crack was initiated in the standard SENT specimen. The side faces of the specimen were then re-machined in order to obtain an initial crack length of 120 mm. Fatigue tests were carried out at a 136 and 218 MPa at a stress ratio of R 0:1, p which corresponds to an initial K 3 and 4.8 MPa m, respectively. The applied stresses are signi®cantly smaller than the yield stress and the length of the pre-crack is much larger than the characteristic microstructural length, the lamellar spacing (because the front of the crack crosses lamellae). Therefore, such a crack can be considered as an extrinsically (physically) short crack where the R-curve concept should be applicable. Both values are below the long crack threshold of this microstructure. At 136 MPa no failure occurred. The crack started to propagate with a progressively decreasing growth rate and the crack stopped the propagation after an extension of 15 mm (after about 20.00 cycles). At 218 MPa the specimen failed after 250.000 cycles. For the investigated case, the
Fig. 11. Comparison of the fatigue crack growth behavior in a da=dN vs. Kmax plot at R=0.1 and 0.5.
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p MPa m (at R=0.1) in the DFL and FG microstructures, respectively. . The in¯uence on the long crack growth behavior of the two microstructures is similar to the long crack threshold. References
Fig. 12. Representation of the application of the R-curve technique. Crack driving force vs. crack length for two load amplitudes and the R-curve for the threshold.
R-curve for the threshold of stress intensity range and the crack driving forces K as a function of the crack length for both stress amplitudes are depicted in Fig. 12 according to the R-curve concept. One can see that these coincide with the R-curve prediction. At 136 MPa the crack should stop propagation after an extension of about 10 mm, similar to the deep notched specimens, and at a larger stress amplitude the specimen should fail. 7. Conclusion The fatigue crack propagation behavior in a g-TiAl sheet alloy with dierent microstructures, a designed fully lamellar (DFL) and a ®ne-grained near g (FG) microstructure, has been investigated. A special technique has been applied to separate the dierent mechanisms which control the fatigue crack growth behavior. . Both microstructures exhibit an R-curve behavior for the threshold of stress intensity range. p . At crack extension below 10 mm (K43 MPa m) the microstructure has no signi®cant in¯uence on the R-curve for the threshold. . For larger crack extensions the R-curve is much steeper in the DFL-microstructure. . The long crack threshold value is reached after a crack extension of about 0.5 mm and is 8.5 and 4.5
[1] Chan KS, Shih DS. Metall Trans 1998;29a:73. [2] Campbell JD, Kruzic JJ, Lillibridge S, Venkateswara RaÂo KF, Ritchie RO. Scripta Materialia 1997;37:707. [3] Larsen JM, Rosenberger AH, Worth BD, Li K, Maxwell DC, Porter WJ. In: Gamma titanium aluminides 1999. TMS-Symp. Proc., 1999. p. 463. [4] Huang ZW, Bowen P. In: Gamma titanium aluminides 1999. TMS-Symp. Proc. 1999. p. 473. [5] Kruzic JJ, Campbell JP, McKelvey AL, Choe H, Ritchie RO. In: Gamma titanium aluminides 1999. TMS-Symp. Proc., 1999, p. 495. [6] Chan KS. In: Gamma titanium aluminides 1999. TMS-Symp. Proc., 1999. p. 517. [7] HeÂna G, Mabru C, Tonneau A, Petit J. In: Gamma titanium aluminides 1999. TMS-Symp. Proc. 1999. p. 549. [8] Venkateswara RaÂo KT, Odette GR, Ritchie RO. Acta Metall Mater 1994;42:893. [9] Choi C, Lee YT, Lee CS. Scripta Materialica 1997;36:821. [10] Shiota H, Tokaj K, Ohta Y. Materials Science and Engineering A243:169 [11] Clemens H, Lorich A, Eberhardt N, Glatz W, Knabl W, Kestler H. Zeitschrift fuÈr Metallkunde 1999;90:569. [12] Koeppe C, Bartels A, Clemens H, Schretter P, Glatz W. Materials Science and Engineering A201:181 [13] Appel F, Wagner R. Materials Science and Engineering 1998;R22:186. [14] Chatterjee A, Bauer H, Appel F, Bartels A, Knabl W, Kestler H, Clemens H. In: Gamma titanium aluminides 1999. TMS-Symp. Proc., 1999, p. 401. [15] Ritchie RO. Materials Science and Engineering 1998;103:15. [16] Lawn B. Fracture of brittle solids, Cambridge University Press, 1993. [17] Suresh S. Fatigue of materials, Cambridge University Press, 1998. [18] Suresh S, Ritchie RO. International Metals Reviews 1984;29:445. [19] Damani RJ, Schuster C, Danzer R. Scienti®c report, University of Leoben, 1996. [20] Tabernig B, Pippan R, Powell P. In Fatigue crack growth thresholds, endurance limits and design, STP 1372. ASTM, 2000, p. 90. [21] Pippan R, PloÈchl L, Klanner F, StuÈwe HP. Journal of Testing and Evaluation 1994;22:98. [22] Tanaka K, Akinawa Y. Engineering Fracture Mechanics 1988;30:863. [23] Hebesberger T, Semprimoschnig COA, Pippan R, Kolednik O, Clemens H. In Gamma titanium aluminides 1999. TMS-Symp. Proc., 1999. p. 573. [24] Mao X, Qiao L, Li X. Scripta Materialia 1998;39:519.
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Fatigue threshold and crack propagation in g-TiAl sheets R. Pippan a,*, P. Hageneder b, W. Knabl c, H. Clemens d, T. Hebesberger a, B. Tabernig a a
Erich Schmid Institut fuÈr Materialwissenschaft der OÈsterreichischen Akademie der Wissenschaften, 8700 Leoben, Austria b Institut fuÈr Metallphysik, MontanuniversitaÈt Leoben, Austria c Plansee AG, Reutte, Austria d Institut fuÈr Metallkunde, UniversitaÈt Stuttgart, Germany Received 2 May 2000; received in revised form 24 August 2000; accepted 24 August 2000
Abstract The fatigue crack propagation behaviour of two dierent microstructures Ð a coarse-grained designed fully lamellar (DFL), and a ®ne-grained near g (FG) Ð of a Ti±46.5 at.% Al±4 at.% (Cr, Nb, Ta, B) alloy was studied. Both the threshold of stress intensity range and standard long crack growth behavior were determined. A special technique was applied to separate the dierent mechanisms Ð intrinsic and extrinsic eects Ð and their changes with crack length. The fatigue crack propagation rate of long cracks is much smaller in the DFL microstructure than in the FG microstructure at the same stress intensity range. The eective p threshold of stress intensity range of both microstructures is about 1.7 MPa m. The threshold of stress intensity range shows a strong R-curve behavior. In other words the propagation±non-propagation conditions of cracks are signi®cantly in¯uenced by the crack extension. The long crack thresholds of stress intensity range at the stress ratio 0.1 are relatively large; they are about 4.5 and p 8 MPa m in the DFL and the FG microstructure, respectively. The dierences in the crack growth behavior between the two microstructures are mainly induced by extrinsic resistance mechanisms. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Titanium aluminides based on TiAl; B. Fatigue resistance and crack growth
1. Introduction Titanium aluminide alloys based on g-TiAl are of considerable interest as advanced high temperature structural materials. Their structural applications demand a certain reliability and damage tolerance. In recent years the fatigue and fracture behavior of g-TiAl alloys have been studied extensively (see, for example [1±10]). The fracture toughness and the fatigue crack propagation behavior of long cracks are well established. However, there are many problems in the case of short cracks and in the transition from short to the long crack behavior for both static and fatigue loading. Therefore, useful data and design tools for a damage tolerant description in these regimes are required. In this study a new technique is applied to determine the threshold of stress intensity range for extrinsically * Corresponding author. Tel.: +43-3842-455-110; fax: +43-3842455-1216. E-mail address: [email protected] (R. Pippan).
short cracks. Two microstructures, a coarse-grained fully lamellar and a ®ne-grained near g-microstructure, have been investigated. The reason for the dierent behavior and the consequences for the application of data are discussed. 2. Material The nominal composition for the studied sheet material is Ti±46.5 at.% Al±4 at.% (Cr, Nb, Ta, B). Two dierent heat treatments were performed to obtain a ®ne-grained primary annealed (FG) and a designed fully lamellar microstructure (DFL). The FG microstructure shown in Fig. 1a predominantly consists of equiaxed g grains with a small amount of a2 phases at the grain boundaries and the triple points. The average grain size varies between 15 and 20 mm. The DFL microstructure (Fig. 1b) consists of colonies of parallel g-TiAl and a2-Ti3Al laths with a colony size of about 200 mm. More details about the fabrication of the sheets, the
0966-9795/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(00)00111-4
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Fig. 1. Scanning electron micrographs of the ®ne-grained near g (FG) (a) and the designed fully lamellar microstructure (DFL) (b) of the sheet surfaces, the rolling direction is vertical, (c) and (d) are the micrographs from the corresponding cross-section.
microstructure and the creep and fatigue properties are given in [11±13] and [14], respectively. 3. General remarks At ®rst, it is appropriate to de®ne few terms regarding crack propagation resistance and short crack problems. 3.1. Extrinsic and intrinsic fatigue resistance Microstructures, temperature and environment signi®cantly aect the fatigue crack propagation behavior, especially near the threshold of stress intensity range. A vast amount of mechanisms are responsible for this eect. It is very helpful to divide the dierent mechanisms into classes. Here we will follow the classi®cation of Ritchie [15], which is schematically depicted in Fig. 2a. The ®rst class is that of the intrinsic mechanisms, which determine the inherent resistance of a material against fatigue crack propagation. In ductile metals the plastic blunting of the crack tip during loading (where a certain amount of cracking can be involved) which produces the new fracture surfaces and the resharpening of the crack tip during unloading is the intrinsic growth mechanism. In ceramics, fatigue crack propagation is caused predominately by a degradation of crack tip shielding [16±18], whereas the intrinsic mechanism is a
cleavage process. In g-TiAl the intrinsic mechanism may be induced by plastic blunting and re-sharpening in combination with a cleavage crack propagation process. The second class is that of the extrinsic mechanisms which cause a local reduction in the crack driving force at the crack tip. For this reason they are often called shielding mechanisms. The most important extrinsic mechanisms in the case of fatigue crack property which may play a signi®cant role in intermetallics are: geometrical shielding (crack de¯ection and crack branching), contact shielding (plasticity, roughness and corrosion debris induced closure, and crack bridging) and zone shielding (microcracks, and eects which are induced from the mismatch of the dierent phases). 3.2. The short crack behavior The basic problem with the short crack behavior is that the similitude concept of fracture mechanics Ð cracks with the same stress intensity range, K, will propagate with the same rate Ð does not hold. They grow at K-values below that of the threshold of stress intensity range determined in a standard crack growth test in this case called the threshold of long cracks, and they grow at the same K faster than long cracks (da=dN vs. K curve determined in a standard test). Hence, the estimation of the fatigue limit or the prediction
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Fig. 2. Representation of the dierent mechanisms which contribute to the fatigue crack growth resistance (i.e. the necessary K to cause a certain crack propagation rate, da=dN). In the case of da=dN 0, it corresponds to the threshold of stress intensity range and the dierent contribution to threshold (a) and the change of the dierent contributions of the resistance as a function of the crack extension (b).
of life time of components which contain a small ¯aw based on long crack data is non-conservative. In order to classify the observations and to identify the applicability of concepts it is helpful to divide the dierent types of short cracks into groups: microstructurally, mechanically, chemically and extrinsically short cracks [17,18]. Microstructurally short cracks are smaller than the characteristic length scale of the microstructure. In the ®ne-grained microstructure the characteristic length corresponds to the grain size; and in the designed fully lamellar microstructure it depends on the propagation mode. In the case of a ``interlamellar'' propagation (i.e. transcrystalline mode within a certain lamellae or intercrystalline mode at the phase or domain boundary of a lamellae) the characteristic length is the colony size and in the case of a translamellar fracture mode it is the lamellar spacing. At mechanically short cracks the plastic zone is no longer within the K dominated stress ®eld. Therefore, the linear elastic fracture mechanics relation between stress intensity factor and the plastic deformation of the crack tip breaks down. Most extrinsic mechanisms act in the wake of the crack tip. Cracks smaller than a certain value cannot build up the full shielding. They are called extrinsically small cracks (often designated as physically small cracks [17,18]). Such build-up of crack tip shielding induces an increase of the crack propagation resistance (usually called R-curve behavior). Ligament bridging is one of the best known mechanisms in TiAl alloys which induces such an R-curve behavior of toughness (see, for example [1,6,8]). In fatigue, this build-up of shielding should cause a behavior of the propagation resistance as schematically depicted in Fig. 2b.
4. Experimental method The basic idea of the applied technique is, to start the fatigue crack growth experiment on precracked specimens with a minimum contribution of crack tip shielding. The loading procedure, the resulting crack extension and the obtained data are schematically shown in Fig. 3 and a typical result is depicted in Fig. 4. The standard fracture mechanics specimen is pre-cracked in cyclic compression. The advantage of pre-cracking specimens in cyclic compression is that the crack closure load at the beginning of the real crack growth test is below zero (i.e. the crack closes only under a certain amount of compression load). Since the pre-crack is not perfectly plane, a certain amount of crack tip shielding induced by crack de¯ection or crack bridging cannot be avoided. In order to minimize this eect and to diminish the eects of prefatigue, we used very short pre-cracks (lengths between 10±50 mm) produced by small load amplitudes on specimens with very sharp notches (root radius about 10 mm) which were machined by a razor blade polishing technique [19]. An example of a typical notch and precrack is depicted in Fig. 5. In order to determine the threshold of stress intensity range and the long crack propagation behavior, the experiment is performed at constant load ratio by increasing the load amplitude in steps until the threshold value for a long crack is reached. If the load amplitude corresponds to a stress intensity range, K, which is smaller than a certain critical value, the crack will not propagate. In the case of the FG sheet material depicted p in Fig. 4 this occurred for K < 1:6 MPa m. If crack tip shielding of the pre-crack can be ignored, this procedure allows to determine an upper and a lower limit
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Fig. 3. Schematic illustration of the stepwise increasing load amplitude test [(a) and (b), load and crack extension vs. number of load cycles, respectively] and the resulting data [(c) crack growth curve and (d) R-curve for the threshold].
for the intrinsic threshold, Ki th. If only crack closure at the beginning of the test can be ignored and other shielding contributions are not changed during further crack extension, this permits to determine the eective threshold of stress intensity range Keff th. As long as the load amplitude corresponds to a K smaller than the long crack threshold of stress intensity range, Ki th, the crack starts to propagate and stops after a certain extension. The reduction of the growth rate until the crack stops propagation is caused by the increase of the eect of crack tip shielding. Finally, there is a step where the crack does not stop. From there on the test can be continued to measure the conventional da=dN vs K curve. The stress intensity factor range where the crack stops for the last time and the K value where the crack does not stop growing, provides an upper and lower bound for the long crack threshold of stress intensity range. In the depicted case of Fig. 4 of thepFG microstructure, Kth lies between 4.3 and 4.7 MPa m. In addition, a plot of the extension of the crack where it stops growing versus the corresponding K gives the Rcurve for the threshold of stress intensity range, which under certain circumstances can be used as the R-curve for static loading [20±23]. The fatigue crack growth experiments were performed on single edge notch tension (SENT)-specimens in LT and TL orientation with a width of 20 mm, thickness 1 mm, notch depth of about 5 mm, at room temperature and in laboratory air. The test frequency was about 100 Hz and the stress ratio R Kmin =Kmax 0:1. In the DFL-microstructure an additional test was also performed at R 0:5. The crack length was monitored by a DC-potential drop-technique. The accuracy to measure a change in crack length was about 1 mm.
Fig. 4. Typical measured crack extension with the potential drop technique in a stepwise increasing load amplitude test of a FG microstructure at K values below the long crack threshold stress intensity range.
Fig. 5. Optical micrograph of typical used notch and pre-crack.
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5. Results Figs. 6 and 7 summarize the measured R-curves for the threshold of stress intensity range Ð i.e. the stress intensity factor range where the crack stops propagation versus the corresponding crack extension Ð and the long crack growth behavior, respectively. Specimens machined from both directions Ð loading axis in the rolling direction (LT) and perpendicular to the rolling direction (TL), were investigated. The results indicate:
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. no signi®cant in¯uence of the loading direction was observed, . the threshold of both microstructures exhibit a strong R-curve eect, . the long crack threshold as well as the growth behavior of the long cracks is signi®cantly in¯uenced by the microstructure, Kth is about 4.5 and p 8 MPa m in the FG and the DFL microstructure, respectively, . in both microstructures the stress intensity range where the ®rst propagation of the p crack is observed, is very similar, about 1. 7 MPa m, . the stress ratio in¯uences signi®cantly both Kth and the da=dN vs K curve. 6. Discussion
Fig. 6. Stress intensity range vs. crack extension where the crack stops the propagation for both microstructures, (a) FG and (b) DFL microstructure in LT and TL orientation. These curves can be denoted as R-curve for the threshold of stress intensity range.
Fig. 7. Summary of the measured crack growth rates vs. K for both microstructures, FG and DFL, in the LT and TL direction. The arrow marks the last K level where a stopping of the crack was observed.
Fig. 8 shows the scanning electron microscope (SEM) image of the fracture surface of the pre-crack and the fracture surface produced during the ®rst few steps of the fatigue crack growth experiment with increasing load amplitude. The crack morphology of the pre-crack induced by cyclic compression and those produced in tension is very similar. Only in few regions along the crack front one can distinguish between the two fracture surfaces. The typical crack de¯ection angle on the microscale of the pre-crack and the ensuing fracture surface is comparable. Only the mean deviations from the macroscopic crack plane increases with the extension of crack. Hence, in the stepwise increasing load amplitude experiment the shielding induced by crack de¯ection should not signi®cantly change with crack extension. Since the length of the pre-crack was typically about 20 mm, the shielding contribution induced by crack bridging should be relatively small. The ®rst propagation of the crack should take place when the stress intensity range is larger than the intrinsic threshold plus a certain contribution of crack tip shielding induced by crack de¯ection. Therefore, it should be a measure for the eective threshold. In all fatigue crack propagation experiments, no extension of the p crack was observed at K values smaller than 1.4 MPa m. Or more exactly, if any crack extension occurred, it was below the detection limit of 1 mm. The ®rst extension of 2 or 3 mm was p measured at K values between 1.5±1.9 MPa m. This value is not signi®cantly in¯uenced by the microstructure, the loading direction and the stress ratio. Only two exceptions in the DFL microstructure were observed, where pthe ®rst propagation was determined at about 2.3 MPa m. (If we look to the more detailed plot in Fig. 10 it seems that this is only a problem of the detection limit.) The scatter of the extension of the crack where it stops the propagation is relatively large at K values p smaller than 3 MPa m. No signi®cant eect of the
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microstructure orp the loading direction can be observed. At K 3 MPa m, the crack stops the propagation after an extension between 5 and 20 mm. This is larger than the lamellar spacing and about equal to the grain size in the FG microstructure. In principle, it may be possible that the crack propagates only in few grains or few lamellae along the crack front. Since the pre-crack is relatively straight this may be the case at very short crack extensions of 1 or 2 mm. At larger extensions the crack should propagate along the whole crack front (not necessary over the same distance) because the typical structural features on the fracture surfaces are in the order of 1 or 2 microns. Despite the scatter in the stress intensity necessary for the ®rst propagation, the scatter p of the crack extension at K smaller than 3 MPa m, the possible variation of the crack extension along the
crack front (variation of propagation±non-propagation condition along the crack front) and some uncertainties which extrinsic mechanism acts at the beginning of the stepwise increasing load amplitude test, the trend in Fig. 9 suggests an eective threshold of about 1.7 for both microstructures. p At K larger than 3 MPa m or the crack extensions larger than 20 mm the behavior changes. The microstructure signi®cantly in¯uences both the R-curve for the threshold and the long crack fatigue crack propagation behavior. In the stepwise increasing load amplitude experiment in the DFL microstructure, the crack propagation stops after a certain extension till K reaches the long crack threshold value of about 8 and 4.5 p MPa m at R=0.1 and 0.5, respectively. The long crack threshold is reached after an extension of about 0.4 mm
Fig. 9. Stress intensity range vs. crack extension where the crack stops the propagation in the FG and DFL microstructure for K smaller p than 3 MPa m (detail of Fig. 6).
Fig. 8. SEM-fractographs of the fatigue fracture surface in the vicinity of the notch root. Material with the DFL (a) and in the FG microstructure (b).
Fig. 10. Change of crack length measured with a potential drop technique during the change of the load amplitude in a stepwise increasing load amplitude test (detail of Fig. 4). The crack length has been measured in intervals of about 40.000 cycles.
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at R=0.1 and at somewhat smaller values at R=0.5. The maximum stress intensity factor at the long crack threshold in the DFL microstructure is somewhat larger than the initiation fracture toughness, i.e. starting value of the R-curve for the fracture toughness (see, for p example, [23]), which is typically about 7 MPa m in both microstructures. In the FG microstructure, the opposite behavior is observed; the maximum stress intensity factor at the long crack threshold is somewhat smaller than the initiation fracture toughness. The rising of the R-curve for the threshold is much smaller in the FG microstructure than in the DFL microstructure, and the extension of the crack where the long crack threshold is reached in the FG microstructure is somewhat smaller than in the DFL microstructure. Why p is the eect of microstructure small below K 3 MPa p m and large above? At K smaller than 3 MPa m, the crack propagates only over a distance of about 10 mm, which is about 10 times the lamellar spacing and about equal to the grain size of the FG microstructure. A comparison of the topography of the fracture surface on the level of few micrometers (see Fig. 8) shows that the characteristic length of the fracture facets is in the order of 1 mm for both microstructures. However, on a level of few hundred micrometers, the fracture surfaces exhibit signi®cant dierences between the two microstructures which may be responsible for this eect. This is similar to the R-curve for the fracture toughness, where the initial toughness and the R-curve in the ®rst few microns is very similar. Possible mechanisms for the explanation of the steep rising R-curve of the threshold at the beginning are: . building up of a plasticity induced crack closure, . building up of roughness induced crack closure by ``nano roughness on the fracture facets' and contacts on dierent facets, . formation of a cloud of nanocracks in the vicinity of the main crack, or the formation of nanobridges as observed in dierent in situ transmission electron microscope studies [13,24]. At crack extensions larger than 10 mm, the increase of the eect of crack closure, crack bridging and a (possible) small amount of crack shielding induced by de¯ection and crack branching is then signi®cantly in¯uenced by the dierence in the microstructure. In the FG microstructure, this additional shielding contribution at the long crack threshold Ð which is reached after an extensionpof about 0.2 mm Ð is relatively small about p 1.5 MPa m compared to 5 MPa m in the DFL microstructure. The question whether a certain mechanism is responsible for the dierence in the crack propagation behavior at larger crack extension, can not be solved with this experiment, because it is only possible to measure the change of crack growth resistance, but not the change of each contribution to the resistance.
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From the change of the crack extension in Fig. 4, one would suggest that a simple static fracture process takes place after the increasing of the load amplitude. A more detailed plot of the crack extension versus the number of cycles in Fig. 10 shows that the crack propagation is really a fatigue process; only the growth rate is relatively large after the increase of the load amplitude. Furthermore, one can see that the large growth rate drops very quickly to zero. The comparison of R=0.1 and 0.5 crack growth results shows a further interesting behavior. One can see that Kmax at the threshold is about equal. This may be explained by a Kmax controlled crack growth mechanism or a very large crack closure stress intensity range which is not in¯uenced by Kmax. However, the crack propagation curves da=dN vs. Kmax do not coincide (see Fig. 11), which indicates that it is not a (pure) Kmax controlled crack growth process. In order to test the applicability of the R-curve concept, a fatigue test on a through thickness short crack was performed in the DFL microstructure. The pre-crack was initiated in the standard SENT specimen. The side faces of the specimen were then re-machined in order to obtain an initial crack length of 120 mm. Fatigue tests were carried out at a 136 and 218 MPa at a stress ratio of R 0:1, p which corresponds to an initial K 3 and 4.8 MPa m, respectively. The applied stresses are signi®cantly smaller than the yield stress and the length of the pre-crack is much larger than the characteristic microstructural length, the lamellar spacing (because the front of the crack crosses lamellae). Therefore, such a crack can be considered as an extrinsically (physically) short crack where the R-curve concept should be applicable. Both values are below the long crack threshold of this microstructure. At 136 MPa no failure occurred. The crack started to propagate with a progressively decreasing growth rate and the crack stopped the propagation after an extension of 15 mm (after about 20.00 cycles). At 218 MPa the specimen failed after 250.000 cycles. For the investigated case, the
Fig. 11. Comparison of the fatigue crack growth behavior in a da=dN vs. Kmax plot at R=0.1 and 0.5.
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p MPa m (at R=0.1) in the DFL and FG microstructures, respectively. . The in¯uence on the long crack growth behavior of the two microstructures is similar to the long crack threshold. References
Fig. 12. Representation of the application of the R-curve technique. Crack driving force vs. crack length for two load amplitudes and the R-curve for the threshold.
R-curve for the threshold of stress intensity range and the crack driving forces K as a function of the crack length for both stress amplitudes are depicted in Fig. 12 according to the R-curve concept. One can see that these coincide with the R-curve prediction. At 136 MPa the crack should stop propagation after an extension of about 10 mm, similar to the deep notched specimens, and at a larger stress amplitude the specimen should fail. 7. Conclusion The fatigue crack propagation behavior in a g-TiAl sheet alloy with dierent microstructures, a designed fully lamellar (DFL) and a ®ne-grained near g (FG) microstructure, has been investigated. A special technique has been applied to separate the dierent mechanisms which control the fatigue crack growth behavior. . Both microstructures exhibit an R-curve behavior for the threshold of stress intensity range. p . At crack extension below 10 mm (K43 MPa m) the microstructure has no signi®cant in¯uence on the R-curve for the threshold. . For larger crack extensions the R-curve is much steeper in the DFL-microstructure. . The long crack threshold value is reached after a crack extension of about 0.5 mm and is 8.5 and 4.5
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