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Cyclic deformation and fatigue in TiAl intermetallic compound under plastic strain control
International Journal of Fatigue 32 (2010) 698–702
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Cyclic deformation and fatigue in TiAl intermetallic compound under plastic strain control Masahide Satoh 1, Susumu Horibe *, Morihiko Nakamura, Hiroyuki Uchida 2 Department of Modern Mechanical Engineering, Waseda University, 3-4-1, Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan
a r t i c l e
i n f o
Article history: Received 6 May 2009 Received in revised form 24 August 2009 Accepted 12 October 2009 Available online 21 October 2009 Keywords: Low cycle fatigue Cyclic deformation TiAl intermetallic compound Hysteresis loop Energy parameter
a b s t r a c t For Mn-containing Ti–48 at.%Al intermetallic compound with a lamellar structure and an equiaxed nearc structure obtained by heat treatment, a tension–compression fatigue test under plastic strain control was conducted to clarify the fatigue behavior of TiAl. Cyclic hardening occurs significantly in the equiaxed near-c structure but not in the lamellar structure. The lamellar structure shows the pointed hysteresis loop, whereas the equiaxed near-c structure exhibits the relatively rounded loop. The variation of the hysteresis loops during cycling was investigated by using the modified energy parameter b0E , and it has been clarified that the strain localization process depends greatly on the microstructure. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Since the TiAl intermetallic compound maintains a considerably favorable strength property even in the high-temperature range, possible applications in the aircraft and automobile industries are expected. Up to now, from a report based on the influence of three types of structures, near-c, duplex, and fully lamellar, for fatigue behavior [1], it has been found that the existence of lamellar colonies improves fatigue properties. Furthermore, the studies to capture fatigue behavior from cyclic stress strain (CSS) behavior using total strain amplitude control have already been performed [2–4]. However, the relation between a microscopic structure and fatigue behavior has yet to be grasped by a fatigue test controlling plastic strain amplitude. In order to estimate the fatigue damage process under the plastic strain control, Abel [5], Mughrabi [6], and Polak et al. [7] have investigated the configurational change of stress–strain hysteresis loops and the change of dislocation structure during the fatigue test of copper single crystals and polycrystals. They have reported that the beginning and completion of the localization of strain can be assumed by using the change of loop configuration.
* Corresponding author. Tel./fax: +81 3 5286 3306. E-mail address: [email protected] (S. Horibe). 1 Present address: Social Welfare Corporation, Kashinoki, 5-12, Kaminikou, Kure, Hiroshima 737-0817, Japan. 2 Present address: Sumitomo Electric Inc., 30, Hinokigaoka, Minakuchi, Koka, Shiga 528-0036, Japan. 0142-1123/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2009.10.009
In the present study, for the purpose of clarifying the fatigue damage development process of the TiAl intermetallic compound material, a plastic strain amplitude control fatigue test has been conducted for the lamellar structure and equiaxed near-c structure, and the strain localization behavior is examined on the basis of the change of the stress–strain hysteresis loop configuration during cycling. 2. Experimental procedure 2.1. Materials and heat treatment Mn-containing TiAl forged material is employed in the present study, since it has been reported that room temperature ductility in TiAl intermetallics is improved with the addition of Mn [8]. The material is a casted one of 260 mm in diameter and 150 mm in height prepared by vacuum arc remelting, which is subjected to soaking of 1200 °C (24 h), and then HIP treatment of 1200 °C (2 h). Subsequently, forging at 80% was carried out isothermally at 1150 °C with the deformation rate of 5 104 s1. Table 1 shows the chemical composition of this forged material. In order to obtain the following two microstructures from the forged material, the heat treatment shown in Table 2 is performed in an Ar atmosphere: (1) the lamellar structure in which a few c particles exist in grain boundaries and (2) the equiaxed near-c structure which mainly consists of equiaxed c grains and a2 grains situated at grain boundary nodes. Fig. 1 shows the optical micrographs of each structure.
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M. Satoh et al. / International Journal of Fatigue 32 (2010) 698–702 Table 1 Chemical composition of TiAl forged material (wt.%). Ti
Al
Mn
Fe
O
N
H
Bal.
34.5 (48.41 at.%)
1.7 (1.17 at.%)
0.15
0.044
0.0025
0.0006
Table 2 Heat treatment conditions of each structure. Structure
Heat treatment conditions (in Ar-gas)
Lamellar microstructure Equiaxed near-c structure
1400 °C 10 min/AC/900 °C 60 min reheating 1300 °C 120 min/AC/900 °C 60 min reheating
Fig. 3. Mounting of test piece and jig.
p
Fig. 1. Microstructure of the specimens used. (a) Lamellar microstructure and (b) equiaxed near-c microstructure.
2.2. Fatigue test In the plastic strain control fatigue test, a hydraulic type servopulser fatigue tester, EHF-EB50kN-10L (Shimadzu Corporation), is employed. The configuration of the specimen is shown in Fig. 2. A clip gauge type extensometer was used for measuring the strain of the test piece. The test piece was fixed onto a jig with force in the form of compression applied to both ends of the specimen using a screw (Fig. 3). A method outlining how to control the plastic strain is as follows. The total strain from the extensometer and the load signal are the input on a subtraction circuit. The signal obtained by subtracting the elastic strain from the total strain is then inputted on an external control of the tester for controlling the plastic strain amplitude. The plastic strain amplitude in this work is defined as shown in Fig. 4. The fatigue test is conducted at two levels of plastic strain amplitudes, Dep/2 of 2 104 and 6 104 for both the lamellar structure and the equiaxed near-c structure until the test piece
plastic strain amplitude =
p
/2
Fig. 4. Definition of plastic strain amplitude Dep/2 in this work.
rupture. The waveform of the fatigue test is sinusoidal. Its frequency is 0.1 Hz. Since it takes a long time for the test to exceed 10,000 cycles, the frequency is increased in steps until 1 Hz after 1000 cycles. The stress–strain hysteresis loops during cycles were recorded and analyzed. 2.3. Measurement of CSSR and energy parameters (bE and b0E ) The cyclic stress–strain response (CSSR) which is a relation between the stress amplitude ra and the number of repetitions has been measured. For the estimation of the strain localization during cycling in relatively simple metallic materials, such as single phase fcc metals, much attention is paid to the configurational changes in hysteresis loops during cycling, as previously described, and the energy parameter bE, which is expressed by the following formula (1), or the hysteresis loop shape parameter VH has been used [5–7]:
bE ¼
Fig. 2. Configuration of test piece.
2ra Dp
I
I
rd
rd
ð1Þ
Both parameters (bE, VH) are connected in the following equation; VH = 1/(1 + bE). However, asymmetry of the hysteresis loop caused by the generation of microcracks, etc., as described later,
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a
p p
/ 2 = 6× 10 / 2 = 2× 10
b
4 4
/ 2 = 6× 10 p / 2 = 2× 10 p
4 4
Fig. 5. Cyclic stress strain response. (a) Lamellar microstructure and (b) equiaxed near-c microstructure.
a
a
MPa
MPa
400
400
300
300
200
200
100
100
p
p
(1 10-4)
-10
-8
-6
-4
-2
2 -100
b
4
6
8
10
(1 10-4)
-10
-8
-6
-4
-2
2 -100
-200
-200
-300
-300
-400
-400
b
MPa
6
8
400
300
300
200
200 100
p
p
(1 10-4)
(1 10-4)
-10
-8
-6
-4
-2
2 -100
4
6
8
10
10
MPa
400
100
4
-10
-8
-6
-4
-2
2 -100
-200
-200
-300
-300
-400
-400
4
6
8
10
Fig. 6. Examples of stress–strain hysteresis loops in lamellar microstructure. (a) Dep/2 = 6 104 and (b) Dep/2 = 2 104.
Fig. 7. Examples of stress–strain hysteresis loops in equiaxed near-c microstructure. (a) Dep/2 = 6 104 and (b) Dep/2 = 2 104.
makes the analysis of loop configuration difficult. Therefore, in place of the conventional energy parameter bE, we have proposed the modified energy parameter b0E , assuming that a genuine plastic behavior is reflected in the compression side of the stress–strain
hysteresis loop. That is, by using the hysteresis loop area only in the compression side (i.e., during the compressive loading and the subsequent unloading) and the corresponding rectangular area, the estimation similar to the formula (1) has been conducted. In
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M. Satoh et al. / International Journal of Fatigue 32 (2010) 698–702
a
b p p
p p
/ 2 = 6× 10 / 2 = 2× 10
/ 2 = 6× 10 / 2 = 2× 10
4 4
4 4
Fig. 8. Variation of bE during cycling. (a) Lamellar microstructure and (b) equiaxed near-c microstructure.
order to analyze the fatigue damage process in the present material, the above both energy parameters have been calculated in addition to the CSSR. 3. Experimental result 3.1. Cyclic stress–strain response (CSSR) Fig. 5 shows CSSR in the lamellar microstructure and equiaxed near-c microstructure under the plastic strain control fatigue test (Dep/2 = 2 104, Dep/2 = 6 104). Both structures show cyclic hardening to failure. Especially, the equiaxed near-c structure shows a remarkable hardening, which coincides with the result by Berteaux et al. [1], and the final fracture occurred not at the gauge section but at the part clamped with the jig, which implies that the fatigue properties of this microstructure has high sensitivity to stress concentration. 3.2. Characteristics of stress–strain hysteresis behavior Figs. 6 and 7 show examples of the stress–strain hysteresis loop at 20 cycles and 160 cycles under the plastic strain control testing (Dep/2 = 2 104, 6 104) for both structures. It is characteristic for an unloading region to have considerable curvature down to a zero stress after tension or compression. It can be assumed that back stress is operating strongly, and there is significant dislocation movement to the opposite direction during the unloading process. Since this tendency is especially remarkable in the lamellar microstructure, it is suggested that the pile-up of the dislocation is strongly involved in this structure. Therefore, outwardly, the lamellar structure shows the pointed hysteresis
a
loop, whereas the equiaxed near-c structure exhibits the relatively rounded loop. Stress dependency of the Young’s modulus has been reported in various materials [9]. It is presumable that its dependency exists in the present intermetallic compound as well. That is, the stress– strain response observed during gradual unloading after tension differs from that observed during unloading after compression. Since the present material tends to harden during cycling, a higher stress is gradually produced by a repetitive plastic strain. At the early stage of cycling with lower stress values, the stress dependency of the Young’s modulus does not influence the unloading region of the hysteresis loop so much, i.e., the unloading portion just after tension or compression is almost parallel to the ordinate. However, when the stress value becomes gradually higher due to cycling, the unloading portion after tension has a positive gradient, while on the other hand, the unloading portion after compression comes to possess a negative gradient, as seen in Fig. 7. This stress dependence of the Young’s modulus makes a precise strain control extremely difficult. Furthermore, since the strain repetition creates a number of microcracks [10,11], the gradient of the unloading curve after tension becomes smaller and the asymmetry of the hysteresis loop should be produced. Coincidentally, it becomes extremely difficult to distinguish the change of the gradient caused by the stress dependency of the Young’s modulus and that caused by microcracking. Taking such a matter into consideration, it seemed difficult to assume fatigue damage process by the conventional energy parameter bE. Therefore, we also tried to analyze the loop by using the energy parameter b0E , which is only for the hysteresis loop of the compression side. Figs. 8 and 9 show the variation of energy parameters bE and b0E with the repetitive strain, respectively. The lamellar structure has
b / 2 = 6× 10 p / 2 = 2× 10 p
/ 2 = 6× 10 p / 2 = 2× 10 p
4 4
4 4
Fig. 9. Variation of b0E during cycling. (a) Lamellar microstructure and (b) equiaxed near-c microstructure.
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larger values for bE and b0E , compared to the equiaxed near-c structure. For the lamellar structure, in the case of Dep/2 = 2 104, b0E shows the maximum value in the vicinity of 70 cycles and the minimum value in the vicinity of 300 cycles, and continues to increase thereafter. In the case of Dep/2 = 6 104, b0E shows the maximum value in the vicinity of 30 cycles and the minimum value in the vicinity of 300 cycles, showing increase thereafter. From these results with the present fatigue conditions, it is suggested that at several tens of cycles PSBs-like structure begin to form, and at several hundreds of cycles the increase of that structure ceases, leading to the microcracking. In Fig. 8, however, bE does not clearly show the maximum point, although the minimum point is indicated as similarly shown in Fig. 9. It seems, therefore, that the analysis using b0E might be preferable. For the equiaxed near-c structure, b0E continues to decrease right after the beginning, showing the minimum value in the vicinity of 150 cycles at Dep/ 2 = 2 104 and in the vicinity of 100 cycles at Dep/2 = 6 104, respectively. There is insignificant difference between bE and b0E in this microstructure. 4. Discussion In the lamellar microstructure, the relatively moderate cyclic hardening has been observed, which is considered to be relevant to a2/c boundaries restricting dislocation motion. Yasuda et al. [12] have conducted the fatigue test controlling a lamellar orientation in the TiAl–PST crystal and obtained the following results. When the angle between a load axis and lamellar boundary surface is / = 0°, rapid cyclic hardening is observed since a2/c lamellar boundaries act as effective barriers to the motion of dislocations while at / = 45°, c/c domain boundaries have little effect as obstacles and cyclic hardening is small. It is assumed, therefore, that in the present lamellar microstructure with random orientations also the dislocation motion is similarly reversible which suppresses the cyclic hardening. Appel et al. [13] also studied electron microscopical structures of a TiAl alloy with a nearly lamellar structure fatigued at various temperatures under strain control. Parthasarathy et al. [14] reported the flow behavior of PST crystal of Ti–48Al with different orientations in the microstrain regime (from 105 to 2 102) at room temperature. On the other hand, the equiaxed near-c structure shows a remarkable hardening, compared with the lamellar microstructure. In the equiaxed near-c structure the a2 phase (or lath [15]) is produced in the form of plates in the c in the c phase. These a2 plates become obstacles against the dislocation motion in the c grain, and the interaction of the dislocations is caused by the action of multiple slip systems in the c grain, which is considered to be the reason for the significant cyclic hardening in this structure. In the lamellar microstructure, the unloading region in the hysteresis loop has a significant curvature (Fig. 6), and the energy parameters show a larger value (Figs. 8 and 9), compared with the equiaxed near-c structure. This is attributed to the microstructure, in which the dislocation can move along the lamellar phase. The tangling of the dislocation does not occur frequently so that the mobile dislocations pile up in the lamellar grain boundaries over a wide range. On the other hand, in the equiaxed near-c structure, cyclic loading causes a remarkable tangling of dislocations. Furthermore, in the present study, the energy parameter b0E based on the consideration that a genuine plastic behavior should be seen at the compression side of the stress–strain hysteresis loop
is proposed in place of the conventional energy parameter bE. From comparing Figs. 7 and 8, it has been suggested that the variation of b0E gives us more precise information in strain localization during cycling than that of bE. 5. Conclusion The fatigue behavior of the lamellar structure and equiaxed near-c structure in TiAl intermetallic compound was studied by plastic strain controlled testing and the following conclusions were obtained; (1) Cyclic hardening was observed significantly in the equiaxed near-c structure but not so much in the lamellar structure. (2) The lamellar structure shows the pointed hysteresis loop suggesting the back stress generation during the loading process, whereas the equiaxed near-c structure exhibits the relatively rounded loop. (3) The variation of the hysteresis loops during cycling was analyzed by using the modified energy parameter b0E in place of bE, and it has been clarified that the strain localization process depends greatly on the microstructure.
Acknowledgement The authors wish to thank Dr. T. Kumagai, National Defense Academy of Japan for helpful discussion in specimen preparation. References [1] Berteaux O, Jouiad M, Thomas M, Henaff G. Microstructure c-low cycle fatigue behaviour relationships in a PM c-TiAl alloy. Intermetallics 2006;14: 1130–5. [2] Park YS, Ahn WS, Nam SW, Hwang SK. The enhancement of low cycle fatigue life by carbon addition in lamellar TiAl alloy. Mater Sci Eng A 2002;336:196–201. [3] Henaff G, Gloanec AL. Fatigue properties of TiAl alloys. Intermetallics 2005;13:543–58. [4] Gloanec AL, Jouiad M, Bertheau D, Grange M, Henaff G. Low-cycle fatigue and deformation substructures in an engineering TiAl alloy. Intermetallics 2007;15:520–31. [5] Abel A. Fatigue of copper single crystals at low constant plastic strain amplitudes. Mater Sci Eng 1978;36:117–24. [6] Mughrabi H. The cyclic hardening and saturation behaviour of copper single crystals. Mater Sci Eng 1978;33:207–23. [7] Polak J, Obrtlik K, Helesic J. Cyclic slip localization in fatigue of copper polycrystals. Fatigue 1990;90:217–23. [8] Tsujimoto T, Hashimoto K, Nobuki M. Alloy design for improvement of ductility and workability of alloys based on intermetallic compound TiAl. Mater Trans JIM 1992;33:989–1003. [9] Sommer C, Christ H-J, Mughrabi H. Non-linear elastic behaviour of the roller bearing steel SAE 52100 during cyclic loading. Acta Metall Mater 1991;39:1177–87. [10] Jha SK, Larsen JM, Rosenberger AH. The role of competing mechanisms in the fatigue life variability of a nearly fully-lamellar c-TiAl based alloy. Acta Mater 2005;53:1293–304. [11] Huang ZW, Bowen P. Persistent microslip bands in the lamellar TiAl structure subjected to room temperature fatigue. Scripta Mater 2001;45:931–7. [12] Yasuda HY, Nakano T, Umakoshi Y. Cyclic deformation behaviour of Ti–Al alloys containing oriented lamellae. Philos Mag A 1995;71:127–38. [13] Appel F, Heckel TK, Christ H-J. Electron microscope characterization of low cycle fatigue in a high-strength multiphase titanium aluminide alloy. Int J Fatigue, in press. doi:10.1016/j.ijfatigue.2009.04.001. [14] Parthasarathy TA, Mendiratta MG, Dimiduk DM. Flow behavior of PST and fully lamellar polycrystals of Ti–48Ti in microstrain regime. Acta Mater 1998;46:4005–16. [15] Kumagai T, Abe E, Kimura T, Nakamura M. The c ? a phase transformation in c-based TiAl alloy. Scripta Mater 1996;34:235–42.
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Cyclic deformation and fatigue in TiAl intermetallic compound under plastic strain control Masahide Satoh 1, Susumu Horibe *, Morihiko Nakamura, Hiroyuki Uchida 2 Department of Modern Mechanical Engineering, Waseda University, 3-4-1, Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan
a r t i c l e
i n f o
Article history: Received 6 May 2009 Received in revised form 24 August 2009 Accepted 12 October 2009 Available online 21 October 2009 Keywords: Low cycle fatigue Cyclic deformation TiAl intermetallic compound Hysteresis loop Energy parameter
a b s t r a c t For Mn-containing Ti–48 at.%Al intermetallic compound with a lamellar structure and an equiaxed nearc structure obtained by heat treatment, a tension–compression fatigue test under plastic strain control was conducted to clarify the fatigue behavior of TiAl. Cyclic hardening occurs significantly in the equiaxed near-c structure but not in the lamellar structure. The lamellar structure shows the pointed hysteresis loop, whereas the equiaxed near-c structure exhibits the relatively rounded loop. The variation of the hysteresis loops during cycling was investigated by using the modified energy parameter b0E , and it has been clarified that the strain localization process depends greatly on the microstructure. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Since the TiAl intermetallic compound maintains a considerably favorable strength property even in the high-temperature range, possible applications in the aircraft and automobile industries are expected. Up to now, from a report based on the influence of three types of structures, near-c, duplex, and fully lamellar, for fatigue behavior [1], it has been found that the existence of lamellar colonies improves fatigue properties. Furthermore, the studies to capture fatigue behavior from cyclic stress strain (CSS) behavior using total strain amplitude control have already been performed [2–4]. However, the relation between a microscopic structure and fatigue behavior has yet to be grasped by a fatigue test controlling plastic strain amplitude. In order to estimate the fatigue damage process under the plastic strain control, Abel [5], Mughrabi [6], and Polak et al. [7] have investigated the configurational change of stress–strain hysteresis loops and the change of dislocation structure during the fatigue test of copper single crystals and polycrystals. They have reported that the beginning and completion of the localization of strain can be assumed by using the change of loop configuration.
* Corresponding author. Tel./fax: +81 3 5286 3306. E-mail address: [email protected] (S. Horibe). 1 Present address: Social Welfare Corporation, Kashinoki, 5-12, Kaminikou, Kure, Hiroshima 737-0817, Japan. 2 Present address: Sumitomo Electric Inc., 30, Hinokigaoka, Minakuchi, Koka, Shiga 528-0036, Japan. 0142-1123/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2009.10.009
In the present study, for the purpose of clarifying the fatigue damage development process of the TiAl intermetallic compound material, a plastic strain amplitude control fatigue test has been conducted for the lamellar structure and equiaxed near-c structure, and the strain localization behavior is examined on the basis of the change of the stress–strain hysteresis loop configuration during cycling. 2. Experimental procedure 2.1. Materials and heat treatment Mn-containing TiAl forged material is employed in the present study, since it has been reported that room temperature ductility in TiAl intermetallics is improved with the addition of Mn [8]. The material is a casted one of 260 mm in diameter and 150 mm in height prepared by vacuum arc remelting, which is subjected to soaking of 1200 °C (24 h), and then HIP treatment of 1200 °C (2 h). Subsequently, forging at 80% was carried out isothermally at 1150 °C with the deformation rate of 5 104 s1. Table 1 shows the chemical composition of this forged material. In order to obtain the following two microstructures from the forged material, the heat treatment shown in Table 2 is performed in an Ar atmosphere: (1) the lamellar structure in which a few c particles exist in grain boundaries and (2) the equiaxed near-c structure which mainly consists of equiaxed c grains and a2 grains situated at grain boundary nodes. Fig. 1 shows the optical micrographs of each structure.
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M. Satoh et al. / International Journal of Fatigue 32 (2010) 698–702 Table 1 Chemical composition of TiAl forged material (wt.%). Ti
Al
Mn
Fe
O
N
H
Bal.
34.5 (48.41 at.%)
1.7 (1.17 at.%)
0.15
0.044
0.0025
0.0006
Table 2 Heat treatment conditions of each structure. Structure
Heat treatment conditions (in Ar-gas)
Lamellar microstructure Equiaxed near-c structure
1400 °C 10 min/AC/900 °C 60 min reheating 1300 °C 120 min/AC/900 °C 60 min reheating
Fig. 3. Mounting of test piece and jig.
p
Fig. 1. Microstructure of the specimens used. (a) Lamellar microstructure and (b) equiaxed near-c microstructure.
2.2. Fatigue test In the plastic strain control fatigue test, a hydraulic type servopulser fatigue tester, EHF-EB50kN-10L (Shimadzu Corporation), is employed. The configuration of the specimen is shown in Fig. 2. A clip gauge type extensometer was used for measuring the strain of the test piece. The test piece was fixed onto a jig with force in the form of compression applied to both ends of the specimen using a screw (Fig. 3). A method outlining how to control the plastic strain is as follows. The total strain from the extensometer and the load signal are the input on a subtraction circuit. The signal obtained by subtracting the elastic strain from the total strain is then inputted on an external control of the tester for controlling the plastic strain amplitude. The plastic strain amplitude in this work is defined as shown in Fig. 4. The fatigue test is conducted at two levels of plastic strain amplitudes, Dep/2 of 2 104 and 6 104 for both the lamellar structure and the equiaxed near-c structure until the test piece
plastic strain amplitude =
p
/2
Fig. 4. Definition of plastic strain amplitude Dep/2 in this work.
rupture. The waveform of the fatigue test is sinusoidal. Its frequency is 0.1 Hz. Since it takes a long time for the test to exceed 10,000 cycles, the frequency is increased in steps until 1 Hz after 1000 cycles. The stress–strain hysteresis loops during cycles were recorded and analyzed. 2.3. Measurement of CSSR and energy parameters (bE and b0E ) The cyclic stress–strain response (CSSR) which is a relation between the stress amplitude ra and the number of repetitions has been measured. For the estimation of the strain localization during cycling in relatively simple metallic materials, such as single phase fcc metals, much attention is paid to the configurational changes in hysteresis loops during cycling, as previously described, and the energy parameter bE, which is expressed by the following formula (1), or the hysteresis loop shape parameter VH has been used [5–7]:
bE ¼
Fig. 2. Configuration of test piece.
2ra Dp
I
I
rd
rd
ð1Þ
Both parameters (bE, VH) are connected in the following equation; VH = 1/(1 + bE). However, asymmetry of the hysteresis loop caused by the generation of microcracks, etc., as described later,
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a
p p
/ 2 = 6× 10 / 2 = 2× 10
b
4 4
/ 2 = 6× 10 p / 2 = 2× 10 p
4 4
Fig. 5. Cyclic stress strain response. (a) Lamellar microstructure and (b) equiaxed near-c microstructure.
a
a
MPa
MPa
400
400
300
300
200
200
100
100
p
p
(1 10-4)
-10
-8
-6
-4
-2
2 -100
b
4
6
8
10
(1 10-4)
-10
-8
-6
-4
-2
2 -100
-200
-200
-300
-300
-400
-400
b
MPa
6
8
400
300
300
200
200 100
p
p
(1 10-4)
(1 10-4)
-10
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4
6
8
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10
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400
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4
-10
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2 -100
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-400
4
6
8
10
Fig. 6. Examples of stress–strain hysteresis loops in lamellar microstructure. (a) Dep/2 = 6 104 and (b) Dep/2 = 2 104.
Fig. 7. Examples of stress–strain hysteresis loops in equiaxed near-c microstructure. (a) Dep/2 = 6 104 and (b) Dep/2 = 2 104.
makes the analysis of loop configuration difficult. Therefore, in place of the conventional energy parameter bE, we have proposed the modified energy parameter b0E , assuming that a genuine plastic behavior is reflected in the compression side of the stress–strain
hysteresis loop. That is, by using the hysteresis loop area only in the compression side (i.e., during the compressive loading and the subsequent unloading) and the corresponding rectangular area, the estimation similar to the formula (1) has been conducted. In
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a
b p p
p p
/ 2 = 6× 10 / 2 = 2× 10
/ 2 = 6× 10 / 2 = 2× 10
4 4
4 4
Fig. 8. Variation of bE during cycling. (a) Lamellar microstructure and (b) equiaxed near-c microstructure.
order to analyze the fatigue damage process in the present material, the above both energy parameters have been calculated in addition to the CSSR. 3. Experimental result 3.1. Cyclic stress–strain response (CSSR) Fig. 5 shows CSSR in the lamellar microstructure and equiaxed near-c microstructure under the plastic strain control fatigue test (Dep/2 = 2 104, Dep/2 = 6 104). Both structures show cyclic hardening to failure. Especially, the equiaxed near-c structure shows a remarkable hardening, which coincides with the result by Berteaux et al. [1], and the final fracture occurred not at the gauge section but at the part clamped with the jig, which implies that the fatigue properties of this microstructure has high sensitivity to stress concentration. 3.2. Characteristics of stress–strain hysteresis behavior Figs. 6 and 7 show examples of the stress–strain hysteresis loop at 20 cycles and 160 cycles under the plastic strain control testing (Dep/2 = 2 104, 6 104) for both structures. It is characteristic for an unloading region to have considerable curvature down to a zero stress after tension or compression. It can be assumed that back stress is operating strongly, and there is significant dislocation movement to the opposite direction during the unloading process. Since this tendency is especially remarkable in the lamellar microstructure, it is suggested that the pile-up of the dislocation is strongly involved in this structure. Therefore, outwardly, the lamellar structure shows the pointed hysteresis
a
loop, whereas the equiaxed near-c structure exhibits the relatively rounded loop. Stress dependency of the Young’s modulus has been reported in various materials [9]. It is presumable that its dependency exists in the present intermetallic compound as well. That is, the stress– strain response observed during gradual unloading after tension differs from that observed during unloading after compression. Since the present material tends to harden during cycling, a higher stress is gradually produced by a repetitive plastic strain. At the early stage of cycling with lower stress values, the stress dependency of the Young’s modulus does not influence the unloading region of the hysteresis loop so much, i.e., the unloading portion just after tension or compression is almost parallel to the ordinate. However, when the stress value becomes gradually higher due to cycling, the unloading portion after tension has a positive gradient, while on the other hand, the unloading portion after compression comes to possess a negative gradient, as seen in Fig. 7. This stress dependence of the Young’s modulus makes a precise strain control extremely difficult. Furthermore, since the strain repetition creates a number of microcracks [10,11], the gradient of the unloading curve after tension becomes smaller and the asymmetry of the hysteresis loop should be produced. Coincidentally, it becomes extremely difficult to distinguish the change of the gradient caused by the stress dependency of the Young’s modulus and that caused by microcracking. Taking such a matter into consideration, it seemed difficult to assume fatigue damage process by the conventional energy parameter bE. Therefore, we also tried to analyze the loop by using the energy parameter b0E , which is only for the hysteresis loop of the compression side. Figs. 8 and 9 show the variation of energy parameters bE and b0E with the repetitive strain, respectively. The lamellar structure has
b / 2 = 6× 10 p / 2 = 2× 10 p
/ 2 = 6× 10 p / 2 = 2× 10 p
4 4
4 4
Fig. 9. Variation of b0E during cycling. (a) Lamellar microstructure and (b) equiaxed near-c microstructure.
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larger values for bE and b0E , compared to the equiaxed near-c structure. For the lamellar structure, in the case of Dep/2 = 2 104, b0E shows the maximum value in the vicinity of 70 cycles and the minimum value in the vicinity of 300 cycles, and continues to increase thereafter. In the case of Dep/2 = 6 104, b0E shows the maximum value in the vicinity of 30 cycles and the minimum value in the vicinity of 300 cycles, showing increase thereafter. From these results with the present fatigue conditions, it is suggested that at several tens of cycles PSBs-like structure begin to form, and at several hundreds of cycles the increase of that structure ceases, leading to the microcracking. In Fig. 8, however, bE does not clearly show the maximum point, although the minimum point is indicated as similarly shown in Fig. 9. It seems, therefore, that the analysis using b0E might be preferable. For the equiaxed near-c structure, b0E continues to decrease right after the beginning, showing the minimum value in the vicinity of 150 cycles at Dep/ 2 = 2 104 and in the vicinity of 100 cycles at Dep/2 = 6 104, respectively. There is insignificant difference between bE and b0E in this microstructure. 4. Discussion In the lamellar microstructure, the relatively moderate cyclic hardening has been observed, which is considered to be relevant to a2/c boundaries restricting dislocation motion. Yasuda et al. [12] have conducted the fatigue test controlling a lamellar orientation in the TiAl–PST crystal and obtained the following results. When the angle between a load axis and lamellar boundary surface is / = 0°, rapid cyclic hardening is observed since a2/c lamellar boundaries act as effective barriers to the motion of dislocations while at / = 45°, c/c domain boundaries have little effect as obstacles and cyclic hardening is small. It is assumed, therefore, that in the present lamellar microstructure with random orientations also the dislocation motion is similarly reversible which suppresses the cyclic hardening. Appel et al. [13] also studied electron microscopical structures of a TiAl alloy with a nearly lamellar structure fatigued at various temperatures under strain control. Parthasarathy et al. [14] reported the flow behavior of PST crystal of Ti–48Al with different orientations in the microstrain regime (from 105 to 2 102) at room temperature. On the other hand, the equiaxed near-c structure shows a remarkable hardening, compared with the lamellar microstructure. In the equiaxed near-c structure the a2 phase (or lath [15]) is produced in the form of plates in the c in the c phase. These a2 plates become obstacles against the dislocation motion in the c grain, and the interaction of the dislocations is caused by the action of multiple slip systems in the c grain, which is considered to be the reason for the significant cyclic hardening in this structure. In the lamellar microstructure, the unloading region in the hysteresis loop has a significant curvature (Fig. 6), and the energy parameters show a larger value (Figs. 8 and 9), compared with the equiaxed near-c structure. This is attributed to the microstructure, in which the dislocation can move along the lamellar phase. The tangling of the dislocation does not occur frequently so that the mobile dislocations pile up in the lamellar grain boundaries over a wide range. On the other hand, in the equiaxed near-c structure, cyclic loading causes a remarkable tangling of dislocations. Furthermore, in the present study, the energy parameter b0E based on the consideration that a genuine plastic behavior should be seen at the compression side of the stress–strain hysteresis loop
is proposed in place of the conventional energy parameter bE. From comparing Figs. 7 and 8, it has been suggested that the variation of b0E gives us more precise information in strain localization during cycling than that of bE. 5. Conclusion The fatigue behavior of the lamellar structure and equiaxed near-c structure in TiAl intermetallic compound was studied by plastic strain controlled testing and the following conclusions were obtained; (1) Cyclic hardening was observed significantly in the equiaxed near-c structure but not so much in the lamellar structure. (2) The lamellar structure shows the pointed hysteresis loop suggesting the back stress generation during the loading process, whereas the equiaxed near-c structure exhibits the relatively rounded loop. (3) The variation of the hysteresis loops during cycling was analyzed by using the modified energy parameter b0E in place of bE, and it has been clarified that the strain localization process depends greatly on the microstructure.
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