The relationships of microstructure and properties of a fully lamellar TiAl alloy

Intermetallics 8 (2000) 647±653

The relationships of microstructure and properties of a fully lamellar TiAl alloy Guoxin Cao *, Lianfeng Fu, Jianguo Lin, Yonggang Zhang, Changqi Chen Department of Materials Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, 100083, PR China

Abstract The relationship between the yield strength and microstructure parameters of a fully lamellar TiAl alloy has been studied systematically. The grain size and the lamellar spacing were chosen as microstructure parameters. The experimental results showed that the yield strength increases with the decrease of grain size and more obviously with the decrease of the lamellar spacing. The relationship between yield strength and grain size and lamellar spacing can be approximately described by Hall±Petch relation. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Titanium aluminides, based on TiAl; B. Mechanical properties at ambient temperature; B. Phase diagram; C. Heat treatment; D. Grain boundaries, structure

1. Introduction

2. Materials and experiments

It is widely accepted that the microstructural features of two-phase TiAl alloys are responsible for their mechanical properties and much work has been carried out to relate the properties to the microstructure of the alloys, such as grain size and the distribution of a2 and g phases [1±3]. The fully lamellar (FL) microstructure is currently regarded as the most attractive because the overall balance of properties is more suitable for hightemperature structures, and the combination of yield strength, fracture toughness and creep resistance is markedly better than the duplex or nearly gamma microstructural forms [4]. This kind of microstructure can be mainly characterized by microstructural parameters, such as grain size and lamellar spacing. At present, there is obviously controversy among the results reported for fully lamellar microstructures. The reason is that there are two main microstructure parameters, grain size and lamellar spacing in fully lamellar microstructure, both of which can in¯uence properties. The two parameters are usually related to each other, and the available experimental results did not separate the two parameters properly. Therefore, the further work must be done to establish the relationship between one parameter and properties under the condition of keeping the other parameter constant.

The primary alloy used for this study has a nominal composition of Ti±45.5 Al±2Cr±1.5Nb-1V (at%). This alloy was prepared using vacuum arc melting technology. The obtained ingot (approximately 30250 mm) was HIP processed (1260 C, 175 MP/3 h) to seal casting porosity. Samples were prepared for heat treatment by wrapping in Ta foil and sealing in quartz tubes back-®lled with Ar to 250 mm Hg. The microstructure was controlled through heat treatment method schematically depicted in Fig. 1. Four di€erent grain sizes with a constant lamellar spacing and four di€erent lamellar spacings with a constant grain size have been obtained, as described in Table 1. The grain sizes of the specimens tested in this study were determined using optical microscopy. The lineintercept method was used to obtain an average grain size (D). The mean lamellar spacings were measured using transmission electron microscopy (TEM). The lamellar spacing (l) is de®ned as the edge-to-edge dimension (measured perpendicular to the lamellar interface) without regarding the phase type of adjacent lamellae. Compression specimens with a size of f 48 mm were prepared for mechanical testing. The specimens were tested at room temperature in air at a nominal strain rate of 210ÿ4 sÿ1. At least three specimens were tested for each material condition, and the mean yield-stress value is reported.

*Corresponding author.

0966-9795/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0966-9795(99)00128-4

648

G. Cao et al. / Intermetallics 8 (2000) 647±653

Fig. 1. Schematic temperature±time path used for microstructural control: (a) to obtain the di€erent grain sizes with a constant lamellar spacing; (b) to obtain the di€erent lamellar spacings with a constant grain size. Table 1 Heat treatmenta Sample

Heat treatment

1320 C/5 min+FC (75 C/min) 1320 C/10 min+FC (75 C/min) 1320 C/20 min+FC (75 C/min) 1320 C/60 min+FC (75 C/min) 1320 C/10 min+WQ+700 C/1 h 1320 C/10 min+AC (150 C/min) 1320 C/10 min+FC (75 C/min) 1320 C/10 min+FC (4 C/min)

a b c d e f g h a

Microstructure Grain size (mm)

Lamellar spacing (nm)

260 390 690 920 370 360 390 380

160 About 160±170 About 160±170 170 15 95 160 500

FC, furnace cooling; AC, air cooling; WQ, water quenching.

3. Results Optical micrographs are shown in Fig. 2 for four different grain sizes of FL microstructure. The lamellar spacing distributions for samples (a) and (d) are shown in Fig. 3. It can be seen that the lamellar spacing of samples (a) and (d) are nearly the same. The same results have been found for samples (b) and (c). The TEM micrographs of samples (e)±(h) with di€erent lamellar spacings are showed in Fig. 4. The grain size of the four samples was estimated to be the same. The microstructure parameters of grain sizes and lamellar spacings of all the samples tested in the present study are presented in Table 1. Fig. 5 shows the 0.2% yield strength (y ) plotted against Dÿ1=2 for the samples (a)±(d) with the same lamellar spacing. A linear relationship has been found and, therefore, Hall±Petch relationship, i.e. y ˆ 0 ‡ ky Dÿ1=2 is followed. 0 and p ky were determined to be 387 MPa and 2.07 MPa m, respectively, by linear regression. Fig. 6 shows the 0.2% yield strength (y ) plotted against lÿ1=2 for the samples (e)±(h) with a constant grain size. Hall±Petch relationship, i.e. y ˆ 00 ‡ k0y lÿ1=2 was also found to be applicable in this case. 00

and p k0y were determined to be 334 MPa and 0.06 MPa m, respectively. All the data of 0 and ky obtained in present study are listed in Table 2, together with available data in literatures. From Table 2, we can see that the ky (fully lamellar) > ky (single l) > ky PST (soft orientation). For PST (soft orientation), ky shows the strengthen e€ect of domain boundaries; in single l, ky shows the strengthen e€ect of grain boundaries; in full lamellar, ky shows the strengthen e€ect of the grain boundaries and lamellar surfaces. From this result, we can conclude that the strengthen e€ect of grain boundaries+lamellar surfaces>strengthen e€ect of grain boundaries>strengthen e€ect of domain boundaries. In Table 2, the value of ky and 0 of single are about 126200 MPa and 0.91.4 MPa mÿ1/2, respectively. From the result of nos. 4±7 in Table 2, there is little di€erence between them. But there is a big di€erence between the previous study results and present work in fully lamellar microstructure. In nos. 8± 9 of Table 2, the value of ky and 0 is larger than the results in this paper because the e€ect of lamellar spacing is not considered in these two studies, and the lineally dependent coecient of Hall±Petch relationship is very low. In no. 11 of Table 2, the e€ect of grain size is not considered in this study. In no. 10, the Hall±Petch relationships are built between the l lamellae spacing and yield stress and between the a2 lamellae spacing and yield stress, respectively but in the present work, we do not distinguish them? 4. Discussion There are three kinds of obstacles, domain boundary, lamellar interface, and grain boundary, to resist the dislocations glide in fully lamellar TiAl alloys. Among these three boundaries, the resistance of domain boundary which is described as 120 -rotational type boundary is the least to the dislocations glide [12]. In this study, therefore, only the resistance of dislocation glide from lamellar interface and grain boundary is considered.

G. Cao et al. / Intermetallics 8 (2000) 647±653

649

Fig. 2. Optical micrographs of the full lamellar TiAl alloys with di€erent grain size.

In the literature, the relationship between yield strength and grain boundary and interface spacing has been studied for single phase g alloy [5,6], fully lamellar structure alloy [10,11] and polysynthetically twinned (PST) crystals which contain only a single set of lamellae [13]. Therefore, present discussion will be based on these results. 4.1. PST crystals In the soft mode deformation of PST (the angle between the lamellae and the loading axis is about 45 ), the slip is mainly parallel to the lamellar interfaces, and therefore, the only obstacle for dislocations glide is the domain boundary. The yield stress y may be related to the domain size (d) as follows [13]. n  1=2 o …1† y ˆ M1 0 ‡ …2 ÿ †1 b=…2…1 ÿ †d† Where M1 is Taylor factor, 0 is the shear stress to move a dislocation through a single crystal of the layer materials,  is the Poisson's ratio,  is the shear modulus, and b is the Burgers vector, 1 is the barrier strength for the domain boundary. The value of 1 is estimated to be close to 0.01 , i.e. 66 MPa [10].

In the hard mode deformation of PST (the angle between the lamellae and the loading axis is either 0 or 90 ), slip crosses the lamellar boundaries, and the dislocations pile up at the lamellar interfaces. The yield stress y may be related to the lamellar spacing (l) [13]: n  1=2 o y ˆ M2 0 ‡ 42 b=l …2† where 2 is the barrier strength for the lamellar interface. It is estimated to be 0.015 , i.e. 99 MPa [10].  is 1 for screw dislocation and (1 ÿ ) for edge dislocation ( ˆ 0:33). In this study, we take screw dislocations and edge dislocations as 50%, respectively. So  ˆ 1=2 ‰1 ‡ …1 ÿ †Š ˆ 0:84. 0 depends on type of dislocations. For ordinary dislocation 1=2 < 110Š, 0 ranges from 40 to 250 MPa; for superdislocation < 101Š, 0 ranges from 25 to 120 Mpa [14]. The experimental measurements at 300 K showed that it is about 50 MPa, the same for twinning, ordinary, and superdislocations [15]. In the soft mode of deformation of PST crystals, Taylor factor M1 lies between 2.0 and 3.0; in the hard mode of deformation of PST crystals, Taylor factor M2 is 3.7 for 90 , and 2.5 for 0 [15].

650

G. Cao et al. / Intermetallics 8 (2000) 647±653

4.3. Assumed fully lamellar TiAl alloy with all grains in soft mode In this case, slip is similar to the slip in the single phase alloy and, therefore, the value of y is equal to that of single phase g-TiAl alloys, and can be expressed by Eq. (3). 4.4. Assumed fully lamellar TiAl alloy with all grains in hard mode In this model, slip may encounter resistance both from lamellar interface and grain boundary, but the resistance from the interface is dominant and, therefore, y can be calculated by adding the model of PST in hard orientation into the model of single-phase alloy as follows, n  1=2  1=2 o y ˆ M4 0 ‡ …2 ÿ †3 b=…2…1 ÿ †D† ‡ 44 l …4† The third item of Eq. (4) is from PST in hard orientation, i.e. Eq. (2). M4 is the Taylor factor of the assumed fully lamellar TiAl alloy with all grains in hard mode, and 4 is the resistance from the lamellar interface in polycrystals. 4.5. Real fully lamellar polycrystalline TiAl alloys Fig. 3. Lamellar spacing distribution of specimens (a) and (d).

4.2. Single phase -TiAl alloys In the single phase g-TiAl alloys, the only obstacle for dislocations glide is the grain boundary. Slip in the single phase alloys may be considered to be similar to slip in PST crystal in soft mode, but in the former case the obstacle for dislocation glide is grain boundary, in the later case the obstacle for dislocations glide is the domain boundary. Therefore, if we replace the domain size (d) with grain size (D) and replace the Taylor factor of PST in soft mode deformation with polycrystalline apparent Taylor factor in Eq. (1), y may be related to the grain size for the single phase alloy as, n  1=2 o …3† y ˆ M3 0 ‡ …2 ÿ †3 b=…2…1 ÿ †D† where 3 is the barrier strength for grain boundary. M3 is Taylor factor for polycrystalline single g alloy, but it is no longer a simple physical quantity, and can be calculated by experimental data. If ÿassume
1=2 0 ˆ M3 0 and , and take the ky ˆ M3 ‰…2 ÿ †b=2…1 ÿ †Š1=2 3 data shown in Table 2 for single phase alloys 0 ˆ 200 Mpa, ky ˆ 1:37 MPa mÿ1/2) [5], we can obtain M3 ˆ 4, and 3 ˆ 1125 MPa (0 ˆ 50 MPa,  ˆ 0:33,  ˆ 66 GPa, b ˆ 4  10ÿ4 mm).

In this model, we assume the soft orientation deformation and the hard orientation deformation are 50%, respectively, and in the hard orientation deformation, 0 and 90 are also 50%, respectively. Thus, y of the fully lamellar TiAl alloys can be related to both D and l as: 1 y ˆ …M3 ‡ M4 †0 2  1=2 1 ‡ …M3 ‡ M4 † …2 ÿ †3 b=…2…1 ÿ †D† 2  ÿ1=2 ‡ M4 44 b=l

…5†

The ®rst item of Eq. (5) is the shear stress to move a dislocation in fully lamellar TiAl alloys, which is the average of soft orientation deformation and hard orientation deformation. The second item represents the resistance from the grain boundary, which is also the average of soft orientation deformation and hard orientation deformation. The third item represents the resistance from the lamellar interface, which is from the hard orientation deformation grain only. In order to calculate M4 and 4 , we can use the experiment data of the relationship of lamellar spacing and yield strength with a constant size (00 ˆ 334 MPa, k0y ˆ 0:06 MPa m1/2, D ˆ 375 mm) showed in Table 2. In Eq. (5), the ®rst item and the second item are not in¯uenced by lamellar spacing (l). For fully lamellar alloys with a constant grain

G. Cao et al. / Intermetallics 8 (2000) 647±653

651

Fig. 4. TEM micrographs of microstructure of specimens (e), (f), (g) and (h).

Fig. 5. Yield stress as a function of grain size with a constant lamellar spacing of 150 nm.

size, the ®rst item and the second item is a constant, as a result, Eq. (5) may be simpli®ed as: n  1=2 o 1 y ˆ …M3 ‡ M4 †0 ‡ g ‡ M4 0 ‡ 64 b=l 2 …6† here g is the resistance from the grain boundary and can be calculated using Eq. (3). The ®rst item of Eq. (3)

Fig. 6. Yield stress as a function of lamellar spacing with a constant grain size of 360 mm.

can be removed when calculating g , because g only represents the resistance from grain boundary. When the value of D is 375 mm, the value of g is calculated to be 71 MPa. From the experiment data, in terms of Hall±Petch 00 ˆ 1=2 relationship: y ˆ 00 ‡ k0y lÿ1=2 , we assumed 1=2 ÿ 
1=2 0 …M3 ‡ M4 † ‡ g , and ky ˆ M4 …4b=l† 4 , and,

652

G. Cao et al. / Intermetallics 8 (2000) 647±653

Table 2 The values of 0 and ky of alloys No.

Microstructure

0 (MPa)

ky (MPa m-1/2)

Reference

1 2 3 4 5 6 7 8 9 10a 11a 12 13a

PST (soft orientation) PST (hard orientation, 0 ) PST (hard orientation, 90 ) Single g Single g Single g Single g Full lamellar Full lamellar Fully lamellar with a constant grain size (75 mm) Full lamellar Fully lamellar with a constant lamellar spacing Fully lamellar with a constant grain size

65 ÿ149 50 150 200 193 126 581 370 57 About 180 387 334

0.27 0.41 0.5 1.1 1.4 1.21 0.91 2.7 2.3 0.19 About 0.22 2.07 0.06

[7,8] [7,8] [7,8] [5] [5] [6] [6] [11] [10] [10] [16] Present work Present work

a

The Hall±Patch relationship between the lamellar spacing (l) and yield stress.

Fig. 7. Comparison between y from experiment data (dots) and y from Eq. (7) (solid lines): (a) the relationship between grain size and yield strength, (b) the relationship between lamellar spacing and yield strength.

as mentioned above  ˆ 0:84, the value of M4 and 4 were calculated to be M4 ˆ 6:5, and 4 ˆ 2:13 MPa. Eq. (6) can be simpli®ed as: y ˆ A0 ‡ BDÿ1=2 ‡ Clÿ1=2

…7†

where A ˆ 1=2…M3 ‡ M4 † ˆ 5:3;  1=2 ˆ 1:82; B ˆ 1=2…M3 ‡ M4 † …2 ÿ †3 b=2…1 ÿ †   1=2 C ˆ M4 44 b= ˆ 0:06: Eq. (7) may correctly simulate the experimental results obtained in present work as shown in Fig. 7 solid line. From the above two Hall±Petch relations, we can see that s00 (334) is less than 0 (387). 0 is equal to the ®rst item and the third item of Eq. (7) which represent the resistance from lamellar interface and shear stress to move a dislocation through polycrystalline fully lamellar alloy; 00 is equal to the ®rst item and the second item which represents the resistance from the grain size and shear stress to move a dislocation through polycrystal-

line fully lamellar alloy. We assumed that the shear stress to move a dislocation through polycrystalline fully lamellar alloy is a constant. The conclusion that the resistance from lamellar interface is larger than that of grain size can be gotten. 5. Conclusion 1. The relationship between grain size and yield strength with a constant lamellar spacing is conform to the Hall±Petch relation, i.e. y ˆ 0 ‡ ky Dÿ1=2 . 0 and p ky were determined to be 387 MPa and 2.07 MPa m, respectively. 2. The relationship between lamellar spacing and yield strength with a constant grain size is conform to the Hall±Petch relation, i.e. y ˆ 0 ‡ k0y lÿ1=2 , 00 and ky0 were p determined to be 334 MPa and 0.06 MPa m, respectively. 3. The in¯uence of lamellar spacing on yield strength is more obvious than that of grain size.

G. Cao et al. / Intermetallics 8 (2000) 647±653

Acknowledgement This work is supported by China National Nature Science Foundation under the contract number 59895153-03.

References [1] [2] [3] [4]

Kim Y. Jom 1995;47(6):39. Kim Y. Mater Sci Eng 1995;A192(193):529. Kim Y, Dimiduk DM. J Met 1991;43:40. Kim Y. Dimiduk DM. Proc. JIMIS-7 on high temperature deformation and fracture. Japan Institute for Metals, Sendai. 1993, p. 82. [5] Huang S, Shih DS. In: Kim Y et al., editors. Titanium aluminides and alloys. Warrendale (PA): TMS, 1990. p. 105.

653

[6] Vasudeva VK, Count SA, Kurath P, Fraser HL. Scripta Metall 1989;23:467. [7] Umakoshi Y, Nakano T, Yamane T. Mater Sci Eng 1992;A152:81. [8] Umakoshi Y, Nakano T. Acta Metall Mater 1993;41:1135. [9] Kim Y, Dimiduk D M. In: Darolia R et al., editors. Structural intermetallics. Warrendale (PA): TMS, 1997. p. 531. [10] Dimiduk DM, Hazzledine PM, Parthasarathy TA, Seshagiri S, Mendiratta MG. Metall Trans 1998;29A:37. [11] Chan KS, Kim Y. Metall Trans 1994;25A:1217. [12] Zhang YG, He ZN, Xu Q, Chen CQ, Chaturvedi MC. In: Kim Y et al., editors. Gamma titanium aluminides. Warrendale (PA): TMS, 1995. p. 283. [13] Li J, Chou Y. Metall Trans 1970;3:1145. [14] Rao SI, Woodward C, Simmons JP, Dimiduk DM. In: Horton JA et al., editors. High temperature ordered intermetallic alloys VI. Pittsburgh (PA): MRS, 1995. p. 3. [15] Inui H, Nakamura A, Oh MH, Yamaguchi M. Acta Metall Mater 1992;40:7. [16] Maziasz PT, Liu CT. Metall Trans 1998;29A:105.