twinning planes at lamellar boundaries in fatigued TiAl polysynthetically twinned crystals

ARTICLE IN PRESS SCITEC187

S C I E N C E A N D TECHNOLOGY OF

1

ADVANCED MATERIALS

2 3 4

Science and Technology of Advanced Materials 00 (2002) 000±000

www.elsevier.com/locate/stam

5

57 58 59 60 61

6

62

7

63

Selection and change in deformation mode to maintain continuity of strains and slip/twinning planes at lamellar boundaries in fatigued TiAl polysynthetically twinned crystals

8 9 10 11 12

71

74 75

27 28 29 30 31 32 33 34 35

F

Keywords: Ti±Al; TiAl-PST; Fatigue; Lamellar boundary; g Domain; Twin; Ordinary dislocation; Continuity of strain; Slip/twinning transfer; Anomalous accumulation of strain energy

90

O

78

O

26

36 37

44 45 46 47 48 49 50 51 52 53 54 55 56

R

43

R

42

O

41

A harmonic design of materials by combining different phases with different suitable properties is necessary for development of new functional and/or structural materials. Ni-based super alloys are an example of materials developed successfully on the basis of the harmonic design, and progress has been of sought in Ni-base and other L12based alloys to improve the registered temperature for practical use [1±4]. A novel combination of intermetallic phases with no disordered phase has recently been focused

C

40

N

39

1. Introduction

* Corresponding author. Department of Materials Science and Engineering, Graduate School of Engineering, Osaka University, 2-1, Yamada-Oka, Suita, Osaka 565-0871, Japan. Tel.: 181-6-6879-7496; fax: 181-6-68797497. E-mail address: [email protected] (T. Nakano). 1 Present address: Research and Development Center, Sumitomo Light Metal Industries Ltd, 3-1-12, Chitose, Minatoku, Nagoya, Aichi 455-8670, Japan.

U

38

77

Change in deformation mode in six types of g domain (AM ±CT) and a2 plates in TiAl polysynthetically twinned (PST) crystals fatigued at a loading axis parallel to lamellar planes with stress amplitude (Ds ) of 420±450 MPa was examined by the transmission electron microscope focusing on continuity of macroscopic strains and slip/twinning planes at lamellar boundaries. At Ds ˆ 420 and 450 MPa, the strain continuity is always maintained at lamellar boundaries by activation of one of the symmetric twinning systems in A-type domain and selection of the dominant deformation mode between ordinary dislocations and twins in (B and C)-type g domain. The (B and C)-type g domains of BM, BT, CM and CT behave as two sets of (BM,CT) and (BT,CM) because each set selects either the deformation mode of ordinary dislocations or twins as a dominant system in order to keep macroscopic strain continuity. The set (BT,CM) which accounts for a larger volume fraction than the set (BM,CT) in TiAl-PST crystals used in this study selected a twinning system at Ds ˆ 450 MPa, while ordinary dislocations were selected at Ds ˆ 420 MPa. At Ds ˆ 450 MPa, twinning deformation prevented the further motion of ordinary dislocations with a Burgers vector parallel to lamellar boundaries, and rapid fatigue hardening occurred accompanied by reduction of the accumulative plastic strain energy. Anomalous change in strain energy during fatigue is in¯uenced by the volume fraction of a set of (B and C)-type domain and the anomalous behavior in fatigued TiAl-PST crystals may disappear when each type of g domain is equally distributed. q 2002 Elsevier Science Ltd. All rights reserved.

PR

25

76

D

24

Abstract

EC TE

23

72 73

Received 15 December 2001; revised 4 January 2002; accepted 4 January 2002

19

22

68

Department of Materials Science and Engineering, Graduate School of Engineering, Osaka University, 2-1, Yamada-Oka, Suita, Osaka 565-0871, Japan b Frontier Research Center, Graduate School of Engineering, Osaka University, 2-1, Yamada-Oka, Suita, Osaka 565-0871, Japan

18

21

67

70

a

17

20

66

69

14 16

65

Takayoshi Nakano a,b,*, Yasuhiro Nakai a,1, Yukichi Umakoshi a,b

13 15

64

80 81 82 83 84 85 86 87 88 89 91 92 93

on the usage of their superior strength at high temperatures. TiAl/Ti3Al and MoSi2/NbSi2 containing peculiar lamellae showing good stability at high-temperatures are the most promising candidates because of their excellent oxidation resistance, relatively light weight and superior hightemperature strength. Many excellent reviews and reports on aluminides and silicides have been published [5±13]. Since intermetallics in general show lower crystallographic symmetry than fcc and bcc alloys in disordered state, the operative deformation modes are restricted and deformation transfer at boundaries often affects the macroscopic plastic deformation in duplex intermetallic phases. The transfer mechanisms of deformation in TiAl polysynthetically twinned (PST) crystals with oriented lamellae were investigated as an ideal model for understanding continuity of strains and slip/twinning planes at different types of lamellar boundary such as g/g domain boundaries and g/a2 interfaces [14±18]. Detailed transmission electron microscopic studies were also performed in polycrystalline TiAl/Ti3Al

1468-6996/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 1468-699 6(02)00018-9 Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

79

article

ap

Alden

94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

ARTICLE IN PRESS

121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158

162 163 164 165 166 167 168

2. Experimental procedure

N

161

TiAl-PST crystals containing Ti±49.1at.%Al were prepared and cyclic deformation was performed in a tension/compression mode under a stress amplitude of Ds ˆ 450 MPa at a frequency of 10 Hz in air at room temperature. The beginning was done in tension. The load was applied at f ˆ 08 and x ˆ 08 where x is the angle  in g domains. The between the loading axis and k112l

U

160

C

159

169 170 171 172 173 174 175 176 177 178 179 180 181 182 183

3. Results

184

3.1. Geometrical classi®cation of lamellar boundaries

186

Strain continuity at boundaries is often calculated based on the decomposed reaction of Burgers vector [15±20,22± 25]. Lamellar boundaries in TiAl-PST crystals fatigued at Ds ˆ 420 MPa were classi®ed into 13 types composed of three g/g true twin, three g/g pseudo twin, three g/g 1208rotation and four g/a2 interfaces [18]. Since such classi®cation made it possible to understand the roles of slip/twinning transfer at each boundary, the same method was applied to the geometrical classi®cation of boundaries in TiAl-PST crystals fatigued at Ds ˆ 450 MPa where anomalous accumulation of plastic strain energy appeared. Since TiAl-PST crystals consist of six types of g domain, AM, BM, CM, AT, BT and CT, and a single-oriented a2 phase maintaining Blackburn's orientation relationship, the relationship among g domains and a2 phase are described on  in AT, BT and CT and on (111) plane in AM, BM and CM, …1 1 1† the (0001) plane in the a2 phase in Fig. 1. The ‰X; Y; ZŠ standard coordinates (S) are also de®ned in this ®gure. The loading direction and lamellar plane normal at f ˆ 08 are parallel to the X and Z axes, respectively. Although the L10 structure of g domain shows a slight tetragonality, the g phase is regarded as a cubic lattice for simplicity. Since in TiAl-PST crystals deformed at f ˆ 08 and x ˆ 08 slip/twinning occurs on {111} octahedral planes in g  phase and on {1100} prism planes in the a2 phase [8,10± 12,14,18,26±31], these important crystallographic planes are denoted as , , and in AM, BM and CM domains, , , and in AT, BT and CT and , and in the a2 phase, respectively, as shown in Fig. 2. They are de®ned on the basis of the relative orientation relationship to the loading axis and lamellar planes. The same de®nition was used in our previous paper [18]. The lamellar boundaries can ®rst be classi®ed into three types of g/g domain boundary and one g/a2 interface. The true twin boundary is formed between AM and AT, between BM and CT or between BT and CM; the pseudo twin boundary between AM and BT, between AM and CT, between BM and

188

185

F

120

O

119

O

118

PR

117

fatigue test was stopped at 1 £ 10 5 cycles. Experimental details were given in our previous paper [26]. Thin foils were cut parallel to the loading axis and perpendicular to the lamellar planes. As a result, the foil  directions in the g normal was thus selected to be k110l  domains and ‰1210Š in the a2 phase. The direction is for  in AM. The foils were thinned to 60 mm example ‰110Š thickness and then electrolytically perforated by a twin jet method using a solution of 1:2:7 by volume of perchloric acid/glycerin/methanol at 230 8C. Deformation substructure and continuity of deformation modes in the fatigued samples were examined in a Hitachi H-800 TEM operated at 200 kV.

EC TE

116

R

115

lamellar crystals to determine the reaction and preservation of strain component in two neighboring g domains and a pair of a g domain and an a2 plate [19±25]. Zhang et al. for example, showed that the most important factor for slip transfer across g/a2 interfaces is existence of a common intersection of slip/twinning planes at the interface [22]. The similar transfer was also observed at g/g domain boundaries [15±17,23,24]. More recently, lamellar boundaries in TiAl-PST crystals fatigued at f ˆ 08 where f is the angle between the loading axis and lamellar plane, at Ds ˆ 420 MPa were classi®ed into 13 groups composed of three g/g true twin, three g/g pseudo twin, three g/g 1208 rotation boundaries and four g/ a2 interfaces on the basis of the Schmid factor for possible slip and twinning systems [18]. They were subdivided into two groups composed of continuous and discontinuous geometry. Detailed analysis of dominant deformation mode by the transmission electron microscope (TEM) showed that macroscopic strain continuity was maintained at all the boundaries. At several boundaries strain continuity was maintained by activation of deformation modes unexpected from Schimid factor consideration. Continuity of macroscopic strains was concluded to be a more effective factor than the continuity of slip/twinning planes and Schimid factors for deformation transfer across the boundary. In TiAl-PST crystals fatigued at f ˆ 08 under a constant applied stress amplitude, anomalous behavior in accumulated plastic strain energy appeared with increasing stress amplitude [26]. The energy for each cycle increased with increasing stress amplitude but an anomalous energy drop was observed at around Ds ˆ 440 MPa. This anomalous behavior was thought to be related to change in the dominant deformation mode from the motion of ordinary dislocations to twinning with increasing stress amplitude in several types of g domain, but no detailed TEM observation was performed, especially above Ds ˆ 440 MPa where anomalous accumulation of plastic strain energy appeared in the slip transfer mechanism at lamellar boundaries. In this article, the continuity of macroscopic strain components at lamellar boundaries was examined geometrically and experimentally in TiAl-PST crystals fatigued at Ds ˆ 450 MPa in comparison with that at Ds ˆ 420 MPa reported earlier [18]. The focus was on cause of the anomalous change in plastic strain energy with stress amplitude between 420 and 450 MPa.

R

114

O

113

T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

D

2

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

article

ap

Alden

187 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224

ARTICLE IN PRESS T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

3 281

226

282

227

283

228

284

229

285

230

286

231

287

232

288

233

289

234

290

235

291

236

292

237

293

238

294

239

295

240

296

241

297

242

298

243

299

244

300

F

225

245 247 249 251 252

258 259 260 261 262 264 266 268 270

278 279 280

314 315 316 317 318

322 323 324 325 326 327 328 329 330 331 332 333

 Fig. 2. Schematic illustrations of {111} octahedral slip/twinning planes in g domains and {1100} prism plane in the a2 phase in TiAl-PST crystals deformed at f ˆ 08 and x ˆ 08: The important crystallographic planes are denoted as , , and in AM, BM and CM domains, , , and in AT, BT and CT and , and in the a2 phase.

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

313

321

U

277

312

320

N

272

310

319

C

271

309 311

of g domain. Schmid factors for possible deformation modes in each g domain are shown in Table 1. Since the twinning partial moves in one preferential direction, positive and negative values of Schmid factors in compression and tension, respectively, are favorable for twinning. According to Schmid factor consideration, g domains in

O

269

276

308

R

267

275

307

R

265

274

306

D

AT, between BM and BT, between CM and AT or between CM and CT; and the 1208 rotation boundary between AM and BM, between BM and CM, between CM and AM, between AT and BT, between BT and CT or between CT and AT. Furthermore, the direction of loading axis should be considered since activated deformation modes roughly depend on the type

263

273

305

EC TE

257

304

Fig. 1. Geometrical orientation relationship among six g domains, AM, BM, CM, AT, BT and CT, and the a2 phase under Blackburn's orientation relationship on  in AT ±CT and (0001) in the a2 phase. The ‰X; Y; ZŠ standard coordinate (S) is de®ned in this ®gure. (111) in AM ±CM, …111†

255 256

303

PR

250

254

302

O

248

253

301

O

246

article

ap

Alden

334 335 336

ARTICLE IN PRESS 341 342

Slip plane

Type of domain

343 344 345 346 347 348 349 350 351 352 353 354

 110Š  …111†‰  …111†‰101Š   …111†‰01 1Š  11  2Š  …111†‰  1†‰110Š  …11  1†‰  101Š  …11  1†‰0  11Š  …11  1†‰1  12Š  …11   …111†‰1 10Š  10  1Š  …111†‰  …11†‰011Š  …111†‰112Š

AM, AT

BM, BT

CM, CT

0.272 0.136 0.408 10.314 0.272 0.408 0.136 10.314 0 0.272 0.272 10.314

0.136 0.272 0.408 20.393 0.272 0 0.272 20.157 0.408 0.272 0.136 10.079

0.272 0.272 0 20.157 0.136 0.408 0.272 20.393 0.408 0.136 0.272 10.079

355 356 358 359 360 361 362 363 364 365 366 367 368 369 370 371

TiAl-PST crystals loaded at f ˆ 08 and x ˆ 08; are classi®ed into two groups of A-type and (B and C)-type, although such a simple classi®cation was ®nally concluded not to be appreciable in our previous paper [18]; the same conclusion was reached and the simple classi®cation is also not in this article due to the macroscopic strain continuity across the lamellar boundary. For simplicity, however, the Schmid factor is considered in this initial geometrical classi®cation. Operative deformation modes markedly changed in (B and C)-type g domain of TiAl-PST crystals fatigued below and above Ds ˆ 440 MPa [26]. In almost all the (B and C)-type domain, dominant deformation modes seemed to change from the motion of ordinary dislocations with a Burgers vector parallel to lamellar boundaries to twinning

EC TE

357

372 373 374 375 376 378 380 382

387 388 389

392

399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427

434 435 436 437 438 439 440 441 442 443 444 445 446

390 391

398

433

U

386

397

432

N

384

396

431

C

383

395

430

O

381

394

429

R

379

393

428

R

377

385

F

340

across lamellae. Based on Schmid factor and TEM observation in the majority of (B and C)-type domain, dominant deformation modes and their relative incidence in each domain and a2 phase of TiAl-PST crystals fatigued at 450 MPa above the critical stress amplitude of 440 MPa are represented by the number of arrows in Fig. 3. The operative deformation modes and their relative incidence are depicted by Burgers vectors projected on the X±Z plane and the number of arrows. The deformation mode with the maximum number of arrows is regarded as the dominant mode in each g domain or the a2 phase. A similar description was given at Ds ˆ 420 MPa below 440 MPa in Fig. 2 in our previous paper [18]. The principal difference depending on stress amplitude between 420 and 450 MPa appears in (B and C)-type domain. In CM domain, for exam 1†‰1  1 2Š  twinning in tension and …11  1†‰  101Š  ple, …11 slip in compression are dominant deformation modes at   Ds ˆ 450 MPa, while …111†‰1 10Š slip in tension and compression is dominant at Ds ˆ 420 MPa. Two equivalent deformation modes on symmetrical octahedral {111} planes exist in A-type domain and the a2 phase, while there are no symmetrical planes for the possible operative deformation modes in (B and C)-type domain in tension or compression. Anyway, Schmid factor consideration leads to classi®cation of three groups composed of (AM, AT), (BM, BT, CM, CT) and the a2 phase independent of the stress amplitude. These three can reconstruct eight types of boundaries similar to the previous classi®cation at Ds ˆ 420 MPa [18] as shown in Table 2, but the dominant deformation mode at Ds ˆ 450 MPa is quite different from that at Ds ˆ 420 MPa as shown in Fig. 3. In this article, hereafter the eight types of boundaries in Table 2 are abbreviated as TT1±In2.

O

339

Table 1 Schmid factors for possible slip/twinning system in TiAl-PST crystals deformed at f ˆ 08 and x ˆ 08 in g domains. Twinning in tension and compression is represented by 2 and 1, respectively (twinning in tension: 2, twinning in compression: 1)

O

338

PR

337

T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

D

4

Fig. 3. The dominant operative deformation modes and their relative intensity in each g domain and the a2 phase of TiAl-PST crystals fatigued at Ds ˆ 450 MPa in tension and compression. The relative intensity are qualitatively represented by the number of arrows.

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

article

ap

Alden

447 448

ARTICLE IN PRESS T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

AM/AT BM/CT, BT/CM AM/BT, AM/CT, AT/BM, AT/CM BM/BT, CM/CT AM/BM, AT/BT, AM/CM, AT/CT BM/CM, BT/CT a2/AM, a2/AT a2/BM, a2/BT, a2/CM, a2/CT

455 456 457 458 459 460 461 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481

3.2. Strain continuity through lamellar boundaries So far, slip/twinning transfer has been discussed by total strain components represented by Burgers vector before and after the transmission through lamellar boundaries [15±17,22±25]. The same method in our previous paper [18] was applied for the TiAl-PST crystals fatigued at Ds ˆ 450 MPa. Macroscopic strain components for each dominant operative deformation mode in TiAl-PST crystals fatigued at Ds ˆ 450 MPa are given at the true twin boundaries of TT1 and TT2 in Fig. 4, at the pseudo twin boundaries of PT1 and PT2 in Fig. 5, at the 1208 rotation boundaries of R1 and R2 in Fig. 6 and at the g/a2 interfaces of In1 and In2 in Fig. 7. The depicted dominant deformation modes are based on those in Fig. 3. The components for each mode are regarded as k110] for two 1/2k110] ordinary dislocations, k101] for one k101] superlattice dislocation, 1/2k112] for  three 1/6k112] twinning partials and 1=3k1210Š for one

EC TE

462

482 483 484 485 486 487 488 490 492 494

499 500 501 502 503 504

511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537

544 545 546 547 548 549 550 551 552 553 554 555 556

Fig. 4. Continuous and discontinuous components of macroscopic strain projected on the X±Z and Y±Z planes at true twin boundaries (TT1-a, TT1-b and TT2) in TiAl-PST crystals fatigued at Ds ˆ 450 MPa in tension and compression (labeled T and C, respectively). Continuous and discontinuous components of the macroscopic strain along the X, Y and Z axes are shown by black and white arrows, respectively. The slip/twinning systems assumed in each g domain are described.

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

510

543

U

498

509

542

N

496

508

541

C

495

507

540

O

493

506

539

R

491

505

538

R

489

497

F

True twin-1 (TT1) True twin-2 (TT2) Pseudo twin-1 (PT1) Pseudo twin-2 (PT2) Rotation-1 (R1) Rotation-2 (R2) Interface-1 (In1) Interface-2 (In2)

454

O

Adjacent phases at boundary

O

Type of boundary

453

 1=3k1210Š prism dislocation to evaluate the continuity of macroscopic strains at boundaries. The macroscopic components in tension and compression are projected as each vector individually along the X, Y and Z axes on the X±Z plane and Y±Z plane. Conservative and non-conservative components of macroscopic strains through lamellar boundaries are shown by black and white arrows, respectively. According to our previous study on the continuity of macroscopic strains and slip/twinning planes in TiAl-PST crystals fatigued at Ds ˆ 420 MPa, the component along the Y-axis is the most important to understand the continuity and slip/twinning transfer [18]. The boundaries are distinguished into two groups based on whether the Y component was reserved or not through the boundaries because the direction of this component is useful to determine continuity of the macroscopic strains and slip/twinning planes at boundaries. In A-type g domain, choice of the operative mode on the two symmetrical slip/twinning planes determines direction of the Y-component, and affects the continuity of the strains and planes. The boundaries neighboring the A-type domain are therefore distinguished as a-type and b-type where the macroscopic strain continuity along the Yaxis is or is not maintained, respectively, as seen in TT1, PT1, R1 and In1 boundaries. Although small white arrow at the end of black bar along Y-direction can be seen even in atype boundary, macroscopic strain continuity is assumed to be maintained in the present study. A similar classi®cation is possible even at the In2 interface containing no A-type domain because the prism slip in the a2 phase can be selected on the symmetrical slip planes. At several boundaries, the strain components are not maintained perfectly

PR

452

450

D

451

Table 2 Types of boundary formed by adjacent phases in TiAl-PST crystals with oriented lamellae

449

5

article

ap

Alden

557 558 559 560

ARTICLE IN PRESS 6

T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000 617

562

618

563

619

564

620

565

621

566

622

567

623

568

624

569

625

570

626

571

627

572

628

573

629

574

630

575

631

576

632

577

633

578

634

579

635

580

636

F

561

581

586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 602 604 606

612 613

616

643 644 645 646 647 648 649

655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670

614 615

642

654

U

611

641

653

N

608

640

652

C

607

639

651

O

605

638

650

R

603

610

crystals fatigued at Ds ˆ 450 MPa is summarized in Table 3. Although change in strain energy during cyclic deformation is different between Ds ˆ 420 and 450 MPa, the same classi®cation of boundaries is obtained (see Table 3 in Ref. [18]). However, the dominant deformation mode in (B and C)-type g domain varied depending on the stress amplitude: the motion of ordinary dislocations with a Burgers vector parallel to lamellar boundaries was dominant at Ds ˆ 420 MPa, while twinning occurred across lamellar

R

601

609

O

along the X and Z axes, but such small discordance may be accommodated by local instigation of the minor deformation mode as observed by several researchers [15±17,19± 25]. On the other hand, the continuity of macroscopic strains and slip/twinning planes is essentially maintained at the TT2 boundary and not at PT2 or R2 boundary by the dominant deformation mode expected by Schmid factor consideration. The continuity for all types of boundary in TiAl-PST

O

585

PR

584

D

583

637

Fig. 5. Continuous and discontinuous components of macroscopic strain projected on the X±Z and Y±Z planes at pseudotwin boundaries (PT1-a, PT1-b and PT2) in TiAl-PST crystals fatigued at Ds ˆ 450 MPa in tension and compression (labeled T and C, respectively).

EC TE

582

Fig. 6. Continuous and discontinuous components of macroscopic strain projected on the X±Z and Y±Z planes at 1208 rotation boundaries (R1-a, R1-b and R2) in TiAl-PST crystals fatigued at Ds ˆ 450 MPa in tension and compression (labeled T and C, respectively).

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

article

ap

Alden

671 672

ARTICLE IN PRESS T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

7 729

674

730

675

731

676

732

677

733

678

734

679

735

680

736

681

737

682

738

683

739

684

740

685

741

686

742

687

743

688

744

689

745

690

746

691

747

692

748

F

673

693 695 697 699 700 701 702 704 706 707 708 709 710 711 712

723 724 725 726 727 728

O

C

boundaries at Ds ˆ 450 MPa. The g/g domain boundaries and g/a2 interfaces at Ds ˆ 450 MPa ®nally can be divided into 13 combinations composed of six continuous and seven discontinuous boundaries similar to those at Ds ˆ 420 MPa.

N

722

756 757 758 759 760 761 762 763 764 765 766 767 768 769 770

Fig. 7. Continuous and discontinuous components of macroscopic strain projected on the X±Z and Y±Z planes at g/a2 interfaces (In1-a, In1-b, In2-a and In2-b) in TiAl-PST crystals fatigued at Ds ˆ 450 MPa in tension and compression (labeled T and C, respectively).

U

721

755

R

714

720

754

R

713

719

753

EC TE

705

718

752

D

703

717

751

PR

698

716

750

O

696

715

749

O

694

3.3. Fatigued microstructure and its analysis in TiAl-PST crystals at D s ˆ 450 MPa on the basis of macroscopic strain continuity through lamellar boundaries Deformation substructures in TiAl-PST crystals fatigued

at Ds ˆ 450 MPa at room temperature to N ˆ 1 £ 10 5 cycles were observed by TEM, focusing on slip/twinning transfer through lamellar boundaries on the basis of the 13 classi®cations in Table 3. The types of g domain, operative dominant deformation modes and boundary types were determined by tilting and g´b analyses in the TEM. Details of the method were described in our previous papers [18,26]. In this crystal, the volume fraction of the (BT, CM) set is relatively larger than that of the (BM, CT) set. Fig. 8 shows a bright ®eld image and a corresponding schematic illustration in a TiAl-PST crystal fatigued at

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

article

ap

Alden

771 772 773 774 775 776 777 778 779 780 781 782 783 784

ARTICLE IN PRESS 8 785 786 787 788 789 790

T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

Table 3 Classi®cation of the boundaries on the basis of continuity (C, continuous; NC, non-continuous) of macroscopic strains and slip/twinning planes in TiAl-PST crystals fatigued at f ˆ 08 and x ˆ 08 at Ds ˆ 450 MPa Type of boundary (wide classi®cation)

Continuity of slip plane (Continuous/Non-continuous)

791 792 793 794 795 796 797 798 799 800 801 802 803

True twin-1 (TT1) True twin-2 (TT2) Pseudo twin-1 (PT1) Pseudo twin-2 (PT2) Rotation-1 (R1) Rotation-2 (R2) Interface-1 (In1) Interface-2 (In2)

C NC C C NC NC C NC NC C NC C NC

Type of boundary (narrow classi®cation) TT1-a TT1-b TT2 PT1-a PT1-b PT2 R1-a R1-b R2 In1-a In1-b In2-a In2-b

F

804

Ds ˆ 450 MPa. Highly dense deformation twins are observed in all g domains belonging to both A-type and (B and C)-type in this ®gure, while BM and CT domains as the minor constituent do not exist in this area. Since all twinning planes are edged on at the incident beam parallel  in AM, they are determined to be …11 1†  ( ) in AM, to ‰011Š       …111† ( ) in CM, …111† ( ) in AT and …111† ( ) in BT. This beam direction was obtained by the foil rotated 608   about the [111] zone axis. Moreover, the …1100†‰ 1120Š prism slip was operative on plane in the a2 phase. Continuity of macroscopic strains and slip/twinning planes is therefore maintained and all boundaries are the continuous type in Table 3. It should be noted that the slip/twinning plane in AM domain and the prism slip plane in the a2 phase are selected between two symmetrical planes so that macroscopic strain transfer occurs through the boundaries. In addition, k101] superlattice dislocations are also operative on the plane parallel to the deformation twinning planes in AM, AT, BT and CM domains. The Burgers vector of k101] dislocations is parallel to the lamellar boundaries as shown in Fig. 3 and often decomposes into 1/2k112] and 1/2k110] dislocations as reported by several researchers [14,32,33].

805

O

806 807 809 811 812 813 814 816 818 819 820 821 822 823 824 826 828 830

834 835 836 837

840

852 853 854 855 856 857 858 859 860 861 862 863

874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894

838 839

851

873

U

833

850

872

N

832

849

871

C

831

848

870

O

829

847

869

R

827

846

868

R

825

845

867

EC TE

817

844

866

D

815

843

865

PR

810

842

864

O

808

841

5

Fig. 8. A bright-®eld image and the corresponding schematic illustration in TiAl-PST crystals fatigued at Ds ˆ 450 MPa to 1 £ 10 cycles. The beam direction  in AM. is parallel to ‰011Š

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

article

ap

Alden

895 896

ARTICLE IN PRESS T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

9 953

898

954

899

955

900

956

901

957

902

958

903

959

904

960

905

961

906

962

907

963

908

964

909

965

910

966

911

967

912

968

913

969

914

970

915

971

916

972

F

897

917 919

O

920 921

930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952

976 977 5

PR

lamellar boundaries. This result indicates that the continuity of macroscopic strains has priority over Schmid factor consideration as suggested in TiAl-PST crystals fatigued at Ds ˆ 420 MPa [18]. The operative deformation mode of ordinary dislocations in the minor set of BM and CT domains at Ds ˆ 450 MPa is in good accordance with that in the major set of BT and CM domains at Ds ˆ 420 MPa. Since the dominant deformation mode in the major set of BT and CM domains with the larger volume fraction becomes twinning at Ds ˆ 450 MPa, a favorable applied stress to activate twins as well as ordinary dislocations in (B and C)-type domain must be reached on the viewpoint of Schmid factor consideration, while twins hardly appear in the set of BM and CT domains with the smaller volume fraction. This result strongly suggests that the continuity of macroscopic strains and slip/twinning planes is the most important factor in selecting the deformation mode in g domains and the a2 plate. Fig. 10 shows the fatigued microstructure containing the a2 phase bounded by In1 and In2 boundaries. In the a2  phase, the to-and-fro motion of 1=3‰1 120Š prism dislocations  occurs on the …1100† plane ( ). As a result, macroscopic continuity is maintained at the interfaces of In1-a and In2-a, and almost all slip traces of the prism dislocations in the a2 phase immediately connect to twinning traces in the neighboring g domains. In TiAl-PST crystals fatigued at Ds ˆ 420 MPa, the prism slip in the a2 phase was induced by the operation of twins, but by ordinary dislocations in the

D

929

975

EC TE

928

R

927

R

926

Of course, minor slip/twinning modes were activated to accommodate local residual strain, and the detailed analysis on the fatigued TiAl-PST crystals was done in our previous paper [26]. Fig. 9 shows the fatigued microstructure containing BM and CT domains which are not seen in Fig. 8. In this area, all types of boundary under the wide classi®cation in Table 3 exist: TT1, TT2, PT1, PT2, R1, R2, In1 and In2. Detailed TEM observation and its analysis clari®ed that the 1/2k110] ordinary dislocations with a Burgers vector parallel to lamellar boundaries were dominantly activated in BM and CT domains which account for a relatively smaller volume fraction than BT and CM in lamellae. The ordinary disloca  ( ) plane in BM and ‰110Š  on …1 11†  tions by ‰110Š on …1 11† ( ) plane in CT were found to operate. Low-dense traces for twins were also observed to maintain the continuity of local strains but dominant strains. If the twins are dominantly activated in spite of the activation of ordinary dislocations on the basis of Schmid factor consideration in BM and CT domains, boundaries surrounding the domains would behave as discontinuous boundaries which could not maintain the continuity of macroscopic strains and slip/ twinning planes. Such possible discontinuous boundaries of PT1-b, PT2, R1-b and R2 are represented by bold lines in Fig. 9, but change in the dominant deformation mode from twins to ordinary dislocations in the BM and CT domains indeed makes it possible to maintain the continuity of macroscopic strains and slip/twinning planes through

O

925

C

924

974

Fig. 9. A bright-®eld image and the corresponding schematic illustration in TiAl-PST crystals fatigued at Ds ˆ 450 MPa to 1 £ 10 cycles. The Beam  direction is parallel to ‰110Š in AM.

N

923

U

922

973

O

918

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

article

ap

Alden

978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008

ARTICLE IN PRESS 10

T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000 1065

1010

1066

1011

1067

1012

1068

1013

1069

1014

1070

1015

1071

1016

1072

1017

1073

1018

1074

1019

1075

1020

1076

1021

1077

1022

1078

1023

1079

1024

1080

1025

1081

1026

1082

1027

1083

1028

1084

F

1009

1029 1031

1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055

1058 1059 1060 1061 1062 1063 1064

D

1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109

4. Discussion

1110 1111 1112 1113

N

1057

In TiAl-PST crystals fatigued at Ds ˆ 450 MPa where plastic strain energy was anomaly accumulated, the continuity of macroscopic strains and slip/twinning planes was maintained through all lamellar boundaries similar to that at Ds ˆ 420 MPa. The major difference at stress amplitudes of both 450 and 420 MPa appears in dominant deformation modes in (B and C)-type domain: twins at

U

1056

1094

EC TE

1041

1093

R

1040

1090 1092

R

1039

1089 1091

O

1038

neighboring g domains due to the stress concentration [18]. In the crystal fatigued at Ds ˆ 450 MPa twinning is a dominant deformation mode in AM, AT, BT and CM, accounting for almost the entire volume fraction in lamellae (as shown later in Fig. 11). Thus, highly dense traces by the prism slip may become marked as shown in Fig. 10. This TEM observation corresponds to the slip trace on prism planes in the a2 phase on the surface of TiAl-PST crystals becoming remarkable and more uniform with increasing stress amplitude over Ds ˆ 440 MPa, where anomalous strain energy accumulation occurs as shown in the previous paper [18]. According to the high resolution X-ray measurement, the residual strain accumulated in the a2 phase in TiAl-PST crystals fatigued at Ds ˆ 450 MPa is smaller than that at Ds ˆ 420 MPa [34]. This suggests that activation of uniform and highly-dense prism dislocations induced by highly dense twins in g domains accommodates and reduces the residual elastic strain in the a2 phase.

C

1037

1088

Fig. 10. A bright-®eld image and the corresponding schematic illustration in TiAl-PST crystals fatigued at Ds ˆ 450 MPa to 1 £ 10 5 cycles. The beam  in AM. direction is parallel to ‰011Š

1035 1036

1087

PR

1034

1086

O

1032 1033

1085

O

1030

1114 1115

Fig. 11. Schematic illustration showing traces of operative dominant slip/ twinning in TiAl-PST crystals below and above Ds ˆ 440 MPa. Volume fraction of the set of (BT and CM) is assumed to be larger than that of (BM and CT) in this ®gure. The macroscopic shear direction is changed below and above Ds ˆ 440 MPa. Continuity of macroscopic strains and slip/twinning planes is maintained.

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

article

ap

Alden

1116 1117 1118 1119 1120

ARTICLE IN PRESS T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176

Table 4 Schematic illustration showing macroscopic shape change on lamellar planes in TiAl-PST crystals fatigued at f ˆ 08; x ˆ 08 below and above Ds ˆ 440 MPa in tension/compression modes. Volume fraction of the set of (BT and CM) is assumed to be larger than that of (BM and CT) in this table

1211

F

1132

O

1131

O

1130

PR

1129

D

1128

1177

EC TE

1127

R

1126

(B and C)-type domain changes the relative activation of dominant deformation mode between the ordinary and twins in the two sets, resulting in the anomalous fatigue behavior. This alludes to disappearance of the anomalous change in accumulated plastic strain energy in TiAl-PST crystals when six types of g domain with equal volume fraction are uniformly distributed in lamellae. Thus, distribution in volume fraction for each (B and C)-type domain, especially between the two sets (BT and CM) and (BM and CT), is an important factor for controlling the fatigue hardening behavior in TiAl-PST crystals with a loading axis parallel to lamellar boundaries. Kishida et al. clearly showed that macroscopic shape change during deformation proceeds in an anisotropic manner in TiAl-PST crystals deformed at f ˆ 08 [14]. The crystals tend to increase the width along the Y-axis but not to change it along the Z-axis. This is explained by negligible value of the normal strain in the direction perpendicular to the lamellar boundaries. Similar anisotropic shape change was observed in TiAl-PST crystals fatigued at f ˆ 08 at both Ds ˆ 420 MPa and Ds ˆ 450 MPa. In the fatigued crystals, dominant operative slip/twinning planes vary with selection of a deformation mode depending on the distribution of (B and C)-type domain; a schematic illustration of anisotropic shape change is predicted in Table 4. In this table, the volume fraction in the set (BT and CM) is assumed to be larger than that in the set (BM and CT). Since the shear direction changes above and below Ds ˆ 440 MPa where anomalous plastic strain energy accumulation occurs as shown in Fig. 11, the shape change on lamellar plane of the X±Y plane is symmetrical under both stress conditions. This suggests that the spatial distribution of g domains in lamellae possibly controls the

Tension

Initial state

Compression

1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1212 1213 1214 1215 1216 1217

Below Ds ˆ 440 Mpa

1218 1219

R

1125

O

1124

C

1123

Ds ˆ 450 MPa and ordinary dislocations at Ds ˆ 420 MPa in the set of (BT and CM) domains with the larger volume fraction than the (BM and CT) set. The g domains of AM ±CT are produced during a±g transformation, avoiding an increase in crystal strain, thus the six types of g domain are ideally distributed having equal volume fraction for each domain. However, lamellar boundaries in TiAl-PST crystals are not necessarily parallel or perpendicular to the direction of crystal growth and heat transfer. Inui et al. also reported that there is priority in the selection of types of boundary due to their different energies [35]. As a result, distribution of g domain type AM ±CT is not necessarily equal as reported by Zghal et al. [36]. This uneven distribution of volume fraction for each g domain plays as an important role in the anomalous strain energy accumulation and is discussed in this section. Fig. 11 shows a schematic illustration of traces parallel to the dominantly operative slip/twinning planes in TiAl-PST crystals fatigued below and above Ds ˆ 440 MPa. Volume fraction of the set of (BT and CM) is assumed to be larger than that of (BM and CT) in accordance with the TEM observation. Since the macroscopic continuity of strains through boundaries is maintained independent of stress amplitude, the similar deformation mode appears in each set of g domains: below Ds ˆ 440 MPa, twins in AM, AT, BM and CT and ordinary dislocations in BT and CM and above Ds ˆ 440 MPa, twins in AM, AT, BT and CM and ordinary dislocations in BM and CT. However, the direction of operative dominant slip/twinning traces and the volume fraction for activation of each mode are, of course, quite different as described in Fig. 11. Since the dominant deformation mode does not change remarkably in A type domain, a discontinuous change in fatigue behavior with increasing stress amplitude is closely related to the deformation mode in (B and C)-type domain. The dominant deformation mode in each set of (BM and CT) or (BT and CM) is selected depending on the relative volume fraction of the two sets in the initial stage of fatigue deformation. Twinning observed frequently in the (B and C)-type domain is a possible dominant deformation mode in tension, while that in A-type domain is possible in compression. The twin formation in (B and C)-type domain is known to restrict the following operation of ordinary dislocations on another symmetrical slip plane [18,26]. Although in the initial stage of TiAl-PST crystals fatigued at Ds ˆ 450 MPa slip by the ordinary dislocations is selected as a dominant deformation mode due to suf®ciently high applied stress for activation of the slip, an increase in the number of twin interrupts the to-and-fro motion of the ordinary dislocations in the crystal fatigued above Ds ˆ 440 MPa and the slip/twinning planes different from those below Ds ˆ 440 MPa are selected. The restriction of motion of ordinary dislocations by the twins introduced earlier may contribute to rapid fatigue hardening and the following reduction of accumulated plastic strain energy. The uneven distribution of volume fraction for two sets of

1220 1221 1222

Above Ds ˆ 440 MPa

1223 1224 1225

N

1122

1226 1227

U

1121

11

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

1228 1229 1230 1231 1232

article

ap

Alden

ARTICLE IN PRESS

1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279

For TiAl-PST crystals fatigued at f ˆ 08 and Ds ˆ 450 MPa where anomalous accumulation of plastic strain energy appeared, geometrical classi®cation of lamellar boundaries and detailed TEM observation of dominant deformation mode were carried out focusing on continuity of macroscopic strains and slip/twinning planes. The following conclusions were reached. 1. Lamellar boundaries can be classi®ed into thirteen groups in the TiAl-PST crystal fatigued at Ds ˆ 450 MPa with f ˆ 08 and x ˆ 08; and subdivided into two groups of six continuous-types and seven discontinuous-types on the basis of continuity of macroscopic strains and slip/twinning planes. 2. In TiAl-PST crystal fatigued at Ds ˆ 450 MPa, the dominant deformation mode in the (BM and CT) set occupying the relatively smaller volume fraction changes from twins to ordinary dislocations with the Burgers vector parallel to lamellar boundaries to maintain continuity of macroscopic strains and slip/twinning planes. In another set of (BT and CM), highly dense twins are activated as the dominant mode. Distribution of (B and C)type domain is one of the most important controlling factors for rapid accumulation of plastic strain energy because the dominant deformation modes are shifted from the ordinary dislocations to twins and vice versa in each set of (BM and CT) and (BT and CM) or below and above Ds ˆ 440 MPa. Twinning in the (B and C)type domain in the initial stage of fatigue deformation restricts the subsequent to-and-fro motion of the ordinary dislocations, resulting in the rapid fatigue hardening. 3. Since the shear direction is changed above and below Ds ˆ 440 MPa where an anomalous peak of accumulated plastic strain energy appears, the shape change on the lamellar plane of X±Y plane is symmetrical under both stress conditions. This macroscopic shape change is opposite in tension and compression. 4. A large number of twins promote introduction of homogeneous slip traces on the prism planes in the a2 phase.

1282 1283 1284 1285 1286 1287 1288

Acknowledgements

U

1281

N

1280

This work was supported by a Grant-in-Aid for Scienti®c Research Development from the Ministry of Education, Sports, Culture, Science and Technology of Japan. This work has partly been carried out at the Strategic Research Base `Handai Frontier Research Center' supported by the

1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301

References

1302

[1] C.T. Sims, W.C. Hagel, The superalloys, Wiley series on the science and technology of materials, Wiley, Canada, 1972 pp. 1±614. [2] Y. Yamabe-Mitarai, Y. Ro, T. Maruko, H. Harada, Ir-base refractory superalloys for ultra-high temperatures, Metall. Mater. Trans. A 29A (1998) 537±549. [3] E.O. Ezugwu, Z.M. Wang, A.R. Machado, The machinability of nickel-based alloys: a review, J. Mater. Process. Technol. 86 (1999) 1±16. [4] X.H. Yu, Y. Yamabe-Mitarai, Y. Ro, H. Harada, Design of quaternary Ir±Nb±Ni±Al refractory superalloys, Metall. Mater. Trans. A 31A (2000) 173±178. [5] M. Yamaguchi, Y. Umakoshi, The deformation behaviour of intermetallic superlattice compounds, Progr. Mater. Sci. 34 (1990) 1±148. [6] A.K. Vasudevan, J.J. Petrovic, A comparative overview of molybdenium disilicide composite, Mater. Sci. Engng A 155 (1992) 1±17. [7] W.J. Boettinger, J.H. Perepezko, P.S. Frankwicz, Application of ternary phase diagrams to the development of MoSi2-based materials, Mater. Sci. Engng A155 (1992) 33±44. [8] M. Yamaguchi, H. Inui, in: R. Darolia, J.J. Lewandowski, C.T. Liu, P.L. Martin, D.B. Miracle, M.V. Nathal (Eds.), Structural Intermetallics, Minerals, Metals and Materials Society, Warrendale, Pennsylvania, 1993, pp. 127±142. [9] Y.W. Kim, D.M. Dimiduk, Designing gamma TiAl alloys: fundamentals, strategy and production, in: M.V. Nathal, R. Darolia, C.T. Liu, P.L. Martin, D.B. Miracle, R. Wagner, M. Yamaguchi (Eds.), Structural Intermetallics, Minerals, Metals and Materials Society, Warrendale, Pennsylvania, 1997, pp. 531±543. [10] F. Appel, R. Wagner, Microstructure and deformation of two-phase gtitanium aluminides, Mater. Sci. Engng: R: Rep. 22 (1998) 187±268. [11] M. Yamaguchi, H. Inui, K. Ito, High-temperature structural intermetallics, Acta Mater. 48 (2000) 307±322. [12] F. Appel, Recent progress in the development of gamma titanium aluminide alloy, Adv. Engng Mater. 2 (2000) 699±720. [13] J.J. Petrovic, A.K. Vasudevan, Key developments in high temperature structural silicides, Mater. Sci. Engng A 261 (1999) 1±5. [14] K. Kishida, H. Inui, M. Yamaguchi, Deformation of lamellar structure in TiAl±Ti3Al two-phase alloy, Phil. Mag. A 78 (1998) 1±28. [15] S. Zghal, A. Coujou, A. Couret, Transmission of the deformation through gamma±gamma interfaces in a polysynthetically twinned TiAl alloy -1. Ordered domain interfaces (120 degrees rotational), Phil. Mag. A 81 (2001) 345±364. [16] F. Appel, P.A. Beaven, R. Wagner, Acta Metall. Mater. 41 (1993) 1721. [17] S. Zghal, A. Couret, Transmission of the deformation through gamma±gamma interfaces in a polysynthetically twinned TiAl alloy -2. Twin interfaces (180 degrees rotational), Phil. Mag. A 81 (2001) 365±382. [18] T. Nakano, H. Biermann, M. Riemer, H. Mughrabi, Y. Nakai, Y. Umakoshi, Classi®cation of g/g (and (g/a2 lamellar boundaries

1304

1303

F

1241

O

1240

5. Conclusions

O

1239

PR

1238

Japanese Government's Special Coordination Fund for Promoting Science and Technology. The framework of this project was created when Dr T. Nakano worked in Prof. H Mughrabi's laboratory in 1997. The authors would like to thank Prof. H Biermann (now of Freiberg University), and Mr M. Riemer and Prof. H. Mughrabi, Institut fur Werkstoffwissenschaften, Lehrstuhl 1, Universitat Erlangen-Nurnberg, Germany for their detailed discussions and valuable comments. They would also like to thank Dr F. Appel, GKSS Research Center, Institut for Materials Research, Germany, for his valuable comments.

EC TE

1237

R

1236

R

1235

macroscopic deformation, especially fatigue deformation. In particular, twin formation plays an important role in restricting the further operative deformation mode in both tension and compression.

O

1234

C

1233

T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

D

12

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

article

ap

Alden

1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344

ARTICLE IN PRESS T. Nakano et al. / Science and Technology of Advanced Materials 00 (2002) 000±000

1348 1349

[19] [20]

1350 1351

[21]

1352 1353 1354

[22]

1355 1356 1357

[23]

1358 1359 1360 1361 1362

[24]

1363 1365 1366 1367 1368 1369 1370

[25] [26]

PR

1364

[27] H. Inui, M.H. Oh, A. Nakamura, M. Yamaguchi, Room-temperature tensile deformation of polysynthetically twinned (PST) crystals of TiAl, Acta Metall. Mater. 40 (1992) 3095±3104. [28] Y. Umakoshi, T. Nakano, The role of ordered domains and slip mode of a2s phase in the plastic behaviour of TiAl crystals containing oriented lamellae, Acta Metall. Mater. 41 (1993) 1155±1161. [29] H. Inui, Y. Toda, M. Yamaguchi, Plastic deformation of single crystals of a DO19 compound with an off-stoichiometric composition (Ti± 36.5at percent Al) at room temperature, Phil. Mag. A 67 (1993) 1315±1332. [30] A. Godfrey, D. Hu, M.H. Loretto, The role of the a2 phase in the transmission of slip in lamellar TiAl-based alloys, Phil. Mag. A 77 (1998) 287±297. [31] J.M.K. Wiezorek, X.D. Zhang, W.A.T. Clark, H.L. Fraser, Activation of slip in lamellae of a2-Ti3Al in TiAl alloys, Phil. Mag. A 78 (1998) 217±238. [32] G. Hug, A. Loiseau, A. Lasalmonie, Nature and dissociation of the dislocations in TiAl deformed at room temperature, Phil. Mag. A 54 (1986) 47±65. [33] H.Y. Yasuda, T. Nakano, Y. Umakoshi, The effect of Schmid factor on [011] superdislocation decomposition observed in cyclically deformed TiAl PST crystals, Phil. Mag. A Lett. 73 (1996) 225±231. [34] T. Nakano, H. Biermann, M. Riemer, H. Mughrabi, Y. Nakai, Y. Umakoshi, unpublished data. [35] H. Inui, M.H. Oh, A. Nakamura, M. Yamaguchi, Ordered domains in TiAl coexisting with Ti3Al in the lamellar structure of Ti-rich TiAl compounds, Phil. Mag. A 66 (1992) 539±555. [36] S. Zghal, S. Naka, A. Couret, A qualitative analysis of the lamellar microstructure in TiAl based alloys, Acta Mater. 45 (1997) 3005± 3015.

F

1347

on the basis of continuity of strains and slip/twinning planes in fatigued TiAl PST crystals, Phil. Mag. A 81 (2001) 1447±1471. S. Wardle, I. Phan, G. Hug, Analysis of twin intersections in TiAl, Phil. Mag. A 67 (1993) 497±514. Y.Q. Sun, P.M. Hazzledine, J.W. Christian, Intersections of deformation twins in TiAl 1. Experimental observations, Phil. Mag. A 68 (1993) 471±494. F. Appel, P.A. Beaven, R. Wagner, Deformation processes related to interfacial boundaries in 2-phase gamma-titanium aluminides, Acta Metall. Mater. 41 (1993) 1721±1732. Y.G. Zhang, F.D. Tichelaar, F.W. Schapink, M.C. Chaturvedi, Interaction of deformation twins with a2 plates in g-TiAl base alloy deformed at room temperature, Mater. Sci. Engng A219 (1996) 162±179. J.M.K. Wiezorek, X.D. Zhang, M.J. Mills, H.L. Fraser, On the role of lamellar interfaces on the strength and ductility of two-phase titanium±aluminum, in: E.P. George, M.J. Mills, M. Yamaguchi (Eds.), High Temperature Ordered Alloys 13, vol. 552, Minerals, Materials Research Society, Warrendale, PA, 1999, pp. KK3.5.1± KK3.5.8. M.A. Gibson, C.T. Forwood, Slip transfer of deformation twins in duplex g-based Ti±Al alloys. Part 1. Transfer across g±g coherent twin interfaces, Phil. Mag. A 80 (2000) 2747±2783. C.T. Forwood, M.A. Gibson, Slip transfer of deformation twins in duplex g-based Ti±Al alloys. Part 2. Transfer across g±a2 interfaces, Phil. Mag. A 80 (2000) 2785±2811. T. Nakano, H.Y. Yasuda, N. Higashitanaka, Y. Umakoshi, Anomalous behaviour of cyclic deformation and fatigue properties of TiAl PST crystals under constant applied stress, Acta Mater. 45 (1997) 4807±4821.

O

1346

O

1345

1371 1372 1373 1374 1376 1378 1379 1380 1381 1382 1383 1384 1386 1388 1390

1395 1396 1397

1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426

1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451

U

1394

1407

1433

N

1392

1406

1432

C

1391

1405

1431

O

1389

1404

1430

R

1387

1403

1429

R

1385

1402

1428

EC TE

1377

1401

1427

D

1375

1393

13

1452 1453

1398

1454

1399

1455

1400

1456

Science and Technology of Advanced Materials ± Model 5 ± Ref style 1 ± AUTOPAGINATION 2 22-02-2002 15:49

article

ap

Alden