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µÈ¾¶½ÇÇ¿ÖÆ¼·Ñ¹×éÖ¯ÑݱäTexture evolution in equal-channel angular extrusion Irene J. Beyerlein£»L¨¢szl¨® S. T¨®th Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 2. Background. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 2.1. Severe plastic deformation (SPD) processes . . . . . .. . . . . . . . . . . . . 431 2.1.1. Equal-channel angular extrusion (ECAE). . . . . . . . . . . . . . . . . . . 431 2.1.2. Definitions of deformation and velocity gradient in ECAE. . . . . . . . . . 431 2.1.3. Simple shear model . . . . . . . . . . . . . . . . . . 432 2.1.4. Distortions and rotations of material elements in ECAE . . . . . .. . 433 2.1.5. Multiple passes: rotations and strain path changes . . . . . . 433 2.1.6. Relationship to other deformation processes: drawing, rolling, plane strain compression, torsion . . . . . . . . . . . . . . 435 2.1.7. Other SPD techniques. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 435 2.2. Ideal texture orientations in simple shear. . . . . . . .. . . . . . . . . . . . . . . 436 2.2.1. Fcc crystal structure . . . . . . . . . . . . . . . . . . . . . . . . . 436 2.2.2. Bcc crystal structure. . . . . . . . . . . . . . . . . . . . . . . . 436 2.2.3. Hcp crystal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436 2.3. Ideal texture orientations in ECAE . . . . . . . . . . . . . . . . . . . . . 438 3. ECAE texture measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 3.1. Cubic textures in ECAE . . . . . . . . . . . . . . . . . . . . . . . . . . 441 3.1.1. Influence of die angle . . . . . . . . . . . . . . . . . . . . . . . . . . 441 3.1.2. First-pass textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 3.1.3. Influence of route and pass number . . . . . . . . . . . . . . 442 3.1.4. Fcc example: copper. . . . . . . . . . . . . . . . . . . . . . 443 3.1.5. Bcc example: IF-steel . . . . . . . . . . . . . . . . . . . . . . . . 445 3.1.6. Deviations from ideal texture positions . . . . . . . . . . . . . . . . . 446 3.1.7. Texture strength . . . . . . . . . . . . . . . . . . . . . . 448 3.1.8. Saturation of texture with pass number . . . . . . . . . . . . . . . . 449 3.1.9. Effect of stacking fault energy . . . . . . . . . . . . . .. . . 449 3.1.10. Effect of deformation twinning . . . . . . . . . . . . . . . . . 449 3.1.11. Effect of substructure evolution . . . . . . . . . . . 450 3.1.12. Effect of temperature . . . . . . .. . . . . . . . . . . . . . 452 3.2. Hcp textures in ECAE . . . . . . . . . . . . . . . . . . . . . . . . 453 3.2.1. Slip and twinning modes . . . . . . . . . . . . . . . . . 453 3.2.2. First-pass textures and effect of die angle . . . . . . . . . . . . . 453 3.2.3. Effect of route and pass number . . . . . . . . . . . . . . . . . 456 3.2.4. Effect of alloying. . . . . . . . . . . . .. . . . . . . . . . . . . . 456 3.2.5. Effect of deformation twinning . . . . . . . . . . . . . . . . . . 457 3.2.6. Effect of temperature . . . . . . . . . . . . .. . . . . . . . . . . . 457 3.3. Effect of initial texture . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 3.3.1. ECAE of single crystals . . . . . . . . . . . . .. . . . . . . . . . . 458 3.3.2. Cubic polycrystals. . . . . . . . . . . . . . . . . . . . . . . 459 3.3.3. Hexagonal polycrystals. . . . . . . . . . . . . . . . . . . 463 3.3.4. Recommendations . . . . . . . . . . . . . . . . . . . . . . 465 3.4. Dynamic recrystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 3.4.1. Cubic metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 3.4.2. Hexagonal metals . . . . . . . . . . . . . . . . . . . . . 467 4. Modeling texture evolution . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 468 4.1. Polycrystal models for SPD processes . . . . . . . . . . . . . .. . . . . . . . . . . 468 4.1.1. Full constraints (FC) Taylor polycrystal model . . . . . . . . . . . . . . 469 4.1.2. Visco-plastic self-consistent (VPSC) polycrystal model . . . . . . . . . 469 4.2. Assessment of model performance . . . . . . . . .. . . . . . . . . 469 4.3. Polycrystal model performance . . . . . . . . . . . .. . . . . . . . . . 470 4.4. VPSC predictions using the simple shear (SS) model . . . . . . . . . . . . . . . . . 470 5. Alternative deformation models for ECAE . . . . . . . . . . .. . . . . . . . 471 5.1. 2D and 3D finite element models . . . . . . . . . . . . . . . . . . . . . 471 5.1.1. Corner gaps and plastic deformation zones (PDZ) . . . . . . 472 5.1.2. Inhomogeneous deformation . . . . . . . . . . .. . . . . . . . . . . . 473 5.1.3. Three-dimensional effects . . . . . . . . . . . . . . . . . . . 474 5.2. Nonphysical factors affecting assessment of model performance . . . . . . . . . . . . . . . . . . . . . . . 475 5.3. Texture calculations with finite element . . . . . . . . . . . . . . . 476 5.4. Heterogeneity in texture evolution . . . . . . . . . . . . . . . . . . . . . . . 477 5.5. Route A: heterogeneity and end-effects. . . . . . . . . . . 478 5.6. Analytical flow models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 5.7. Texture calculations with analytical flow models. . . . . . . . . . . . . . . . . . . . 483 6. Extended texture calculations including grain-scale and subgrain-scale effects 484 6.1. Grain¨Cgrain interactions . . . . . . . . . . . . . . . 486 6.2. Grain shape effects . . . . . . . . . . . . . . . . . . . . . 486 6.3. Substructure models . . . . . . . . . . . . . 489 6.4. Deformation twinning. . . . . . . . . . . . . 490 6.5. Application: Modeling texture evolution in route C . . . . . . . . . . 491 6.5.1. Grain¨Cgrain interactions . . . . . . . . . . . . . . . . . 492 6.5.2. Inhomogeneous deformation . . . . . . . . . . . . . . . . . . . . 492 6.5.3. Grain hardening and substructure evolution . . . . .. . . . . . . . 492 6.5.4. Imperfect reversal. . . . . . . .. . . . . . . . . . . . . . . 494 6.6. Sensitivity of texture to microstructural evolution (grain refinement) . . . . . 499 6.7. Influence of texture on post deformation of SPD materials . . . . . .. . 500 7. Concluding remarks and recommendations . . . . . . . . . . . . . 502 8. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 References . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 |
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