J. Mater. Sci. Technol. ›› 2021, Vol. 91: 58-66.DOI: 10.1016/j.jmst.2021.03.015
• Research Article • Previous Articles Next Articles
Yi Yanga, Bohua Zhanga, Zhichao Mengb, Lei Quc, Hao Wanga,*(
), Sheng Caod, Jianan Hua, Hao Chena, Songquan Wua,*(
), Dehai Pinge, Geping Lib, Lai-Chang Zhangf, Rui Yangb, Aijun Huangg
Received:2020-12-27
Revised:2021-03-21
Accepted:2021-03-28
Published:2021-11-20
Online:2021-11-20
Contact:
Hao Wang,Songquan Wu
About author:sqwu@usst.edu.cn(S. Wu).Yi Yang, Bohua Zhang, Zhichao Meng, Lei Qu, Hao Wang, Sheng Cao, Jianan Hu, Hao Chen, Songquan Wu, Dehai Ping, Geping Li, Lai-Chang Zhang, Rui Yang, Aijun Huang. {332}<113> Twinning transfer behavior and its effect on the twin shape in a beta-type Ti-23.1Nb-2.0Zr-1.0O alloy[J]. J. Mater. Sci. Technol., 2021, 91: 58-66.
| Chosen grains | Observed twins | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Grain No. | Euler angle (°) | Top 5 SFs for {332}<113> twinning | Twin No. | Euler angle (°) | TS | SF | ||||||||
| φ1 | ϕ | φ2 | SF1 | SF2 | SF3 | SF4 | SF5 | φ1 | ϕ | φ2 | ||||
| G01 | 140 | 42 | 54 | 0.458 | 0.446 | 0.423 | 0.303 | 0.234 | T01 | 258 | 24 | 6 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.423 |
| G02 | 146 | 50 | 53 | 0.459 | 0.451 | 0.400 | 0.244 | 0.232 | T02 | 262 | 21 | 8 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.459 |
| G03 | 149 | 40 | 56 | 0.475 | 0.419 | 0.408 | 0.304 | 0.188 | T03 | 277 | 23 | 85 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.475 |
| G04 | 145 | 28 | 44 | 0.499 | 0.378 | 0.368 | 0.364 | 0.313 | T04 | 273 | 33 | 71 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.364 |
| G05 | 135 | 29 | 61 | 0.480 | 0.427 | 0.419 | 0.311 | 0.291 | T05 | 286 | 30 | 64 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.419 |
| G06 | 229 | 31 | 33 | 0.483 | 0.420 | 0.383 | 0.366 | 0.228 | — | — | — | — | — | — |
| G07 | 99 | 24 | 12 | 0.456 | 0.449 | 0.426 | 0.301 | 0.255 | T07 | 318 | 36 | 30 | (332)[$11\bar{3}$] | 0.426 |
| G08 | 250 | 34 | 1 | 0.483 | 0.399 | 0.396 | 0.300 | 0.205 | — | — | — | — | — | — |
| G09 | 144 | 36 | 49 | 0.483 | 0.426 | 0.411 | 0.324 | 0.286 | T09 | 268 | 29 | 85 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.411 |
| G10 | 209 | 8 | 42 | 0.480 | 0.440 | 0.348 | …… | 0.218 (7th) | T10a | 55 | 27 | 68 | ($\bar{3}23$)[$13\bar{1}$] | 0.440 |
| T10b | 259 | 41 | 34 | ($32\bar{3}$)[$\bar{1}31$] | 0.218 | |||||||||
| G11 | 337 | 20 | 40 | 0.492 | 0.410 | 0.370 | 0.336 | 0.261 | T11 | 148 | 36 | 79 | ($\bar{2}33$)[$\bar{3}\bar{1}\bar{1}$] | 0.492 |
| G12 | 23 | 18 | 87 | 0.489 | 0.417 | 0.370 | 0.330 | 0.247 | T12a | 142 | 43 | 5 | (323)[$\bar{1}31$] | 0.417 |
| T12b | 73 | 44 | 3 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.247 | |||||||||
| G13 | 338 | 19 | 46 | 0.474 | 0.415 | 0.403 | 0.326 | 0.258 | T13 | 155 | 39 | 79 | ($\bar{2}33$)[$\bar{3}\bar{1}\bar{1}$] | 0.474 |
| G14 | 195 | 12 | 56 | 0.477 | 0.445 | 0.342 | 0.297 | 0.280 | — | — | — | — | — | — |
| G15 | 224 | 40 | 34 | 0.460 | 0.450 | 0.404 | 0.326 | 0.214 | — | — | — | — | — | — |
| G16 | 358 | 25 | 34 | 0.427 | 0.422 | 0.376 | 0.357 | 0.240 | T16 | 157 | 33 | 90 | ($\bar{2}33$)[$\bar{3}\bar{1}\bar{1}$] | 0.427 |
| G17 | 44 | 28 | 67 | 0.489 | 0.416 | 0.404 | 0.331 | 0.296 | — | — | — | — | — | — |
| G18 | 132 | 34 | 45 | 0.464 | 0.446 | 0.360 | 0.315 | 0.283 | T18 | 328 | 40 | 45 | ($23\bar{3}$)[$3\bar{1}1$] | 0.446 |
| G19 | 4 | 16 | 21 | 0.460 | 0.450 | 0.351 | 0.328 | 0.273 | T19 | 151 | 42 | 88 | ($\bar{2}33$)[$\bar{3}\bar{1}\bar{1}$] | 0.450 |
| G20 | 50 | 46 | 52 | 0.420 | 0.413 | 0.385 | 0.355 | 0.237 | — | — | — | — | — | — |
| G21 | 50 | 41 | 51 | 0.442 | 0.425 | 0.387 | …… | 0.069 (9th) | T21 | 352 | 43 | 48 | (323)[$\bar{1}31$] | 0.069 |
| G22 | 132 | 26 | 21 | 0.467 | 0.442 | 0.422 | 0.310 | 0.265 | T22 | 73 | 42 | 34 | ($23\bar{3}$)[$3\bar{1}1$] | 0.467 |
| G23 | 47 | 35 | 31 | 0.466 | 0.448 | 0.398 | 0.340 | 0.229 | T23 | 204 | 23 | 29 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.466 |
| G24 | 58 | 32 | 33 | 0.460 | 0.436 | 0.378 | 0.314 | 0.285 | T24 | 218 | 26 | 28 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.460 |
| G25 | 217 | 35 | 43 | 0.490 | 0.417 | 0.390 | 0.354 | 0.275 | T25a | 41 | 20 | 11 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.490 |
| T25b | 21 | 44 | 43 | ($32\bar{3}$)[$\bar{1}31$] | 0.354 | |||||||||
| T25c | 146 | 16 | 73 | ($\bar{3}23$)[$13\bar{1}$] | 0.275 | |||||||||
| G26 | 47 | 35 | 35 | 0.474 | 0.435 | 0.373 | 0.371 | 0.211 | T26 | 210 | 20 | 25 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.474 |
| G27 | 229 | 31 | 43 | 0.469 | 0.448 | 0.353 | 0.307 | 0.287 | T27a | 53 | 26 | 11 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.469 |
| T27b | 35 | 49 | 41 | ($32\bar{3}$)[$\bar{1}31$] | 0.448 | |||||||||
| G28 | 63 | 18 | 3 | 0.470 | 0.445 | 0.399 | 0.341 | 0.236 | T28 | 195 | 43 | 27 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.470 |
| G29 | 44 | 44 | 78 | 0.473 | 0.420 | 0.413 | 0.300 | 0.195 | T29 | 260 | 41 | 11 | ($32\bar{3}$)[$\bar{1}31$] | 0.420 |
Table 1 Euler angles of the labeled grains and top 5 Schmid factors (SFs) for {332}<113> twinning systems (TS) in them, as well as Euler angles and SFs for the observed {332}<113> twins shown in Fig. 1.
| Chosen grains | Observed twins | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Grain No. | Euler angle (°) | Top 5 SFs for {332}<113> twinning | Twin No. | Euler angle (°) | TS | SF | ||||||||
| φ1 | ϕ | φ2 | SF1 | SF2 | SF3 | SF4 | SF5 | φ1 | ϕ | φ2 | ||||
| G01 | 140 | 42 | 54 | 0.458 | 0.446 | 0.423 | 0.303 | 0.234 | T01 | 258 | 24 | 6 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.423 |
| G02 | 146 | 50 | 53 | 0.459 | 0.451 | 0.400 | 0.244 | 0.232 | T02 | 262 | 21 | 8 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.459 |
| G03 | 149 | 40 | 56 | 0.475 | 0.419 | 0.408 | 0.304 | 0.188 | T03 | 277 | 23 | 85 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.475 |
| G04 | 145 | 28 | 44 | 0.499 | 0.378 | 0.368 | 0.364 | 0.313 | T04 | 273 | 33 | 71 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.364 |
| G05 | 135 | 29 | 61 | 0.480 | 0.427 | 0.419 | 0.311 | 0.291 | T05 | 286 | 30 | 64 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.419 |
| G06 | 229 | 31 | 33 | 0.483 | 0.420 | 0.383 | 0.366 | 0.228 | — | — | — | — | — | — |
| G07 | 99 | 24 | 12 | 0.456 | 0.449 | 0.426 | 0.301 | 0.255 | T07 | 318 | 36 | 30 | (332)[$11\bar{3}$] | 0.426 |
| G08 | 250 | 34 | 1 | 0.483 | 0.399 | 0.396 | 0.300 | 0.205 | — | — | — | — | — | — |
| G09 | 144 | 36 | 49 | 0.483 | 0.426 | 0.411 | 0.324 | 0.286 | T09 | 268 | 29 | 85 | ($3\bar{3}2$)[$1\bar{1}\bar{3}$] | 0.411 |
| G10 | 209 | 8 | 42 | 0.480 | 0.440 | 0.348 | …… | 0.218 (7th) | T10a | 55 | 27 | 68 | ($\bar{3}23$)[$13\bar{1}$] | 0.440 |
| T10b | 259 | 41 | 34 | ($32\bar{3}$)[$\bar{1}31$] | 0.218 | |||||||||
| G11 | 337 | 20 | 40 | 0.492 | 0.410 | 0.370 | 0.336 | 0.261 | T11 | 148 | 36 | 79 | ($\bar{2}33$)[$\bar{3}\bar{1}\bar{1}$] | 0.492 |
| G12 | 23 | 18 | 87 | 0.489 | 0.417 | 0.370 | 0.330 | 0.247 | T12a | 142 | 43 | 5 | (323)[$\bar{1}31$] | 0.417 |
| T12b | 73 | 44 | 3 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.247 | |||||||||
| G13 | 338 | 19 | 46 | 0.474 | 0.415 | 0.403 | 0.326 | 0.258 | T13 | 155 | 39 | 79 | ($\bar{2}33$)[$\bar{3}\bar{1}\bar{1}$] | 0.474 |
| G14 | 195 | 12 | 56 | 0.477 | 0.445 | 0.342 | 0.297 | 0.280 | — | — | — | — | — | — |
| G15 | 224 | 40 | 34 | 0.460 | 0.450 | 0.404 | 0.326 | 0.214 | — | — | — | — | — | — |
| G16 | 358 | 25 | 34 | 0.427 | 0.422 | 0.376 | 0.357 | 0.240 | T16 | 157 | 33 | 90 | ($\bar{2}33$)[$\bar{3}\bar{1}\bar{1}$] | 0.427 |
| G17 | 44 | 28 | 67 | 0.489 | 0.416 | 0.404 | 0.331 | 0.296 | — | — | — | — | — | — |
| G18 | 132 | 34 | 45 | 0.464 | 0.446 | 0.360 | 0.315 | 0.283 | T18 | 328 | 40 | 45 | ($23\bar{3}$)[$3\bar{1}1$] | 0.446 |
| G19 | 4 | 16 | 21 | 0.460 | 0.450 | 0.351 | 0.328 | 0.273 | T19 | 151 | 42 | 88 | ($\bar{2}33$)[$\bar{3}\bar{1}\bar{1}$] | 0.450 |
| G20 | 50 | 46 | 52 | 0.420 | 0.413 | 0.385 | 0.355 | 0.237 | — | — | — | — | — | — |
| G21 | 50 | 41 | 51 | 0.442 | 0.425 | 0.387 | …… | 0.069 (9th) | T21 | 352 | 43 | 48 | (323)[$\bar{1}31$] | 0.069 |
| G22 | 132 | 26 | 21 | 0.467 | 0.442 | 0.422 | 0.310 | 0.265 | T22 | 73 | 42 | 34 | ($23\bar{3}$)[$3\bar{1}1$] | 0.467 |
| G23 | 47 | 35 | 31 | 0.466 | 0.448 | 0.398 | 0.340 | 0.229 | T23 | 204 | 23 | 29 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.466 |
| G24 | 58 | 32 | 33 | 0.460 | 0.436 | 0.378 | 0.314 | 0.285 | T24 | 218 | 26 | 28 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.460 |
| G25 | 217 | 35 | 43 | 0.490 | 0.417 | 0.390 | 0.354 | 0.275 | T25a | 41 | 20 | 11 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.490 |
| T25b | 21 | 44 | 43 | ($32\bar{3}$)[$\bar{1}31$] | 0.354 | |||||||||
| T25c | 146 | 16 | 73 | ($\bar{3}23$)[$13\bar{1}$] | 0.275 | |||||||||
| G26 | 47 | 35 | 35 | 0.474 | 0.435 | 0.373 | 0.371 | 0.211 | T26 | 210 | 20 | 25 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.474 |
| G27 | 229 | 31 | 43 | 0.469 | 0.448 | 0.353 | 0.307 | 0.287 | T27a | 53 | 26 | 11 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.469 |
| T27b | 35 | 49 | 41 | ($32\bar{3}$)[$\bar{1}31$] | 0.448 | |||||||||
| G28 | 63 | 18 | 3 | 0.470 | 0.445 | 0.399 | 0.341 | 0.236 | T28 | 195 | 43 | 27 | ($32\bar{3}$)[$\bar{1}\bar{3}\bar{1}$] | 0.470 |
| G29 | 44 | 44 | 78 | 0.473 | 0.420 | 0.413 | 0.300 | 0.195 | T29 | 260 | 41 | 11 | ($32\bar{3}$)[$\bar{1}31$] | 0.420 |
Fig. 1. (a, c, e) SEM images and (b, d, f) EBSD orientation maps of: (a, b) 5% and (c-f) 10% cold-compressed specimens. (g, h) point-to-point misorientations along the corresponding arrows in (b) and (d). The compression direction is horizontal. G: grain; T: twin.
| No. | Grain pair (A-B) | TT | MA (°) | θn | θb | m’ | SF TA | SF TB |
|---|---|---|---|---|---|---|---|---|
| 1 | G01-G09 | Yes | 7 | 3 | 7 | 0.991 | 0.423 (T01) | 0.411 (T09) |
| 2 | G02-G01 | Yes | 10 | 3 | 10 | 0.985 | 0.459 (T02) | 0.423 (T01) |
| 3 | G05-G04 | Yes | 10 | 9 | 6 | 0.983 | 0.419 (T05) | 0.364 (T04) |
| 4 | G03-G02 | Yes | 11 | 9 | 7 | 0.978 | 0.475 (T03) | 0.459 (T02) |
| 5 | G23-G24 | Yes | 13 | 12 | 9 | 0.966 | 0.466 (T23) | 0.460 (T24) |
| 6 | G03-G05 | Yes | 15 | 5 | 15 | 0.962 | 0.475 (T03) | 0.419 (T05) |
| 7 | G13-G12 | Yes | 15 | 15 | 14 | 0.937 | 0.474 (T13) | 0.417 (T12a) |
| 8 | G16-G11 | Yes | 16 | 15 | 10 | 0.952 | 0.427 (T16) | 0.492 (T11) |
| 9 | G11-G12 | Unclear | 15 | 12 | 13 | 0.953 | 0.492 (T11) | 0.417 (T12a) |
| 10 | G16-G12 | Partly | 18 | 18 | 17 | 0.910 | 0.427 (T16) | 0.417 (T12a) |
| 11 | G02-G04 | Partly | 24 | 1 | 24 | 0.913 | 0.459 (T02) | 0.364 (T04) |
| 12 | G04-G07 | Partly | 26 | 25 | 16 | 0.867 | 0.364 (T04) | 0.426 (T07) |
| 13 | G16-G17 | No | 25 | 25 | 25 | 0.820 | 0.427 (T16) | 0.296 |
| 14 | G26-G29 | No | 42 | 26 | 41 | 0.673 | 0.474 (T26) | 0.300 |
| 15 | G22-G25 | No | 42 | 36 | 40 | 0.618 | 0.467 (T22) | 0.275 |
| 16 | G11-G10 | No | 43 | 42 | 28 | 0.656 | 0.492 (T11) | 0.218 |
| 17 | G16-G20 | No | 45 | 44 | 41 | 0.539 | 0.427 (T16) | 0.017 |
| 18 | G11-G14 | No | 46 | 45 | 27 | 0.625 | 0.492 (T11) | 0.211 |
| 19 | G29-G27 | No | 46 | 157 | 134 | 0.638 | 0.420 (T29) | 0.448 |
| 20 | G22-G27 | No | 47 | 145 | 138 | 0.607 | 0.467 (T22) | 0.049 |
| 21 | G27-G22 | No | 47 | 137 | 142 | 0.577 | 0.448 (T27b) | 0.074 |
| 22 | G12-G14 | No | 49 | 45 | 27 | 0.630 | 0.417 (T12a) | 0.211 |
| 23 | G22-G26 | No | 49 | 20 | 44 | 0.674 | 0.467 (T22) | 0.474 |
| 24 | G07-G08 | No | 50 | 49 | 37 | 0.527 | 0.426 (T07) | 0.161 |
| 25 | G10-G16 | No | 51 | 51 | 43 | 0.461 | 0.440 (T10a) | 0.175 |
| 26 | G12-G18 | No | 51 | 49 | 38 | 0.516 | 0.417 (T12a) | 0.136 |
| 27 | G18-G12 | No | 51 | 48 | 39 | 0.518 | 0.446 (T18) | 0.247 |
| 28 | G05-G06 | No | 53 | 36 | 51 | 0.515 | 0.419 (T05) | 0.086 |
| 29 | G26-G25 | No | 53 | 128 | 133 | 0.425 | 0.474 (T26) | 0.031 |
| 30 | G28-G27 | No | 53 | 129 | 147 | 0.532 | 0.470 (T28) | 0.049 |
| 31 | G24-G25 | No | 54 | 17 | 61 | 0.469 | 0.460 (T24) | 0.026 |
| 32 | G25-G24 | No | 54 | 126 | 142 | 0.465 | 0.490(T25a) | 0.097 |
| 33 | G26-G27 | No | 54 | 126 | 140 | 0.449 | 0.474 (T26) | 0.049 |
| 34 | G27-G26 | No | 54 | 20 | 63 | 0.432 | 0.469 (T27a) | 0.021 |
| 35 | G27-G26 | No | 54 | 179 | 126 | 0.583 | 0.448 (T27b) | 0.108 |
| 36 | G18-G19 | No | 55 | 53 | 45 | 0.422 | 0.446 (T18) | 0.123 |
| 37 | G19-G18 | No | 55 | 53 | 46 | 0.423 | 0.450 (T19) | 0.136 |
| 38 | G12-G15 | No | 56 | 45 | 38 | 0.552 | 0.417 (T12a) | 0.049 |
| 39 | G21-G27 | No | 58 | 28 | 56 | 0.449 | 0.069 (T21) | 0.063 |
| 40 | G27-G21 | No | 58 | 169 | 122 | 0.527 | 0.448 (T27b) | 0.442 |
| 41 | G22-G21 | No | 60 | 10 | 61 | 0.483 | 0.467 (T22) | 0.153 |
Table 2 Situations of the interactions between twins and grain boundaries based on the SEM images and EBSD orientation maps shown in Fig. 1. For the situations of twinning transfer (TT) occurring and TT partly occurring, misorientation angle (MA) of grain pairs, crystallographic alignment factors (m’=cosθn·cosθb, where θn is the angle between two twinning plane normals and θb is the angle between two twinning Burgers vectors) and Schmid factors (SFs) for the observed {332}<113> twin pairs in Fig. 1 are listed. For the situation of TT not occurring, the highest m’ for the observed incoming and possible outgoing {332}<113> twin variants and the corresponding SFs (SF TA and SF TB) are listed.
| No. | Grain pair (A-B) | TT | MA (°) | θn | θb | m’ | SF TA | SF TB |
|---|---|---|---|---|---|---|---|---|
| 1 | G01-G09 | Yes | 7 | 3 | 7 | 0.991 | 0.423 (T01) | 0.411 (T09) |
| 2 | G02-G01 | Yes | 10 | 3 | 10 | 0.985 | 0.459 (T02) | 0.423 (T01) |
| 3 | G05-G04 | Yes | 10 | 9 | 6 | 0.983 | 0.419 (T05) | 0.364 (T04) |
| 4 | G03-G02 | Yes | 11 | 9 | 7 | 0.978 | 0.475 (T03) | 0.459 (T02) |
| 5 | G23-G24 | Yes | 13 | 12 | 9 | 0.966 | 0.466 (T23) | 0.460 (T24) |
| 6 | G03-G05 | Yes | 15 | 5 | 15 | 0.962 | 0.475 (T03) | 0.419 (T05) |
| 7 | G13-G12 | Yes | 15 | 15 | 14 | 0.937 | 0.474 (T13) | 0.417 (T12a) |
| 8 | G16-G11 | Yes | 16 | 15 | 10 | 0.952 | 0.427 (T16) | 0.492 (T11) |
| 9 | G11-G12 | Unclear | 15 | 12 | 13 | 0.953 | 0.492 (T11) | 0.417 (T12a) |
| 10 | G16-G12 | Partly | 18 | 18 | 17 | 0.910 | 0.427 (T16) | 0.417 (T12a) |
| 11 | G02-G04 | Partly | 24 | 1 | 24 | 0.913 | 0.459 (T02) | 0.364 (T04) |
| 12 | G04-G07 | Partly | 26 | 25 | 16 | 0.867 | 0.364 (T04) | 0.426 (T07) |
| 13 | G16-G17 | No | 25 | 25 | 25 | 0.820 | 0.427 (T16) | 0.296 |
| 14 | G26-G29 | No | 42 | 26 | 41 | 0.673 | 0.474 (T26) | 0.300 |
| 15 | G22-G25 | No | 42 | 36 | 40 | 0.618 | 0.467 (T22) | 0.275 |
| 16 | G11-G10 | No | 43 | 42 | 28 | 0.656 | 0.492 (T11) | 0.218 |
| 17 | G16-G20 | No | 45 | 44 | 41 | 0.539 | 0.427 (T16) | 0.017 |
| 18 | G11-G14 | No | 46 | 45 | 27 | 0.625 | 0.492 (T11) | 0.211 |
| 19 | G29-G27 | No | 46 | 157 | 134 | 0.638 | 0.420 (T29) | 0.448 |
| 20 | G22-G27 | No | 47 | 145 | 138 | 0.607 | 0.467 (T22) | 0.049 |
| 21 | G27-G22 | No | 47 | 137 | 142 | 0.577 | 0.448 (T27b) | 0.074 |
| 22 | G12-G14 | No | 49 | 45 | 27 | 0.630 | 0.417 (T12a) | 0.211 |
| 23 | G22-G26 | No | 49 | 20 | 44 | 0.674 | 0.467 (T22) | 0.474 |
| 24 | G07-G08 | No | 50 | 49 | 37 | 0.527 | 0.426 (T07) | 0.161 |
| 25 | G10-G16 | No | 51 | 51 | 43 | 0.461 | 0.440 (T10a) | 0.175 |
| 26 | G12-G18 | No | 51 | 49 | 38 | 0.516 | 0.417 (T12a) | 0.136 |
| 27 | G18-G12 | No | 51 | 48 | 39 | 0.518 | 0.446 (T18) | 0.247 |
| 28 | G05-G06 | No | 53 | 36 | 51 | 0.515 | 0.419 (T05) | 0.086 |
| 29 | G26-G25 | No | 53 | 128 | 133 | 0.425 | 0.474 (T26) | 0.031 |
| 30 | G28-G27 | No | 53 | 129 | 147 | 0.532 | 0.470 (T28) | 0.049 |
| 31 | G24-G25 | No | 54 | 17 | 61 | 0.469 | 0.460 (T24) | 0.026 |
| 32 | G25-G24 | No | 54 | 126 | 142 | 0.465 | 0.490(T25a) | 0.097 |
| 33 | G26-G27 | No | 54 | 126 | 140 | 0.449 | 0.474 (T26) | 0.049 |
| 34 | G27-G26 | No | 54 | 20 | 63 | 0.432 | 0.469 (T27a) | 0.021 |
| 35 | G27-G26 | No | 54 | 179 | 126 | 0.583 | 0.448 (T27b) | 0.108 |
| 36 | G18-G19 | No | 55 | 53 | 45 | 0.422 | 0.446 (T18) | 0.123 |
| 37 | G19-G18 | No | 55 | 53 | 46 | 0.423 | 0.450 (T19) | 0.136 |
| 38 | G12-G15 | No | 56 | 45 | 38 | 0.552 | 0.417 (T12a) | 0.049 |
| 39 | G21-G27 | No | 58 | 28 | 56 | 0.449 | 0.069 (T21) | 0.063 |
| 40 | G27-G21 | No | 58 | 169 | 122 | 0.527 | 0.448 (T27b) | 0.442 |
| 41 | G22-G21 | No | 60 | 10 | 61 | 0.483 | 0.467 (T22) | 0.153 |
Fig. 3. (a) Relationships between twinning transfer (TT) and Schmid factors (SFs) of the incoming and outgoing twins, (b) crystallographic alignment factors (m’) for the observed {332}<113> twin pairs and (c) misorientation angles (MA) of grain pairs. For the situation of TT not occurring, the highest m’ for the observed incoming (solid shapes in (a)) and possible outgoing {332}<113> twin variants (open shapes in a) are selected. Situations of TT: Squares- Yes; Triangles- Partly; Circles- No.
Fig. 4. Bright-field TEM image of {332}<113> twinning transfer in the 10% cold-compressed specimen, showing the interaction between twins and grain boundary (GB), and twinning shear strain inducing zigzag-shaped GB. The dashed line indicates the possible original position of GB between matrix grains A and B before twinning, and the dashed arrows indicates the shear strain direction. m: matrix; t: twin.
Fig. 5. The initial configuration of MD simulation and the rotation angles between grains G2 and G1, G3 and G1, G4 and G1 are n, 2n, 3n (n = 10°-70°), respectively. The corresponding direction of the coordinate axis is X: [113], Y: [$33\bar{2}$], Z: [$1\bar{1}0$].
Fig. 6. MD simulation results for the behaviors of TT and TT-N with different MA, as well as the stress component distribution. The atoms are colored by shear strain. TT: twinning transfer occurring; TT-N: twinning transfer not occurring. The compression direction is horizontal.
Fig. 7. Illustration of the interaction between {332}<113> twin and grain boundary (GB). (a-c) The grain pair A-B with SFA=0.5, SFB=0.088, θn=40°, θb=40° and m’=0.587 for ($3\bar{3} \bar{2}$)[$1\bar{1}3$] twinning system. (d-f) The grain pair A-C with SFA=0.5, SFC=0.433, θn=15°, θb=15° and m’=0.933 for ($3\bar{3} \bar{2}$)[$1\bar{1}3$] twinning system. (a, d) Before deformation. (b, e) Compressed deformation in the situation of the grain pair with nil strength GB, i.e., matrix grains A and B deform individually and do not interact with each other. A crack is formed on the GB. (c, f) Compressed deformation in the situation of the grain pair deforming accommodatingly.
| [1] | O. Muránsky, M.R. Barnett, D.G. Carr, S.C. Vogel, E.C. Oliver, Acta Mater. 58(2010) 1503-1517. |
| [2] | X.L. Wu, Y.T. Zhu, Phys. Rev. Lett. 101(2008) 025503. |
| [3] | Y.T. Zhu, J. Narayan, J.P. Hirth, S. Mahajan, X.L. Wu, X.Z. Liao, Acta Mater. 57(2009) 3763-3770. |
| [4] | J.W. Christian, S. Mahajant, Prog. Mater. Sci. 39(1995) 1-157. |
| [5] | K.P.D. Lagerlöf, Acta Metall.Mater. 41(1993) 2143-2151. |
| [6] | L. Wang, P. Eisenlohr, Y. Yang, T.R. Bieler, M.A. Crimp, Scr. Mater. 63(2010) 827-830. |
| [7] | L. Wang, Y. Yang, P. Eisenlohr, T.R. Bieler, M.A. Crimp, D.E. Mason, Metall. Mater. Trans. A 41 (2010) 421-430. |
| [8] | S. Xu, C. Schuman, J.S. Lecomte, Scr. Mater. 116(2016) 152-156. |
| [9] | M.A. Kumar, I.J. Beyerlein, R.A. Lebensohn, C.N. Tomé, Modell. Simul. Mater. Sci. Eng. 25(2017) 064007. |
| [10] | M.A. Kumar, I.J. Beyerlein, R.J. McCabe, C.N. Tomé, Nat. Commun. 7(2016) 13826. |
| [11] | J. Wang, I.J. Beyerlein, C.N. Tomé, Scr.Mater. 63(2010)741-746. |
| [12] | S. Xu, T.M. Liu, Y. Zhang, J.J. He, W. Zeng, J.X. Wang, Mater. Sci. Technol. 29(2013) 1144-1147. |
| [13] | R.L. Xin, Y.C. Liang, C.H. Ding, C.F. Guo, B.S. Wang, Q. Liu, Mater. Des. 86(2015) 656-663. |
| [14] | I. Chelladurai, D. Adams, D.T. Fullwood, M.P. Miles, S. Niezgoda, I.J. Beyerlein, M. Knezevic, Int. J. Plast. 117(2019) 21-32. |
| [15] | X. Hong, A. Godfrey, W. Liu, Scr. Mater. 123(2016) 77-80. |
| [16] | Q.L. Huang, R.L. Xin, Adv. Eng. Mater. 19(2017) 1600614. |
| [17] | M.A. Kumar, I.J. Beyerlein, R.A. Lebensohn, C.N. Tomé, Mater. Sci. Eng. A 706 (2017) 295-303. |
| [18] | H.C. Chen, T.M. Liu, D.W. Hou, D.F. Shi, Mater. Sci. Eng. A 667 (2016) 402-408. |
| [19] | D.F. Shi, T.M. Liu, T.Y. Wang, D.W. Hou, S.Q. Zhao, S. Hussain. J. Alloy. Compd. 690(2017) 699-706. |
| [20] | Z.Z. Shi. J. Alloy. Compd. 716(2017) 128-136. |
| [21] | Z.Z. Shi, X.F. Liu. J. Alloy. Compd. 692(2017) 274-279. |
| [22] | L. Capolungo, P.E. Marshall, R.J. McCabe, I.J. Beyerlein, C.N. Tomé , Acta Mater. 57(2009) 6047-6056. |
| [23] | Y. Yang, G.P. Li, G.M. Cheng, H. Wang, M. Zhang, F. Xu, K. Yang, Scr. Mater. 58(2008) 9-12. |
| [24] | Y. Yang, G.P. Li, H. Wang, S.Q. Wu, L.C. Zhang, Y.L. Li, K. Yang, Scr. Mater. 66(2012) 211-214. |
| [25] | P. Castany, Y. Yang, E. Bertrand, T. Gloriant, Phys. Rev. Lett. 117(2016) 245501. |
| [26] | T. Furuhara, K. Kishimoto, T. Maki, Mater. Trans. 35(1994) 843-850. |
| [27] | M.J. Lai, C.C. Tasan, D. Raabe, Acta Mater. 111(2016) 173-186. |
| [28] | X.H. Min, K. Tsuzaki, S. Emura, T. Sawaguchi, S. Ii, K. Tsuchiya, Mater. Sci. Eng. A 579 (2013) 164-169. |
| [29] | H. Tobe, H.Y. Kim, T. Inamura, H. Hosoda, S. Miyazaki, Acta Mater. 64(2014) 345-355. |
| [30] | Y. Yang, G.P. Li, G.M. Cheng, Y.L. Li, K. Yang, Appl. Phys. Lett. 94(2009) 061901. |
| [31] | Y. Yang, S.Q. Wu, G.P. Li, Y.L. Li, Y.F. Lu, K. Yang, P. Ge, Acta Mater. 58(2010) 2778-2787. |
| [32] | Y. Yang, D. Xu, S. Cao, S.Q. Wu, Z.W. Zhu, H. Wang, L. Li, S.W. Xin, L. Qu, A.J. Huang. J. Mater. Sci. Technol. 73(2021) 52-60. |
| [33] | J.H. Gao, Y.H. Huang, D.K. Guan, A.J. Knowles, L. Ma, D. Dye, W.M. Rainforth, Acta Mater. 152(2018) 301-314. |
| [34] | M. Marteleur, F. Sun, T. Gloriant, P. Vermaut, P.J. Jacques, F. Prima, Scr. Mater. 66(2012) 749-752. |
| [35] | X.H. Min, X.J. Chen, S. Emura, K. Tsuchiya, Scr. Mater. 69(2013) 393-396. |
| [36] | X.H. Min, S. Emura, X.J. Chen, X.Y. Zhou, K. Tsuzaki, K. Tsuchiya, Mater. Sci. Eng. A 659 (2016) 1-11. |
| [37] | S. Sadeghpour, S.M. Abbasi, M. Morakabati, A. Kisko, L.P. Karjalainen, D.A. Porter, Scr. Mater. 145(2018) 104-108. |
| [38] | F. Sun, J.Y. Zhang, M. Marteleur, T. Gloriant, P. Vermaut, D. Laillé, P. Castany, C. Curfs, P.J. Jacques, F. Prima, Acta Mater. 61(2013) 6406-6417. |
| [39] | W.L. Wang, X.L. Wang, W. Mei, J. Sun, Mater. Charact. 120(2016) 263-267. |
| [40] | J.Y. Zhang, J.S. Li, Z. Chen, Q.K. Meng, F. Sun, B.L. Shen. J. Alloy. Compd. 699(2017) 775-782. |
| [41] | L. Ren, W.L. Xiao, C.L. Ma, R.X. Zheng, L. Zhou, Scr. Mater. 156(2018) 47-50. |
| [42] | T. Saito, T. Furuta, J.H. Hwang, S. Kuramoto, K. Nishino, N. Suzuki, R. Chen, A. Yamada, K. Ito, Y. Seno, T. Nonaka, H. Ikehata, N. Nagasako, C. Iwamoto, Y. Ikuhara, T. Sakuma, Science 300 (2003) 464-467. |
| [43] | L. Qu, Y. Yang, Y.F. Lu, L. Feng, J.H. Ju, P. Ge, W. Zhou, D. Han, D.H. Ping, Scr. Mater. 69(2013) 389-392. |
| [44] | Y.D. Im, Y.K. Lee, K.H. Song, Met. Mater. Int. 24(2018) 913-917. |
| [45] | X.Y. Zhou, X.H. Min. J. Mater. Sci. 53(2018) 8604-8618. |
| [46] | F.X. Lin, M. Marteleur, P.J. Jacques, L. Delannay, Int. J. Plast. 105(2018) 195-210. |
| [47] | S. Plimpton. J. Comput. Phys. 117(1995) 1-19. |
| [48] | J. Li, Modell. Simul. Mater. Sci. Eng. 11(2003) 173-178. |
| [49] | R. Ravelo, T.C. Germann, O. Guerrero, Q. An, B.L. Holian, Phys. Rev. B 88 (2013) 134101. |
| [50] | Y.F. Zhang, P.C. Millett, M. Tonks, B. Biner, Scr. Mater. 66(2012) 117-120. |
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