TY - JOUR
T1 - Variant selection of primary–secondary extension twin pairs in magnesium
T2 - an analytical calculation study
AU - Liu, Hong
AU - Lin, Fengxiang
AU - Liu, Pei
AU - Yue, Yuan
AU - Shin, Kwang Seon
AU - Peng, Liming
AU - Delannay, Laurent
AU - Nie, Jian Feng
AU - Moelans, Nele
N1 - Funding Information:
HL acknowledges the support from the FWO and European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 665501 . NM and HL acknowledge the funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (INTERDIFFUSION, Grant Agreement No. 714754 ). FXL acknowledges the funding from the European Research Council (ERC Grant Agreement No. 788567 M4D). JFN is grateful to the support from the Australian Research Council. LMP acknowledges the funding from National Nature Science Foundation of China (Grant No. 51771113 ). LD is mandated by the FSR-FNRS Belgium. Prof. Q. Liu is highly acknowledged for providing experimental samples.
Publisher Copyright:
© 2021
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/10/15
Y1 - 2021/10/15
N2 - Twining is an important deformation mode in magnesium. In a deformed magnesium sample, an extension twin crystal, i.e., {101¯2} twin, can form inside a {101¯2} primary twin, which is named {101¯2}–{101¯2} secondary twin. These secondary twins often appear at the intersection of two primary twins, and form primary–secondary twin pairs. Experimental observations show that the most frequently observed primary–secondary twin pairs have a unique misorientation, i.e., twin variant selection exists. Such variant selection of the primary–secondary twin pairs is studied in this work. The crystallographic analysis reveals that the twin planes of the primary and secondary twins that form a twin pair have coincident intersection lines with the boundary where the twin pair adjoins. An analytical calculation method based on Eshelby's inclusion theory is developed, and the calculation results show that only for this unique misorientation, the stress fields concentrated at the rims of the primary and the secondary twins are mutually favoured. The analysis is further extended to the incoming–outgoing twin pairs across ordinary grain boundaries, and compared with the commonly used geometrical compatibility factor m′. It is found that m′ only gives good prediction for twin transmission when the shear stress component on the twin plane along the twin shear direction of the incoming twin is the major contributor to the resolved shear stress of the outgoing twin. When other stress components play a dominant role, m′ becomes ineffective in prediction, which is the case for the primary–secondary twin pairs.
AB - Twining is an important deformation mode in magnesium. In a deformed magnesium sample, an extension twin crystal, i.e., {101¯2} twin, can form inside a {101¯2} primary twin, which is named {101¯2}–{101¯2} secondary twin. These secondary twins often appear at the intersection of two primary twins, and form primary–secondary twin pairs. Experimental observations show that the most frequently observed primary–secondary twin pairs have a unique misorientation, i.e., twin variant selection exists. Such variant selection of the primary–secondary twin pairs is studied in this work. The crystallographic analysis reveals that the twin planes of the primary and secondary twins that form a twin pair have coincident intersection lines with the boundary where the twin pair adjoins. An analytical calculation method based on Eshelby's inclusion theory is developed, and the calculation results show that only for this unique misorientation, the stress fields concentrated at the rims of the primary and the secondary twins are mutually favoured. The analysis is further extended to the incoming–outgoing twin pairs across ordinary grain boundaries, and compared with the commonly used geometrical compatibility factor m′. It is found that m′ only gives good prediction for twin transmission when the shear stress component on the twin plane along the twin shear direction of the incoming twin is the major contributor to the resolved shear stress of the outgoing twin. When other stress components play a dominant role, m′ becomes ineffective in prediction, which is the case for the primary–secondary twin pairs.
KW - Eshelby's inclusion theory
KW - Secondary twin
KW - Twin transmission
KW - Twin-twin interaction
KW - Variant selection
UR - http://www.scopus.com/inward/record.url?scp=85114672255&partnerID=8YFLogxK
U2 - 10.1016/j.actamat.2021.117221
DO - 10.1016/j.actamat.2021.117221
M3 - Article
AN - SCOPUS:85114672255
VL - 219
JO - Acta Materialia
JF - Acta Materialia
SN - 1359-6454
M1 - 117221
ER -