Review Article

Atomistic Energetics and Critical Twinning Stress Prediction in Face and Body Centered Cubic Metals: Recent Progress

[+] Author and Article Information
Piyas Chowdhury

Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
1206 W. Green Street,
Urbana, IL 61801

Huseyin Sehitoglu

Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
1206 W. Green Street,
Urbana, IL 61801
e-mail: huseyin@illinois.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received March 8, 2017; final manuscript received November 19, 2017; published online January 19, 2018. Assoc. Editor: Irene Beyerlein.

J. Eng. Mater. Technol 140(2), 020801 (Jan 19, 2018) (19 pages) Paper No: MATS-17-1069; doi: 10.1115/1.4038673 History: Received March 08, 2017; Revised November 19, 2017

This paper recounts recent advances on the atomistic modeling of twinning in body-centered cubic (bcc) and face-centered cubic (fcc) alloy. Specifically, we have reviewed: (i) the experimental evidence of twinning-dominated deformation in single- and multi-grain microstructures, (ii) calculation of generalized planar fault energy (GPFE) landscapes, and (iii) the prediction of critical friction stresses to initiate twinning-governed plasticity (e.g., twin nucleation, twin–slip and twin–twin interactions). Possible avenues for further research are outlined.

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Grahic Jump Location
Fig. 1

A perspective on the goal of using atomistics to develop physically based theories that can capture the phenomenology of deformation, and thus formulate strategies for property enhancement in novel alloys of wide technological importance

Grahic Jump Location
Fig. 2

(a) The Co-Ni crystal under ⟨111⟩ tension plastically deforms predominantly via twinning and twin-slip interactions as confirmed by DIC, EBSD, and TEM [52]. (b) Co-Ni compressed along the ⟨001⟩ orientation demonstrates parallel twinning as the primary deformation mechanism [52]. (c) The deformation of electrodeposited nanocrystalline (as indicated by EBSD analysis) Ni-Co alloys with pre-existent annealing twins shows a strong composition effect [52]. The deformation behavior is found to be characterized by massive slip–twin boundary interactions via electron microscopy.

Grahic Jump Location
Fig. 3

(a) Fe-Cr single crystal under [01¯0] tension deforms via interacting deformation twins as evidenced in DIC, EBSD, and SEM analyses [34]. (b) The deformation mechanism of Fe-Cr single crystal under [101] begins with slip activities followed by twin nucleation, which causes a stress drop [34]. Subsequently, twin–twin interactions give rise to hardening as substantiated by DIC, EBSD, and TEM techniques. (c) Polycrystalline Fe-Cr stress–strain response is found to be governed by massive strain transfer across grain boundaries [35] (as confirmed by combined EBSD and DIC studies).

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Fig. 4

Nucleation of a twin embryo through the pole mechanism in fcc lattice is proposed to be controlled by a simultaneous process of mobile jog formation and dislocation loop expansion [4446]. Expanding slip loops from two adjoining planes eventually interconnect to form a continuous spiral, ultimately leading to the twin nucleation.

Grahic Jump Location
Fig. 10

Evolution of energy barriers for various slip–twin interaction mechanisms with respect to the number of incident slip (nslip) and the predicted frictional stresses (τCRSStwin−slip) [105]

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Fig. 9

To generate a γ surface, crystal blocks consisting of atoms are rigidly sheared in atomic simulations. The atomic structures of the perfect lattice and the one corresponding to an intrinsic stacking fault are shown [52] as computed from DFT simulations.

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Fig. 8

The atomistic configuration of a deformation twin produced from lattice shearing induced by consecutive glide of slip [52]

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Fig. 7

Full dislocations dissociate into partials connected by intrinsic stacking faults [47]. Two extended dislocations from adjoining planes form a two-layer fault, i.e., an extrinsic stacking fault. Interaction between two extrinsic stacking faults leads ultimately to twin formation.

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Fig. 6

The dissociation of a screw dislocation with three-fold core in bcc materials into three fraction dislocations under applied stress [4043]. Two of the fractional dislocations (the most stress ones) cross-glide and become parallel to the third one, thereby forming a three-layer twin nucleus.

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Fig. 5

An illustration of twin nucleation model via pole mechanism in bcc lattice [30,36]. An expanding slip loop stemming from sessile dislocation (pole) cross-slips into a perpendicular plane. Subsequently, the dislocation continues to revolve around the pole assisted by further cross-slips and hence generates layers of stacking faults, i.e., the twin embryo.

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Fig. 11

(a) GSFE for Co-Ni alloys, which represents the energy pathway for the nucleation of an extended dislocation [52] connected by an intrinsic stacking fault. (b) GPFE for Co-Ni alloys [52] as an example. The GPFE represents the twinning energy pathway encompassing the formation of a single-layer intrinsic stacking fault first, then a two-layer extrinsic stacking fault, and finally a three-layer twin nucleus. Further shearing on consecutive planes results in the twin growth (migration) process. (c) Comparison among the GSFE and GPFE in bcc Fe and Fe-Cr alloys. There are two distinct types of twin boundaries in bcc alloys, namely, isosceles and reflective ones [71], which are favored differently from one material (e.g., Fe) to another (e.g., Fe-Cr).

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Fig. 12

(a) Relative sizes of the fault energetics (GSFE and GPFE) and their implication regarding the preference for a certain defect nucleation for fcc lattice [3,5860] and (b) possible shapes of fault energy surfaces and the likely defect mechanism scenario in bcc lattice

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Fig. 14

Five different types of slip–twin boundary interaction mechanisms studied in molecular dynamics simulations: transmission [23], incorporation [27] (shown after 1.3 picoseconds from the beginning, to) Lomer lock formation [25], transmission-incorporation [98] and multiplication [94]

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Fig. 15

The “tracing atom” method for computing the extrinsic magnitude of γus from molecular dynamics simulations [104]. The convergence criteria of the energy parameter are obtained at high l and low w, which are the length and width of the tracing area, respectively.

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Fig. 16

Fault energy profile for various slip-coherent twin boundary interaction mechanism in fcc Cu [94]. Incorporation process has the lowest energy barrier while the blockage case has the highest. The curves designated “baseline” represents the GSFE profile for bulk lattice shearing (i.e., absence of residual slip br). The reason the GSFE curves specific to the reactions are elevated is that br creates local stress, which makes glide difficult for subsequent incidence.

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Fig. 17

An approaching twin consisting of three (a/6)[111¯]  type twinning partials intercept a pre-existent twin boundary [71] in bcc Fe-Cr alloy. The resultant reaction is the incorporation of the twinning partials on the boundary leaving a residual dislocation (br) behind at the interception site. Depending on the magnitude of br (which can be obtained by modulating the Schmid factor or changing single crystal loading direction), the GSFE profile will be altered as shown on the right.

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Fig. 18

Comparison between the predicted twin–twin interaction stress (τCRSStwin−twin) and the experimental one in several bcc alloys [71]

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Fig. 13

Modeling of twin–slip interaction based on dislocation mechanics whereby a propagating three-layer twin approaches a dislocation dipole arrangement [52]. The atomistic contributions are considered in the form of GPFE representing the discrete lattice during the process.

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Fig. 19

Comparison between the predicted and experimental critical resolved shear stresses in polycrystalline NiCo alloys (in the presence of annealing twins) [52]

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Fig. 20

Molecular dynamics simulation of polycrystalline deformation behaviors. From left to right: Nucleation of twins from grain boundaries in nanocrystalline Al [115]; a nanocrystalline Cu structure with annealing twins, which upon deformation results in massive slip–interface interactions [117]; Shockley partials emerging from grain boundaries in Cu [116].

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Fig. 21

Study of crack-tip twinning behavior using atomistics concept. Competition between twin and slip nucleation from a crack is correlated with the relative size/shape of GSFE/GPFE curves [59,60,69,123].



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