The synergistic effects of energy barriers and shear directions on twinning in face centered cubic metals

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Highlights

  • A theoretical descriptor was proposed to estimate the twinning propensities of face-centered cubic metals.

  • We demonstrate that deformation twins form readily in: Al, Ir, Ni, Rh, Co, Au, Cu, Yb, Ag, Sr, and Ca, but have difficulty forming in: Ce, Pt, Pb, and Pd.

  • The descriptor predicts well in Cu-Al alloys where there exists a highest twinning propensity at 6 at.% Al.

Abstract

The formation of twins in face-centered cubic (FCC) crystals is influenced by both the energy barriers and associated shear directions. In this study, we formulate and implement a theoretical framework to study 15 pure FCC metals in an effort to propose a twinning propensity descriptor to predict the tendency for twin formation in FCC metals under different shear directions. Our calculations demonstrate that deformation twins form readily in: Al, Ir, Ni, Rh, Co, Au, Cu, Yb, Ag, Sr, and Ca, but have difficulty forming in: Ce, Pt, Pb, and Pd, and this trend is consistent with available experiment results. Using this descriptor, we further predict that in the case of Cu-Al alloys the highest twinning propensity is achieved at ~6 at. % Al concentration, which is also consistent with experimental observations. These results provide insight into the nature of deformation twins, and furthermore help establish the framework necessary to design FCC metals and alloys with a high tendency for twin formation.

Introduction

Metals play an irreplaceable role as structural materials in the aircraft and automotive industries, partly due to their broad availability but also due to their mechanical and physical attributes, such as strength, fracture toughness and conductivity [1], [2]. In many applications, however, it is their inherently low strength/weight ratio that hinders their applicability [3]. Grain refinement has been proposed by many researchers as a strategy to enhance strength, and although some progress has been documented to date, challenges related to conductivity or toughness have limited this approach [4], [5], [6], [7], [8], [9]. Alternatively, twinning is an effective way to improve the strength/weight ratio while not sacrificing other properties. Accordingly, several experimental [10], [11], [12] and theoretical [13], [14], [15] studies have been devoted to investigating the factors that affect twinning and propose some methods to predict the tendency for twin formation.

Normally, it is widely accepted that metals with a low stacking fault energy (SFE) values have a high tendency for twin formation. This relationship is mainly attributed to the separation of twin dislocations from the dissociation site and extension of a stacking fault. For example, Cu (~42 mJ/m2) and Ag (~15 mJ/m2) have low SFEs, facilitating the formation of twins [16], [17], [18]. However, deformation twins can also form in Ir (~339 mJ/m2) and Ni (~143 mJ/m2), whose SFE values are significantly larger than those of Cu and Ag [19], [20]. To understand this “contradiction”, Tadmor et al. [13], [21] suggested that not only SFE but also the unstable stacking fault energy (USFE), and unstable twin fault energy (UTFE) affect the formation of twins [22], [23]. Accordingly, they developed a homogenized formula to evaluate the twinning tendency depending on the ratio of USFE and UTFE. This criterion works well in common FCC metals like Cu, Ag, and Au and conventional alloys [24], [25]. However, broad application of this criterion is limited to the fact that their original formulation was based on the condition that exists at a crack-tip [26]. Besides the ratio of USFE and UTFE, the shear direction is also known to play an important role in the formation of twins [15], [27], [28], [29]. For example, although deformation twins are typically formed in polycrystalline Cu, an inhomogeneous occurrence of deformation twins was found in different grains and was attributed to different shear directions [30], [31], [32].

Recent studies have proposed that the effect of shear directions can override the intrinsic energy barriers. For instance, Li et al. [26] suggested that the tendency for twin formation can be evaluated by the competition between twinning partial nucleation and trailing partial nucleation. Jo et al. [14] transformed the intrinsic energy barriers into effective energy barriers based on the increase of effective shear stress along a particular direction. This method clearly describes the changes of deformation mechanisms depending on the shear directions along with the energy barriers.

In this contribution, we carried out density-functional theory (DFT) calculations to systematically investigate the formation of twins in FCC metals and alloys. Based on the synergistic influence of intrinsic energy barriers and shear direction of external shear stress, we consider the critical condition of shear direction and propose a descriptor η, termed as “twinning propensity”, to describe the tendency for twin formation. This descriptor η can be applied to compare the twinning propensities between metals under different shear directions. According to the magnitude of η, deformation twins form readily in: Al, Ir, Ni, Rh, Co, Au, Cu, Yb, Ag, Sr, and Ca, due to the positive values of η. But twins have difficulty forming in: Ce, Pt, Pb, and Pd, which have negative or zero values. Furthermore, the highest η is achieved at ~6 at.% Al concentration when applying this descriptor to Cu-Al alloys, which is close to the experimental findings that twinning occurs readily around 8 at.% Al. These findings provide a physical explanation to the formation of a twin. Our results obtained with Cu alloys further support our original hypothesis that η provides a general principle to screen alloying concentrations for high twinning propensity.

Section snippets

Method

All DFT computations were carried out using the Vienna ab initio simulation package (VASP) code [33], [34]. The projector augmented wave (PAW) basis was utilized to describe the interaction between the valence electrons and ionic cores [35]. We used the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) as the exchange-correlation functional [36], [37].

As shown in Fig. 1(a), we established a periodic supercell consisting of 12 FCC layers with four atoms per layer to

Results and discussion

A twin is the most common manifestation of plastic deformation in crystalline solids. The formation of a twin always corresponds to lattice shearing, and the extreme of the corresponding energy path is the same as for the GSFE curve resulting from the idealized rigid shift [22]. In FCC metals, the (111) plane and 110 direction are the dominant slip plane and slip direction, respectively [43]. The dislocation gliding with the Burgers vector 12[011-] would form a perfect dislocation (termed as

Conclusions

We have carried out density-funtional theory calculations to systematically model the twin formation in face-centered cubic (FCC) metals and alloys. We find that the tendency of twin formation can be described by the synergistic influence of intrinsic energy barriers and shear direction of external shear stress. Importantly, a theoretical descriptor, η, was proposed to estimate the twinning propensities of FCC metals. We show that when η is positive twin is preferential to form in most FCC

CRediT authorship contribution statement

Haoran Sun: Methodology, Investigation, Writing - original draft, Formal analysis, Investigation, Data curation. Zhigang Ding: Conceptualization, Writing - review & editing. Hao Sun: Software, Investigation. Shuang Li: Validation. Enrique J. Lavernia: Writing - review & editing. Wei Liu: Resources, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Key R&D Program of China (Grant 2017YFA0204403). W.L. is grateful for support from the NSFC (21773120, 51722102, 51931003), the Fundamental Research Funds for the Central Universities (30919011405). E.J.L. acknowledges support from NSF CMMI-1729829.

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