Elsevier

Acta Materialia

Volume 58, Issue 19, November 2010, Pages 6554-6564
Acta Materialia

Simulations of stress-induced twinning and de-twinning: A phase field model

https://doi.org/10.1016/j.actamat.2010.08.020Get rights and content

Abstract

Twinning in certain metals or under certain conditions is a major plastic deformation mode. Here we present a phase field model to describe twin formation and evolution in a polycrystalline fcc metal under loading and unloading. The model assumes that twin nucleation, growth and de-twinning is a process of partial dislocation nucleation and slip on successive habit planes. Stacking fault energies, energy pathways (γ surfaces), critical shear stresses for the formation of stacking faults and dislocation core energies are used to construct the thermodynamic model. The simulation results demonstrate that the model is able to predict the nucleation of twins and partial dislocations, as well as the morphology of the twin nuclei, and to reasonably describe twin growth and interaction. The twin microstructures at grain boundaries are in agreement with experimental observation. It was found that de-twinning occurs during unloading in the simulations, however, a strong dependence of twin structure evolution on loading history was observed.

Introduction

Deformation twinning is a major plastic deformation mode in some cubic and in most non-cubic materials [1], [2], [3], [4]. For example, in hcp crystals, where deformation by slip along some directions either is not possible or requires very high stresses, twinning is a dominant deformation mechanism. Although plastic deformation predominantly occurs via dislocation nucleation and slip in coarse grained fcc metals and alloys with medium to high stacking fault energies, deformation twinning becomes important in nanocrystalline materials as grain sizes decreases [5], [6], [7], [8], [9]. Twin formation during crystal growth from the melt due to crucible contact stresses or growth stresses can be problematic in the processing of single crystals, such as CdTeZn growth via the vertical gradient freeze method [10], [11]. A fundamental understanding of the effect of microstructure, defects and external stresses on twin nucleation and growth is helpful in designing advanced or improving existing materials and materials processing methods.

Experiments and atomistic simulations show that deformation twinning in nanocrystalline fcc metals forms and evolves via partials dislocations emitted from grain boundaries [5], [6], [7], [8], [9]. The stacking fault energy and energy pathways are predicted using first principle calculations [12], [13], [14]. Molecular dynamics (MD) simulations have been successfully used to investigate how grain boundary structure influences dislocation nucleation and in examining the twinning mechanisms [9], [15], [16]. Stacking fault core fields in fcc metals have been analyzed by MD simulations and continuous models [17]. The critical twinning stress was estimated using a continuous mechanical model [3], [12], which suggests that the shear stress on the habit plane and slip direction of the twin controls twin nucleation. In addition, one of the commonly accepted mechanisms in both coarse grained and nanocrystalline fcc metals is that a twin nucleates and evolves via the nucleation and slip of partial dislocations with the same Burgers vectors. In the present work we assume that twin nucleation, growth and de-twinning is a process of partial dislocation nucleation and slip on successive habit planes under internal and external stresses. A phase field model is proposed to describe the dynamics of partial dislocations and to study both stress-induced partial dislocation nucleation and twin structure evolution. Compared with atomistic simulation methods, the main advantage of the mesoscale phase field method is that it permits simulations at relatively large length and long time scales. Furthermore, it is possible to incorporate the effect of long-range elastic interactions on deformation twin evolution due to second phases, such as inclusions/precipitates, once the elastic constants and lattice mismatches are known. The capability of our model is demonstrated by modeling twin microstructure evolution in a polycrystalline fcc solid.

Section snippets

Phase field model

Fig. 1 illustrates the formation of the thinnest possible twin in the matrix formed by the nucleation and passage of three partial dislocation loops on successive planes. Since the partial dislocation is the smallest unit cell in the twin structure, we study twin evolution using partial dislocation dynamics similar to the phase field model of dislocation dynamics [18], [19], [20]. In this work an arbitrary fcc crystal is used as an example. With the assumption that a twin consists of partial

Results and discussion

To demonstrate the capability of the proposed phase field model we constructed a two-dimensional simulation cell consisting of four differently orientated grains. The orientations of grains 1–3 are shown in Fig. 5a. θi (i = 1, 2, 3) denotes the angle between direction [112¯] or [011¯] and the x-axis. The orientation of grain 4 was the same as grain 1, which ensured that the simulation cell was periodic in the x direction. As shown in Fig. 5b, two twin variants, their habit planes perpendicular to

Conclusion

In this work we have proposed, for the first time, a phase field model to predict both nucleation and evolution of twin structures in a polycrystalline material with defects and subject to external applied loads. The model was developed for fcc Al and was based on the assumption that a twin evolves via the nucleation and glide of partial dislocations. Stacking fault energies, energy pathways (γ surfaces), ideal critical shear stresses for the formation of stacking faults and dislocation core

Acknowledgements

This research was supported by the US Department of Energy NA22 Project “Property improvement in CZT via processing and modeling innovations” in the Pacific Northwest National Laboratory, which is operated by Battelle Memorial Institute for the US Department of Energy under Contract No. DE-AC05-76RL01830. S.H. would like to thank Drs. X. Sun and Y.F. Shen at Pacific Northwest National Laboratory and Drs. Y. Wang and T.W. Heo at The Pennsylvania State University for helpful discussions.

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