Dislocation slip or deformation twinning: confining pressure makes a difference

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Abstract

While b.c.c. metals deform plastically by dislocation motion or deformation twinning, the atomistic mechanisms governing the choice of deformation modes are not well established. Molecular dynamics simulations using the Finnis–Sinclair potential were carried out to explore the pressure dependence of the deformation response of b.c.c. molybdenum. The crystal was sheared in (1 1 2)[1̄ 1̄ 1] under various confining pressures. The homogeneous nucleation stress of deformation twinning was found to increase with increasing confining pressure. Under sufficient pressure (0 1 1)[1̄ 1̄ 1] dislocations were nucleated instead of twins. Details of the dislocation and twin nucleations were analyzed with the help of the multi-layer generalized stacking fault energies. A two-fault (n=2) metastable twin state was found, in contrast to previous results using pair potentials.

Introduction

Dislocation glide and deformation twinning are the two major plastic deformation modes in metals and alloys. Their nucleation and multiplication/growth under stress govern the mechanical behavior of materials. Various models have been proposed for the nucleation of twin from dislocations [1], [2], [3], [4], [5], [6], [7]. But direct experimental confirmations of these models are rare. A measure of the “twinning tendency” at the crack tip of f.c.c. metals has recently been derived within the Peierls framework [8], which is still to be tested. Under extreme conditions such as shock-wave loading, the material deforms at very high strain rate and twinning may play an important role; however, large discrepancies exist with respect to the volume fraction of shock-induced twin, so the factors controlling twin nucleation are yet to be clearly identified [9]. In nanoindentation experiments, homogeneous nucleation of defects inside a perfect crystal can occur at extremely high stresses. A so-called Λ-criterion predicts the location and critical stress of homogeneous nucleation [10], [11], by ascertaining when a local elastic wavelet starts to possess imaginary frequency and subsequently grows in amplitude. This criterion also provides some clues as to what kinds of defects may result after the instability. If the unstable elastic wave is longitudinal (sound wave), then a microcrack is likely to be nucleated. If the unstable elastic wave is transverse (shear wave), then a dislocation loop or twinning embryo may be nucleated. However, the atomistic details of this runaway dynamics are not yet clear. Also, it is noted that even in cases of shear wave instability, the nanoindentation setup induces a significant subsidiary pressure at the defect nucleation site (on the order of tens of GPa) in addition to the resolved shear stress, so it is important to study the influence of the confining pressure [19].

In this paper, nucleation and growth of deformation twins in b.c.c. Mo was simulated atomistically using the Finnis–Sinclair empirical potential [12]. Shear deformations were carried out under (initially) hydrostatic tension and compression to ascertain the effects of pressure. The atomic configurations of the homogeneously nucleated twin embryos were analyzed. Further interpretations were made by considering the static multi-layer generalized stacking fault energetics of a quasi 1D chain model.

Section snippets

Simulation method and setup

We perform molecular dynamics simulations at constant strain rate loading using the Finnis–Sinclair second-moment many body potential for molybdenum [12]. Simulation cells containing up to 0.5 million Mo atoms were employed in the calculations, with periodic boundary condition in all three directions. Shear displacements were imposed along [1̄ 1̄ 1] direction on (1 1 2) plane (both twinning and anti-twinning sense); the confining pressure being adjusted by changing the lattice parameter. Most of

Nucleation of twin and dislocation under confinement in b.c.c. Mo perfect crystal

At zero pressure, when the applied shear strain approached the ideal shear strain of the crystal, shear wave fluctuations became more and more localized. Finally a twin was nucleated in the perfect crystal sheared, via amplification and condensation of the shear waves of the lattice, in a manner similar to a four-stage scenario described previously [10], [11]. The effect of pressure on the shear strength is shown in Fig. 2. The x-axis in this figure is the ratio of the simulation cell vector

Conclusions

Atomistic investigations of the pressure dependence of twin and dislocation nucleation behavior in perfect b.c.c. Mo are carried out using the Finnis–Sinclair interatomic potential. An energetic analysis based on the concept of multi-layer stacking faults is presented to elucidate the nucleation behavior. The following conclusions can be drawn:

  • (1)

    The confining pressure has an appreciable effect on defect nucleation behavior. Increase of pressure will not facilitate the nucleation of twin; instead,

Acknowledgements

The support from the Ministry of Science and Technology of China under grant TG2000067105 is gratefully acknowledged. D.S. Xu acknowledges support from K.C. Wong Fellowship for his visit to MIT.

References (20)

  • K.D.P. Lagerlöf

    Acta Metall. Mater

    (1993)
  • S. Mahajan

    Acta Metall

    (1975)
  • J.W. Christian et al.

    Prog. Mater. Sci

    (1995)
  • E.B. Tadmor et al.

    J. Mech. Phys. Solids

    (2003)
  • K. Wongwiwat et al.

    Mater. Sci. Eng

    (1978)
  • J.P. Chang, PhD Thesis, MIT,...
  • V. Vitek

    Scripta Metall

    (1970)
  • S. Ogata et al.

    Science

    (2002)
  • A.H. Cottrell et al.

    Philos. Mag

    (1951)
  • A.W. Sleeswyk

    Philos. Mag

    (1974)
There are more references available in the full text version of this article.

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