The kinetics and energetics of dislocation mediated de-twinning in nano-twinned face-centered cubic metals

Abstract

Polycrystalline Cu with hierarchy microstructures – ultrafined grains about 500 nm and included twins several to tens of nanometers thick – show maximum strength at an averaged twin thickness of 15 nm. Li et al. Nature 464 (2010) 877–880 (Ref. [1]), reported that the primary plastic deformation transits from inclined dislocation gliding to de-twinning in nano-twinned (nt) Cu when twin thicknesses decrease from 25 nm to 4 nm. Their investigation showed that enhanced de-twinning accounts for the strength softening in nt-Cu. From the kinetic and energetic aspects of de-twining process, we present respectively two models. In the kinetic model, we assume that thermally activated dislocation nucleation is the controlling mechanism for plastic deformation, while the transformation energy associated with de-twinning is considered to be governing in the energetic model. Applications of the models on strain-rate sensitivity and temperature dependence of strengths in nt-Cu suggest that the energetic mechanism also plays an important role for de-twinning in nt-Cu.

Introduction

With increasing volume fraction of grain boundaries (GBs) as grain sizes reduce, nanocrystalline (nc) metals often exhibit substantial increasing in strength [2], [3], [4], but poor deformability, low thermal conductivity, and high electrical resistance [4], [5], [6]. Manipulating the GB structures in nc metals such that desired properties can be realized, which is often called GB engineering [4], [6], [7], [8], [9], [10], has been one of the foci for material synthesis in recent years. The ways to replace general GBs by low energy, coherent twin boundaries (TBs) have been broadly explored [5], [11], [12], [13], [14], [15], [16], for the well known strengthening mechanism by TBs yet their minimum impairment to mechanical, thermal and electrical properties of polycrystalline metals. A hierarchy structure in polycrystalline Cu, with ultrafine grains and included twins at tens of nanometers thick, has been revealed to be an optimal microstructure [5]. In contrast to conventional coarse-grained Cu, such nt-Cu shows high strength, intermediate ductility, and almost no loss in electrical conductivity [5]. Comprehensive summary on the progress in this field is documented in [6] and [17].

More interestingly, Lu et al. [18] have revealed that, in samples with similar grain sizes but different twin thicknesses, the strength of nt-Cu first increases as twin thickness λ decreases to 15 nm, then decreases as λ gets even smaller (see Fig. 1). The strength softening with further decreasing of λ from 15 nm to 4 nm is particularly intriguing. In nc metals without embedded twins, there is a strength softening as grain sizes reach about 10 nm and smaller. Such softening is generally related to the shift of major plastic deformation mechanisms – from dislocation mediated plastic deformation to GB associated mechanisms such as GB sliding, GB diffusion and grain rotation [7], [8], [9] when grains become smaller than 10 nm, which are intensively investigated by experiments [7], [19], [20], [21], molecular dynamics (MD) simulations [22], [23], [24], [25], [26], [27], and continuum level models [28], [29], [30], [31], [32], [33], [34]. Nevertheless, the experience for strength softening in regular nc metals cannot be applied to nt-Cu. In nt-Cu, plastic deformation mainly comes from three sources: (I) GB associated deformation, (II) motion and/or nucleation of dislocations inclined to TBs, and (III) nucleation, motion and/or multiplication of dislocations parallel to TBs (see Fig. 2 for demonstration). For case (I), it is known from experiments that the grain sizes for those samples with different twin thicknesses are close, and the contribution by GB deformation, if it exists, should be similar in all samples. Indeed, the enhanced ductility in nt-Cu may suggest that plastic deformation in GBs is very small, since we know that non-creep deformation in GBs usually leads to poor ductility in polycrystalline materials. As to case (II), nucleation and motion of dislocations inclined to TBs account for the strengthening mechanism as λ decreases instead of softening. Because dislocation activities are confined by the twin space λ, it renders the difficulty in the motion and nucleation of such inclined dislocations. Therefore, to shed light on the observed strength softening in nt-Cu as λ gets smaller, it is necessary to investigate case (III) – the nucleation, motion, and/or multiplication of dislocations parallel to TBs. The motion of leading partial dislocations in TBs will result in de-twinning, also called TB migration in f.c.c. metals, since the gliding of a leading partial dislocation in the TB renders the TB behind the dislocation to migrate by one (1 1 1) lattice space. For now and in what follows, we refer leading partial dislocations in TBs as twinning partials.

Deformation mechanisms in such nano-twinned metals have been studied by experiments [35], [36], [37], [38], [39], [40], [41], MD simulations [42], [43], [44], [45], [46], [47], [48], [49], [50], and finite-element simulations [51], [52]. However, the softening mechanism in nt-Cu has not been studied in depth. The initial dislocation density observed in nt-Cu [18] could contribute roughly 0.2% plastic strain if all initial dislocations are mobile. After the exhaustion of those initial dislocations, the flow stress in samples with narrower twins is still much lower than those with wider twins in a wide strain range, say from 2% to 10% strain in the stress–strain curve (Ref. [18], their Fig. 3). It hence indicates that, in addition to the influence by initial dislocations, there might be other mechanisms responsible for the strength softening of nt-Cu. MD simulations by Kulkarni and Asaro [53] showed that pre-existing dislocations influence the initial strength of nt-metals. They also speculated that the influence of twin–twin interactions may contribute to strength softening. Large scale MD simulations by Li et al. [1] show that there exists a transition of dislocation activities: from nucleation of inclined dislocations (with respect to TBs) to nucleation of twinning partials as twin thickness narrows; the refinement of twin structure at a fixed grain size increases the density of nucleation sites for twinning partials and therefore softens the material by easy nucleation mechanism. Here we will show that, in addition to the kinetics of twinning partial nucleation controlled de-twining, the energetics of de-twinning also plays an important role for strength softening in nt-Cu in order to explain the strain-rate sensitivity and temperature dependence of this material. The energetic mechanism predicts that the strength τ is proportional to twin thickness λ and inversely proportional to grain size d, i.e., τ ∝ λ/d.

The remainder of this paper is organized as follows. In Section 2, we briefly discuss the MD simulations by Li et al. [1] to motivate our subsequent discussion. In Section 3, we then describe modeling on twinning partial mediated de-twinning. Two situations are considered separately: one is the nucleation of twinning partials being the controlling mechanism; the other corresponds to easy twinning partial sources (either nucleated, pre-existing, or by multiplication) but their successful motion to accommodate plastic deformation is controlled by free energy change during de-twinning. Both mechanisms lead to strength softening in nt-Cu as TB thickness decreases. Two characteristics of those mechanisms – strain-rate sensitivity and temperature dependence – are discussed in Section 4. We conclude in Section 5 with some suggestions on further experiments which might better our understanding on the deformation of nt-metals.