S.I. Rao

Estimating the strength of single-ended dislocation sources in micron-sized single crystals

Three-dimensional (3D) discrete dislocation dynamics simulations were used to calculate the effects of anisotropy of dislocation line tension (increasing Poissons ratio, ν) on the strength of single-ended dislocation sources in micron-sized volumes with free surfaces and to compare them with the strength of double-ended sources of equal length. Their plastic response was directly modelled within a 1 µm3 volume composed of a single crystal fcc metal. In general, double-ended sources are stronger than single-ended sources of an equal length and exhibit no significant effects from truncating the long-range elastic fields at this scale. The double-ended source strength increases with ν, exhibiting an increase of about 50% at ν = 0.38 (value for Ni) as compared to the value at ν = 0. Independent of dislocation line direction, for ν greater than 0.20, the strengths of single-ended sources depend upon the sense of the stress applied. The value for α in the expression for strength, τ = α(L)µb/L is shown to vary from 0.4 to 0.84 depending on the character of the dislocation and the direction of operation of the source at ν = 0.38 and L = 933b. By varying the lengths of the sources from 933 to 233b, it was shown that the scaling of the strength of single-ended and double-ended sources with their length both follow a ln(L/b)/(L/b) dependence. Surface image stresses are shown to have little effect on the critical stress of single-ended sources at a length of ∼250b or greater. This suggests that for 3D discrete dislocation dynamics simulations of the plastic deformation of micron-sized crystals in the size range 0.5–20 µm, image stresses making the surface traction-free can be neglected. The relationship between these findings and a recent statistical model for the hardening of small volumes is discussed.

Discrete dislocation simulations of precipitation hardening in superalloys

The low-temperature yield stress of a nickel-based superalloy, containing up to 40% Ni3A1 precipitates (γ′), is calculated by discrete dislocation simulations. A pair of screw or 60°(a/2) ⟨110⟩ dislocation glides under external stress across a {111} plane of γ phase, intersected by a random distribution of either spherical or cubic γ′ precipitates. The stress is raised until the dislocations can cut or bow round all the obstacles. In this paper the emphasis is on the cutting regime which is prevalent when the precipitates are small and/or have low antiphase-boundary (APB) energies. From a large number of simulations in the cutting regime, the effects of size, shape, volume fraction and APB energy are found to be as follows: The yield stress is proportional to the square root of the volume fraction of γ′. The yield stress depends weakly on the precipitate size in the size range 20–400 nm, for APB energies of 150, 250 and 320 mJ m−2. The yield stress depends linearly on the APB energy for APB energies up to 320 mJ m−2 in the size range 50–200 nm. At a precipitate size of 100 nm, cubes are weaker obstacles than equivalent spheres by about 25% for an APB energy of 320 mJ m−2; however, the shape effect on strengthening decreases with decreasing APB energy and decreasing precipitate size. When a coherency stress (from a lattice parameter mismatch of 0.3%) is added, the yield stress increases by about 10%. When solid-solution strenthening is added, it is potent when the solute is in the γ matrix, but much less potent when the solute is in γ′. When the γ′ precipitates are larger than 400 nm across and the APB energy greater than 250 mJ m−2, significant Orowan looping occurs. The yield stress drops inversely as the precipitate size and becomes insensitive to the APB energy but sensitive to the shear modulus. Many of these results from the full simulations differ from the analytical models of strengthening in superalloys but they can be rationalized from the results of simulations on simple homogenized precipitate structures.

Atomistic simulations of cross-slip nucleation at screw dislocation intersections in face-centered cubic nickel

The Escaig model for thermally activated cross-slip in face-centered cubic (fcc) materials assumes that cross-slip preferentially occurs at obstacles that produce large stress gradients on the Shockley partials of the screw dislocations. However, it is unclear as to the source, identity and concentration of such obstacles in single-phase fcc materials. Embedded atom potential, molecular-statics simulations of screw character dislocation intersections with 120° forest dislocations in fcc Ni are described that illustrate a mechanism for cross-slip nucleation. The simulations show how such intersections readily produce cross-slip nuclei and thus may be preferential sites for cross-slip. The energies of the dislocation intersection cores are estimated and it is shown that a partially cross-slipped configuration for the intersection is the most stable. In addition, simple three-dimensional dislocation dynamics simulations accounting for Shockley partials are shown to qualitatively reproduce the atomistically determined core structures for the same dislocation intersections.

Spontaneous athermal cross-slip nucleation at screw dislocation intersections in FCC metals and L12 intermetallics investigated via atomistic simulations

In this manuscript, we extend on our prior work to show that under certain conditions cross-slip nucleation is athermal and spontaneous with zero activation energy in FCC elemental metals such as Ni and Cu, and L12 intermetallic compounds such as Ni3Al. Using atomistic simulations (molecular statics), we show that spontaneous cross-slip occurs at mildly repulsive intersections. Further, the local Shockley partial dislocation interactions at such repulsive intersections are found to be attractive leading to junction formation. The line orientation of the intersecting dislocation determines whether the spontaneous cross-slip nucleation occurs from either the glide plane to the cross-slip plane or vice versa. Collectively, these results suggest that cross-slip should be preferentially observed at selected screw dislocation intersections in FCC-derviative metals and alloys.

Cast aluminium single crystals cross the threshold from bulk to size-dependent stochastic plasticity

Metals are known to exhibit mechanical behaviour at the nanoscale different to bulk samples. This transition typically initiates at the micrometre scale, yet existing techniques to produce micrometre-sized samples often introduce artefacts that can influence deformation mechanisms. Here, we demonstrate the casting of micrometre-scale aluminium single-crystal wires by infiltration of a salt mould. Samples have millimetre lengths, smooth surfaces, a range of crystallographic orientations, and a diameter D as small as 6 μm. The wires deform in bursts, at a stress that increases with decreasing D. Bursts greater than 200 nm account for roughly 50% of wire deformation and have exponentially distributed intensities. Dislocation dynamics simulations show that single-arm sources that produce large displacement bursts halted by stochastic cross-slip and lock formation explain microcast wire behaviour. This microcasting technique may be extended to several other metals or alloys and offers the possibility of exploring mechanical behaviour spanning the micrometre scale.