Peter M. Hazzledine

Dislocation-Based Deformation Mechanisms in Metallic Nanolaminates

The appeal of nanolayered materials from a mechanical viewpoint is that, in principle, plastic deformation can be confined to small volumes of material by Controlling both the frequency and magnitude of obstacles to dislocation motion. As we shall see, the spacing of obstacles can be used to impart large plastic anisotropy and work hardening. However, how strong can such materials be made as layer thickness (and therefore obstacle spacing) is decreased to the nanoscale level? In perspective, large, micron-scale, polycrystalline materials generally display improved yield strength (and fracture toughness) as grain size is decreased. This behavior at the micron scale can be explained via modeis that are built on two assumptions: (1) the strength of obstacles to crystal slip is sufficiently large to require pileups of numerous dislocations in order to slip past them; and (2) the strength of such obstacles does not change, even if their spacing is decreased. The modeling presented here shows that these assumptions may break down at the nanometer scale. The result is that there is a critical layer thickness in the nanometer range, below which improvement in strength does not occur. Our discussion to follow briefly outlines a more macroscopic, micron-scale approach to determine yield strength, and then contrasts that with a sequence of events leading up to yield in nanolayered materials. We also address whether nanoscale materials are expected to exhibit more uniform or coarse slip than micron-scale materials. Finally, a semi-quantitative model of yield strength is developed which requires, as input, the strength of an interface to crystal slip transmission across it. We discuss several contributions to the interfacial strength and apply the theory to demonstrate a peak in strength for a 50 vol% Cu-50 vol% Ni multilayered sample.

The geometry and nature of pinning points of ½ 〈110] unit dislocations in binary TiAl alloys

Abstract The b = ½ 〈110] unit dislocations in deformed TiAl alloys exhibit a unique morphology, consisting of numerous pinning points along the dislocation line aligned roughly along the screw dislocation direction, and bowed-out segments between the pinning points. The three-dimensional arrangement of these dislocations has been characterized in detail, based on post-mortem weak-beam transmission electron microscopy observations in deformed binary Ti-50 at.% Al and Ti-52 at.% Al alloys. The bowed segments glide on parallel {111} primary planes, and the pinning points are jogs with a range of heights, up to a maximum of about 40 nm. The substructure evolution is consistent with dislocation glide involving frequent double cross-slip and consequent jog formation. The dislocations experience a large glide resistance during the forward (non-conservative) motion of these jogs. Pinning of unit dislocations is an intrinsic process in these alloys and is not related to the presence of interstitial-containing prec...

Shear boundaries in lamellar TiAl

Abstract Small-angle tilt boundaries and small-angle twist boundaries are familiar features of crystalline microstructures but small-angle shear boundaries are much less well known. Shear boundaries may be composed of cross-grids of either edge or screw dislocations. This paper reports some observations of shear boundaries on {111} planes in tetragonal TiAl which consist only of screw dislocations. In the electron microscope, shear boundaries look very similar to twist boundaries but they differ in that their two sets of dislocations have the same sign whereas twist boundaries have two sets with opposite signs. Asymmetric shear boundaries, composed of two sets of dislocations with different spacings, can be described as a superposition of a symmetric shear boundary and a twist boundary. An extreme case is a simple shear boundary which has just one set of screw dislocations.

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.

Monte Carlo simulations of grain growth and Zener pinning

Abstract This paper describes computer simulations of Zener pinning in two and three dimensional grain growth, in the presence of dispersions of shaped particles. The two dimensional simulations are embedded on square or hexagonal lattices of 2000 × 2000 Potts elements. In these simulations, if they are large enough, the grain growth exponent is n = 0.38 for the initial growth and stagnation occurs at a grain size which is proportional to the particle size and proportional to f −1/2 where f is the area fraction of particles. In three dimensions the simulations are embedded on simple or face-centered cubic lattices with up to 235 × 235 × 235 Potts elements. In these simulations, the kinetics are similar to those in two dimensions ( n = 0.38) and the stagnant grain size is proportional to ƒ −1/3 . The stagnant grain shape does not depend strongly on the particle shape (sphere, needle or plate), but the grain size exhibits a mild dependence on the precipitate shape. However, these three dimensional simulations are often not big enough to give reliable results and, in particular, they violate the principle that the grain size should be proportional to the particle size. This problem becomes more acute as the volume fraction of particles decreases. The ranges of allowable volume fractions and particle sizes in a simulation of given size are discussed.

Discrete dislocation simulations of precipitation hardening in inverse superalloys

The low-temperature yield stress of a γ′ (Ni3Al) matrix–γ (Ni) precipitate ‘inverse’ superalloy, containing 40% Ni precipitates (γ), is calculated by discrete-dislocation simulations. Two different precipitate sizes and two anti-phase boundary energies are considered. The results of these simulations are compared with corresponding results from γ–γ′ superalloys (S. Rao, T.A. Parthasarathy, D. Dimiduk, et al., Phil. Mag. 84 3195 (2004)). In general, the results show that precipitation hardening in inverse superalloys is weaker than for regular superalloys. Similar to studies of superalloys, many of these results can be rationalized from the results of simulations on simple homogenized precipitate structures. The Hirsch, Kelly and Ardell precipitation-strengthening model (Metall. Trans. A 16 2131 (1985); Phil. Mag. 12 881 (1965); Trans. Jpn. Inst. Metals 9 1403 (1968).), developed for low-stacking-fault-energy spherical precipitates in a high-stacking-fault-energy matrix, adapted for inverse superalloys, shows qualitative agreement with the simulation results for spherical γ precipitates.

Design-tool representations of strain compatibility and stress-strain relationships for lamellar gamma titanium aluminides

Abstract Engineering use of gamma titanium aluminides requires further development of design models of the material. Presently, modeling tools are limited by computational capability, uncertainty in experimental data, and physical accuracy. Lamellar Ti–Al alloys are plastically inhomogeneous and exhibit anisotropic flow. The origin of this behavior is that there are at least four different length scales in the microstructure: the grain size, the domain size, the lamellar thickness and the separation between either dislocations or twins. They range from mm to nm and give rise to strain incompatibilities and internal stresses over a similar range of lengths. Traditional engineering finite-element analysis of plastic deformation ignores all microstructural length-dependent aspects of deformation, but uses instead constitutive equations to describe plasticity. The gap between the scientific and engineering analyses of plasticity might be bridged by using Ashbys strain-gradient arguments. These capture most of the microstructural scale effects and may deliver descriptions of plasticity that are capable of being used in simulations. In this study, strain-gradient arguments are used to interpret experimental stress–strain measurements of both PST (poly-synthetically-twinned) and polycrystalline TiAl.

Internal Stresses in TiAl Based Lamellar Composites

In the in situ lamellar γ-TiAl based composites, very large elastic stresses (≈ 1GPa) would be generated at coherent interfaces between close packed planes for three reasons: the tetragonality of TiAl, the larger atomic spacing in α 2 -Ti 3 Al than in γ and the differences between thermal expansion coefficients in α 2 and γ. These stresses appear to be partially relaxed by the creation of van der Merwe dislocations, diffusion across α 2 /γ interfaces and cracking along interfaces. Measurements of lattice parameters by Convergent Beam Electron Diffraction (CBED) reveal stresses of the order of 100MPa. The presence of these stresses and the very specific form of the resulting stress tensor are used to discuss the hard/soft mode deformation of TiAl composites.

The Critical Stress for Transmission of a Dislocation Across an Interface: Results From Peierls and Embedded Atom Models

A continuum Peierls model of a screw dislocation being pushed through an interface and an atomistic EAM study of dislocation transmission across a [0 0 1] Al-Ni interface suggest that core spreading into the interface and misfit dislocations in the interface are both potent effects that can significantly increase barrier strength of interfaces.

Dislocation Confinement and Ultimate Strength in Nanoscale Polycrystals

Nanoscale polycrystalline metals typically exhibit increasing hardness with decreasing grain size down to a critical value on the order of 5 to 30 nm. Below this, a plateau or decrease is often observed. Similar observations are made for nanoscale multilayer thin films. There, TEM observations and modeling suggest that the hardness peak may be associated with the inability of interfaces to contain dislocations within individual nanoscale layers. This manuscript pursues the same concept for nanoscale polycrystalline metals via an analytic study of dislocation nucleation and motion within a regular 2D hexagonal array of grains. The model predicts a hardness peak and loss of dislocation confinement in the 5 to 30 nm grain size regime, but only if the nature of dislocation interaction with grain boundaries changes in the nanoscale regime.