[1] Modeling the overall solidification kinetics for undercooled single-phase solid-solution alloys. I. Model derivation

H Wang et al

Departing from the volume-averaging method, the equiaxed solidification model was extended to describe the overall solidification kinetics of undercooled single-phase solid-solution alloys. In this model, a single grain, whose size is given assuming site saturation, is divided into three phases, i.e. the solid dendrite, the inter-dendritic liquid and the extra-dendritic liquid. The non-equilibrium solute diffusion in the inter-dendritic liquid and the extra-dendritic liquid, as well as the heat diffusion in the extra-dendritic liquid, is considered. The growth kinetics of the solid/liquid interface is given by the solute or heat balance, where a maximal growth velocity criterion is applied to determine the transition from thermal-controlled growth to solutal-controlled growth. A dendrite growth model, in which the nonlinear liquidus and solidus, the non-equilibrium interface kinetics, and the non-equilibrium solute diffusion in liquid are considered, is applied to describe the growth kinetics of the grain envelope. On this basis, the solidification path is described.

[2] Interactions between carbon solutes and dislocations in bcc iron

H Hanlumyuang et al

Carbon solute–dislocation interactions and solute atmospheres for both edge and screw dislocations in body-centered cubic (bcc) iron are computed from first principles using two approaches. First, the distortion tensor and elastic constants entering Eshelby’s model for the segregation of C atoms to a dislocation core in Fe are computed directly using an electronic-structure-based the total energy method. Second, the segregation energy is computed directly via first-principles methods. Comparison of the two methods suggests that the effects of chemistry and magnetism beyond those already reflected in the elastic constants do not make a major contribution to the segregation energy. The resulting predicted solute atmospheres are in good agreement with atom probe measurements.

[1] In situ study of nucleation and growth of the irregular α-Al/β-Al5FeSi eutectic by 3-D synchrotron X-ray microtomography

S Terzi et al

In order to better understand the formation of β-Al5FeSi intermetallic plates during solidification of Al–Si casting alloys, an Al–8% Si–4% Cu–0.8% Fe alloy has been studied by in situ microtomography using high-energy X-rays in the synchrotron. After formation of the aluminium dendrites, the β phase forms as an irregular eutectic together with eutectic α-Al. Only four plates were nucleated in the sample, and all nucleated in the very early stage of the eutectic reaction and subsequently developed into complex connected three-dimensional plates. The plates display very rapid lateral growth and slow thickening, which, together with the observation of imprints of dendrites and ridges in the plates, suggest a very weakly coupled eutectic.

[2] Deformation of hierarchically twinned martensite

P Muellner and A H King

Shape-memory alloys deform via the reorganization of a hierarchically twinned microstructure. Twin boundaries themselves present obstacles for twin boundary motion. In spite of a high density of obstacles, twinning stresses of Ni–Mn–Ga Heusler alloys are very low. Neither atomistic nor dislocation-based models account for such low yield stresses. Twinning mechanisms are studied here on a mesoscopic length scale making use of the disclination theory. In a first approach, a strictly periodic twin pattern containing periodic disclination walls with optimally screened stress fields is considered. Strict periodicity implies that the twin microstructure reorganizes homogeneously. In a second approach, a discontinuity of the fraction of secondary twins is introduced and modeled as a disclination dipole. The stress required for nucleation of this discontinuity is larger than the stress required for homogeneous reorganization. However, once the dipole is formed, it can move under a much smaller stress in agreement with experimental findings.

[3] New Interpretation of the Haasen Plot for Solute-strengthened Alloys

W A Curtin

The Haasen plot (inverse activation area 1/Δa versus offset flow stress σ-σs) for solute-strengthened alloys is usually assumed additive, 1/Δa=1/Δas+1/Δaf, with 1/Δafnot, vert, similarβ(σ-σs) due to forest interactions. Experiments often show a slope < β. Here, a model for the dislocation activation enthalpy is proposed that predicts a slope 1/(Δasσs) determined only by solute parameters Δas and σs and not directly connected to forest hardening. This parameter-free prediction agrees well with a wide range of experiments on Al-X alloys at T=78K.

[1] Dislocation dynamics simulations of dislocation interactions and stresses in thin films

R S Fertig III and S P Baker

The dislocation interactions that stop threading dislocations (threads) during relaxation at increasing applied strains in single-crystal thin films are investigated using large-scale three-dimensional dislocation dynamics simulations. Threads were observed to stop via interactions with both threads and misfit dislocations (misfits). Both types of interactions were shown to depend on stress inhomogeneity. Low-stress regions enabled threads to stop in weak thread–misfit interactions even at high average film stresses. Threads were also concentrated in low-stress regions, which facilitated their interaction with other threads. Threads accumulated in thread–thread interactions, and stopped only temporarily in thread–misfit interactions. The mean free path for dislocation motion is shown to be accurately predicted from details of the inhomogeneous stress state arising from the applied strain and the misfit structure. These behaviors are analyzed to present a more complete picture of film strength, strain hardening and relaxation.

[2] Comparing grain boundary energies in face centered cubic metals: Al, Au, Cu and Ni

E A Holm et al

The energy of 388 grain boundaries in Al, Au, Cu and Ni were calculated using atomistic simulations. Grain boundary energies in different elements are strongly correlated. Consistent with a dislocation model for grain boundary structure, the boundary energy scales with the shear modulus. Boundaries with substantial stacking fault character scale with the stacking fault energy. There is more scatter in the data for Al, which has a high stacking fault energy, than for the low stacking fault energy elements.

Shearing of γ′ precipitates by a<1 1 2> dislocation ribbons in Ni-base superalloys: A phase field approach

V.A. Vorontsov et al

The phase field model of dislocations has been used to study the propagation of dislocation ribbons with an overall Burgers vector of a through a simulated Ni-base superalloy. The driving force for dislocation dissociation reactions and formation of planar faults is incorporated into the free energy functional using periodic functions specially fitted to ab initio γ-surface data. The model shows that the mechanism of cutting of the γ′ precipitates by these ribbons exhibits significant dependence on stress magnitude, orientation and precipitate shape. In the case of mixed screw–edge ribbons a change of shearing mode is observed, from stacking fault shear to anti-phase boundary shear, when the applied stress approaches the yield of the material. This transition is absent in pure edge ribbons.