## Lattice Boltzmann modeling of dendritic growth

### January 31, 2009

Lattice Boltzmann modeling of dendritic growth in a forced melt convection

D Sun et al

A two-dimensional (2D) lattice Boltzmann-based model is developed to simulate solutal dendritic growth of binary alloys in the presence of forced flow. The model adopts the lattice Boltzmann method (LBM) that describes transport phenomena by the evolution of distribution functions of moving pseudoparticles to numerically solve fluid flow and solute transport governed by both convection and diffusion. Based on the LBM-calculated solutal field, the dynamics of dendritic growth is determined according to a previously proposed local solutal equilibrium approach. After detailed model analysis and validation, the model is applied to simulate single and equiaxed multidendritic growth of Al–Cu alloys with forced convection. The results demonstrate the quantitative, numerically stable and computationally efficient capabilities of the proposed model. It is found that the solute distribution and dendritic growth are strongly influenced by convection, producing asymmetrical dendrites that grow faster in the upstream direction, but mostly slower in the downstream direction.

## Crystal plasticity using DFT

### January 31, 2009

Crystal plasticity simulations using discrete Fourier transforms

M Knezevic, H F Al-Harbi, and S R Kalidindi

In this paper, we explore efficient representation of all of the functions central to crystal plasticity simulations in their complete respective domains using discrete Fourier transforms (DFTs). This new DFT approach allows for compact representation and fast retrieval of crystal plasticity solutions for a crystal of any orientation subjected to any deformation mode. The approach has been successfully applied to a rigid–viscoplastic Taylor-type model for face-centered cubic polycrystals. It is observed that the novel approach described herein is able to speed up the conventional crystal plasticity computations by two orders of magnitude. Details of this approach are described and validated in this paper through a few example case studies.

## Internal strain around crack-tip

### January 31, 2009

In situ neutron-diffraction measurements were performed to investigate the lattice-strain evolution around a fatigue crack under five different loading conditions (i.e., fatigued, tensile overloaded, compressive underloaded, tensile overloaded-compressive underloaded, and compressive underloaded-tensile overloaded) during fatigue crack growth. The results show that different crack-growth behaviors are closely related to the distinct strain distributions developed near the crack tip under the various loading conditions.

## Morphological instabilities during solidification

### January 29, 2009

Effect of a high magnetic field on the morphological instability and irregularity of the interface of a binary alloy during directional solidification

X Li et al

The influence of an axial high magnetic field (up to 12 T) on the stability and morphology of the liquid–solid interface of a binary alloy has been investigated experimentally during the directional solidification of the Al–0.85 wt.% Cu and Zn–2.0 wt.% Cu alloys. Experimental results indicate that the high magnetic field caused the breakdown of a planar interface into cellular undulations and the formation of an irregular shape. Specifically, for the Zn–2.0 wt.% Cu peritectic alloy, a wavy band-like structure appears under a high magnetic field. Moreover, the high magnetic field promoted the enrichment of the solute Cu element in the diffusion boundary layer. A theory about the magnetization and solute build-up in the diffusion boundary layer under a high magnetic field for a binary alloy has been proposed. This magnetization and solute build-up could be partly responsible for the breakdown of the planar interface and the formation of the band-like structure in a peritectic alloy. Moreover, the stresses in the solid near the interface under a high magnetic field were analyzed, measured and simulated numerically. It is suggested that they are responsible to the interface irregularity, and are also capable of inducing the interface instability.

## Mechanical alloying of yttria dispersed steel

### January 28, 2009

Bacause the first author happens to be a close friend on whose work I want to keep tabs on, and, because yttria can be dispersed in steel:

M P Phaniraj, D-I Kim, J-H Shim and Y W Cho

Austenitic oxide dispersion strengthened (ODS) alloys containing 0.5 and 5 wt.% yttria were prepared from elemental powders (Fe–20% Ni–14% Cr–2.5% Mo–2.5% Al–2% Mn) by mechanical alloying. The powders were analyzed using X-ray diffraction (XRD), X-ray photoelectron spectroscopy and transmission electron microscopy (TEM), paying particular attention to the behavior of yttria. XRD and high-resolution TEM analyses show that yttria does not form a solid solution with austenite; unlike in ferritic ODS alloys, where it dissolves. Milling induces the formation of the thermodynamically favorable yttrium aluminum perovskite (YAP). Alumina from the aluminum powder in the starting blend, formed in the initial stages of milling using oxygen available from the other elemental powders, combines with yttria to form YAP. The yttria content does not affect alloy formation but reduces the crystallite size and strain significantly in the 5% yttria composition. TEM analysis of hot-pressed compacts reveals nanocrystalline particles of yttria, yttrium aluminum garnet and YAP.

## Cottrell on strain hardening

### January 25, 2009

Alan Cottrell in the latest Phil Mag on some mysteries and surprises in strain hardening that are yet to be understood:

The independence of temperature shown by the strain hardening coefficient of face centred cubic metals appears to be at variance with several other features of this strain hardening that depend on temperature. However, on the forest theory of this hardening, thermal activation is expected to have opposite effects on two underlying aspects. First, it reduces the applied stress required to enable glide dislocations to cut through forest obstacles. Second, it increases the density of the secondary dislocations that form these obstacles so that the forest becomes harder to penetrate.

## In-situ nucleation and movement of dislocations

### January 24, 2009

Thanks to Eddie‘s sharing the link in Google Reader, I found this interesting paper in Nature Materials:

In situ observation of dislocation nucleation and escape in a submicrometre aluminium single crystal

S H Oh et al

‘Smaller is stronger’ does not hold true only for nanocrystalline materials but also for single crystals. It is argued that this effect is caused by geometrical constraints on the nucleation and motion of dislocations in submicrometre-sized crystals. Here, we report the first in situ transmission electron microscopy tensile tests of a submicrometre aluminium single crystal that are capable of providing direct insight into source-controlled dislocation plasticity in a submicrometre crystal. Single-ended sources emit dislocations that escape the crystal before being able to multiply. As dislocation nucleation and loss rates are counterbalanced at about 0.2 events per second, the dislocation density remains statistically constant throughout the deformation at strain rates of about 10-4 s-1. However, a sudden increase in strain rate to 10-3 s-1 causes a noticeable surge in dislocation density as the nucleation rate outweighs the loss rate. This observation indicates that the deformation of submicrometre crystals is strain-rate sensitive.

## Mechanical behaviour of alloys during solidification

### January 18, 2009

A mesoscale granular model for the mechanical behavior of alloys during solidification

S Vernede, J A Dantzig and M Rappaz

We present a two-dimensional granular model for the mechanical behavior of an ensemble of globular grains during solidification. The grain structure is produced by a Voronoi tessellation based on an array of predefined nuclei. We consider the fluid flow caused by grain movement and solidification shrinkage in the network of channels that is formed by the faces of the grains in the tessellation. We develop the governing equations for the flow rate and pressure drop across each channel when the grains are allowed to move, and we then assemble the equations into a global expression that conserves mass and force in the system. We show that the formulation is consistent with dissipative formulations of non-equilibrium thermodynamics. Several example problems are presented to illustrate the effect of tensile strains and the availability of liquid to feed the deforming microstructure. For solid fractions below gs=0.97, we find that the fluid is able to feed the deformation at low strain, even if external feeding is not permitted. For solid fractions above gs=0.97, clusters of grains with “dry” boundaries form and fluid flow becomes highly localized.

## Plastic deformation in single crystal copper

### January 16, 2009

A very interesting paper from the latest Phil Mag.

Mapping mesoscale heterogeneity in the plastic deformation of a copper single crystal

K R Magid et al

Part of a ‘multiscale characterization’ study of heterogeneous deformation
patterns in metals is reported. A copper single crystal was oriented for single slip
in the (111)[101] slip system and tested to \$10% strain in roughly uniaxial
compression. The macroscopic strain field was monitored during the test by
optical ‘image correlation’. The strain field was measured on orthogonal surfaces,
one of which (the x-face) was oriented perpendicular to [121] and contained the
[101] direction of the preferred slip system. The macroscopic strain developed in
an inhomogeneous pattern of broad, crossed shear bands in the x-face. One, the
primary band, lay parallel to (111). The second, the ‘conjugate’ band, was
oriented perpendicular to (111) with an overall (101) habit that contains no
common slip plane of the fcc crystal. The mesoscopic deformation pattern was
explored with selected area diffraction, using a focused synchrotron radiation
polychromatic beam with a resolution of 1–3 mm. Areas within the primary,
conjugate and mixed (primary þ conjugate) strain regions of the x-face were
identified and mapped for their orientation, excess defect density and shear stress.
The mesoscopic defect structure was concentrated in broad, somewhat irregular
primary bands that lay nominally parallel to (111) in an almost periodic
distribution with a period of about 30 mm. These primary bands were dominant
even in the region of conjugate strain. There were also broad conjugate defect
bands, almost precisely perpendicular to the primary bands, which tended to
bridge primary bands and terminate at them. The residual shear stresses were
large (ranging to well above 500 MPa) and strongly correlated with the primary
shear bands; interband stresses were small. The maximum resolved shear stresses
within the primary bands were oriented out of the plane of the bands, and, hence,
could not recover the dislocation structure in the bands. The maximum resolved
shear stresses in the interband regions lay predominantly in {111} planes. The
results are compared to the mesoscopic defect patterns found in Cu in etch pit
studies done some decades ago, which also revealed a mesoscopic dislocation
structure made up of orthogonal bands.

## Structure and mobility of dislocations in BCC iron using MD

### January 11, 2009

Structure and mobility of the $\frac{1}{2} \langle 11\bar{1} \rangle \{112\}$ edge dislocation in BCC iron studied by molecular dynamics

G Monnet and D Terentyev

In this paper, we carried out atomistic calculations to investigate in detail the core structure and motion mechanism of the $\frac{1}{2} \langle 11\bar{1} \rangle \{112\}$ edge dislocation in α-iron. First, molecular statics simulations are used to characterise the dislocation-core structure in the framework of the Peierls–Nabarro model. It is shown that the accommodation of the distortion due to the insertion of the extra half-planes is not equivalent in the planes above and below the dislocation slip plane and that the relative atomic-displacement profile in the dislocation-core region is asymmetrical. Then, molecular dynamics simulations are used to study the mechanism of the dislocation motion at different temperatures. At low temperature, the dislocation is found to move by nucleation and propagation of kink-pairs along its line. Independently of temperature, when loading is performed in the twinning direction, the critical stress is found to be lower than the one corresponding to the antitwinning loading direction.