Twinning dislocation multiplication at a coherent twin boundary

N Li et al

Using in situ nanoindentation in a high-resolution transmission electron microscope we have studied the interaction of glide dislocations with a Σ3 {1 1 1} coherent twin boundary (CTB) of growth type in Cu. These high-resolution observations indicate that, in addition to acting as barriers to slip transmission, CTB can react with a lattice dislocation to facilitate the multiplication of partial dislocations, resulting in translation of the CTB. On the basis of dislocation theory and molecular dynamics (MD) simulations we propose a dislocation multiplication mechanism by which successive dissociation reactions, starting with a single glide dislocation trapped at a CTB, can lead to a continuous source under certain applied stress states. No evidence of deformation twinning was noted in the nanotwinned lamellae in the indented foils. These findings provide insights into understanding the plastic deformation mechanisms, the migration of CTBs the high strength, and work hardening of highly twinned face-centered cubic metals.

[1] Formation of Stray Grains during Directional Solidification of a Nickel-Based Superalloy

Y Zhou

Superalloy CMSX-4 is directionally solidified and initiated by bi-crystal seeds. It has been found that diverging boundaries are the most favorable location for stray grain formation. The phenomenon cannot be attributed to nucleation of crystals. Reasonable mechanism is bending or detachment of side arms during extension of secondary arms and development of tertiary branches at the diverging boundaries. Solute interaction of the neighboring dendrites promotes likelihood of bending or detachment and then leads to an enhanced frequency of stray grains.
Highlights

► Stray grains are formed particularly around re-entrant features such as the platforms or shroud regions of the turbine blade airfoils and lead to rejection of single crystal superalloy components since the boundSuperalloy CMSX-4 is directionally solidified and initiated by bi-crystal seeds. It has been found that diverging boundaries are the most favorable location for stray grain formation. The phenomenon cannot be attributed to nucleation of crystals. Reasonable mechanism is bending or detachment of side arms during extension of secondary arms and development of tertiary branches at the diverging boundaries. Solute interaction of the neighboring dendrites promotes likelihood of bending or detachment and then leads to an enhanced frequency of stray grains.

[2] Sapphire surface pits as sources of threading dislocations in hetero-epitaxial GaN layers

F Y Meng et al

Sapphire substrates showed nanosized surface pits after the growth of GaN layers using a two-step process by hydride vapor phase epitaxy. Threading dislocations with Burgers vectors of c and c+a were found to originate from the pits. Mechanism of their generation is developed from cross-sectional transmission electron microscopy observations.

Twinning dislocations

April 5, 2011

Twinning dislocations on {-1 0 1 1} and {-1 0 1 3} source planes in hexagonal close-packed crystals

J Wang et al

The objective of this investigation was to identify the elementary twinning dislocations (TDs) for {-1 01 1} and {-1 0 1 3} twins by fully characterizing their structure for an Mg crystal. For both {-1 0 1 1} and {-1 0 1 3} twins, we conclude that the 2-layer TD, not the 4-layer TD, is the active TD in twinning. The 4-layer TD can be considered as the combination of two 2-layer TDs with opposite-sign screw components. Molecular statics simulations of the Peierls energy show why the TDs of both twinning modes (for c/a ratios > 1.5) are only activated when the c-axis experiences a compressive strain. The simulations predict that 2-layer TDs are more mobile than 4-layer TDs and that the mobility of these twinning dislocations depends strongly on dislocation character. Correspondingly, the influence of TDs involved in deformation twinning processes on deformation twins is discussed.

[1] Interaction of a dislocation with a crack tip: From stimulated emission to avalanche generation

G Michot

Stress relaxation at a crack tip relies on the material’s ability to generate dislocations. Despite the extensive literature devoted to crack–dislocation interaction, no one has yet explained how dislocations appear and multiply in order to build a fully plastic zone. Here we will show how a simple event, such as the intersection of a unique incoming dislocation with a crack front, induces the generation of new dislocations: this effect is called “stimulated emission”. Submitted to the applied crack stress field, these dislocations can repeat the stimulation process step by step all along the crack front, through a cross-slip mechanism. Such a rapidly increasing rate of dislocations nucleation leads to a sudden growth of the plastic zone (avalanche).

[2] Modeling the recrystallized grain size in single phase materials

S Wang et al

A model is proposed for post-recrystallization grain size. The model is based on the coarsening of subgrain networks as present after deformation and recovery. It is shown that the orientation spread in the subgrain network is the key variable in predicting the density of abnormal subgrains and, hence, the recrystallized grain size. The model explains the strong dependence of the post-recrystallization grain size on prior strain and the lack of a dependence on the annealing temperature.

On the reversibility of dislocation slip during cyclic deformation of Al alloys containing shear-resistant particles

W Z Han et al

The cyclic deformation behavior of a model Al–4Cu–0.05Sn (wt.%) alloy containing a homogeneous and well-defined distribution of shear-resistant θ′ (Al2Cu) precipitate plates was used to study the effect of precipitate state on the cyclic slip irreversibility. The precipitate spacing was controlled so that it was less than the self-The cyclic deformation behavior of a model Al–4Cu–0.05Sn (wt.%) alloy containing a homogeneous and well-defined distribution of shear-resistant θ′ (Al2Cu) precipitate plates was used to study the effect of precipitate state on the cyclic slip irreversibility. The precipitate spacing was controlled so that it was less than the self-trapping distance of dislocations. The cyclic deformation tests were conducted under constant plastic stain amplitude mode and the evolution of the cyclic stress and cyclic hardening rate with cumulative plastic strain were monitored. The deformed and undeformed microstructures were characterized using transmission electron microscopy. The cyclic deformation behavior and the corresponding dislocation structures depend on both precipitate state and imposed plastic strain amplitude. An expression for the cyclic slip irreversibility that explicitly depends on microstructural and deformation parameters was derived based on proposed mechanisms of interaction between the mobile dislocations and the precipitates. The cyclic deformation curve was calculated using the expression for the slip irreversibility and shown to describe most features of the cyclic deformation curves well, as a function of precipitate state and imposed plastic strain amplitude, as well as describing the results of plastic strain amplitude jump tests.trapping distance of dislocations. The cyclic deformation tests were conducted under constant plastic stain amplitude mode and the evolution of the cyclic stress and cyclic hardening rate with cumulative plastic strain were monitored. The deformed and undeformed microstructures were characterized using transmission electron microscopy. The cyclic deformation behavior and the corresponding dislocation structures depend on both precipitate state and imposed plastic strain amplitude. An expression for the cyclic slip irreversibility that explicitly depends on microstructural and deformation parameters was derived based on proposed mechanisms of interaction between the mobile dislocations and the precipitates. The cyclic deformation curve was calculated using the expression for the slip irreversibility and shown to describe most features of the cyclic deformation curves well, as a function of precipitate state and imposed plastic strain amplitude, as well as describing the results of plastic strain amplitude jump tests.

PS: Recently, I heard one of the authors, Chris Hutchinson give a talk in the Department on this work, and liked it quite a lot.

Modeling displacive–diffusional coupled dislocation shearing of γ′ precipitates in Ni-base superalloys

N Zhou et al

In Ni-base superalloys, superlattice extrinsic stacking fault (SESF) shearing of γ′ precipitates involves coupled dislocation glide and atomic diffusion. A phase-field model is developed to study this process, in which the free energy of the system is formulated as a function of both displacement and long-range order parameter. The free energy surface is fitted to various fault energy data obtained from experiments and ab initio calculations. Three-dimensional simulations at experimentally relevant length scales are carried out to investigate systematically the influence of microstructural features on the critical resolved shear stress. The simulations reveal that the critical resolved shear stress for SESF shearing is determined not only by the SESF energy itself, but also by the complex stacking fault energy and by the shape (interface curvature) and spacing of γ′ precipitates. The effect of reordering kinetics (i.e. temperature effect) is also investigated. It is found that viscous deformation can only occur within certain domain of intermediate temperatures.
Highlights

► The displacive–diffusional coupled dislocation shearing of γ′ precipitates in Ni-Base superalloys are modeled with phase field method. ► The influences of a variety of material parameters and temperature on the critical stress of initiating SESF (superlattice extrinsic stacking fault) shearing and microtwinning are analyzed. ► It was found that temperature, γ′ particle’s size, shape and spatial distribution as well as the complex stacking fault energy have significant impact on the deformation mode for Ni-base disk alloys.

[1] Formation mechanism of coarse columnar γ grains in as-cast hyperperitectic carbon steels

S Tsuchiya et al

Abstract

The formation mechanism of as-cast coarse columnar γ grain (CCG) structure in hyperperitectic carbon steels is investigated by means of a rapid unidirectional solidification method. This method achieves cooling conditions similar to those in the vicinity of a practically continuously cast slab surface. The microstructural observation of the quenched samples indicates that the CCG structure develops from the mold side along the direction of the temperature gradient. In the solidifying samples, fine columnar γ grains (FCG) always exist ahead of the CCG region. Instead of continuous growth into large grains, FCG always shrink and vanish as a result of the growth of CCG initially formed near the mold side. Therefore, the grain size at a fixed point in the ingot discontinuously changes from the FCG to the CCG. The validity of this process is supported by numerical analyses. This finding is in marked contrast to the assumption made in conventional grain growth analysis on the CCG structure.
Highlights

► We examine the formation process of as-cast coarse columnar γ grains (CCG) in steels. ► Fine columnar γ grains (FCG) exist ahead of the CCG region during the solidification. ► The FCG do not continuously grow into the CCG and they always shrink. ► We find that the CCG develop by the mechanism of the discontinuous grain growth.

[2] Dislocation junction formation and strength in magnesium

L Capolungo et al

Adaptative meshing finite-element-based discrete dislocation dynamics simulations are employed to predict dislocation junction formation in magnesium as well as their resulting strength. Apart from coplanar and collinear interactions, all possible interactions between basal, prismatic and pyramidal slip are considered. Among others it is found that while non-coplanar prismatic junctions are more likely than basal–prismatic junctions, the latter are more stable. However, pyramidal–prismatic junctions appear more stable than pyramidal–basal junctions. Finally, non-coplanar pyramidal junctions are more likely than any other junction formation, and these junctions also appear to be amongst the strongest.

Crystal plasticity finite-element analysis versus experimental results of pyramidal indentation into (0 0 1) fcc single crystal

B Eidel

Pyramidal microindentation into the (0 0 1) surface of an face-centered cubic (fcc) single crystal made of a Ni-base superalloy is analyzed in experiment and crystal plasticity finite-element simulations. The resultant material pile-up at the surface reflects the material’s symmetry and turns out to be insensitive to different loading scenarios as induced by (i) different azimuthal orientations of the pyramidal indenter, (ii) different indenter shapes (sphere or pyramid) and (iii) the elastic anisotropy. Experiments and simulations are in agreement and suggest that pile-up deformation patterns merely depend on the geometry of discrete slip systems but are invariant to different anisotropic stress distributions as induced by (i)–(iii). The local adaption of pile-up to the pyramidal indenter leads to convex or concave indent shapes corresponding to the indenter orientation. We contrast the present findings for curved indent shapes of fcc single crystals to similar, well-known observations for quasi-isotropic polycrystals. Although phenomenologically similar in kind, the driving mechanisms are different: for the single crystal it is the discrete and anisotropic nature of plastic glide in certain slip systems; for isotropic polycrystals it is the rate of strain-hardening caused by the cumulative response of dislocations.

Phase transformation in free-standing SMA nanowires

F R Phillips et al

The primary focus of this work is on determining if the phase transformation of shape memory alloy (SMA) nanowires exhibits a critical size below which the phase transformation is inhibited. The SMA nanowires are fabricated through the use of the mechanical pressure injection method. The mechanical pressure injection method is a template-assisted nanowire fabrication method in which an anodized aluminum oxide (AAO) template is impregnated with liquid metal. The fabrication of SMA nanowires with different diameters is accomplished through the fabrication of AAO templates of varying diameters. The phase transformation behavior of the fabricated SMA nanowires is characterized using transmission electron microscopy. By analysis of the fabricated SMA nanowires, it is found that the phase transformation of SMA nanowires is not affected for nanowires ranging in diameter from 650 to 10 nm.

The role of strain accommodation during the variant selection of primary twins in magnesium

J J Jonas et al

Samples of magnesium alloys AM30 and AZ31 were deformed in tension at room temperature and a strain rate of 0.1 s−1 to strains of 0.08 and 0.15. Of the numerous contraction twins that formed, the orientations of 977 were determined by electron backscatter diffraction techniques. The orientations of their host grains were also measured, so that the Schmid factors (SFs) applicable to each of the six contraction twins that could potentially form in each grain could also be calculated. About half of the observed twins were of the “high SF” (0.3–0.5) type, while nearly half had “low” SFs (0.15–0.30). Furthermore, 5% of the observed twins had associated Schmid factors of only 0.03–0.15, i.e. these were of the “very low SF” type. Of particular interest is the observation that many potential “high Schmid factor” twins did not form. The presence of the low and very low SF twins and the absence of many potential high SF twins are explained in terms of the accommodation strains that are or would be required to permit their formation. These were calculated by rotating the twinning shear displacement gradient tensor into the crystallographic reference frame of the neighboring grain. It is shown that the very high plastic anisotropy of Mg grains permits the “easy” accommodations to take place but conversely prevents accommodation of the potential twinning shears when these are “difficult” (when these involve high critical resolved shear stresses). The twins that appear require little or no “difficult” accommodation.

[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] 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.