[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.

Advertisements

Equilibrium morphology

March 30, 2011

After Ni, it is WC now.

The equilibrium morphology of WC particles – A combined ab initio and experimental study

Y Zhong et al

We report an ab initio density functional theory study, complemented by parallel experimental work, of the equilibrium shape of WC particles. The equilibrium shape is simulated under the condition of little or no liquid-phase sintering. The effects of the carbon-rich and carbon-deficient conditions and the adsorption of Co and Ni atoms on the surface of WC particles are investigated. The equilibrium shape of WC particles is found to be a truncated triangular prism under both carbon-rich and carbon-deficient conditions. The adsorption of Co and Ni on the WC surface can promote the formation of either truncated triangular prisms or near-hexagonal prisms, depending on their specific combination with the carbon chemical potential. Under all the conditions investigated, the equilibrium shapes of WC crystals can be described as “bulky” rather than “plate-like”. The findings in this study are consistent with the experimental observations.

Martensitic aging

March 29, 2011

Stabilizing internal stress as the thermodynamic factor of martensite aging effects

A Kosogor et al

The symmetry-conforming Landau theory has been developed for the description of interplay between the symmetry of the deformable crystal lattice and the configuration of crystallographic defects in martensitic alloys. For this purpose, the multi-component non-scalar order parameter describing the slow reconfiguration of defects after the deformation of crystal lattice has been introduced within the framework of the Landau theory of martensitic transformations (MTs). Due to the transformational equivalence of the configurational order parameter and strain/stress tensor components, the conception of stabilizing internal stress (SIS), which is linearly related to this parameter, has been formulated. The complete agreement between the developed theory and the symmetry-conforming short-range-order principle formulated by Ren and Otsuka has been established. The effect of stabilizing the product (martensitic) phase after aging has been described by considering the stress–temperature phase diagram, which was constructed by taking into account the time dependence of SIS. The applicability of the theory to the aging effects in the Au–Cd shape memory alloy has been demonstrated. The time dependencies of the experimentally observed slow changes in the MT temperatures, lattice parameters and yield stress values have been derived from the SIS conception.
Highlights

► A martensite aging is accompanied by reconfiguration of the crystal defects system. ► The reconfiguration causes an internal stressing of crystal lattice. ► The internal stressing elevates the martensitic transformation temperature. ► A theory that accounts for the internal stress adequately describes aging effects. ► A quantitative description of aging effects observed in Au–Cd alloys is presented.

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] Systematic study of the microstructure, entropy change and adiabatic temperature change in optimized La–Fe–Si alloys

J Liu et al

A systematic study of the microstructure and magnetocaloric effect in LaFe11.8Si1.2 and LaFe11.6Si1.4 alloys over a large range of annealing temperatures and times has been carried out. With the aim of obtaining the pure 1:13 phase and maximum magnetic entropy change the annealing temperature was optimized at 1373 K for LaFe11.8Si1.2 and 1323 K for LaFe11.6Si1.4. We found a unique morphology of eutectoid-type lamellae, which is suggested to be an intermediate phase upon formation of the 1:13 phase. Adiabatic temperature change ΔTad measurements were employed to directly assess the magnetocaloric effect. By application of a magnetic field of 1.9 T large ΔTad values of 7.3 K and 7.0 K in the vicinity of the transition temperatures were found for LaFe11.8Si1.2 and LaFe11.6Si1.4, respectively, after optimized annealing. By considering the partial irreversibility of magnetostructural transition the influence of thermal and magnetic hysteresis on magnetic entropy change and ΔTad is also discussed.
Highlights

► Optimized annealing temperature and time in La-Fe-Si. ► Lamellar structure as an intermediate phase ► Large adiabatic temperature change of about 7 K for La-Fe-Si.

[2] Modeling of excess vacancy annihilation at different types of sinks

F D Fischer et al

The equilibrium site fraction of vacancies increases with temperature and, thus, annealing and rapid quenching may lead to states with a significant vacancy supersaturation. Excess vacancies can then gradually annihilate at available sinks represented by jogs at dislocations, by grain boundaries or free surfaces. Significant supersaturation by vacancies may also lead to the nucleation and growth of Frank loops acting as additional sinks. Three models corresponding to three different annihilation mechanisms are developed in this paper. They refer to annihilation of excess vacancies at jogs at dislocation with a constant density, at homogeneously distributed Frank loops with a constant density and at grain boundaries. The simulations based on the models are performed for individual annihilation mechanisms under isothermal and non-isothermal conditions as well as for simultaneous annihilation of vacancies at Frank loops and dislocation jogs and grain boundaries using different cooling conditions.
Highlights

► The kinetics of generation and annihilation of vacancies is modeled. ► Dislocation jogs, grain boundaries and Frank loops act as sources and sinks. ► The kinetics is determined by the densities of considered objects. ► The vacancy concentration kinetics reflects the thermo-mechanical treatment.

[3] The equilibrium crystal shape of nickel

H Meltzman et al

The crystal shape of Ni particles, dewetted in the solid state on sapphire substrates, was examined as a function of the partial pressure of oxygen (P(O2)) and iron content using scanning and transmission electron microscopy. The chemical composition of the surface was characterized by atom-probe tomography. Unlike other face-centered cubic (fcc) equilibrium crystal shapes, the Ni crystals containing little or no impurities exhibited a faceted shape, indicating large surface anisotropy. In http://dx.doi.org/10.1016/j.actamat.2011.02.021addition to the {1 1 1}, {1 0 0} and {1 1 0} facets, which are usually present in the equilibrium crystal shape of fcc metals, high-index facets were identified such as {1 3 5} and {1 3 8} at low P(O2), and {0 1 2} and {0 1 3} at higher P(O2). The presence of iron altered the crystal shape into a truncated sphere with only facets parallel to denser planes. The issue of particle equilibration is discussed specifically for the case of solid-state dewetting.
Highlights

► The ECS of pure Ni is completely facetted with both dense and high-index planes. ► The partial pressure of oxygen has a significant effect on the surface anisotropy. ► The addition of Fe decreased the anisotropy and de-stabilized high-index planes. ► During solid dewetting nucleation barriers prevent equilibration of the top facet.

[4] Triple junction effects in solids

B Zhao et al

The grain boundary–free surface triple line tension and grain boundary triple line tension were investigated in copper using a recently introduced novel approach. The effect of triple line tension on grain growth, Zener drag and Gibbs–Thompson relation was studied. The results showed that the triple line tension has a considerable effect on grain growth, particle–boundary interactions and void shape, especially for nanocrystalline materials.
Highlights

► The effect of triple junctions on a variety of metallurgical phenomena was investigated. ► For copper the groove root triple line energy was determined as 1.5 E-8 J/m. ► For copper the grain boundary triple line energy was determined as 6 E-9 J/m ► In nanocrystalline materials the triple line energy contributes to the driving force for grain growth. The triple line energy prevents a grain boundary to wet nanoscopic particles and voids.

Some interesting papers

March 19, 2011

[1] Study of spinodal decomposition and formation of nc-Al2O3/ZrO2 nanocomposites by combined ab initio density functional theory and thermodynamic modeling

S H Sheng et al

Using ab initio density functional theory, the equilibrium properties, such as the total energy, the molar volume, the bulk modulus and its first derivative, as well as the formation enthalpy of monoclinic ZrO2 and hexagonal α-Al2O3 phases, were calculated and compared with the published theoretical and experimental data. Based on the good agreement of these data, we calculated the lattice instabilities of hypothetical binary hexagonal Zr2O3 and monoclinic AlO2, and the interaction parameters of ternary Zr1−xAlxOy solid solutions. The binodal and spinodal diagrams were then constructed to predict the possibility of the formation of oxide-based nanocomposites which may display hardness enhancement above that of the solid solutions. It is shown that exponential dependence of the interaction parameter on temperature yields the most reliable results. The system should undergo spinodal phase segregation within the composition range that is relevant for the formation of hard or superhard nanocomposites with high thermal and oxidation stability, which are important for their applications.

[2] Direct characterization of phase transformations and morphologies in moving reaction zones in Al/Ni nanolaminates using dynamic transmission electron microscopy

J S Kim et al

Phase transformations and transient morphologies are examined as exothermic formation reactions self-propagate across Al/Ni nanolaminate films. The rapid evolution of these phases and sub-micrometer morphological features requires nanoscale temporal and spatial resolution that is not available with traditional in situ electron microscopy. This work uses dynamic transmission electron microscopy to identify intermetallic products and phase morphologies, as exothermic formation reactions self-propagate in nanolaminate films grown with 3:2, 2:3 and 1:1 Al/Ni atomic ratios. Single-shot diffraction patterns with 15 ns temporal resolution reveal that the NiAl intermetallic forms within not, vert, similar15 ns of the reaction front’s arrival in all three types of films and is the only intermetallic phase to form, as the reactions self-propagate and quench very rapidly. Time-resolved imaging reveals a transient cellular morphology in the Al-rich and Ni-rich foils, but not in the equiatomic films. The cellular features in the Al-rich and Ni-rich films are attributed to a cooling trajectory through a two-phase field of liquid + NiAl.

[3] Crystal plasticity modeling of texture evolution and heterogeneity in equal channel angular pressing of aluminum single crystal

C Lu et al

A crystal plasticity finite element method (CPFEM) model has been developed to investigate the texture evolution and heterogeneity during equal channel angular pressing (ECAP) of an aluminum single crystal. The developed model has been validated by comparison with experimental observations. The simulation results show that the lattices rotate predominantly around the Z axis (transverse direction) during ECAP. After deformation the billet is subdivided into three matrix bands along the thickness by the Z-axis rotation. The Z-axis rotation angles within three matrix bands are about 60°, 0° and 90°, respectively. It has been found that the die geometry plays a very important role on the texture evolution and heterogeneity in ECAP. In the large strain gradient region, multi-slip can be activated and the material rotation induced by slips is negligible. The lattices must rotate to accommodate the whole material rotation required by deformation. When the strain gradient is small, the single dominant slip is the main slip mechanism. The material remains roughly at the initial orientation after deformation. There is a rigid-rotation region in the lower part of the die corner where the lattices rotate by the die angle Φ.

[4] In situ synchrotron analysis of lattice rotations in individual grains during stress-induced martensitic transformations in a polycrystalline CuAlBe shape memory alloy

S Berveiller et al

Two synchrotron diffraction techniques, three-dimensional X-ray diffraction and Laue microdiffraction, are applied to studying the deformation behaviour of individual grains embedded in a Cu74Al23Be3 superelastic shape memory alloy. The average lattice rotation and the intragranular heterogeneity of orientations are measured during in situ tensile tests at room temperature for four grains of mean size not, vert, similar1 mm. During mechanical loading, all four grains rotate and the mean rotation angle increases with austenite deformation. As the martensitic transformation occurs, the rotation becomes more pronounced, and the grain orientation splits into several sub-domains: the austenite orientation varies on both sides of the martensite variant. The mean disorientation is not, vert, similar1°. Upon unloading, the sub-domains collapse and reverse rotation is observed.
Highlights

► 3DXRD, Laue microdiffraction measurements of grain rotation in a shape memory alloy. ► During stress-induced martensitic transformation, the austenite grains rotate. ► This rotation reverses with the reverse transformation. ► The austenite grains splits into various orientations with martensite formation.

[5] Twin relationships of 5M modulated martensite in Ni–Mn–Ga alloy

Z Li et al

For Ni–Mn–Ga ferromagnetic shape memory alloys, the characteristic features of modulated martensite (including the number/shape of constituent variants, the inter-variant orientation relationship and the geometrical distribution of variant interfaces) determine the attainability of the shape memory effect. In the present work, a comprehensive microstructural and crystallographic investigation has been conducted on a bulk polycrystalline Ni50Mn28Ga22 alloy. As a first attempt, the orientation measurements by electron backscatter diffraction (EBSD) – using the precise information on the commensurate 5M modulated monoclinic superstructure (instead of the conventionally simplified non-modulated tetragonal structure) – were successfully performed to identify the crystallographic orientations on an individual basis. Consequently, the morphology of modulated martensite, the orientation relationships between adjacent variants and the characters of twin interfaces were unambiguously determined. With the thus-obtained full-featured image on the configuration of martensitic variants, the possibility of microstructural modification by proper mechanical “training” was further discussed. This new effort makes it feasible to explore the crystallographic/microstructural correlations in modulated martensite with high statistical reliability, which in turn provides useful guidance for optimizing the microstructure and shape memory performance.
Highlights

► We determine orientation relationships of 5M modulated martensite in NiMnGa alloy. ► Accurate EBSD mapping is performed using monoclinic superstructure. ► Four distinct variants mutually twin-related to each other are revealed. ► Three twinning types and full twinning elements are identified. ► Twin interfaces do coincide with respective twinning planes.

[6] Chemistry and structure of core/double-shell nanoscale precipitates in Al–6.5Li–0.07Sc–0.02Yb (at.%)

C Monachon et al

An Al–6.3Li–0.07Sc–0.02Yb (at.%) alloy is subjected to a double-aging treatment to create nanoscale precipitates, which are studied by atom-probe tomography and transmission electron microscopy. After homogenization and quenching, Yb atoms form clusters exhibiting L12-like order. A first aging step at 325 °C leads to a doubling of microhardness as a result of the formation of coherent precipitates with an Al3Yb-rich core and an Al3Sc-rich shell. The core and shell both exhibit the L12 structure and both contain a large concentration of Li, which substitutes for up to 50% of the Sc or Yb atoms at their sublattice positions. These core/single-shell precipitates provide excellent resistance to overaging at 325 °C. Subsequent aging at 170 °C increases the microhardness by an additional 30%, through precipitation of a metastable δ′-Al3Li second shell on the core/single-shell precipitates, thereby forming a chemically and structurally complex core/double-shell structure. The metastable δ′-Al3Li phase is observed to form exclusively on pre-existing core/shell precipitates.
Highlights

► An Al–Li alloy with dilute Sc and Yb-additions was double-aged for strengthening. ► Due to kinetic effects, core/shell precipitates form during the first aging. ► Lithium, though fast-diffusing, delays overaging of the alloy. ► A second aging treatment resulted in core/double-shell precipitates. ► Distinct hardening events correspond to the core, first shell, and second shell.

[7] An in situ transmission electron microscopy study of interface growth during martensitic transformation in an Fe–Ni–Mn alloy

J Wu et al

Frame-by-frame analysis of the austenite/lath martensite interface during in situ heating using transmission electron microscopy was used to provide direct information on the mechanisms of the martensite interface motion in an Fe–20Ni–5.5Mn (wt.%) alloy. When the temperature was increased to not, vert, similar550 °C, the tip of the lath martensite receded slightly, and then decomposed into ledges on only one side of the lath. With further time at 550 °C, the ledges migrated in a start–stop fashion; the highest velocity observed was 0.79 μm s−1. When the temperature was increased to not, vert, similar580 °C, the interface on the mobile side of the lath preferentially receded within certain transformation twins formed during the earlier quenching treatment. Based on these experimental observations, it appears that the austenite may form an array of parallel twins during the martensitic transformation, which coalesce to form a lath shape. This lath then thickens in one direction only to establish the final morphology by a ledge mechanism displaying start–stop growth behavior.
Highlights

► Movement of martensite interfaces was investigated using in situ heating in the TEM. ► Martensite interfaces moved by a ledge mechanism rather than advancing uniformly. ► Martensite ledges vary from atomic dimensions to several tens of nanometers in height. ► Martensite lath dissolution occurred preferentially on one side.