Simulation of dendritic microstructures
February 24, 2011
[1] Phase-field simulation of micropores constrained by the dendritic network during solidification
H Meidani and A Jacot
A phase-field model has been developed to describe the morphology of pores constrained by a dendritic solid network, and are forced to adopt complex non-spherical shapes. The distribution of the solid, liquid and gas phases was calculated with a multiphase-field approach which accounts for the pressure difference between the liquid and the gas. The model considers the partitioning of the dissolved gas at interfaces, gas diffusion and capillary forces at the solid/liquid, liquid/gas and gas/solid interfaces. The model was used to study the influence of the dendrite arm spacing (DAS) and the solid fraction on the state of a pore. The calculations show that a pore constrained to grow in a narrow liquid channel exhibits a substantially higher mean curvature, a larger pressure and a smaller volume than an unconstrained pore. Comparisons with simple geometrical models indicate that analytical approaches show a good trend but tend to underestimate the pore curvature, in particular at high solid fractions, where pores have to penetrate the thin liquid channels. For pores spanning over distances larger than the average DAS, the simulations showed that the radius of curvature can vary between two limits, which are given by the size of the narrowest section that the pore needs to pass in order to expand and by the largest sphere that can be fitted in the interdendritic liquid. The pore curvature is therefore a complex non-monotonic function of the DAS, the solid fraction, the hydrogen content and statistical variations of the liquid channel width.
[2] Simulation of a dendritic microstructure with the lattice Boltzmann and cellular automaton methods
H Yin et al
A new modeling approach combining the lattice Boltzmann method (LB) and the cellular automaton technique (CA) was developed to simulate solidification at the microscale. The LB method was used for the coupled calculation of temperature, solute content and velocity field, while the CA method was used to compute the liquid/solid phase change. To validate the accuracy of the LB–CA model and its efficiency for the simulation of dendrite growth under convection, comparisons of the tip characteristics and dendrite morphologies under various simulation conditions were made with those obtained by analytical means and by a finite element model coupled with the cellular automaton technique (FE–CA model). The results show that the LB–CA model is computationally much more efficient than the FE–CA model for simulations of dendritic microstructures under convection. The tip splitting phenomenon was captured for high cooling rates and with comparatively coarse grids due to mesh-induced anisotropy and thermal instabilities. The simulated dendrite morphologies obtained with various anisotropy and Gibbs–Thomson coefficients were discussed. The results show that the dendrite growth direction does not always follow the crystallographic direction and high branching phenomena can occur with small anisotropy and/or Gibbs–Thomson coefficients.
Microstructural evolution, twinning, nanoporous superalloys and deformation mechanisms
February 20, 2011
A Deschamps et al
The kinetics of the microstructural evolution during ageing at 200 °C of an Al–2.5%Cu–1.5%Mg (wt.%) alloy is evaluated using nuclear magnetic resonance and in situ small-angle X-ray scattering. This alloy is known to exhibit “rapid hardening” upon artificial ageing, where 50–70% of the total age hardening increment is reached within minutes at elevated temperatures. It is shown that formation of small solute-rich entities which correspond to Cu–Mg clusters or GPB zones occurs within seconds at 200 °C. These entities have radius not, vert, similar0.5 nm, volume fraction not, vert, similar2% and Cu concentration not, vert, similar30 at.%. Within the stage of constant yield strength (rapid hardening plateau) at this temperature, they are shown to be the dominant constituent of the precipitate microstructure and to be extremely stable in terms of size and volume fraction. The S phase is observed to nucleate within the hardening plateau, but remains a minor constituent until the end of this stage. Based on the quantitative measurement of their size and volume fraction, the obstacle strength of these solute-rich clusters is calculated to be about one-tenth of the Orowan strength. The energy required to shear these clusters (not, vert, similar0.5 eV) is shown to be compatible with existing atomistic calculations of similar objects.
Markus Chmielus et al
Twinning is the primary deformation mechanism in magnetic shape memory alloys (MSMAs). Obstacles such as inclusions, precipitates and defects hinder or even prevent twin boundary motion in the bulk of Ni–Mn–Ga MSMA single crystals. Here, we study the effect of surface damage on the mechanical properties and twin structure of Ni–Mn–Ga single crystals. Any methods that produce defects may be considered for modifying the near-surface microstructure. In this study deformations were produced by grinding and mechanical polishing using abrasive particles. The amount of damage was characterized with X-ray diffraction: damage causes peak broadening. Deformation and damage localized near the surface increases the twinning stress. Surface damage stabilizes a densely twinned microstructure. The twins are thin but extend over the entire sample and allow a large strain to be accommodated at moderate stress. This effect is critical for preventing damage accumulation in high-cycle magnetomechanical actuation and for achieving high dynamic performance.
[3] Production of nanoporous superalloy membranes by load-free coarsening of γ′-precipitates
B Hinze et al
Nickel-based superalloys are predominantly used as structural materials in high-temperature applications due to their exceptional high-temperature strength based on precipitation hardening by the coherent γ′-phase. In modern superalloys, the γ′-phase fraction can amount to 75%, at which γ′-precipitates align as cubes parallel to the left angle bracket0 0 1right-pointing angle bracket directions of the crystal lattice. At high temperatures and under a mechanical load, e.g. during service in gas turbines, the γ′-cubes coalesce to γ′-rafts, generating an interpenetrating microstructure of γ and γ′. By extracting one phase of this interpenetrated network, nanoporous superalloy membranes containing channel-like interconnected pores are produced. So far, this can only be achieved by applying simultaneously thermal and mechanical loads during tensile creep deformation. Here, a new production process is presented. Due to internal stresses, load-free aging of single-crystalline superalloys, e.g. CMSX-4, also generates an interpenetrating microstructure of γ and γ′. This can be utilized to manufacture nanoporous superalloy membranes in the absence of an external mechanical load. The advantage of this process is its simplicity and the potential to fabricate larger membranes than possible by the costly tensile creep deformation process currently used.
[4] Deformation mechanisms of nanograined metallic polycrystals
Saada and Kruml
This paper is an attempt to discuss the relevance of the physical concepts used to describe the plastic flow behaviour of a wide class of nanograined metallic polycrystals, by critically analyzing recent experimental observations on nanograined Ni and Cu. The paper focuses on the description of the elastic–plastic transition, and of the strain rate sensitivity. Using the generally accepted assumption that plastic flow results from dislocation nucleation at grain boundaries, it is shown that two deformation regimes must be distinguished: a nucleation-controlled mechanism at low strain rates, and a combined nucleation and propagation mechanism at high strain rates. At low deformation rates, the average nucleation rate is determined either from knowledge of the stress–strain curve, or from analysis of creep or relaxation kinetics. The strain rate sensitivity is shown to be related to the effect of stress on the nucleation rate.
Phase field modelling: shape memory ferromagnets
February 14, 2011
Phase-field simulation of magnetoelastic couplings in ferromagnetic shape memory alloys
L J Li et al
Ferromagnetic shape memory alloys (FSMAs) possess coupled ferroelastic and ferromagnetic orderings simultaneously, making it possible to manipulate ferroelastic twins of FSMAs via a magnetic field or magnetic domains via mechanical loading. In this paper, we develop a phase-field model to simulate the formation and evolution of magnetoelastic domains in FSMAs under combined mechanical and magnetic loadings, taking into account both variant rearrangement and magnetization rotation. It is found that the large magnetic field induced strain in FSMAs results from a variant rearrangement process, yet such variant rearrangement can be blocked by a relatively large compressive stress, substantially reducing the magnetic field induced strain. Furthermore, either pseudoelastic or quasiplastic behavior is exhibited in FSMAs subjected to varying compressive stress, depending on the strength of the constant magnetic field applied. These results agree well with experiments, and can be used to guide the design and optimization of FSMAs.
Ni-Mn-Ga and faceted bicrystals
February 8, 2011
Z B Li et al
For Ni–Mn–Ga ferromagnetic shape memory alloys, a large magnetic-field-induced strain could be reached through the reorientation of martensitic variants in the martensite state. Owing to the collective and displacive nature of the austenite to martensite transformation, a certain orientation relationship (OR) between the parent and the product phase is required to minimize the transformation strain and the strain energy generated, which brings about self-accommodating groups of martensitic variants with specific orientation correlations. In this work, the microstructural and crystallographic characteristics of martensitic variants in a polycrystalline Ni50Mn30Ga20 alloy were investigated by electron backscatter diffraction analysis. With accurate orientation measurement on inherited martensitic variants, the local orientations of parent austenite grains were predicted using four classical OR for the martensitic transformation. Furthermore, a specific OR, namely the Pitsch relation with (1 0 1)A//(1 View the MathML source View the MathML source)7M and [1 0 View the MathML source]A//[View the MathML source View the MathML source 1]7M, was unambiguously determined by considering the magnitude of discontinuity between the lattices of the product and parent phases and the structural modulation of the incommensurate 7M modulated martensite. The present procedure to determine the OR, without recourse to the presence of retained austenite, is in general applicable to a variety of materials with modulated superstructure for insight into their martensitic transformation processes.
[2] Size and shape evolution of faceted bicrystal nanoparticles of gold on sapphire
O Malyi et al
We produced an array of Au nanoparticles on the basal plane of sapphire via solid-state dewetting of a thin film, and followed the size and shape evolution of individual particles during a 950 °C anneal in air. The particles exhibited {1 0 0} and {1 1 1} facets and shapes that tend to be far from those predicted based upon equilibrium considerations. Most of the single-crystal particles exhibited remarkable size and shape stability up to the longest annealing time, 65 h. The bicrystal particles rapidly transformed into single crystals after the shortest annealing time, 1 h. This transformation was accompanied by an apparent rotation of one of the grains and its alignment along its immobile counterpart. We interpreted both phenomena in terms of very slow mass transport along the singular {1 1 1} and {1 0 0} facets. In the case of bicrystal particles, the fast migration and escape of the boundary from the particle changed the crystallography of the facets in the grain swept by the boundary from a crystallographically singular orientation to a non-special orientation. Such surfaces exhibit high diffusivity and, hence, rapid shape evolution via curvature-driven surface diffusion. A quantitative model of this rotation was proposed and showed to confirm our qualitative description. Based on these findings, we conclude that grain-boundary migration, rather than surface diffusivity, controls the kinetics of mid- and late-term agglomeration of thin polycrystalline films of Au.
Fe-Ga atomic mechanisms of magnetostriction and stress induced martensitic transformations
February 6, 2011
Boise et al
The Fe–Ga body-centered cubic (bcc) alloys within the 15–20 at.% Ga composition range have abnormally high magnetostriction. There is growing evidence that this effect is associated with the magnetic field-induced flip of tetragonal axes of nanoparticles of the ordered phase formed in this range. We studied structural transformations within this composition range at 550 °C by using computer modeling of the atomic-scale ordering and clustering in the atomic density field approximation. It is shown that the initial stage of equilibration of the compositionally homogeneous bcc solid solution with 19 at.% Ga results in bcc → B2 congruent ordering followed by a precipitation of Ga-rich B2 particles, which eventually transform to particles of the DO3 phase. At the composition 21 at.% Ga, the congruently ordered B2 phase undergoes further B2 → DO3 congruent ordering, which is followed by decomposition into an equilibrium mixture of the bcc and DO3 phases. An important result is that the phase transformations at 0.15 < c < 0.19 produce nanoparticles of transient B2 phase. We assume that the nanoprecipitates of the transient B2 phase undergo a diffusionless cubic → tetragonal transformation, forming the L10 phase during cooling to the room temperature, and that this involves a magnetic field-induced flipping of tetragonality of these nanoprecipitates which may be responsible for the giant magnetostriction.
[2] Effect of stress triaxiality and Lode angle on the kinetics of strain-induced austenite-to-martensite transformation
Beese and Mohr
The effect of the stress state on the transformation kinetics of stainless steel 301LN sheets at room temperature is investigated using newly developed experimental techniques for simple shear and large strain in-plane compression. In addition, uniaxial and equi-biaxial tension experiments are performed. Two-dimensional and stereo digital image correlation techniques are used to measure the surface strain fields. In situ magnetic permeability measurements are performed to monitor the evolution of martensite content throughout each experiment. The experimental results indicate that the martensitic transformation kinetics cannot be described solely by a monotonically increasing function of stress triaxiality: for instance, less martensite is developed under equi-biaxial tension than under uniaxial tension for the same increment in equivalent plastic strain. A stress-state-dependent transformation kinetics law is proposed that incorporates the effect of the Lode angle parameter in addition to the stress triaxiality. In the proposed model, the rate of martensite formation increases monotonically with the stress triaxiality and the Lode angle parameter. The comparison with the experimental data demonstrates that the proposed transformation kinetics law provides an accurate description of the evolution of the martensite content in stainless steel 301LN over a wide range of stress states.
Nanotwinned copper, martensitic thin films, and growth mechanism of nanowire oxides
February 3, 2011
[1] Fracture toughness and fatigue crack growth characteristics of nanotwinned copper
A Singh et al
Recent studies have shown that nanotwinned copper (NT Cu) exhibits a combination of high strength and moderate ductility. However, most engineering and structural applications would also require materials to have superior fracture toughness and prolonged subcritical fatigue crack growth life. The current study investigates the effect of twin density on the crack initiation toughness and stable fatigue crack propagation characteristics of NT Cu. Specifically, we examine the effects of tailored density of nanotwins, incorporated into a fixed grain size of ultrafine-grained (UFG) copper with an average grain size of 450 nm, on the onset and progression of subcritical fracture under quasi-static and cyclic loading at room temperature. We show here that processing-induced, initially coherent nanoscale twins in UFG copper lead to a noticeable improvement in damage tolerance under conditions of plane stress. This work strongly suggests that an increase in twin density, at a fixed grain size, is beneficial not only for desirable combinations of strength and ductility but also for enhancing damage tolerance characteristics such as fracture toughness, threshold stress intensity factor range for fatigue fracture and subcritical fatigue crack growth life. Possible mechanistic origins of these trends are discussed, along with issues and challenges in the study of damage tolerance in NT Cu.
[2] Structure of martensite in deformed Ti–Ni–Cu thin films
Meng et al
Microstructural evolution in a high-Cu-content Ti50.2Ni30Cu19.8 shape-memory thin film deformed in the B19 martensite state was studied by transmission electron microscopy, and the deformation mechanisms were clarified. The thin film was prepared by magnetron sputtering deposition. In the undeformed film, the B19 martensite has mainly {0 1 1}B19 twins with a small number of {1 1 1}B19 twins. The tensile deformation involves a reorientation of the {0 1 1}B19 twin domains, de-twinning of the {0 1 1}B19 and {1 1 1}B19 twins, and a stress-induced B19–B19′ transformation with the production of (0 0 1)B19′ compound twins. The film shows a large recoverable strain of 5.5%, which is far beyond the stress plateau.
Yuan et al
The spontaneous formation of oxide nanowires (and whiskers) from the oxidation of metals is a well-established phenomenon that has, however, long resisted interpretation. Here we report new fundamental insights into this phenomenon by studying CuO nanowire formation during the thermal oxidation of copper. It is shown that the volume change associated with the solid-state transformation at the CuO/Cu2O interface produces compressive stresses, which stimulate CuO nanowire growth to accompany the interface reaction. A kinetic model based on the stress-driven grain-boundary diffusion followed by rapid surface diffusion of cations on the sidewall of nanowires is developed to account for CuO nanowire growth. The mechanism proposed explains our observations on CuO nanowires and other past observations.
