Phase field study of precipitate growth: Effect of misfit strain and interface curvature

We have used phase field simulations to study the effect of misfit and interfacial curvature on diffusion-controlled growth of an isolated precipitate in a supersaturated matrix. Treating our simulations as computer experiments, we compare our simulation results with those based on the Zener–Frank and Laraia–Johnson–Voorhees theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the Zener–Frank theory is very good in one-dimensional systems. In two-dimensional systems with interfacial curvature (with and without misfit), we find good agreement between theory and simulations, but only at large supersaturations, where we find that the Gibbs–Thomson effect is less completely realized. At small supersaturations, the convergence of instantaneous growth coefficient in simulations towards its theoretical value could not be tracked to completion, because the diffusional field reached the system boundary. Also at small supersaturations, the elevation in precipitate composition matches well with the theoretically predicted Gibbs–Thomson effect in both misfitting and non-misfitting systems.     

Accelerated precipitate coarsening due to a concomitant secondary phase transformation

The effect of a concomitant secondary phase transformation on the coarsening of spherical precipitates inherited from a previous primary phase transformation is investigated. An extended period of accelerated coarsening and a non-monotonic evolution of the normalized size distribution are found. These results are illustrated using approximate asymptotic solutions to the coarsening equation and computer simulations of coarsening dynamics. Experimental results found in silicon nitride systems, which cannot be explained by the classical coarsening theories, are in good agreement with our model predictions.     

Using ECAP to achieve grain refinement, precipitate fragmentation and high strain rate superplasticity in a spray-cast aluminum alloy

An aluminum 7034 alloy, produced by spray casting and with an initial grain size of ˜2.1 μm, was processed by equal-channel angular pressing (ECAP) at 473 K to produce an ultrafine grain size of ˜0.3 μm. It is shown that the rod-like MgZn₂ precipitates present in the as-received alloy are broken into very small spherical particles during ECAP and these particles become distributed reasonably uniformly throughout the material. The presence of these fine MgZn₂ particles, combined with a distribution of fine Al₃Zr precipitates, is very effective in restricting grain growth so that submicrometer grains are retained at elevated temperatures up to at least ˜670 K. Tensile testing of the pressed material revealed high elongations to failure, including elongations of >1000% when testing at a temperature of 673 K at initial strain rates at and above 10⁻² s⁻¹. These results confirm the occurrence of high strain rate superplasticity in the spray-cast alloy.     

The hillock formation on the basal planes of graphite due to ion interaction

Highly oriented graphite materials were modified by the introduction of foreign species, i.e. doped by iron and implanted by energetic ions. On irradiated surfaces, hillocks were observed and assessed using STM. An increase in atomic weight of the implanted energetic ions led to an increase in area of the damaged surface of graphite and a low RRR value indicated a high density of hillocks in iron-doped graphite. The formation of hillocks is based on the displacement of carbon atoms in graphite basal planes: cascade collision due to implanted ions and protuberances created along the carbon layers by diffusion of species due to iron doping. The heat treatment of the irradiated graphite led to an increase in height of the pre-existing hillocks by diffusion of the trapped atoms towards the surface. The heat treatment of iron-doped graphite at 2800°C allowed the increase in hillock number due to the diffusion of trapped atoms along the graphite layers.     

The effect of elastic misfit strain on the morphological evolution of γ’-precipitates in a model Ni-base superalloy

The morphological evolution of coherent γ’-precipitates in a Ni-23.4Co-4.7Cr-4Al-4.3Ti (wt%) alloy has been observed under systematically varying heat-treatment conditions. By deeply etching the matrix and observing under a scanning electron microscope, the precipitate morphologies are determined accurately. By quenching after solution treatment and aging isothermally, high initial precipitate density is obtained, and the cuboidal precipitates cluster and align to form regularly spaced arrays. The dimensionality of the aligned structure increases with increasing precipitate volume fraction as the aging temperature decreases. By directly cooling to an aging temperature after the solution treatment intermediate precipitate density is obtained. During the isothermal aging, the cuboidal precipitates split into octets and clusters of several pieces which disintegrate subsequently into aligned cuboids. Upon further aging the coherency is broken. When directly cooled to aging temperatures very close to the solvus temperature, the dispersed precipitates grow dendritically along the 〈111〉 directions. Various thermodynamic and kinetic theories for the elastic strain effect stemming from the lattice misfit agree quantitatively with the observed clustering, alignment, and splitting, but presently there is no complete theory which accurately describes the observed morphologies.     

The superposition of flow stress contributions in a precipitate hardened Ni-based alloy studied by strain rate sensitivity measurements

The strain rate sensitivity of the flow stress of underaged, peakaged and overaged samples of the γ′-hardened Ni-based superalloy Inconel X-750 has been measured. The experimental data are presented in the form of Haasen plots, which help to analyze the flow stress superposition rules. It was found that a progressive increase of the slope in the Haasen plot, during Stage II of work hardening, is correlated with the increase in the γ′-precipitate size. The analysis of the results was carried out in the framework of the theory developed by Kocks, Argon and Ashby (Kocks UF, Argon AS, Ashby MF. Prog Mater Sci, 1975;19:1) for two contributions to the flow stress. It was found that the square superposition rule leads to a slight curvature but more important, it predicts an increase of the effective slope in the Haasen plots in agreement with the experimental results.     

Structural changes in low-carbon steel due to rolling friction strain

Changes in the strongly strained structure of low-carbon steel appearing in the process of operation of suspended-belt conveyors are studied. The effect of micropores in the steel on the kind of fracture and wear of the surface layers of the pipe is determined. Correlation is established for the structure, the yield point, the fracture toughness, and the level of wear of commercial iron. The possibility of realization of the process of dynamic recrystallization of ferrite under the action of high strain is considered. __________ Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 8, pp. 39–43, August, 2007.     

Elastic energy of metadislocations in complex metallic alloys

A parameterized expression for the Burgers vectors of metadislocations is derived. On this basis we calculate the elastic line energy of metadislocations and demonstrate that the experimentally observed occurrence of Fibonacci relations between the members of a metadislocation series is due to energy minimization. All complex metallic alloy phases in which metadislocations have been experimentally observed are considered.     

Bond stress development at a surface coating-substrate interface due to the action of a nucleus of thermo-elastic strain

The class of problems dealing with surface reinforced elastic media is encountered in many areas of materials engineering, notably in connection with surface layers that are used to provide protection to an otherwise softer substrate. These problems are of particular importance to the assessment of the mechanical behaviour of thin films and other forms of industrial coatings. This paper examines the problem related to the flexure of a plate-like surface layer that is bonded to an elastic halfspace region, and where the flexure of the coating is induced by a nucleus of thermo-elastic strain acting within the halfspace region.     

Changes in mechanical characteristics of a cast and deformed lead-containing nickel silver with a low stacking-fault energy due to annealing

Processes that occur during the annealing of a cast and deformed lead-containing nickel silver have been studied. The hardness of the alloy measured at room temperature is insusceptible to the melting of lead. The strengthening of the alloy upon annealing is governed by short-range-ordering effects.     

Structural transformations and strain effects in copper and copper-base alloys due to dynamic loading

The strain behavior and phase transformations in Cu-37 wt.% Zn brass, Cu-12.5 wt.% Al bronze, and copper (99.97%) are studied under two variants of pulse loading, i.e., converging shock waves and a flux of powder particles accelerated by explosion. The effects connected with uniform and localized strain caused by the action of shock waves are determined and the disperse structures formed in the materials under dynamic loading are analyzed. __________ Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 3, pp. 28–34, March, 2007.     

Effects of volume strain due to Li–Sn compound formation on electrode potential in lithium-ion batteries

Sn and Sn-based compounds have attracted great interest as candidates for anode materials in lithium-ion batteries. Despite the great deal of attention focused on the effects of the volume change of the Sn anode during the lithiation/delithiation process on the cyclic property of the batteries, its influence on the electrode potential is still not well understood. In this study, by constructing a simple Sn–Li battery system, we have investigated the effects of the volume change associated with the formation of Li–Sn compounds on the electrode potential from the viewpoint of the Gibbs free energy and associated elastic-strain energy. Our experimental results show that (i) α-Sn, which is a low-temperature phase and in thermodynamic non-equilibrium at around 298 K (our experimental temperature), is also formed together with usual β-Sn after several cycles of the lithiation and delithiation processes and (ii) when a Sn plate-shape electrode is lithiated, the experimental electrode potential underruns the value expected thermodynamically. These experimental results can be consistently explained by considering the contribution of the elastic-strain energy to the chemical free energy of formation.     

Structural analysis of a new precipitate phase in high-temperature TiNiPt shape memory alloys

Aging of the high-temperature shape memory alloy Ti₅₀Ni₃₀Pt₂₀ (at.%) results in precipitation of a previously unidentified phase, which plays a key role in achieving desirable shape memory properties. The precipitate phase has been analyzed with electron diffraction, high-resolution scanning transmission electron microscopy and three-dimensional atom probe tomography. The experimental observations show that the precipitates have unique crystallography due to their non-periodic character along one of the primary crystallographic directions. It will be shown that the structure can be explained in terms of crystal intergrowth of three variants of a monoclinic crystal. The monoclinic crystal structure is closely related to the high-temperature cubic B2 phase; the departure of the structure from the B2 phase can be attributed to ordering of Pt atoms on the Ni sublattice and relaxation of the atoms (shuffle displacements) from the B2 sites. The shuffle displacements and the overall structural refinement were deduced from ab initio calculations.     

Magnetic method for the measurement of precipitate particle sizes in a Cu-Co alloy

Extremely small ferromagnetic precipitate particles in a nonmagnetic matrix behave like a paramagnetic substance of very large moment. Magnetization curves of such substances can be used to determine precipitate particle sizes and size distributions. By this means the precipitation of cobalt in a 2 pct Co-Cu alloy has been followed, the effective particle radii growing from 12 to 70Å with increasing aging time. The cobalt particles are shown not to be hexagonal, but rather to be either spherical or plate-shaped.     

Modelling of energy attenuation due to powder flow-laser beam interaction during laser cladding process

Laser cladding is becoming an emergent process with high interest for industries dedicated to high added value parts production. Laser cladding introduces new manufacturing concepts such as direct manufacturing of parts, avoiding in this way the excessive waste of material in the form of chips, inherent to traditional machining processes. This process is based on the use of a source of high energy density, such as laser beams, to generate a melt pool on a substrate where a filler material is injected. Thus, when studying the process it is necessary to know the effective energy that reaches the base material. This energy does not correspond to the one provided by the laser beam, considering that the laser beam has to go through a cloud of injected powder before it reaches the substrate. In this region there is an interaction between the laser beam and the filler material in which a significant amount of energy is absorbed by the powder. As a result, attenuation values can reach up to high percentages of the initial energy value.This paper presents a model based on the shadow created by powder particles on the substrate, with capabilities of estimating the attenuation suffered by the beam and characterizing the density of energy that reaches the surface of the substrate. The model starts from the initial energy density of the laser and the powder concentrations obtained from a CFD model, which has been experimentally validated. In addition, three different approaches have been introduced for the model solution. Initially a constant powder particle size and a perfectly cylindrical laser beam are considered. Subsequently, an experimentally measured particle size distribution and the divergence of the beam are introduced in order to accurately adjust the model and the real process. The attenuation model has been experimentally adjusted and validated. The error average is below 10% of measured values.