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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

The partition of elastic strain energy in solid foams and lattice structures

Rapid advances in additive manufacturing techniques promise that, in the near future, the fabrication of functional cellular structures will be achieved with the desired cellular microstructures tailored to specific applications. It is therefore essential to develop a detailed understanding of the relationship between macroscopic mechanical response and cellular microstructure. The present study reports on the results of a series of computational experiments that explore the effect of topology and microstructural irregularity (or non-periodicity) on deformation modes of cellular structures under both uniaxial and biaxial stress states. A simple quantitative technique based on the partition of elastic strain energy into bending and stretch components is used to identify the distribution of deformation modes at a microstructural level. The relationship between nodal connectivity, morphological regularity and deformation modes is then explored through their influence on biaxial yield surfaces as obtained from finite element analyses.     

Structure analysis of a precipitate phase in an Ni-rich high-temperature NiTiHf shape memory alloy

Thermal aging of the high-temperature shape memory alloy 50.3Ni–29.7Ti–20Hf (at.%) introduces a novel precipitate phase that plays an important role in improving shape memory properties. The precipitate phase was investigated by conventional electron diffraction, high-resolution scanning transmission electron microscopy (STEM) and three-dimensional atom probe tomography. An unrelaxed orthorhombic atomic structural model is proposed based on these observations. This model was subsequently relaxed by ab initio calculations. As a result of the relaxation, atom shuffle displacements occur, which in turn yields improved agreement with the STEM images. The relaxed structure, which is termed the “H phase”, has also been verified to be thermodynamically stable at 0 K.     

Contribution of precipitate on migrated grain boundaries to ductility-dip cracking in Alloy 625 weld joints

We investigated the crack properties in Alloy 625 weld metals and their characteristics using experimentally designed filler wires fabricated by varying the niobium and manganese contents in the flux with the shield metal arc welding (SMAW) process. The fast diffusivity of niobium on the migrated grain boundary (MGB) under strong restraint tensile stress, which was induced by the hardened matrix in weld metal containing high niobium and manganese, accelerated the growth of niobium carbide (NbC) in multipass deposits. Coalescence of microvoids along with incoherent NbC and further propagation induced ductility-dip cracking (DDC) on MGB.     

Quantitative evaluations for strain amplitude dependent organization of dislocation structures due to cyclic plasticity in austenitic stainless steel 316L

This study is a quantitative evaluation of dislocation structures due to cyclic plasticity with small strain amplitudes in austenitic stainless steel 316L. First, dislocation structures in specimens after 100 cycles of cyclic loading with strain amplitudes of 0.25%, 0.75% and 1.0% were observed by transmission electron microscopy (TEM). The observations showed that cyclic loading with larger strain amplitudes results in the organization of more uniform dislocation cell structures. Secondly, an image analysis method for evaluation of the TEM images is proposed. The proposed method quantitatively evaluates the strain amplitude dependency of the organization of dislocation structures. Finally, the accumulation of shear slips on slip systems during cyclic loading is estimated by using crystal plasticity finite element analysis. The distribution of the accumulated shear slips correlates with the organization of dislocation structures.     

Incremental recrystallization/grain growth driven by elastic strain energy release in a thermomechanically fatigued lead-free solder joint

A single shear lap solder joint specimen with lead-free eutectic Sn–Ag solder on copper substrates was exposed to 1500 thermomechanical fatigue (TMF) cycles between −15° (3.5 h) and 150 °C (20 min) to generate intrinsic thermal strains. The 0.15-mm-thick solder joint had a cross-sectional area of 1 mm². Orientation imaging microscopy was used to examine changes in the tin microstructure as a function of the number of TMF cycles. The tin phase consisted of embedded minority orientations within an initial dominant orientation, which varied by about 25° from one end of the joint to the other, by means of lattice curvature and low angle boundaries. Between about 150 and 750 cycles, an incremental recrystallization/grain growth process occurred where a minority solidification twin orientation grew and consumed the dominant initial orientation. An elastic FEM analysis incorporating anisotropic thermal expansion and elastic constants indicated that the final orientation had an internal stress state that was 20–100% smaller than the initial orientation, when subjected to a temperature change. The release of elastic strain energy provided the thermodynamic driving force for recrystallization/grain growth.     

Yield point elongation due to twinning in a magnesium alloy

Fine-grained magnesium alloy AZ31 displays a yield elongation when deformed such that yielding occurs by twinning. That is, following yielding there is a plateau in the stress-strain curve. The present paper presents a microstructural analysis of the twins in deformed samples. A major aim is to explain the yield elongation and in particular why it decreases and eventually disappears with increasing grain size. It is shown that during the Lüders yield elongation twins initiate twinning events in neighbouring grains and in this manner twinning spreads its way progressively over the sample. This occurs at a twinning frequency of approximately one twin per grain. A criterion for the presence of a Lüders strain is developed based on twin transfer across boundaries. It is shown that higher Lüders strains and stresses are expected for finer grain sizes. The key to understanding the effect is that it arises from the condition for Lüders band propagation whereby the twins on the Lüders band front must stimulate, on average, one twin each within the fresh material ahead of the front, at a constant value of applied stress. An important part of the derivation followed here is that at the higher stresses seen in fine-grained samples, the twin aspect ratio is larger and consequently the strain at the grain level corresponding to a single twinning event is higher in finer-grained samples.