Influence of directional solidification variables on the cellular and primary dendrite arm spacings of PWA1484

A series of directional solidification experiments have been performed to elucidate the effects of thermal gradient G and growth velocity V on the solidification behavior and microstructural development of the multicomponent Ni-base superalloy PWA 1484. A range of aligned as-cast microstructures were exhibited by the alloy: (i) aligned dendrites with well developed secondary and tertiary arms; (ii) flanged cellular dendrites aligned with the growth direction and without secondary arms; and (iii) cells with no evidence of flanges or secondary arms. The role of the imposed process parameters on the primary arm spacings that developed in the Bridgman-grown samples were examined in terms of current theoretical models. The presence of secondary arms increases the spacings between dendrites and leads to a greater sensitivity of ₁ on G ^–1/2 V ^–1/4. The exponent of V was analyzed and found to depend upon the imposed gradient G. High withdrawal velocities and low thermal gradients were found to cause radial non-uniformity of the primary dendrite arm spacing. Such behavior was associated with off-axis heat flows.     

Coarsening during solidification of aluminium-copper alloys

Coarsening of directionally solidified -phase dendrites and of particulate -phase/liquid mixtures was investigated in Al-4, 10 and 20 wt% Cu alloys, as a function of temperature, composition and presence or absence of forced convection. Isothermal dendritic coarsening in the absence of convection operated in two stages. In stage I the dendritic structure broke down through remelting into fragments which spheroidized quickly; in stage II the spherical particles coarsened slowly. The coarsening rate of the dendritic or particulate solid increased with temperature and copper dilution. Alloy inoculation with titanium slowed coarsening, yielding finer dendritic microstructures. The effect of turbulent flow on coarsening was manifested only for longer holding times. At higher impeller angular velocities the dendritic structure breaks down into fragments which spheroidize rapidly. At lower shear rates (below 650 rev min^–1) solid particles in solid-liquid mixtures coalesce into clusters, whereas at higher rates the clusters break up again into individual particles. A coarsening model was introduced which showed that coarsening is faster in the presence of forced convection, because of the resulting decrease in solute diffusion-boundary layer thickness.     

Effect of medium-density direct current on dendrites of directionally solidified Pb–50Sn alloy

This paper investigated the effect of coupling of direct current (DC) and pulling rate on dendrites and cooling behaviours of directionally solidified Pb–50Sn alloy. Experimental results indicated that the secondary dendritic arm spacing (SDAS) decreased and temperature gradient increased as increasing current densities. Moreover, temperature rise and SDAS under positive DC were higher than those under negative DC. It was speculated that Joule heating and electromigration were obviously induced by the present DC. The effect of DC on the microstructure and solidification parameters was weakened as the pulling rate increases. The coarsening rate reduced from tf^1/3 toward a value of tf^0.29 when DC of ±200?A?cm^–2 were applied. The refinement mechanism of SDAS was discussed.     

Mechanisms of phase transformations during laser treatment of grey cast iron

Pearlitic grey cast iron was surface melted using a 500 W CW CO₂ laser at travel speeds 0.5–100 cm s^–1. Detailed structural analysis of the laser modified layer was performed by optical and scanning electron microscopy (SEM), and microhardness depth profiles were measured. Temperature distribution was calculated from a three dimensional moving point source model, taking only the heat transfer into account. From the structural details observed in the austenitized zone some conclusions on the mechanism and kinetics of the pearlite austenite transformation at high heating rates were drawn. The melted zone consisted of primary austenite and ledeburite. At lower scanning speeds the structure was dendritic, at higher scanning speeds transition to dendritic-cellular structure was observed. From the secondary dendrite arm spacings the cooling rate during solidification was estimated as a function of the depth. Some discrepancies were found between our measurements and the literature data as well as predictions by the simple model neglecting convection in the melt.     

Effects of dendritic arm coarsening on macroscopic modelling of solidification of binary alloys

Abstract

A pure macroscopic two-dimensional numerical model has been developed, capable of capturing the effects of dendritic arm coarsening on the transport phenomena occurring during a binary alloy solidification process. The general continuum conservation equations are aptly modified to take into account shrinkage induced fluid flow. Simultaneously, the effective permeability of the mushy zone is numerically modelled according to the microscopic coarsening kinetics. Moreover, a new nodal latent heat updating algorithm is proposed that takes into account dendritic arm coarsening considerations. The numerical results are first tested against experimental results reported in the literature, corresponding to the solidification of an Al-Cu alloy in a bottom cooled cavity. It is concluded that dendritic arm coarsening leads to an increased effective permeability of the mushy region as well as an enhanced eutectic fraction of the solidified ingot. Consequently, an enhanced macrosegregation is predicted, compared with that dictated by shrinkage induced fluid flow alone. Physical insights are also developed regarding the effects of various parameters on the overall macrosegregation.     

Coarsening of hafnium carbide particles in tungsten

The coarsening behaviour of finely dispersed HfC particles in a W-HfC alloy was investigated by monitoring the growth rate of the particles. An activation energy of 480 kJ mol^–1 was obtained for the process. Diffusion experiments of hafnium in tungsten were conducted at temperatures between 1773 and 2573 K using a secondary ion mass spectroscopy technique to determine the diffusion contribution to the coarsening process. The diffusion process at high temperature is controlled by lattice diffusion with an activation energy of 335 kJ mol^–1 whereas that at low temperature is governed by grain-boundary diffusion with an activation energy of 170 kJ mol^–1. It appears that the coarsening process is controlled by two energy barriers: one dictated by the diffusivity of hafnium and the other by the solubility limit as a function of temperature. The strain energy required to dissociate the carbide particles into individual species was also considered. The effects of the coarsening of HfC particles in a dispersion-strengthened W-0.4 mol% HfC alloy on recrystallization and creep deformation were illustrated using a concerted experimental modelling analysis. Results show that the strengthening effect of the HfC particles is significantly reduced at temperatures above 1800 K, due to particle coarsening.     

The role of secondary carbide precipitation on the fracture toughness of a reduced carbon white iron

The fracture toughness of a high chromium, reduced carbon white cast iron was measured using the K_Ic fracture toughness test. The toughness was found to increase with increasing heat treatment temperature for the temperature range of 1273–1423 K. Increases in the fracture toughness were due to crack deflection into the dendritic phase. Cracking in the dendrites was promoted by the presence of secondary carbides which formed during the high temperature heat treatment employed. The characteristic distance for brittle fracture as calculated by the Ritchie–Knott–Rice model correlated well with the centre to centre mean free path of the secondary carbides on the fracture plane.     

Flow of Molten Arsenic Selenide in a Cylindrical Channel

The flow rate of molten arsenic selenide in cylindrical channels is measured at channel diameters of 3.0 to 5.5 mm, channel lengths of 40 to 120 mm, temperatures of 285–320 and 375–470°C, and inert gas gage pressures of up to 1.5 × 10⁵ Pa. It is found that there is a motionless melt layer on the inner surface of the channel. For a channel 4.6 mm in diameter, its thickness is 0.7 mm at 290°C and 0.1 mm at 420°C. In the temperature range 280–315°C, there is a threshold gas pressure below which the melt does not flow. Partial crystallization may occur in the flowing melt. Its effect on the melt flow rate grows as the holding time at 270–320°C increases. The data obtained can be used to choose conditions for producing As₂Se₃ optical fibers by the crucible method.     

Quantitative phase analysis of metastable structure in a laser melted Fe-C alloy

Pure Fe-3.5wt% C alloy was surface melted using a cw C0₂ laser and the microstructure of the laser tracks was investigated by scanning and transmission electron microscopy. Structure of the melted zones consisted of dendrites of partially transformed primary austenite and of very fine lamellar ledeburite. The secondary dendrite arm spacings were indicative of a cooling rate of 10⁵ Ks^–1, in good accord with calculations based on the model of a moving Gaussian beam. Using methods of quantitative metallography the volume fraction of dendrites within the melted zone and the volume fractions of the carbide and ferrite phases in the decomposed ledeburite were estimated. These data were combined with the results of a quantitative X-ray diffraction phase analysis (see Part II) and compared with the equilibrium phase diagram. It was found that the volume fraction of dendrites was near the equilibrium value while the volume content of cementite in the rapidly solidified structures was considerably higher than predicted from the equilibrium phase diagram.     

Numerical study on the prediction of microstructure parameters by multi-scale modeling of directional solidification of binary aluminum–silicon alloys

In order to create a model to predict microstructural quantities like grain size, primary and secondary dendrite arm spacing a multi-phase and multi-scale model based on the work of Wang and Beckermann [C. Wang, C. Beckermann, Metallurgical and Materials Transactions A 27A (1996) 2754–2764] was combined with a front tracking technique [A. Wu, A. Ludwig, in: C.-A. Gandin, M. Bellet (Eds.), Modeling of Casting, Welding, and Advanced Solidification Processes – XI, TMS, 2006, pp. 291–298], micro-models for nucleation [M. Rappaz, P. Thevoz, Acta Metallurgica 35 (7) (1987) 1487–1497], primary [J. Hunt, S.-Z. Lu, Metallurgical and Materials Transactions A 27A (1996) 611–623], secondary [W. Kurz, D. Fisher, Fundamentals of Solidification, Trans Tech Publication, 1986, ISBN 0-87849-522-3] dendrite arm spacing and a control volume based finite element solver for axial-symmetric problems. As most of the micro-models are just valid for pure diffusive conditions, the model just takes into account macroscopic diffusion in the melt and thus neglects the influence of melt flow. The new software was used for a comprehensive comparison to several test cases. The validation includes investigation of the correlation of calculated and measured grain size distributions for inoculated alloys. Experimental and numerical data for the primary and secondary dendrite arm spacing for steady state and transient directional solidification were compared in a second step. A good correlation is found for all test cases.     

Instabilities with reduced frictional drag in the rotating channel flow of dilute polymer solutions

Summary A numerical investigation is conducted on secondary flows and roll-cell instabilities in the laminar channel flow of dilute polymer solutions subjected to a steady spanwise rotation. Finite difference calculations of the full nonlinear equations of motion for a Maxwell fluid and a Rivlin-Ericksen fluid of the second grade are presented which indicate that there is a double-vortex secondary flow at weak and rapid rotation rates with an instability in the form of longitudinal roll cells at intermediate rotation rates (regimes analogous to those for a Newtonian fluid). However, for a given physical pressure gradient and rotation rate, the introduction of a minute amount of a polymeric additive to a Newtonian fluid so that the Weissenberg number is of the order of 10^–5 has a stabilizing effect on rotating channel flow and gives rise to secondary flows with a substantially reduced frictional drag. Comparisions with previously conducted experimental and analytical studies are made along with a brief discussion of potential applications to the field of polymeric drag reduction.With 14 Figures     

Local heat transfer on the entrance segment of a tube with a sharp inlet edge. 1. Nature and behavior of heat transfer intensity extrema

Experimental results on local heat transfer on the entrance segment of a round smooth tube with a sharp leading edge when Re _d =(13–110)·10³, X/d=0.1–13, which support the previously proposed model for separated flow, are examined. It is shown that under separated flow conditions the usual sequence of flow transitions in a boundary layer for mixed nonseparated flows and Re _d >10⁴ is still retained. Formulas are obtained for calculating local heat transfer coefficients on a segment where a laminar boundary layer occurs, including cross sections where these coefficients acquire extreme values.Kiev Polytechnic Institute, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 2, pp. 131–138, August, 1993.     

Effects of growth rate on carbides and microporosity in DS200 + Hf superalloy

The effects of growth rate on the carbide morphology and microporosity were investigated using DS200 + Hf superalloy, between 16.7×10^–6 and 266.7×10^–6 m s^–1. The fact that the shape factor remained almost unchanged with the growth rate indicates that the shape of the carbide particles does not directly depend on the cooling rate in this alloy. The stability of carbide particles was considered in terms of the interfacial energy between the carbide and matrix interface and the fluctuation of carbide composition. It was observed that the carbide/--matrix interfacial area per unit volume as a function of growth rate remained almost unchanged (especially above 66.7×10^–6 m s^–1), indicating that the rate of coarsening of carbides during solidification is not affected by the carbide/matrix specific interface energy. One of the factors which determines the rate controlling step for the coarsening of carbide particles is suggested to be Ti in the interdendritic and grain-boundary regions, and Hf in the vicinity of the incipient melting region.     

Microtomographic characterization of columnar Al–Cu dendrites for fluid flow and flow stress determination

During the twin roll casting of Al alloys, the interdendritic liquid may flow as the two solidification fronts are compressed together between the rolls. This can lead to defects such as centerline segregation. To understand the flow properties of the interdendritic liquid, samples of Al–12 wt.% Cu were solidified directionally in a Bridgman furnace and quenched to capture the growing columnar dendritic structures. The quenched samples were scanned using a laboratory X-ray microtomography (XMT) unit to obtain the 3D structure with a voxel resolution of 7.2 μm. Image analysis was used to separate the Al dendrite from the interdendritic Al–Al₂Cu eutectic. Flow between the dendrites was simulated by solving the Stokes equation to calculate the permeability tensor as a function of the fraction solid. The results were compared to prior experimental measurements and calculations using synchrotron tomography observations of equiaxed structures. Elasto–plastic finite element (FE) simulations were performed on the dendritic structures to determine flow stress behavior as a function of fraction solid. It was found that the standard approximations for the reduction in flow stress in the semi-solid have a variation in excess of 100% from that calculated using the true structure. Therefore, it is critical to simulate the actual dendrite for effective flow stress determination.     

Melt flow properties of polypropylene/EPDM/glass bead ternary composites

The flow properties of polypropylene(PP)/ethylene-propylene-diene monomer copolymer(EPDM)/glass bead (GB) ternary composites were measured in a wide scope of shear rates by using a Rosand capillary rheometer. The apparent shear rates varied from 10 to 10⁵ s^–1, and the test temperature was from 210 to 240°C. The results showed that the flow behavior of the composite melts may be considered to approximate that of a power law fluid although the slope of the melt flow curves somewhat varied around shear rate of 700 s^{– 1}. The dependence of the melt shear viscosity on the test temperature was roughtly consistent with the Arrhenius expression. The melt shear viscosity increased dramatically with increasing the volume fraction (_g) of GB under lower shear rate level, white it increased gently with an addition of _g under higher shear rate level. Furthermore, there were certain effects of the filler surface treatment on the melt shear viscosity and its sentivity to the filler content at higher concentration of the beads at lower shear rates.     

Application of a wedge-type Fabry-Perot etalon to the study of low-density air flows

A Fabry-Perot etalon with a wedge-shaped arrangement of the mirrors is applied to the study of low-density air flows. Interferograms of a gas flow past a cylinder at a pressure of 5 · 10^–2 torr are presented.     

Evaluation of small hydrogen sulfide concentrations in calibrating commercial gas analyzers for hydrogen sulfide

Conclusions Small concentrations (10^–5–10^–2 by volume) of hydrogen sulfide in gas mixtures can be analyzed by means of the photocolorimetric method based on the formation of molybdenum blue by the interaction of hydrogen sulfide with ammonium molybdate in an acidic medium.The optimum conditions for reducing molybdate by hydrogen chloride are provided by a content of 50 mg/ml of ammonium molybdate in the absorbing solution, a sulfuric solution with an acidity of 0.6 N, and a coloration ripening time of 15–20 min.     

The growth of oriented ceramic eutectics

Controlled microstructures of the two eutectics in the alumina-titania system have been grown using a special electron beam heating technique. In the aluminium titanate-titania system, the eutectic interlamallar spacing varies with the freezing rate R as =AR ^–n where n=0.5 and the value of the constant A is 8.5×10^–6 cm^3/2sec^–1/2. Primary plate-like dendrites of aluminium titanate in a matrix of discontinuous aluminium titanate-titania eutectic are formed on solidifying a composition TiO₂-20 wt % Al₂O₃. These dendrites appear to deflect cracks in this ceramic. In the alumina-aluminium titanate system, primary rod-like dendrites of alumina were grown in a ribbon-like eutectic of alumina and aluminium titanate on solidifying a composition Al₂O₃–38.5% TiO₂.     

Serrated flow and related microstructures in an Al-8.4 at.% Li alloy

Serrated flow in as-quenched and aged Al-8.4 at.% Li alloys has been investigated between 253 K and 353 K at strain rates ranging from 8.9 × 10^–5 s^–1 to 1.2 × 10^–2 s^–1. Size and volume fraction of precipitates were determined by small angle scattering and transmission electron microscopy. Growth and coarsening of the precipitates induces different trends of critical strain of serrated flow changing with temperature and strain rate. The stress drop of serrations increases to some extent with increasing ageing time, increasing deformation temperature and decreasing strain rate. The volume fraction of precipitates decreases as deformation proceeds. The characteristics of serrated flow are related to the changes in microstructures during deformation.