Models for the isothermal coarsening of secondary dendrite arms in multicomponent alloys

Models for the isothermal coarsening of secondary dendrite arms for binary alloys are simply expanded to correlate the secondary dendrite arm spacing to local solidification time, melting temperature of the liquid, and the properties of the solute elements in multicomponent alloys. An equation is derived. Calculations using the equation show reasonable qualitative agreement with experiment.     

Effect of dendrite coarsening on the solidification of interdendritic liquid in iron alloys

The solidification of the interdendritic liquid in austenitic 110G13L steel and white cast iron is studied. In the absence of dendrite coarsening, the solidification mechanism of the interdendritic liquid in the manganese steel is shown to change and solidification occurs in the form of polycrystalline aggregates around dendrites from different centers. The relation between the standard solidification of the interdendritic liquid and the dendrite coarsening in iron alloys is grounded.     

On the drag of model dendrite

An experimental study of low Reynolds number drag on laboratory models of dendrite fragments has been conducted. The terminal velocities of the dendrites undergoing free fall along their axis of symmetry were measured in a large Stokes flow facility. Corrections for wall interference give nearly linear dragvs Reynolds number curves. Corrections for both wall interference and inertia effects show that the dendrite Stokes settling velocities are always less than that of a sphere of equal mass and volume. In the Stokes limit, the settling speed ratio is found to correlate well with the primary dendrite arm aspect ratio and a second dimensionless shape parameter which serves as a measure of the fractal-like nature of the dendrite models. These results can be used to estimate equiaxed grain velocities and distance of travel in metal castings. The drag measurements may be used in numerical codes to calculate the movement of grains in a convecting melt in an effort to determine macrosegregation patterns caused by the sink/float mechanism.     

The dendrite arm spacings of aluminum-copper alloys solidified under steady-state conditions

Aluminum-copper alloys of different composition have been solidified under steady-state conditions with known growth velocities and temperature gradients. Specimens were quenched during solidification to reveal the dendrite growth morphology and to allow the solute content at dendrite tips to be analyzed. Primary and secondary arm spacings have been measured as a function of the distanced behind the growing dendrite tips, the tip velocityR the temperature gradient in the liquid G_l and the solute content. The primary arm spacing λ₁ is described for each alloy by the empirical relation: λ₁ = kG_L ^-aR^-b wherek is a constant, and both a and b are close to 1/2; λ₁ is also found to increase with solute content. The secondary arm spacing λ₂ for each alloy increases with timeθ spent in the liquid/solid region, being directly proportional to θⁿ where n is close to 1/3; increasing solute content however causes a reduction in λ₂. It is suggested that the observed “coarsening” of the secondary arms is primarily a coalescence phenomenon. Formerly at Sheffield University     

On the influence of coarsening on microsegregation

An analytical treatment of the influence of coarsening by ripening on microsegregation is presented. Comparison of results from the model with data on Al-4.5 wt pct Cu and Sn-Bi alloys indicates that an overestimation of the reduction in microsegregation results if it is assumed that ripening proceeds throughout the solidification range. This is attributed to the changing nature of coarsening processes, in which coalescence processes predominate over ripening at higher volume fractions solid.     

Refinement of dendrite arm spacings in aluminum ingots through heat flow control

A model for heat flow during solidification of alloys is presented which treats the heat of fusion released during solidification separately for three distinct regions of a casting: portions released isothermally at the liquidus temperature, between the liquidus and solidus in a specified manner and the remainder released at the solidus. The model is solved numerically by a finite difference technique for unidirectional and two-dimensional heat flow in end-chilled thin plates. Effects of heat transfer coefficient at the chill, superheat, heat input, liquid convection and amount of sidewise heat loss are considered. Results are presented in terms of position of liquidus and solidus isotherms as a function of time, width of the mushy zone and local solidification time and secondary dendrite arm spacingvs distance from the chill. Results from experimental castings made under controlled heat flow conditions are compared with computer calculations. The local solidification time and resultant dendrite arm spacing are shown to decrease at a given location as a) the chill heat transfer coefficient increases, b) superheat increases, c) the gradient of temperature at the solidification front increases, and d) the multidimensionality of the heat flow path increases. Formerly Graduate Students in the Department of Materials Science and Engineering, M.I.T., Cambridge, MA, Department of Metallurgy and Mining Engineering.     

On the coarsening of gas-filled pores in solids

An analytical study is presented of the asymptotic coarsening kinetics of both monatomic and diatomic-gas-filled pores in solids, the rate-controlling process being assumed to be the volume diffusion of gas atoms within the host solid. It is shown that the asymptotic size-distribution functions can be expressed in terms of appropriate similarity transformations, and exact expressions are derived for both the frequency and cumulative distributions for each of the two cases considered. The fact that the order in size between pores is maintained as coarsening proceeds is used, together with the cumulative distribution functions, to derive expressions which describe the temporal evolution of individual pores. The behavior of gross properties of the pore distributions, such as pore concentration, mean radius, and volume fraction is also evaluated.     

Prediction of dendrite arm spacings in unsteady-and steady-state heat flow of unidirectionally solidified binary alloys

Various theoretical dendrite and cell spacing formulas have been tested against experimental data obtained in unsteady- and steady-state heat flow conditions. An iterative assessment strategy satisfactorily overcomes the circumstances that certain constitutive parameters are inadequately established and/or highly variable and that many of the data sets, in terms of gradients, velocities, and/or cooling rates, are unreliable. The accessed unsteady- and steady-state observations on near-terminal binary alloys for primary and secondary spacings were first examined within conventional power law representations, the deduced exponents and confidence limits for each alloy being tabularly recorded. Through this analysis, it became clear that to achieve predictive generality the many constitutive parameters must be included in a rational way, this being achievable only through extant or new theoretical formulations. However, in the case of primary spacings, all formulas, including our own, failed within the unsteady heat flow algorithm while performing adequately within their steady-state context. An earlier untested, heuristically derived steady-state formula after modification,

连铸坯枝晶臂间距检测方法的优化与应用实践

介绍了连铸坯凝固组织中树枝晶臂间距检测方法的优化试验及其应用效果。通过对连铸坯凝固冷却过程的分析及批量数据的采集,确定了测定连铸坯树枝晶臂间距的代表性区域,建立了一种科学测量枝晶臂间距的方法。将该方法应用于连铸圆坯生产检验中,能快速准确地找出铸坯枝晶臂间距随连铸二冷强度变化的规律,采取调整连铸二冷强度的措施,来控制一、二次枝晶臂间距大小,达到了减轻或消除铸坯开裂缺陷、提高连铸质量的目的。     

On the elastic stabilization of precipitates against coarsening under applied load

A simple procedure is developed for examining the stability against coarsening of two misfitting spherical precipitates subjected to an applied uniaxial tensile stress. Analytic expressions are obtained defining regions of stability and metastability. It is found that the applied stress can act to stabilize the precipitates for certain precipitate orientations with respect to the applied stress and destabilize the precipitates for other orientations. Conditions are also delineated in which small precipitates should be expected to grow at the expense of larger precipitates. These results are found to be in agreement with experiment for an applied stress field less than a threshold stress.     

The effect of grain refining on macrosegregation and dendrite arm spacing of direct chill cast AA5182

The effect of titanium and titanium diboride inoculation on the spatial variation of local solidification time for direct chill (DC) cast ingots of aluminum alloy 5182 (AA5182) was studied. The results have been compared to those of an ingot cast without grain refining. To accomplish this, the effect of grain refining on a number of ingot characteristics such as grain size, macrosegregation, spatial variation of dendrite arm spacing, and thermal conductivity was investigated. Furthermore, the effect of grain refining on the well-known relationship between dendrite arm spacing and local solidification time had to be established for AA5182. The results indicated that the spatial variation of dendrite arm spacing in the industrial ingots was independent of grain refining, although the nonrefined ingot produced significantly finer dendrite arm spacings in its center. This was attributed to the influence of showering crystals in the nonrefined ingot. The relationship between dendrite arm spacing and local solidification time was also found to be independent of grain refining.     

The coarsening of liquid Al-Pb-dispersions

The behaviour of a dispersion with liquid Pb particles moving at their Stokes velocities relative to the liquid Al matrix has been investigated. In order to provide a stable dispersion a special experimental arrangement has been used that minimizes effects due to settling of the heavier Pb droplets. It is shown that the measured stationary droplet size distribution coincides with the authors′ theoretical prediction for Ostwald ripening by convective diffusion.     

Effect of plastic deformation on the coarsening of

Particle coarsening has been studied in a rapidly solidified Al-8.8 wt pct Fe-3.7 wt pct Ce alloy subjected to isothermal annealing for various times at 425 °C. The effect of static and dynamic loading on the particle coarsening rates at the same temperature also has been examined. The dispersed particles in all specimens of the present study are the equilibrium Al¹³Fe⁴ and Al¹⁰Fe²Ce phases. They are incoherent with the matrix and constitute 23 pct of the total volume. The coarsening rate in isothermally annealed specimens is orders of magnitude greater than predicted by the modified Lifshitz-Slyozov-Wagner theory for volume diffusion controlled coarsening but can be explained using Kirchner’s model for coarsening by diffusion along grain boundaries. In the case of intragranular particles, coarsening by diffusion along dislocation cores also is likely to be significant. Creep loading is seen to cause a significant enhancement of the coarsening rate. Fatigue testing with a hold period at the maximum tensile stress also accelerates coarsening whereas continuous cycling appears initially to retard the increase in the average particle size. Dislocations connecting dispersed phase particles are observed more frequently in crept specimens and specimens fatigued with a hold period than in specimens fatigued with no hold period. The effects of plastic deformation on particle coarsening rates are discussed in terms of excess vacancy generation, short circuiting along dislocations, and fine precipitation during fatigue.     

On the effect of plastic deformation on the coarsening of ϑ-phase precipitation in an Al-Cu alloy

In the present investigation, the focus is on dynamic coarsening of the equilibrium ϑ phase in an Al-4wt pct Cu alloy. For this purpose, specimens containing a uniform ϑ particle distribution have been produced and deformed in compression at two different temperatures (200 °C and 250 °C) and strain rates in the ranges of 200 °C to 250 °C and 10⁻⁵ to 10⁻² s⁻¹, respectively. The particle size distribution measurements performed in a scanning microscope in back-scattered mode demonstrated a double peak behavior depending on temperature: at the lowest test temperature, the dynamic coarsening is enhanced at the highest strain rate, while at 250 °C, the coarsening seems to be affected by crushing of small and medium size particles during straining.     

Abnormal growth in the presence of coarsening particles

The possibility of occurrence of abnormal growth in a matrix which is pinned by coarsening particles is examined by means of a simple theoretical model. Abnormal growth is found to depend on a parameter ϵ which is the interplay of several quantities. Low values of ϵ mean that the matrix approaches the behaviour of a particle-free material whilst for large values of ϵ the matrix behaves more like it were pinned by stable particles.     

Activation energies for the coarsening of compound precipitates

The theory of diffusion-controlled coarsening is extended to the case of compound precipitates of the typeA _αB_β growing in a matrix of a third elementM. The bulk of the existing theory for coarsening in binary systems is found to apply in this case as well. The rate constant for coarsening is conveniently expressed as a preexponential term and an activation energy. Although the activation energy is dependent on the activation energy for diffusion of one or the other components, other terms are involved. In general, the activation energy for coarsening is considerably greater than the activation energy for diffusion. Rules are presented for deducing the coarsening rate from atomic mobilities, thermo-chemical data, alloy composition, and coarsening atmosphere. This paper is based upon a thesis submitted by S. K. BHATTACHARYYA in partial fulfillment of the degree of Doctor of Science at M.I.T.