Robert D. Pehlke

Mathematical Modeling of Porosity Formation in Solidification

Shrinkage porosity and gas porosity occur simultaneously and at the same location when conditions are such that both may exist in a solidifying casting. Porosity formation in a solidifying alloy is described numerically, including the possible evolution of dissolved gases. The calculated amount and size of the porosity formed in Al-4.5 pct Cu plate castings compares favorably with measured values. The calculated distribution of porosity in sand cast Al-4.5 pct Cu plates of 1.5 cm thickness matches experimental measurements. The decrease of the hydrogen content by strong degassing and the increase of mold chilling power are recommended to produce sound aluminum alloy castings. The calculated results for steel plate castings are in agreement with the experimental work of Pellini. The present modeling has clarified the basis of empirical rules for soundness and suggests that the simultaneous occurrence of shrinkage and gas evolution is an essential mechanism in the formation of porosity defects.

Metal-Mold interfacial heat transfer

During the solidification of metal castings, an interfacial heat transfer resistance exists at the boundary between the metal and the mold. This heat transfer resistance usually varies with time even if the cast metal remains in contact with the mold, due to the time dependence of plasticity of the freezing metal and oxide growth on the surface. The present work has studied interfacial heat transfer on two related types of castings. In the first type, a copper chill was placed on the top of a cylindrical, bottom gated casting. Using the techniques of transducer displacements and electrical continuity, a clearance gap was detected between the solidified metal and the chill. The second type of casting had a similar design except that the chill was placed at the bottom. Owing to the effect of gravity, solid to solid contact was maintained at the metal-chill interface, but the high degree of interface nonconformity resulted in a relatively low thermal conductance as indicated by solution of the inverse heat conduction problem. Finally, the influence of interfacial heat transfer on solidification time with three mold ma-terials is compared by a numerical example, and criteria for utilizing Chvorinovs rule are discussed.

Thermodynamic properties of solid alloys of chromium with nickel and iron

The thermodynamic properties of chromium have been determined in the Ni-Cr and Fe-Cr binary systems and in the Fe-corner of the Fe-Ni-Cr system. These properties are based on experimental measurements using solid oxide electrolyte cells of the type: Cr, Cr2O3 I ThO2-Y2O3Cr (alloy), Cr2O3. In the Ni-Cr system, between 900 and 1300°, the activity of chromium exhibits negative deviation from ideality up to about 25 at. pct chromium. For alloys higher in chromium content, the activity of chromium exhibits positive deviation from ideality. In the Fe-Cr system, between 900 and 1200°, and 0 and 63 at. pct Cr, the chromium activity when referred to solid pure chromium exhibits positive deviation from ideality in both the γ and α phases, approaching ideality with increasing temperature. The nickel and iron activities in these two respective binary systems were calculated by a Gibbs-Duhem integration. The activity of chromium, referred to solid pure chromium, was measured between 900 and 1200° in solid Fe-Ni-Cr alloys with chromium concentrations of 9, 20, and 30 at. pct and Ni concentrations of 8, 18, and 30 at. pct. Additions of nickel to Fe-Cr alloys in the above concentration range are found to increase the chromium activity. The effect of nickel in increasing the chromium activity is greater at both greater chromium contents and lower temperatures.

Mathematical Modeling of Microsegregation in Binary Metallic Alloys

A mathematical model was developed to calculate microsegregation in binary metallic alloys. This model utilized the mathematical techniques of the method of lines combined with invariant imbedding (MOL/II) to solve the problem of combined heat and mass transfer during and after solidification. Model predictions were compared to experimental measurements in the Al-Cu system and to other microsegregation models. The MOL/II model predicted nonequilibrium second-phase contents within ±3 pct at low and intermediate cooling rates, when dendrite-arm coarsening was included in the model. It also was able to reproduce concentration profiles reasonably well. The analytical models commonly used (equilibrium cooling, Scheil equation, Brody/ Flemings model, Clyne/Kurz model, Solari/Biloni model, and Basaran equation) in micro-segregation calculations were shown to be considerably less accurate than the numerical models (MOL/II and the Ogilvy/Kirkwood model).

Nitrogen solution and titanium nitride precipitation in liquid Fe-Cr-Ni alloys

The solubility of nitrogen in liquid Fe-Cr, Fe-Ni, Ni-Cr, and Fe-Cr-Ni alloys up to 20 wt pct Ni and 40 wt pct Cr was measured by the Sieverts’ method. The first and second order interactions in iron between nitrogen and chromium, and nitrogen and nickel were determined. Chromium increases the nitrogen solubility at lower chromium concentrations but the second order interaction term which is of the opposite sign becomes significant at higher chromium levels and compensates partly for the effect of the first order interaction term. Nickel decreases the nitrogen solubility in iron. Titanium nitride formation in liquid Fe-Cr, Fe-Ni, and Fe-Cr-Ni alloys also was investigated. The first and second order interactions between titanium and chromium or nickel were determined at 1600°C. Chromium increases the solubility product of TiN, principally by decreasing the activity of nitrogen in the melt. Nickel decreases the solubility product of TiN by increasing the activities of nitrogen and titanium.

Equilibrium partition coefficients in iron-based alloys

Accurate relationships between equilibrium partition coefficients and solute concentration are required for the prediction of solute redistribution during solidification. Thermodynamic analyses are presented to relate these coefficients to fundamental thermodynamic quantities. Using the most accurate data available, partition coefficients are calculated for ten Fe−X (X=Al, C, Cr, Mn, Ni, N, P, Si, S, Ti) binary systems and compared with literature values. Equations are presented to allow for prediction of these partition coefficients as a function of temperature, as well as liquidus temperature as a function of composition. In addition, partition coefficient values are examined for the ternary systems Fe−Cr−C, Fe−Mn−Ni, and Fe−Ni−S.

Nitrogen solubility in liquid Fe-V and Fe-Cr-Ni-V alloys

AbstractNitrogen solubility in liquid Fe, Fe-V, Fe-Cr-V, Fe-Ni-V and Fe-18 pct Cr-8 pet Ni-V alloys has been measured using the Sieverts’ method for vanadium contents up to 15 wt pct and over the temperature range from 1775 to 2040 K. Nitrogen solution obeyed Sieverts’ law for all alloys investigated. Nitride formation was observed in Fe-13 pet V, Fe-15 pet V and Fe-18 pet Cr-8 pet Ni-10 pet V alloys at lower temperatures. The nitrogen solubility increases with increasing vanadium content and for a given composition decreases with increasing temperature. In Fe-V alloys, the nitrogen solubility at 1 atm N2 pressure is 0.72 wt pet at 1863 K and 15 pct V. The heat and entropy of solution of nitrogen in Fe-V alloys were determined as functions of vanadium content. The first and second order interaction parameters were determined as functions of temperature as:

Mass transfer during dissolution of a solid into liquid in the iron-carbon system

e_N^V = \frac{{ - 463.6}}{T} + 0.148 and e_N^{VV} = \frac{{17.72}}{T} - 0.0069