David R Poirier

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• Poirier, D. R. (2014). Density, Viscosity, and Diffusion Coefficients in Hypoeutectic Al-Si Liquid Alloys: An Assessment of Available Data. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science, 1-10.
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  Abstract: This article is a review of empirical and calculated data on density, viscosity, and diffusion coefficients in hypereutectic Al-Si liquid alloys. Many regressions of the data were effected in order to consolidate the data as functions, which can be used to calculate each property as a function of temperature and concentration of Si. The chemical diffusion coefficient in the alloys was derived based on the Sutherland model, which relates the diffusion coefficient to viscosity. © 2014 The Minerals, Metals & Materials Society and ASM International.
• Hoose, J. V., Grugel, R. N., Tewari, S. N., Brush, L. N., Erdmann, R. G., & Poirier, D. R. (2012). Observation of misoriented tertiary dendrite arms during controlled directional solidification in aluminum-7 wt pct silicon alloys. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 43(12), 4724-4731.
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  Abstract: Electron backscattered diffraction (EBSD) examination of transverse cross sections from a directionally solidified aluminum-7 wt pct silicon alloy revealed tertiary dendrite arms that appeared in place but in reality had orientations that significantly differed from their parent arm. The maximum extent of spuriously orientated arms occurred at an intermediate growth velocity and was more pronounced at subgrain boundaries that separated uniquely oriented dendritic arrays. Mechanisms for tertiary arm misorientations are discussed, and attention is called to the practical consequences of these in-situ defects. © 2012 The Minerals, Metals & Materials Society and ASM International.
• Erdmann, R. G., Poirier, D. R., & Hendrick, A. G. (2010). Permeability in the mushy zone. Materials Science Forum, 649, 399-408.
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  Abstract: When modeled at macroscopic length scales, the complex dendritic network in the solid-plus-liquid region of a solidifying alloy (the "mushy zone") has been modeled as a continuum based on the theory of porous media. The most important property of a porous medium is its permeability, which relates the macroscopic pressure gradient to the throughput of fluid flow. Knowledge of the permeability of the mushy zone as a function of the local volume-fraction of liquid and other morphological parameters is thus essential to successfully modeling the flow of interdendritic liquid during alloy solidification. In current continuum models, the permeability of the mushy zone is given as a deterministic function of (1) the local volume fraction of liquid and (2) a characteristic length scale such as the primary dendrite arm spacing or the reciprocal of the specific surface area of the solid-liquid interface. Here we first provide a broad overview of the experimental data, mesoscale numerical flow simulations, and resulting correlations for the deterministic permeability of both equiaxed and columnar mushy zones. A extended view of permeability in mushy zones which includes the stochastic nature of permeability is discussed. This viewpoint is the result of performing extensive numerical simulations of creeping flow through random microstructures. The permeabilities obtained from these simulations are random functions with spatial autocorrelation structures, and variations in the local permeability are shown to have dramatic effects on the flow patterns observed in such microstructures. Specifically, it is found that "lightning-like" patterns emerge in the fluid velocity and that the flows in such geometries are strongly sensitive to small variations in the solid structure. We conclude with a comparison of deterministic and stochastic permeabilities which suggests the importance of incorporating stochastic descriptions of the permeability of the mushy zone in solidification modeling. © (2010) Trans Tech Publications.
• Huang, H., & Poirier, D. R. (2009). Computer simulation of directional solidification of binary alloy calculated under personal computer platform. Tamkang Journal of Science and Engineering, 12(3), 239-248.
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  Abstract: The objective of this paper is to demonstrate the ability of simulating thermal-solute double diffusivities problem, which is usually calculated via mini-supercomputer or supercomputer, by using typical personal computer (PC). The "plume" phenomena due to buoyant force of lighter liquid solute during solidification will be illustrated. The conduction, convection and macrosegregation predicted by numerical simulations of a directionally solidified binary alloy (Pb-23.2 wt% Sn) are calculated on Pentium-4 1.6 GHz Personal Computer (PC) platform and presented. The casting was solidified at a rate of 6 μm s-1 and a thermal gradient of approximately 7.2 x 103 Km-1 which is a rather high thermal gradient that has not been numerical simulated before. The calculated results showed channels at the vertical casting surface and segregated internal pockets in the mushy zone, in agreement with the observation of freckles in the experimental casting. They also showed plumes phenomena at the early stage of solidification process. The simulator calculates a set of equations. They are mass conservation, momentum, energy and solute equations. The simulator ported to IBM-compatible PC platform can provide instant information on casting process for manufacturers as compared to obtain calculations under Convex C240 mini-super computer before.
• Neri, M. A., Poirier, D. R., & Erdmann, R. G. (2007). Effect of casting over-pressure on the fatigue resistance of aluminum alloy A356-T6. TMS Annual Meeting, 275-282.
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  Abstract: The fatigue resistance of an Al-Si casting alloy (A356) solidified under pressures up to 20 atm and under a vacuum was investigated. Pressures of 10 and 20 atm mitigated microporosity in plate-castings, and this enhancement significantly improved fatigue resistance. Cooling rate during solidification, which affects the dendrite arm spacing (DAS), was also varied. Also studied were Sr-modification and the use of a flux to capture oxide-bifilms. Fatigue life increased as the maximum pore size decreased, which resulted from the over-pressures and/or a decrease in DAS. The use of flux in the mold and Sr-modification, especially when employed simultaneously, also increased fatigue life.
• Zhao, P., Heinrich, J. C., & Poirier, D. R. (2007). Numerical simulation of crystal growth in three dimensions using a sharp-interface finite element method. International Journal for Numerical Methods in Engineering, 71(1), 25-46.
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  Abstract: A sharp-interface numerical model is presented to simulate thermally driven crystal growth in three-dimensional space. The model is formulated using the finite element method and works directly with primitive variables. It solves the energy equation in a fixed volume mesh while explicitly tracking the motion of the solid-liquid interface. The three-dimensional interface is represented by connected planar triangles that form a surface mesh. To accurately capture the morphology of the growing dendrite, the surface mesh is updated every few time-steps so that the quality of the triangles is maintained and the size of the triangles is always kept in a range associated with the element size of the fixed volume mesh. The interface curvature is calculated by a least-squares paraboloid-fitting to neighbouring nodes. The model is validated through a comparison with an exact solution of a three-dimensional Stefan problem, a mesh refinement study, a mesh orientation test and a comparison with solvability theory. It is shown that the interface position is tracked to second-order accuracy. Simulations are performed under different combinations of the undercooling and surface energy. The effects of these parameters on the growth and morphology of the dendrites are studied. Copyright © 2006 John Wiley & Sons, Ltd.
• Zhao, P., Heinrich, J. C., & Poirier, D. R. (2006). Numerical modeling of fluid-particle interactions. Computer Methods in Applied Mechanics and Engineering, 195(41-43), 5780-5796.
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  Abstract: Finite elements based techniques for the simulation of flow interacting with particles which can be rigid, deformable or changing in size are presented. Numerical methods first developed to simulate dendritic growth of binary alloys in two dimensions and without convection are extended to treat a variety of flow-particle interactions including forced or natural convection as well as forced or free particle motion. The calculations rely on various ways to use fixed and changing meshes to achieve the flexibility needed to model a wide variety of physical situations involving moving interfaces of complex geometry in the presence of fluid motion. © 2005 Elsevier B.V. All rights reserved.
• Felicelli, S. D., & Poirier, D. R. (2005). Modeling of solidification and filling of thin-section castings. Proceedings of the ASME Summer Heat Transfer Conference, 3, 207-212.
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  Abstract: A finite element model for simulating dendritic solidification of multicomponent-alloy castings is used to study the filling and solidification of castings of thin cross section. The model solves the conservation equations of mass, momentum, energy, and alloy components and couples the solution with the thermodynamic of the multicomponent alloy through a phase diagram equation. The transport of mass and energy in the mushy zone is done considering the mushy zone as a porous medium of variable porosity. The same set of conservations equations are used for the liquid, solid and mushy zones, in which the volume fraction of liquid acts as the variable that makes the equations transition continuously from one zone to another (Felicelli et al. [1]). During filling, the model tracks the advancing front as the metal flows into the thin mold, and solidification is calculated as the metal loses energy by convection and radiation to the mold, including the dynamic calculation of view factors. The code supports two fluid models that emulate the flow behavior under equiaxed or columnar solidification. In the former case a slurry fluid model is used in which the viscosity is determined by the volume fraction of solid. In this slurry state, the solid and liquid move at the same velocity. For the case of columnar solidification, the solid is fixed and the liquid flows through a porous structure of dendrictic solid. The model development is based on the work by Felicelli et al. [2], to which several features were added, including a front-tracking technique (Gao [3]) and thermal radiation boundary conditions. Calculations for Ni and Al alloys were performed to illustrate the effect of several physical and operation parameters in the filling of a horizontal channel of thin thickness. A wide range of process parameters was tested in order to determine how much of the channel length could be filled before blockage of flow by solidification occurred. In a separate section, the effect of alloy concentration on the fluidity was studied using a Pb-Sn hypoeutectic system, and the importance that the dendrite breaking phenomenon can have on the results is shown. Conclusions about the parameters that most influence the filling process are presented, as well as recommendations on which experimental data are more critical in order to conduct a proper validation of this type of models. Copyright © 2005 by ASME.
• Heinrich, J. C., Poirier, D. R., & Zhao, P. (2005). Simulating dendritic growth with convection. 3rd M.I.T. Conference on Computational Fluid and Solid Mechanics, 668-671.
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  Abstract: Starting with the effect of forced flows on the morphologies of growing dendrites, previous work on simulating dendritic growth with convection is summarized. In our work a fixed mesh for the temperature and a conformable mesh for velocity and concentration in a binary alloy are used; this method captures the morphology and motion of the complex solid-liquid interface. Convection is driven by thermo-solutal buoyancy and solidification contraction. Examples include: the natural convection near a dendrite of a pure substance growing in its under-cooled liquid; the dendritic growths of a pure substance and an alloy in their undercooled liquids, in which the convection is driven by buoyancy and solidification contraction; and the effects of convection driven by thermosolutal buoyancy and solidification contraction during the directional solidification of an alloy. Solidification contraction dominates the convection pattern, when the concentration of the alloy-element is dilute. © 2005 Elsevier Ltd.
• Zhao, P., Heinrich, J. C., & Poirier, D. R. (2005). Dendritic solidification of binary alloys with free and forced convection. International Journal for Numerical Methods in Fluids, 49(3), 233-266.
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  Abstract: Dendritic solidification with forced convection and free convection driven by contraction and thermosolutal buoyancy is simulated in two-dimensional space using a sharp-interface model. Both pure substances and alloys are considered. The model is formulated using the finite element method and works directly with primitive variables. The coupled energy- and solutal concentration-equations, along with the Navier-Stokes equations for incompressible flow, are solved using different meshes. Temperature is solved in a fixed mesh that covers the whole domain (solid + liquid) where the solid-liquid interface is explicitly tracked using marker points. The concentration and momentum equations are solved in the liquid region using an adaptive mesh of triangular elements that conforms to the interface. The velocity boundary conditions are applied directly on the interface. The model is validated using a series of problems that have analytical, experimental and numerical results. Four simulations are presented: (1) crystal growth of succinonitrile with thermal convection under two small undercoolings; (2) dendritic growth into an undercooled pure melt with a uniform forced flow; (3) equiaxial dendritic growth of a pure substance and an alloy with contraction-induced convection; and (4) directional solidification of Pb-0.2 wt% Sb alloy with convection driven by the combined action of contraction, thermal and solutal buoyancy. Some of the simulation results are compared to those reported using other methods including the phase-field method; others are new. In each case, the effects of convection on dendritic solidification are analysed. Copyright © 2005 John Wiley & Sons, Ltd.
• Heinrich, J. C., & Poirier, D. R. (2004). Convection modeling in directional solidification. Comptes Rendus - Mecanique, 332(5-6), 429-445.
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  Abstract: Mathematical and numerical models of solidification of binary and multicomponent dendritic alloys that can model the dynamics of the mushy zone as well as the all liquid region are examined. The discussion is centered around models based on finite element discretization of the governing equations that have been developed by the authors during the last fifteen years. The capabilities of existing simulation codes to model the effects of convection and the resulting macrosegregation in castings, and in particular, the development of 'freckles' in vertically solidified dendritic monocrystals are discussed. The current capabilities of the models as well as the areas in which more improvement is needed are noted. Numerical examples are presented to illustrate the different aspects of the simulations. To cite this article: J.C. Heinrich, D.R. Poirier, C. R. Mecanique 332 (2004). © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.
• Heinrich, J. C., & Poirier, D. R. (2004). The effect of volume change during directional solidification of binary alloys. Modelling and Simulation in Materials Science and Engineering, 12(5), 881-899.
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  Abstract: The effect of solidification contraction is examined through numerical simulations of hypoeutectic Pb-Sn alloys. In addition, particular attention is given to numerically approximating the solidification of the eutectic liquid. In order to predict the inverse segregation at the cooled surface accurately, the contribution of the boundary integral is retained in the weak formulation of the solute conservation equation. This procedure eliminates the false flux, which incorrectly causes a negative segregation at the cooled surface. In the case of vertical solidification under gravity, when channels form, the shrinkage turns the flow inside the channel downwards and towards the solidifying eutectic. Without including shrinkage, the flow in an entire channel is upwards.
• Westra, D. G., Heinrich, J. C., & Poirier, D. R. (2004). Simulating the effect of space vehicle environments on directional solidification of a binary alloy. AIAA Paper, 6113-6125.
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  Abstract: Simulations were conducted to study the effect of spacecraft vibrations on the directional solidification of a dendritic alloy. Finite element calculations were done with a simulator based on a continuum model of dendritic solidification, using the Fractional Step Method (FSM). An important difficulty common to all solidification models in which the energy equation is expressed in terms of temperature, and that are based on finite elements or finite differences, arises when the interdendritic liquid reaches the eutectic temperature and concentration. When a node reaches eutectic temperature, it is assumed that the solidification of the eutectic liquid continues at constant temperature until all the eutectic is solidified. With this approach, solidification is not achieved continuously across an element; rather, the element is not considered solidified until the eutectic isotherm overtakes the top nodes. To overcome this difficulty, a more accurate method is employed for predicting the rate of change of fraction of liquid as the liquid in an element solidifies. The new method enables us to contrast results of simulations in which the alloy is subjected to no gravity or a steady-state acceleration versus simulations when the alloy is subjected to vibration disturbances; therefore, the effect of vibration disturbances can be assessed more accurately. To assess the impact of these vibration perturbations, transient accelerometer data from a space shuttle mission are used as inputs for the simulation.
• Zhao, P., Heinrich, J. C., & Poirier, D. R. (2004). Effect of variable density in dendritic solidification. AIAA Paper, 6097-6105.
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  Abstract: Dendritic solidification with natural convection caused by solidification contraction and thermal and solutal buoyancy in two-dimensional space is numerically studied using a sharp-interface model. The model is formulated using the finite element method and works directly with primitive variables. Both pure substances and binary alloys are considered. The model solves the coupled energy and solutal concentration equations and the Navier-Stokes equations for incompressible flow while tracking the solid-liquid interface explicitly using marker points. The energy equation is solved on a fixed mesh that covers the whole domain of the solid and liquid phases. The solutal concentration and Navier-Stokes equations are solved on an adaptive mesh of triangular elements that covers only the liquid phase. The adaptive mesh conforms to the interface and the velocity boundary conditions are applied directly at the nodes on the interface. Three examples that consider solidification contraction, thermal buoyancy and all three of contraction and thermal and solutal buoyancy are presented. The simulations show that, for equiaxial dendritic growth into an undercooled pure melt, the contraction-induced convection enhances the solidification rate symmetrically while the thermal convection causes the dendrite to grow faster in the downward direction and slower in the upward direction. For directional solidification with the growth direction perpendicular to the gravity, thermo-solutal buoyancy causes circulatory convection while contraction induces unidirectional flow. The mixed convection alters the concentration distribution in the solutal-boundary layer ahead of the interface and changes the local solidification rate.
• Zhao, P., Heinrich, J. C., & Poirier, D. R. (2004). Fixed mesh front-tracking methodology for finite element simulations. International Journal for Numerical Methods in Engineering, 61(6), 928-948.
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  Abstract: A direct front-tracking method using an Eulerian-Lagrangian formulation is developed in two space dimensions. The front-tracking method is general in that it can track any type of interface once its local velocity is specified or has been determined by calculation. The method uses marker points to describe the interface position and tracks the interface evolution on a fixed finite-element mesh, including growth, contraction, splitting and merging. Interfacial conditions are applied directly at the interface position. The method is applied to three scenarios that involve different interface conditions and are based on energy and mass diffusion. The three calculations are for the dendritic solidification of a pure substance, the cellular growth of an alloy, and the Ostwald ripening of silica particles in silicon. Numerical results show that very complicated interface morphologies and topological changes can be simulated properly and efficiently. © 2004 John Wiley and Sons, Ltd.
• Chen, J., Sung, P. K., Tewari, S. N., Poirier, D. R., & de, H. (2003). Directional solidification and convection in small diameter crucibles. Materials Science and Engineering A, 357(1-2), 397-405.
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  Abstract: Pb-2.2 wt.% Sb alloy was directionally solidified in 1, 2, 3 and 7 mm diameter crucibles. Pb-Sb alloy presents a solutally unstable case. Under plane-front conditions, the resulting macrosegregation along the solidified length indicates that convection persists even in the 1 mm diameter crucible. Al-2 wt.% Cu alloy was directionally solidified because this alloy was expected to be stable with respect to convection. Nevertheless, the resulting macrosegregation pattern and the microstructure in solidified examples indicated the presence of convection. Simulations performed for both alloys show that convection persists for crucibles as small as 0.6 mm of diameter. For the solutally stable alloy, Al-2 wt.% Cu, the simulations indicate that the convection arises from a lateral temperature gradient. © 2003 Elsevier Science B.V. All rights reserved.
• Frueh, C., Poirier, D. R., Erdmann, R. G., & Felicelli, S. D. (2003). On the length-scale and location of channel nucleation in directional solidifaction. Materials Science and Engineering A, 345(1-2), 72-80.
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  Abstract: This work provides evidence that channels in directionally solidified hypoeutectic Pb-Sn alloy nucleate at the dendrite tips. Using a finite-element simulator, distinctive 'convective signatures' are shown to exist for stable and unstable cases, where the stability of a system is shown to be largely a function of the thickness of an inverted density layer that can exist ahead of the moving solidification front. The thickness of this layer, and therefore, the stability of the systems studied, is shown to largely be a function of the length scale D/V, where it is shown that channeling can be turned on or off simply by changing this length scale. © 2002 Elsevier Science B.V. All rights reserved.
• Zhao, P., Heinrich, J. C., & Poirier, D. R. (2003). Stability of numerical simulations of dendritic solidification. JSME International Journal, Series B: Fluids and Thermal Engineering, 46(4), 586-592.
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  Abstract: Novel developments in the numerical simulation of diffusion limited dendritic growth are discussed in the context of two-dimensional simulations of solidification of pure substances and of binary alloys. The three most important numerical difficulties encountered in the simulations of dendritic growth of binary alloys are discussed : 1) the need to accurately calculate the position and velocity of the interface as part of the solution; 2) the disparity of length scales between the thermal diffusion length and the solute diffusion length ; and 3) the instability of the solid-liquid interface, particularly at high concentrations of solute. Dealing with the third difficulty constitutes the main objective of this paper. The stability of calculations is studied using the continuity condition on the heat flux across the interface and numerical simulations. The latter are used to assess the current modeling capabilities and the hurdles faced to produce more powerful simulators.
• Zhao, P., Vénere, M., Heinrich, J. C., & Poirier, D. R. (2003). Modeling dendritic growth of a binary alloy. Journal of Computational Physics, 188(2), 434-461.
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  Abstract: A two-dimensional model for simulation of the directional solidification of dendritic alloys is presented. It solves the transient energy and solute conservation equations using finite element discretizations. The energy equation is solved in a fixed mesh of bilinear elements in which the interface is tracked; the solute conservation equation is solved in an independent, variable mesh of quadratic triangular elements in the liquid phase only. The triangular mesh is regenerated at each time step to accommodate the changes in the interface position using a Delaunay triangulation. The model is tested in a variety of situations of differing degrees of difficulty, including the directional solidification of Pb-Sb alloys. © 2003 Elsevier Science B.V. All rights reserved.
• Frueh, C., Poirier, D. R., & Felicelli, S. D. (2002). Predicting freckle-defects in directionally solidified Pb-Sn alloys. Materials Science and Engineering A, 328(1), 245-255.
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  Abstract: This work validates a finite element model of dendritic solidification by comparing predicted results to data resulting from 11 directionally solidified hypoeutectic Pb-Sn samples, which were produced under various thermal gradients and solidification growth rates. For all but one of the cases, which was thought to be borderline between freckling and not freckling, predictions of whether freckles formed were supported by experiments. It was also determined that freckling could be predicted by running a simulation with convection turned on only after a mushy zone was fully developed; this saves computational time and lends credibility to the notion of using a non-dimensional freckling criterion such as a Rayleigh number. Finally, with D as the diffusivity of Sn in the liquid and V the growth rate, setting the mesh spacing in the growth direction at only D/V at the dendrite tips, and allowing the element size to be coarser throughout the rest of the domain, the simulations accurately predicted freckling consistent with results produced using a uniform mesh spacing of D/V. By testing the simulated system to see whether convection produces freckles after a completely developed mushy zone evolves and by employing a non-uniform mesh, a considerable saving in computational time for predicting freckles was achieved. © 2002 Elsevier Science B.V. All rights reserved.
• Frueh, C., Sung, P. K., Poirier, D. R., Erdmann, R. G., & Miszkiel, M. E. (2002). Microporosity in A356.2 aluminum alloy cast under pressure. Advances in Aluminum Casting Technology II, 99-105.
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  Abstract: The effect of pressure on porosity in cast A356.2 was investigated. Alloys were melted in an induction furnace under vacuum and then pressurized with argon and 0.2 atm hydrogen to a total overpressure of either 1 atm, 10 atm, or 20 atm. Hydrogen was intentionally added to effect porosity, so that the role of overpressure on suppressing the porosity could be examined. While maintaining an overpressure, the alloys were poured into bottom-chilled molds, resulting in castings that were in turn sectioned, polished, and analyzed for porosity. The resulting data show that an increase in overpressure reduces the amount of porosity and shifts the pore size distribution to smaller pores. These findings were further supported by modeling the casting process with a finite element model of the formation of porosity during solidification using the same alloy and experimental conditions. By solving the redistribution and transport phenomena of hydrogen during solidification and comparing its Sievert's pressure to the local pressure within the alloy cast under pressure, it was found that the predicted results agreed reasonably well with the experimental data.
• Poirier, D. R., & Sung, P. K. (2002). Thermodynamics of hydrogen in Al-Si alloys. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 33(12), 3874-3876.
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  Abstract: The thermodynamics of hydrogen in Al-Si alloys was discussed. The solubility of the hydrogen was deduced. It was found that the interaction coefficient for the solid alloys applied to the mixture of the two phase and not to the individual phase. The analysis showed that both the solubility of hydrogen in α and the partition ratio of hydrogen with lesser silicon were greater than the solubility and partition ratio for the equilibrium ratio.
• Sung, P. K., Poirier, D. R., & Felicelli, S. D. (2002). Continuum model for predicting microporosity in steel castings. Modelling and Simulation in Materials Science and Engineering, 10(5), 551-568.
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  Abstract: Using a finite element model for simulating dendritic solidification of multicomponent-alloy castings, the pressure and redistribution of gas-forming elements during solidification and cooling in AISI 8620 steel casting alloy were calculated. The model solves the conservation equations of mass, momentum, energy, each alloy component and gas-forming elements (i.e. hydrogen and nitrogen). By solving for the concentrations of hydrogen and nitrogen in the intergranular liquid and comparing the sum of their Sievert's pressures with the local pressure within the mushy zone of the alloy, the model predicts regions of possible formation of porosity. The thermal boundary conditions on test-bar castings were deduced from a thermal calculation performed with a commercial code, ProCAST™. With these realistic thermal boundary conditions, our porosity-simulations were carried out for many cases with combinations of different initial contents of the gas-forming elements: Hydrogen in the range of 3-7 ppm and nitrogen in the range of 0-100 ppm. The calculated results are summarized in a plot that separates castings expected to have porosity from those with no porosity. The effect of adding titanium to form TiN inclusions and inhibit the development of porosity during solidification was also investigated.
• Sung, P. K., Poirier, D. R., & Felicelli, S. D. (2001). Sensitivity of mesh spacing on simulating macrosegregation during directional solidification of a superalloy. International Journal for Numerical Methods in Fluids, 35(3), 357-370.
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  Abstract: The sensitivity of mesh spacing on simulations of macrosegregation, particularly 'freckles', during vertical directional solidification of a superalloy in a rectangular mold was systematically analyzed to achieve accurate predictions in finite element calculations. It was observed that a coarser mesh spacing in the x-direction horizontal tends to minimize the simulated macrosegregation, whereas a coarser mesh spacing in the y-direction vertical artificially tends to make the system appear to have more macrosegregation. When solidification conditions either lead to a well-established freckling case or to a well-established non-freckling case, the simulated results are not sensitive to the mesh spacing provided the elements are no larger than about 2d1 by 2 D/V and 3d1 by 4 D/V respectively, where d1 is the primary dendrite arm spacing, D is the diffusivity of the alloy solute with the smallest diffusivity in the liquid, and V is the growth rate. However, when solidification conditions are very close to the transition between freckling and no freckling, the simulated results are sensitive to the mesh spacing, especially in the y-direction. Based on the mesh sensitivity analysis from the two-dimensional simulations of rectangular castings of Rene N5, the mesh with element dimensions no larger than 2d1 in the x-direction and 1.5 D/V in the y-direction are recommended as the most stringent element size. Copyright © 2001 John Wiley & Sons, Ltd.
• Sung, P. K., Poirier, D. R., & Felicelli, S. D. (2001). Simulating the initiation of a channel during directional solidification of a superalloy. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 32(1), 202-207.
• Sung, P. K., Poirier, D. R., Felicelli, S. D., Poirier, E. J., & Ahmed, A. (2001). Simulations of microporosity in IN718 equiaxed investment castings. Journal of Crystal Growth, 226(2-3), 363-377.
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  Abstract: A finite element model for simulating dendritic solidification of multicomponent-alloy castings has been enhanced to include the calculation of pressure and redistribution of gas-forming elements during solidification and cooling. The model solves the conservation equations of mass, momentum, energy and alloy components, and the gas-forming elements, hydrogen and nitrogen. By solving the transport of gas solutes and comparing their Sievert's pressure with the local pressure, the model can predict regions of possible formation of intergranular porosity. Calculations were performed on equiaxed Ni-base superalloy (IN718) plate castings. The potential to form microporosity was analyzed with different variables including the mass transfer of hydrogen and nitrogen from the casting to the casting/mold gap, the final grain size, a grain-shape parameter and the thickness of the plate casting. The most important factor was found to be the mass transfer coefficient. The results were also affected by the final grain size and grain-shape parameter. © 2001 Elsevier Science B.V.
• Felicelli, S. D., Poirier, D. R., & Sung, P. K. (2000). A model for prediction of pressure and redistribution of gasforming elements in multicomponent casting alloys. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science, 31(6), 1283-1292.
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  Abstract: A finite element model for simulating macrosegregation in multicomponent alloys is extended to include the calculation of pressure and redistribution of gas-forming elements during solidification. The model solves the conservation equations of mass, momentum, energy, and alloy components, including gas-forming elements such as hydrogen and nitrogen. The results of transport calculations are contrasted with thermodynamic equilibrium conditions to establish the possible formation of pores, assuming that there is no barrier to nucleation of the pores. By solving the transport of gaseous solutes and comparing their Sievert's pressure with the local pressure, the new model can predict regions of possible formation of intergranular porosity. Simulations were performed for a nickel-base alloy (INCONEL 718) in plate castings with equiaxed structure, and the evolution of microporosity for different initial concentrations of hydrogen and nitrogen was analyzed. The simulations showed that during solidification and cooling, a large fraction of the hydrogen escapes and a smaller fraction of nitrogen escapes from the casting. The initial gas concentration is an important factor in porosity formation, but the pressure drop due to shrinkage flow is not very significant. The resulting gas porosity is rather insensitive to initial nitrogen concentration, but sensitive to the concentration of hydrogen.
• Frueh, C., Poirier, D. R., & Felicelli, S. D. (2000). Effect of computational domain size on the mathematical modeling of transport processes and segregation during directional solidification. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 31(12), 3129-3135.
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  Abstract: Using a finite-element simulator, a directionally solidified hypoeutectic Pb-Sn alloy was modeled in two dimensions to determine the effect of the height of the overlying liquid on convective transport and macrosegregation. It was determined that, while the strength of the convection in the overlying liquid depends on the square root of its height, one need not model the entire domain to predict freckling. Furthermore, the assumption of a constant thermal gradient in the liquid causes the predicted convection to be somewhat weaker than the convection in the temperature field used in directional solidification processing.
• Poirier, D. R., Heinrich, J. C., Erdmann, R. G., & Bhat, M. S. (2000). Permeability for flow through equiaxed-dendritic alloys. Proceedings of the Merton C. Flemings Symposium on Solidification and Materials Processing, 287-296.
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  Abstract: The permeability for flow of intergranular liquid through fixed equiaxed grains was calculated for volume fraction of liquid in the range of 0.40 to 0.932. These permeabilities were obtained by calculation in order to augment empirical data which are restricted to volume fraction of liquid less than 0.48. The calculated permeabilities are based on calculated flow in actual microstructures of equiaxed grains, obtained by quenching during early stages of solidification. A special method of processing the images of the microstructures and of building a finite-element mesh was adopted to effect the calculations of two-dimensional flows. Permeabilities extracted from the two-dimensional flows were corrected for three-dimensional flows by deducing the ratio of the permeability for three-dimensional flows through random arrays of uniform spheres to the permeabilities for two-dimensional flows past the circles formed by a plane intersecting randomly placed spheres. The permeabilities are given in nondimensional form by selecting the reciprocal of the specific area of the solid (Sv-1) as the characteristic length scale of the microstructure. These calculated permeabilities are combined with empirically measured permeabilities and results from sedimentation experiments to make a set of 82 data and regressions for calculating permeability as a function of fraction solid and Sv-1.
• Zhang, B., Chen, W., & Poirier, D. R. (2000). Effect of solidification cooling rate on the fatigue life of A356.2-T6 cast aluminium alloy. Fatigue and Fracture of Engineering Materials and Structures, 23(5), 417-423.
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  Abstract: The effect of the cooling rate during solidification on the fatigue life of a cast aluminium alloy (A356.2-T6) is examined. The fatigue lives were determined for specimens removed from ingots with a gradient in cooling rates along their heights. Low- and high-cycle fatigue tests were conducted under both axial loading and reciprocating-bending conditions at a stress (strain) ratio (R) of -1.0, 0.1 and 0.2. Results show that the fatigue life decreases by a factor of three in low-cycle fatigue (R = -1.0) and by a factor of 100 in high-cycle fatigue (R = 0.1) as solidification cooling rate decreases from ∼10 to ∼0.3 Ks-1, as indicated by measurements of the secondary dendrite arm spacings in the ingots. Fatigue cracks initiated from porosity in the material solidified at slower cooling rates. When pore size is below a critical size of ∼80 μm, as a result of increasing the cooling rate, the fatigue cracks initiated from near-surface eutectic-microconstituent. When present at or near the surface, large oxide inclusions initiated fatigue cracks. © 2000 Blackwell Science Ltd.
• Mcbride, E., Heinrich, J. C., & Poirier, D. R. (1999). Numerical simulation of incompressible flow driven by density variations during phase change. International Journal for Numerical Methods in Fluids, 31(5), 787-800.
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  Abstract: A change in density during the solidification of alloys can be an important driving force for convection, especially at reduced levels of gravity. A model is presented that accounts for shrinkage during the directional solidification of dendritic binary alloys under the assumption that the densities of the liquid and solid phases are different but constant. This leads to a non-homogeneous mass conservation equation, which is numerically treated in a finite element formulation with a variable penalty coefficient that can resolve the velocity field correctly in the all-liquid region and in the mushy zone. The stability of the flow when shrinkage interacts with buoyancy flows at low gravity is examined.
• Sung, P. K., & Poirier, D. R. (1999). Liquid-solid partition ratios in nickel-base alloys. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 30(8), 2173-2181.
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  Abstract: The equilibrium partition ratios of Al, Ta, and Cr in Ni-rich alloys of the Ni-Al-Ta-Cr system were experimentally determined by isothermally holding at a temperature in the liquid/solid range of the alloys followed by quenching. The partition ratios apply to equilibria between melts and γ phase (fcc) in the range of 1615 to 1694 K. It was found that the equilibrium partition ratios in this system depend mainly on the concentration of Ta. The equilibrium partition ratio of Ta varies from approximately 0.6 at dilute Ta to 0.85 at 17 wt pct Ta. For the same range of Ta contents, less variability is seen in the partition ratios of Al and Cr, which range from about 0.92 to 0.96. In addition to the partition ratios, the liquidus temperatures of the liquid in equilibrium with γ in the Ni-Al-Ta-Cr system were estimated with a multidimensional regression analysis. The experimental results reported herein are complemented by a compilation of partition ratios of many solutes in binary and multicomponent Ni-base alloys.
• Zhang, B., Poirier, D. R., & Chen, W. (1999). Microstructural effects on high-cycle fatigue-crack initiation in A356.2 casting alloy. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 30(10), 2659-2666.
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  Abstract: The effects of various microconstituents on crack initiation and propagation in high-cycle fatigue (HCF) were investigated in an aluminum casting alloy (A356.2). Fatigue cracking was induced in both axial and bending loading conditions at strain/stress ratios of -1, 0.1, and 0.2. The secondary dendrite arm spacing (SDAS) and porosity (maximum size and density distribution) were quantified in the directionally solidified casting alloy. Using scanning electron microscopy, we observed that cracks initiate at near-surface porosity, at oxides, and within the eutectic microconstituents, depending on the SDAS. When the SDAS is greater than ∼ 25 to 28 μm, the fatigue cracks initiate from surface and subsurface porosity. When the SDAS is less than ∼ 25 to 28 μm, the fatigue cracks initiate from the interdendritic eutectic constituents, where the silicon particles are segregated. Fatigue cracks initiated at oxide inclusions whenever they were near the surface, regardless of the SDAS. The fatigue life of a specimen whose crack initiated at a large eutectic constituent was about equal to that when the crack initiated at a pore or oxide of comparable size.
• Apprill, J. M., Poirier, D. R., Maguire, M. C., & Gutsch, T. C. (1998). GASAR porous metals process control. Materials Research Society Symposium - Proceedings, 521, 291-296.
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  Abstract: GASAR porous metals are produced by melting under a partial pressure of hydrogen and then casting into a mold that ensures directional solidification. Hydrogen is driven out of solution and usually grows as quasi-cylindrical pores normal to the solidification front. Experiments with pure nickel have been carried out under processing conditions of varying H2 partial pressure, total pressure (H2 + Ar), and superheat. An analysis that considers heterogeneous bubble nucleation was developed that identifies processing conditions in which hydrogen bubbles are stable in the liquid before solidification. It is hypothesized that these conditions lead to low porosity because these bubbles float out of the melt and 'escape' the advancing solidification front. Experimental data are shown to support this hypothesis.
• Chen, W., Zhang, B., Wu, T., Poirier, D., Sung, P., & Fang, Q. T. (1998). Microstructure dependence of fatigue life for A356.2. TMS Annual Meeting, 99-113.
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  Abstract: Fatigue life of a cast aluminum alloy (A356.2) was measured in specimens removed from ingots with a gradient of microstructures. The variation of microstructures in an ingot, quantified by the secondary dendrite arm spacing (DAS), was controlled by varying the cooling rate along the ingot height during solidification. Low- and high-cycle, completely reversal fatigue tests were conducted under both axial and reciprocating bending loading conditions. Experimental results indicated that secondary dendrite arm spacing was closely related to the total fatigue life which decreased at least three times as DAS increased from 15 μm to 50 μm. Fatigue cracks initiated from near-surface eutectic regions in microstructures with fine DAS, whereas porosity became the dominate crack initiation site for microstructures with large DAS. Secondary cracks interacted with the dominant fatigue crack under both low- and high-cycle fatigue.
• Felicelli, S. D., Heinrich, J. C., & Poirier, D. R. (1998). Finite element analysis of directional solidification of multicomponent alloys. International Journal for Numerical Methods in Fluids, 27(1-4 Special Issu), 207-227.
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  Abstract: A finite element model of dendritic solidification of multicomponent alloys is presented that includes solutal convection and is an extension of a previously developed model for solidification of binary alloys. The model is applied to simulation of the solidification of ternary and quaternary Ni-based alloys. The role of solutal convection in the macrosegregation and the formation of freckles is analysed. Calculations shows the effects of geometry and material properties on the convection patterns and the attendant segregation.
• Felicelli, S. D., Heinrich, J. C., & Poirier, D. R. (1998). Three-dimensional simulations of freckles in binary alloys. Journal of Crystal Growth, 191(4), 879-888.
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  Abstract: A tridimensional finite-element model was developed to calculate the thermosolutal convection and macrosegregation during the solidification of dendritic alloys. A single set of conservation equations is solved in the mushy zone, all-liquid, and all-solid regions without internal boundary conditions. The model is applied to simulate the directional solidification of a Pb-Sn alloy in cylinders of square and circular cross section. The calculations are started from an all-liquid state and the evolution of convection, solute and energy transport, and the mushy zone growth are followed in time. The results show details of the channels, which result in freckles, that are not observable in existing two-dimensional simulations. Several qualitative features of channels and freckles previously observed in experiments with transparent systems, like chimney convection, preference of channels to be on surfaces, and enhanced solid growth at the channel mouth ("volcanoes") are successfully reproduced. © 1998 Elsevier Science B.V. All rights reserved.
• Felicelli, S. D., Poirier, D. R., & Heinrich, J. C. (1998). Modeling freckle formation in three dimensions during solidification of multicomponent alloys. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science, 29(4), 847-855.
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  Abstract: The formation of macrosegregation defects known as "freckles" was simulated using a three-dimensional finite element model that calculates the thermosolutal convection and macrosegregation during the dendritic solidification of multicomponent alloys. A recently introduced algorithm was used to calculate the complicated solidification path of alloys of many components, which can accommodate liquidus temperatures that are general functions of liquid concentrations. The calculations are started from an all-liquid state, and the growth of the mushy zone is followed in time. Simulations of a Ni-Al-Ta-\V alloy were performed on a rectangular cylinder until complete solidification. The results reveal details of the formation of freckles not previously observed in two-dimensional simulations. Liquid plumes in the form of chimney convection emanate from channels within the mushy zone, with similar qualitative features previously observed in transparent systems. Associated with the formation of channels, there is a complex three-dimensional flow produced by the interaction of the different solutal buoyancies of the alloy solutes. Regions of enhanced solid growth develop f around the channel mouths, which are visualized as volcanoes on top of the mushy zone. The prediction of volcanoes differs from our previous calculations with multicomponent alloys in two dimensions, in which the volcanoes were not nearly as apparent. These and other features of freckle formation phenomena are illustrated.
• Felicelli, S. D., Sung, P. K., Poirier, D. R., & Heinrich, J. C. (1998). Transport properties and transport phenomena in casting nickel superalloys. International Journal of Thermophysics, 19(2-6), 1657-1669.
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  Abstract: Nickel superalloys that are used in the high-temperature regions of gas-turbine engines are cast by directional solidification (DS). In the DS processes, the castings are cooled from below, and three zones exist during solidification: (1) an all-solid zone at the bottom, (2) a "mushy zone" that is comprised of solid and liquid material, and (3) an overlying all-liquid zone. Computer simulations can be useful in predicting the complex transport phenomena that occur during solidification, but realistic simulations require accurate values of the transport properties. In addition to transport properties, the thermodynamic equilibria between the solid and liquid during solidification must also be known with reasonable accuracy. The importance of using reasonably accurate estimations of the transport properties is illustrated by two-dimensional simulations of the convection during solidification and the coincidental macrosegregation in the DS castings of multicomponent Ni-base alloys. In these simulations, we examine the sensitivity of the calculated results to measured partition ratios, thermal expansion coefficients, and viscosities that are estimated by regression analyses and correlations of existing property data. © 1998 Plenum Publishing Corporation.
• Poirier, D. R., Yin, H., Suzuki, M., & Emi, T. (1998). Interfacial Properties of Dilute Fe-O-S Melts on Alumina Substrates. ISIJ International, 38(3), 229-238.
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  Abstract: Compilations and data pertaining to the wettability and interfacial properties of Fe-melts and dilute Fe-O-S alloys on alumina substrates have been collected and compared. The properties included the surface tension of liquid Fe; the surface tension of Al2O3; measurements of work of adhesion and contact angles; and the effects of sulfur and oxygen on the surface tension of liquid Fe and on the contact angle. Based on the comparisons, recommendations for estimating these interfacial properties as well as the tension of the Fe-O-S (liquid)/Al2O3 interface are given.
• Shibata, H., Poirier, D. R., & Emi, T. (1998). Modeling the Behavior of AI₂O₃ Inclusions during the Dendritic Solidification of Steel. ISIJ International, 38(4), 339-347.
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  Abstract: Starting with a distribution of single-particle alumina inclusions, estimates of their collision frequencies and the number concentrations of two- and three-particle clusters in the interdendritic liquid during solidification were made. The alumina clusters possibly serve as pore-nucleation sites, so their number concentrations that form during solidification are of interest. We also show that the smaller alumina inclusions are not entrapped in the dendritic solid during solidification, based on estimates of the interdendritic solidification rates and empirical data on the engulfment of AI2O3 inclusions by solidifying steel. Engulfment by the interdendritic liquid, however, is enhanced by the gradients of the concentrations of oxygen and sulfur in the interdendritic liquid during solidification. These elements are surface active on the liquid-steel/alumina interface and, in turn, introduce very strong capillary forces on the interdendritic alumina inclusions.
• Sung, P. K., & Poirier, D. R. (1998). Estimation of densities and coefficients of thermal expansion of solid Ni-base superalloys. Materials Science and Engineering A, 245(1), 135-141.
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  Abstract: To calculate the densities of solid Ni-base superalloys as functions of temperature and composition, lattice parameters of 18 alloys at 20°C and coefficients of thermal expansion (CTEs) of 17 alloys were estimated by combining available data. To estimate the lattice parameters of the alloys at 20°C, the changes in the lattice parameter of Ni caused by additions of the elements were simply summed to get the lattice parameters of alloys. This procedure results in calculated densities that are < 1% in error for all 18 alloys. For the densities of the alloys at an elevated temperature, the CTEs were then estimated. The CTEs of the 17 Ni-base alloys were gathered and regressed to yield the CTE as a function of temperature and composition. The CTEs calculated from the regressions are < 10% in error for all 17 alloys at 400, 700, 1000 and 1300 K. These errors of the CTEs also result in densities that are within 0.5% error or less in the overall temperature range. © 1998 Elsevier Science S.A. All rights reserved.
• Felicelli, S. D., Poirier, D. R., & Heinrich, J. C. (1997). Macrosegregation patterns in multicomponent Ni-base alloys. Journal of Crystal Growth, 177(1-2), 145-161.
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  Abstract: A mathematical model of the dendritic solidification of multicomponent alloys, that includes thermosolutal convection and macrosegregation, is presented. The model is an extension of one previously developed for binary alloys. Numerical simulations are given for ternary and quaternary Ni-base alloys, and the evolution of macrosegregation during solidification is studied. The results show that the segregation patterns vary greatly with cooling conditions, adopting several shapes and levels of intensity. Calculations of segregation in rectangular molds and in molds with smooth and abrupt variations of the cross sections exhibit significant differences in the distribution of macrosegregation due to the change in geometry. In addition, the segregation patterns are found to be particularly sensitive to the values of the equilibrium partition coefficients of the alloy components.
• Felicelli, S. D., Poirier, D. R., Giamei, A. F., & Heinrich, J. C. (1997). Simulating convection and macrosegregation in superalloys. JOM, 49(3), 21-25.
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  Abstract: Numerical simulations using a mathematical model of the dendritic solidification of multicomponent alloys that includes thermosolutal convection and macrosegregation were conducted on nickel-based alloys. The results show that segregation patterns vary greatly with cooling conditions, adopting several shapes and levels of intensity. In addition, the segregation patterns are particularly sensitive to the values of the equilibrium partition coefficients of the alloy components.
• Frueh, C., Poirier, D. R., & Maguire, M. C. (1997). The effect of silica-containing binders on the titanium/face coat reaction. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science, 28(5), 919-926.
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  Abstract: The interactions of CP-Ti and Ti-6Al-4V with investment molds containing alumina/silica and yttria/silica face coat systems were studied. "Containerless" melting in argon was employed and small test samples were made by drop casting into the molds. The effects of the face coat material and mold preheat temperatures on the thickness of the alpha case in the drop castings were evaluated with microhardness and microprobe measurements. It was found that the thickness of the alpha case was the same, whether a yttria/silica or alumina/silica face coat was used, indicating that the silica binder can reduce the apparent inertness of a more stable refractory, such as yttria. It was also found that the alloyed titanium castings had a thinner alpha case than those produced from CP-Ti, which suggests that the thickness of the alpha case depends on the crystal structure of the alloy during cooling from high temperatures. Furthermore, the small drop castings made in small yttria crucibles used as molds exhibited little or no alpha case.
• Poirier, D. R., & McBride, E. (1997). Thermal conductivities of hypoeutectic Al-Cu alloys during solidification and cooling. Materials Science and Engineering A, 224(1-2), 48-52.
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  Abstract: The thermal conductivity of hypoeutectic Al-Cu alloys during solidification and cooling was estimated by combining available data on electrical resistivity and thermal conductivity. To estimate the thermal conductivity of the solid alloys, the Smith-Palmer equation was used. This equation enables one to closely estimate the thermal conductivities from known data on electrical conductivities. The electrical resistivities of Al-Cu melts were also gathered. The Smith-Palmer equation was tested successfully for pure Al-melt and assumed to apply to Al-Cu melts, so that their thermal conductivities - could be estimated. Finally simple-mixture models were applied to estimate the electrical resistivities and thermal conductivities of the alloys during solidification. © 1997 Elsevier Science S.A.
• Sung, P. K., Poirier, D. R., & McBride, E. (1997). Estimating densities of liquid transition-metals and Ni-base superalloys. Materials Science and Engineering A, 231(1-2), 189-197.
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  Abstract: To estimate the densities of liquid Ni-base superalloys, the densities and temperature coefficients of density (dρ/dT) of the liquid transition-metals, which are used as alloy elements in Ni-base superalloys, were gathered, reviewed, and applied to a simple correlation. The correlation is particularly useful to estimate dρ/dT of many transition-metals for which there are no data available. To demonstrate how the results can be applied, the densities of liquid Ni-rich Ni-Al-Cr-Ta alloys were considered and regressed to yield the liquid density as a function of temperature and composition. As a verification of this approach, the liquid densities of five Ni-base superalloys were also estimated. By including a regression estimate of the molar mixing volume, the estimates of the liquid densities agreed with the measured values to ±2.5%. © 1997 Elsevier Science S.A.
• Frueh, C., Poirier, D. R., Maguire, M. C., & Harding, R. A. (1996). Attempts to develop a ceramic mould for titanium casting - A review. International Journal of Cast Metals Research, 9(4), 233-239.
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  Abstract: Although past efforts in universities, government laboratories and industry have tried many materials in an attempt to find a mould suitable for casting titanium alloys, no ceramic mould that is completely resistant to titanium has been developed. Because much of this work was conducted more than 30 years ago and because much data are recorded in difficult-to-find government reports, investigators can and have unknowingly repeated past experiments. This review, therefore, serves as a reference for future mould developers and will hopefully encourage renewed interest in a problem which, if solved, could have a tremendous impact on the titanium casting industry.
• Heinrich, J. C., Poirier, D. R., & Nagelhout, D. F. (1996). Mesh generation and flow calculations in highly contorted geometries. Computer Methods in Applied Mechanics and Engineering, 133(1-2), 79-92.
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  Abstract: We present a method to define the solid-liquid boundaries in complex dendritic geometries and construct finite element meshes using quadrilateral isoparametric elements. Calculations of flow at low Reynolds numbers through the dendritic network are also performed. The results of the calculations are used to estimate the average pressure drop as a function of the fraction of liquid in the region, from which permeabilities can be obtained to model the full domain as a porous medium.
• Huang, H. -., Heinrich, J. C., & Poirier, D. R. (1996). Technical note: Numerical anomalies in simulating directional solidification of binary alloys. Numerical Heat Transfer; Part A: Applications, 29(6), 639-644.
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  Abstract: In a numerical model of the directional solidification of a binary alloy, unreasonable results and/or oscillatory values of the concentration can occur when simulations of solidification scenarios with large thermal gradients approaching plane front conditions are attempted.
• Huang, H. W., Heinrich, J. C., & Poirier, D. R. (1996). Simulation of directional solidification with steep thermal gradients. Modelling and Simulation in Materials Science and Engineering, 4(3), 245-259.
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  Abstract: The convection and macrosegregation predicted by a simulation of a directionally solidified binary alloy (Pb-23.2 wt%Sn) are presented, and the simulated macrosegregation is compared with the macrosegregation in an experimental casting. The casting was solidified at a rate of 6 μm s-1 and a thermal gradient of approximately 7.2 × 103 K m-1; such thermal gradients are much greater than those previously simulated. The calculated results showed channels at the vertical casting surfaces and segregated internal pockets in the mushy zone, in agreement with the observation of freckles in the experimental casting.
• Ocansey, P. M., & Pourier, D. R. (1996). Equilibrium partition ratios of C, Mn, and Si in a high carbon steel. Materials Science and Engineering A, 211(1-2), 10-14.
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  Abstract: As part of a program to study solid-liquid equilibria in continuously cast steels, the equilbrium partition ratios of C, Mn and Si between solid (austenite) and liquid Fe have been experimentally determined as a function of the solidification path in Fe-C-Mn-Si alloy (AISI 91125). The experimental results show that the partition ratios of Si and Mn depend on the solidification path. The partition ratio of Si decreases with temperature and increases as composition of carbon in the liquid increases. Specifically, as the concentration of carbon in the liquid changes from 1.37 to 2.72 wt.% C, the partition ratio of Si increases from 0.83 to 1.08. On the other hand, the partition of Mn increases with temperature but decreases with the carbon content in the liquid. The equilibrium partition ratio for C, however, showed little variation with temperature and composition of the liquid.
• Bhat, M. S., Poirier, D. R., & Heinrich, J. C. (1995). A permeability length scale for cross flow through model structures. Metallurgical and Materials Transactions B, 26(5), 1091-1092.
• Bhat, M. S., Poirier, D. R., & Heinrich, J. C. (1995). Permeability for cross flow through columnar-dendritic alloys. Metallurgical and Materials Transactions B, 26(5), 1049-1056.
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  Abstract: Experiments for measuring permeability in columnar-dendritic microstructures have provided data only up to a volume fraction of liquid of 0.66. Hence, the permeability for flow perpendicular to the primary dendrite arms in columnar-dendritic microstructures was calculated, extending our data base for permeability to volume fractions of liquid as high as 0.98. Analyses of the dendritic microstructures were undertaken first by detecting the solid-liquid interfaces with a special computer program and then by generating a mesh for a finite-element fluid flow simulation. Using a Navier-Stokes solver, the velocity and pressure at the nodes were calculated at the microstructural level. In turn, the average pressure gradient was used to calculate the Darcy permeability. Permeabilities calculated by this versatile technique provided data at high volume fractions of liquid that merged with the empirical data at the lower volume fractions. © 1995 THE MINERALS, METALS & MATERIALS SOCIETY and ASM INTERNATIONAL.
• Liu, S. H., Poirier, D. R., & Ocansey, P. N. (1995). Electrical resistivity of pb and pb-10 wt pct sn during solidification. Metallurgical and Materials Transactions A, 26(3), 741-745.
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  Abstract: The electrical resistivities of Pb and Pb-10 wt pct Sn alloy were measured during cooling and solidification. Three regimes corresponding to events when the metals were all liquid, liquid plus solid, and all solid were eminent. In particular, the nucleation and growth of the solid were captured by measuring the electrical resistivity. The resistivities of the liquid at the nucleation temperature of lead and of Pb-10 wt pct Sn are 94.7 and 85.7 μΩ. cm, respectively, and nucleation in these systems occurred at 326.9 °C and 301 °C, respectively. In lead, it was found that the ratio of resistivity of the liquid at the melting temperature to the resistivity of the solid was 1.92. The resistivity data were used to estimate the mass fraction of solid as a function of temperature during solidification. The method of measuring resistivity and temperature or the models for predicting electrical resistivity of two-phase mixtures should be improved before this method can be made quantitative. © 1995 The Minerals, Metals & Material Society.
• Nagelhout, D., Bhat, M. S., Heinrich, J. C., & Poirier, D. R. (1995). Permeability for flow normal to a sparse array of fibres. Materials Science and Engineering A, 191(1-2), 203-208.
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  Abstract: Solutions for flow normal to an array of fibers (visualized as circular cylinders) arranged in a square array were determined using a finite element formulation. The calculated results were used to obtain the permeability for flow through the system with as little as 0.01 volume fraction solid and for a Reynolds number up to 40. These results can be used to estimate permeabilities for infiltrating fiber composites or for modeling the solidification of dendritic alloys with transport phenomena in porous media. © 1995.
• Bhat, M. S., Poirier, D. R., Heinrich, J. C., & Nagelhout, D. (1994). Permeability normal to columnar dendrites at high fraction liquid. Scripta Metallurgica et Materiala, 31(3), 339-344.
• Poirier, D. R., & Heinrich, J. C. (1994). Continuum model for predicting macrosegregation in dendritic alloys. Materials Characterization, 32(4), 287-298.
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  Abstract: "Macrosegregation" represents a class of defects in cast products of serious concern to both alloy producers and users. Many types of macrosegregation result from thermosolutal convection in the solid plus liquid and all-liquid regions of a solidifying alloy, and this has spurred modeling and simulations, which treat the solid plus liquid region (i.e., the mushy zone) as a porous medium of variable porosity and permeability. Simulations include scenarios in which the convection is strong enough to make channels in the mushy zone region, and these channels lead to localized segregates known as "freckles". Using Pb-10 wt.% Sn as a model alloy, we simulated vertical solidification with various solidification rates. By sufficiently increasing the cooling rate at the bottom surface, convection can be suppressed enough to prevent the formation of freckles. The simulation is an example of relating microstructural metrics to a macroscopic property of the porous medium used in continuum theory. In this case, the property is the permeability, which is governed by two microstructural metrics: the volume fraction of liquid and a characteristic length in the dendritic microstructure. Permeability data, relevant to columnar dendritic solidification, are reviewed, and recommendations for future work on determining the permeability in terms of microstructural metrics are given. © 1994.
• Poirier, D. R., & Ocansey, P. (1993). Permeability for flow of liquid through equiaxial mushy zones. Materials Science and Engineering A, 171(1-2), 231-240.
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  Abstract: An experimental method for measuring the permeability for flow through equiaxial mushy zones of PbSn alloys was devised. With PbSn alloys, dendritic structures could be maintained during the permeability tests. The volume fraction of liquid was varied from 0.31 to as high as 0.49. With the results presented as dimensionless permeabilities, reasonably good agreement among globular, dendritic-globular, and dendritic microstructures was obtained for previous data on borneol-paraffin and Al-15.6wt.%Cu alloys, and the PbSn alloys studied herein. The empirical data agree approximately with the analytical results for flow through regular arrays of spheres, which suggests that the analytical results can be used for extrapolations of permeability when gL > 0.49. © 1993.
• Ganesan, S., Chan, C. L., & Poirier, D. R. (1992). Permeability for flow parallel to primary dendrite arms. Materials Science and Engineering A, 151(1), 97-105.
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  Abstract: The permeability for the flow of interdendritic liquid parallel to primary dendrite arms in columnar structures was calculated using the boundary element method for fully developed flow. The permeability was calculated because when the volume fraction of liquid (gL)exceeds approximately 0.60 -0.65, experiments fail. The calculated results, based on the microstructures of directionally solidified alloys, agreed with analytical results for flow parallel to circular cylinders arranged in square and triangular arrays. It appears that there is a transition in the behavior of the permeability at gL ≈ 0.65. © 1992.
• Poirier, D. R., & Ganesan, S. (1992). Permeabilities for flow of interdendritic liquid in equiaxial structures. Materials Science and Engineering A, 157(1), 113-123.
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  Abstract: Permeabilities for the flow of interdendritic liquid in Al-15.6wt.%Cu alloy with equiaxial structures were measured and found to be structure sensitive. The center-to-center distance between grains (153-259 μm), specific surface area (2.57 × 10-2-6.96 × 10-1 μm-1) and volume fraction of liquid (0.166-0.434) were the structural parameters studied in this investigation. During a test, coarsening of the dendrites occurred, wherein the solid morphology went from dendritic to dendritic-globular and ultimately to globular for longer times. The permeabilities of the globular structures (non-dendritic) were found to be approximately one order of magnitude greater than the permeabilities for the dendritic-globular structures, when the volume fraction of liquid is approximately 0.3. The dimensionless permeability, based on the specific surface, was found to represent best the empirical data for the globular and dendritic morphologies and the theoretical results for flow through different arrays of uniform spheres. © 1992.
• Poirier, D. R., & Heinrich, J. C. (1992). Simulation of solidification of dendritic alloys with a porous media model. American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD, 206-2, 167-174.
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  Abstract: 'Macrosegregation' represents a class of defects in cast products and is of serious concern to both alloy producers and users. Most types of macrosegregation result from thermosolutal convection that takes place in the solid plus liquid and all-liquid regions of a solidifying alloy. Mathematical modeling of convection in solidifying alloys has been done since about 1970, but only in the past five years has analysis of thermosolutal convection been incorporated into solidification theory. This has resulted in simulations, which treat the solid plus liquid region as a porous medium of variable porosity and permeability. Simulations include scenarios in which the convection is strong enough to make channels in the solid plus liquid region, and these channels are responsible for making localized segregates known as 'freckles.' Using Pb-10 wt pct Sn as a model alloy, we simulated vertical solidification with two different solidification rates; both exhibited freckles. By an increase of the cooling rate at the bottom surface, convection was suppressed for the first minute of solidification, but thereafter the convection was sufficient to cause the formation of freckles.
• Felicelli, S. D., Heinrich, J. C., & Poirier, D. R. (1991). Simulation of freckles during vertical solidification of binary alloys. Metallurgical Transactions B, 22(6), 847-859.
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  Abstract: A mathematical model of solidification that simulates the formation of channel segregates or freckles is presented. The model simulates the entire solidification process starting with the initial melt to the solidified cast, and the resulting segregation is predicted. Emphasis is given to the initial transient, when the dendritic zone begins to develop and the conditions for the possible nucleation of channels are established. The mechanisms that lead to the creation and eventual growth or termination of channels are explained in detail and illustrated by several numerical examples. Predictions of the pattern and location of channels in different cooling situations are in good agreement with experimental observations. © 1991 The Minerals, Metals & Material Society.
• Heinrich, J. C., Felicelli, S., & Poirier, D. R. (1991). Vertical solidification of dendritic binary alloys. Computer Methods in Applied Mechanics and Engineering, 89(1-3), 435-461.
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  Abstract: This paper addresses the effect of thermosolutal convection in the formation of defects in directionally solidified (DS) alloys. Three different models have been used as the basis for numerical simulations of the solidification process, and all use the Boussinesq approximation. In increasing order of complexity, the three are the plane-front model, an extension of the plane-front model that includes a dendritic region with a time-independent volume fraction of liquid, and a model where the dendritic region is free to develop according to local equilibrium conditions and that is capable of predicting channel segregates or freckles. Finite element models of thermosolutal convection have been developed for all three cases and have been used to investigate nonlinear convection when the systems are unstable. The dendritic or mushy region is treated as a porous medium with variable porosity; the algorithm is based on a Petrov-Galerkin and penalty function formulation using the four-noded bilinear Lagrangian element with reduced integration of the penalty term. Calculations are presented for lead-tin alloys at different concentrations of tin and for various temperature gradients. Also shown are calculations in which freckles develop in DS alloys - the first of their kind. The results of the numerical calculations are discussed and compared to experimental observations and other theoretical analyses. © 1991.
• Nandapurkar, P. J., Poirier, D. R., & Heinrich, J. C. (1991). Momentum equation for dendritic solidification. Numerical Heat Transfer; Part A: Applications, 19(3), 297-311.
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  Abstract: For analyzing dendritic solidification, convection in the mushy zone is based on a momentum equation for a porous medium with a spatially varying fraction of liquid. Results are compared with those obtained with a less complete momentum equation. Calculations are done for directional solidification, with isotherms and isoconcentrates that move with a constant velocity. Thermosolutal convection as a function of time is studied by perturbing the solutal field. The total kinetic energy, the nature of the convection cells, and the isoconcentrates are significantly different for the two models. Hence the complete form of the momentum equation should be used.
• Poirier, D. R., & Speiser, R. (1991). Surface tension of aluminumrich Al-Cu liquid alloys. Metallurgical Transactions A, 22(1), 1156-1160.
• Poirier, D. R., Ganesan, S., Andrews, M., & Ocansey, P. (1991). Isothermal coarsening of dendritic equiaxial grains in Al15.6wt.%Cu alloy. Materials Science and Engineering A, 148(2), 289-297.
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  Abstract: The isothermal coarsening of equiaxial dendritic grains in Al15.6wt.%Cu alloy at 826 K (5 K above the eutectic temperature) was studied. For very short times (less than 60 s), the structure ripened by the usual increase in the secondary dendrite arm spacing. The secondary arms also coalesced and liquid inclusions formed within the grains. Simultaneously there was some fragmentation, in that the average center-to-center distance λ between grains at first decreased and then, at approximately 400 s, λ increased chth time. For times greater than 900 s, λ increased very slowly, and the morphology of the grains changed from dendritic globular to globular, when the original dendritic structure was no longer discernible. Using the surface-area-to-volume ratio Sv of the solid as the characteristic metric, a kinetic analysis showed that Ostwald ripening could not explain the results. Coalescence was identified as a mechanism, but unlike previous work, a t- 1 3 dependence of Sv on time t was not observed. © 1991.
• Poirier, D. R., Nandapurkar, P. J., & Ganesan, S. (1991). The energy and solute conservation equations for dendritic solidification. Metallurgical Transactions B, 22(6), 889-900.
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  Abstract: The energy equation for solidifying dendritic alloys that includes the effects of heat of mixing in both the dendritic solid and the interdendritic liquid is derived. Calculations for Pb-Sn alloys show that this form of the energy equation should be used when the solidification rate is relatively high and/or the thermal gradients in the solidifying alloy are relatively low. Accurate predictions of transport phenomena in solidifying dendritic alloys also depend on the form of the solute conservation equation. Therefore, this conservation equation is derived with particular consideration to an accounting of the diffusion of solute in the dendritic solid. Calculations for Pb-Sn alloy show that the distribution of the volume fraction of interdendritic liquid g L in the mushy zone is sensitive to the extent of the diffusion in the solid. Good predictions of g L are necessary, especially when convection in the mushy zone is calculated. © 1991 The Minerals, Metals & Material Society.
• Ganesan, S., & Poirier, D. R. (1990). Conservation of mass and momentum for the flow of interdendritic liquid during solidification. Metallurgical Transactions B, 21(1), 173-181.
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  Abstract: In this paper, mass and momentum conservation equations are derived for the flow of interdendritic liquid during solidification using the volume-averaging approach. In this approach, the mushy zone is conceived to be two interpenetrating phases; each phase is described with the usual field quantities, which are continuous in that phase but discontinuous over the entire space. On the microscopic scale, the usual conservation equations along with the appropriate interfacial boundary conditions describe the state of the system. However, the solution to these equations in the microscopic scale is not practical because of the complex interfacial geometry in the mushy zone. Instead, the scale at which the system is described is altered by averaging the microscopic equations over some representative elementary volume within the mushy zone, resulting in macroscopic equations that can be used to solve practical problems. For a fraction of liquid equal to unity, the equations reduce to the usual conservation equations for a single-phase liquid. It is also found that the resistance offered by the solid to the flow of interdendritic liquid in the mushy zone is best described by two coefficients, namely, the inverse of permeability and a second-order resistance coefficient. For the flow in columnar dendritic structures, the second-order coefficient along with the permeability should be evaluated experimentally. For the flow in equiaxial dendritic structures (i.e., isotropic media), the inverse of permeability alone is sufficient to quantify the resistance offered by the solid. © 1990 The Minerals, Metals & Material Society.
• Ganesan, S., & Poirier, D. R. (1989). Solute redistribution in dendritic solidification with diffusion in the solid. Journal of Crystal Growth, 97(3-4), 851-859.
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  Abstract: An investigation of solute redistribution during dendritic solidification with diffusion in the solid has been performed using numerical techniques. The extent of diffusion in the solid during solidification is characterized by two parameters, namely the instantaneous and average diffusion parameters, respectively. These parameters are functions of the diffusion Fourier number, the partition ratio and the fraction solid. The diffusion Fourier number is that originally defined by Brody and Flemings; it is Dstf/ λ 2 with Ds = solute diffusivity in the solid, tf = local solidification time and λ = one-half of the characteristic dendrite arm spacing. The numerical results are presented as an approximate model, which is used to predict the average diffusion parameter. In turn, the average diffusion parameter can be used to calculate the composition of the interdendritic liquid during solidification in a simple manner. Also, an approximate model is presented to predict the solute distribution at the end of solidification. This result is put in a convenient form and is useful to those who wish to consider homogenization kinetics of as cast alloys. © 1989.
• Heinrich, J. C., Felicelli, S., Nandapurkar, P., & Poirier, D. R. (1989). Thermosolutal convection during dendritic solidification of alloys: Part II. Nonlinear convection. Metallurgical Transactions B, 20(6), 883-891.
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  Abstract: A mathematical model of thermosolutal convection in directionally solidified dendritic alloys has been developed that includes a mushy zone underlying an all-liquid region. The model assumes a nonconvective initial state with planar and horizontal isotherms and isoconcentrates that move upward at a constant solidification velocity. The initial state is perturbed, nonlinear calculations are performed to model convection of the liquid when the system is unstable, and the results are compared with the predictions of a linear stability analysis. The mushy zone is modeled as a porous medium of variable porosity consistent with the volume fraction of, interdendritic liquid that satisfies the conservation equations for energy and solute concentrations. Results are presented for systems involving lead-tin alloys (Pb-10 wt pct Sn and Pb-20 wt pct Sn) and show significant differences with results of plane-front solidification. The calculations show that convection in the mushy zone is mainly driven by convection in the all-liquid region, and convection of the interdendritic liquid is only significant in the upper 20 pct of the mushy zone if it is significant at all. The calculated results also show that the systems are stable at reduced gravity levels of the order of 10-4 g 0 (g 0=980 cm·s-1) or when the lateral dimensions of the container are small enough, for stable temperature gradients between 2.5≤G l≤100 K·cm-1 at solidification velocities of 2 to 8 cm·h-1. © 1989 The Minerals, Metals & Materials Society and ASM International.
• Nandapurkar, P., Poirier, D. R., Heinrich, J. C., & Felicelli, S. (1989). Thermosolutal convection during dendritic solidification of alloys: Part i. Linear stability analysis. Metallurgical Transactions B, 20(5), 711-721.
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  Abstract: This paper describes the simulation of thermosolutal convection in directionally solidified (DS) alloys. A linear stability analysis is used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. In the unperturbed and nonconvecting state . e.}, the basic state), isotherms and isoconcentrates are planar and horizontal. The mushy zone is realistically treated as a medium with a variable volume fraction of liquid that is con-sistent with the energy and solute conservation equations. The perturbed variables include tem-perature, concentration of solute, and both components of velocity in a two-dimensional system. As a model system, an alloy of Pb-20 wt pct Sn, solidifying at a velocity of 2 X 10-3 cm s-1 was selected. Dimensional numerical calculations were done to define the marginal stability curves in terms of the thermal gradient at the dendrite tips, G L, vs the horizontal wave number of the perturbed quantities. For a gravitational constant of 1 g, 0.5 g, 0.1 g, and 0.01 g, the marginal stability curves show no minima; thus, the system is never unconditionally stable. Nevertheless, such calculations quantify the effect of reducing the gravitational constant on reducing convection and suggest lateral dimensions of the mold for the purpose of suppressing convection. Finally, for a gravitational constant of 10-4 g, calculations show that the system is stable for the thermal gradients investigated (2.5 ≤G L ≤ 100 K-cm-1). © 1989 The Minerals, Metals & Material Society.
• Yeum, K. S., Laxmanan, V., & Poirier, D. R. (1989). Efficient estimation of diffusion during dendritic solidification. Metallurgical Transactions A, 20(12), 2847-2856.
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  Abstract: A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing our computed results to the results of an analytical solution derived by Kobayashi[4] for the as-sumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a par-abolic rate of the advancement of the solid/liquid interface. The flexibility of our method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy. © 1989 The Metallurgical Society of AIME.
• Yeum, K. S., Speiser, R., & Poirier, D. R. (1989). Estimation of the surface tensions of binary liquid alloys. Metallurgical Transactions B, 20(5), 693-703.
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  Abstract: A simple method to estimate the surface tensions of binary alloys has been developed by assuming that the partial molar excess free energies are proportional to the number of nearest neighbors in both the bulk solution and in the surface itself. In order to estimate the surface tension of the alloys, excess free energies of the alloys and the surface tensions of the pure components are required. This method has been applied to ten alloys exhibiting positive, positive as well as negative, and negative deviations from ideal solution behavior. The method depends upon the reliability of the thermodynamic data for the bulk solutions, and, further, it is important to use an interpolation scheme that is consistent with the Gibbs-Duhem requirement, when the thermodynamic data are presented in tabular form as a function of composition. To accomplish this interpolation, a special calculation technique is presented. © 1989 The Minerals, Metals & Material Society.
• Chen, J. -., Poirier, D. R., Damento, M. A., Demer, L. J., Biancaniello, F., & Cetas, T. C. (1988). Development of Ni-4 wt.% Si thermoseeds for hyperthermia cancer treatment. Journal of Biomedical Materials Research, 22(4), 303-319.
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  PMID: 3372551;Abstract: The thermoseeds were prepared by using either a special casting technique or casting and swaging followed by homogenization. The effects of these different processing schedules on the magnetic behavior of these alloys are discussed. In particular, the importance of minimizing oxidation during melting and heat treating, and the effects of homogenizing the thermoseeds on the relative permeability at temperatures near the Curie temperature are pointed out. The best processing schedule is casting small ingots while avoiding oxidation, followed by swaging, drawing, and homogenization. These thermoseeds can be used to obtain nearly uniform and constant temperatures in tumors with variable blood flows.
• Nandapurkar, P., & Poirier, D. R. (1988). Heat of mixing and morphological stability. Journal of Crystal Growth, 92(1-2), 88-96.
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  Abstract: A mathematical model, which incorporates heat of mixing in the energy balance, has been developed to analyze the morphological stability of a planar solid-liquid interface during the directional solidification of a binary alloy. It is observed that the stability behavior is almost that predicted by the analysis of Mullins and Sekerka at low growth velocities while deviations in the critical concentration of about 20-25% are observed under rapid solidification conditions for certain systems. Our calculations indicate that a positive heat of mixing makes the planar interface more unstable, whereas a negative heat of mixing makes it more stable, in terms of the critical concentration. © 1988.
• Poirier, D. R. (1988). Densities of Pb-Sn alloys during solidification. Metallurgical transactions. A, Physical metallurgy and materials science, 19 A(9), 2349-2354.
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  Abstract: Data for the densities and expansion coefficients of solid and liquid alloys of the Pb-Sn system are consolidated in this paper. More importantly, the data are analyzed with the purpose of expressing either the density of the solid or of the liquid as a function of its composition and temperature. In particular, the densities of the solid, during dendritic solidification are derived. Finally, the solutal and thermal coefficients of volume expansion for the liquid are given as functions of temperature and composition.
• Poirier, D. R., & Nandapurkar, P. (1988). Enthalpies of a binary alloy during solidification. Metallurgical transactions. A, Physical metallurgy and materials science, 19 A(12), 3057-3061.
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  Abstract: The purpose of the paper is to present a method of calculating the enthalpy of a dendritic alloy during solidification. The enthalpies of the dendritic solid and interdendritic liquid of alloys of the Pb-Sn system are evaluated, but the method could be applied to other binaries as well. The enthalpies are consistent with a recent evaluation of the thermodynamics of Pb-Sn alloys and with the redistribution of solute during dendritic solidification. Because of the heat of mixing in Pb-Sn alloys, the interdendritic liquid of hypoeutectic alloys (Pb-rich) of less than 50 wt pct Sn has enthalpies that increase as temperature decreases during solidification. For some concentrations of Sn, the enthalpy of the dendritic solid at the solid-liquid interface also increases with decreasing temperature during solidification. Of particular concern in formulating the energy equation is the fact that the heat of fusion during solidification increases as much as 80 pct for hypoeutectic alloys and decreases as much as 325 pct for hypereutectic alloys. Thus the often applied assumptions of a constant specific heat and/or a constant heat of solidification could lead to errors in numerical modeling of temperature fields for dendritic solidification processes.
• Ganesan, S., & Poirier, D. R. (1987). DENSITIES OF ALUMINUM-RICH ALUMINUM-COPPER ALLOYS DURING SOLIDIFICATION.. Metallurgical transactions. A, Physical metallurgy and materials science, 18 A(4), 721-723.
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  Abstract: Authors reevaluated the available data on the density of both the liquid- and solid-phases and to reduce them to a form suitable for our studies on the permeability for the flow of interdendritic liquid in partially melted alloys and for modeling macrosegregation phenomena in Al-Cu alloys. More generally, our results can be used to calculate the densities of the solid and liquid phases as functions of temperature and composition. To estimate the composition of the primary solid and hence its density, an assume that during dendritic freezing, the solute partitions according to the Scheil equation.
• Ganesan, S., & Poirier, D. R. (1987). Densities of aluminum-rich. Metallurgical Transactions A, 18(5), 721-723.
• Ganesan, S., Speiser, R., & Poirier, D. R. (1987). Viscosities of aluminum-rich Al-Cu liquid alloys. Metallurgical Transactions B, 18(2), 421-424.
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  Abstract: Viscosity data for Al-Cu liquid alloys in the ranges of 0≤C L≤33.1 wt pct Cu and 1173≤T ≤973 K are reviewed. It was found that Andrade's equation can be used to represent the variation of viscosity with temperature for a given composition, but that each of the two parameters in Andrade's equation shows no systematic variation with composition of the liquid-alloys. Consequently, arithmetic averages of the parameters were used and assumed to apply to all compositions in the range 0≤C L ≤33.1 wt pct Cu. Such a procedure implies that the viscosity happens to vary with composition solely because the specific volume varies with composition. In order to establish the predictability of extrapolating such simple behavior, a more complex model was considered. The latter model was recently presented by Kucharski and relates viscosity to the structure and thermodynamics of liquid alloys. Viscosities obtained by interpolating Andrade's equation and Kucharski's model compare closely; furthermore, values obtained by extrapolations to lower temperatures also compare favorably. Finally the simpler model was used to calculate the viscosity of the interdendritic liquid during solidification. © 1987 The Metallurgical Society and ASM INTERNATIONAL.
• Poirier, D. R. (1987). Permeability for flow of interdendritic liquid in columnar-dendritic alloys. Metallurgical Transactions B, 18(1), 245-255.
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  Abstract: Permeability data for the flow of interdendritic liquid in partially solid Pb-Sn and borneol-paraffin columnar-alloys are summarized. The data are used in regression analyses and simple flow models to arrive at relationships between permeability and the morphology of the solid dendrites. When flow is parallel to the primary dendrite arms, the important morphological aspects are the volume fraction liquid (g L) and the primary dendrite arm spacing (d 1). When flow is normal to the primary dendrite arms, the permeability depends upon the secondary dendrite arm spacing (d 2) as well as d 1 and g L. The parallel permeability is best described by a model based on the Hagen-Poiseuille law for laminar flow through a tube; for the normal permeability an empirical multilinear regression gives the best fit to the data. However, those models are not appropriate for extrapolations beyond the range of the available data (0.19≤g L≤0.66), particularly as g L approaches 1. For extrapolations, models based upon the Blake-Kozeny equation for flow through porous media are recommended. © 1987 The Metallurgical Society of American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., and American Society for Metals.
• Poirier, D. R., & Speiser, R. (1987). SURFACE TENSION OF ALUMINUM-RICH Al-Cu LIQUIDS ALLOYS.. Metallurgical transactions. A, Physical metallurgy and materials science, 18 A(6), 1156-1160.
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  Abstract: In order to model microporosity during soldification, the surface tension of the interdendritic liquid should be known. The surface tension is a function of both temperature and composition. This communication gives an example of treating surface tension data for a binary alloy based upon a thermodynamic model, then extrapolating the results to the lower temperatures within the solidification range of the alloy.
• Poirier, D. R., & Speiser, R. (1987). Surface tension of aluminumrich Al-Cu liquid alloys. Metallurgical Transactions A, 18(13), 1156-1160.
• Speiser, R., Poirier, D. R., & Yeum, K. (1987). Surface tension of binary liquid alloys. Scripta Metallurgica, 21(5), 687-692.
• Demer, L. J., Chen, J. -., Buechler, D. N., Damento, M. A., Poirier, D. R., & Cetas, T. C. (1986). FERROMAGNETIC THERMOSEED MATERIALS FOR TUMOR HYPERTHERMIA.. IEEE/Engineering in Medicine and Biology Society Annual Conference, 1448-1453.
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  Abstract: Ferromagnetic thermoseed materials with adequate thermal input and thermal regulation characteristics have been developed for hyperthermia treatments of localized tumors. Thermoseed encasement and coating techniques have been developed, and in vivo testing has demonstrated that they result in implants that are compatible with living tissues. The manner of obtaining biocompatibility for both short-term and long-term ferromagnetic implants is discussed. An in vivo example of the use of such thermoseeds and their behavior in a situation of variable blood flow is presented.
• C., S. L., & Poirier, D. R. (1985). STRUCTURE AND PROPERTIES OF THERMITE WELDS IN PREMIUM RAILS.. United States, Federal Railroad Administration, Office of Research and Development, (Report) FRA/O.
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  Abstract: Thermite welds were used to join combinations of premium rails and AREA Controlled Cooled Carbon rails (i. e. , standard rails). The premium rails comprised head-hardened rails and CrMo, CrV and Cr alloy rails. A major objective was to determine the feasibility of joining premium rails to each other and to standard rails with the thermite welding process. The objective was met in that metallurgically sound welds were produced using either 'standard' or 'alloy' thermite charges. Other objectives were to determine mechanical properties and metallurgical structures of the weld-metal and of the heat-affected zones. The 'alloy' weld-metal was stronger than 'standard' weld metal but had less tensile ductility. Both types exhibit ductilities of only 2-6 percent reduction in area and impact energies of only 1. 5-2. 8 Joules at 20 degree C. Tensile and impact specimens show tensile ductilities of 19-60 percent reduction in area and only 2. 6-6. 9 Joules for impact energy.
• Nasser-Rafi, R., Deshmukh, R., & Poirier, D. R. (1985). Flow of interdendritic liquid and permeability in pb-20 Wt Pct Sn alloys. Metallurgical Transactions A, 16(12), 2263-2271.
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  Abstract: Directionally solidified Pb-20 wt pct Sn alloys of uniform microstructures were produced with various primary and secondary dendrite arm spacings. Permeabilities of these alloys were investigated with approximately 0.19 and 0.29 volume fraction liquid, for flow parallel to the direction of primary dendrite arms. The permeabilities of the samples with approximately 0.19 volume fraction liquid were also obtained for flow normal to the primary dendrite arms. It was found that for flow parallel to the primary dendrite arms, permeability varied with d 1 2 and g L 2 (d1 is the primary arm spacing and gL is the volume fraction of liquid). There appears to be no relation between permeability for this parallel flow and the secondary dendrite arm spacing. For flow perpendicular to the primary dendrite arms, permeability is approximately 0.06 to 0.20 that for parallel flow, and in this case the permeability appears to be strongly dependent upon the secondary dendrite arm spacing. © 1985 The Metallurgical of Society of AIME.
• Maples, A. L., & Poirier, D. R. (1984). Convection in the two-phase zone of solidifying alloys. Metallurgical Transactions B, 15(1), 163-172.
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  Abstract: The analysis is applicable to alloy solidification which proceeds horizontally to the center of a mold. The model follows the growth of the solid-liquid zone adjacent to the chill face (the initial transient), the movement of the zone across the mold, and the region of final solidification adjacent to the centerline (the final transient). During solidification the density of the liquid varies across the twophase zone. Consequently, there is natural convection which is treated as flow through a porous medium. The equations for convection are coupled with the equation of solute redistribution between the phases in order to calculate macrosegregation after solidification is complete. Results were computed for alloys which show: (1) "inverse segregation≓ at a cooled-surface; (2) macrosegregation resulting from solidification with the initial transient, a period with a complete two-phase zone, and a final transient; and (3) macrosegregation when the width of the two-phase zone exceeds the semi-width of the mold. © 1984 The Metallurgical of Society of AIME.
• Schroeder, L. C., & Poirier, D. R. (1984). Improving the structure and properties of thermite weld metal. Materials Science and Engineering, 63(1), 23-33.
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  Abstract: In this study, normalizing thermite welds produced a significant improvement in the tensile ductility of the weld metal. For example, by normalizing weld metal with 0.55 wt.% C and 0.06 wt.% V, ductilities in the range 10%-20% reduction in area were achieved when the cooling rate exceeded 37 K min-1 through the transformation range, whereas the tensile ductility of "as-cast" thermite weld metal was only 2%-6% reduction in area. Tensile strengths comparable with those of the weld metal used in current practice were obtained together with the enhanced tensile ductility. In addition, attempts were made to filter the molten thermite steel by passing it through zirconia-mullite filters. These attempts were only partly successful in that the filters partially dissolved in this application; even so, the filters did reduce the inclusion content of the thermite weld metal. It was concluded that it is possible to produce more ductile thermite welds by judicious control of composition and the application of post-weld normalizing and that, with suitable ceramic filters, filtering could be employed to reduce the amount and sizes of inclusions in thermite weld metal. © 1984.
• Schroeder, L. C., & Poirier, D. R. (1984). The mechanical properties of thermite welds in premium alloy rails. Materials Science and Engineering, 63(1), 1-21.
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  Abstract: In this paper the results of an investigation into the properties of 13 thermite rail welds produced using CrMo, CrV and chromium alloy rails, American Railway Engineering Association controlled-cooled rails (i.e. standard rails) and heat-hardened rails are reported. Various combinations of the rails were joined with weld metal produced by the aluminothermic reaction of "standard" and "alloy" thermite charges. After welding, the hardness profiles, the tensile properties, the impact energies and the macrostructures and microstructures of the welds were determined. Detailed examinations of the microstructures of the heat-affected zones and of the weld metals revealed that the thermite welding process produced welds compatible with rail service in that no martensite was ever observed in any of the welds regardless of the rail composition or of the weld metal composition. Despite the absence of martensite, very low impact energies (1.5-2.8 J at 293 K) were measured in Charpy V-notch specimens removed from the weld metals. The weld metals also exhibited only a 2%-6% reduction in area for tensile ductility. Predictably, all the weld metal fracture surfaces showed brittle-type transgranular cleavage. It was also shown that alloy weld metal is harder and stronger than standard weld metal. Depending on the preheat time, the Rockwell C hardness of alloy weld metal is approximately 28-34 HRC whereas that of standard weld metal is 20-27 HRC. Correspondingly, the tensile strengths and yield strengths of alloy weld metal were about 100-150 MPa greater than those of standard weld metal. Also studied were the properties and structures of specimens which straddled the region of minimum hardness along the outer edge of the heat-affected zone. © 1984.
• Fujii, T., Poirier, D. R., & Flemings, M. C. (1982). COARSENING OF SiO//2 PARTICLES IN COPPER AND MnS INCLUSIONS IN STEEL.. Metallurgical transactions. A, Physical metallurgy and materials science, 13 A(12), 2143-2153.
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  Abstract: A model to simulate the diffusion-controlled coarsening and dissolution kinetics of particles within a metallic matrix is formulated. The change in size distribution of particles, average radius of particles, volume fraction, average distance between particles, surface area, and matrix composition are also calculated. Kinetics do not generally obey the Lifshitz-Slyozov-Wagner theory for diffusion controlled coarsening based upon concentration profiles around isolated spheres. Calculations are on silica particles in a copper matrix and manganese sulfide inclusions in iron, with emphasis on the latter, in order to predict behavior during homogenization or soaking treatments. The effect of manganese from 0. 1 to 1. 2 wt pct on the coarsening of sulfides in a high sulfur (0. 017 wt pct) and a low sulfur (0. 003 wt pct) steel was investigated. The model predicts that manganese strongly reduces the rate of coarsening, particularly for times of ten hours or less in the temperature range 1100 to 1400 degree C. The rate of dissolution is low at temperatures greater than the solvus for manganese sulfide inclusions in austenite.
• Myers, J., Geiger, G. H., & Poirier, D. R. (1982). STRUCTURE AND PROPERTIES OF THERMITE WELDS IN RAILS.. Welding Journal (Miami, Fla), 61(8), 258-s.
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  Abstract: This paper gives the results of the first phase of research in which standard controlled-cooled (SCC) and high silicon (HiSi) rails were welded using the processes and materials of two thermite-welding suppliers. Specimens removed from welds are characterized by low tensile ductility and low impact toughness due to microporosity and inclusions.
• Poirier, D. R., & Maples, A. L. (1982). ANALYSIS OF CONVECTION IN THE TWO-PHASE ZONE OF SOLIDIFYING ALLOYS.. Array, 141-143.
• Fujii, T., Poirier, D. R., & Flemings, M. C. (1979). Macrosegregation in a multicomponent low alloy steel. Metallurgical Transactions B, 10(3), 331-339.
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  Abstract: Macrosegregation theory is extended to predict the formation of channel-type segregation for multicomponent systems. Specifically, calculations are carried out for 0.7 pct C steel, by considering heat, mass and momentum transport in the mushy zone. In the model used for calculations the momentum transport equation and the energy equation were solved simultaneously. It is confirmed, by comparing calculated results with experimental results, that this model successfully predicts the occurrence of channel-type segregation. This analysis is also more rigorous than previous works on macrosegregation because previous analyses were done by solving for convection in the mushy zone with an "uncoupled" temperature field. Using the model, the effects of adjusting the compositions of silicon and molybdenum in steel were quantitatively evaluated in order to show how channel-type segregates can be avoided by adjusting alloy composition. A method of optimizing composition to minimize segregation is presented. It is recommended that this methodology be applied to alloy design so that ingots of alloys amenable to commercial practice can be obtained readily with a minimum amount of "trial-and-error" development work and expense. © 1979 American Society for Metals and the Metallurgical Society of AIME.
• Kou, S., Poirier, D. R., & Flemings, M. C. (1978). Macrosegregation in Rotated Remelted Ingots. Metallurgical Transactions B, 9(4), 711-719.
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  Abstract: A computer model is presented for predicting macrosegregation in rotated electroslag or vacuum arc remelted ingots. Sample calculations of segregation are carried out for ingots of the model alloy Sn-12 pet Pb in which the liquid density increases during solidification and for two hypothetical alloys; in one, the liquid density decreases during solidification, and in the other, liquid density first increases and then decreases during solidification. In alloys such as Sn-Pb in which liquid density increases during solidification, segregation is positive at the ingot centerline and if solidification is sufficiently slow, "freckles" form near the centerline. Positive segregation and freckles are found at the outer periphery of the ingot when liquid density decreases during solidification. Positive segregation and freckles are found at midradius when liquid density first increases and then decreases during solidification, and when the solidus isotherm changes shape abruptly at midradius (with density increasing during solidification). Ingot rotation, by introducing a radial component to the force field, alters interdendritic flow behavior and therefore macrosegregation. Modest rotation speeds eliminate "freckles" and reduce macrosegregation in all modeling studies conducted. Greater rotational speeds can accentuate the segregation. Experiments were conducted on simulated remelted ingots of Sn-Pb alloy. The ingots were 8 cm diam, rotated at speeds up to 119 rpm and solidified at rates from 5.3 × 10-3 to 1.36 × 10-2 cm/s. Segregation behavior obtained agrees qualitatively and quantitatively with theory. © 1978 American Society for Metals and the Metallurgical Society of AIME.
• Poirier, D. R., & Gandhi, N. V. (1977). OPTIMIZATION OF RISER DESIGNS WITH INSULATING SLEEVES TO ACHIEVE MINIMUM COST.. Trans Am Foundrymen's Soc, 84, 577-584, 819.
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  Abstract: A model is developed for the design and costs of risers for metal castings. The model determines riser height and diameter, riser cost, optimum design and minimum cost, and it compares the costs of risers incorporating insulating sleeves with risers without sleeves. The model includes costs for the sleeve, the cost for removing the riser, conversion costs for providing molten metal in the foundry, and a cost for the metal lost during the removal of the riser. Results of calculations for aluminum casting alloy 356. 0 are presented, but the model is suitable for general applications. The savings possible by using the sleeves are very substantial.
• Poirier, D. R., & Kieras, A. P. (1975). ANISOTROPIC CUTTING BEHAVIOR OF FREE-MACHINING STEELS.. J Eng Ind Trans ASME, 97 Ser B(3), 1094-1104.
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  Abstract: Paper No. 74-WA/Prod-12.
• Poirier, D. R., & Kieras, A. P. (1974). ANISOTROPIC CUTTING BEHAVIOR OF FREE-MACHINING STEELS.. American Society of Mechanical Engineers (Paper).
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  Abstract: A determination of the anisotropy in the shear strength during machining of a group of free-machining steels including 1117, 11L17, and 1215 and a plain steel, 1018, is presented. The three free-machining steels are anisotropic in the as-received condition, but the nonfree-machining steel is not anisotropic. Since tensile ductility depends on inclusion content and the orientation of inclusions relative to the specimen axis, and the same is true for the shear strength during machining, then, as expected, there is a relationship between the two for the steels all at the same strength level of 50,000 psi; the effective shear strength during machining decreases with decreasing tensile ductility.
• FLEMINGS, M. C., POIRIER, D. R., BARONE, R. V., & BRODY, H. D. (1970). MICROSEGREGATION IN IRON-BASE ALLOYS. J Iron Steel Inst (London), 208(pt 4), 371-381.
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  Abstract: Results are given of dendrite morphology studies and microsegregation measurements on a series of iron-base alloys, including Fe-Ni, Fe- Cr, Fe- Ni- C, and Fe- Cr- C alloys. The bulk of the results are from unidirectionally solidified ingots. Effects of homogenization and working on microsegregation are examined for one alloy (Fe-1. 5%Cr- 1. 0%C). An improved numerical analysis procedure is given for calculation of microsegregation. This procedure is applicable for idealized rod-like or plate- like dendrites, and when significant solid diffusion occurs during and/or after solidification.
• ROBERTS, R. A., LOPER, J. C., & POIRIER, D. R. (1969). RISER DESIGN AND FEEDING DISTANCE OF MANGANESE BRONZE CASTINGS -2. Am Foundrymen's Soc-Trans, 77, 387-397.
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  Abstract: An effective riser must solidify after that portion of the casting it is intended to feed, and provide adequate feed metal to the casting. From these principles and experimental results, an engineering method is presented for design o risers. Examples of riser design curves are presented which can be used by determining effective volume to surface area ratio of the feeding path, volume of the casting to be fed by the riser, and geometrical considerations of the particular casting-riser system.