An inverse finite element method with an application to extrusion with solidification

The flow and solidification of planar jets are analysed by means of an efficient inverse isotherm finite element method. The method is based on a tessellation that is constructed by isotherms as characteristic co-ordinate lines transverse to the flow direction. Thus opposite sides of finite elements lie on isotherms. The method allows the simultaneous determination of the location of the isotherms with the primary unknowns, namely, the velocity, the pressure, the temperature and the location of the free surface. Thus the determination of the location of the solidification front (which is known to pose significant computational difficulties) is automatic. This facilitates the control of the location of the solidification front by controlling macroscopic variables such as the flow rate, the cooling rate and the capillary design. The location of the solidification may then be suitably chosen to influence the frozen-in orientation and structure in extrusion of high-performance materials such as composites and polymers, in continuous casting of metals and in growth of crystals.     

Morphology of solidified polysulfone structures obtained by wet phase separation

Evidence is presented that all three theoretically predicted modes of phase separation take place in the ternary system polysulfone(PSf)/N,N-dimethyl acetamide(DMA)/water during the process of wet phase separation (WPS). The elementary process of solidification is reconsidered with regard to the (non-) equilibrium phase separation. Cast solutions with more than 15 wt% of PSf undergo nucleation and growth of the polymer lean phase with formation of separation membranes characterised by a cellular structure. When cast solutions with about 5-7 wt% of PSf undergo WPS, somewhere inside the ternary system conditions are established so that alongside other solidified PSf structures the bicontinuous spinodal structures superimposed by bead-like structures are also formed. Variety of lacy PSf structures with less/more polymer beads is the manifestation of the primary phase separation by the spinodal mode superimposed by the secondary phase separation taking place by heterogeneous nucleation and growth of the polymer rich phase mode. Latex formation during the WPS will also be explained. Skin formation on the cast solution - coagulation bath interface by direct accumulation of polymer is established regardless of the PSf content in the cast solution.     

Oriented tin on the metal surface obtained by crystallization in magnetic field

¹¹⁹Sn NMR showed that β-tin areas that formed upon freezing at magnetic field 9.4 T on the surface of tin polycrystalline samples have their symmetry axes strongly aligned along a particular direction. The fraction of the oriented frozen tin was found to approach the total amount of the Sn melt on the sample surface.     

The development of a cellular automaton-finite volume model for dendritic growth

A cellular automaton to track the solid–liquid interface movement is linked to finite volume computations of solute diffusion to simulate the behavior of dendritic structures in binary alloys during solidification. A significant problem encountered in the CA formulation has been the presence of artificial anisotropy in growth kinetics introduced by a Cartesian CA grid. A new technique to track the interface movement is proposed to model dendritic growth in different crystallographic orientations while reducing the anisotropy due to grid orientation. The model stability with respect to the numerical parameters (cell size and time step) for various operating conditions is examined. A method for generating an operating window in Δt and Δx has been identified, in which the model gives a grid-independent set of results for calculated dendrite tip radius and tip undercooling. Finally, the model is compared to published experimental and analytical results for both directional and equiaxed growth conditions.     

Short shots and industrial case studies: Understanding fluid flow and solidification in high pressure die casting

The geometric complexity and high fluid speeds involved in high pressure die casting (HPDC) combine to give strongly three dimensional fluid flow with significant free surface fragmentation and splashing. A simulation method that has proved particularly suited to modelling HPDC is Smoothed Particle Hydrodynamics (SPH). Materials are approximated by particles that are free to move around rather than by fixed grids, enabling more accurate prediction of fluid flows involving complex free surface motion. Three practical industrial case studies of SPH simulated HPDC flows are presented; aluminium casting of a differential cover (automotive), an electronic housing and zinc casting of a door lock plate. These show significant detail in the fragmented fluid free surfaces and allow us to understand the predisposition to create defects such as porosity in the castings. The validation of flow predictions coupled with heat transfer and solidification is an important area for such modelling. One powerful approach is to use short shots, where insufficient metal is used in the casting or the casting shot is halted part way through, to leave the die cavity only partially filled. The frozen partial castings capture significant detail about the order of fill and the flow structures occurring during different stages of filling. Validation can occur by matching experimental and simulated short shots. Here we explore the effect of die temperature, metal super-heat and volume fill on the short shots for the casting of a simple coaster. The bulk features of the final solid castings are found to be in good agreement with the predictions, but the fine details appear to depend on surface behaviour of the solidifying metals. This potentially has significant implications for modelling HPDC.     

Microanalytical Techniques Applied to Phase Identification and Measurement of Solute Redistribution at the Solid/Liquid Interface of Frozen Fe-4.3Ni Doublets

 A Fe-4.3Ni alloy has been solidified directionally by using the Bridgman system. The solidification conditions were chosen to obtain an oriented cellular structure of δ-ferrite. These are: a positive temperature gradient of about 60 K/cm and a growth rate of 6.6 μm/s. A change in these conditions can lead either to the formation of austenite or to the competitive growth of δ-ferrite/γ-austenite. The solid/liquid interface of δ-ferrite cells has been frozen and double instability has been revealed at the tip of the cells. The instability is described as the first harmonic wave of fundamental undulation, which appeared at the formerly planar solid/liquid interface. This means that a doublet structure is formed only with the imposed specific conditions of solidification. The Ni-solute redistribution after back-diffusion has been measured across the δ-ferrite doublet. Results of energy dispersive X-ray (EDX) measurements on the distribution of Ni and Fe correspond well to the theoretical prediction for redistribution developed especially for oriented structure formation (two dimensional solidification). Additionally, electron backscattered diffraction from the bulk Fe-4.3Ni alloy sample allowed us to determine the local structure, i.e. the distribution of single crystallite orientations in the microstructure. A unique correlation between fluctuations of the Ni-solute redistribution and crystalline orientations in the δ-ferrite doublets has been demonstrated. Moreover, a relationship between geometrical asymmetry of the doublets and solute redistribution has also been found.     

Compositional changes in cement-stabilized waste during leach tests--comparison of SEM/EDX data with predictions from geochemical speciation modeling

Cement-based stabilization/solidification (s/s) is a widely used treatment process for hazardous wastes containing toxic metals. The treated waste consists of a complex mixture of several solid phases produced by cement hydration reactions. Understanding and predicting the effects of leaching on these individual phases is essential for assessing the long-term immobilization of metal contaminants in s/s waste exposed to rain and groundwater. In this paper, particles of crushed Portland cement doped with copper, lead, and zinc nitrates were leached with nitric acid solutions maintained at constant pH in the range pH 4-7. Changes in solid composition at the microscopic scale were measured by scanning electron microscopy and energy dispersive X-ray spectrometry (SEM/EDX). The geochemical equilibrium model SOLTEQ-B, which accounts for the incongruent solubility behavior of calcium silicate hydrate, was used to simulate the compositional changes in the hydration gel for increasing extents of leaching. Measured concentrations of calcium, silicon, and sulfur were successfully predicted at all extents of leaching. Aluminum, lead, and zinc concentrations were also in good agreement with model predictions, except in the remineralization zones that form when metals solubilized in the outer regions of the s/s waste particles diffuse toward the interior and reprecipitate at higher pH. Copper was less accurately modeled at high extents of leaching. Accounting for the incorporation of contaminant metals into the cement hydration gel (in opposition to assuming the presence of individual metal hydroxides) is crucial for successfully predicting contaminant metal concentrations in the hydration gel at low and intermediate extents of leaching.     

Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process

A technique to determine the thermal boundary conditions existing during the solidification of metallic alloys in the investment casting process is presented. Quantitative information about these conditions is needed so that numerical models of heat transfer in this process produce accurate results. In particular, the variation of the boundary conditions both spatially and temporally must be known. The method used involves the application of a new inverse heat conduction method to thermal data recorded during laboratory experiments of aluminium alloy solidification in investment casting shell moulds. The resultant heat transfer coefficient for the alloy/mould interface is calculated. An experimental programme to determine requisite mould thermal properties was also undertaken. It was observed that there is significant variation of the alloy/mould heat transfer coefficient during solidification. It is found to be highly dependent on the alloy type and on the vertical position below the initial free surface of the liquid metal. The aluminium casting alloys used in this study were 413, A356, 319 (Aluminum Association designations), and commercially pure aluminium. These alloys have significantly different freezing ranges. In particular, it was found that alloys with a high freezing range solidify with rates of heat transfer to the mould which are very sensitive to metallostatic head.     

CALCULATION OF THE YOUNG''''S MODULUS OF AN ADSORBED POLYMER LAYER

Polymer layers adsorbed to a surface or in a confined environment often change their mechanical properties. There is even the possibility of solidification of the confined layer. To judge the stiffness of such a layer, we used the Hertz model to calculate the Young's modulus of the polymer layer in the confinement of AFM experiments with silicon nitride tip with a radius of curvature of R≈50 nm and a glass sphere attached to the cantilever R = 5μm. Since there is no visible indentation of the layer in the AFM experiments, the layer is either penetrated very easily, or the indentation is too small to be seen in a force curve. The latter would be the case for a polymer layer with a Young's modulus above 4×108 Pa in case of an experiment with a silicon nitride tip and 4×105 Pa in case of a glass sphere.     

Analysis of high-speed continuous casting with inverse finite elements

A recently proposed inverse isotherm finite element method is further extended in order to account for processes with distorted isotherms. With this method a variety of problems can be solved which require the explicit calculation of characteristic material lines along with the common field of unknowns in transport phenomena. The method is applied to high-speed metal casting, where the location and shape of the extensive solidification front is calculated simultaneously with the primary unknowns, the velocity and the pressure, whereas the temperature is fixed at the moving nodes of the finite element tessellation. This is achieved by solving the energy equation inversely along with the rest of the conservation equations, i.e. the temperature field is fixed and its location is calculated. Empirical correlations may be derived which give the shape of the solidification front as a function of the process parameters. This may be used to improve the control means of metal casting, which is currently based on one-dimensional approximate analyses.