A three-phase model of hydrogen pore formation during the equiaxed dendritic solidification of aluminum-silicon alloys

A computational model for the prediction of porosity due to dissolved hydrogen in binary aluminum-silicon alloys has been developed. The model combines the cellular automata technique for the simulation of the growth of the solid phase, the finite-difference technique for the simulation of diffusion of the dissolved species, and a quasi-equilibrium model for the growth of individual bubbles. The growth of the solid and gas phases is initiated by a stochastic nucleation model, depending upon the undercooling (for the solid) or the supersaturation ratio (for the gas). The results agree favorably with experiments. The low supersaturation values needed to simulate the experimental results are consistent with a nucleation mechanism of gas pockets entrained within the melt.     

A volume-averaged two-phase model for transport phenomena during solidification

A basic model of the transport phenomena occurring during solidification of multicomponent mixtures is presented. The model is based on a two-phase approach, in which each phase is treated separately and interactions between the phases are considered explicitly. The macroscopic transport equations for each phase are derived using the technique of volumetric averaging. The basic forms of the constitutive relations are developed. These relations link the macroscopic transport phenomena to microscopic processes such as microstructure development, interfacial stresses, and interfacial heat and mass transfer. Thermodynamic relations are presented, and it is shown that nonequilibrium effects can be addressed within the framework of the present model. Various simplifications of the model are examined, and future modeling needs are discussed.     

A transparent model for simulation of ingot front solidification

Conclusion Observations of the macroscopic freezing front in water and solutions of water with ammonium chloride reveal anisotropies identical in nature to those noted in metallic alloys. The variables which govern the anisotropies are similar for both types of materials, a fact which allows us to confirm our conclusions already stated about metals. The observations made with water are also direct ones and not inferential as must be the case for metals; we are therefore surer about other effects connected with this phenomenon of anisotropic growth. For example, cracking of the ice was often observed when the anisotropy occurred but was absent otherwise; it then appears that cracking in some metals may owe its origins to the effect of interface front anisotropy.     

A three-phase model of retirement decision making.

The present article organizes prominent theories about retirement decision making around three different types of thinking about retirement: imagining the possibility of retirement, assessing when it is time to let go of long-held jobs, and putting concrete plans for retirement into action at present. It also highlights important directions for future research on retirement decision making, including perceptions of declining person–environment fit, the role of personality traits, occupational norms regarding retirement, broader criteria for assessing older workers' job performance, couples' joint decision making about retirement, the impact of self-funded and self-guided pension plans on retirement decisions, bridge employment before total withdrawal from the work force, and retirement decisions that are neither entirely forced nor voluntary in nature. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

A multivariate mixed linear model for meta-analysis.

A multivariate mixed-effects approach for meta-analysis is presented. The approach (a) incorporates as outcomes multiple effect sizes per study; (b) allows different studies to have different subsets of effect sizes; and (c) treats each study's effect sizes as random realizations from a population of possible effect sizes. Application is illustrated via reanalysis of data from studies assessing the effects of coaching on verbal and mathematical subtests of the Scholastic Aptitude Test. Covariance components are estimated via restricted maximum likelihood (REML); inferences about regression coefficients and specific study effect sizes are based on their joint conditional distribution given the REML covariance component estimates. The approach can be implemented via now-standard software for unbalanced hierarchical data. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A Markov mixed effect regression model for drug compliance

Patient compliance (adherence) with prescribed medication is often erratic, while clinical outcomes are causally linked to actual, rather than nominal medication dosage. We propose here a hierarchical Markov model for patient compliance. At the first stage, conditional upon individual random effects and a set of individual-specific nominal daily dose times, we assume that (i) the subject-specific probability of taking zero, one, or more than one dose associated with a given nominal dose time depends on the value of certain covariates, and on the number of doses associated with the immediate previous time, but is independent of any other previous or future dosing events (the Markov hypothesis); and (ii) the set of 'errors' between actual dose times associated with each nominal time is multivariate normally distributed, conditional on covariates and the number of such actual dose times, as in (i). At the second stage, a multivariate normal distribution is assumed for the individual random effects. We fit this model by maximum likelihood to data collected over three months using an electronic system for recording actual dose times in HIV-positive patients assigned to a regimen of zidovudine thrice daily. Beyond its value for describing and quantifying compliance behaviour, as illustrated here, the model may prove useful for explanatory analyses of clinical trials.     

A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures

A three-dimensional (3-D) model for the prediction of dendritic grain structures formed during solidification is presented. This model is built on the basis of a 3-D cellular automaton (CA) algorithm. The simulation domain is subdivided into a regular lattice of cubic cells. Using physically based rules for the simulation of nucleation and growth phenomena, a state index associated with each cell is switched from zero (liquid state) to a positive value (mushy and solid state) as solidification proceeds. Because these physical phenomena are related to the temperature field, the cell grid is superimposed to a coarser finite element (FE) mesh used for the solution of the heat flow equation. Two coupling modes between the microscopic CA and macroscopic FE calculations have been designed. In a so-called “weak” coupling mode, the temperature of each cell is simply interpolated from the temperature of the FE nodes using a unique solidification path at the macroscopic scale. In a “full” coupling mode, the enthalpy field is also interpolated from the FE nodes to the CA cells and a fraction of solid increment is computed for each mushy cell using a truncated Scheil microsegregation model. These fractions of solid increments are then fed back to the FE nodes in order to update the new temperature field, thus accounting for a more realistic release of the latent heat (i.e., the solidification path is no longer unique). Special dynamic allocation techniques have been designed in order to minimize the computation costs and memory size associated with a very large number of cells (typically 10⁷ to 10⁸). The potentiality of the CAFE model is demonstrated through the predictions of typical grain structures formed during the investment casting and continuous casting processes.     

The alstruc microstructure solidification model for industrial aluminum alloys

The model predicts the solidification path in the aluminum corner of the AlCuFeMgMnSi phase diagram, with compensation for solid-state diffusion and particle growth undercoolings. Input is the composition and the rate of cooling. Output is the temperature vs fraction solid; the solid-state concentration profiles; the type, volume fraction, and size of the intermetallic particles; and also the temperature-dependent thermal conductivity, density, specific heat, and heat of fusion for use in thermal models.     

A thermomechanical model for simulation of carbon steel solidification in mould in continuous casting

Abstract

The 17th Annual Conference of the Sheffield Metallurgical and Engineering Association (SMEA), held on 17–18 June 2008 at the Endcliffe Conference Centre, University of Sheffield, attracted 120 delegates. The aim of the conference was to explore the effect of hot rolling and forging processes on the quality and performance of steels and high duty alloys. Five technical sessions and 20 presentations explored process developments and their influence on product quality, how the hot working process can be optimised to influence microstructure and properties, and the influence of new technologies.     

A nonlinear mixed model framework for item response theory.

Mixed models take the dependency between observations based on the same cluster into account by introducing 1 or more random effects. Common item response theory (IRT) models introduce latent person variables to model the dependence between responses of the same participant. Assuming a distribution for the latent variables, these IRT models are formally equivalent with nonlinear mixed models. It is shown how a variety of IRT models can be formulated as particular instances of nonlinear mixed models. The unifying framework offers the advantage that relations between different IRT models become explicit and that it is rather straightforward to see how existing IRT models can be adapted and extended. The approach is illustrated with a self-report study on anger. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An analytical model for nodular eutectic grain predictions during solidification

In this work, analytical expressions are derived for the globular eutectic transformation, which occurs during the solidification of nodular iron. The model incorporates heat and mass balance equations in considering nucleation and growth of nodular eutectic grains. In particular, an expression is found that relates the volumetric density of nodular eutectic grains to the maximum degree of undercooling. The proposed expression includes various experimental constants, which are well defined in nodular iron. Accordingly, good agreement is found to exist between the experimental and predicted data on the density of nodular eutectic grains and the maximum degree of undercooling.     

Diffusion-based model for isothermal solidification kinetics during transient liquid-phase sintering

Results from a diffusion-based model for transient liquid-phase sintering (TLPS) were used to predict the influence that the solute diffusivity (D), base-metal particle size (a), base-metal grain size (d), alloy partition coefficient (k), and the extent of solute saturation (X _max/X _o) had on the rate of isothermal solidification (where both X _max/X _o and k determine the initial liquid weight fraction in the system W _{A o}). The solidification rate increases with an increase in D and a decrease in a, d, X _o, and W _{A o}, but decreases with an increase in k. Model predictions are close to, but slightly underestimate, results for the solidification rate measured in a Pb-Sn TLPS system.     

An analytical model for optimal directional solidification using liquid metal cooling

In what follows, a model is developed that describes the optimal processing parameters for directional solidification using liquid metal cooling (LMC). The model considers a sample with a flat geometry and, as a first approximation, can be used to treat the flat sections of a turbine blade. The model predicts (1) the optimal withdrawal rate of the casting from the hot zone, (2) the temperature gradient in the liquid at the solidification interface, and (3) the temperature profile along the length of the casting. The model is then used to perform a sensitivity analysis of the LMC process. Cooling bath temperature, baffle thickness, shell thickness, and shell thermal conductivity are shown to have a strong influence on system performance.     

Heat flow model for surface melting and solidification of an alloy

The heat flow model previously developed for a pure metal is extended to the solidification of an alloy over a range of temperatures. The eq11Ations are then applied to rapid surface melting and solidification of an alloy substrate. The substrate is subjected to a pulse of stationary high intensity heat flux over a circular region on its bounding surface. The finite difference form of the heat transfer eq11Ation is written in terM_s of dimensionless nodal temperature and enthalpy in an oblate spheroidal coordinate system. A numerical solution technique is developed for an alloy which precipitates a eutectic at the end of solidification. Generalized solutions are presented for an Al-4.5 wt pct Cu alloy subjected to a uniform heat flux distribution over the circular region. Dimensionless temperature distributions, size and location of the “mushy” zone, and average cooling rate during solidification are calculated as a function of the product of absorbed heat flux,q, the radius of the circular region,a, and time. General trends established show that for a given product ofqa all isotherM_s are located at the same dimensionless distance for identical Fourier numbers. The results show that loss of superheat and shallower temperature gradients during solidification result in significantly larger “mushy” zone sizes than during melting. Furthermore, for a given set of process parameters, the average cooling rate increases with distance solidified from the bottom to the top of the melt pool.     

A three-step procedure for assessing bioequivalence in the general mixed model framework

Bioavailability data arising from a standard two-period cross-over study are routinely analysed to establish bioequivalence between test and reference formulations. Current regulatory guidelines only require evidence of equivalence in average bioavailability for the assessment of bioequivalence. Under normality assumptions, this is achieved by demonstrating equivalence between the formulation means (step 1). However, the equivalence of formulation variances should also be assessed to get evidence of population bioequivalence (step 2), since a difference in variability of bioavailability may also pose significant problems in drug safety and efficacy. On the other hand, even population bioequivalence does not ensure that an individual subject could be expected to respond similarly to the two formulations. Therefore, whenever individual bioequivalence is the ultimate goal, the magnitude of intra-subject correlation should always be examined as the final stage (step 3). In this paper, these three successive concepts of bioequivalence are cast into the general mixed model framework and a stepwise testing procedure for the global assessment of bioequivalence is proposed. In addition to this, important issues addressed in the regulatory guidelines, such as verification of the model assumptions and application of the log-transformation, are discussed. Lastly, an example is presented to illustrate the proposed three-step procedure on the original and log-transformed scale of measurement.