Alan J. Markworth

Modelling studies applied to functionally graded materials

This review contains a description of modelling studies relative to functionally graded materials (FGMs). Two principal topics are covered: models for microstructure-dependent thermophysical properties, and models for the design, processing, and performance of FGMs. The former is a particularly important input to FGM modelling because of the wide variety of microstructures that can exist across the graded direction of a single material. Based on the work described in this review, recommendations are made regarding areas in which additional modelling studies would be beneficial. Suggested approaches to the modelling include the application of a number of powerful techniques, such as percolation theory, fractal analysis, lattice-based microstructure models, the renormalization group, neural networks, and fuzzy logic.

Splat-quench solidification of freely falling liquid-metal drops by impact on a planar substrate

Results are presented of a study of the splat-quench solidification of small, freely falling liquid drops of the alloy Nitronic 40W, which were allowed to impact on a solid, planar, horizontal substrate. The principal variable was the substrate material, with substrates of copper, alumina and fused quartz being used. The shapes of the solidified splats were correlated with a simplified model for the energetics of the splatting process and with the thermal conductivity of the substrate. The measured results are qualitatively in agreement with theoretical predictions, and suggestions are offered for a more comprehensive model of splat-quench solidification. A relationship between sessile droplet diameter and parent wire diameter is also presented and discussed.

Thermal conductivity of graded composites: Numerical simulations and an effective medium approximation

We describe two methods for modeling the thermal conductivity and temperature profile in a graded composite film. The film consists of a random binary composite, whose concentration varies in the direction perpendicular to the film surface, and a fixed temperature difference is applied across the film. In the first method, the temperature profile is modeled directly, using a finite element technique in which the film is represented as a discrete network of thermal conductances, randomly distributed according to the assumed composition profile. The temperature at each node, and the effective thermal conductance, is then obtained by a transfer matrix technique. In the second approach, the film is treated by an effective-medium approximation, suitably generalized to account for the composition gradient. The methods are in rough agreement with each other, and suggest that thermophysical properties of the film can be treated reasonably well by approaches generalized from those which succeed in conventional composites.

On the coarsening of gas-filled pores in solids

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

A model of structure optimization for a functionally graded material

Abstract A simple model is developed for the spatial variation of composition of a metal/ceramic functionally graded material. The composition profile is optimized, subject to certain constraints, such that the flow of heat through the material is either maximized or minimized. Normal thermal-stress profiles are calculated and are found to exhibit unusual behavior in some cases.

Controlling chaos in a model of thermal pulse combustion

We describe methods for automating the control and tracking of states within or near a chaotic attractor. The methods are applied in a simulation using a recently developed model of thermal pulse combustion as the dynamical system. The controlled state is automatically tracked while a parameter is slowly changed well beyond the usual flame‐out point where the chaotic attractor ceases to exist because of boundary crisis. A learning strategy based on simple neural networks is applied to map‐based proportional feedback control algorithms both with and without a recursive term. Adaptive recursive proportional feedback is found to track farther beyond the crisis (flame‐out) boundary than does the adaptive non‐recursive map‐based control. We also found that a continuous‐time feedback proportional to the derivative of a system variable will stabilize and track an unstable fixed point near the chaotic attractor. The positive results suggest that a pulse combustor, and other nonlinear systems, may be suitably cont...

The kinetic behavior of precipitate particles under Ostwald ripening conditions

Abstract The theory advanced by other investigators, on the asymptotic nature of particle size distributions undergoing Ostwald ripening, is used to evaluate the kinetic behavior of individual particles of which the distributions are constituted. Assuming asymptotic conditions, expressions are derived for the particle radius as a function of time and initial conditions for both diffusion-controlled and interface-controlled ripening. These expressions are then used to calculate the dissolution time for particles as a function of initial conditions.

The theory of bubble migration applied to irradiated materials

Abstract Methods of crystal growth are reviewed and then applied to the problem of bubbles migrating in solids. The distribution of driving force between the reversible and irreversible processes occurring at the bubble surface is summarized in a coupling equation which illustrates the contributions made by surface curvature, atomic attachment kinetics, impurities contained within the bubble, and vapor diffusion. The shape assumed by a migrating bubble is reviewed, and the special case in which kinetic effects dominate is examined in detail. Lenticular shaped bubbles are shown to be a form of cellular growth, resulting from the accumulation of impurities within the bubble. The trails of small bubbles behind such voids reveal the entrainment of impurities as in the grooves of a cellular interface. A procedure is briefly described for evaluating bubble shapes and temperature profiles in the matrix when all features such as capillarity, diffusion and kinetics are considered.

Comments on foam stability, Ostwald ripening, and grain growth

Abstract A discussion is presented of the applicability of well-established theories of interface-reaction-controlled Ostwald ripening of second-phase precipitate distributions, and of the evolution of grain distributions in polycrystalline materials, to the problem of foam evolution by interbubble gas diffusion. Two limiting cases are developed in detail: evolution of a narrow size distribution of foam bubbles, and characteristics of a bubble distribution at asymptotically large times.

Chaotic dynamics in a model of metal passivation

The dynamic behavior of a model for the passivation of a metal surface in contact with an aqueous solution is investigated. The model, which is characterized by a three-dimensional state space and five-dimensional parameter space, is obtained by combining elements from passivation models developed by Talbot and Oriani and by Sato. A three-dimensional subspace of parameter space has been studied; the remaining two dimensions are not thought to provide any additional interesting dynamics. The model exhibits remarkably rich dynamics, including the period-doubling, intermittency, and crisis routes to chaos, folds and bubbles in periodic portions of the attractor, and multiple attractors with complex, intertwined basins of attraction.