S.G.R. Brown

A review of measurement techniques for the thermal expansion coefficient of metals and alloys at elevated temperatures

Metallurgical operations at elevated temperatures, such as those that involve solidification and/or mechanical deformation, can be critically influenced by the thermal stresses and strains that result from expansion and contraction of the material as a function of temperature. With the increasing use of computer-based process models for these operations, there arises a greater need for quantitative data on the thermal expansion coefficient of the relevant alloy at the temperatures involved. After briefly reviewing some existing sources of data for this property, the various techniques for its measurement at elevated temperatures are then described. These include mechanical dilatometry, optical imaging and interference systems, x-ray diffraction methods and electrical pulse heating techniques. Finally the implications, for process modelling, of the available data and measurement techniques are discussed.

A cellular automaton model of steady-state columnar-dendritic growth in binary alloys

A two-dimensional cellular automaton model has been developed to examine the evolution and coarsening behaviour of solid-solution dendrites during steady-state columnar freezing. Using an empirical rule to account for interface growth, realistic dendrite geometries were obtained for different assumed compositions and process conditions. Coarsening occurred by a coalescence mechanism associated with bridging of adjacent dendrite arms.

Numerical determination of liquid flow permeabilities for equiaxed dendritic structures

Abstract Darcys law has been applied to the 3D finite difference numerical determination of the influence of solid fraction and geometry on the permeability of equiaxed dendritic structures. The micro-model computes the permeability for flow through a domain equivalent to the volume ultimately occupied by a single solid solution dendritic grain in an Al3Cu3Si alloy. Evolution of the dendrite shape during solidification was simulated using a novel cellular automaton-finite difference technique. Numerically determined permeabilities compare well with reported experimental data for aluminium alloys. For solid fractions in excess of ∼20%, there is also reasonable correlation with the Kozeny–Carman (KC) expression for a KC constant of unity. A significant feature of the micro-model is that it is able to account for the isolation of interdendritic liquid pools in calculating the effective values of the solid–liquid interfacial area and of the fraction liquid.

Creep strain and creep life prediction for the cast nickel-based superalloy IN-100

Abstract A new approach to creep, termed the θ projection concept, is illustrated by reference to high precision data obtained for IN-100. This new approach envisages normal creep curves as the sum of a decaying primary and an accelerating tertiary component so that the increase in creep strain ϵc with time t can be described as ϵ c = θ 1 {1− exp (−θ 2 t} + θ 3 { exp (θ 4 t)−1} where θ1 and θ3 define the extent with respect to strain and θ2 and θ4 quantify the curvatures of the primary and tertiary stages of creep respectively. Once the stress and temperature dependences of the four θ functions and the rupture ductility are established, any creep strain or creep life parameter can be computed directly, offering major theoretical and practical advantages over traditional approaches which rely on the measurement of only a few quantities such as the minimum creep rate and rupture life.

Modelling of non-equilibrium solidification in ternary alloys: comparison of 1D, 2D, and 3D cellular automaton–finite difference simulations

Abstract A cellular automaton–finite difference (CAFD) computer model is presented that describes the solidification of multicomponent multiphase alloys at the microscopic level. The objective of the model is to enable the prediction of microsegregation patterns and the appearance of non-equilibrium constituents during non-equilibrium freezing. To support the development of the model, coupling with a thermodynamic software package, ThermoCalc, has been achieved to obtain accurate thermodynamic data for multicomponent alloys. The CAFD model has been used to generate evolving dendritic structures in two and three dimensions. A simple one-dimensional (1D) CAFD plate model, which assumes that adjacent dendrite arms are plates, has also been developed. Recently, experimental results of a study carried out on a directionally solidified Al–3.95Cu–0.8 Mg alloy (cooling rate of 0.378 K s-1) have been reported. In the present investigation, a comparison between 1D, 2D, and 3D simulations of microsegregation and these experimental results is made, with respect to the amounts of non-equilibrium constituents and solute profiles in the primary -Al phase, for the same alloy and solidification conditions.

A cellular automaton model of the steady-state “free” growth of a non-isothermal dendrite

Abstract A 2D cellular automaton model has been developed to study the steady-state “free” growth of a non-isothermal dendrite. The model incorporates rules to account for heat diffusion, the influence of curvature on the equilibrium freezing temperature and latent heat evolution. The model predicts a V ∝ δTb growth rate-undercooling relationship for the various dendrite tip growth temperatures selected. The prediction of the values of b accords reasonably with analytical models and reported experimental observations.

Powder Bed Layer Characteristics: The Overseen First-Order Process Input

Powder Bed Additive Manufacturing offers unique advantages in terms of manufacturing cost, lot size, and product complexity compared to traditional processes such as casting, where a minimum lot size is mandatory to achieve economic competitiveness. Many studies—both experimental and numerical—are dedicated to the analysis of how process parameters such as heat source power, scan speed, and scan strategy affect the final material properties. Apart from the general urge to increase the build rate using thicker powder layers, the coating process and how the powder is distributed on the processing table has received very little attention to date. This paper focuses on the first step of every powder bed build process: Coating the process table. A numerical study is performed to investigate how powder is transferred from the source to the processing table. A solid coating blade is modeled to spread commercial Ti-6Al-4V powder. The resulting powder layer is analyzed statistically to determine the packing density and its variation across the processing table. The results are compared with literature reports using the so-called “rain” models. A parameter study is performed to identify the influence of process table displacement and wiper velocity on the powder distribution. The achieved packing density and how that affects subsequent heat source interaction with the powder bed is also investigated numerically.

Simulation of diffusional composite growth using the cellular automaton finite difference (CAFD) method

A model is described of directional coupled two-phase composite growth in three dimensions using a combined cellular automaton finite difference (CAFD) approach. The modelling strategy and some preliminary results are presented here for the first time. The model incorporates solute diffusion and a simple cellular automaton growth rule containing a pseudo-curvature algorithm. Despite its limitations, the model is able to simulate some of the structural effects that take place during coupled growth. As a demonstration application the model is applied to eutectic growth in the Pb–Sn system and compared to experimental measurements. The scale of predicted microstructures in the model is close to that measured after directional freezing of Pb–Sn eutectic.

The scandium effect in multicomponent alloys

Despite its excellent elemental properties, lightweight nature and good alloying potential, scandium has received relatively little attention in the manufacturing community. The abundance of scandium in the Earths crust is quite high. It is more abundant than silver, cobalt, lead and tin. But, because scandium is so well dispersed in the lithosphere, it is notoriously difficult to extract in commercial quantities – hence low market availability and high cost. Scandium metallurgy is still a largely unexplored field – but progress is being made. This review aims to summarise advances in scandium metallurgical research over the last decade. The use of scandium as a conventional minor addition to alloys, largely in structural applications, is described. Also, more futuristic functional applications are discussed where details of crystal structures and peculiar symmetries are often of major importance. This review also includes data obtained from more obscure sources (especially Russian publications) which are much less accessible to the wider community. It is clear that more fundamental research is required to elevate the status of scandium from a laboratory-based curiosity to a mainstream alloying element. This is largely uncharted territory. There is much to be discovered.

Three-dimensional cellular automaton models of microstructural evolution during solidification

The evolution of microstructural features during solidification involves complex interactions between several physical phenomena. Cellular automata (CA) models are often characterized as being simple in their construction and yet able to produce very complicated behaviour. This property of CA models has been exploited to produce computer simulations of various aspects of microstructural evolution occurring during solidification. Results of a series of three-dimensional simulations of non-isothermal “free” dendritic growth are presented and the changes in dendrite morphology for different conditions are quantified and discussed. A modification of this model was also developed to examine the effects of composition on microstructural evolution for a simple eutectic system. As the composition moves towards the eutectic the simulated microstructures change from combined dendritic/lamellar to completely lamellar.