I. V. Samarasekera

Heat transfer and microstructure during the early stages of metal solidification

Transient heat transfer in the early stages of solidification of an alloy on a water-cooled chill and the consequent evolution of microstructure, quantified in terms of secondary dendrite arm spacing (SDAS), have been studied. Based on dip tests of the chill, instrumented with thermocouples, into Al-Si alloys, the influence of process variables such as mold surface roughness, mold material, metal superheat, alloy composition, and lubricant on heat transfer and cast structure has been determined. The heat flux between the solidifying metal and substrate, computed from measurements of transient temperature in the chill by the inverse heat-transfer technique, ranged from low values of 0.3 to 0.4 MW/m2 to peak values of 0.95 to 2.0 MW/m2. A onedimensional, implicit, finite-difference model was applied to compute heat-transfer coefficients, which ranged from 0.45 to 4.0 kW/m2 °C, and local cooling rates of 10 °C/s to 100 °C/s near the chill surface, as well as growth of the solidifying shell. Near the chill surface, the SDAS varied from 12 to 22 (µm while at 20 mm from the chill, values of up to 80/smm were measured. Although the SDAS depended on the cooling rate and local solidification time, it was also found to be a direct function of the heat-transfer coefficient at distances very near to the casting/chill interface. A three-stage empirical heat-flux model based on the thermophysical properties of the mold and casting has been proposed for the simulation of the mold/casting boundary condition during solidification. The applicability of the various models proposed in the literature relating the SDAS to heat-transfer parameters has been evaluated and the extension of these models to continuous casting processes pursued.

Mathematical model of the thermal processing of steel ingots: Part II. Stress model

A mathematical model has been developed to predict the internal stresses generated in a steel ingot during thermal processing. The thermal history of the ingot has been predicted by a finite-element, heat-flow model, the subject of the first part of this two-part paper, which serves as input to the stress model. The stress model has been formulated for a two-dimensional transverse plane at mid-height of the ingot and is a transient, elasto-viscoplastic, finite-element analysis of the thermal stress field. Salient features of the model include the incorporation of time-temperature and temperature-dependent mechanical properties, and volume changes associated with nonequilibrium phase transformation. Model predictions demonstrate that the development of internal stresses in the ingot during thermal processing can be directly linked to the progress of the phase transformation front. Moreover, the low strain levels calculated indicate that metallurgical embrittlement must be very important to the formation of cracks in addition to the development of high tensile stresses.

Comparison of numerical modeling techniques for complex, two-dimensional, transient heat-conduction problems

The accuracy, stability, and cost of the standard finite-element method, (Standard), Matrix method method of Ohnaka, and alternating-direction, implicit finite-difference method (ADI) have been compared using analytical solutions for two problems approximating different stages in steel ingot processing. The Standard and Matrix methods both employ triangular elements and were compared using the Dupont, Lees, and Crank-Nicolson time-stepping techniques. Other variables include mesh and time-step refinement, type of boundary condition formulation, and the technique for simulating phase change. The best overall combination of methods investigated for modeling two-dimensional, transient, heat conduction problems involving irregular geometry was the Dupont-Matrix method with a lumped boundary condition formulation and temperature dependent properties evaluated at time level two, coupled with the Lemmon latent-heat evolution technique if phase change is involved. For problems with simple geometry, the ADI method was found to be more cost effective.

Mathematical model of the thermal processing of steel ingots: Part I. Heat flow model

A two-dimensional mathematical model has been developed to predict stress generation in static-cast steel ingots during thermal processing with the objective of understanding the role of stress generation in the formation of defects such as panel cracks. In the first part of a two-part paper the formulation and application of a heat-flow model, necessary for the prediction of the temperature distribution which governs thermal stress generation in the ingot, are described. A transverse plane through the ingot and mold is considered and the model incorporates geometric features such as rounded corners and mold corrugations by the use of the finite-element method. The time of air gap formation between mold and solidifying ingot skin is input, based on reported measurements, as a function of position over the ingot/mold surface. The model has been verified with analytical solutions and by comparison of predictions to industrial measurements. Finally, the model has been applied to calculate temperature contours in a 760×1520 mm, corrugated, low-carbon steel ingot under processing conditions conducive to panel crack formation. The model predictions are input to an uncoupled stress model which is described in Part II.

Mold behavior and its influence on quality in the continuous casting of steel slabs: Part i. Industrial trials, mold temperature measurements, and mathematical modeling

An extensive study has been conducted to elucidate mold behavior and its influence on quality during the continuous casting of slabs. The study combined industrial measurements, mathe matical modeling, and metallographic examination of cast slab samples. The industrial mea surements involved instrumenting an operating slab mold with 114 thermocouples in order to determine the axial mold wall temperature profiles for a wide range of casting conditions. A three-dimensional (3-D) heat-flow model of the mold wall was developed to characterize the heat fluxes in the mold quantitatively from the measured mold temperature data. Furthermore, heat-flow models were developed to examine steel solidification phenomena and mold flux behavior at the meniscus. Slab samples collected during the industrial trials were examined metallographically to evaluate the cast structure and defects. Owing to the length of the study, it is presented in two parts, the first of which describes the experimental techniques employed in the instrumentation of the mold together with the details of the industrial trials and mold temperature measurements. Also, the mathematical modeling technique applied to determine the axial heat-flux profiles from the measured mold temperature data is presented. It is shown that a fully 3-D model of the mold wall is needed to convert the measured temperatures to heat-flux profiles properly.

Heat transfer in the hot rolling of metals

The heat-transfer coefficient (HTC) in the roll gap during the hot rolling of AA5XXX-series (aluminum-magnesium) alloys has been measured in a laboratory mill with the aid of thermocouples attached to the surface and embedded in the interior of test samples. The heat-transfer coefficient was calculated from the sample temperature response using an implicit finite-difference model over a range of temperatures, strain rates, and pressures. Values of 200 to 450 kW/m2 °C were obtained by backcalculation. A comparison of the results from this study with those measured in a previous investigation on two steel alloys has led to the development of an equation which characterizes the HTC as a function of the ratio of the rolling pressure to the flow stress at the surface of the workpiece. This relationship has been employed to explain the apparent differences in the heat-transfer behavior of different metals at similar rolling pressures.

Analysis of thermomechanical behaviour in billet casting with different mould corner radii

Abstract A finite element thermal stress model to compute the thermomechanical state of the solidifying shell during continuous casting of steel in a square billet casting mould has been applied to investigate longitudinal cracks. A two-dimensional thermoelastoviscoplastic analysis was carried out within a horizontal slice of the solidifying strand which moves vertically within and just below the mould. The model calculates the temperature distributions, the stresses, the strains in the solidifying shell, and the intermittent air gap between the casting mould and the solidifying strand. Model predictions were verified with both an analytical solution and a plant trial. The model was then applied to study the effect of mould corner radius on longitudinal crack formation for casting in a typical 0·75%/m tapered mould with both oil and mould powder lubrication. With this inadequate linear taper, a gap forms between the shell and the mould in the corner region. As the corner radius of the billet increases from 4 to 15 mm, this gap spreads further around the corner towards the centre of the strand and becomes larger. This leads to more temperature non-uniformity around the billet perimeter as solidification proceeds. Longitudinal corner surface cracks are predicted to form only in the large corner radius billet, owing to tension in the hotter and thinner shell along the corner during solidification in the mould. Off corner internal cracks form more readily in the small corner radius billet. They are caused by bulging below the mould, which bends the thin, weak shell around the corner, creating tensile strain on the solidification front where these longitudinal cracks are ultimately observed.

Modeling the microstructural changes during hot tandem rolling of AA5XXX aluminum alloys: Part I. Microstructural evolution

AbstractA comprehensive mathematical model of the hot tandem rolling process for aluminum alloys has been developed. Reflecting the complex thermomechanical and microstructural changes effected in the alloys during rolling, the model incorporated heat flow, plastic deformation, kinetics of static recrystallization, final recrystallized grain size, and texture evolution. The results of this microstructural engineering study, combining computer modeling, laboratory tests, and industrial measurements, are presented in three parts. In this Part I, laboratory measurements of static recrystallization kinetics and final recrystallized grain size are described for AA5182 and AA5052 aluminum alloys and expressed quantitatively by semiempirical equations. In Part II, laboratory measurements of the texture evolution during static recrystallization are described for each of the alloys and expressed mathematically using a modified form of the Avrami equation. Finally, Part III of this article describes the development of an overall mathematical model for an industrial aluminum hot tandem rolling process which incorporates the microstructure and texture equations developed and the model validation using industrial data. The laboratory measurements for the microstructural evolution were carried out using industrially rolled material and a state-of-the-art plane strain compression tester at Alcan International. Each sample was given a single deformation and heat treated in a salt bath at 400 °C for various lengths of time to effect different levels of recrystallization in the samples. The range of hot-working conditions used for the laboratory study was chosen to represent conditions typically seen in industrial aluminum hot tandem rolling processes, i.e., deformation temperatures of 350 °C to 500 °C, strain rates of 0.5 to 100 seconds and total strains of 0.5 to 2.0. The semiempirical equations developed indicated that both the recrystallization kinetics and the final recrystallized grain size were dependent on the deformation history of the material i.e., total strain and Zener-Hollomon parameter (Z), where

Mathematical modeling of the extrusion of 6061/Al2O3/20p composite

Z = \dot \varepsilon exp \left( {\frac{{Q_{def} }}{{RT_{def} }}} \right)