Predicting the columnar-to-equiaxed transition for a distribution of nucleation undercoolings

A deterministic mathematical model for steady-state unidirectional solidification is proposed to predict the columnar-to-equiaxed transition. In the model, which is an extension to the classic model proposed by Hunt [Hunt JD. Mater Sci Eng 1984;65:75], equiaxed grains nucleate according to either a normal or a log-normal distribution of nucleation undercoolings. Growth maps are constructed, indicating either columnar or equiaxed solidification as a function of the velocity of isotherms and temperature gradient. The fields A columnar and equiaxed growth change significantly with the spread of the nucleation undercooling distribution. Increasing the spread Favors columnar solidification if the dimensionless velocity of the isotherms is larger than 1. For a velocity less than 1, however, equiaxed solidification is initially favored, but columnar solidification is enhanced for a larger increase in the spread. This behavior was confirmed by a stochastic model, which showed that an increase in the distribution spread Could change the grain structure from completely columnar to 50% columnar grains. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Modeling of columnar-to-equiaxed transition in solidified Al-Si alloys

A Cellular-Automaton Finite-Volume-Method (CAFVM) algorithm has been developed, coupling with macroscopic model for heat transfer calculation and microscopic models for nucleation and growth. The solution equations have been solved to determine the time-dependent constitutional undercooling and interface retardation during solidification. The constitutional undercooling is then coupled into the CAFVM algorithm to investigate both the effects of thermal and constitutional undercooling on columnar growth and crystal selection in the columnar zone, and formation of equiaxed crystals in the bulk liquid. The model cannot only simulate microstructures of alloys but also investigates nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies.

An atomistic simulation of solid state sintering using Monte Carlo methods

This paper presents results on the simulation of the solid state sintering of copper wires using Monte Carlo techniques based on elements of lattice theory and cellular automata. The initial structure is superimposed onto a triangular, two-dimensional lattice, where each lattice site corresponds to either an atom or vacancy. The number of vacancies varies with the simulation temperature, while a cluster of vacancies is a pore. To simulate sintering, lattice sites are picked at random and reoriented in terms of an atomistic model governing mass transport. The probability that an atom has sufficient energy to jump to a vacant lattice site is related to the jump frequency, and hence the diffusion coefficient, while the probability that an atomic jump will be accepted is related to the change in energy of the system as a result of the jump, as determined by the change in the number of nearest neighbours. The jump frequency is also used to relate model time, measured in Monte Carlo Steps, to the actual sintering time. The model incorporates bulk, grain boundary and surface diffusion terms and includes vacancy annihilation on the grain boundaries. The predictions of the model were found to be consistent with experimental data, both in terms of the microstructural evolution and in terms of the sintering time. (C) 2002 Elsevier Science B.V. All rights reserved.

Microhardness mapping and the hardness-yield strength relationship in high-pressure diecast magnesium alloy AZ91

Microhardness maps of cross-sections of high-pressure diecast test bars of AZ91 have been determined. Specimens with rectangular cross-sections, 1, 2 and 3 mm thick, or with a circular cross-section 6.4 mm in diameter, have been studied. The hardness is generally higher near the edges in all specimens, and more so near the corners of the rectangular specimens. The hardness at the center of the castings is generally lower, due to a coarser solidification microstructure and the concentration of porosity. The evidence confirms that the surface of the castings is harder than the core, but it does not support the concept of a skin with a sharp. and definable boundary. This harder layer is irregular in hardness and depth and is not equally hard on opposite sides of the casting. The mean hardness obtained by integrating the microhardness maps over the entire cross-section increased with decreasing thickness of the bars, and was found to be in good correlation with each bar's yield strength. (c) 2005 Elsevier B.V. All rights reserved.

Segregation of particles and its influence on the morphology of the eutectic silicon phase in Al-7 wt.% Si alloys

A new modification phenomenon is reported for Al-Si alloys, where the Al-Si eutectic is refined by segregated TiB2 particles. The TiB2 particles are pushed to the Al-Si phase boundary during solidification of the eutectic and it is believed that at high concentrations the TiB2 particles restrict solute redistribution causing refinement of the Si. (c) 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Grain refinement of Mg-Al(-Mn) alloys by SiC additions

The addition of SiC particles effectively grain refined a range of Mg-Al alloys. The greatest reductions in grain size were found for the alloys with lower Al contents. The presence of Mg2Si in the microstructure after that SiC addition, and consideration of phase equilibria suggested that the SiC transforms to Al4C3, and this is the actual nucleant. The addition of Mn poisoned the grain refining effect of the SiC addition, probably due to the formation of less potent Al-Mn-carbides. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Modelling of microstructure formation and evolution during solidification

A comprehensive probabilistic model for simulating microstructure formation and evolution during solidification has been developed, based on coupling a Finite Differential Method (FDM) for macroscopic modelling of heat diffusion to a modified Cellular Automaton (mCA) for microscopic modelling of nucleation, growth of microstructures and solute diffusion. The mCA model is similar to Nastac's model for handling solute redistribution in the liquid and solid phases, curvature and growth anisotropy, but differs in the treatment of nucleation and growth. The aim is to improve understanding of the relationship between the solidification conditions and microstructure formation and evolution. A numerical algorithm used for FDM and mCA was developed. At each coarse scale, temperatures at FDM nodes were calculated while nucleation-growth simulation was done at a finer scale, with the temperature at the cell locations being interpolated from those at the coarser volumes. This model takes account of thermal, curvature and solute diffusion effects. Therefore, it can not only simulate microstructures of alloys both on the scale of grain size (macroscopic level) and the dendrite tip length (mesoscopic level), but also investigate nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies. The calculated results are compared with values of grain sizes and solidification morphologies of microstructures obtained from a set of casting experiments of Al-Si alloys in graphite crucibles.

Abrasive wear study of white cast iron with different solidification rates

The abrasive wear resistance of white cast iron was studied. The iron was solidified using two solidification rates of 1.5 and 15 degrees C/s. Mass loss was evaluated with tests of the type pin on abrasive disc using alumina of different sizes. Two matrices were tested: one predominantly austenitic and the other predominantly martensitic, containing M(3)C carbides. Samples with cooling rate of 15 degrees C/s showed higher hardness and more refined microstructure compared with those solidified at 1.5 degrees C/s. During the test, the movement of successive abrasives gave rise to the strain hardening of the austenite phase, leading to the attainment of similar levels of surface hardness, which explains why the wear rate showed no difference compared to the austenite samples with different solidification rates. For the austenitic matrix the wear rate seems to depend on the hardness of the worn surface and not on the hardness of the material without deformation. The austenitic samples showed cracking and fracture of M(3)C carbides. For the predominantly martensitic matrix, the wear rate was higher at the solidification rate of 1.5 degrees C/s, for grain size of 66 and 93 mu m. Higher abrasive sizes were found to produce greater penetration and strain hardening of austenitic matrices. However, martensitic iron produces more microcutting, increasing the wear rate of the material. The analysis of the worn surface by scanning electron microscopy indicated abrasive wear mechanisms such as: microcutting, microfatigue and microploughing. Yet, for the iron of austenitic matrix, the microploughing mechanism was more severe. (C) 2009 Elsevier B.V. All rights reserved.

Microstructure and texture of duplex stainless steel after melt-spinning processing

The microstructure and texture of melt-spun UNS S31803 (DIN W. Nr. 1. 4462) duplex stainless steel were analyzed after casting and solution treatment. The cast ribbons contained austenite (gamma) and ferrite (alpha or delta) with roughly equal compositions. The alpha and gamma had < 100 > and < 110 > partial fiber textures, respectively. After solution treatment, the texture was maintained, the amount of gamma phase increased, and the alloying elements were partitioned as expected, according to whether they were ferrite or austenite stabilizers. (c) 2006 Elsevier Inc. All rights reserved.

Rheological behaviour of the mushy zone and its effect on the formation of casting defects during solidification

A new conceptual framework has been developed which explains the formation of shear-related casting defects such as porosity, segregation and tears. The theory relates defect formation to the mechanical behaviour of the partially solidified microstructure when shear stresses are developed during the filling of a casting and by the subsequent feeding processes during solidification. Two transition points, the dendrite coherency point and the maximum packing solid fraction, divide the mushy zone into three regions of different mechanical and feeding behaviours. The response of the mush to shear is related to the presence of these zones during solidification of a casting. The resulting defects are rationalized by considering the governing local shear stress and shear rate, local strength and time available for fluid flow. The design of the casting, the casting process used and the alloy composition all influence the relative importance of shearing on defect formation. (C) 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.

Shear deformation at 29% solid during solidification of magnesium alloy AZ91 and aluminium alloy A356

Partially solid commercial Al-Si and Mg-Al alloys have been deformed in shear during solidification using vane rheometry. The dendritic mush was deformed for a short period at 29% solid and allowed to cool naturally after deformation. Both alloys exhibited yield point behaviour and deformation was highly localised at the surface of maximum shear stress. The short period of deformation was found to have a distinct impact on the as-cast microstructure leading to fragmented dendrites in the deformation region of both alloys. In the case of the Mg-Al alloy, a concentrated region of interdendritic porosity was also observed in the deformation region. Concentrated porosity was not observed in the Al-Si alloy. (c) 2005 Elsevier B.V. All rights reserved.

Numerical simulation of dendrite growth during solidification

A comprehensive probabilistic model for simulating dendrite morphology and investigating dendritic growth kinetics during solidification has been developed, based on a modified Cellular Automaton (mCA) for microscopic modeling of nucleation, growth of crystals and solute diffusion. The mCA model numerically calculated solute redistribution both in the solid and liquid phases, the curvature of dendrite tips and the growth anisotropy. This modeling takes account of thermal, curvature and solute diffusion effects. Therefore, it can simulate microstructure formation both on the scale of the dendrite tip length. This model was then applied for simulating dendritic solidification of an Al-7%Si alloy. Both directional and equiaxed dendritic growth has been performed to investigate the growth anisotropy and cooling rate on dendrite morphology. Furthermore, the competitive growth and selection of dendritic crystals have also investigated.

Eutectic solidification in hypoeutectic Al-Si alloys: electron backscatter diffraction analysis

Nucleation and growth of the eutectic, in hypoeutectic Al-Si foundry alloys has been investigated by the electron backscatter diffraction (EBSD) mapping technique using a scanning electron microscope (SEM). Sample preparation procedures for optimizing mapping have been developed. To obtain a sufficiently smooth surface from a cast Al-Si eutectic microstructure for EBSD mapping, an appropriate preparation technique by ion milling was developed and applied instead of conventional electropolishing. By comparing the orientation of the aluminum in the eutectic to that of the surrounding primary aluminum dendrites, the growth mechanism of the eutectic can be determined. Two different results were found, in isolation or sometimes together, but distinct for different strontium contents: (1) crystallographic orientations of aluminum in eutectic and surrounding primary dendrites are identical, and (2) wide variation in orientations of the aluminum in the eutectic. (C) 2001 Elsevier Science Inc. All rights reserved.

Characterization of the Al-3wt.%Si alloy in unsteady-state horizontal directional solidification

The main purpose of this paper is to investigate both the columnar to equiaxed transition and primary dendritic arm spacings of Al-3wt.%Si alloy during the horizontal directional solidification. The transient heat transfer coefficient at the metal-mold interface is calculated based on comparisons between the experimental thermal profiles in castings and the simulations provided by a finite difference heat flow program. Simulated curve of the interfacial heat transfer coefficient was used in another numerical solidification model to determine theoretical values of tip growth rates, cooling rates and thermal gradients that are associated with both columnar to equiaxed transition and primary dendritic arm spacings. A good agreement was observed between the experimental values of these thermal variables and those numerically simulated for the alloy examined. A comparative analysis is carried out between the experimental data of this work and theoretical models from the literature that have been proposed to predict the primary dendritic spacings. In this context, this study may contribute to the understanding of how to manage solidification operational parameters aiming at designing the microstructure of Al-Si alloys.