The effect of pore size on cell adhesion in collagen-GAG scaffolds.

The phase-field method is reviewed against its historical and theoretical background. Starting from Van der Waals considerations on the structure of interfaces in materials the concept of the phase-field method is developed along historical lines. Basic relations are summarized in a comprehensive way. Special emphasis is given to the multi-phase-field method with extension to elastic interactions and fluid flow which allows one to treat multi-grain multi-phase structures in multicomponent materials. Examples are collected demonstrating the applicability of the different variants of the phase-field method in different fields of materials science.

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Phase-field models in materials science

Modelling of inoculation of metallic melts : Application to grain refinement of aluminium by Al-Ti-B

A new approach to the modelling of grain structure formation in solidification processes is proposed. Based upon a two-dimensional cellular automata technique, the model includes the mechanisms of heterogeneous nucleation and of grain growth. Nucleation occurring at the mould wall as well as in the liquid metal are treated by using two distributions of nucleation sites. The location and the crystallographic orientation of the grains are chosen randomly among a large number of cells and a certain number of orientation classes, respectively. The growth kinetics of the dendrite tip and the preferential 〈100〉 growth directions of cubic metals are taken into account. The model is then applied to small specimens of uniform temperature. The columnar-to-equiaxed transition, the selection and extension of columnar grains which occur in the columnar zone and the impingement of equiaxed grains are clearly shown by this technique. The calculated effect of the alloy concentration and cooling rate upon the resultant microstructure agree with experimental observations.

Probabilistic modelling of microstructure formation in solidification processes

A new criterion for the appearance of hot tears in metallic alloys is proposed. Based upon a mass balance performed over the liquid and solid phases, it accounts for the tensile deformation of the solid skeleton perpendicular to the growing dendrites and for the induced interdendritic liquid feeding. This model introduces a critical deformation rate (
 
$$\dot \varepsilon _{p,\max } $$

 ) beyond which cavitation, i.e., nucleation of a first void, occurs. As should be expected, this critical value is an increasing function of the thermal gradient and permeability and a decreasing function of the viscosity. The shrinkage contribution, which is also included in the model, is shown to be of the same order of magnitude as that associated with the tensile deformation of the solid skeleton. A hot-cracking sensitivity (HCS) index is then defined as 
$$\dot \varepsilon _{_{p,\max } }^{ - 1} $$

 . When applied to a variable-concentration aluminum-copper alloy, this HCS criterion can reproduce the typical “Λ curves” previously deduced by Clyne and Davies on a phenomenological basis. The calculated values are in fairly good agreement with those obtained experimentally by Spittle and Cushway for a non-grain-refined alloy. A comparison of this criterion to hot cracks observed in ring-mold solidification tests indicates cavitation depression of a few kilo Pascal and tensile stresses in the coherent mushy zone of a few mega Pascal. These values are discussed in terms of those obtained by other means (coherency measurement, microporosity observation, and simulation). Even though this HCS criterion is based only upon the appearance of a first void and not on its propagation, it sets up for the first time a physically sound basis for the study of hot-crack formation.

/pdf/a-new-hot-tearing-criterion-2z5ivwusns.pdf

A New Hot-Tearing Criterion

Introduction Atom Transfer at the Solid/Liquid Interface Morphological Instability of a Solid/Liquid Interface Solidification Microstructure: Cells and Dendrites Solidification Microstructure: Eutectic and Peritectic Solute Redistribution Rapid Solidification Microstructures Summary Appendices Symbols Index

W. Kurz

Papers

Fundamentals of Solidification