Progress in modelling solidification microstructures in metals and alloys: dendrites and cells from 1700 to 2000

Abstract

This is the first account of the history of our understanding of, and ability to model, solidification microstructures. Its objective is to retrace the scientific steps made, from the earliest observations of the eighteenth century to our present-day understanding of dendrites and eutectics. Because of the abundance of information, especially that added during the present century, sub-division was essential: this being the first of three articles. They cover dendrites and cells from 1700 to 2000, and then from 2001 to 2015 and finally eutectics and peritectics from 1700 to 2015. The authors have striven always to identify the genesis of every advance made, being aware that such a compact history must leave many worthy contributions by the wayside; others will doubtless complete the history. This review shows how crossfertilisation between theory and experiment, and basic and applied research led to both the posing and answering of challenging fundamental questions, thus rewarding society with beneficial results.

Morphological stability diagram for slowly and rapidly solidifying binary systems

“…Indeed, an intensive atoms attachment to the solid-liquid interface leads to the fast decrease in the interface undercooling with the formation of crystalline ensemble of cellular or dendritic morphology (see Refs. [4][5][6] and references therein). In appearance of such morphologies a key role plays an establishing balance between destabilizing and stabilizing forces which are competing at the interface leading it to the planar or cellular/dendritic form.…”

CALPHAD Based Cellular Model of Dendrite Growth in Welds

“…Solidification theory and observations predict a parabolic dendrite tip shape [15]. Unlike the dendrite body, close to the tip, the S/L interface is smooth under steady-state growth (Figure-1.9).…”

“…Second, there is no unique solution for and , because, mathematically, there are two unknowns and one equation. Temkin [15] solved the first problem by including the capillarity effect in Ivantsov's model, so the tip radius cannot reach zero because the capillarity will blunt a too sharp tip. The most common solution to the second problem is the marginal stability assumption.…”

“…Originally, the cellular automaton (CA) algorithm was developed by John von Neumann to model complex physical phenomena using simple laws [21]. The first numerical modeling of a dendritic structure evolution was performed by Umantsev et al in 1986 [15].…”

“…15 shows the developed duplex microstructure, and it is found that the developed microstructure is around 4.1% ferrite and 95.9% austenite.…”