Last-stage solidification of alloys: Theoretical model of dendrite-arm and grain coalescence

Abstract

Hot tearing in castings is closely related to the difficulty of bridging or coalescence of dendrite arms during the last stage of solidification. The details of the process determine the temperature at which a coherent solid forms; i.e., a solid that can sustain tensile stresses. Based on the disjoining-pressure concept used in fluid dynamics, a theoretical framework is established for the coalescence of primaryphase dendritic arms within a single grain or at grain boundaries. For pure substances, approaching planar liquid/solid interfaces coalesce to a grain boundary at an undercooling (⌬T b ), given bywhere ␦ is the thickness of an isolated solid-liquid interface, and ⌬⌫ b is the difference between the grain-boundary energy, ␥ gb , and twice the solid/liquid interfacial energy, 2␥ sl , divided by the entropy of fusion. If ␥ gb Ͻ 2␥ sl , then ⌬T b Ͻ 0 and the liquid film is unstable. Coalescence occurs as soon as the two interfaces get close enough (at a distance on the order of ␦ ). This situation, typical of dendrite arms belonging to the same grain (i.e., ␥ gb ϭ 0), is referred to as "attractive". The situation where ␥ gb ϭ 2␥ sl is referred to as "neutral"; i.e., coalescence occurs at zero undercooling. If ␥ gb Ͼ 2␥ sl , the two liquid/solid interfaces are "repulsive" and ⌬T b Ͼ 0. In this case, a stable liquid film between adjacent dendrite arms located across such grain boundaries can remain until the undercooling exceeds ⌬T b . For alloys, coalescence is also influenced by the concentration of the liquid film. The temperature and concentration of the liquid film must reach a coalescence line parallel to, but ⌬T b below, the liquidus line before coalescence can occur. Using one-dimensional (1-D) interface tracking calculations, diffusion in the solid phase perpendicular to the interface (backdiffusion) is shown to aid the coalescence process. To study the interaction of interface curvature and diffusion in the liquid film parallel to the interface, a multiphase-field approach has been used. After validating the method with the 1-D interface tracking results for pure substances and alloys, it is then applied to twodimensional (2-D) situations for binary alloys. The coalescence process is shown to originate in small necks and involve rapidly changing liquid/solid interface curvatures.

Phase-field-crystal study of grain boundary premelting and shearing in bcc iron

“…The formation of those films below the bulk melting point, typically referred to as GB premelting, can dramatically reduce shear resistance and lead to catastrophic materials failure. This phenomenon is of interest for predicting the formation of solidification defects associated with the formation of those intergranular films, which can lead to hot cracking during the late stages of solidification [3][4][5] , and more generally for understanding the microstructure and mechanical behavior of structural alloys at high homologous temperature. GB premelting has been widely studied experimentally [6][7][8][9][10][11][12][13][14][15][16] as well as theoretically.…”

“…(1) defines it in the Gibbs ensemble for MD simulations, we shall also use the grand canonical and canonical ensembles for PFC and amplitude equation simulations, respectively. In the simplest formulation of the disjoining potential, W can be viewed as the width of a liquid layer sandwiched between two atomically sharp solid-liquid phase boundaries 3 . Furthermore, V (W ) is assumed to have a simple exponentially decaying form (see e.g.…”

Structural short-range forces between solid-melt interfaces

“…This phenomenon, known as GB premelting, can result in a dramatic reduction of the shear resistance and hence to material failure, e.g. during hot cracking in the late stages of solidification [3][4][5] .…”

Simulation of Semi-Solid Material Mechanical Behavior Using a Combined Discrete/Finite Element Method

“…[36] This behavior creates clusters of increasing size, which ultimately percolate throughout the domain (i.e., spread over the entire domain width). In Section III, it will be shown that the percolated solid at high g s controls the mechanical resistance of the mushy zone.…”

“…The mechanical behavior of these solid elements is assumed to be elastoviscoplastic. For the simulations at low g s (i.e., g s < 0.94), no solid bridges have formed between the grains, [36,37] and the mechanical behavior of the free solid grains is relatively unimportant because most deformation is concentrated in the liquid films and because the stresses in the solid rarely exceed the yield stress. However, for simulations at high g s , the mechanical behavior of a domain containing numerous grain clusters is dictated increasingly by the behavior of the percolated grains.…”