Cellular Automaton Modeling of Microporosity Formation during Solidification of Aluminum Alloys

Abstract

A two-dimensional (2D) cellular automaton (CA)-finite difference method (FDM) model is proposed to simulate the dendrite growth and microporosity formation during solidification of aluminum alloys. The model involves a three-phase system of liquid, gas, and solid. The growth of both dendrite and gas pore is simulated using a CA approach. The diffusion of solute and hydrogen is calculated using the FDM. The model is applied to simulate the formation and interactions of dendrites and micropores in an Al-7wt.%Si alloy. The effects of initial hydrogen concentration and cooling rate on microporosity formation are investigated. It is found that the porosity nuclei with larger size grow preferentially, while the growth of the small porosity nuclei is restrained. The competitive growth between porosities and dendrites is also observed. With the increase of initial hydrogen concentration, the incubation time of porosity nucleation and growth decreases, and the percentage of porosity increases, while porosity density does not increase apparently. With the decrease of cooling rate, porosity nucleates and starts to grow at higher temperatures, and the percentage of porosity increases, but the porosity density displays a decreasing trend. In addition, at a slower cooling rate, the competitive growth between porosities and dendrites becomes more evident, leading to a more non-uniform distribution of porosity size, and an increased maximum porosity size. The simulation results agree reasonably with the experimental data in the literature.

Notch Stress Intensity Factor (NSIF)-Based Fatigue Design to Assess Cast Steel Porosity and Related Artificially Generated Imperfections

“…In order to establish artificial casting defects numerically, the algorithm of cellular automata (CA) is utilized. As already proposed in recent publications, the application of CA leads to satisfying results concerning the modelling of porosity formation and pore growth [69][70][71]. The presented results within this paper demonstrate the basic applicability of the developed tool, further details are provided in a preceding scientific work [72].…”

Three-dimensional cellular automaton simulation of coupled hydrogen porosity and microstructure during solidification of ternary aluminum alloys

“…Thus, pores are not able to grow immediately after nucleation as the local hydrogen concentration is lower than the local hydrogen solubility. The incubation time which appears in pore nucleation and in pore growth has been previously reported 27 . As solidification proceeds, the local hydrogen concentration in the melt continues increasing.…”

“…Secondly, gaseous pore nucleation only occurs when the gas dissolves in the liquid () and exceeds the critical supersaturation 27 . The hydrogen saturation in melt Al-Si-Mg can be described based on Sievert’s law as: (mL/100 g Al) 3,18 , where is the internal pressure of a gas pore, P 0 is the standard atmospheric pressure, γ is the surface tension of the G/L interface, r p is the pore radius, and and are the solute concentrations of Si and Mg in melt Al, respectively.…”

“…The geometrical factor G G for 2-D system proposed by Zhu et al . 27 is extended to 3-D system as follows: , , where S I , S II and S III are the state of the nearest 6 neighbor cells, the second-nearest 12 neighbor cells, and the third-nearest 8 neighbor cells, respectively.…”

“…Zhu et al . 27 proposed a 2-D CA-FDM model to simulate the growth of microporosity and dendrite during solidification of Al-Si alloys, but was not able to extend the model to the third dimension. Du et al .…”