Hydrogen porosity in directionally solidified aluminium–copper alloys: a mathematical model

Abstract

A combined continuum and stochastic model of diffusion-controlled growth was developed to simulate the formation of porosity during the solidification of aluminium alloys. The whole population of pores was tracked, rather than just the average values. A finite difference solution of the diffusion equations was used, combined with a stochastic model of nucleation. The growth of each individual pore was simulated, assuming the shape to be spherical until it impinged on the developing dendrites, at which point the growth was modelled as a hemispherically capped segmented cone, with the growth radius limited by the liquid space between the dendrites. A previously published model by one of the authors was used to predict the dendritic spacing as a function of the thermal conditions. The model was compared with in situ observations of the formation of porosity during the solidification of aluminium–copper alloys, where the size, distribution and morphological evolution of pores were measured as a function of temperature/time. The predicted development of the porosity, including the distribution in size and morphology, compared well with that observed experimentally. The qualitative agreement between the model predictions and experimental results supports the hypothesis that the effect of hydrogen and its diffusion must be incorporated into any accurate model of pore formation in aluminium alloys.