Effects of melt-pool geometry on crystal growth and microstructure development in laser surface-melted superalloy single crystals: Mathematical modeling of single-crystal growth in a melt pool (part I)
Abstract The effects of melt-pool geometrical parameters on crystal growth and microstructure development during laser surface melting of single-crystal alloys were studied by means of mathematical modeling and experiments. A mathematical model was developed for the three-dimensional (3-D) melt-pool geometry and single-crystalline melt-pool solidification in laser surface melting. The 3-D melt-pool geometry corresponding to the solidification interface is described by four geometrical parameters ( w , l , h , α ). The model was used to study the effects of variations in the geometrical parameters on crystal growth and microstructure development in the melt pool. Laser surface melting experiments with single-crystal nickel-base superalloys were conducted to verify the computational results of microstructure development in the melt pool. Results indicate that the melt-pool geometrical parameters have profound influences on the dendrite growth velocity and growth pattern in the melt pool. For the (0 0 1)/[1 0 0] substrate orientation, variations in l / w and α can influence both the number and the relative sizes of growth regions while the variation in h / w can only influence the relative sizes of the growth regions. Unidirectional dendrite growth along the [0 0 1] crystallographic direction can be achieved for an α value of 45° or below. The maximum ratio of dendrite-growth velocity to the beam velocity in the melt pool is related to α and l / w . Experimental microstructure observations agreed well with the computational results. These findings show that the desired dendrite growth velocity and microstructure can be obtained through proper control of the 3-D melt-pool geometry.
Controlling fusion zone shape and peak temperature produced by laser or electron beam
The fusion zone shape and peak temperature in melting or welding encountered in packaging and manufacturing technologies can be generally correlated as a function of four independent working parameters. They are dimensionless beam power, Marangoni, Prandtl and modified Peclet numbers. Dimensionless beam power includes the beam power and beam radius, Marangoni number represents the driving force, namely, surface-tension gradient coefficient and viscosity, Prandtl number stands for the ratio between momentum and thermal diffusivities, and the modified Peclet number includes scanning speed, specific heat, solid-to-liquid thermal conductivity ratio, difference in melting and ambient temperatures and latent heat. Determination of the fusion zone shape and peak temperature is crucial due to its close relationship with the strength and properties of the packaging and manufacturing products. The correlated results agree with numerical data, and available experimental data. This unified work can thus be successfully used to control the fusion zone shape and peak temperature prior to welding and melting.
Microsegregation in rapidly solidified Ag-15wt%Cu alloys
Spacings and composition profiles of cellular structures formed in Ag-15wt%Cu alloys at growth rates between 0.1 and 18 cm/s are measured. Cells of the Ag-rich phase occur with intercellular regions composed of eutectic or the Cu-rich phase. At the highest rates the cell spacings exceed the characteristic diffusion length D/V (ratio of liquid diffusion coefficient to growth rate) by a factor of ten. The rate of increase of the average cell composition with growth velocity is larger than predicted by existing diffusion models of the cell tip. Increases in cell compositions beyond the Ag metastable solidus retrograde are accounted for quantitatively by the use of non-equilibrium interface conditions (solute trapping).