Solute transport and composition profile during direct metal deposition with coaxial powder injection
Highlights
► Composition profile is important for microstructure and mechanical performance. ► We simulate concentration distribution evolution of elements using a self-developed model. ► Different elements have similar concentration distribution patterns. ► Strong convective motion dominates the species transportation in laser cladding. ► The model helps to achieve appropriate microstructure and target mechanical properties.
Introduction
DMD involves complex physical phenomena, such as laser–powder interactions, heat transfer, melting, fluid flow and solidification. Many analytical and numerical models were developed for heat transfer and fluid flow. They were summarized by the authors in another publication [1].
During DMD with coaxial powder injection, addition of powder particles leads to the interaction between laser and powder, and also the redistribution of solute. Attenuation of laser power during interaction between a laser and powder was investigated a lot [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. Qi et al. [2] considered the coaxial laser powder interaction while modelling heat transfer and fluid flow during DMD. A semi-empirical method of evaluating the laser energy redistribution during CO2 laser cladding with lateral powder injection was reported by Gedda et al. [5]. It was found that 50% of the laser power was reflected off the cladding melt, 10% was reflected off the powder cloud, 30% was used to heat the substrate, and 10% was used to melt the clad layer. Lin [6], [7] studied the laser attenuation and powder temperature distribution in a focused coaxial powder stream both experimentally and theoretically. A Gaussian distribution of coaxial powder concentration was used in his calculations and verified by experimental observation. Similar studies with a powder jet originating from a point source were conducted by Neto and Vilar [8]. Liu and Lin [9] studied, through a numerical model, the heating, melting and evaporation processes of a single spherical powder particle when irradiated by a CO2 laser beam in coaxial powder flow cladding process. The laser energy, initial powder velocity and size have been shown to have important effects on the temperature profile of the powder stream. Kaplan and Groboth [10] developed an analytical model of laser cladding based on balances of mass and energy, which can calculate the temperature distribution in the workpiece. It was found that the powder catchment efficiency and the beam energy redistribution in the material can be optimized by the powder mass flow rate and geometrical properties of the beam and powder jet. An analytical model was presented by Fu et al. [11], in which a powder injection angle was introduced to enable the analysis for both coaxial and lateral powder flows. Formulations for divergent or attenuated laser beams were also given in their model for possible analytical solutions of attenuated energy distribution. Partes [12] developed an analytical model to evaluate the catchment efficiency for the laser cladding process at high processing speeds. It was concluded that the influence of the particles melting during the flight on the catchment efficiency was growing with increasing speed, laser power and powder feed rate. Brückner et al. [13] investigated the influence of process parameters such as feed rate and heat input on the residual stresses of cladding bead by an analytical model, including the powder–beam interaction, the powder catchment by the molten pool, and the self-consistent calculation of temperature field and bead shape. Huang et al. [14], [15] introduced the classical optical theory to calculate the interaction between laser beam and powder stream and investigated the effect of powder feeding rate on the laser intensity and temperature of the particles. They found that the laser intensity distribution and the temperature of the particles at different sites on the surface of the workpiece tended to be even.
Pinkerton and Li [16] constructed a model to describe the variation in powder stream concentration along the axis of a coaxial nozzle. It related directly to nozzle dimensions, material mass and volume flow rates, and was sufficiently simple not to rely on numerical techniques. Lin [17] simulated the powder flow structures of a coaxial nozzle for laser cladding with various arrangements of the nozzle exit. The results showed that more than 50% powder concentration can be increased in a gas stream through a specific nozzle arrangement for coaxial laser cladding. Liu and Li [18] investigated the effects of powder concentration distribution on fabrication of thin-wall parts in coaxial laser cladding. They found that increase in concentration distribution led to decrease in wall thickness and increase in wall growing rate.
In some laser manufacturing processes, such as laser dissimilar welding, laser alloying and laser cladding, there exists solute redistribution, besides mass, momentum and energy transfer. The composition profiles in the molten pool have been simulated by solving the coupled momentum, energy, and species conservation equations for laser dissimilar welding [19], [20] and laser alloying [21], [22], [23], [24], [25]. However, for laser cladding, few researchers have tried to simulate the solute transport process. Kar and Mazumder [26] determined the one-dimensional composition of extended solid solution based on the transport of energy and mass in laser cladding process. They solved governing equations analytically and predicted the extended solubility in clad with the continuous growth model. Huang et al. [27] simulated the mass transfer in the molten pool in the process of laser cladding. The concentration distribution on different sides of the interface between cladding layer and substrate was calculated separately and coupled at the co-boundary.
In previous work, He and Mazumder mainly investigated the heat transfer, fluid flow and energy distribution during single-track laser cladding [1], and the temperature and composition profile of the overlap region for double-track laser cladding [28]. In this study, the solute transport and composition profile evolution by single track during coaxial laser cladding is simulated by a self-consistent three dimensional numerical model, in which some important physical phenomena including melting and solidification, phase changes, mass addition, and interactions between the laser beam and the coaxial powder flow are considered.
Section snippets
Mathematical modelling
A numerical model to simulate heat transfer, fluid flow and mass transfer during laser cladding has been developed. Following assumptions are made in order to simplify calculations:
- (1)
The fluid motion in the molten pool is assumed to be Newtonian, laminar and incompressible.
- (2)
The thermo-physical properties of powder are considered the same as those of substrate, and these properties are assumed to be temperature-independent.
- (3)
The input heat from laser is assumed to have Gaussian distribution. The beam
Concentration profile of carbon
During coaxial laser cladding processes, the addition of powder leads to the interaction of laser and powder, and also the redistribution of solute. Powder particles are heated by the laser beam and their temperature rises under irradiation by the laser, even accompanied by the phase transformation. They also accumulate energy, which is finally transmitted to the substrate. Meanwhile, the laser beam gets attenuated by absorption, reflection and scattering effects of the clouded particles. The
Conclusions
A self-consistent three-dimensional model has been developed to simulate the solute transport and composition profile during DMD with coaxial powder injection. The model is based on the solution of the equations of mass, momentum, energy conservation and solute transport in the molten pool, incorporating heat transfer, phase changes, mass addition, fluid flow and interactions between laser beam and coaxial powder flow. Some of the important findings are as follows:
- (1)
The solute transport and
Acknowledgements
The work is supported by a grant from the Department of Commerce Advanced Technology Program (ATP), under grant number 70NANB4H3027. Dr. Jean Louis Steademann is the Program Manager.
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