Simulation of thermal behaviours and powder flow for direct laser metal deposition process

. Laser engineering net-shaping (LENS), based on directed energy deposition (DED), is one of the popular AM technologies for producing fully dense complex metal structural components directly from laser metal deposition without using dies or tooling and hence greatly reduces the lead-time and production cost. However, many factors, such as powder-related and laser-related manufacturing parameters, will affect the final quality of components produced by LENS process, especially the powder flow distribution and thermal history at the substrate. The powder concentration normally determines the density and strength of deposited components; while the thermal behaviours of melt pool mainly determines the cooling rate, residual stress and consequent cracks in deposited components. Trial and errors method is obviously too expensive to afford for diverse applications of different metal materials and various manufacturing input parameters. Numerical simulation of the LENS process will be an effective means to identify reasonable manufacturing parameter sets for producing high quality crack-free components. In this paper, the laser metal powder deposition process of LENS is reported. The gas-powder flow distribution below the deposition nozzle is obtained via CFD simulation. The thermal behaviours of substrate and as-deposited layer/track during the LENS process are investigated by using FEM analysis. Temperature field distributions caused by the moving laser beam and the resultant melt pool on the substrate, are simulated and compared. The research offers a more accurate and practical thermal behaviour model for LENS process, which could be applied to further investigation of the interactions between laser, melt pool and powder particles; it will be particularly useful for manufacturing key components which has more demanding requirement on the components’ functional performance.


Introduction
Laser engineering net-shaping (LENS), based on a kind of directed energy deposition (DED), is one of the popular AM technologies for producing complex metal structural components production.It could be used to fabricate complex, fully-dense metal components from CAD files directly without using dies, tooling or further machining, which hence greatly reduces the lead-time and production cost.Although LENS is a promising additive manufacturing process, it has not been widely used until recently.One of the main reasons is the high temperature and cooling rate during the LENS process will produce large residual stresses which may cause detrimental cracks and geometrical distortion to the deposited components.Besides, the range of deposited component size, imperfect surface quality and high cost of metal powder also limited LENS applications.Many factors, such as the laser-related and powder-related input manufacturing parameters will affect the final quality of components produced by LENS process, especially the thermal history of laser metal-powder deposition process mainly determining the cooling rate, residual stress and consequent cracks on the surface of deposited components.Trial and errors method is obviously too expensive to afford for diverse applications of different metal materials and various manufacturing input parameters.Numerical simulation of the LENS process will be an effective means to identify reasonable manufacturing parameter sets for producing high quality crack-free components.
Many researches have already tried to investigate the LENS or direct laser metal deposition (LMD) process numerically or experimentally [1][2][3][4].Peyre et al [5] developed a three-step analytical and numerical approach to predict the shapes of manufactured structures and thermal loadings induced by the LMD process using multi-physics COMSOL.This approach takes into account the moving interface during metal deposition which allows the conductivity front to move simultaneously with the moving laser source and hence could accurately represent the LMD process.Liu et al. [ where, k is the thermal conductivity; ρ s is the substrate material density; C s is the specific heat; T is the temperature and t is time variables.The typical boundary conditions are represented as where n refers to the direction vertical to the substrate surface; k n is the thermal conductivity vertical to the substrate surface; h c is the surface heat transfer coefficient; ε c is emissivity constant; σ S-B is Stefan-Boltzmann constant; T R is the reference temperature, respectively.The 1 st term on the right-hand side in Eq. [4] represents heat energy being transferred to the substrate due to thermal conduction from the surface whose unit normal is n.The 2 nd and the 3 rd terms on the right-hand side refer to convection and radiation from the surface open to air.For laser beam heat source which follows Gaussian distribution, the heat flux, q s , transferring from laser beam to the substrate surface could be expressed as: where P is the laser power; η is the thermal absorption coefficient of the laser beam, r lb the radius of the laser beam spot; d is the beam distribution parameter, respectively.The values of d, r lb , and η are considered as 3.0, 0.26 mm, and 0.28, respectively.It is worthy to mention that the high value of d(>2.0)allows the distribution of the applied heat flux to follow a high peak with a steep descent within a small focused area, which is typical for the type of laser used in the LENS machine.
The effective beam radius r lb could be obtained by measuring several melt pool radii that are produced by the LENS system's laser on a SS316 substrate without any powder material.The absorption coefficient, η, of the laser beam is a complex function of substrate temperature, incident surface quality, and shielding atmosphere.To avoid complexity, an average value of η is estimated following Bramson's equation as [3,11] where R is the temperature-dependent electrical resistivity of the material and λ is the wavelength of the laser beam, the latter being equal to 1.067um in the present case.
During the LENS processing, the powders travel through the passages within the laser deposition head and are then ejected out from the nozzles; they will fly to the focus of the laser beam and finally fall into the melt pool if not fully being melt when flying via the focus of laser beam.It is too complicate to track the real-time position and temperature of the individual powders.It is a reasonable assumption that most of the incident powders will be trapped by the molten pool at melting points and some of them may be renounced by the substrate due to large momentum and keeps the room temperature.
In this paper, three-dimensional 8-node heat transfer brick element (DC3D8 in ABAQUS) with temperature as the nodal degree of freedom is used for modelling the moving laser caused thermal behaviours on the substrate.The transient heat transfer calculations are performed using a uniform time-step and a number of very small time increments within each time-step.For the moving laser beam of a moving speed 5m/s and spot diameter of 0.26mm, the simulated temperature field around the laser spot on the substrate are obtained in Section 4. The realization and the application of the heat input to the heat transfer elements in the substrate are realized through an ABAQUS user subroutine DFlux.

Gas-powder flow
As mentioned in Fig. 2, there are many output variables from CFD simulation, such as particle velocity, particle mass concentration (PMC), DPM number of collision and trajectory of powders after being ejected from the nozzles.PMC is the most important variable https://doi.org/10.

Table 1 .
Input parameters from CFD simulation of gas-powder flow

Thermal behaviour modelling in LENS 3.1. Laser heat source caused temperature field on the substrate A
3D FE model for simulation of the thermal transfer when laser heat source moving on the substrate is established with user subroutine DFlux in ABAQUS.The transient heat conduction equation between the moving laser heat source and the substrate could be expressed as follow in the 3D Cartesian coordinate system :