Coupled heat transfer, fluid flow and solidification kinetics for laser additive manufacturing applications

Abstract

A new coupled heat transfer and solidification kinetics model is developed for the optimization of microstructure during laser additive manufacturing applications. The Johnson–Mehl–Avrami–Kolmogorov equation is applied in a self-consistent manner for modeling of the rapid phase change on the substrate. The numerical simulations using the OpenFOAM framework are conducted for Ni-based superalloy single track laser cladding. Single track laser cladding experiments were carried out to verify the results of our calculations. A rather good coincidence with the experimental data is shown for the developed model. The influence of processing parameters on the macro and micro parameters of the tracks is analyzed. A method for changing the average crystalline size and simultaneous preservation of the height and width of the track is presented. The possibility of controlling the microstructure of similar tracks gives an opportunity to preserve the scanning strategy for building parts with a defined quality.

Introduction

Laser cladding (LC) and its additive manufacturing (AM) applications enable a substantial reduction of the production cycle of complex shape parts. Direct numerical simulation (DNS) is an efficient tool for the reduction of the experimental work needed for complex technology optimization. The models of LC cease to investigate single phenomena and advance in incorporating a wide range of processes [1]. Coupling of different phenomena especially on multiple scales is still a challenge. The simulation results focus not only on the prediction of the temperature dynamics or track macroparameters but also on the final properties of the cladded material.

The correlation between individual or combined processing parameters at laser cladding and the resulting single track characteristics has been investigated by many authors [[2], [3], [4], [5]]. Experimental evidence in the optimal processing window of laser cladding shows the direct correlation of the main single track macroparameters to the laser power while having the opposite for the scanning speed [[2], [3], [4]]. Though the overall microstructure evaluation is rather complex, it is also known that a finer microstructure can be obtained using laser cladding at an increased scanning speed, which is usually associated with an increase in the cooling rate at the crystallization front in this case [5]. While not underestimating the importance of obligatory experimental research, the numerical simulations are attracting high attention, giving an opportunity to look inside the complex phenomena as experimental optimization of the laser cladding process is generally very expensive in terms of cost and time.

The state-of-art models of laser cladding include almost every phenomenon that occurs in the melt pool. Wen and Shin [6] considered both the powder aerodynamics and laser-particle interaction and the melt pool hydrodynamics during laser cladding. In their recent publication Kovalev et al. presented in detail the powder distribution on a flat substrate after the feeding stage but ignored the fluid flow in the melt pool [7]. Though the particle trajectory is critical in determining the laser particle interaction time both papers show a similar particle distribution pattern. It is seen that particles irradiated by the laser beam are rapidly heated to the high temperatures and the powder in the peripheral zone of the powder jet is rather cold. This could be used for the simplification of laser-powder interaction simulation.

Lee and Farson [8] presented the hydrodynamic model for multiple layer additive manufacturing and demonstrated the change of the melt pool shape from layer to layer due to the spreading of the melt. This reveals that the fluid flow could not be reduced to the thermal conduction with effective coefficients for the multilayer process. The powder catchment efficiency was included in the hydrodynamic model and typical cladding dissipation geometries (a massive substrate, an edge and corner of the bulk part and a thin wall) were considered for the process planning purposes in our previous paper [9]. The phase change is considered to be equilibrium and is simulated in most models by shock-capturing methods [10].

Rapid crystallization of the added material during laser cladding is known to result in the material properties different from the conventional technologies [11]. Laser additive manufacturing (LAM) is a multiscale technology and processes on different scales strongly influence each other but the problem is considered on each scale separately [1,12], or the consistency is limited by one side [13]. The phase change on a macroscale is supposed to be equilibrium [14] which could not be justified for rapid crystallization in the course of laser additive manufacturing applications. The assumption of equilibrium phase change on the macroscale results in information loss on microscale also because the temperature history gained on macroscale determines the process on the microscale [12]. For example, Liu et al. developed a phase-field model to predict dendrite evolution for the TiC composite LC [15] using the results of macromodel [6]. This causes the loss of the information on the nonequilibrium phase change. Self-consistent models of dendrite growth are published for selective laser melting [16], but to our knowledge, there are no such models for laser cladding and its additive applications. The authors reduce the problem into two 2D cross-sections and show microsegregation and microstructure evolution with temperature variation. Nevertheless for the accurate quantitative prediction of solidification microstructure 3D modeling is needed.

Three dimensional model of grain structure evolution at laser welding of aluminum alloy is developed recently by Wei et al. [17]. The authors show powerful capabilities of the numerical modeling in the investigating of the microstructure comparing to the experimental investigation which is constrained to 2D cross sections. The grain structure and topology dependence on main processing parameters is revealed for single track laser welding. Generous dependences of output parameters on the processing conditions narrow the search area in the processing map, but still much experimental work is needed to find optimal processing parameters. The further development of the numerical modeling to make direct engineering recommendations is essentially vital to reduce the labour intensive experimental work.

In this paper, we present in all details the developed self-consistent model of the microstructure calculation during LC and its verification. The heat transfer, fluid flow and solidification kinetics are considered in a coupled manner for a single track LC of a Ni-based superalloy. The developed model does not require a multiscale approach and helps us to predict the resulting microstructure along with the growth macroparameters of the metal part before its actual fabrication. Using the developed model we make engineering recommendations for the building parts with a defined quality.