Thermal Study of a Cladding Layer of Inconel 625 in Directed Energy Deposition (DED) Process Using a Phase-Field Model

In an effort to simulate the involved thermal physical effects that occur in direct energy deposition (DED) a thermodynamically-consistent of phase-field method is developed. Two state parameters, characterizing phase change and consolidation, are used to allocate the proper material properties to each phase. The numerical transient solution is obtained via a finite element analysis. A set of experiments for single tracks scanning were carried out to provide dimensional data of the deposited cladding lines. By relying on a regression analytical formulation to establish the link between process parameters and geometries of deposited layers from experiments, an activation of passive elements in the finite element discretization is considered. The single-track cladding of Inconel 625 powder on tempered steel 42CrMo4 was printed with different power, scanning speed and feed-rate to assess their effect on the morphology of the melt pool and the solidification cooling rate. The predicted dimensions of melt pools were compared with experiments reported in the literature. In addition, this research correlated the used process parameter in the modelling of localized transient thermal with solidification parameters, namely, the thermal gradient ( 𝐺 ) and the solidification rate ( 𝑅 ).


Introduction
Additive manufacturing (AM) is a transformative approach to industrial production that enables the creation of lighter and stronger parts with higher flexibility in the design to achieve desirable mechanical properties and high dimensional accuracy. The AM processes consolidate feedstock materials such as powder, wire or sheets into a dense metallic part by melting and solidification with the aid of an energy source such as laser, electron beam or electric arc, in a layer by layer manner [1] [2].
Directed Energy Deposition (DED) covers a range of terminology including laser engineered net shaping products, directed light fabrication, direct metal deposition and 3D laser cladding [3]. DED is a complex printing process commonly used to repair or add additional material to existing components [4] [5]. DED involves injecting a stream of metallic powder that is melted by a laser beam as a heat source in order to deposit material layer-by-layer on a built platform [6]. In DED process, solidification and solid-state transformations, upon heating and cooling, deeply affect the mechanical properties of deposited layer induced by the high-energy input and high cooling rate during the process [7]. The control of the involved physical phenomena like melting, phase changing, vaporization, and Marangoni convection is extremely difficult and sometimes impossible exclusively by means of experimental analyses [8]. Furthermore, it is rather time-consuming and expensive to produce DED fabricated parts. Computational simulation can give precious information on the complex process-structure-property relations and therefore be useful to its design and optimization.
The phenomenon has a multi-scale inherent nature which is computationally complex and challenging that, so far, must be tackled at different stages. Temperature prediction and solid-liquid phase fields detection can be defined as the initial stage in the process simulation, that can then be utilized subsequently in thermal-mechanical and material microstructure evolution. The model needs to properly consider the material properties with respect to solid-liquid phase changing, powder-dense material status. Lee et al. presented enhanced models for temperature evolution and phasedependent thermal conductivity and heat capacity in selective laser melting (SLM) process [9] [10]. Roy et al. proposed a purely thermal model which explicitly incorporates two state variables for both the phase and the porosity in SLM. Their model has the ability to capture the consolidation of the material and allowed them to investigate the phase-dependent laser absorptivity [11]. It is worth noting that although a broad number of numerical modeling approaches for selective laser melting (SLM) can be found in recent years, capable of predicting the temperature field, melting and solidification [12] [13], there is a lack of the detailed studies on phase detecting on DED. The origin of this inattention comes from another existing challenge in DED simulation, including the dynamic incorporation of the additive material as the deposited layer into the numerical model. Through activation of a new set of elements in each time step of the finite element solution. Moreover, DED process has a highly localized thermal behavior which leads to undesirable microstructural features [14] and inconsistent mechanical properties of the fabricated parts. Nevertheless, some significant efforts have been made to simulate solidification kinetics [15] and investigation results on the correlation microstructural features and mechanical properties between thermal characterization of melt pool and solidification parameters, including thermal gradient and solidification rate, have been reported [16]. The effect of increasing the laser speed and decreasing the power simultaneously on the melt pool size, thermal gradients and cooling rates were illustrated in [17]. Correlation between solidification parameters which can be derived from numerical thermal models based on the Finite Element Method (FEM) were reported in [18] [19]. Subsequently, the microstructure was predicted using the solidification map of the specific material. Finally, indirect microstructure control was achieved by relating the predicted microstructure to the derived melt pool dimensional map. To the best of the authors' knowledge, very little attention has been given, so far, to the development of a transient heat numerical model on DED process involving phase changing to predict of the melt pool boundary with varying laser power to extract the solidification parameters.
The present article focuses on the development of a thermal powder deposition evolution for DED process using the commercial FEM software ABAQUS. The transient heat transfer model associated with the phase field concept is implemented by user coding in FORTRAN language, taking into consideration the latent heat of fusion and vaporization. In the present model, the volume fraction of the deposited material is modeled based on the synergistic interactions from experiment-driven equations. Subsequently, the validation procedure is carried out based on experimentally measured melt pool dimensions related to single track fabrication of IN 625 on a 42CrMo4 baseplate. Then the calculated solidification parameters ( , ) were compared across the melt pool by changing laser power to shed light on its effect on the microstructure map.
The paper is organized as follows. Section 2 contains the numerical approach consisting of governing equations, describing the transient heat transfer model associated with the phase change concept, material allocations for both deposition and substrate with the concept of the phase-field model and heat source modeling. Section 3 presents the experimental study for single-track lines of IN625 on the tempered substrate 42CrMo4 with different power, scanning speed and feed rate to achieve various penetrations. In section 4, the thermal phenomena based on finite element formulation is implemented in ABAQUS through relevant user interface routines. Subsequently, in section 5 the results from the proposed numerical method are compared with experimental data to assess the efficiency of the model. In Section 6, conclusions are drawn and summarized.

Proposed Numerical Approaches
The direct energy deposition (DED) process modelling is presented in detail in the following sections, in terms of heat transfer constitutive equations, allocated material properties with respect to temperature and material states and energy source modelling; The energy density is expressed in terms of the temperature and state variables as below; Here , and , are the volumetric heat capacities in the solid and liquid states, the latent heat of fusion-melting [21] [22] and latent heat of vaporization respectively. is the average melting temperature, taken as = 0.5 * ( + ), where and are liquidus and solidus temperatures [23].
The used function ( ) in Equation 4 is defined based on the thermodynamically consistent phase-field approach proposed by Wang et al. [20] such that (0) = 0 and (1) = 1 and = = 0 = 0 and = 1 [23], where is the phase parameter. It takes the following form: In Equation 5 the phase parameters , are defined as: where is the vaporized temperature, is the temperature at the liquid-vapor transition and is the average vaporization temperature taken as = 0.5 * ( + ).
Some conditions are considered: = 0 if < and = 1 if < . When ≤ ≤ then 0 < < 1 , representing the mushy region. Moreover, = 1 if < , indicating whether the material is vaporized or not. The parameter determines the steepness of change transition [10]. The effect of the choice of on the profile of the phase parameter ( ) (for sharp transition = 10 and for diffuse transition = 5) is shown in Figure. 1. When = 0 the material is still in the powder state and = 1 refers to the fully dense region. Table   1 shows the material state relation with the state variables.
According to Equation 8, which is related to the history of the fusion phase parameter at each material point. The mentioned volumetric heat capacity ( ) and thermal conductivity ( ) in Equations 1 and 2 are determined by the degree of consolidation ( ) defined in Equations 9-10 where and are the thermal conductivity in the powder and dense material, respectively. The volumetric heat capacity depends on the consolidation and , the latter being the heat capacity of the fully dense material and 0 represents the initial porosity of powder and assumed 0.6. In general, the thermal conductivity and heat capacity are also temperature dependent. In the next section, the correlation between materials' thermo-physical properties with state variables are presented.

Material Properties Module
Nickel-based super alloy powder (MetcoClad625®) as cladding powder and 42CrMo4 tempering steel as substrate are considered in this research. MetcoClad625 is used as a blown powder cladding layer and tempering steel is employed as a solid substrate part. Figures 2 and 3 along with the Table 2 represent the thermo-physical material properties depending on the temperature for MetcoClad625 (both powder and solid phase) and steel 42CrMo4. In the DED process, a great part of the blown powder particle undergoes a phase change and turns into a liquid state by a heat source, while the rest of the material remains in mushy powder-melt state. Thereafter, as the material cools down, the melted parts change to a solid state. Since the difference of material properties between the liquid area with mushy zones and the solid state is very large, the current state of the material should be identified in order to utilize appropriate properties according to the phase change history.  Table 2. Thermo-physical properties of the material  Figure 4 shows the different phases throughout deposition process between solid and liquid phases. which is schematically represented in Figure 5, Figure 5 The schematic of heat source with exponentially decaying method where is the laser power, is the distribution of power factor, is laser beam radius corresponding to the distance between the beam center and the point at coordinates ( , ), is the laser speed moving. Figure 6 illustrates the schematic profile of power density with respect to the distribution factor.

Experimental procedure
A tempered steel (42CrMo4) plate with size of 100 × 120 × 15 was used as a substrate. In the preparation process, the surface was machined and then cleaned by ethanol. The used powder is commercially the gas-atomised Nickel-based super alloy (MetcoClad 625), similar to Inconel 625. Figure 7 shows the micrography of the powder. Laser cladding experiments were performed by a coaxial laser machine "LDF 3000 -100" with a fibre-coupled high power laser diode (adjustable wavelength 900-1030 nm that changes depend on power), with 6000 W maximum beam power output. The laser machine was equipped with a 6-axes KUKA KR90 R3100 industrial robot. Based on  Figure 8 (a -f) shows the geometrical measures of the clad section of the molten pool for some samples using software ImageJ.

Numerical implementation with finite element method (FEM)
To obtain the thermal model for DED process, including subsequent results such as temperature, melt pool dimensions, interfacial phenomena, a thermal finite element analysis framework was built using the commercial software ABAQUS/Standard. ABAQUS provides the interface for mesh designing, programming user-defined material behavior and boundary conditions. Hereby, the specific features and numerical models of DED introduced in Section 2 associated with experimental results, in section 3, are implemented using provided user subroutines as follows.

Finite element solution for heat transfer
Using the Galerkin weighted residual method it is possible to obtain from Equations 1 and 2 the following classical integral (weak) form as Equation 16; where = ( ) is a weighting function, and from which, utilizing the finite element method, a system of ordinary differential equations can be written, in a matrix form as Equation 17: In Equation 17, is the nodal temperature vector, ̇ its time derivative, ( ) a temperature dependent equivalent capacity matrix, resulting terms that include temperature time derivative in Equation 16, ( ) is the equivalent conductivity matrix, resulting from terms that include temperature in Equation 16 and is the equivalent time dependent heat source, resulting from independent terms in Equation 16.
Using an implicit time integration scheme to solve Equation 17, in which it is assumed that Then final nonlinear system of equations to be solved results in Equation 19; The nonlinear system of equations is iteratively solved, within each time step, resorting to the Newton method, in a three-step procedure at each iteration as below; Therefore, the material state can be defined by the state variables , with respect to temperature. Finally, a USDFLD subroutine is developed to manage the material states at the end of each time increment. In Figure 9, a general flowchart summarizes the structure combination of used subroutines in ABAQUS.

Time and space discretization
The dimensional size of the modeled substrate is 100mm×120mm×15mm and the cladding lines are modeled with 5 mm×5 mm×100mm dimensions above the substrate as shown schematically in Figure   9. During the simulation, only a specific volume of the cladding line is activated based on the fed process parameters. This methodology makes the affordable balance for the computational time with the resolution of the results, thus making the simulation times reasonable. In this research, for both deposition layer and substrate, 3D thermal finite element mesh DC3D8 is utilized. The resolution of FEM model was selected to be high enough guarantee stabilization as well as an accurate cooling rate but keeping an affordable computational time. Thus artificial dispersion control introduces a stability limit on the size of the time increment and mesh size such that the local Courant number as Equation 25 [26].
where | | is the velocity and ∆ and ∆ represent the time increment and characteristic element size in the direction of flow respectively. The larger elements were used far away from the scanned region to reduce calculation time in the substrate. Meanwhile, to ensure a good link between the clad layers surface and the substrate, the mesh is refined as much as to avoid numerical temperature fluctuation due to very high temperature gradient.

Initial and Thermal boundary condition
All the surfaces of the cladding welding line and the substrate were initially fixed at 0 = 298.15 and the sink temperature was also fixed at 0 in the bottom of the baseplate. Besides, the tie constraint is applied between the top surface of baseplate and bottom surface of cladding layer to transfer the temperature between the contacted nodes.

Numerical model validation
Three single-track laser scans are simulated firstly to validate the proposed numerical model using the experimentally measured melt pool dimensions. The processing parameters used in the simulation of is shown in Table 3. The real scanning speed, feed rate, laser power are used in the numerical model to better mimic the real phenomena. The predicted melt pool dimension using the described numerical model and the experimental results are shown in Figures 11 and 12. The results show that both melt pool dimensions including width and depth increase as more laser power is used. In other words, by increasing the laser power, the heat per unit time increases as well, and so the melt pool volume increases. The predicted results are also in good agreement with the experimental datadriven. In particular, Table 4 illustrates the comparison between width, depth of melt pool area and height of cladding lines derived from associated regression-based information experimentally and numerically.   The red triangles and purple squares in Figure 13 show the average widths and depths of the simulated melt tracks at different scanning speeds. In the Figure, results from the simulation illustrate that both the width and depth of the melt track decrease with increasing scanning speed. Figure 14 provides evidence that by increasing the laser velocity the volume of the melt pool decrease. When the scanning speed is low, the laser remains longer around a local point, thereby generating more heat and resulting in a larger melt volume. width-Exp. Depth-Num. Depth-Exp.

Transient heat model associated with phase field approach
The presented graphs in Figure 15     the variation in the morphology and size is presented in Figure 18. As can be seen the dendrite morphology, orientations, and micro segregation are different at different locations within the melt pool. This is primarily due to different positions and orientations of the initial nuclei combined with different thermal gradients and solidification velocities along the melt pool boundary.
The growth rate is geometrically derived as the projection of laser velocity onto the normal vector of solidification front, using the angle , which is the local angle between the surface normal to the liquidus isotherm boundary and the welding direction as in Equation 23 and Figure 19;  Figure 20 (a, b), the variation of the and along with the centerline of melt pool boundary with increasing depth is explicitly shown. The results reveal that there is an inverse relationship between and . The maximum is calculated near the top of the melt pool (with a low solidification front depth) while the minimum is found near the bottom of the melt pool (with a high solidification front depth). In contrast, the maximum is calculated at the bottom of the melt pool as the minimum is observed at the top. In the bottom region is exposed at high and low and hence corresponds to the planar grains as shown in Figure 18