Integrated Computational Materials Engineering to Predict Melt-Pool Dimensions and 3D Grain Structures for Selective Laser Melting of Inconel 625

The melt-pool simulation is the third step of the multi-scale simulation procedure in AMP² (Fig. 1). The macro- and meso-scale simulations are on a length scale of millimeters. The micro-scale melt-pool simulation is on a length scale of ~ 10* (melt-pool length). Since the melt-pool length is unknown a priori, the micro-scale length scale is set automatically by the iterative solution, which computes the melt-pool dimensions. The thermal boundary conditions for the melt-pool simulation at a given location are generated from the macro- and meso-scale simulations. Although the temperature distribution at the part and layer scale is non-uniform, the thermal boundary conditions for the melt-pool simulation are assumed to be steady state, corresponding to the temperature distribution on a plane perpendicular to the longitudinal axis of the laser track at the location of interest. In Fig. 1, such a plane would be a radial cross section through the wall of the part. Accordingly, the melt-pool thermal-CFD simulation solves the incompressible Navier-Stokes equations and the thermal energy equation with a solid–liquid phase change for steady-state melt-pool physics. The simulation uses inputs of material property data and AM process setup parameters to perform detailed parametric analyses. From the numerical analysis, the melt-pool geometry, flow field, and temperature distribution are predicted. The melt-pool cross-section geometry and length are computed iteratively such that the thermal and fluid flow equilibrium conditions are fulfilled.

The thermal-CFD melt-pool solution accounts for the effects of phase change, heat of fusion, and heat of vaporization. It uses a Eulerian, steady-state, CFD solver to simulate melt-pool shape, temperature, and fluid flow [11]. Equations (1), (2), and (3) are utilized to model the conservation of mass, momentum, and energy, respectively.where, u_i is liquid velocity, V_i is the laser scan velocity, x_i is the Cartesian coordinate, T is temperature, δ_ij is the Kronecker delta, p is the dynamic pressure (total minus hydrostatic pressure), μ is the dynamic viscosity, H_f is latent heat of fusion, g is the gravitational constant, h_d is the depth from the top surface of the melt pool, c_p is specific heat, k is thermal conductivity, and ρ is density. D_c is the D’arcy type phase coefficient which is used to switch between constant velocity in the solid and momentum conservation in the liquid. α is the phase fraction and equal to 0 in the solid region and 1 in the liquid region. The last two terms in Eq. (3) represent the laser energy absorption (\( {\dot{Q}}_{\mathrm{L}} \)) and the energy lost to evaporation (\( {\dot{Q}}_{\mathrm{E}} \)). The rate of material evaporation is computed using a scaled form of the Langmuir equation [12]:where a_i is the activity of element i in the liquid alloy, \( {P}_{\mathrm{i}}^{\mathrm{o}} \) is the equilibrium vapor pressure of element i over pure liquid at temperature T, and M_i is the molecular weight of element i. To calculate \( {P}_{\mathrm{i}}^{\mathrm{o}} \), the Clausius-Clapeyron equation is used as follows:where P_ATM is the ambient pressure, T_boil is the boiling temperature, H_{v, i} is the enthalpy of vaporization for the element i, and R is the universal gas constant. The rate of mass loss (J_v) is used to compute a rate of energy loss due to evaporation as follows:where H_v is the enthalpy of evaporation for the alloy. The Marangoni shear stress at the gas-liquid interface is modeled using Eqs. (7) and (8):where \( {\hat{n}}_{\mathrm{i}} \) is the normal vector at the gas-liquid interface boundary and \( \frac{d\gamma}{d T} \) is the derivative of surface tension with respect to temperature. The thermal-CFD solver uses a pressure-corrector formulation to solve the incompressible conservation equations. Accordingly, the out-flow faces are set to zero-gauge pressure, and all other faces are assigned a zero-pressure gradient in the direction of the surface normal, or:

A comparison of the predictions of melt-pool dimensions with the experimental work reported by Heigel and Lane [13] and Criales et al. [14] is given in Appendixes 1 and 2. The experimental data includes the melt-pool geometry for scan passes on a bare plate as well as with powder recoat for alloy IN625 for laser power ranging from 49 to 195 W and scan speed between 200 and 875 mm/s. The thermophysical properties of IN625 were obtained from Capriccioli and Frosi [15]. Table 1 contains the remaining material properties with the corresponding reference citations. Material properties with asterisks in Table 1 are data reported for alloy IN718 and are thus approximate values for alloy IN625.

Criales et al. [14] studied the powder bed scan passes; the width and depth of the melt pool were measured. These experiments consisted of multiple tracks alternating scan direction, which resulted in higher substrate temperature at the beginning of subsequent tracks. The melt-pool width and depth were measured close to the end of the substrate, which provided two distinct melt-pool dimensions. For a cooler substrate, the simulations had an average error of 4% and 18% for the prediction of width and depth, respectively. For the subsequent track where the substrate was at higher temperature, the simulations had an average error of 18% and 24% for width and depth, respectively.

The scan passes on a bare plate were performed by Heigel and Lane [13]; the length was measured experimentally, and the simulation predictions had an error ranging from 5 to 65%. We observed that for higher laser power, the error percentage was larger.

The solidification grain structure simulation was performed using the CA-Solidification software developed by AO. This software uses the temperature and melt-pool dimension data generated by the melt-pool simulation as input. It uses a 3D uniform discretization to represent the CA grid (Fig. 2). At the start of simulation, each cell in the CA grid is initialized with a random distribution of grain size and crystal orientation using the DREAM.3D software [19]. Then, for each track in the simulation, the melt-pool thermal profile from the melt-pool simulation is mapped onto the CA grid. Next, the solidification grain structure is updated based on the melt-pool solidification front parameters as it moves through the CA grid.

The CA growth rules for the CA grid cells define the process for the growth of solidification grain structures. These rules utilize the growth model from Rai et al. [20]. This growth model considers that there is a “grain envelope” at the center of each CA cell, which emulates the dendrite arms. The salient steps for the CA calculation using this model are as follows: (1) At each time step, the grain envelopes are considered to grow in the epitaxial direction. (2) The solid cells on the solid-liquid interface are grown based on the simulation time step, easy growth directions, and the dendrite tip velocity which is computed as a function of the melt-pool geometry and the liquid-to-solid interface velocity. (3) Next, the liquid cells are considered to become solid with the orientation of the neighboring cell that has grown the furthest into the liquid cell. If no neighboring growing cells have sufficiently grown into the liquid cell, it remains liquid for the present time step. (4) This process of mapping the melt pool at each time step and the growth and solidification of CA cells is repeated for the entire length of each track.

The AM-Bench experimental work was performed by NIST. The experiment was designed to isolate the effect of individual tracks printed on a bare plate of alloy IN625. The plate dimension is 24.82 mm × 24.08 mm × 3.18 mm [21]. The tracks were printed at the center of the plate and were separated by a distance of 0.5 mm. The plate geometry and the track positions are shown in Fig. 3. To avoid heat buildup, each track was printed at 5-min intervals. The nominal temperature of the base plate was 25 °C at the start of experiment. Three different process parameter sets were used to produce the tracks as shown in Table 2. The laser was a continuous-wave ytterbium fiber (Yb-fiber) laser with a wavelength of 1070 nm. The experimental work was performed using two machines, namely Additive Manufacturing Metrology Testbed (AMMT) and Commercial Built Machine (CBM) for which the laser spot sizes were 100 μm and 59 μm, respectively. The cooling rates were measured as shown in Fig. 4.