*2.1. DED Tests*

The DED experiments were performed on a 5-axis laser-processing machine, with a work-piece size capacity of 700 × 360 × 380 mm3. A high-power Yb:YAG fiber laser, Rofin FL010 (ROFIN-SINAR Laser GmbH, Bergkirchen, Germany), with a maximum power output of 1 kW was employed. In addition, the powder was fed by means of a Sulzer Metco Twin 10 C powder feeder (Oerlikon Metco, Pfäffikon, Switzerland), and an in-house designed coaxial nozzle [20], using argon as both the drag and shielding gasses.

In the experimental tests, AISI 1045 (DIN 1.1191) and AISI H13 (DIN 1.2344) were used as the base and filler materials, respectively. AISI 1045 is a medium carbon steel commonly used in structural parts requiring high strength and hardness. AISI H13 is a Cr-Mo-V alloyed tool steel with a high level of resistance to thermal shock and fatigue and good temperature strength, which makes this material particularly valuable for tooling. The filler material was supplied by Flame Spray Technologies (Duiven, The Netherlands) and obtained via gas atomization, consisting of spherical particles with diameters of 53–150 μm. The chemical compositions of the employed materials are detailed in Table 1.


**Table 1.** Chemical compositions (wt %) of AISI 1045 [21] and AISI H13 [22].

First, two specimens of 50 × 50 × 7 mm<sup>3</sup> and 50 × 50 × 5 mm3, respectively, were manufactured by adding AISI H13 over an AISI 1045 substrate via DED, employing the process parameters detailed in Table 2. A zigzag pattern was used to deposit the filler material, alternating longitudinal and transversal directions for the deposition of successive layers, as shown in Figure 1a. This strategy reduces the anisotropic behavior inherent to the DED process and allows the manufacture of larger parts, which enables the transfer of the results obtained to real components. Figure 1b shows a photograph of the manufactured specimens.


**Table 2.** Process parameters employed for the deposition of AISI H13.

**Figure 1.** Schematic of the Directed Energy Deposition (DED) process (**a**) and (**b**) photograph of the manufactured AISI H13 specimens.

## *2.2. Thermal Di*ff*usivity Measurement*

To perform thermal diffusivity measurements, three slabs, each 2 mm thick, were extracted from the deposited material at different depths, as shown in Figure 2. From the 7-mm-thick specimen, two plates were cut: (a) the inner plate, Sample 1, contained the deepest and earliest deposition (0 to 2 mm from the substrate); (b) the outer plate, Sample 2, contained the outermost side of the coating (4 to 6 mm from the substrate). Sample 3 was extracted from the specimen with a 3.5 mm deposition thickness, and the sample spanned the interface between the filler and substrate, from −1 to 1 mm with respect to the interface, to evaluate the influence of the DED process on the substrate. Moreover, for comparison, a 2-mm-thick plate made of cast AISI H13 was also prepared. All samples were extracted by means of wire electrical discharge machining, and the white layer generated on the cut surfaces was ground to eliminate the heat-affected region.

**Figure 2.** Sample extraction for thermal diffusivity measurements.

For each plate, the thermal di ffusivities were measured at room temperature in two perpendicular directions: along the surface, the so-called in-plane thermal di ffusivity (<sup>α</sup>), and in the direction perpendicular to the surface, the so-called through-thickness thermal di ffusivity (<sup>α</sup>⊥).

To measure α⊥, a flash method was used, which was developed by Parker et al. [23]. In this technique, the front surface of the plate was illuminated homogeneously by the brief pulse of a flash lamp (3 kJ energy pulse, 3 ms duration) while the temperature evolution of the back-surface was recorded by a mid-infrared video camera (3–5 μm wavelength) operating at a rate of 950 frames·s<sup>−</sup>1. The thermal di ffusivity was obtained by measuring the time required to reach half of the maximum temperature rise (t1/2), which was related to the thermal di ffusivity through Equation (1), where *L* is the plate thickness:

$$t\_{1/2} = 0.1388 \frac{L^2}{\alpha\_\perp}.\tag{1}$$

In order to enhance both the absorption to the flashlight and the infrared emissivity, the sample surfaces were covered by a very thin graphite layer (≈3 μm thick). According to Maillet et al. [24], the influence of this layer on the accuracy of the thermal di ffusivity values is less than 1% provided the sample is much thicker than the graphite layer (in the present case, 2 mm against 6 μm).

To measure <sup>α</sup>, a lock-in thermography setup with laser spot excitation was used, which was first used by Heath and Winfree [25] and enables measurements of the thermal di ffusivities of the materials with high accuracy. This technology has been widely used for similar applications, for example, Nolte et al. [26] determined the thermal di ffusivity of sheets of brass, stainless, and structural steel. The sample is illuminated by an intensity-modulated laser beam, tightly focused on the surface, and the oscillating component of the temperature rise is detected by an infrared video camera connected to a lock-in module. By analyzing the radial dependence of the temperature phase, the in-plane thermal di ffusivity can be retrieved with ease, based on the linear relationship between the phase of the temperature and the lateral distance to the heating spot, the slope of which ( *m*) is given by Equation (2), where *f* is the modulation frequency:

$$m = -\sqrt{\frac{\pi \times f}{\alpha\_{\parallel}}}.\tag{2}$$

#### *2.3. Thermal Modeling of the Tool Cooling*

In order to quantify the influence of the e ffective thermal conductivity of the laser-deposited AISI H13 on a bimetallic hot stamping tool, two di fferent cases were simulated using the same geometry, shown in Figure 3. The aim of the simulation was to quantify the impact of considering the real DED AISI H13 thermal conductivity or the data from the bibliography. Therefore, no optimization of the geometry of the cooling channels was performed and the cooling channels' position and geometry were maintained. The geometry has a 300 × 170 × 150 mm<sup>3</sup> bounding box and the cooling channels have an 8 mm diameter and are positioned at a 12 mm distance from the contact face with the blank. The tool has an AISI 1045 core, which was coated with a 3-mm-thick DED AISI H13. In Case 1, the thermal conductivity value of the cast AISI H13 was used as a reference, whereas in Case 2, the e ffective thermal conductivity value of the deposited AISI H13 was considered. In both cases, the stamped blank was made of USIBOR 1500 steel (22MnB5), a boron alloyed steel that is well-suited for the entire range of automotive structural parts, which require high resistance to anti-intrusion during impact.

**Figure 3.** Simulated geometry of the bimetallic hot stamping tool.

The simulation was carried out using the thermal transient module of the FEM software ANSYS Workbench 19.2 (Ansys Inc., Canonsburg, PA, U.S.). The employed mesh consists of over 1 million first-order tetrahedral elements, with an average skewness of 0.246 and a maximum of 0.846. The initial temperature of the tools, as well as the reference temperature for the water-cooling convection, was set at 20 ◦C, whereas the temperature of the blank after the loading operation was 810 ◦C [27]. The blank was 1.85 mm thick, which is a typical thickness for an automotive sheet metal structural body part [28]. The geometric parameters of the tools are detailed in Table 3, and the thermal properties of the employed materials are shown in Table 4. The model simulated a 20 s cooling time, which is a typical value for hot stamping already used by other authors [27,29].

**Table 3.** Geometric parameters of the simulated tools.


**Table 4.** Thermal properties of AISI H13, AISI 1045, and USIBOR 1500, data obtained from [21,22,30].


The tools are cooled by the convection of the water that is forced through the cooling channels, a parameter referred to as the convective heat transfer coe fficient (CHTC). For cooling channels manufactured via drilling, Coldwell et al. measured the inner roughness between 0.14 and 0.48 μm [31]. Thus, an intermediate Ra value of 0.31 μm was considered in the present case. According to Arrizubieta et al. [32], for mechanically drilled 8-mm-diameter ducts with a 0.31 μm Ra value and a 20 ◦C cooling water, the CHTC is 4736.7 W·m<sup>−</sup>2·K−1.

The heat transfer between the hot blank and the tools needs to be established as an input parameter in the model. This parameter is referred to as the interfacial heat transfer coe fficient (IHTC). In the present study, the correlation proposed by Hu et al. [33] was taken as a reference. Considering a 15 MPa contact pressure, a value which was already considered by Cortina et al. [34], the IHTC was estimated to be approximately 3000 <sup>W</sup>·m<sup>−</sup>2·K−1, based on the aforementioned approximation.

To compare the cooling performance of the tools using either the e ffective thermal conductivity of DED AISI H13 or the reference thermal conductivity, the time point at which the martensitic transformation was complete (280 ◦C) was calculated. In addition, the time at which the blank was cooled to below 70 ◦C was determined to define the total cycle time before the tools were opened.
