**3. Results and Discussion**

#### *3.1. Quality of the Deposited Material*

Defects such as pores and cracks generate discontinuities within the material, lowering its density and possibly decreasing thermal conductivity. Therefore, the quality of the deposited material must be analyzed to evaluate defects and their impact on thermal properties. Therefore, three details of the cross-section of the DED AISI H13 were evaluated. The cross-sections were polished and etched using Murakami and Marble reagents. The samples are shown in Figure 4.

**Figure 4.** Cross-section of the DED AISI H13 and details of the microstructure.

As can be seen from the figure, clads free of cracks were attained, and this microstructure would be expected to ensure the continuity of the heat transfer within the deposited material. In addition, no defects were found at the interface between the DED AISI H13 and substrate AISI 1045 materials.

#### *3.2. E*ff*ective Thermal Di*ff*usivity and Conductivity Values*

The results of the measurements of the through-thickness thermal di ffusivity, α⊥, are summarized in the third column of Table 5. The statistical uncertainty was obtained by repeating each measurement five times and the uncertainty was thus found to be less than 3%.



As shown in the table, the thermal diffusivity of the laser-deposited AISI H13 was always smaller than that of the cast sample. The thermal diffusivity of each plate was measured in two directions, i.e., from both the front (illuminated) surface and the rear (measured) surface, and the thermal diffusivities thus retrieved were the same. This homogeneity is obtained because the flash method measures the effective (or average) α⊥. Because Sample 3 included two different materials, α⊥ was not measured in that sample.

As for the in-plane thermal diffusivity measurements, <sup>α</sup>, Figure 5 shows the amplitude and phase thermograms of Sample 1, at the surface 0 mm from the substrate, with f = 7 Hz. For each specimen, the thermal diffusivity on both sides was measured. The round shape of the isophases and isotherms in Figure 5 is representative of all the cases analyzed and indicates in-plane thermal isotropy. The in-plane thermal diffusivity was obtained considering the vertical profiles of the phase thermograms (the white vertical line in Figure 5b) since they are free from diffraction effects, like those observed in the horizontal profile in Figure 5b. From the slope of the vertical phase profile, the in-plane thermal diffusivity was obtained, using Equation (2). In order to average local heterogeneities, the measurement was repeated at five different zones at the sample surface. The thermal diffusivities obtained using this method together with the uncertainty (≈3%) are summarized in the fourth column of Table 5. The uncertainty takes into account the standard deviation in the slope of the phase profile and the standard deviation of the five repetitions.

**Figure 5.** (**a**) Amplitude and (**b**) phase thermograms of Sample 1 at the surface 0 mm from the substrate, with a modulation frequency of 7 Hz. The white vertical line corresponds to the phase profile used for thermal diffusivity measurements. The scale of the amplitude is in ◦C and the phase is in degrees.

Although the thermal diffusivity of each surface increased with the surface's height above the substrate, at all heights, the thermal diffusivity of the sample remained below the diffusivity of the reference cast material. Comparing the values of α⊥ and <sup>α</sup>, the DED process did not introduce any thermal anisotropy.

Thermal diffusivity, α, and conductivity, *k*, are related to Equation (3), where ρ and *cp* are the density and specific heat of the material, respectively:

$$\alpha = \frac{k}{\rho \times c\_p}.\tag{3}$$

Equation (3) was used to calculate the thermal conductivity of DED AISI H13, cast AISI H13, and AISI 1045, and the results are shown in Table 6. The perpendicular thermal diffusivity values shown in Table 5 were used because the flash technique is generally acknowledged to be the most reliable method and is covered by standards, such as ASTM International [35], the British Standards Institution [36], and the Japanese Standards Association [37]. The density and specific heat were taken from the material specifications. In the case of DED AISI H13, the heat capacity was calculated using the rule of mixtures given in Equation (4) and considering this material as a mixture of AISI H13 and air.

$$\left(\rho \times c\_p\right)\_\text{DED AISI H13} = \nu\_1 \times \left(\rho \times c\_p\right)\_\text{cast AISI H13} + \nu\_2 \times \left(\rho \times c\_p\right)\_\text{air}.\tag{4}$$


**Table 6.** Thermal conductivities.

In Equation (4), υ1 and υ2 are the volume fractions of cast AISI H13 and air, respectively. Because υ1 > 0.995, the same heat capacity was used for the cast reference and DED AISI H13. This result is consistent with the fact that the heat capacity, unlike the thermal transport properties (α and k), depends only on the composition of the sample, not the microstructure. Therefore, because the DED process does not affect the sample composition, the same heat capacity is expected for AISI H13 regardless of the production process.

In the cast AISI H13 and the base AISI 1045, the measured effective thermal diffusivities presented almost no differences compared to the reference values encountered in the literature [21,22], demonstrating the accuracy of the measurements acquired in this study. In the case of DED AISI H13, the effective thermal conductivity was 15.3% lower than that of cast AISI H13. This is because the thermal conductivity of alloys depends not only on the sample composition but also on the microstructure (grain size, micro-cracks, pores, etc.). Because the micrographs shown in Figure 4 do not indicate the presence of cracks or pores, the thermal conductivity reduction was attributed primarily to the smaller sizes of the grains produced by the fast cooling rate in DED in comparison with conventional manufacturing processes. According to Berman [38], the larger number of interfaces compared to the cast material reduces the electron mean free path and consequently the thermal conductivity. This effect is especially noticeable in the first layers, where the cooling rate is maximum and therefore, the microstructure is finer. As the number of deposited layers increases, the heat dissipation is slowed down, which leads to slower cooling rates and coarser grain sizes. Consequently, the thermal conductivity variation within the deposited material is attributed to the differences in the grain size, thus leading to lower values in the first deposited layers.

Focusing on the variation of thermal conductivity in relation to temperature, Zhang et al. [39] studied the thermal conductivity change of multi-stacked silicon steel sheets under different pressure and temperature conditions. Their results showed that although the thermal conductivity changed under different compressive stresses, the conductivity maintained the same rate of variation in response to temperature change. Therefore, in this study, the thermal conductivity reduction measured at 20 ◦C was assumed to affect the material in proportion to the temperature, and this result was extended to the whole temperature range, as shown in Table 7, and applied to the case study model described in the next section.


**Table 7.** Effective thermal conductivity of the DED AIS H13 considered in the thermal model.

#### *3.3. Thermal Modeling and Cycle-Time Reduction*

The influence of the thermal conductivity differences between the cast and DED AISI H13 tool steels was evaluated by means of thermal simulation of the upper part of an automotive structural body part with a B-pillar type geometry.

Based on the effective thermal conductivity of the laser-deposited AISI H13 tool steel, the cycle times required to lower the blank temperature below 280 and 70 ◦C were calculated, respectively. Figure 6 shows the evolution of the maximum temperature of the blank. The lower thermal conductivity of the laser-deposited AISI H13 can be seen to reduce heat extraction from the blank, and this case thus requires a longer cooling time to achieve an equivalent thermal field. Table 8 presents the results of the simulated case study, as well as the error produced if the effective thermal conductivity of the laser-deposited AISI H13 is not considered in the model.

**Figure 6.** Blank maximum temperature evolution during the hot stamping process.


**Table 8.** Results of the simulated case study.

The errors generated when calculating the thermal fields were relatively low in comparison with the differences in thermal conductivity values. This is because the coating thickness was only 3 mm, and such low thickness values are commonly employed in bimetallic tools. Nevertheless, if fully DED-manufactured structures are employed, much higher errors could be generated in the simulation. Figure 7 shows the thermal field of the blank at 12.89 s in the case where the effective thermal conductivity of the DED AISI H13 coating is considered.

**Figure 7.** Temperature field of the blank at 12.89 s time instant, considering the effective thermal conductivity of the DED AISI H13 coating.
