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Page 18 of 25 Dela Cruz et al. Microstructures 2023;3:2023012 https://dx.doi.org/10.20517/microstructures.2022.33

Effect of residual strain
The far-from-equilibrium processing conditions in LPBF introduce residual strains that may also influence
hardness. Since residual strain is associated with crystal misorientation [121-124] , the relationship between
crystal misorientation and hardness is presented in Figure 10. Comparing the reference alloy and the LPBF
alloy prepared at 0.44 J/mm LED, the hardness of the former was significantly lower (227 HV2) than the
latter (287 HV2). The corresponding average Kernel average misorientation (KAM) in the reference alloy is
also lower (0.44°) than in the LPBF alloy (0.64°). A high residual strain has been associated with a high
[125]
density of low-angle grain boundaries and, as such, the density of these boundaries (2° to 10°
misorientation) in both the reference and LPBF alloys were measured by EBSD to be 3% and 7%,
respectively. Hu et al. reported that in pure Ti sheet, the hardening effect due to low-angle boundaries was
[126]
dependent on the level of strain . At strains up to 30%, the high-angle boundaries (HAGB) contributed to
the hardness, but for strains above 30%, the density of the low-angle boundaries (LAGB) increased. The
latter was suggested to be the biggest contributor to hardness. This was also noted in both 304 L stainless
steel and Ni-Co alloys, whereby the hardness increased with increasing residual strain , and in a Fe-Ni
[127]
[128]
alloy, the hardness decreased when the residual strain was relieved . A dislocation has to overcome the
grain boundary energy, both high- and low-angle, for it to move through the boundary, and the magnitude
[114]
of the LAGB interfacial energy is a function of the degree of crystallographic misalignment . Thus, the
high hardness in the LPBF alloys as compared to the reference alloy was also caused by the inherent residual
strain that resisted the localised deformation.

Figure 10 shows a positive correlation between the average crystal misorientation from EBSD analysis and
the computed temperature gradient using the FEA of the melt pool as a function of LED at differing depths
from the melt pool surface. On the top surface of the melt pool, the highest temperature gradient
(2.32 × 10 K/m) was computed for 0.25 J/mm LED. It then decreased as the LED increased, with 0.88 J/mm
3
2
LED having the lowest temperature gradient (7.72 × 10 K/m). At 50 μm depth from the melt pool surface,
the temperature gradient in 0.25 J/mm LED increased substantially to 1.90 × 10 K/m (~7× increase) while it
4
remained almost constant in 0.88 J/mm LED at 1.15 × 10 K/m (~0.5× increase). This then corresponds to
3
an average misorientation of 0.65° and 0.49°, respectively, and suggests that a high average KAM indeed
correlates with a high temperature gradient.

The residual strain in the LPBF alloy is caused by the local heat application of the laser, which introduces
tensile stress in the molten layer and compressive stress in the solidified lateral and underlying layers .
[129]
These stresses, if not released, result in residual plastic strains. Several authors looked into minimising
thermal stress in the LPBF-fabricated alloy. Vrancken et al., Lu et al., and Liu et al. agreed that a short laser
scan length introduced less thermal stress, while Mishurova et al. emphasised the importance of large melt
pool volume to lessen thermal stress [130-133] . The scan strategy was maintained during the LPBF of
Fe-30Mn-6Si alloy, but the melt pool for 0.88 J/mm LED was comparably large than for the other LEDs
[Figure 6D]. However, Liu et al. added that a low LED is necessary for a small thermal stress, and these
workers pointed out that a low thermal stress in short laser scan length was caused by the release of stress
through cracking . A low average misorientation (0.49°) and a high hardness [Figure 10] in the highest
[132]
LED (0.88 J/mm) suggest otherwise. More so, the ε-martensite formation in 0.88 J/mm LED may be stress
induced and its volume fraction was high (45.8%). This entirely suggests that the residual strain may have
been released through the formation of cracks since the LPBF alloy fabricated at 0.88 J/mm LED had
comparably more cracks than the 0.25 J/mm LED (Figure 2C and D, respectively). A more thorough
investigation is, however, warranted to understand the residual strain in the LPBF alloy fabricated from a
homogeneously mixed Fe-30Mn-6Si powder.