4.1. Microstructure evolution
Figure 1 (b) clearly shows that the 2θ angles of heat-treated samples become lower than that of the as-printed sample, which proves that the lattice distortion inside the sample was alleviated during the heat-treating process. The as-printed sample underwent a rapid solidification during the SLM process layer by layer, the residual stress was very large inside the sample. Thus, the lattice distortion was serious inside the sample [
12]. However, after being heated to a high temperature and kept for a long time, the dislocation network, originating from the solidification process subjected to substantial shrinkage strain, underwent decomposition into individual dislocations, and the lattice distortion inside the sample was alleviated [
11].
The content of HAGBs suffers a drastic decrease from the as-printed sample to the heat-treated samples. This observation aligns well with the findings obtained from XRD analysis. HAGBs often have higher energy than LAGBs. A higher content of HAGBs means a severe lattice distortion [
19,
20]. A further decrease in the content of HAGBs happens when the heat-treating temperature increases to 1100 °C, which means a higher heat-treating temperature of 1100 °C is helpful to release the residual stress [
11]. The 1200W-1 has a similar content of HAGBs as compared to the sample of 1100W-1, which means the residual stress has almost been released over a temperature of 1100 °C, so the content of HAGBs changes little. The heat-treating method has been used to alleviate the residual stress of as-printed samples in many reports [
11,
12].
The BCC phases get larger after heat treatment as shown in
Figure 4 and
Table 2. This is because when a material is heated to such high temperatures, the atoms within the grains diffuse and rearrange themselves to minimize their energy. This can result in the coalescence of smaller grains into larger ones, which would make the BCC phases appear larger. Ostwald [
21] found the Ostwald ripening phenomenon, which shows smaller grains dissolve, and their material reprecipitates on the surface of larger grains. This can lead to the growth of larger BCC grains and a corresponding reduction in the number of smaller ones. The average grain size of BCC phases shows a stable increase after heat-treated at 1000 °C or 1100 °C for 1 hour and then cooled in water, but a drastic increase when heat-treated at 1200 °C for 1 hour and then cooled in water, which means that a higher heat-treated temperature is good for the growth of the BCC grain size.
The size of the FCC phase of the 1000W-1 sample is similar to that of the as-printed sample, as shown in
Figure 4 and
Table 2. The BCC phases with a small average size of 0.82 μm which are distributed along the FCC grain boundaries can pin grain boundaries. Thus, inhibiting the growth of FCC phases during heat treatment. However, after heat-treating at 1100 °C for 1 hour, the FCC phases become more than 3.0 times larger than those of the 1000W-1 sample. The BCC phases of the the1100W-1 sample have a large average size of 1.29 μm and the number of the BCC phases has decreased a lot when compared with as-printed or 1000W-1 samples, the pinning effect is weakened and the FCC phases of the 1100W-1 sample grow up to an average size of 4.33 μm. After heat-treating at a higher heat-treating temperature of 1200°C, the FCC phases grow up to 5.8 μm. Oikawa et al. [
22] found the pinning effects of second-phase particles with an average size of 0.28 μm influencing the grain growth of ferrite in a Fe-0.1C alloy enriched with 5 ppm of boron (B). Li et al. [
23] introduced a phase field model to explore how particle pinning influences the migration of grain boundaries in materials with stored energy variations along the grain boundaries. The outcomes indicated that reducing particle size and increasing particle area fraction could amplify the pinning effect.
The content of FCC phases increases and the content of BCC phases decreases with the increase in heat-treating temperature. At a certain temperature, the BCC phase will convert to the FCC phase, and the heat during heat treatment makes this happen. Panda et al. [
24] heat-treated AlCoCrFeNi (prepared by arc melting, BCC + B2 structure) in the temperature range starting from 1073 K to 1373 K up to 10 hours. Results showed that the formation of the FCC phase was up to 30% ~ 35%. Indicating a long time at a high-temperature range will lead to the BCC phase transforming to the FCC phase.
During heat treatment, nucleation and growth of new phases can occur. HAGBs of the FCC phases provide sites for nucleation of the BCC phases because they often have higher energy. The large BCC phases may have nucleated along these boundaries due to favorable thermodynamic conditions and then grown as heat treatment continued. Zhang et al. [
25] suggested a thermomechanical treatment method capable of adjusting the lamellar structure of duplex stainless steel to form an equiaxed matrix of austenite and ferrite. Their observations revealed a preference for alpha-martensite nucleation at the large-angle grain boundaries (HAGBs) between austenite grains. The small BCC phases that remained among the FCC phases represent that the phase transformation was less severe in these regions because these regions consist of LAGBs with lower energy than HAGBs.
4.2. Strengthening mechanism
The tailorable mechanical properties of Fe32Cr33Ni29Al3Ti3 fabricated via SLM before and after heat treatment can be explained by the following:
(1) The tailorable mechanical strength of Fe32Cr33Ni29Al3Ti3 fabricated via SLM before and after heat treatment is attributed to the tailorable grain size and the influence of dislocation density.
To investigate this trend, the primary mechanisms contributing to strengthening were examined as a combination of dislocation hardening and grain refinement [
26]. This was succinctly expressed in the following equation:
where
represents the yield strength of these samples, and
and
denote the strengthening contributions from grain boundaries and dislocations, respectively.
The lattice frictional strength of the present alloy, denoted as
, can be regarded as 267 MPa, according to (CoCrNi)94Al3Ti3 HEA reported by Zhao et al. [
27]. The
can be regarded as [
15]:
where
represents the average grain size, and
is a grain boundary strengthening coefficient.
is the content of FCC phase of each sample;
is the content of BCC phase of each sample,
,
are the strengthening coefficient of the FCC-FCC interface and the FCC-BCC interface, respectively; the coefficient
and
were considered as 275 MPa∙μm
1/2 and 574 MPa∙μm
1/2, respectively [
28]. The value of
kBCC is higher than
because the BCC phase displays greater resistance to dislocations compared to the FCC phase [
29].
and
represent the average grain sizes of the FCC and BCC phases in each sample, respectively. The data in
Table 2 was brough into Equation (2), and
is calculated to be 396 MPa, 332 MPa, 205 MPa, and 149 MPa for as-printed, 1000W-1, 1100W-1 and 1200W-1 samples, respectively.
In SLM-processed materials, the high dislocation density often plays a crucial role in achieving high strength levels [
30]. The dislocation hardening effect can be described by the Taylor equation, which is expressed as follows [
31,
32]:
where
M is the Taylor factor (3.09 and 2.71 for FCC and BCC materials, respectively),
is a constant (0.20 and 0.24 for FCC and BCC materials, respectively),
is the shear modulus (81 and 57 GPa for FCC and BCC materials, respectively),
is the Burgers vector (0.254 and 0.248 nm for FCC and BCC materials, respectively), and
is the dislocation density. The values of
,
,
,
were achieved from the research of Ren et al [
32]. The dislocation density was calculated using the Williamson-Hall method based on XRD pattern (
Figure 1) [
33,
34]. The measured values of ρ were shown in
Table 4. These data were brought into Equation (3),
could be estimated to be 179 MPa, 133 MPa, 132 MPa and 125 MPa for as-printed, 1000W-1, 1100W-1 and 1200W-1 samples, respectively, as shown in
Table 4.
Upon substituting each strengthening contribution into Equation (1), the predicted yield strengths are approximately 842 MPa, 732 MPa, 604 MPa, and 541 MPa for the as-printed, 1000W-1, 1100W-1, and 1200W-1 samples, respectively. These values demonstrate a satisfactory agreement with our experimental data, as depicted in
Figure 7. The main cause of error between predicted yield strength and actual yield strength is that
K (grain boundary strengthening coefficient) may differ in these samples. Huang et al. [
35] found that the Hall-Petch slopes (
values) slightly increased with offset strain. In this study, the strain shows a decrement with the increase of heat-treating temperature as the dislocation density becomes lower and lower. The value of
was supposed to be getting smaller and smaller with the increase of heat-treating temperature. But in calculation by Equation (2), it was set as the same. So actual yield strength was higher than the predicted yield strength in as-printed and 1000W-1 samples, and lower than the predicted yield strength in 1100W-1 and 1200W-1 samples.
(2) The tailorable ductility of Fe32Cr33Ni29Al3Ti3 fabricated via SLM before and after heat treatment is attributed to the tailorable grain size.
The average grain sizes of as-printed, 1000W-1, 1100W-1, and 1200W-1 samples are 0.69, 1.00, 1.94 and 3.70 μm, respectively. The grains of the as-printed sample are ultra-fine grains, with an average grain size of less than 1 μm. And the grains of other samples are micron grains. The relationship between elongation and the average grain sizes is shown in
Figure 8.
The relationship between elongation and the average grain size fits well with the influence of grain size on elongation studied by other researchers [
36,
37]. The elongation increases with the average grain size increases. The samples with micron grains have an elongation higher than 10%. The as-printed sample shows a sharp decrease in elongation from the 1000W-1 sample because of its ultra-fine grains. When the grain size is less than 1.00 μm, the elongation decreases sharply [
36].
The content of FCC and BCC phases is another factor that influenced the elongation of these samples. The higher content of the FCC phase is good for the ductility of a dual-phase sample [
14]. As the heat-treating temperature increases, the content of the FCC phase also increases, contributing positively to ductility.