Revealing relationships between microstructure and hardening nature of
additively manufactured 316L stainless steel
Luqing Cui
a, Shuang Jiang
a, Jinghao Xu
a, Ru Lin Peng
a, Reza Taherzadeh Mousavian
b, Johan Moverare
a,⁎
aDivision of Engineering Materials, Department of Management and Engineering, Linköping University, Linköping SE-58183, Sweden bI-Form, Advanced Manufacturing Research Centre, Dublin City University, Dublin 9, Ireland
H I G H L I G H T S
• Dislocation-type and their impacts on hardening nature of L-PBF alloys during annealing were studied.
• GND and SSD densities were statistically measured utilizing Hough-based EBSD method and Taylor's hardening model. • Migration of GNDs during recovery
leads to higher concentration of GNDs along new subgrain boundaries. • SSDs decrease faster than GNDs during
annealing, because SSDs largely depend on the release of thermal distortions. • GND type dislocations governing the
hardening nature of the present L-PBF alloys. G R A P H I C A L A B S T R A C T
a b s t r a c t
a r t i c l e i n f o
Article history: Received 5 October 2020Received in revised form 23 November 2020 Accepted 3 December 2020
Available online 7 December 2020 Keywords:
Laser powder bed fusion 316 L stainless steel Dislocation-type Hardening nature Microstructural evolution
Relationships between microstructures and hardening nature of laser powder bed fused (L-PBF) 316 L stainless steel have been studied. Using integrated experimental efforts and calculations, the evolution of microstructure entities such as dislocation density, organization, cellular structure and recrystallization behaviors were charac-terized as a function of heat treatments. Furthermore, the evolution of dislocation-type, namely the geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs), and their impacts on the hardness var-iation during annealing treatments for L-PBF alloy were experimentally investigated. The GND and SSD densities were statistically measured utilizing the Hough-based EBSD method and Taylor's hardening model. With the progress of recovery, the GNDs migrate from cellular walls to more energetically-favourable regions, resulting in the higher concentration of GNDs along subgrain boundaries. The SSD density decreases faster than the GND density during heat treatments, because the SSD density is more sensitive to the release of thermal distor-tions formed in printing. In all annealing condidistor-tions, the dislocadistor-tions contribute to more than 50% of the hardness, and over 85.8% of the total dislocations are GNDs, while changes of other strengthening mechanism contributions are negligible, which draws a conclusion that the hardness of the present L-PBF alloy is governed predominantly by GNDs.
© 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).
⁎ Corresponding author.
E-mail address:johan.moverare@liu.se(J. Moverare).
https://doi.org/10.1016/j.matdes.2020.109385
0264-1275/© 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available atScienceDirect
Materials and Design
1. Introduction
Laser powder bed fusion is one of the most promising additive manufacturing (AM) technologies that has been successfully applied to produce structural components with complex geometries and out-standing performance through a layer-by-layer method [1,2]. Owing to the natural rapid cooling rate (up to 106K/s) of the L-PBF process,
the microstructures are significantly distinct compared with the coun-terparts processed by conventional manufacturing approaches, such as casting, powder metallurgy, and forging [3]. For example, the disloca-tion tangled cellular structure is one of the most significant microstruc-tural features in AM-fabricated alloys, which can remarkably improve the strength and ductility simultaneously [4]. Apart from cellular struc-tures, the microstructural features also include melt pool boundaries (MPBs), columnar grains, highly serrated grain boundaries (GBs) and nanoparticles [5,6], which in turn significantly affect the mechanical properties [4–6]. On the other hand, since the melt pool is highly local-ized and then rapid cooling, distortion and residual stress are commonly introduced into the L-PBF components [7]. Porosity is inevitably formed in the as-built L-PBF alloy as a result of entrapped gases, lack of fusion and solidification shrinkage [8]. Even though these microstructural de-fects always lead to premature failure [9] under the mechanical loading, the mechanical properties of L-PBF alloys are still better than the con-ventionally processed ones [4]. Because of the huge potential of the L-PBF technology, many studies related to the manufacturing of metal parts via L-PBF, such as nickel-based superalloy [10], high entropy alloy [11] and titanium alloy [12], stainless steel [13] have been carried out.
Stainless steels (SS) are widely used in the marine, biomedical and aerospace industries owing to the combination of desirable mechanical properties, relatively low cost and excellent corrosion resistance [13]. Numerous studies have been conducted on the SS structural compo-nents fabricated by L-PBF [6,8,13,14]. In addition, thermal post-processing treatments are usually required for L-PBF SS to achieve the best balance between strength and ductility [6,8]. Typically, the heat treatment reliefs the residual stress, segregation of elements, MPBs and crystallographic anisotropy [6,8]. In the past few years, efforts have been dedicated to understand the effects of heat treatment on the microstructure and mechanical properties of L-PBF SS [6,8,15–17]. Research by Ronneberg et al. [8] showed that the ductility of L-PBF 316L SS had been improved without sacrificing the strengthening con-tributions from cellular structures after annealing treatment at 700 °C. Similarly, the ductility of an L-PBF SS increased by 130% after combined hot isostatic pressing and annealing without sacrificing the tensile strength [18]. Salman et al. [6] reported that the cell size increased with increasing annealing temperature up to 873 K, and the annealing treatments had nearly no impact on the texture of a Fe-Cr-Ni SS. More-over, the yield strength of an L-PBF austenitic SS increased from 586 MPa to 642 MPa with only a small loss in uniform elongation after heat treatment at 400 °C for 60 min [19]. Although the properties of the L-PBF alloys have been improved via heat treatments, the underly-ing mechanisms and the relationships between the post-processunderly-ing thermal treatment, microstructural evolution and mechanical proper-ties are still not well elucidated. Especially the dislocation-type evolu-tion and their impacts on mechanical properties for L-PBF alloys during post-processing heat treatments have not been revealed yet, which are critical issues within AM community.
Dislocations in a polycrystalline aggregate are generally considered into two types: the geometrically necessary dislocations (GNDs) and the statistically stored dislocations (SSDs) [20–22]. GNDs are accumu-lated in plastic strain gradientfields caused by local heterogeneous de-formation, which are considered necessary to maintain the strain compatibility across microstructures; while SSDs are stored in the de-formed polycrystalline aggregate through random trapping processes [21,22]. Moreover, the Burgers vector for GNDs is net non-zero, which leads to an observed lattice curvature [22]. Therefore, the GND density
can be measured using the Hough-based electron backscattered diffrac-tion (EBSD) method [20]. Different from GNDs, SSDs have a net-zero Burgers vector and thus no lattice curvature is presented [22]. As far as we know, no experimental method has been developed for direct quantitative estimation of SSD density in a polycrystalline aggregate [20]. In transmission electron microscopy (TEM) micrographs, the dislo-cation lines of both GNDs and SSDs could be observed. Nevertheless, it is difficult to distinguish SSDs from GNDs, and this method is also very time consuming. Ashby [23] illustrated that the total dislocation density is the sum of GND and SSD density, and both equally contribute to strength. Thus, the density of SSDs can be estimated by subtracting the EBSD-measured GND density from the total dislocation density [20–22]. Based on this, the evolution of GNDs and SSDs, as well as their roles onflow stress for annealed conventional alloys have been carried out [20–22,24]. In contrast to the annealed conventional alloys, which contain very low density of dislocations, a considerable number of dislocations are generated in as-built alloys during L-PBF process, which undoubtedly affects the distribution of GNDs. However, the evo-lution of GNDs and SSDs, and their roles on mechanical behavior for L-PBF alloys have not been studied yet.
In this study, the microstructural evolution of an L-PBF alloy with different post-process treatment scenarios was systematically investi-gated. In addition, the evolution of GNDs and SSDs, and their impacts on the hardness during annealing treatments were experimentally in-vestigated. Both the total dislocation density, quantified using TEM and the Taylor's hardening model, and the microstructure-averaged GND density measured utilizing the Hough-based EBSD method provide a high confidence of accuracy to determine the density of SSDs. The stability of GNDs and SSDs as a function of post-process treatments also has been discussed. Additionally, the contributions from different strengthening components were carefully discussed, which provide new insights on the microstructures tuning and mechanical properties improvements of L-PBF alloys.
2. Materials and experimental procedures 2.1. Material
Gas atomized 316L SS prealloyed powder with a Gaussian size distri-bution ranging from 15 to 50μm was used in this work. The actual chemical composition of the powder determined by optical emission spectrometer (Oxford Instruments - PMI-Master Smart) is listed in
Table 1.
2.2. L-PBF process and post-treatment
A cylindrical bar with a height of 60 mm and a diameter of 10 mm was vertically printed on an EOSINT M280 3D printing system with a discontinuous Yb-fiber laser and maximum power capacity of 200 W. The printing process was conducted under a high purity argon atmo-sphere protection. In order to minimize micro-defects, optimized L-PBF processing parameters were used (Table 2), with a scanning direction rotation of 67° between the adjacent layers (Fig. 1a). The 67° rotation is the most commonly used printing strategies in the L-PBF field, because it achieves the maximum number of layers until the exact same laser scan vector direction appears again [25], leading to rel-atively isotropic mechanical properties and grain refinement. The com-bined parameter energy density (ED) is frequently used to evaluate the printing parameters and is determined as follows [26]:
ED¼ PL
VLHLTL ð1Þ
where PL, VL, HLand TLare laser power (W), scan speed (mm/s), hatch
spacing (mm) and layer thickness (mm), respectively. In the present work, the value of ED is determined to be 100 J/mm3. According to the
research by Nayak [27], regular and uniform tracks are obtained when the ED value ranges from 87.5 to 140 J/mm3. Similarly, with the use of
ED of 104 J/mm3, Cherry [28] also produced nearly zero porosity for an L-PBF SS. Therefore, the printed alloy in the present work is also ex-pected to have very low porosity.
Nine round discs with a thickness of 4 mm were cut from the printed cylindrical bar (Fig. 1b) by electro-discharge machining (EDM) for the following post-processing heat-treatments. Varying degrees of heat treatments ranging from the as-built condition (no post-processing) to the nearly full recrystallization temperature were carried out. The holding temperatures were 700 °C, 900 °C, 1050 °C, 1100 °C and 1200 °C with thefluctuation of ±2 °C using two thermocouples. The discs were annealed in the air-filled, preheated furnace for 10 or 40 min before being taken out to cool down to room temperature in am-bient condition. The internal structures of the as-built and post-treated samples are crack-free with only a few isolated micropores (see Fig. S1, the average size of micropores is 1.8μm with the area fraction of 0.03%), which are supposed to have limited influence on the microstructural characterizations.
2.3. Microstructural characterizations
Phase analysis was conducted by X-ray diffraction (XRD) in Bragg– Brentano geometry using a powder diffractometer Panalytical X'Pert PRO equipped with a graphite curved crystal monochromator and Cu-Kα radiation (λ = 1.5418 Å). Measurements were performed with 2θ angles ranging from 40° to 100° with a step size of 0.02° and a counting time of 1.5 s per step.
The microscopy analysis was performed both for as-built and post-treated samples on the X-Y and X-Z planes, as shown inFig. 1b. Sectioned samples were mounted in the conductive bakelite and then prepared following Struers recommendations.
To further reveal the microstructure, the well-polished samples were chemically etched using Aqua Regia (75% Nitric Acid and 25% Hy-drochloric acid in volume) at room temperature for 5–10 s. The micro-structure was analyzed with a Hitachi SU70 FEG scanning electron microscope (SEM), equipped with an energy dispersive X-ray spec-trometer (EDS). Grain orientation and qualitative analysis of the GND density distribution (Fig. S7) were performed by EBSD mapping with a step size of 400 nm and a binning of 4 × 4 under an accelerating voltage of 20 kV, using a Nordlys-S™ detector. Whilst for GND density calcula-tion (Fig. 4), a binning of 2 × 2 and step size of 200 nm were selected to balance the scanning time and quality required. The EBSD data was then analyzed with HKL Channel 5 software and the MTEX MATLAB toolbox [20,22,29]. The GND mapping and density were calculated based on the Pantleon's theory [30], which has been successfully applied to other alloys in different states to quantify the GND density distribution [20–22,24]. Moreover, the 15° misorientation criterion was used to distinguish the low angle grain boundaries (LAGBs) and high angle grain boundaries (HAGBs), and the minimum grain size is set to 5μm.
Detailed microstructures and dislocation configurations were ob-served in a FEI Tecnai G2 scanning transmission electron microscope (STEM) operating at 200 kV and with an EDAX EDS detector that was used to measure the chemical compositions of cellular structures and precipitates. For TEM sample preparation, twin-jet electro-polishing was carried out at−25 °C in a solution of 10 vol% perchloric acid and 90 vol% ethanol at 25 V. Camera lengths of 140 mm and 2.1 m were applied when taking high angle annular dark field (HAADF) and bright-field images using an annular detector.
2.4. Microhardness measurement
Vickers microhardness was performed on both the as-built and heat-treated samples using a LECO hardness testing machine. Consider-ing the possible indentation size effect (ISE) in the tests [31–33], eight different maximum loads ranging from 0.01 kgf to 0.5 kgf, namely 0.01, 0.02, 0.025, 0.05, 0.1, 0.2, 0.3 and 0.5 kgf, were selected for the indenta-tion tests. All tests were conducted with a 15 s dwell-time. At each load, the schematic illustration of hardness measurement is shown inFig. 1c. Detailed information of hardness measurement can be seen in the Table 1
The actual chemical composition of the stainless steel powders (wt%).
C Mn N P S Cr Mo O Ni Si Cu Fe
0.023 0.897 0.091 0.010 0.005 17.695 2.321 0.032 12.692 0.704 0.011 Bal.
Table 2
Processing parameters used in the present work. Laser power,
W
Laser spot size, μm Scan speed, mm/s Hatch spacing, μm Layer thickness, μm 195 75 1083 90 20
Fig. 1. (a) Schematic illustration of the laser scan vectors with a bidirectional scanning strategy with 67° rotation on subsequent layers. (b) Schematic 3D overview of the heat treatment samples for microstructure analysis and hardness measurement. BD: building direction. (c) The location of the microhardness measurement on the cross section (perpendicular to BD).
Supplementary material (Section S2). As shown in Fig. S2, the distribu-tion of hardness is essentially homogeneous across the diameter of each sample, which illustrates that the hardness is not sensitive to the indentation position. Finally, the hardness of a specific maximum load is determined by the average of 28 indentations.
3. Results
3.1. Effect of annealing on the phase stability and microstructural evolution The XRD patterns of the as-built and the different post-treated samples are given inFig. 2. It can be clearly seen that the Bragg line numbers for the FCC austenite structure corresponds well to the pres-ent XRD profiles. The strongest lines of BCC ferrite should appear at around 43° and 65°, and their absences in Fig. 2illustrates that a fully austenitic structure may be presented in the as-built and post-treated samples. Note that a small amount of ferrite may be formed in the as-built and heat-treated samples; however, probably due to the low content and small size of ferrite particles, they are not de-tected by the XRD instrument.
The microstructural evolution with heat treatment is schemati-cally illustrated inFig. 3a. The typical microstructural features of L-PBF SS mainly include three aspects, namely grains, MPBs and cellular structures. Looking at the grain orientation maps in Figs. 3b1-g1, it seems that up to 1050 °C, the overall grain structure is not greatly affected by the heat treatment, while the 1200 °C sample has a significantly different grain apperance with larger grain size, faceted grain morphology and a great number of anneal-ing twins (ATs, marked by green lines inFig. 3g1). Whereas, the higher magnification images in Figs. 3b2-g2 and 3b3-g3 show that microstructural evolutions do occur on a small scale. After an-nealing treatment at 700 °C-40 min, the MPBs appear to have nearly no change compared to the as-built one. However, when the temperature increases to 900 °C only vague traces are left, and they completely disappear after annealing above 1050 °C, demonstrating that atomic diffusion becomes more significant from 900 to 1200 °C. By further increase of the magnification of SEM micrographs, the cellular structures are observed (Figs. 3b3-g3). Similar to the evolution of MPBs, cellular walls became thinner with increasing annealing temperature and totally vanished after exposure at 900 °C for 40 min (Fig. 3e3). Different from the obvi-ously non-affected MPBs after the 700 °C treatment, the morphol-ogy of the cellular structures keeps the same but the average size increases from 530 for the as-built material to 600 nm, as shown in Figs. 3b3 and c3. It is interesting to note that the evolution
condition is in the sequence of 900 °C-40 min, 1050 °C-10 min and over 1050 °C, which corresponds for the dissolution of cellular structures and MPBs as well as the transition of grain structures, respectively. It means that although these three microstructural configurations are associated with element segregation, the segre-gation on GBs may be higher in comparison to the cellular struc-tures. When chemical segregation is eliminated by atomic diffusion, the microstructure becomes more uniform. Compared with welding or casting alloys, the dendrite arm spacing of AM-fabricated alloys is much narrower, which means that the homogenzation treatment of AM-fabricated alloys is expected to be achieved at lower temperatures and shorter durations. More-over, the grain dimensional evolution with heat treatment also has been calculated and listed inFig. 3h–j. The average size and area fraction of small and large grains remains constant up to 1050 °C, but at 1200 °C the average grain size significantly in-creases to 54.2μm. The same trend was also observed in the rela-tionship between the aspect ratio of grains and anneling temperatures, as shown inFig. 3j.
Different approaches have been proposed to distinguish the recrys-tallization (REX) grains from the deformed ones, such as the grain ori-entation spread (GOS) [34], grain size [35] and image quality (IQ) methods based on EBSD measurements [36]. In the present work, the GOS method is applied for the REX fraction analysis. The GOS values of the recrystallized grains are lower than the originally deformed ones [34,36]. By considering the distribution of GOS values and its corre-sponding microstructures, a critical GOS value of 2° is adopted for the REX determination. The relationship between REX fraction and anneal-ing temperature is shown inFig. 3j, and representative GOS maps are also present in Figs. 3b4-g4. The REX fraction appears to be constant around 6% up to 900 °C, then slowly increasing to 6.59% at 1050 °C, andfinally dramatically raises to 90% at 1200 °C. It should be noted that the microstructures after annealing at 1200 °C for 40 min is not fully recrystallized, which is confirmed by the white grains (Fig. 3g4) filled with LAGBs and tangled dislocations, as shown in Fig. S6d, Fig. S7f andFig. 4d.
3.2. Effect of annealing on the configuration and total density of dislocations Fig. S4 shows the typical microstructures of the as-built material and a sample heated at 700 °C for 40 min. It can be clearly observed from Figs. S4a and b that the microstructure of the as-built alloy is composed of cellular walls with highly tangled dislocations (marked by red arrows in Fig. S4b) and relatively clean cellular interior. The im-ages of the as-built samples also show that the average cell size and thickness of cellular walls are 530 and 33 nm, respectively. The STEM micrographs taken from the samples after annealing at 700 °C for 40 min (Figs. S4c and d) show no obvious differences with the as-built one in general, but the cell size increases to 620 nm. By fur-ther increasing the image magnification, as shown in Fig. S4f, some dislocations are still trapped around the cell boundaries, but the den-sity is significanly reduced, which indicates that the elemental segre-gation on the cell boundaries is reduced after high temperature atomic diffusion. It should also be noted that smaller subgrains, as the comparison of the representative ones marked by the light green dotted lines in Figs. S4a and c, were formed in the 700 °C-40 min sam-ple, illustrating that the recovery has occurred under this condition, which is reported by Ronneberg [8] and Clarebrough [37] as well. The newly formed subgrain boundaries (sub-GBs) consist of a large number of parallel and dense dislocation lines, as displayed in Fig. S4e. In addition, the average subgrain diameter and thickness of sub-GBs in 700 °C-40 min sample were also measured and are 1.18 ± 0.98μm and 69.2 ± 20.8 nm, respectively. For the as-built ma-terial (or the 700 °C-40 min sample), since the mean thickness of the cellular walls (or sub-GB thickness) is much smaller than the average Fig. 2. XRD patterns of the L-PBF 316 L SS after different annealing treatments.
Fig. 3. (a) Microstructural evolution with heat treatment for the L-PBF SS. (b)–(g) Typical microstructure characteristics and recrystallization phenomenon of the L-PBF SS after different annealing treatments. (h)–(j) The evolution of grain dimension and recrystallization fraction of L-PBF SS with different annealing treatments for 40 min.
cell size (or average subgrain diameter), the volume fraction of cellu-lar walls (or sub-GBs) can be calculated as follows [9,38]:
fw≈κwd
c ð2Þ
whereκ is a geometric constant and set as 3 for a regular substructure [38], w is the thickness of cellular walls or the sub-GBs, dcis the average
size of cellular structures or subgrain diameter. Thus, the volume frac-tion of cellular walls for the as-built alloy is about 18.0%, and that of sub-GBs for the 700 °C-40 min sample is around 17.5%.
One of the natures of the L-PBF technique is that it introduces a high density of dislocations (up to 1014–1015/m2) without any other
addi-tional processes [39,40]. Due to the high density dislocation structures, the alloys are hardened. Therefore, in the present study quantitative analysis of dislocation density was also performed from the TEM
micrographs using the intersection measurement method [41]. The dis-location densityρ for one material state can be obtained as follows [41]: ρ ¼ 1 ht ∑nv ∑Lvþ ∑nh ∑Lh ð3Þ where htis the thickness of the TEM foils, which is estimated to be
180 nm [41].∑nvand∑nhare the total intersections of dislocations
with the vertical and horizontal test lines.∑Lvand∑Lhare the total
length of the vertical and horizontal test lines from all TEM micrographs used for a specific material state. For the as-built state, since a large quantity of dislocations are tangled in the cellular wall, it is almost im-possible to directly measure the dislocation density in these regions. On the contrary, the dislocation density within the cellular interior (ρI) is relatively low and can be determined using Eq. (3) to be
(2.45 ± 0.81) × 1014/m2, which is close to the value in an as-built Fig. 4. Magnified EBSD-BC, GB distribution and corresponding GND density maps of the as-built material and samples after different heat treatments. (a) As-built state. (b) 900 °C-40 min. (c) 1100 °C-40 min. (d) 1200 °C-40 min.
L-PBF Inconel 718 alloy [39]. On the other hand, several relationships between the dislocation density along the cellular walls and cellular in-teriors have been proposed [42–46]. For example, as reported by the lit-erature [43–46], the dislocation density in the cellular wall region (ρw)
is about 3–5 times the average density (ρA). In the present work,
assum-ing that this relationship is also appropriate for AM alloys and an inter-mediate value of 4 is selected to calculate the value ofρAandρw.
Therefore, the average dislocation density for the as-built alloy can be estimated as follows:
ρA¼ ρwfwþ ρIð1− fwÞ ð4Þ
ρw¼ 4ρA ð5Þ
where fwis defined previously and calculated to be 18% for the as-built
alloy. Thus,ρAandρware determined to be (7.16 ± 1.19) × 1014/m2and
(2.86 ± 0.29) × 1015/m2. For the 700 °C-40 min sample, as shown in
Fig. S4e and f, since the dislocation density along the cellular walls is sig-nificantly reduced, not highly tangled and can be counted, the disloca-tion density within the subgrains can be obtained using Eq.(3)to be (2.11 ± 0.56) × 1014/m2. Similarly, the average dislocation for the
700 °C-40 min sample can be determined by Eqs.(4) and (5)withρw
andρIbeing the dislocation density in the sub-GBs and subgrain
inte-riors. Consequently, the average dislocation density for the 700 °C-40 min sample is around (5.80 ± 0.82) × 1014/m2.
Figs. S5a–f and g–i show the bright-field micrographs after heat treatment at 900 and 1050 °C for 40 min, respectively. Similar to the mi-crostructure after 700 °C-40 min treatment, a large number of small subgrains surrounded by parallel dense dislocations (marked by blue ar-rows in Fig. S5c, f and i) were formed, which demonstrates the occur-rence of the recovery phenomenon, whereas the dislocation density within the subgrains (as shown in Fig. S5c, f and i) significantly declines. Additionally, the dislocations in the subgrains of 900 °C-40 min and 1050 °C-40 min samples are no longer trapped by the cellular walls and present a more random distribution state (Fig. S5f and i), indicating that a uniform redistribution of elements has been reached, which is con-sistent with the comparison ofFig. 3c3–e3. Ultimately, the average dislo-cation density for 900 °C-40 min and 1050 °C-40 min samples can be obtained using Eqs.(4) and (5)to be (5.17 ± 0.63) × 1014/m2and
(3.75 ± 0.59) × 1014/m2, respectively. Furthermore, some nanoparticles
and dislocation networks also can be found in the subgrains (Fig. S5h). Different from the as-built conditions and the samples heat treated in the temperature range 700–1050 °C, the microstructure of the 1200 °C-40 min sample consists of recrystallized grains with straight GBs (Fig. S6a) and residual recovery onesfilled with small subgrains (Fig. S6d). A small number of dislocation arrays near the GBs (Fig. S6b) and some dislocation networks (Fig. S6c) in the grain interiors can be observed in the recrystallized grains. Moreover, the dislocation density in the recrystallized grains (ρR) was determined from the
STEM micrographs to be (3.28 ± 1.25) × 1013/m2. For the residual
re-covery grains, the average subgrain size and mean dislocation density (ρD) are mearsured to be 1.55 ± 0.47μm and (3.87 ± 0.77) × 1014/
m2, respectively. On the other hand, as shown inFig. 3g4 and j, the
area fraction of recrystallized grains (fR) in the 1200 °C- 40 min sample
is about 90%. Therefore, the average dislocation density (ρA) can be
es-timated using the following equation:
ρA¼ fRρRþ 1− fð RÞρD ð6Þ
Consequently, the value ofρAfor the 1200 °C-40 min sample was
de-termined to be around 6.82 × 1013/m2.
On the whole, the post-processing treatments in this work can be di-vided into the regions of recovery (700–1050 °C) and recrystallization (1100–1200 °C). In the recovery region, rearrangement and annihila-tion of dislocaannihila-tions occur simultaneously, while the latter is proved to be a secondary mechanism by the gradually decreases of dislocation density from (7.16 ± 1.19) × 1014/m2to (3.75 ± 0.59) × 1014/m2.
Part of trapped dislocations around the cellular walls migrate to the energy-favourable regions owing to the reduction of elemental segrega-tion, leading to the arrangement of dense dislocations along the newly formed sub-GBs, which has also been reported in the laser-melted 316 L steel [47] and conventionally deformed materials [48,49]. On the contrary, the annihilation of dislocations becomes the dominant mech-anism at 1200 °C, and thus dislocation density significantly decreases to 6.82 × 1013/m2.
3.3. Effect of annealing on the distribution and density of GNDs
Fig. S7 shows the GND density maps with an area of roughly 638μm by 146μm calculated from EBSD-acquired data for the present L-PBF alloy after different annealing treatments. About 1000 grains are in-cluded in each image and the indexing rates of all maps are above 94%. Therefore, it is sufficiently reliable to qualitatively analyze the dis-tribution of GND density using these datasets. In Fig. S7, the bright colors (red and orange) correspond to high dislocation density, while dark color (blue) corresponds to low density. It can be clearly observed that with the annealing temperature increasing the bright regions grad-ually decrease, illustrating an overall decrease of the GND density. On the other hand, it is interesting to note that the distribution of GND den-sity in the microstructure is significantly non-uniform; the bright colors are predominantly present in thefine grain regions. Due to the higher GND density and GB density in these regions, small grains also provide a greater contribution to alloy strength and a higher resistance for the crack propagation than the large grain regions.
The Hough-based EBSD technique has been successfully used to quantify the GND density in different alloys under different deformation states [20–22,24,30].Fig. 4shows the magnified EBSD-BC (Band Con-trast) maps, GB maps and the corresponding GND density distribution maps of the as-built material and different heat-treated samples. In the as-built and low temperature treated microstructures, nearly no annealing twins were detected in the BC maps (Fig. 4a and b); neverthe-less, some annealing twins (ATs) were formed in the high-temperature treated samples (Fig. 4c and d). It becomes clear that GNDs are hetero-geneously distributed across the microstructures, and most of them are located along sub-GBs (LAGBs). With the progress of annealing treat-ment, the GNDs transform into the configurations of energetically favourable LAGBs, resulting in the formation of new subgrains. The EBSD results correspond well to the TEM observations in Figs. S5-S7. These newly formed LAGBs are similar to the other sub-GBs in micro-structures, and both of them are formed by the arrangement of GNDs [21], which is consistent with the STEM observations of parallel dense dislocations in Figs. S5c and f. The GND density across the LAGBs and within the subgrains are in the order of 1015and 1013-1014/m2[21], which agrees well with our measurements inSection 3.2, giving con fi-dence in the reliability of our calculations. In addition, the GNDs are not concentrated at the GBs, ATs and triple junctions (TJs), which is dif-ferent from the reports for deformed Fe-22Mn-0.6C steel [22] and the simplified model proposed by Ashby [23]. This may be due to the fact that the Ashby's model is suitable when single slip is considered [50]. Whereas, in the present work, multi-slip systems may be activated dur-ing the heat treatment process for the release of internal stresses.
Before quantitatively analyzing the GND density, we need to deter-mine the uncertainty of the EBSD measurement for GND density. Ac-cording to Wilkinson et al. [51], the noise floor (ρnoise) of GND
measurements can be estimated as follows:
ρnoise¼ δ=bλs ð7Þ
whereδ is uncertainly in the crystal orientation measurement. For the present Nordlys-S™ EBSD detector, the upper-bound of δ is about 0.1° [21]. b andλsare Burgers vector (0.2546 nm) and step size (200 nm),
respectively. Therefore, the uncertainties in GND density calculations can be determined to be 1.7 × 1013/m2[21].
The frequency histograms of GND density distribution in logarithmic scale for the present L-PBF alloy after different annealing treatments are shown inFig. 5. As report by Kamaya et al. [52] the intragranular misori-entation distribution of the entire microstructure follows a lognormal distribution function. In addition, the measured GND densities for Fe-22Mn-0.6C steel [22] and polycrystalline Ni [20,21] also obey the same distribution curve. However, it was recently reported that when the cu-mulative strain is high, the misorientation would follow a gamma distri-bution [53]. In the present work, since no deformation is applied to the alloy, a lognormal distribution of GND density is assumed to calculate the microstructure-averaged density, as follows:
fðρGNDjμ, σÞ ¼ 1 σρGND ffiffiffiffiffiffi 2π p exp − ln ρð GND−μÞ 2 2σ2 ! ð8Þ whereμ and σ are the location and scale parameter of lognormal distri-bution, respectively. Under this definition, the microstructure-averaged value of GND density (mGND) and the heterogeneous distribution of
GNDs across the microstructure as quantified by the variance (υGND)
can be expressed as follows: mGND¼ exp μ þσ 2 2 ð9Þ υGND¼ exp 2μ þ σ2 exp σ2 −1 ð10Þ FromFig. 5a, it can be clearly seen that the GND densities of all heat-treated samples are larger than the noisefloor of 1.7 × 1013/m2.
Moreover, at least two EBSD scans were performed for each sample to eliminate the macroscopic variations of GND density in the microstruc-tures.Fig. 5b shows the evolution of mGND(red line) andυGND(black
line) as a function of annealing temperatures. The microstructure-averaged GND density decreases from 5.89 × 1014to 1.32 × 1014/m2
with increasing annealing temperature from room temperature (as-built state) to 1200 °C. The TEM-measured total dislocation density (blue line) is also plotted in Fig. 5b for comparison. The EBSD-measured GND density and the TEM-EBSD-measured total dislocation density nearly have the same magnitude, which is in agreement with the find-ings in polycrystalline nickel [20] and Fe-22Mn-0.6C steel [22] for a small plastic strain of 0.05 and 0.06, respectively. In addition, the rela-tionship betweenυGNDand annealing temperature can be divided into
3 regions, as shown inFig. 5b. At the stage I, the value ofυGNDgradually
decreases until 1050 °C, so the GNDs become more homogeneously dis-tributed in the microstructures. The rearrangement of GNDs during re-covery process at a temperature between 700 and 1050 °C may be
responsible for this, which is supported by the remarkable differance in dislocation density at the cellular walls between the as-built and 700 °C-40 min samples, as shown in Figs. S5b and f. Compared with as-built material (Fig. S4b), the dislocation distribution between cellular wall and cellular interior in the 700 °C-40 min sample becomes much more uniform (Fig. S4f). For the second, stage ranging from 1050 °C to a certain temperature between 1100 and 1200 °C, the significant differ-ence in GND density between the residual recovery grains and the re-crystallized ones may result in the higherυGNDvalue at 1100 °C. For
temperatures ranging from a certain temperature between 1100 and 1200 °C to the beginning of the melting range defines the third stage, where a majority of the grains have been recrystallized, and thusυGND
decreases to a relatively low value.
3.4. Effect of annealing on the evolution of microhardness
To characterize the effect of annealing treatment on the mechanical properties of the present L-PBF alloy, Vicker's microhardness tests were performed.Fig. 6a shows the evolution of hardness as a function of a rel-atively wide range of applied loads. Each plotted point and its error bar are the average value and standard deviation of more than 20 indenta-tion measurements, as shown inFig. 1c. It can be clearly seen that for all samples in the low load range, the hardness value dramatically de-creases as the load inde-creases; nevertheless, it turns to a slow decline or a constant value at higher loads. The same trend is also observed in the relationship between hardness and indentation depth (h) in
Fig. 6b. This means that the ISE occurs in all samples. Nix and Gao [54] explain that the ISE is related to GNDs, whose density is inversely pro-portional to the indentation depth, and this leads to the different inden-tation depths corresponding to different hardness values. Therefore, a depth-independent hardness, sometimes called as“true hardness” [31,55], is necessary to use to accurately evaluate the properties of the present Fe-Ni-Cr SS. Some models are proposed to calculate the true hardness, such as the proportional specimen resistance (PSR) model as-sumed by Li et al. [56] and the modified PSR model put forward by Gong et al. [55]. In the present work, we use the hardness in the limit of in fi-nite depth (H0) as the“true hardness” calculated as follows [33]:
H H0
2
¼ 1 þhh∗ ð11Þ
where H is the hardness for a given indentation depth h. h∗is a charac-teristic length, which is not a constant for a given material but depends on the shape of the indenter, the shear modulus and SSD density [33,54].Fig. 6c shows the relationship between square of hardness (H2) and reciprocal of indentation depth (1/h) byfitting Eq.(11). A good
Fig. 5. (a) Frequency histogram of GND density distribution for the present L-PBF alloy after different annealing treatments in logarithmic scale. (b) Evolutions of TEM-measured total dislocation density, EBSD-measured GND density and variance of microstructure-average GND density as a function of annealing temperature.
straight line is found, the slope of which is H02h∗and the intercept of
which is H02. The measured values of H0for the different state samples
are demonstrated inFig. 6d. With the annealing temperature increasing, H0gradually decreases from 2.322 GPa for the as-built material to
1.457 GPa for the 1200 °C-40 min sample. 4. Discussion
4.1. The hardening nature of the L-PBF 316 L SS
As shown inFig. 6d, the true hardness of the present L-PBF alloy gradually decreases from 2.322 to 1.457 GPa with increasing annealing temperatures. It is acknowledged that hardness is closely related with the strength, which has been investigated by several previous researches [57,58]. For example, in the model put forward by Cahoon et al. [58], the strain hardening exponent (n) of the given material is explicitly considered. In the present study, the Cahoon's model has been successfully applied to L-PBF alloys, and an excellent agreement (error < 3.2%) with tensile test results are established. Therefore, it is possible to quantitatively analysis the hardening mechanisms of the alloy through the factors that affect the strength. The derivation process of the expression can be seen in the Supplementary material (Section S7), and the expression is as follows:
YS¼ H0
3
0:1
ð Þm−1:79 ð12Þ
where YS is the yield strength of the given material. H0is the“true
hard-ness” in Fig. 6d. m is the Meyer's index, which is related to the ISE effect.
Fig. 7a shows the relationship between the values of Meyer's index and annealing temperatures byfitting Eq. (S2). With increasing annealing temperatures, the value of Meyer's index displays a decreasing trend (except 1050 °C), which illustrates that more significant ISE effect oc-curs in the high-temperature annealed samples. The increased inner length scale due to the decreased GND dislocation density as the anneal-ing temperature increases (Fig. 5) is responsible for this phenomenon [33]. Finally, using the values of H0inFig. 6d and m inFig. 7a, the yield
strengths of the present L-PBF alloy after different heat treatments were calculated and displayed inFig. 7b andTable 3. The evolution of yield strength as a function of annealing temperature shows the same trend as that for hardness.
4.1.1. Effects of annealing on hardening mechanisms of the L-PBF 316L SS For comprehensively understanding the hardening mechanisms in the 316 L SS, all strengthening factors that play a role in yield strength were considered. According to the additive strengthening mixture rule, the yield strengthσyis the sum of friction stress (σ0), grain size
strengthening (σGB), solid solution strengthening (σSS), precipitation
strengthening (σP) and dislocation strengthening (σDis):
σy¼ σ0þ σGBþ σSSþ σPþ σDis ð13Þ
Hereσ0is a constant taken as 15 MPa for theγ‑iron at room
temper-ature according to Nabarro [59,60] and Foreman [61]. The grain-size re-finement can also contribute to a yield strength increment. As present in Fig. S3 andFig. 3, due to the significant grain size difference, we consider the microstructure of the L-PBF alloy as consisting of relatively large Fig. 6. (a)–(b) Evolution of hardness as a function of applied load and indentation depth, respectively. (c) The relationship between square of hardness and reciprocal of indentation depth. (d) Bulk hardness (hardness in the limit of infinite depth) in as-built and heat-treated samples.
grains surrounded by small ones up to 1100 °C. Therefore, the value of σGBcan be estimated using a modified Hall–Petch relation as:
σGB¼ fsmall ky ffiffiffiffiffiffiffiffiffiffiffi dsmall p þ flarge ky ffiffiffiffiffiffiffiffiffiffiffi dlarge q ð14Þ
where kyis the strengthening coefficient taken as 452 MPa/μm1/2[62].
fsmall, flargeand dsmall, dlargein Eq.(14)are the area fractions and average
grain sizes of the small and large grains, respectively; and values of them have been plotted inFig. 3h and i. Thus, the increments in yield strength resulting from the grain-size refinement are calculated and listed inTable 3.
The solid solution strengthening also contributes to the increase in yield strength of steels, and has been studied in several previous work [63–68]. For the case of austenitic stainless steel, Van Bohemen pro-posed an expression to obtainσSSas follows [67]:
σSS¼ ∑iBiCi ð15Þ
where Biis the strengthening coefficient of i-th alloying element in the
unit of MPa/wt%, Ciis the concentration of i-th alloying element in wt
%. Since the heat-treated samples have a comparable composition as the powder (as substantiated by Table S1), it results in σSSto be
96.6 MPa for all samples.
The yield strength is somewhat enhanced due to the precipitation of the Si-rich nanoparticles. The strengthening mechanisms of the Si-rich nanoparticles are still highly unclear unfortunately [5,6]. Although there are many uncertainties in the interaction between dislocations
and precipitates [69,70] and the elastic modulus of Si-rich nanoparticles, the model proposed by Russel and Brown [71] was successfully applied in many studies [69,70]. In this model, the precipitates have an attrac-tive interaction with dislocations, and hinder the dislocation move-ments, resulting in a strength increment [69]. The corresponding strengthening can be obtained by assuming dislocations cut through the weak particles, and the equation is expressed as [71]:
σP−Cut¼ MGbL 1− EEp m 2 " #3 4 ; sin−1 Ep Em ≥ 50 ð16Þ
where M is the Taylor factor derived from the EBSD measurements to be 3.06–3.12 (Table S3), b = 0.2546 nm is the magnitude of Burgers vector in austenitic steels, G = 73 GPa is the shear modulus [40], Epand Emare
the dislocation line energy in the Si-rich nanoparticles and matrix, re-spectively. L is the average spacing on the glide plane for nanoparticles. The ratio of Ep/Emis particle size dependent and is suggested as [71]: Fig. 7. (a) Relationship between the values of Meyer's index (m) and annealing temperatures. (b) Evolution of estimated yield strength as a function of annealing temperatures. (c) TEM-measured total dislocation density, estimated total dislocation density from the Taylor's hardening model, EBSD-TEM-measured GND density, and estimated SSD density according to the difference between the total dislocation density from the Taylor's hardening model and the measured GND density. (d) The hardening mix of the L-PBF alloy after different heat treatments.
Table 3
All strengthening components and the estimated yield strength (YSE).
σ0/MPa σGB/MPa σSS/MPa σP/MPa σDis/MPa YSE/MPa
As-built 15.0 89.1 96.6 12.5 343.1 556.3 700 °C 15.0 89.8 96.6 12.0 299.5 512.9 900 °C 15.0 85.7 96.6 12.0 282.0 491.3 1050 °C 15.0 87.2 96.6 11.7 245.9 456.5 1100 °C 15.0 79.1 96.6 14.2 239.7 444.6 1200 °C 15.0 61.4 96.6 13.7 197.6 384.4
Ep Em¼ E∞P E∞m log R r0 log r r0 þlog r RP log r r0 ð17Þ where r and r0is the inner cut-off radius and outer cut-off radius of the
dislocation stressfield, respectively. In the present work, the values of r and r0are taken as 2.5b and 1000r, respectively [72]. EP∞/Em∞=0.62 is the
energy per unit length of a dislocation in an infinite medium [70]. RPis
the mean radius of the Si-rich particles, whose value has been measured and listed in Table S3. The average spacing, L, on the glide plane can be calculated as follows [73]: L¼ ffiffiffiffiffiffiffiffi 2π 3 fP s RP ð18Þ
where fPis the volume fraction of the nanoparticles, which has been
measured and shown in Table S3. Therefore, the strength increment caused by the interaction between dislocations and precipitates are cal-culated and listed in Table S3.
Apart from assuming that the Si-rich nanoparticles are soft and can be cut by dislocations, dislocations are also likely to by-pass the particles via the Orowan strengthening mechanism [5,74]. The contribution to strength resulting from the dislocation looping can be evaluated accord-ing to [5].
σP−Loop¼L−dGb
P ð19Þ
where L has been defined previously, and values are listed in Table S3. dP
is the average diameter of nanoparticles (Table S3). This yields a strengthening effect of 11.7–14.2 MPa, which is very close to the pre-dicted results of Russel-Brown model, and both of them are negligibly small. In the further evaluation and inTable 3the values from the Orowan model has been adopted for the strengthening mechanisms originating from the nanoparticles.
The strength contribution from dislocations can be estimated by subtracting the friction stress, grain size strengthening, solid solution strengthening and precipitation strengthening from the yield strength, and the corresponding values are listed inTable 3. In addition, by using Eq.(12) the corresponding hardness coming from different strengthening components can be calculated. For a better comparison, a schematic map of the different hardening components for the present L-PBF alloy is summarized inFig. 7d. It can be clearly observed that with the increase of annealing temperature, the contributions of dislocations and grain size gradually decreases, but more than 50% of the hardness increment comes from the contribution of dislocations under any condi-tions. Similarfindings were also reported in other L-PBF alloys with dif-ferent microstructures, such as the precipitation strengthened IN738LC superalloy [9] and single-phase steel [40], in which dislocation strength-ening contributed 53.3% and 67.9% of the yield strength, respectively. 4.1.2. Effect of dislocation-type on the hardness of L-PBF 316 L SS
It is widely accepted that GNDs and SSDs have equal contributions to the strength of alloys [22,23,50,75]. Therefore, this part of strength can be expressed by the well-known Taylor relation [23]:
σDis¼ MαGbpffiffiffiffiffiffiffiffiffiρTOT¼ MαGb
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ρGNDþ ρSSD
p
ð20Þ Combining Eqs.(13) and (20), both the density of total dislocations (ρTOT) and SSDs (ρSSD) can be estimated as follow:
ρTOT¼ σ y−σ0−σGB−σSS−σP MαGb n o2 ð21Þ ρSSD¼ ρTOT−ρGND ð22Þ
M, G and b have been defined previously in Eq.(16).α is an empir-ical constant related to the dislocation structures [40,76]. For the
as-built material and samples heat-treated up to 1100 °C, dislocation formed structures (cellular walls or sub-GBs) present in the microstruc-tures, thusα is 0.23 [76]; whereas,α = 0.3 for the no cell-forming dis-location distribution in the 1200 °C-40 min sample [9].ρGNDhas been
evaluated by the EBSD-acquired orientation maps inSection 3.3. The total dislocation density calculated from the dislocation strengthening using Eq.(21)is plotted onFig. 7c, and decreases from 6.86 × 1014to 1.39 × 1014/m2with increasing annealing temperature,
which coincides well with the measured values from TEM micrographs, as illustrated inFig. 7c. In addition, to further confirm the validity of the total dislocation density, the modified Williamson-Hall method was performed on the basis of XRD measurements, see details in the Supple-mentary material (Section S9). The results are consistent with that de-termined from TEM micrographs and the Taylor's hardening model. They are also reasonably comparable to the values measured for an L-PBF Fe-20Cr-16Ni austenitic SS in Ref. [77]. This validation suggests that the acceptable accuracy of the total dislocation density is obtained for the present L-PBF alloy. The average density of SSDs can be obtained by subtracting the EBSD-measured GND density from the total disloca-tion density using Eq.(22). InFig. 7c, the average SSD density shows a decline from 9.73 × 1013for the as-built sample to 7.43 × 1012/m2
after annealing at 1200 °C. Apparently the accuracy of the estimated SSD density will largely depend on the accuracy of the total dislocation density and GND density. The total dislocation density is carefully stud-ied by considering the separate strengthening components and the Taylor's hardening model, whose value agrees well with that measured from TEM micrographs. As for the GND density determination, more than 800 grains were analyzed for each sample, and the GND density of all heat-treated samples are larger than the noisefloor (1.7 × 1013/
m2). In addition, the parameters used for the EBSD scanning, such as
step size, also have a significant impact on GND density. In the present work, a step size of 200 nm is chosen according to the recommendations by Wright [78], which is small enough to reveal the cellular structures (with the average size of 530 nm) and large enough to have an accept-able measurement duration. Therefore, both the TEM-measured and the Taylor's model-estimated total dislocation density as well as the EBSD-measured GND density provide a high confidence of accuracy to esti-mate the SSD density. It also can be seen that the proportion of SSDs in the total density decreases rapidly, from about 14.2% for as-built sam-ple to 5.3% for 1200 °C-40 min samsam-ple, indicating that the SSDs are less stable than GNDs and the strengthening contribution from SSDs dimin-ishes rapidly during heat treatments. As reported by Zhi [22] and Zhu [20], the SSD density largely depends on the degree of deformation, while GND density shows weak dependence. In the present work, the thermal distortions induced during printing process are released in the post-processing treatments, which explains the variation of SSD density as a function of annealing conditions. Further analysis shows that under all annealing conditions the GND type dislocations account for more than 85.8% of total dislocations. Hence, the hardness of present L-PBF alloy is governed predominantly by GND type dislocations. 4.2. Relationship between microstructural evolution and hardening nature
The complete set of the evolution of microscopic data (cellular struc-ture, chemical segregation and dislocation density) and macroscopic data (grain dimension and recrystallization behavior) with annealing conditions studied in this work were collected and summarized sche-matically inFig. 8. The grain shape and size appear largely unaffected by heat treatment up to 1050 °C, but at 1200 °C they changed signi fi-cantly due to the occurrence of recrystallization. Dislocation tangled cel-lular structures can be observed in the as-built and 700 °C-40 min samples, but after the treatment at 900 °C for 40 min the dislocations are no longer trapped by the cellular walls due to a homogeneous redis-tribution of elements within the subgrain interiors. With the progress of recovery, the GNDs migrate from cellular walls to more energetically-favourable regions, which result in the higher concentration of GNDs
along the sub-GBs and formation of new subgrains, as shown byFig. 8b and c. The total dislocation density gradually decreases from 6.86 × 1014/m2 for the as-built alloy to 3.67 × 1014/m2 for the
1050 °C- 40 min sample due to the occurrence of recovery. After heat treatment at 1200 °C for 40 min, the dislocation density significantly de-creases to around 1.39 × 1014/m2; meanwhile, the volume fraction of
re-crystallized grains promptly increases to 90%. During heat treatment, strength contribution from SSDs diminishes more rapidly than that from GNDs, which is due to the SSDs largely depends on the release of thermal distortions formed in printing. Under all annealing conditions, more than 50% of the hardness increment comes from the dislocation strengthening, while changes in the contribution of other strengthening mechanisms are negligible. In addition, since the majority of the total dislocations are the GNDs, the hardness of the present L-PBF alloy is governed predominantly by the GND type dislocations.
5. Conclusions
In the present work, the relationships between microstructure and the hardening nature of the L-PBF 316 L SS through heat treatment ex-periments are revealed. The microstructural evolutions were systematically investigated using integrated experimental efforts and calculations. The density and distribution of GNDs were measured uti-lizing the Hough-based EBSD method, and the SSD density was esti-mated according to the Taylor's hardening model. A fundamental understanding of dislocation-type, namely GNDs and SSDs, their stabil-ity during annealing treatments, as well as their impacts on the harden-ing nature of the L-PBF alloy has been accessed. The main conclusions are summarized as follows:
(1) The significant microstructural features of the present L-PBF alloy are cellular structures, MPBs and highly serrated GBs, whose transi-tion conditransi-tions are 900 °C-40 min, 1050 °C-10 min and over 1050 °C, respectively. Dislocations are no longer trapped by the cel-lular walls after treatment at 900 °C for 40 min due to the homoge-neous redistribution of elements within the subgrain interiors. (2) A model for estimating yield strength of L-PBF alloys from
hard-ness has been established, and the expression is as follows: YS=
H0
3
0:1
ð Þm−1:79, which shows excellent agreement (error < 3.2%)
when calculating the yield strength for various L-PBF alloys with different microstructures.
(3) The total dislocation density determined by Taylor's hardening model agrees well with that measured from TEM micrographs, which gradually decreases from 6.86 × 1014/m2for the as-built
alloy to 3.67 × 1014/m2for the 1050 °C- 40 min sample due to
the occurrence of recovery. After heat treatment at 1200 °C for 40 min, the dislocation density significantly decreases to around 1.39 × 1014/m2; meanwhile, the volume fraction of recrystalliza-tion grains promptly increases to 90%.
(4) The microstructure-averaged GND density decreases from 5.89 × 1014to 1.32 × 1014/m2with increasing temperature from 20 °C (as-built state) to 1200 °C. With the progress of recovery, the GNDs migrate from cellular walls to more energetically-favourable regions, resulting in the higher concentration of GNDs along the sub-GBs and division of grains into small subgrains. (5) Average density of SSDs was estimated by subtracting the
EBSD-measured GND density from the total dislocation density based on the Taylor's hardening model. The average SSD density de-creases from 9.73 × 1013for the as-built material to 7.43 × 1012/
m2for the 1200 °C-40 min sample. The SSDs are less stable than
GNDs during heat treatment due to that the SSD density largely depends on the release of thermal distortions formed in printing. Under all annealing conditions, the dislocation strengthening con-tributes more than half of hardness increment, and the majority of the dislocations are the GNDs. Therefore, the hardness of the pres-ent L-PBF alloy is governed predominantly by the GNDs. Author contributions
All authors have read and agreed to the published version of the manuscript.
Declaration of Competing Interest
The authors declare that they have no conflict of interests or per-sonal relationships that could have appeared to influence the work re-ported in this paper.
Fig. 8. Schematic showing the microstructural evolution dependence of annealing conditions. (For interpretation of the references to color, the reader is referred to the web version of this article.)
Acknowledgements
This study is supported by the Swedish Governmental Agency for In-novation Systems (Vinnova grant 2016-05175) and the Center for Addi-tive Manufacturing-metal (CAM2). This research is also supported in
part by a research grant from Science Foundation Ireland (SFI) under Grant Number 16/RC/3872 and is cofounded under the European Re-gional Development Fund and by the I-Form Industry partners. Also, the assistance of staff and technicians in Dublin City University and Wa-terford Institute of Technology is acknowledged.
Appendix A. Supplementary data
Supplementary data to this article can be found online athttps://doi. org/10.1016/j.matdes.2020.109385.
References
[1] H. Chen, W. Yan, Spattering and denudation in laser powder bed fusion process: multiphaseflow modelling, Acta Mater. 196 (2020) 154–167.
[2]R. Shi, S.A. Khairallah, T.T. Roehling, T.W. Heo, J.T. McKeown, M.J. Matthews, Micro-structural control in metal laser powder bed fusion additive manufacturing using laser beam shaping strategy, Acta Mater. 184 (2020) 284–305.
[3]K. Saeidi, X. Gao, Y. Zhong, Z.J. Shen, Hardened austenite steel with columnar sub-grain structure formed by laser melting, Mater. Sci. Eng. A 625 (2015) 221–229.
[4]L. Liu, Q. Ding, Y. Zhong, J. Zou, J. Wu, Y.-L. Chiu, J. Li, Z. Zhang, Q. Yu, Z. Shen, Dislo-cation network in additive manufactured steel breaks strength–ductility trade-off, Mater. Today 21 (2018) 354–361.
[5] Y.M. Wang, T. Voisin, J.T. McKeown, J.C. Ye, N.P. Calta, Z. Li, Z. Zeng, Y. Zhang, W. Chen, T.T. Roehling, R.T. Ott, M.K. Santala, P.J. Depond, M.J. Matthews, A.V. Hamza, T. Zhu, Additively manufactured hierarchical stainless steels with high strength and ductility, Nat. Mater. 17 (2018) 63–71.
[6]O.O. Salman, C. Gammer, A.K. Chaubey, J. Eckert, S. Scudino, Effect of heat treatment on microstructure and mechanical properties of 316L steel synthesized by selective laser melting, Mater. Sci. Eng. A 748 (2019) 205–212.
[7]D. Deng, R.L. Peng, H. Brodin, J. Moverare, Microstructure and mechanical properties of Inconel 718 produced by selective laser melting: sample orientation dependence and effects of post heat treatments, Mater. Sci. Eng. A 713 (2018) 294–306.
[8] T. Ronneberg, C.M. Davies, P.A. Hooper, Revealing relationships between porosity, microstructure and mechanical properties of laser powder bed fusion 316L stainless steel through heat treatment, Mater. Des. 108481 (2020).
[9]J. Xu, H. Gruber, R. Boyd, S. Jiang, R.L. Peng, J.J. Moverare, On the strengthening and embrittlement mechanisms of an additively manufactured Nickel-base superalloy, Materialia (2020) 100657.
[10] F. Zhang, L.E. Levine, A.J. Allen, M.R. Stoudt, G. Lindwall, E.A. Lass, M.E. Williams, Y. Idell, C.E. Campbell, Effect of heat treatment on the microstructural evolution of a nickel-based superalloy additive-manufactured by laser powder bed fusion, Acta Mater. 152 (2018) 200–214.
[11] H. Wang, Z.G. Zhu, H. Chen, A.G. Wang, J.Q. Liu, H.W. Liu, R.K. Zheng, S.M.L. Nai, S. Primig, S.S. Babu, S.P. Ringer, X.Z. Liao, Effect of cyclic rapid thermal loadings on the microstructural evolution of a CrMnFeCoNi high-entropy alloy manufactured by selective laser melting, Acta Mater. 196 (2020) 609–625.
[12] T.H. Becker, N.M. Dhansay, G.M.T. Haar, K. Vanmeensel, Near-threshold fatigue crack growth rates of laser powder bed fusion produced Ti-6Al-4V, Acta Mater. 197 (2020) 269–282.
[13] A.E. Wilson-Heid, S. Qin, A.M. Beese, Multiaxial plasticity and fracture behavior of stainless steel 316L by laser powder bed fusion: experiments and computational modeling, Acta Mater. 199 (2020) 578–592.
[14] S. Gao, Z. Hu, M. Duchamp, P.S.S.R. Krishnan, S. Tekumalla, X. Song, M. Seita, Recrystallization-based grain boundary engineering of 316L stainless steel pro-duced via selective laser melting, Acta Mater. 200 (2020) 366–377.
[15] M.S.I.N. Kamariah, W.S.W. Harun, N.Z. Khalil, F. Ahmad, M.H. Ismail, S. Sharif, Effect of heat treatment on mechanical properties and microstructure of selective laser melting 316L stainless steel, IOP Conf. Ser. Mater. Sci. Eng. 257 (2017) 1–11.
[16] O. Fergani, A. Bratli Wold, F. Berto, V. Brotan, M. Bambach, Study of the effect of heat treatment on fatigue crack growth behaviour of 316L stainless steel produced by se-lective laser melting, Fatigue Fract. Eng. Mater. Struct. 41 (2018) 1102–1119.
[17] D. Kong, X. Ni, C. Dong, L. Zhang, C. Man, J. Yao, K. Xiao, X. Li, Heat treatment effect on the microstructure and corrosion behavior of 316L stainless steel fabricated by selective laser melting for proton exchange membrane fuel cells, Electrochim. Acta 276 (2018) 293–303.
[18] K. Chadha, Y. Tian, J.G. Spray, C. Aranas, Effect of annealing heat treatment on the mi-crostructural evolution and mechanical properties of hot Isostatic pressed 316L stainless steel fabricated by laser powder bed fusion, Metals 10 (2020).
[19] N. Chen, G. Ma, W. Zhu, A. Godfrey, Z. Shen, G. Wu, X. Huang, Enhancement of an additive-manufactured austenitic stainless steel by post-manufacture heat-treatment, Mater. Sci. Eng. A 759 (2019) 65–69.
[20] C. Zhu, T. Harrington, G.T. Gray, K.S. Vecchio, Dislocation-type evolution in quasi-statically compressed polycrystalline nickel, Acta Mater. 155 (2018) 104–116.
[21] O. Muránsky, L. Balogh, M. Tran, C.J. Hamelin, J.S. Park, M.R. Daymond, On the mea-surement of dislocations and dislocation substructures using EBSD and HRSD tech-niques, Acta Mater. 175 (2019) 297–313.
[22]H. Zhi, C. Zhang, S. Antonov, H. Yu, T. Guo, Y. Su, Investigations of dislocation-type evolution and strain hardening during mechanical twinning in Fe-22Mn-0.6C twinning-induced plasticity steel, Acta Mater. 195 (2020) 371–382.
[23] M.F. Ashby, The deformation of plastically non-homogeneous materials, Philos. Mag. 21 (1970) 399–424.
[24] Y. Guo, D.M. Collins, E. Tarleton, F. Hofmann, A.J. Wilkinson, T.B. Britton, Dislocation density distribution at slip band-grain boundary intersections, Acta Mater. 182 (2020) 172–183.
[25] Pakkanen J.A., Designing for additive manufacturing-product and process driven de-sign for metals and polymers (Doctoral dissertation, Polytechnic University of Turin, Turin, Italy), 2018https://doi.org/10.6092/polito/porto/2714732.
[26] T. Kurzynowski, K. Gruber, W. Stopyra, B. Kuźnicka, E. Chlebus, Correlation between process parameters, microstructure and properties of 316 L stainless steel processed by selective laser melting, Mater. Sci. Eng. A 718 (2018) 64–73.
[27] S.K. Nayak, S.K. Mishra, C.P. Paul, A.N. Jinoop, K.S. Bindra, Effect of energy density on laser powder bed fusion built single tracks and thin wall structures with 100μm preplaced powder layer thickness, Opt. Laser Technol. 125 (2020), 106016, .
[28]J.A. Cherry, H.M. Davies, S. Mehmood, N.P. Lavery, S.G.R. Brown, J. Sienz, Investiga-tion into the effect of process parameters on microstructural and physical properties of 316L stainless steel parts by selective laser melting, Int. J. Adv. Manuf. Technol. 76 (2015) 869–879.
[29] C. Zhu, T. Harrington, V. Livescu, G.T. Gray, K.S. Vecchio, Determination of geometri-cally necessary dislocations in large shear strain localization in aluminum, Acta Mater. 118 (2016) 383–394.
[30] W. Pantleon, Resolving the geometrically necessary dislocation content by conven-tional electron backscattering diffraction, Scr. Mater. 58 (2008) 994–997.
[31]X. Rao, F. Zhang, X. Luo, F. Ding, Characterization of hardness, elastic modulus and fracture toughness of RB-SiC ceramics at elevated temperature by Vickers test, Mater. Sci. Eng. A 744 (2019) 426–435.
[32] K. Durst, B. Backes, O. Franke, M. Goken, Indentation size effect in metallic materials: modeling strength from pop-in to macroscopic hardness using geometrically neces-sary dislocations, Acta Mater. 54 (2006) 2547–2555.
[33] K. Durst, B. Backes, M. Göken, Indentation size effect in metallic materials: correcting for the size of the plastic zone, Scr. Mater. 52 (2005) 1093–1097.
[34] Y. Wu, X. Qin, C. Wang, L. Zhou, Influence of phosphorus on hot deformation micro-structure of a Ni-Fe-Cr based alloy, Mater. Sci. Eng. A 768 (2019), 138454, .
[35]S. Mandal, S.K. Mishra, A. Kumar, I. Samajdar, P.V. Sivaprasad, T. Jayakumar, B. Raj, Evolution and characterization of dynamically recrystallized microstructure in a titanium-modified austenitic stainless steel using ultrasonic and EBSD techniques, Philos. Mag. 88 (2008) 883–897.
[36] Y. Cao, H. Di, J. Zhang, J. Zhang, T. Ma, R.D.K. Misra, An electron backscattered diffrac-tion study on the dynamic recrystallizadiffrac-tion behavior of a nickel–chromium alloy (800H) during hot deformation, Mater. Sci. Eng. A 585 (2013) 71–85.
[37] L.M. Clarebrough, M.E. Hargreaves, G.W. West, The release of energy during anneal-ing of deformed metals, Proc. R. Soc. Lond. A 232 (1955) 252–270.
[38] E. Nes, Modelling of work hardening and stress saturation in FCC metals, Prog. Mater. Sci. 41 (1997) 129–193.
[39] T.G. Gallmeyer, S. Moorthy, B.B. Kappes, M.J. Mills, B. Amin-Ahmadi, A.P. Stebner, Knowledge of process-structure-property relationships to engineer better heat treatments for laser powder bed fusion additive manufactured Inconel 718, Addit. Manuf. 31 (2020), 100977, .
[40] Y.J. Yin, J.Q. Sun, J. Guo, X.F. Kan, D.C. Yang, Mechanism of high yield strength and yield ratio of 316 L stainless steel by additive manufacturing, Mater. Sci. Eng. A 744 (2019) 773–777.
[41] J. Pešička, R. Kužel, A. Dronhofer, G. Eggeler, The evolution of dislocation density during heat treatment and creep of tempered martensite ferritic steels, Acta Mater. 51 (2003) 4847–4862.
[42] M.R. Staker, D.L. Holt, The dislocation cell size and dislocation density in copper de-formed at temperatures between 25 and 700°C, Acta Metall. 20 (1972) 569–579.
[43] D. Griffiths, J.N. Riley, Dislocation arrangements in deformed polycrystalline 3% silicon-iron, Acta Metall. 14 (1966) 755–773.
[44] D. Kuhlmann-wilsdorf, A critical test on theories of work-hardening for the case of drawn iron wire, Metall. Trans. A. 1 (1970) 3173–3179.
[45] J.E. Bailey, The dislocation density,flow stress and stored energy in deformed poly-crystalline copper, Philos. Mag. 8 (1963) 223–236.
[46] J.E. Bailey, P.B. Hirsch, The dislocation distribution,flow stress, and stored energy in cold-worked polycrystalline silver, Philos. Mag. 5 (1960) 485–497.
[47] K. Saeidi, F. Akhtar, Subgrain-controlled grain growth in the laser-melted 316 L pro-moting strength at high temperatures, R. Soc. Open Sci. 5 (2018).
[48] I.Z. Awan, A.Q. Khan, Recovery, recrystallization, and grain-growth, J. Chem. Soc. Pak. 41 (2019) 1–42.
[49] E.J. Mittemeijer, Fundamentals of Materials Science, Springer, Berlin, 2011.
[50] D.A. Hughes, N. Hansen, D.J. Bammann, Geometrically necessary boundaries, inci-dental dislocation boundaries and geometrically necessary dislocations, Scr. Mater. 48 (2003) 147–153.
[51] A.J. Wilkinson, D. Randman, Determination of elastic strainfields and geometrically necessary dislocation distributions near nanoindents using electron back scatter dif-fraction, Philos. Mag. 90 (2010) 1159–1177.
[52] M. Kamaya, A.J. Wilkinson, J.M. Titchmarsh, Quantification of plastic strain of stain-less steel and nickel alloy by electron backscatter diffraction, Acta Mater. 54 (2006) 539–548.
[53] D.N. Githinji, S.M. Northover, P.J. Bouchard, M.A. Rist, An EBSD study of the deforma-tion of service-aged 316 austenitic steel, Metall. Mater. Trans. A 44 (2013) 4150–4167.
[54] W.D. Nix, H. Gao, Indentation size effects in crystalline materials: a law for strain gradient plasticity, J. Mech. Phys. Solids 46 (1998) 411–425.
[55] J. Gong, J. Wu, Z. Guan, Examination of the indentation size effect in low-load vickers hardness testing of ceramics, J. Eur. Ceram. Soc. 19 (1999) 2625–2631.
[56] H. Li, R.C. Bradt, The microhardness indentation load/size effect in rutile and cassit-erite single crystals, J. Mater. Sci. 28 (1993) 917–926.
[57] J.R. Cahoon, W.H. Broughton, A.R. Kutzak, The determination of yield strength from hardness measurements, Metall. Trans. A. 2 (1971) 1979–1983.
[58] J.R. Cahoon, An improved equation relating hardness to ultimate strength, Metall. Mater. Trans. B Process Metall. Mater. Process. Sci. 3 (1972) 3040.
[59] F.R.N. Nabarro, Dislocations in a simple cubic lattice, Proc. Phys. Soc. 59 (1947) 256–272.
[60] F.R.N. Nabarro, Fifty-year study of the Peierls-Nabarro stress, Mater. Sci. Eng. A 234–236 (1997) 67–76.
[61] A.J. Foreman, M.A. Jaswon, J.K. Wood, Factors controlling dislocation widths, Proc. Phys. Soc. Lond. Sect. A 64 (1951) 156–163.
[62] C.X. Huang, G. Yang, C. Wang, Z.F. Zhang, S.D. Wu, Mechanical behaviors of ultrafine-grained 301 austenitic stainless steel produced by equal-channel angular pressing, Metall. Mater. Trans. A 42 (2011) 2061–2071.
[63] A. Eres-Castellanos, I. Toda-Caraballo, A. Latz, F.G. Caballero, C. Garcia-Mateo, An integrated-model for austenite yield strength considering the influence of temper-ature and strain rate in lean steels, Mater. Des. 188 (2020), 108435, .
[64] H. Sieurin, J. Zander, R. Sandström, Modelling solid solution hardening in stainless steels, Mater. Sci. Eng. A 415 (2006) 66–71.
[65] R. Labusch, A statistical theory of solid solution hardening, Phys. Status Solidi 41 (1970) 659–669.
[66] K.J. Irvine, The strength of austenitic stainless steels, J. Iron Steel Inst. 207 (1969) 1017–1028.
[67] S.M.C. van Bohemen, Exploring the correlation between the austenite yield strength and the bainite lath thickness, Mater. Sci. Eng. A 731 (2018) 119–123.
[68] P. Kusakin, A. Belyakov, D.A. Molodov, R. Kaibyshev, On the effect of chemical com-position on yield strength of TWIP steels, Mater. Sci. Eng. A 687 (2017) 82–84.
[69] Z.B. Jiao, J.H. Luan, Z.W. Zhang, M.K. Miller, W.B. Ma, C.T. Liu, Synergistic effects of Cu and Ni on nanoscale precipitation and mechanical properties of high-strength steels, Acta Mater. 61 (2013) 5996–6005.
[70] H.J. Kong, C. Xu, C.C. Bu, C. Da, J.H. Luan, Z.B. Jiao, G. Chen, C.T. Liu, Hardening mech-anisms and impact toughening of a high-strength steel containing low Ni and Cu ad-ditions, Acta Mater. 172 (2019) 150–160.
[71] K.C. Russell, L.M. Brown, A dispersion strengthening model based on differing elastic moduli applied to the iron-copper system, Acta Metall. 20 (1972) 969–974.
[72]C.R. Hutchinson, M. Gouné, A. Redjaïmia, Selecting non-isothermal heat treatment schedules for precipitation hardening systems: an example of coupled process– property optimization, Acta Mater. 55 (2007) 213–223.
[73] A. Deschamps, M. Militzer, W.J. Poole, Precipitation kinetics and strengthening of a Fe-0.8wt%Cu alloy, ISIJ Int. 41 (2001) 196–205.
[74] S. Lozano-Perez, M.L. Jenkins, J.M. Titchmarsh, Evidence for deformation-induced transformations of Cu-rich precipitates in an aged FeCu alloy, Philos. Mag. Lett. 86 (2006) 367–374.
[75] S. Brinckmann, T. Siegmund, Y. Huang, A dislocation density based strain gradient model, Int. J. Plast. 22 (2006) 1784–1797.
[76] B.B. He, B. Hu, H.W. Yen, G.J. Cheng, Z.K. Wang, H.W. Luo, M.X. Huang, High disloca-tion density–induced large ductility in deformed and partidisloca-tioned steels, Science 357 (2017) 1029–1032.
[77] M. Shamsujjoha, S.R. Agnew, J.M. Fitz-Gerald, W.R. Moore, T.A. Newman, High strength and ductility of additively manufactured 316L stainless steel explained, Metall. Mater. Trans. A 49 (2018) 3011–3027.
[78] S.I. Wright, Review of automated orientation imaging microscopy (OIM), J. Comput.-Assist. Microsc. 5 (1993) 207–221.
