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1 In the format provided by the authors and unedited. Additively-manufactured hierarchical stainless steels with high strength and ductility Y. Morris Wang 1*, Thomas Voisin 1, Joseph T. McKeown 1, Jianchao Ye 1, Nicholas P. Calta 1, Zan Li 1, Zhi Zeng 2, Yin Zhang 2, Wen Chen 1, Tien Tran Roehling 1, Ryan T. Ott 3, Melissa K. Santala 4, Philip J. Depond 1, Manyalibo J. Matthews 1, Alex V. Hamza 1, Ting Zhu 2 1 Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 2 Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA 3 Division of Materials Sciences and Engineering, Ames Laboratory (USDOE), Ames, IA 50011, USA 4 School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97331, USA *ymwang@llnl.gov This Supplementary Information (SI) contains four supplementary tables (Tables S1-S4) and fifteen supplementary figures (Figures S1-S15). NATURE MATERIALS 1

2 Table S1. Processing parameters used in this work to fabricate near fully-dense 316L stainless steel samples. See Table S3 for the detailed laser power and speed for each individual sample. Parameters Concept Fraunhofer Laser spot size (μm) Laser power (W) Scan speed (mm/s) Layer thickness (μm) NATURE MATERIALS 2

3 Table S2. Compositions of 316L stainless steels made by laser powder-bed-fusion (L-PBF), in comparison with the composition of an AISI 316L SS 1. The reported values are averaged from two measurements made by the Concept and Fraunhofer machines, respectively. Fe Cr Ni Mo C Mn P S Si O N H L-PBF 316L SS Bal (Concept) (wt.%) L-PBF 316L SS (Fraunhofer) (wt.%) Bal AISI 316L SS (wt.%) Bal NATURE MATERIALS 3

4 Table S3. A summary of tensile yield strength, uniform elongation, and build parameters for the samples reported in Fig. 2b. Three types of combination were used for the build direction and tensile test direction. 1) Concept horizontal (H): the rectangular plate (40 (L) 20 (W) 2 (T) mm 3 ) was built with the width (W) parallel to the build direction. The tensile tests were performed parallel (P) to the plate length (L) direction. 2) Fraunhofer vertical (V): the square plate (40 (L) 40 (W) 3 (T) mm 3 ) was built with the thickness (T) vertical to the build direction. The tensile tests were conducted along the build direction. 3) Fraunhofer flat (F): the square plate (40 (L) 40 (W) 3 (T) mm 3 ) was built with the thickness parallel to the build direction. The tensile tests were performed vertical to the build direction. Build Machine Sample Yield Strength (MPa) Uniform Elongation (%) Laser Power (W) Laser Speed (mm/s) Hatch Spacing (µm) Build Direction Tensile Test Direction H P H P Concept H P H P H P V P Fraunhofer 2* F V 3* F V *These two samples were tested by using two different gauge length (6.5 mm and 3.5 mm, respectively). A nearly identical uniform elongation was observed. NATURE MATERIALS 4

5 Table S4. Elastic constants of specific reflections (unit: GPa) for austenitic stainless steel 2. E111 E200 E220 E NATURE MATERIALS 5

6 Fig. S1 Synchrotron X-ray diffraction (XRD) patterns of L-PBF 316L stainless steels. The data were collected at APS beamline 11-ID-B, using kev X-rays (λ = Å). Two pillar samples made by the Concept machine were examined. NATURE MATERIALS 6

7 Fig. S2 Grain area distribution measured from the EBSD image shown in Fig. 1b. NATURE MATERIALS 7

8 Fig. S3. Compositional analysis (in wt.%) of precipitates observed in an L-PBF 316L SS made by the Concept machine. a. A STEM image of three selected particles, marked with 1-3. Location 4 is for the matrix as a reference. b. Corresponding energy dispersive spectra (EDS) for three particles and the matrix. c. Quantitative composition information indicates that these particles are rich in Si, O, and Mn. However, Mn and Cr content varies from particle to particle. NATURE MATERIALS 8

9 Fig. S4 Compositional analysis (in wt.%) of cell walls and cell interior for an L-PBF 316L SS made by the Fraunhofer machine. a. A bright-field TEM image of cells. b. A high-angle annular dark field (HAADF) image of a selected region with corresponding Ni, Fe, Si, Mn, Mo, Cr, O elemental maps. c. Detailed compositions of the regions along the cell interiors and cell walls, respectively. There is little evidence of elemental segregation. NATURE MATERIALS 9

10 Fig. S5 Normalised processing diagram for L-PBF 316L SS reported in this work. Contours of normalized equivalent energy density, EE 0, are delineated as dashed lines. The processing windows for the Concept and Fraunhofer machines are highlighted inside two separate dashed circles. Some characteristic microstructure length scale (e.g., cell size) and the range of mechanical properties (namely, yield strength (YS) and uniform elongation (UE)) obtainable from two L-PBF machines are summarized. As discussed in ref. 3, note that the same EE 0 value does not warrant the same microstructure and subsequent properties. NATURE MATERIALS 10

11 Fig. S6 The Kocks-Mecking strain hardening plot for L-PBF 316L SS reported in Fig. 2a, in comparison with those of as-cast and as-wrought 316L SS. The normalized work hardening rate is defined as θθ = 1 σσ ( ) TT, where σ and ɛ are true stress and true strain, respectively, and T the temperature. NATURE MATERIALS 11

12 Fig. S7 The Hall-Petch fitting plot obtained from the literature data 4,5. Note that only 316L stainless steels with the austenitic phase are included. NATURE MATERIALS 12

13 Fig. S8 Microstructure of a Fraunhofer L-PBF 316L SS sample (blue curve in Fig. 2a). a. An EBSD image acquired with a 2-µm step size. b. Grain size distribution based on a. c. A brightfield TEM image of the as-built microstructure, showing a mixture of large and small grains, as well as cellular structures and dislocations. d. A HAADF image of the same region in c, highlighting HAGBs and solidification cells. NATURE MATERIALS 13

14 Fig. S9 Focused-ion-beam cross-sectional view of oxides in an L-PBF 316L SS (Concept sample). Some particles are highlighted by red solid circles with the corresponding diameters labelled. NATURE MATERIALS 14

15 Fig. S10 A 2D X-ray diffraction pattern acquired for an L-PBF 316L SS before deformation, collected at APS beamline 6-ID-D. The beam size is 1 mm (width) 0.2 mm (height), and the sample thickness is 0.5 mm. Peaks for which complete rings were collected are labelled with Miller index, and the tensile load direction is labelled as LD. Q is the scattering vector, and the azimuthal angle. NATURE MATERIALS 15

16 Fig. S11 A magnified plot of the second unloading-reloading segment shown in Fig. 3a. σf is the flow stress, σ * the thermal component of the flow stress, and σr the reverse yield stress. The back stress at ~3.3% strain is estimated to be ~300 MPa, based on the method reported in reference 6. NATURE MATERIALS 16

17 Fig. S12 Elastic lattice strain (ɛ hkl ) as a function of true stress along the transverse direction. a. The ɛ hkl in the initial loading period, with the 0.2% offset yield strength (σ0.2%) marked as a dashed line. b. The ɛ hkl evolution during the second reloading (R2). All reflections show nearly linear compressive response of lattice strain with applied stress, until the flow stress reached a value of ~ 650 MPa, where strong deviations from linear elasticity occurred. NATURE MATERIALS 17

18 Fig. S13 Full-Width at Half-Maximum (FWHM) of the scattering vector of (400) plane as a function of true strain in the second reloading up to 6% strain. See Fig. 3 for the details. NATURE MATERIALS 18

19 Fig. S14 I Deformation microstructure of an L-PBF 316L SS after ~36% uniform tensile strain. a. Deformation twins and cellular structures. The orientations of cellular walls and twin boundaries are marked with white and dark dashed lines, respectively. b. A magnified image of a, showing the intersections of high density deformation twins with cellular walls. NATURE MATERIALS 19

20 a b 0.12 z Volume fraction x y Grain volume ( m 3 ) c d 1200 True stress (MPa) True strain Fig. S15 I Microstructure sensitive finite element simulations of uniaxial compression of L- PBF SS produced by the Concept machine. a. A polycrystal model with a wide distribution of grain sizes. Grain colour represents grain orientation, randomly assigned. b. The grain volume/size distribution (symbols) in the polycrystal model shown in a matches the experimental measurement (solid line). c. Comparison of the stress-strain curves from experiment (black curve), a model with an effective strength-controlling length of L (red curve), a model with a wide distribution of grain sizes (green curve), and a mixture model containing 60% volume fraction of sub-grain cellular structures (blue curve). d. A mixture model containing the grains without cellular structures (coloured in green) and grains with cellular structures (coloured in red), the latter of which occupy ~60% volume fraction of the sample. The effect of tension-compression asymmetry is not considered in the model. NATURE MATERIALS 20

21 References for SI 1 Yan, F. K., Liu, G. Z., Tao, N. R. & Lu, K. Strength and ductility of 316L austenitic stainless steel strengthened by nano-scale twin bundles. Acta Mater. 60, , doi: /j.actamat (2012). 2 Clausen, B., Lorentzen, T. & Leffers, T. Self-consistent modelling of the plastic deformation of FCC polycrystals and its implications for diffraction measurements of internal stresses. Acta Mater. 46, , doi: /s (98) (1998). 3 Thomas, M., Baxter, G. J. & Todd, I. Normalised model-based processing diagrams for additive layer manufacture of engineering alloys. Acta Mater. 108, 26-35, doi: /j.actamat (2016). 4 Chen, X. H., Lu, J., Lu, L. & Lu, K. Tensile properties of a nanocrystalline 316L austenitic stainless steel. Scr. Mater. 52, , doi: /j.scriptamat (2005). 5 Kashyap, B. P. & Tangri, K. On the Hall-Petch relationship and substructural evolution in type 316L stainless-steel. Acta Metall. Mater. 43, , doi: / (95)00110-h (1995). 6 Wu, X. L. et al. Heterogeneous lamella structure unites ultrafine-grain strength with coarse-grain ductility. Proc. Natl. Acad. Sci. U. S. A. 112, , doi: /pnas (2015). NATURE MATERIALS 21