Hall-Petch relationship in selective laser melting additively manufactured metals: using grain or cell size?

Abstract

The mechanical properties of many materials prepared by additive manufacturing technology have been greatly improved. High strength is attributed to grain refinement, formation of high density dislocation and existence of cellular structures with nanoscale during manufacturing. In addition, the super-saturated solid solution of elements in the matrix and the solid solution segregation along the wall of the cellular structures also promote the improvement of strength by enhancing dislocation pinning. Hence, the existence of cellular structure in grains leads to differences in the prediction of material strength by Hall-Petch relationship, and there is no unified calculation method to determine the d value as grain size or cell size. In this work, representative materials including austenite 316L SS were printed by selective laser melting (SLM), and the strength was predicted. The values of cell size and grain size were substituted into Hall-Petch formula, and the results showed that the calculation error for 316L is increased from 4.1% to 11.9%. Therefore, it is concluded that the strength predicted by grain size is more accurate than that predicted by cell size in additive manufacturing materials. When calculating the yield strength of laser additive manufacturing metal materials through the Hall-Petch formula, the grain size should be used as the basis for calculation.

Keywords

additive manufacturing / Hall-Petch relationship / grains / cellular structures / mechanical property

References

[1] Al-MangourB, MongrainR, IrissouE, YueS. Improving the strength and corrosion resistance of 316L stainless steel for biomedical applications using cold spray [J]. Surface and Coatings Technology, 2013, 216: 297-307

[2] AhmadiA, MirzaeifarR, MoghaddamN S, TurabiA S, KaracaH, ElahiniaM. Effect of manufacturing parameters on mechanical properties of 316L stainless steel parts fabricated by selective laser melting: A computational framework [J]. Materials and Design, 2016, 112: 328-338

[3] ZhongY, RännarL E, LiuL-f, KoptyugA, WikmanS, OlsenJ, CuiD-q, ShenZ-jian. Additive manufacturing of 316L stainless steel by electron beam melting for nuclear fusion applications [J]. Journal of Nuclear Materials, 2017, 486: 234-245

[4] AlmangourB, KimY K, GrzesiakD. Novel TiB2-reinforced 316L stainless steel nanocomposites with excellent room- and high-temperature yield strength developed by selective laser melting [J]. Composites Part B: Engineering, 2019, 156(1): 51-63

[5] JohnsonL, MahmoudiM, ZhangB, SeedeR, HuangX-q, MaierJ T, MaierH J, KaramanI, ElwanyA. Assessing printability maps in additive manufacturing of metal alloys [J]. Scripta Materialia, 2019, 176(1): 199-210

[6] SongB, ZhaoX, LiS, HanC, WeiQ-s, WenS-f, LiuJ, ShiY-sheng. Differences in microstructure and properties between selective laser melting and traditional manufacturing for fabrication of metal parts: A review [J]. Frontiers of Mechanical Engineering, 2015, 10(2): 111-125

[7] ZinovievaO, ZinovievA, PloshikhinV. Three-dimensional modeling of the microstructure evolution during metal additive manufacturing [J]. Computational Materials Science, 2018, 141: 207-220

[8] LinK-J, GuD-d, XiL-x, YuanL-h, NiuS-q, LvP, GeQ. Selective laser melting processing of 316L stainless steel: Effect of microstructural differences along building direction on corrosion behavior [J]. International Journal of Advanced Manufacturing The Technology, 2019, 104(5–8): 2669-2679

[9] LiR-d, NiuP-d, YuanT-c, CaoP, ChenC, ZhouK-chao. Selective laser melting of an equiatomic CoCrFeMnNi high-entropy alloy: Processability, non-equilibrium microstructure and mechanical property [J]. Journal of Alloys and Compounds, 2018, 746: 125-134

[10] MurrL E, GaytanS M, RamirezD A, MartinezE, HernandezJ, AmatoK N, ShindoP W, MedinaF R, WickerR B. Wicker. Metal fabrication by additive manufacturing using laser and electron beam melting technologies [J]. Journal of Materials Science & Technology, 2012, 28(1): 1-14

[11] LiR-d, WangM-b, LiZ-m, CaoP, YuanT-c, ZhuH-bin. Developing a high-strength Al-Mg-Si-Sc-Zr alloy for selective laser melting: Crack-inhibiting and multiple strengthening mechanisms [J]. Acta Materialia, 2020, 193: 83-98

[12] JeonJ M, ParkJ M, YuJ-h, KimJ G, SeongY, ParkS H, KimH S. Effects of microstructure and internal defects on mechanical anisotropy and asymmetry of selective laser-melted 316L austenitic stainless steel [J]. Materials Science and Engineering A, 2019, 763: 138152

[13] ZhangZ-y, ChuB-b, WangL, LuZ-hua. Comprehensive effects of placement orientation and scanning angle on mechanical properties and behavior of 316L stainless steel based on the selective laser melting process [J]. Journal of Alloys and Compounds, 2019, 791166-175

[14] ZhuZ G, NguyenQ B, NgF L, AnX H, LiaoX Z, LiawP K, NaiS M L, WeiJ. Hierarchical microstructure and strengthening mechanisms of a CoCrFeNiMn high entropy alloy additively manufactured by selective laser melting [J]. Scripta Materialia, 2018, 154(9): 20-24

[15] WangY M, VoisinT, MckeownJ T, YeJ, CaltaN P, LiZ, ZengZ, ZhangY, ChenW. Additively manufactured hierarchical stainless steels with high strength and ductility [J]. Nature Materials, 2018, 17(1): 67-71

[16] BahlS, MishraS, YazarK U, KolaI R, ChatterjeeK, SuwasS. Non-equilibrium microstructure, crystallographic texture and morphological texture synergistically result in unusual mechanical properties of 3D printed 316L stainless steel [J]. Additive Manufacturing, 2019, 28: 65-77

[17] LiJ C M, ChouY T. The role of dislocations in the flow stress grain size relationships [J]. Metallurgical & Materials Transactions B, 1970, 1(5): 1145-1159

[18] ChiaK H, JungK, ConradH. Dislocation density model for the effect of grain size on the flow stress of a Ti-15.2 at.% Mo β-alloy at 4.2–650 K [J]. Materials Science and Engineering A, 2005, 409(12): 32-38

[19] KubinL P, MortensenA. Geometrically necessary dislocations and strain-gradient plasticity: A few critical issues [J]. Scripta Materialia, 2003, 48(2): 119-125

[20] KashyapB P, TangriK. On the Hall-Petch relationship and substructural evolution in type 316L stainless steel [J]. Acta Metallurgica et Materialia, 1995, 43(11): 3971-3981

[21] XiL X, ZhangH, WangP, LiH C, PrashanthK G, LinK J, KabanI, GuD D. Comparative investigation of microstructure, mechanical properties and strengthening mechanisms of Al-12Si/TiB₂, fabricated by selective laser melting and hot pressing [J]. Ceramics International, 2018, 44(15): 17635-17642

[22] JiaQ-b, RometschP, KürnsteinerP, ChaoQ, HuangA-j, WeylandM, BourgeoisL, WuX-hua. Selective laser melting of a high strength AlMnSc alloy: Alloy design and strengthening mechanisms [J]. Acta Materialia, 2019, 171: 108-118

[23] PengP, WangK-s, WangW, HanP, ZhangT, LiuQ, ZhangS-y, WangH-d, QiaoK. Relationship between microstructure and mechanical properties of friction stir processed AISI 316L steel produced by selective laser melting [J]. Materials Characterization, 2020, 163: 110283

[24] BirnbaumA J, SteubenJ C, BarrickE J, IliopoulosA P, MichopoulosJ G. Intrinsic strain aging, Σ3 boundaries, and origins of cellular substructure in additively manufactured 316L [J]. Additive Manufacturing, 2019, 29100784

[25] NiuP D, LiR D, YuanT C, ZhuS Y, ChenC, WangM B, HuangL. Microstructures and properties of an equimolar AlCoCrFeNi high entropy alloy printed by selective laser melting [J]. Intermetallics, 2019, 10424-32

[26] HuangJ, YanX-c, ChangC, XieY-c, MaW-y, HuangR-z, ZhaoR-m, LiS-h, LiuM, LiaoH-lin. Pure copper components fabricated by cold spray (CS) and selective laser melting (SLM) technology [J]. Surface and Coatings Technology, 2020, 395: 125936

[27] Kuhlmann-WilsdorfD, CominsN. Dislocation cell formation and work hardening in the unidirectional glide of f.c.c. metals I: Basic theoretical analysis of cell walls parallel to the primary glide plane in early stage II [J]. Mater Sci Eng, 1983, 607-24

[28] Galindo-NavaE I, Rivera-Díaz-Del-CastilloP E J. A thermodynamic theory for dislocation cell formation and misorientation in metals [J]. Acta Materialia, 2012, 60(11): 4370-4378

[29] MughrabiH. Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals [J]. Acta Metellurgica, 1983, 31(9): 1367-1379

[30] RamirezD A, MurrL E, MartinezE, HernandezD H, MartinezJ L, MachadoB I, MedinaF, FrigolaP, WickerR B. Novel precipitate-microstructural architecture developed in the fabrication of solid copper components by additive manufacturing using electron beam melting [J]. Acta Materialia, 2011, 59(10): 4088-4099

[31] ASMASM metals reference book [M], 1984, Materials Park, OH, ASM International

[32] ShanmugasundaramT, HeilmaierM, MurtyB S, SarmaV S. On the Hall-Petch relationship in a nanostructured Al-Cu alloy [J]. Materials Science and Engineering A, 2010, 527(2930): 7821-7825

[33] YanQ, SongB, ShiY-sheng. Comparative study of performance comparison of AlSi₁₀Mg alloy prepared by selective laser melting and casting [J]. Journal of Materials Science and Technology, 2020, 41: 199-208

[34] FiteJ, EswarappaP S, SlotwinskiJ A, WeihsT P. Evolution of the microstructure and mechanical properties of additively manufactured AlSi₁₀Mg during room temperature holds and low temperature aging [J]. Additive Manufacturing, 2020, 36: 101429

[35] AlghamdiF, SongX, HadadzadehA, Shalchi-AmirkhizB, MohammadiM, HaghshenasM. Post heat treatment of additive manufactured AlSi₁₀Mg: On silicon morphology, texture and small-scale properties [J]. Materials Science and Engineering A, 2020, 783139296

[36] KempfA, HilgenbergK. Influence of sub-cell structure on the mechanical properties of AlSi₁₀Mg manufactured by laser powder bed fusion [J]. Materials Science and Engineering A, 2020, 776138976

[37] AboulkhairN T, MaskeryI, TuckC, AshcroftI, EverittN M. The microstructure and mechanical properties of selectively laser melted AlSi₁₀Mg: The effect of a conventional T6-like heat treatment [J]. Materials Science and Engineering A, 2016, 667139-146

[38] AboulkhairN T, TuckC, AshcroftI, MaskeryI, EverittN M. On the precipitation hardening of selective laser melted AlSi₁₀Mg [J]. Metallurgical and Materials Transactions A, 2015, 46(8): 3337-3341

[39] ZhouL, MehtaA, SchulzE, McwilliamsB, ChoK, SohnY. Microstructure, precipitates and hardness of selectively laser melted AlSi₁₀Mg alloy before and after heat treatment [J]. Materials Characterization, 2018, 143: 5-17

[40] Gutierrez-UrrutiaI, Muñoz-MorrisM A, MorrisD G. Contribution of microstructural parameters to strengthening inan ultrafine-grained Al-7% Si alloy processed by severe deformation [J]. Acta Materialia, 2007, 55(4): 1319-1330

[41] DixitM, MishraR S, SankaranK K. Structure-property correlations in Al 7050 and Al 7055 high-strength aluminum alloys [J]. Materials Science and Engineering A, 2008, 478(12): 163-172

[42] LiX P, JiG, ChenZ, AddadA, WuY, WangH W, VleugelsJ, VanH J, KruthJ P. Selective laser melting of nano-TiB2 decorated AlSi₁₀Mg alloy with high fracture strength and ductility [J]. Acta Materialia, 2017, 129: 183-193

[43] ChenB, MoonS K, YaoX, BiG, ShenJ, UmedaJ, KondohK. Strength and strain hardening of a selective laser melted AlSi₁₀Mg alloy [J]. Scripta Materialia, 2017, 141: 45-49

[44] ZouZ-x, XiangJ-z, XuS-yong. Theoretical derivation of Hall-Petch relationship and discussion of its applicable range [J]. Physics Examination and Testing, 2012, 6(30): 13-17(in Chinese)

[45] ValievR Z, EnikeevN A, MurashkinM Y, AleksandrovS E, GoldshteinR V. Superstrength of ultrafine-grained aluminum alloys produced by severe plastic deformation [J]. Doklady Physics, 2010, 55(6): 267-270

[46] GodonA, CreusJ, CohendozS, ConfortoE, FeaugasX, GiraultP, SavallC. Effects of grain orientation on the Hall-Petch relationship in electrodeposited nickel with nanocrystalline grains [J]. Scripta Materialia, 2010, 62(6): 403-406

[47] JinZ-z, ZhaM, YuZ-y, MaP-k, LiY-k, LiuJ-m, JiaH-l, WangH-yuan. Exploring the Hall-Petch relation and strengthening mechanism of bimodal-grained Mg-Al-Zn alloys [J]. Journal of Alloys and Compounds, 2020, 833155004

[48] HyerH, ZhouL, BensonG, McwilliamsB, ChoK, SohnY. Additive manufacturing of dense WE43 Mg alloy by laser powder bed fusion [J]. Additive Manufacturing, 2020, 33101123

[49] BenmessaoudF, CheikhM, VelayV, VidalV, MatsumotoH. Role of grain size and crystallographic texture on tensile behavior induced by sliding mechanism in Ti-6Al-4V alloy [J]. Materials Science and Engineering A, 2020, 774138835

[50] XieZ-y, DaiY, OuX-q, NiS, SongM. Effects of selective laser melting build orientations on the microstructure and tensile performance of Ti-6Al-4V alloy [J]. Materials Science and Engineering A, 2020, 776139001