Abstract
This paper presents a numerical model for the simulation of resistance sintering. It involves an electro-thermo-mechanical coupling, where each model is simulated as a continuum with the influence of porosities included through the distribution of relative density, i.e., the ratio of the apparent density to that of the corresponding fully dense bulk material. For the mechanical response, this involves a plasticity model based on a porous formulation. Other material data have to be supplied as a function of relative density and temperature, as, for example, the electrical resistivity. The numerical modeling is compared to experimentally resistance sintered titanium with good agreement in terms of pre-compaction and developed relative density and temperature during the sintering process.
References
1.
Castro
, R. H. R.
, 2013
, “Overview of Conventional Sintering,” Sintering
, R. H. R.
Castro
, and K.
van Benthem
, eds., Springer
, New York
, pp. 1
–16
.2.
Olevsky
, E. A.
, and Dudina
, D. V.
, 2018
, Resistance Sintering
, Springer International Publishing
, Cham
.3.
Lagos
, M. A.
, Agote
, I.
, Schubert
, T.
, Weissgaerber
, T.
, Gallardo
, J. M.
, Montes
, J. M.
, Prakash
, L.
, Andreouli
, C.
, Oikonomou
, V.
, Lopez
, D.
, and Calero
, J. A.
, 2017
, “Development of Electric Resistance Sintering Process for the Fabrication of Hard Metals: Processing, Microstructure and Mechanical Properties
,” Int. J. Refract. Met. Hard Mater.
, 66
, pp. 88
–94
. 4.
Yang
, Y. F.
, and Qian
, M.
, 2015
, Spark Plasma Sintering and Hot Pressing of Titanium and Titanium Alloys
, Elsevier Inc.
, Cambridge, MA
.5.
Cuevas
, F. G.
, Andreouli
, D.
, Gallardo
, J. M.
, Oikonomou
, V.
, Cintas
, J.
, Torres
, Y.
, and Montes
, J. M.
, 2019
, “Ceramic Dies Selection for Electrical Resistance Sintering of Metallic Materials
,” Ceram. Int.
, 45
(12
), pp. 14555
–14561
. 6.
Forno
, I.
, Actis Grande
, M.
, and Fais
, A.
, 2015
, “On the Application of Electro-Sinter-Forging to the Sintering of High-Karatage Gold Powders
,” Gold Bull.
, 48
(3–4
), pp. 127
–133
. 7.
Fais
, A.
, Leoni
, M.
, and Scardi
, P.
, 2012
, “Fast Sintering of Nanocrystalline Copper
,” Metall. Mater. Trans. A
, 43
(5
), pp. 1517
–1521
. 8.
Cuevas
, F.
, Gallardo
, J.
, Torres
, Y.
, Astacio
, R.
, Weissgaerber
, T.
, Lagos
, M.
, Montes
, J.
, and Cintas
, J.
, 2019
, “Production of Ultrafine Grained Hardmetals by Electrical Resistance Sintering
,” Metals
, 9
(2
), p. 159
. 9.
Lagos
, M. A.
, Agote
, I.
, Leizaola
, I.
, Lopez
, D.
, and Calero
, J. A.
, 2020
, “Fabrication of Chromium Carbide Cermets by Electric Resistance Sintering Process: Processing, Microstructure and Mechanical Properties
,” Int. J. Refract. Met. Hard Mater.
, 95
, pp. 1
–8
. 10.
Montes
, J. M.
, Rodríguez
, J. A.
, Cuevas
, F. G.
, and Cintas
, J.
, 2011
, “Consolidation by Electrical Resistance Sintering of Ti Powder
,” J. Mater. Sci.
, 46
(15
), pp. 5197
–5207
. 11.
Cannella
, E.
, Nielsen
, C. V.
, and Bay
, N.
, 2019
, “Process Investigation and Mechanical Properties of Electro Sinter Forged (ESF) Titanium Discs
,” Int. J. Adv. Manuf. Technol.
, 104
(5–8
), pp. 1985
–1998
. 12.
Leich
, L.
, Röttger
, A.
, Theisen
, W.
, and Krengel
, M.
, 2018
, “Densification of Nanocrystalline NdFeB Magnets Processed by Electro-Discharge Sintering—Microstructure, Magnetic, and Mechanical Properties
,” J. Magn. Magn. Mater.
, 460
, pp. 454
–460
. 13.
Cannella
, E.
, Nielsen
, C. V.
, and Bay
, N.
, 2020
, “Resistance Sintering of NdFeBCo Permanent Magnets and Analysis of Their Properties
,” CIRP J. Manuf. Sci. Technol.
, 29
(Part A
), pp. 88
–98
. 14.
Di Napoli
, P.
, Cagliero
, R.
, and Maizza
, G.
, 2015
, “Micro-Macro Analysis of Capacitor Discharge Sintering in Copper-Diamond Bead
,” J. Am. Ceram. Soc.
, 98
(11
), pp. 3538
–3546
. 15.
Maizza
, G.
, and Tassinari
, A.
, 2009
, “Modelling of Micro/Macro Densification Phenomena of Cu Powder During Capacitor Discharge Sintering
,” COMSOL Conference
, Milan, Italy
, Oct. 14–16
, pp. 1
–7
.16.
McWilliams
, B.
, Zavaliangos
, A.
, Cho
, K. C.
, and Dowding
, R. J.
, 2006
, “The Modeling of Electric-Current-Assisted Sintering to Produce Bulk Nanocrystalline Tungsten
,” JOM
, 58
(4
), pp. 67
–71
. 17.
Zhang
, Y.
, Wu
, L.
, Guo
, X.
, Jung
, Y. G.
, and Zhang
, J.
, 2016
, “Molecular Dynamics Simulation of Electrical Resistivity in Sintering Process of Nanoparticle Silver Inks
,” Comput. Mater. Sci.
, 125
, pp. 105
–109
. 18.
Wei
, X.
, Giuntini
, D.
, Maximenko
, A. L.
, Haines
, C. D.
, and Olevsky
, E. A.
, 2015
, “Experimental Investigation of Electric Contact Resistance in Spark Plasma Sintering Tooling Setup
,” J. Am. Ceram. Soc.
, 98
(11
), pp. 3553
–3560
. 19.
Tiwari
, D.
, Basu
, B.
, and Biswas
, K.
, 2009
, “Simulation of Thermal and Electric Field Evolution During Spark Plasma Sintering
,” Ceram. Int.
, 35
(2
), pp. 699
–708
. 20.
Braginsky
, M.
, Tikare
, V.
, and Olevsky
, E.
, 2005
, “Numerical Simulation of Solid State Sintering
,” Int. J. Solids Struct.
, 42
(2
), pp. 621
–636
.21.
Garcia
, C.
, and Olevsky
, E.
, 2010
, “Numerical Simulation of Spark Plasma Sintering
,” Adv. Sci. Technol.
, 63
, pp. 58
–61
. 22.
Allen
, J. B.
, and Walter
, C.
, 2012
, “Numerical Simulation of the Temperature and Stress Field Evolution Applied to the Field Assisted Sintering Technique
,” ISRN Mater. Sci.
, 2012
, pp. 1
–9
. 23.
Nielsen
, C. V.
, Zhang
, W.
, Perret
, W.
, Martins
, P. A. F.
, and Bay
, N.
, 2015
, “Three-Dimensional Simulations of Resistance Spot Welding
,” Proc. Inst. Mech. Eng. Part D.
, 229
(7
), pp. 885
–897
.24.
Nielsen
, C. V.
, Zhang
, W.
, Martins
, P. A. F.
, and Bay
, N.
, 2015
, “3D Numerical Simulation of Projection Welding of Square Nuts to Sheets
,” J. Mater. Process. Technol.
, 215
, pp. 171
–180
. 25.
Nielsen
, C. V.
, Zhang
, W.
, Alves
, L. M.
, Bay
, N.
, and Martins
, P. A. F.
, 2013
, “Coupled Finite Element Flow Formulation,” Modelling of Thermo-Electro-Mechanical Manufacturing Processes With Applications in Metal Forming and Resistance Welding
, J. P.
Davim
, ed., Springer-Verlag
, London
, pp. 11
–36
.26.
Cannella
, E.
, Nielsen
, C. V.
, and Bay
, N.
, 2019
, “On the Process and Product Fingerprints for Electro Sinter Forging (ESF)
,” Micromachines
, 10
(4
), p. 218
. 27.
GoodFellow
, 2017
, “Titanium Powder (Ti)-Material Information
,” http://www.goodfellow.com/E/Titanium-Powder.html, Accessed March 20, 2017.28.
Ness Engineering
, 2020
, “Technical Data
,” http://www.nessengr.com/techdata/metalresis.html, Accessed October 22, 2020.29.
MatWeb
, 2017
, “Material Property Data—Titanium Grade 2
,” http://www.matweb.com/search/datasheet.aspx?MatGUID=24293fd5831941ec9fa01dce994973c7, Accessed October 22, 2017.30.
Montes
, J. M.
, Cuevas
, F. G.
, and Cintas
, J.
, 2007
, “Electrical Resistivity of Metal Powder Aggregates
,” Metall. Mater. Trans. B
, 38
(6
), pp. 957
–964
. 31.
Montes
, J.
, Cuevas
, F.
, Ternero
, F.
, Astacio
, R.
, Caballero
, E.
, and Cintas
, J.
, 2017
, “A Method to Determine the Electrical Resistance of a Metallic Powder Mass Under Compression
,” Metals
, 7
(12
), p. 479
. 32.
Montes
, J. M.
, Cuevas
, F. G.
, and Cintas
, J.
, 2011
, “Electrical Resistivity of a Titanium Powder Mass
,” Granular Matter
, 13
(4
), pp. 439
–446
. 33.
Weiner
, L.
, Chiotti
, P.
, and Wilhelm
, H. A.
, 1952
, “Temperature Dependence of Electrical Resistivity of Metals
,” Ames Lab. ISC Tech. Reports, Ames Lab., 12.5
.34.
Shima
, S.
, and Oyane
, M.
, 1976
, “Plasticity Theory for Porous Metals
,” Int. J. Mech. Sci.
, 18
(6
), pp. 285
–291
. 35.
Marques
, M. J. M. B.
, and Martins
, P. A. F.
, 1991
, “A General Three-Dimensional Finite Element Approach for Porous and Dense Metal-Forming Processes
,” Proc. Inst. Mech. Eng. Part B
, 205
(4
), pp. 257
–263
. 36.
Alves
, L. M. M.
, Martins
, P. A. F.
, and Rodrigues
, J. M. C.
, 2006
, “A New Yield Function for Porous Materials
,” J. Mater. Process. Technol.
, 179
(1–3
), pp. 36
–43
. 37.
Montes
, J. M.
, Cuevas
, F. G.
, Cintas
, J.
, and Urban
, P.
, 2014
, “A One-Dimensional Model of the Electrical Resistance Sintering Process
,” Metall. Mater. Trans. A
, 46
(2
), pp. 963
–980
. Copyright © 2021 by ASME
You do not currently have access to this content.
