Abstract
This paper presents predictions of the mechanical response of sintered FGH96 Ni-based superalloy powder compacts at high temperatures, obtained by the analysis of 3D representative volume elements generated by both X-ray tomography and a virtual technique. The response of the material to a multi-axial state of stress/strain for porosities as large as 0.3 is explored, obtaining the yield surfaces and their evolution as well as scaling laws for both elastic and plastic properties. The two modeling approaches are found in good agreement. The sensitivity of the predictions to particle size, inter-particle friction, applied strain rate, and boundary conditions is also examined.
Issue Section:
Research Papers
References
1.
Fedotov
, A.
, 2017
, “Analysis of the Adequacy and Selection of Phenomenological Models of the Elastic Properties of Porous Powder Materials
,” J. Mater. Sci.
, 52
(5
), pp. 2964
–2973
. 10.1007/s10853-016-0593-12.
Pabst
, W.
, and Gregorová
, E.
, 2015
, “Critical Assessment 18: Elastic and Thermal Properties of Porous Materials–Rigorous Bounds and Cross-Property Relations
,” Mater. Sci. Technol.
, 31
(15
), pp. 1801
–1808
. 10.1080/02670836.2015.11146973.
Pabst
, W.
, and Gregorová
, E.
, 2014
, “Young’s Modulus of Isotropic Porous Materials With Spheroidal Pores
,” J. Eur. Ceram. Soc.
, 34
(13
), pp. 3195
–3207
. 10.1016/j.jeurceramsoc.2014.04.0094.
Bruck
, H. A.
, Shabana
, Y. M.
, Xu
, B.
, and Laskis
, J.
, 2007
, “Evolution of Elastic Mechanical Properties During Pressureless Sintering of Powder-Processed Metals and Ceramics
,” J. Mater. Sci.
, 42
(18
), pp. 7708
–7715
. 10.1007/s10853-007-1675-x5.
Gregorová
, E.
, Pabst
, W.
, Nečina
, V.
, Uhlířová
, T.
, and Diblíková
, P.
, 2019
, “Young’s Modulus Evolution During Heating, Re-Sintering and Cooling of Partially Sintered Alumina Ceramics
,” J. Eur. Ceram. Soc.
, 39
(5
), pp. 1893
–1899
. 10.1016/j.jeurceramsoc.2019.01.0056.
Lambrinou
, K.
, Lauwagie
, T.
, Chalvet
, F.
, De Portu
, G.
, Tassini
, N.
, Patsias
, S.
, Lube
, T.
, and Van der Biest
, O.
, 2007
, “Elastic Properties and Damping Behaviour of Alumina–Alumina/Zirconia Laminates
,” J. Eur. Ceram. Soc.
, 27
(2–3
), pp. 1307
–1311
. 10.1016/j.jeurceramsoc.2006.04.1247.
Pabst
, W.
, Gregorová
, E.
, and Černý
, M.
, 2013
, “Isothermal and Adiabatic Young’s Moduli of Alumina and Zirconia Ceramics at Elevated Temperatures
,” J. Eur. Ceram. Soc.
, 33
(15–16
), pp. 3085
–3093
. 10.1016/j.jeurceramsoc.2013.06.0128.
Choren
, J. A.
, Heinrich
, S. M.
, and Silver-Thorn
, M. B.
, 2013
, “Young’s Modulus and Volume Porosity Relationships for Additive Manufacturing Applications
,” J. Mater. Sci.
, 48
(15
), pp. 5103
–5112
. 10.1007/s10853-013-7237-59.
Hentschel
, M.
, and Page
, N.
, 2006
, “Elastic Properties of Powders During Compaction. Part 3: Evaluation of Models
,” J. Mater. Sci.
, 41
(23
), pp. 7902
–7925
. 10.1007/s10853-006-0875-010.
Elruby
, A.
, and Nakhla
, S.
, 2019
, “Extending the Ramberg–Osgood Relationship to Account for Metal Porosity
,” Metall. Mater. Trans. A
, 50
(7
), pp. 3121
–3131
. 10.1007/s11661-019-05236-711.
Siegkas
, P.
, Petrinic
, N.
, and Tagarielli
, V.
, 2016
, “Measurements and Micro-Mechanical Modelling of the Response of Sintered Titanium Foams
,” J. Mech. Behav. Biomed. Mater.
, 57
, pp. 365
–375
. 10.1016/j.jmbbm.2016.02.02412.
Zacharopoulos
, P.
, and Tagarielli
, V. L.
, 2017
, “Numerical Modelling of the Mechanical Response of Cellular Solids Made From Sintered Titanium Powders
,” Int. J. Solids Struct.
, 113–114
, pp. 241
–254
. 10.1016/j.ijsolstr.2017.03.00413.
Muñoz
, S.
, Castillo
, S.
, and Torres
, Y.
, 2018
, “Different Models for Simulation of Mechanical Behaviour of Porous Materials
,” J. Mech. Behav. Biomed. Mater.
, 80
, pp. 88
–96
. 10.1016/j.jmbbm.2018.01.02614.
Pabst
, W.
, Uhlířová
, T.
, and Gregorová
, E.
, 2018
, “Shear and Bulk Moduli of Isotropic Porous and Cellular Alumina Ceramics Predicted From Thermal Conductivity Via Cross-Property Relations
,” Ceram. Int.
, 44
(7
), pp. 8100
–8108
. 10.1016/j.ceramint.2018.01.25415.
Zhu
, W.
, Blal
, N.
, Cunsolo
, S.
, and Baillis
, D.
, 2017
, “Micromechanical Modeling of Effective Elastic Properties of Open-Cell Foam
,” Int. J. Solids Struct.
, 115
, pp. 61
–72
. 10.1016/j.ijsolstr.2017.02.03116.
Uhlířová
, T.
, and Pabst
, W.
, 2019
, “Conductivity and Young’s Modulus of Porous Metamaterials Based on Gibson-Ashby Cells
,” Scr. Mater.
, 159
, pp. 1
–4
. 10.1016/j.scriptamat.2018.09.00517.
Schiffer
, A.
, Zacharopoulos
, P.
, Foo
, D.
, and Tagarielli
, V. L.
, 2019
, “A Coarse Model for the Multiaxial Elastic-Plastic Response of Ductile Porous Materials
,” J. Appl. Mech.
, 86
(8
), p. 081002
. 10.1115/1.404343918.
Madej
, L.
, 2017
, “Digital/Virtual Microstructures in Application to Metals Engineering—A Review
,” Arch. Civ. Mech. Eng.
, 17
(4
), pp. 839
–854
. 10.1016/j.acme.2017.03.00219.
Doroszko
, M.
, and Seweryn
, A.
, 2017
, “A New Numerical Modelling Method for Deformation Behaviour of Metallic Porous Materials Using X-Ray Computed Microtomography
,” Mater. Sci. Eng. A
, 689
, pp. 142
–156
. 10.1016/j.msea.2017.02.05520.
Doroszko
, M.
, and Seweryn
, A.
, 2015
, “Numerical Modeling of the Tensile Deformation Process of Sintered 316L Based on Microtomography of Porous Mesostructures
,” Mater. Des.
, 88
, pp. 493
–504
. 10.1016/j.matdes.2015.09.00621.
Singh
, R.
, Lee
, P.
, Lindley
, T.
, Kohlhauser
, C.
, Hellmich
, C.
, Bram
, M.
, Imwinkelried
, T.
, and Dashwood
, R.
, 2010
, “Characterization of the Deformation Behavior of Intermediate Porosity Interconnected Ti Foams Using Micro-Computed Tomography and Direct Finite Element Modeling
,” Acta Biomater.
, 6
(6
), pp. 2342
–2351
. 10.1016/j.actbio.2009.11.03222.
Fiedler
, T.
, Belova
, I.
, and Murch
, G.
, 2012
, “μ-CT-Based Finite Element Analysis on Imperfections in Open-Celled Metal Foam: Mechanical Properties
,” Scr. Mater.
, 67
(5
), pp. 455
–458
. 10.1016/j.scriptamat.2012.06.00223.
Zhu
, X.
, Ai
, S.
, Lu
, X.
, Cheng
, K.
, Ling
, X.
, Zhu
, L.
, and Liu
, B.
, 2014
, “Collapse Models of Aluminum Foam Sandwiches Under Static Three-Point Bending Based on 3D Geometrical Reconstruction
,” Comput. Mater. Sci.
, 85
, pp. 38
–45
. 10.1016/j.commatsci.2013.12.05524.
Lee
, D. J.
, Jung
, J. M.
, Latypov
, M. I.
, Lee
, B.
, Jeong
, J.
, Oh
, S. H.
, Lee
, C. S.
, and Kim
, H. S.
, 2015
, “Three-Dimensional Real Structure-Based Finite Element Analysis of Mechanical Behavior for Porous Titanium Manufactured by a Space Holder Method
,” Comput. Mater. Sci.
, 100
, pp. 2
–7
. 10.1016/j.commatsci.2014.10.02025.
Roy
, S.
, Khutia
, N.
, Das
, D.
, Das
, M.
, Balla
, V. K.
, Bandyopadhyay
, A.
, and Chowdhury
, A. R.
, 2016
, “Understanding Compressive Deformation Behavior of Porous Ti Using Finite Element Analysis
,” Mater. Sci. Eng. C
, 64
, pp. 436
–443
. 10.1016/j.msec.2016.03.06626.
Richter
, H.
, 2017
, “Mote3D: An Open-Source Toolbox for Modelling Periodic Random Particulate Microstructures
,” Modell. Simul. Mater. Sci. Eng.
, 25
, p. 035011
. 10.1088/1361-651x/aa629a27.
Panico
, M.
, and Brinson
, L.
, 2008
, “Computational Modeling of Porous Shape Memory Alloys
,” Int. J. Solids Struct.
, 45
(21
), pp. 5613
–5626
. 10.1016/j.ijsolstr.2008.06.00528.
Luther
, D. I. T.
, 2005
, Homogenization of Damaged Concrete Meso-Structures Using Representative Volume Elements—Implementation and Application to Slang
, Bauhaus-University
, Weimar, Germany
.29.
Al Kassem
, G.
, and Weichert
, D.
, 2009
, “Micromechanical Material Models for Polymer Composites Through Advanced Numerical Simulation Techniques
,” Proc. Appl. Math. Mech
, 9
, pp. 413
–414
.30.
Shen
, H.
, and Brinson
, L. C.
, 2006
, “A Numerical Investigation of the Effect of Boundary Conditions and Representative Volume Element Size for Porous Titanium
,” J. Mech. Mater. Struct.
, 1
(7
), pp. 1179
–1204
. 10.2140/jomms.2006.1.117931.
Systemes
, D.
, 2018
, “ABAQUS 2017 Documentation
,” English Version, 6.32.
Chavoshi
, S. Z.
, Jiang
, J.
, Wang
, Y.
, Fang
, S.
, Wang
, S.
, Shi
, Z.
, and Lin
, J.
, 2018
, “Density-Based Constitutive Modelling of P/M FGH96 for Powder Forging
,” Int. J. Mech. Sci.
, 138
, pp. 110
–121
. 10.1016/j.ijmecsci.2018.02.00333.
Zhang
, M.
, Li
, F.
, Yuan
, Z.
, Li
, J.
, and Wang
, S.
, 2013
, “Effect of Heat Treatment on the Micro-Indentation Behavior of Powder Metallurgy Nickel Based Superalloy FGH96
,” Mater. Des.
, 49
, pp. 705
–715
. 10.1016/j.matdes.2013.02.02434.
Rasband
, W.
, 1997
, ImageJ Software
, National Institutes of Health
, Bethesda, MD
(2012).35.
Dewey
, J. M.
, 1947
, “The Elastic Constants of Materials Loaded With Non-Rigid Fillers
,” J. Appl. Phys.
, 18
(578
), pp. 578
–581
. 10.1063/1.169769136.
Zhao
, Y.
, Tandon
, G.
, and Weng
, G.
, 1989
, “Elastic Moduli for a Class of Porous Materials
,” Acta Mech.
, 76
(1–2
), pp. 105
–131
. 10.1007/BF0117579937.
Arnold
, M.
, Boccaccini
, A.
, and Ondracek
, G.
, 1996
, “Prediction of the Poisson’s Ratio of Porous Materials
,” J. Mater. Sci.
, 31
(6
), pp. 1643
–1646
. 10.1007/BF0035787638.
Nielsen
, L. F.
, 1982
, “Elastic Properties of Two-Phase Materials
,” Mater. Sci. Eng.
, 52
(1
), pp. 39
–62
. 10.1016/0025-5416(82)90068-439.
Spinner
, S.
, Knudsen
, F.
, and Stone
, L.
, 1963
, “Elastic Constant-Porosity Relations for Polycrystalline Thoria
,” J. Res. Nat. Bur. Stand., Sec. C
, 67C
(No.1
), pp. 39
–46
.40.
Dunn
, M. L.
, and Ledbetter
, H.
, 1995
, “Poisson’s Ratio of Porous and Microcracked Solids: Theory and Application to Oxide Superconductors
,” J. Mater. Res.
, 10
(11
), pp. 2715
–2722
. 10.1557/JMR.1995.271541.
Ramakrishnan
, N.
, and Arunachalam
, V.
, 1993
, “Effective Elastic Moduli of Porous Ceramic Materials
,” J. Am. Ceram. Soc.
, 76
(11
), pp. 2745
–2752
. 10.1111/j.1151-2916.1993.tb04011.x42.
Ramakrishnan
, N.
, and Arunachalam
, V.
, 1990
, “Effective Elastic Moduli of Porous Solids
,” J. Mater. Sci.
, 25
(9
), pp. 3930
–3937
. 10.1007/BF0058246243.
Roberts
, A. P.
, and Garboczi
, E. J.
, 2000
, “Elastic Properties of Model Porous Ceramics
,” J. Am. Ceram. Soc.
, 83
(12
), pp. 3041
–3048
. 10.1111/j.1151-2916.2000.tb01680.x44.
Gibson
, I.
, and Ashby
, M. F.
, 1982
, “The Mechanics of Three-Dimensional Cellular Materials
,” Proc. R. Soc. Lond. A
, 382
(1782
), pp. 43
–59
. 10.1098/rspa.1982.008845.
McAdam
, G.
, 1951
, “Some Relations of Powder Characteristics to the Elastic Modulus and Shrinkage of Sintered Ferrous Compacts
,” J. Iron Steel Inst.
, 168
, pp. 346
–358
.46.
Maitra
, A.
, and Phani
, K. K.
, 1994
, “Ultrasonic Evaluation of Elastic Parameters of Sintered Powder Compacts
,” J. Mater. Sci.
, 29
(17
), pp. 4415
–4419
. 10.1007/BF0037626347.
Herakovich
, C.
, and Baxter
, S.
, 1999
, “Influence of Pore Geometry on the Effective Response of Porous Media
,” J. Mater. Sci.
, 34
(7
), pp. 1595
–1609
. 10.1023/A:100452860021348.
Ishai
, O.
, and Cohen
, L.
, 1967
, “Elastic Properties of Filled and Porous Epoxy Composites
,” Int. J. Mech. Sci.
, 9
(8
), pp. 539
–546
. 10.1016/0020-7403(67)90053-749.
Martin
, R. B.
, and Haynes
, R. R.
, 1971
, “Confirmation of Theoretical Relation Between Stiffness and Porosity in Ceramics
,” J. Am. Ceram. Soc.
, 54
(8
), pp. 410
–411
. 10.1111/j.1151-2916.1971.tb12333.x50.
Hashin
, Z.
, 1962
, “The Elastic Moduli of Heterogeneous Materials
,” J. Appl. Mech.
, 29
(1
), pp. 143
–150
. 10.1115/1.363644651.
Hasselman
, D.
, 1962
, “On the Porosity Dependence of the Elastic Moduli of Polycrystalline Refractory Materials
,” J. Am. Ceram. Soc.
, 45
(9
), pp. 452
–453
. 10.1111/j.1151-2916.1962.tb11191.x52.
Bert
, C. W.
, 1985
, “Prediction of Elastic Moduli of Solids With Oriented Porosity
,” J. Mater. Sci.
, 20
(6
), pp. 2220
–2224
. 10.1007/BF0111230753.
Fryxell
, R.
, and Chandler
, B.
, 1964
, “Creep, Strength, Expansion, and Elastic Moduli of Sintered BeO as a Function of Grain Size, Porosity, and Grain Orientation
,” J. Am. Ceram. Soc.
, 47
(6
), pp. 283
–291
. 10.1111/j.1151-2916.1964.tb14417.x54.
Spriggs
, R.
, 1961
, “Expression for Effect of Porosity on Elastic Modulus of Polycrystalline Refractory Materials, Particularly Aluminum Oxide
,” J. Am. Ceram. Soc.
, 44
(12
), pp. 628
–629
. 10.1111/j.1151-2916.1961.tb11671.x55.
Paul
, B.
, 1960
, “Prediction of Elastic Constants of Multiphase Materials
,” Trans. Metall. Soc. AIME
, 218
, pp. 36
–41
.56.
Boccaccini
, A.
, and Fan
, Z.
, 1997
, “A New Approach for the Young’s Modulus-Porosity Correlation of Ceramic Materials
,” Ceram. Int.
, 23
(3
), pp. 239
–245
. 10.1016/S0272-8842(96)00033-857.
Boccaccini
, A.
, 1994
, “Comment on “Dependence of Ceramic Fracture Properties on Porosity”
,” J. Mater. Sci. Lett.
, 13
, pp. 1035
–1037
.58.
Eudier
, M.
, 1962
, “The Mechanical Properties of Sintered Low-Alloy Steels
,” Powder Metall.
, 5
(9
), pp. 278
–290
. 10.1179/pom.1962.5.9.00559.
Knudsen
, F.
, 1962
, “Effect of Porosity on Young’s Modulus of Alumina
,” J. Am. Ceram. Soc.
, 45
(2
), pp. 94
–95
. 10.1111/j.1151-2916.1962.tb11089.x60.
Rossi
, R.
, 1968
, “Prediction of the Elastic Moduli of Composites
,” J. Am. Ceram. Soc.
, 51
(8
), pp. 433
–440
. 10.1111/j.1151-2916.1968.tb11914.x61.
Hasselman
, D.
, and Fulrath
, R.
, 1964
, “Effect of Small Fraction of Spherical Porosity on Elastic Moduli of Glass
,” J. Am. Ceram. Soc.
, 47
(1
), pp. 52
–53
. 10.1111/j.1151-2916.1964.tb14644.x62.
Phani
, K. K.
, and Sanyal
, D.
, 2005
, “Critical Reevaluation of the Prediction of Effective Poisson’s Ratio for Porous Materials
,” J. Mater. Sci.
, 40
(21
), pp. 5685
–5690
. 10.1007/s10853-005-1507-963.
Siegkas
, P.
, Tagarielli
, V.
, Petrinic
, N.
, and Lefebvre
, L.
, 2011
, “The Compressive Response of a Titanium Foam at Low and High Strain Rates
,” J. Mater. Sci.
, 46
(8
), pp. 2741
–2747
. 10.1007/s10853-010-5147-364.
Chavoshi
, S. Z.
, and Xu
, S.
, 2018
, “Tension–Compression Asymmetry in Plasticity of Nanotwinned 3C-SiC Nanocrystals
,” J. Appl. Phys.
, 124
, p. 095103
. 10.1063/1.504694965.
Chavoshi
, S. Z.
, Tschopp
, M. A.
, and Branicio
, P. S.
, 2019
, “Transition of Deformation Mechanisms in Nanotwinned Single Crystalline SiC
,” Philos. Mag.
, 99
(21
), pp. 2636
–2660
. 10.1080/14786435.2019.1637033Copyright © 2019 by ASME
You do not currently have access to this content.
