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Research Papers

Modeling of Microstructure Effects on the Mechanical Behavior of Ultrafine-Grained Nickels Processed by Severe Plastic Deformation by Crystal Plasticity Finite Element Model

[+] Author and Article Information
Thê-Duong Nguyen

Faculty of Civil Engineering,
Duy Tân University,
25/K7, Quang Trung,
Da Nang 55000, Vietnam
e-mail: theduong.nguyen@duytan.edu.vn

Van-Tung Phan

R&D Institute,
Duy Tân University,
25/K7, Quang Trung,
Da Nang 55000, Vietnam
e-mail: phanvantung@dtu.edu.vn

Quang-Hien Bui

R&D Institute,
Faculty of Civil Engineering,
Duy Tân University,
25/K7, Quang Trung,
Da Nang 55000, Vietnam
e-mails: quanghien.bui@duytan.edu.vn, buiquanghien@gmail.com

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received April 20, 2014; final manuscript received January 7, 2015; published online February 2, 2015. Assoc. Editor: Irene Beyerlein.

J. Eng. Mater. Technol 137(2), 021010 (Apr 01, 2015) (11 pages) Paper No: MATS-14-1085; doi: 10.1115/1.4029570 History: Received April 20, 2014; Revised January 07, 2015; Online February 02, 2015

In this study, a crystal plasticity finite element model (CPFEM) has been revisited to study the microstructure effects on macroscopic mechanical behavior of ultrafine-grained (UFG) nickels processed by severe plastic deformation (SPD). The microstructure characteristics such as grain size and dislocation density show a strong influence on the mechanical behavior of SPD-processed materials. We used a modified Hall–Petch relationship at grain level to study both grain size and dislocation density dependences of mechanical behavior of SPD-processed nickel materials. Within the framework of small strain hypothesis, it is quite well shown that the CPFEM predicts the mechanical behavior of unimodal nickels processed by SPD methods. Moreover, a comparison between the proposed model and the self-consistent approach will be shown and discussed.

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References

Sanders, P., Youngdahl, C., and Weertman, J., 1997, “The Strength of Nanocrystalline Metals With and Without Flaws,” Mater. Sci. Eng. A, 234–236, pp. 77–82. [CrossRef]
Atkinson, H. V., and Davies, S., 2000, “Fundamental Aspects of Hot Isostatic Pressing: An Overview,” Metall. Mater. Trans. A, 31(12), pp. 2981–3000. [CrossRef]
Champion, Y., Bernard, F., Guigue-Millot, N., and Perriat, P., 2003, “Sintering of Copper Nanopowders Under Hydrogen: An In Situ X-Ray Diffraction Analysis,” Mater. Sci. Eng. A, 360(1–2), pp. 258–263. [CrossRef]
Segal, V., 1995, “Materials Processing by Simple Shear,” Mater. Sci. Eng. A, 197(2), pp. 157–164. [CrossRef]
Valiev, R., Islamgaliev, R., and Alexandrov, I., 2000, “Bulk Nanostructured Materials From Severe Plastic Deformation,” Prog. Mater. Sci., 45(2), pp. 103–189. [CrossRef]
Valiev, R., Estrin, Y., Horita, Z., Langdon, T., Zechetbauer, M., and Zhu, Y., 2006, “Producing Bulk Ultrafine-Grained Materials by Severe Plastic Deformation,” JOM, 58(4), pp. 33–39. [CrossRef]
Dubravina, A., Zehetbauer, M., Schafler, E., and Alexandrov, I., 2004, “Correlation Between Domain Size Obtained by X-Ray Bragg Profile Analysis and Macroscopic Flow Stress in Severely Plastically Deformed Copper,” Mater. Sci. Eng. A, 387–389, pp. 817–821. [CrossRef]
Kapoor, R., Kumar, N., Mishra, R., Huskamp, C., and Sankaran, K., 2010, “Influence of Fraction of High Angle Boundaries on the Mechanical Behavior of an Ultrafine Grained Al–Mg Alloy,” Mater. Sci. Eng. A, 527(20), pp. 5246–5254. [CrossRef]
Segal, V., 1999, “Equal Channel Angular Extrusion: From Macromechanics to Structure Formation,” Mater. Sci. Eng. A, 271(1–2), pp. 322–333. [CrossRef]
Valiev, R., and Langdon, T., 2006, “Principles of Equal-Channel Angular Pressing as a Processing Tool for Grain Refinement,” Prog. Mater. Sci., 51(7), pp. 881–981. [CrossRef]
Bridgman, P., 1943, “On Torsion Combined With Compression,” J. Appl. Phys., 14(6), pp. 273–283. [CrossRef]
Jiang, H., Zhu, Y. T., Butt, D., Alexandrov, I., and Lowe, T., 2000, “Microstructural Evolution, Microhardness and Thermal Stability of HPT-Processed Cu,” Mater. Sci. Eng. A, 290(1–2), pp. 128–138. [CrossRef]
Alexandrov, I., Dubravina, A., Kilmametov, A., Kazykhanov, V., and Valiev, R., 2003, “Textures in Nanostructured Metals Processed by Severe Plastic Deformation,” Met. Mater. Int., 9(2), pp. 151–156. [CrossRef]
Stolyarov, V., Zhu, Y., Lowe, T., Islamgaliev, R., and Valiev, R., 2000, “Processing Nanocrystalline Ti and Its Nanocomposites From Micrometer-Sized Ti Powder Using High Pressure Torsion,” Mater. Sci. Eng. A, 282(1–2), pp. 78–85. [CrossRef]
Zhilyaev, A., McNelley, T., and Langdon, T., 2007, “Evolution of Microstructure and Microtexture in fcc Metals During High-Pressure Torsion,” J. Mater. Sci., 42(5), pp. 1517–1528. [CrossRef]
Jahedi, M., Paydar, M. H., Zheng, S., Beyerlein, I. J., and Knezevic, M., 2014, “Texture Evolution and Enhanced Grain Refinement Under High-Pressure-Double-Torsion,” Mater. Sci. Eng. A, 611, pp. 29–36. [CrossRef]
Tsuji, N., Ueji, R., and Minamino, Y., 2002, “Nanoscale Crystallographic Analysis of Ultrafine Grained IF Steel Fabricated by ARB Process,” Scr. Mater., 47(2), pp. 69–76. [CrossRef]
Pérez-Prado, M., del Valle, J. A., and Ruano, O., 2004, “Grain Refinement of Mg–Al–Zn Alloys Via Accumulative Roll Bonding,” Scr. Mater., 51(11), pp. 1093–1097. [CrossRef]
Heason, C., and Prangnell, P., 2002, “Texture Evolution and Grain Refinement in Al Deformed to Ultra-High Strains by Accumulative Roll Bonding (ARB),” Mater. Sci. Forum, 408–412, pp. 733–738. [CrossRef]
Kamikawa, N., Tsuji, N., Huang, X., and Hansen, N., 2006, “Quantification of Annealed Microstructures in ARB Processed Aluminum,” Acta Mater., 54(11), pp. 3055–3066. [CrossRef]
Jiang, L., Prado, M. P., Gruber, P., Arzt, E., Ruano, O., and Kassner, M., 2008, “Texture, Microstructure and Mechanical Properties of Equiaxed Ultrafine-Grained Zr Fabricated by Accumulative Roll Bonding,” Acta Mater., 56(6), pp. 1228–1242. [CrossRef]
Saito, Y., Utsunomiya, H., and H Suzuki, T. S., 2008, “Improvement in the R-Value of Aluminum Strip by a Continuous Shear Deformation Process,” Scr. Mater., 42(12), pp. 1139–1144. [CrossRef]
Okamura, Y., Utsunomiya, H., Sakai, T., and Saito, Y., 2003, “Texture and Microstructure of Ultra-Low Carbon IF Steel Strip Processed by Conshearing,” J. Iron Steel Inst. Jpn., 89(6), pp. 666–672.
Utsunomiya, H., Hatsuda, K., Sakai, T., and Saito, Y., 2004, “Continuous Grain Refinement of Aluminum Strip by Conshearing,” Mater. Sci. Eng. A, 372(1–2), pp. 199–206. [CrossRef]
Hall, E. O., 1951, “The Deformation and Aging of Mild Steel. III: Discussion of Results,” Proc. Phys. Soc. London B, 64(9), pp. 747–753. [CrossRef]
Petch, N., 1953, “The Cleavage Strength of Polycrystals,” J. Iron Steel Inst., 174(1), pp. 25–28.
Krasilnikov, N., Lojkowski, W., Pakiela, Z., and Valiev, R., 2005, “Tensile Strength and Ductility of Ultra-Fine-Grained Nickel Processed by Severe Plastic Deformation,” Mater. Sci. Eng. A, 397(1–2), pp. 330–337. [CrossRef]
Jiang, B., and Weng, G., 2004, “A Generalized Self-Consistent Polycrystal Model for the Yield Strength of Nanocrystalline Materials,” J. Mech. Phys. Solids, 52(5), pp. 1125–1149. [CrossRef]
Ramtani, S., Bui, H., and Dirras, G., 2009, “A Revisited Generalized Self-Consistent Polycrystal Model Following an Incremental Small Strain Formulation and Including Grain-Size Distribution Effect,” Int. J. Eng. Sci., 47(4), pp. 537–553. [CrossRef]
Ramtani, S., Dirras, G., and Bui, H., 2010, “A Bimodal Bulk Ultra-Fine-Grained Nickel: Experimental and Micromechanical Investigations,” Mech. Mater., 42(5), pp. 522–536. [CrossRef]
Bui, Q. H., and Pham, X. T., 2011, “Modeling of Microstructure Effects on the Mechanical Behavior of Ultrafine-Grained Nickels Processed by Hot Isostatic Pressing,” Int. J. Mech. Sci., 53(10), pp. 812–826. [CrossRef]
Weng, G. J., 1983, “A Micromechanical Theory of Grain Size Dependence in Metal Plasticity,” J. Mech. Phys. Solids, 31(3), pp. 193–203. [CrossRef]
Berbenni, S., Favier, V., and Berveiller, M., 2007, “Impact of the Grain Size Distribution on the Yield Stress of Heterogeneous Materials,” Int. J. Plast., 23(1), pp. 114–142. [CrossRef]
Raeisinia, B., and Sinclair, C., 2009, “A Representative Grain Size for the Mechanical Response of Polycrystals,” Mater. Sci. Eng. A, 525(1–2), pp. 78–82. [CrossRef]
Nicaise, N., Berbenni, S., Wagner, F., Berveiller, M., and Lemoine, X., 2011, “Coupled Effects of Grain Size Distributions and Crystallographic Textures on the Plastic Behaviour of IF Steels,” Int. J. Plast., 27(2), pp. 232–249. [CrossRef]
Lebensohn, R. A., and Tomé, C. N., 1993, “A Study of the Stress State Associated With Twin Nucleation and Propagation in Anisotropic Materials,” Philos. Mag. A, 67(1), pp. 187–206. [CrossRef]
Clausen, B., Tomé, C., Brown, D., and Agnew, S., 2008, “Reorientation and Stress Relaxation Due to Twinning: Modeling and Experimental Characterization for Mg,” Acta Mater., 56(11), pp. 2456–2468. [CrossRef]
Barai, P., and Weng, G. J., 2008, “The Competition of Grain Size and Porosity in the Viscoplastic Response of Nanocrystalline Solids,” Int. J. Plast., 24(8), pp. 1380–1410. [CrossRef]
Lebensohn, R., Solas, D., Canova, G., and Brechet, Y., 1996, “Modelling Damage of Al–Zn–Mg Alloys,” Acta Mater., 44(1), pp. 315–325. [CrossRef]
Kurzydlowsky, K., 1990, “A Model for the Flow Stress Dependence on the Distribution of Grain Size in Polycrystals,” Scr. Metall. Mater., 5(24), pp. 879–883. [CrossRef]
Kadkhodapour, J., Ziaei-Rad, S., and Karimzadeh, F., 2009, “Finite-Element Modeling of Rate Dependent Mechanical Properties in Nanocrystalline Materials,” Comput. Mater. Sci., 45(4), pp. 1113–1124. [CrossRef]
Wei, Y., and Anand, L., 2004, “Grain-Boundary Sliding and Separation in Polycrystalline Metals: Application to Nanocrystalline fcc Metals,” J. Mech. Phys. Solids, 52(11), pp. 2587–2616. [CrossRef]
Wei, Y., Su, C., and Anand, L., 2006, “A Computational Study of the Mechanical Behavior of Nanocrystalline fcc Metals,” Acta Mater., 54(12), pp. 3177–3190. [CrossRef]
Fu, H.-H., Benson, D. J., and Meyers, M. A., 2004, “Computational Description of Nanocrystalline Deformation Based on Crystal Plasticity,” Acta Mater., 52(15), pp. 4413–4425. [CrossRef]
Wu, B., Liang, L., Ma, H., and Wei, Y., 2012, “A Trans-Scale Model for Size Effects and Intergranular Fracture in Nanocrystalline and Ultra-Fine Polycrystalline Metals,” Comput. Mater. Sci., 57, pp. 2–7. [CrossRef]
Péron-Lührs, V., Jérusalem, A., Sansoz, F., Stainier, L., and Noels, L., 2013, “A Two-Scale Model Predicting the Mechanical Behavior of Nanocrystalline Solids,” J. Mech. Phys. Solids, 61(9), pp. 1895–1914. [CrossRef]
Aoyagi, Y., Kobayashi, R., Kaji, Y., and Shizawa, K., 2013, “Modeling and Simulation on Ultrafine-Graining Based on Multiscale Crystal Plasticity Considering Dislocation Patterning,” Int. J. Plast., 47, pp. 13–28. [CrossRef]
Aoyagi, Y., Tsuru, T., and Shimokawa, T., 2014, “Crystal Plasticity Modeling and Simulation Considering the Behavior of the Dislocation Source of Ultrafine-Grained Metal,” Int. J. Plast., 55, pp. 43–57. [CrossRef]
Dobosz, R., Lewandowska, M., and Kurzydlowski, K. J., 2012, “The Effect of Grain Size Diversity on the Flow Stress of Nanocrystalline Metals by Finite-Element Modelling,” Scr. Mater., 67(4), pp. 408–411. [CrossRef]
Peirce, D., Asaro, R. J., and Needleman, A., 1982, “An Analysis of Nonuniform and Localized Deformation in Ductile Single Crystals,” Acta Mater., 30(6), pp. 1087–1119. [CrossRef]
Huang, Y., 1991, “A User-Material Subroutine Incorporating Single Crystal Plasticity in the Abaqus Finite Element Program,” Division of Applied Sciences, Harvard University, Cambridge, MA, Mechanical Report No. 178.
Ting, T., 1996, “Anisotropy Elasticity: Theory and Applications,” Oxford University Press, Oxford, UK.
Hutchinson, J. W., 1976, “Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials,” Proc. R. Soc. London A., 348(1652), pp. 101–127. [CrossRef]
Asaro, R. J., 1983, “Micromechanics of Crystals and Polycrystals,” Adv. Appl. Mech., 23, pp. 1–15. [CrossRef]
Asaro, R. J., 1983, “Crystal Plasticity,” ASME J. Appl. Mech., 50(4b), pp. 921–934. [CrossRef]
Simulia, 2012, “Abaqus 6.12: Abaqus/CAE User's Manual,” Dassault Systemes, Providence, RI.
Peirce, D., Shih, C. F., and Needleman, A., 1984, “A Tangent Modulus Method for Rate Dependent Solids,” Comput. Struct., 18(5), pp. 875–887. [CrossRef]
Böhlke, T., Risy, G., and Bertram, A., 2006, “Finite Element Simulation of Metal Forming Operations With Texture Based Material Models,” Modell. Simul. Mater. Sci. Eng., 14(3), pp. 365–387. [CrossRef]
Phan, V. T., Jöchen, K., and Böhlke, T., 2012, “Simulation of Sheet Metal Forming Incorporating EBSD Data,” J. Mater. Process. Technol., 212(12), pp. 2659–2668. [CrossRef]
Glavas, V., Böhlke, T., Daniel, D., and Leppin, C., 2012, “Texture Based Finite Element Simulation of a Two-Step Can Forming Process,” Key Eng. Mater., 504–506, pp. 655–660. [CrossRef]
Bui, Q., Pham, X., and Fafard, M., 2013, “Modelling of Microstructure Effects on the Mechanical Behavior of Aluminium Tubes Drawn With Different Reduction Areas,” Int. J. Plast., 50, pp. 127–145. [CrossRef]
Schwartz, A. J., Kumar, M., Adams, B., and Field, D. P., 2009, Electron Backscatter Diffraction in Materials Science, 2nd ed., Springer, New York.
Zhang, C., Enomoto, M., Suzuki, A., and Ishimaru, T., 2004, “Characterization of Three-Dimensional Grain Structure in Polycrystalline Iron by Serial Sectioning,” Metall. Mater. Trans. A, 35(7), pp. 1927–1933. [CrossRef]
Rowenhorst, D., Lewis, A., and Spanos, G., 2010, “Three-Dimensional Analysis of Grain Topology and Interface Curvature in a β-Titanium Alloy,” Acta Mater., 58(16), pp. 5511–5519. [CrossRef]
Cailletaud, G., Forest, S., Jeulin, D., Feyel, F., Galliet, I., Mounoury, V., and Quilici, S., 2003, “Some Elements of Microstructural Mechanics,” Comput. Mater. Sci., 27(3), pp. 351–374. [CrossRef]
Diard, O., Leclercq, S., Rousselier, G., and Cailletaud, G., 2005, “Evaluation of Finite Element Based Analysis of 3D Multicrystalline Aggregates Plasticity: Application to Crystal Plasticity Model Identification and the Study of Stress and Strain Fields Near Grain Boundaries,” Int. J. Plast., 21(4), pp. 691–722. [CrossRef]
Aurenhammer, F., 1991, “Voronoi Diagrams—A Survey of a Fundamental Geometric Data Structure,” ACM Comput. Surv., 23(3), pp. 345–405. [CrossRef]
CEA, 2003, “Cast3M,” CEA, Saclay, France, http://www-cast3m.cea.fr/
Knezevic, M., Drach, B., Ardeljan, M., and Beyerlein, I. J., 2014, “Three Dimensional Predictions of Grain Scale Plasticity and Grain Boundaries Using Crystal Plasticity Finite Element Models,” Comput. Methods Appl. Mech. Eng., 277, pp. 239–259. [CrossRef]
Furukawa, M., Horita, Z., Nemoto, M., and Langdon, T. G., 2002, “The Use of Severe Plastic Deformation for Microstructural Control,” Mater. Sci. Eng. A, 324(1–2), pp. 82–89. [CrossRef]
Bui, Q., Dirras, G., Ramtani, S., and Gubicza, J., 2010, “On the Strengthening Behavior of Ultrafine-Grained Nickel Processed From Nanopowders,” Mater. Sci. Eng. A, 527(13–14), pp. 3227–3235. [CrossRef]
Ebrahimi, F., Bourne, G., Kelly, M., and Matthews, T., 1999, “Mechanical Properties of Nanocrystalline Nickel Produced by Electrodeposition,” Nanostruct. Mater., 11(3), pp. 343–350. [CrossRef]
Xiao, C., Mirshams, R., Whang, S., and Yin, W., 2001, “Tensile Behavior and Fracture in Nickel and Carbon Doped Nanocrystalline Nickel,” Mater. Sci. Eng. A, 301(1), pp. 35–43. [CrossRef]
Hughes, D., and Hansen, N., 2000, “Microstructure and Strength of Nickel at Large Strains,” Acta Mater., 48(11), pp. 2985–3004. [CrossRef]
Neighbours, J. R., Bratten, F. W., and Smith, C. S., 1952, “The Elastic Constants of Nickel,” J. Appl. Phys., 23(4), pp. 389–393. [CrossRef]
Bui, Q., and Nguyen-Thê, D., 2013, “Elasto-Plastic Self-Consistant Model for Nano Metal Fabricated by Top-Down Method,” Proceedings of the 11th National Congress on Mechanics of Deformable Bodies, Vol. 1, Hanoi, Vietnam, December, 8–9, 2012, Vietnam Association for Mechanics, Vietnam, pp. 455–461.
Wu, P., Huang, Y., and Lloyd, D., 2006, “Studying Grain Fragmentation in ECAE by Simulating Simple Shear,” Scr. Mater., 54(12), pp. 2107–2112. [CrossRef]
Fromm, B. S., Adams, B. L., Ahmadi, S., and Knezevic, M., 2009, “Grain Size and Orientation Distributions: Application to Yielding of α-Titanium,” Acta Mater., 57(8), pp. 2339–2348. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) 3D Voronoi FE mesh of a cube 1 × 1 × 1 including 50 tessellations and (b) applied boundary conditions

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Fig. 2

Hall–Petch relation for nickel consolidated from different processing routes [27,31,71-73]. The straight line represents a linear fit on data from Refs. [72] and [73].

Grahic Jump Location
Fig. 3

Fitted curve of the Hall–Petch relationship: (a) stress–strain relation for step 1 with τ∞C=3.077 MPa and k0 = 2600 MPa × nm−1 and (b) comparison of flow stresses to existing data obtained by FEM simulation for step 1

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Fig. 4

(a) True stress–true strain curves of SPD-processed nickels and (b) comparison of flow stresses

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Fig. 5

Distribution of plastic strain (-) at different states of deformation (a) 0.01, (b) 0.025, and (c) 0.04 predicted by CPFEM for all grains and for 15 random grains of RVE model

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Fig. 6

Distribution of von Mises stress (MPa) at different states of deformation: (a) 0.01, (b) 0.025, and (c) 0.04, predicted by CPFEM for all grains and for 15 random grains of the RVE model

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