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Research Papers

A Predictive Framework for Dislocation-Density Pile-Ups in Crystalline Systems With Coincident Site Lattice and Random Grain Boundaries

[+] Author and Article Information
David M. Bond

North Carolina State University,
Raleigh, NC 27695-7190
e-mail: dmbond@ncsu.edu

Mohammed A. Zikry

College of Engineering,
North Carolina State University,
Campus Box 7910/3154 EBIII,
Centennial Campus,
Raleigh, NC 27695-7190
e-mail: zikry@ncsu.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 16, 2016; final manuscript received September 9, 2016; published online February 13, 2017. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 139(2), 021023 (Feb 13, 2017) (8 pages) Paper No: MATS-16-1184; doi: 10.1115/1.4035494 History: Received June 16, 2016; Revised September 09, 2016

Evolving dislocation-density pile-ups at grain-boundaries (GBs) spanning a wide range of coincident site lattice (CSL) and random GB misorientations in face-centered cubic (fcc) bicrystals and polycrystalline aggregates has been investigated. A dislocation-density GB interaction scheme coupled to a dislocation-density-based crystalline plasticity formulation was used in a nonlinear finite element (FE) framework to understand how different GB orientations and GB-dislocation-density interactions affect local and overall behavior. An effective Burger's vector of residual dislocations was obtained for fcc bicrystals and compared with molecular dynamics (MDs) predictions of static GB energy, as well as dislocation-density transmission at GB interfaces. Dislocation-density pile-ups and accumulations of residual dislocations at GBs and triple junctions (TJs) were analyzed for a polycrystalline copper aggregate with Σ1, Σ3, Σ7, Σ13, and Σ21 CSLs and random high-angle GBs to understand and predict the effects of GB misorientation on pile-up formation and evolution. The predictions indicate that dislocation-density pile-ups occur at GBs with significantly misoriented slip systems and large residual Burger's vectors, such as Σ7, Σ13, and Σ21 CSLs and random high-angle GBs, and this resulted in heterogeneous inelastic deformations across the GB and local stress accumulations. GBs with low misorientations of slip systems had high transmission, no dislocation-density pile-ups, and lower stresses than the high-angle GBs. This investigation provides a fundamental understanding of how different representative GB orientations affect GB behavior, slip transmission, and dislocation-density pile-ups at a relevant microstructural scale.

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References

Capolungo, L. , Spearot, D. E. , Cherkaoui, M. , McDowell, D. L. , Qu, J. , and Jacob, K. I. , 2007, “ Dislocation Nucleation From Bicrystal Interfaces and Grain Boundary Ledges: Relationship to Nanocrystalline Deformation,” J. Mech. Phys. Solids, 55(11), pp. 2300–2327. [CrossRef]
Lim, H. , Lee, M. G. , Kim, J. H. , Adams, B. L. , and Wagoner, R. H. , 2011, “ Simulation of Polycrystal Deformation With Grain and Grain Boundary Effects,” Int. J. Plast., 27(9), pp. 1328–1354. [CrossRef]
Zaefferer, S. , Kuo, J.-C. , Zhao, Z. , Winning, M. , and Raabe, D. , 2003, “ On the Influence of the Grain Boundary Misorientation on the Plastic Deformation of Aluminum Bicrystals,” Acta Mater., 51(16), pp. 4719–4735. [CrossRef]
Zhang, Z. F. , Wang, Z. G. , and Eckert, J. , 2003, “ What Types of Grain Boundaries Can Be Passed Through by Persistent Slip Bands?,” J. Mater. Res., 18(5), pp. 1031–1034. [CrossRef]
Shi, J. , and Zikry, M. A. , 2009, “ Grain–Boundary Interactions and Orientation Effects on Crack Behavior in Polycrystalline Aggregates,” Int. J. Solids Struct., 46(21), pp. 3914–3925. [CrossRef]
Sangid, M. D. , Ezaz, T. , and Sehitoglu, H. , 2012, “ Energetics of Residual Dislocations Associated With Slip–Twin and Slip–GBs Interactions,” Mater. Sci. Eng.: A, 542, pp. 21–30. [CrossRef]
Kashihara, K. , and Inoko, F. , 2001, “ Effect of Piled-Up Dislocations on Strain Induced Boundary Migration (SIBM) in Deformed Aluminum Bicrystals With Originally ∑3 Twin Boundary,” Acta Mater., 49(15), pp. 3051–3061. [CrossRef]
Pan, Y. , Adams, B. L. , Olson, T. , and Panayotou, N. , 1996, “ Grain-Boundary Structure Effects on Intergranular Stress Corrosion Cracking of Alloy X-750,” Acta Mater., 44(12), pp. 4685–4695. [CrossRef]
Su, J. , Demura, M. , and Hirano, T. , 2002, “ Grain-Boundary Fracture Strength in Ni3Al Bicrystals,” Philos. Mag. A, 82(8), pp. 1541–1557.
Schuh, C. A. , Kumar, M. , and King, W. E. , 2003, “ Analysis of Grain Boundary Networks and Their Evolution During Grain Boundary Engineering,” Acta Mater., 51(3), pp. 687–700. [CrossRef]
Watanabe, T. , 1994, “ The Impact of Grain Boundary Character Distribution on Fracture in Polycrystals,” Mater. Sci. Eng.: A, 176(1), pp. 39–49. [CrossRef]
Chiba, A. , Hanada, S. , Watanabe, S. , Abe, T. , and Obana, T. , 1994, “ Relation Between Ductility and Grain Boundary Character Distributions in Ni3Al,” Acta Metall. Mater., 42(5), pp. 1733–1738. [CrossRef]
Randle, V. , and Coleman, M. , 2009, “ A Study of Low-Strain and Medium-Strain Grain Boundary Engineering,” Acta Mater., 57(11), pp. 3410–3421. [CrossRef]
Bachurin, D. V. , Weygand, D. , and Gumbsch, P. , 2010, “ Dislocation–Grain Boundary Interaction in <111> Textured Thin Metal Films,” Acta Mater., 58(16), pp. 5232–5241. [CrossRef]
Kobayashi, S. , Tsurekawa, S. , and Watanabe, T. , 2006, “ Structure-Dependent Triple Junction Hardening and Intergranular Fracture in Molybdenum,” Philos. Mag., 86(33–35), pp. 5419–5429. [CrossRef]
Shantraj, P. , and Zikry, M. A. , 2013, “ Microstructurally Induced Fracture Nucleation and Propagation in Martensitic Steels,” J. Mech. Phys. Solids, 61(4), pp. 1091–1105. [CrossRef]
Koning, M. , Miller, R. , Bulatov, V. V. , and Abraham, F. F. , 2002, “ Modelling Grain-Boundary Resistance in Intergranular Dislocation Slip Transmission,” Philos. Mag. A, 82(13), pp. 2511–2527. [CrossRef]
Patriarca, L. , Abuzaid, W. , Sehitoglu, H. , and Maier, H. J. , 2013, “ Slip Transmission in bcc FeCr Polycrystal,” Mater. Sci. Eng.: A, 588, pp. 308–317. [CrossRef]
Guo, Y. , Britton, T. B. , and Wilkinson, A. J. , 2014, “ Slip Band–Grain Boundary Interactions in Commercial-Purity Titanium,” Acta Mater., 76, pp. 1–12. [CrossRef]
Guo, Y. , Collins, D. M. , Tarleton, E. , Hofmann, F. , Tischler, J. , Liu, W. , Xu, R. , Wilkinson, A. J. , and Britton, T. B. , 2015, “ Measurements of Stress Fields Near a Grain Boundary: Exploring Blocked Arrays of Dislocations in 3D,” Acta Mater., 96, pp. 229–236. [CrossRef]
Suzuki, A. , Gigliotti, M. F. X. , and Subramanian, P. R. , 2011, “ Novel Technique for Evaluating Grain Boundary Fracture Strength in Metallic Materials,” Scr. Mater., 64(11), pp. 1063–1066. [CrossRef]
Wu, Q. , and Zikry, M. A. , 2016, “ Microstructural Modeling of Transgranular and Intergranular Fracture in Crystalline Materials With Coincident Site Lattice Grain-Boundaries: Σ3 and Σ17b Bicrystals,” Mater. Sci. Eng.: A, 661, pp. 32–39. [CrossRef]
Zhang, L. , Lu, C. , and Tieu, K. , 2016, “ A Review on Atomistic Simulation of Grain Boundary Behaviors in Face-Centered Cubic Metals,” Comput. Mater. Sci., 118, pp. 180–191. [CrossRef]
Jang, H. , and Farkas, D. , 2007, “ Interaction of Lattice Dislocations With a Grain Boundary During Nanoindentation Simulation,” Mater. Lett., 61(3), pp. 868–871. [CrossRef]
Cheng, Y. , Mrovec, M. , and Gumbsch, P. , 2008, “ Crack Nucleation at the Symmetrical Tilt Grain Boundary in Tungsten,” Mater. Sci. Eng.: A, 483–484, pp. 329–332. [CrossRef]
Sangid, M. D. , Ezaz, T. , Sehitoglu, H. , and Robertson, I. M. , 2011, “ Energy of Slip Transmission and Nucleation at Grain Boundaries,” Acta Mater., 59(1), pp. 283–296. [CrossRef]
Dewald, M. P. , and Curtin, W. A. , 2007, “ Multiscale Modelling of Dislocation/Grain-Boundary Interactions: I. Edge Dislocations Impinging on Σ11 (113) Tilt Boundary in Al,” Modell. Simul. Mater. Sci. Eng., 15(1), p. S193. [CrossRef]
Liu, B. , Raabe, D. , Eisenlohr, P. , Roters, F. , Arsenlis, A. , and Hommes, G. , 2011, “ Dislocation Interactions and Low-Angle Grain Boundary Strengthening,” Acta Mater., 59(19), pp. 7125–7134. [CrossRef]
Liu, B. , Eisenlohr, P. , Roters, F. , and Raabe, D. , 2012, “ Simulation of Dislocation Penetration Through a General Low-Angle Grain Boundary,” Acta Mater., 60(13–14), pp. 5380–5390. [CrossRef]
Ding, R. , Gong, J. , Wilkinson, A. J. , and Jones, I. P. , 2016, “ A Study of Dislocation Transmission Through a Grain Boundary in HCP Ti–6Al Using Micro-Cantilevers,” Acta Mater., 103, pp. 416–423. [CrossRef]
Yang, Y. , Wang, L. , Bieler, T. R. , Eisenlohr, P. , and Crimp, M. A. , 2011, “ Quantitative Atomic Force Microscopy Characterization and Crystal Plasticity Finite Element Modeling of Heterogeneous Deformation in Commercial Purity Titanium,” Metall. Mater. Trans. A, 42(3), pp. 636–644. [CrossRef]
Lim, H. , Carroll, J. D. , Battaile, C. C. , Buchheit, T. E. , Boyce, B. L. , and Weinberger, C. R. , 2014, “ Grain-Scale Experimental Validation of Crystal Plasticity Finite Element Simulations of Tantalum Oligocrystals,” Int. J. Plast., 60, pp. 1–18. [CrossRef]
Bieler, T. R. , Eisenlohr, P. , Roters, F. , Kumar, D. , Mason, D. E. , Crimp, M. A. , and Raabe, D. , 2009, “ The Role of Heterogeneous Deformation on Damage Nucleation at Grain Boundaries in Single Phase Metals,” Int. J. Plast., 25(9), pp. 1655–1683. [CrossRef]
Koning, M. , Kurtz, R. J. , Bulatov, V. V. , Henager, C. H. , Hoagland, R. G. , Cai, W. , and Nomura, M. , 2003, “ Modeling of Dislocation–Grain Boundary Interactions in FCC Metals,” J. Nucl. Mater., 323(2–3), pp. 281–289. [CrossRef]
Lee, T. C. , Robertson, I. M. , and Birnbaum, H. K. , 1989, “ Prediction of Slip Transfer Mechanisms Across Grain Boundaries,” Scr. Metall., 23(5), pp. 799–803. [CrossRef]
Liu, G. S. , House, S. D. , Kacher, J. , Tanaka, M. , Higashida, K. , and Robertson, I. M. , 2014, “ Electron Tomography of Dislocation Structures,” Mater. Charact., 87, pp. 1–11. [CrossRef]
Zikry, M. A. , 1994, “ An Accurate and Stable Algorithm for High Strain-Rate Finite Strain Plasticity,” Comput. Struct., 50(3), pp. 337–350. [CrossRef]
Ziaei, S. , and Zikry, M. A. , 2015, “ Modeling the Effects of Dislocation-Density Interaction, Generation, and Recovery on the Behavior of H.C.P. Materials,” Metall. Mater. Trans. A, 46(10), pp. 4478–4490. [CrossRef]
Asaro, R. J. , and Rice, J. R. , 1977, “ Strain Localization in Ductile Single Crystals,” J. Mech. Phys. Solids, 25(5), pp. 309–338. [CrossRef]
Franciosi, P. , Berveiller, M. , and Zaoui, A. , 1980, “ Latent Hardening in Copper and Aluminium Single Crystals,” Acta Metall., 28(3), pp. 273–283. [CrossRef]
Zikry, M. A. , and Kao, M. , 1996, “ Dislocation Based Multiple-Slip Crystalline Constitutive Formulation for Finite-Strain Plasticity,” Scr. Mater., 34(7), pp. 1115–1121. [CrossRef]
Shanthraj, P. , and Zikry, M. A. , 2011, “ Dislocation Density Evolution and Interactions in Crystalline Materials,” Acta Mater., 59(20), pp. 7695–7702. [CrossRef]
Ma, A. , Roters, F. , and Raabe, D. , 2006, “ Studying the Effect of Grain Boundaries in Dislocation Density Based Crystal-Plasticity Finite Element Simulations,” Int. J. Solids Struct., 43(24), pp. 7287–7303. [CrossRef]
Roters, F. , Eisenlohr, P. , Hantcherli, L. , Tjahjanto, D. D. , Bieler, T. R. , and Raabe, D. , 2010, “ Overview of Constitutive Laws, Kinematics, Homogenization and Multiscale Methods in Crystal Plasticity Finite-Element Modeling: Theory, Experiments, Applications,” Acta Mater., 58(4), pp. 1152–1211. [CrossRef]
Rezvanian, O. , Zikry, M. A. , and Rajendran, A. M. , 2008, “ Microstructural Modeling in fcc Crystalline Materials in a Unified Dislocation-Density Framework,” Mater. Sci. Eng.: A, 494(1–2), pp. 80–85. [CrossRef]
Brandon, D. G. , 1966, “ The Structure of High-Angle Grain Boundaries,” Acta Metall., 14(11), pp. 1479–1484. [CrossRef]
Abuzaid, W. Z. , Sangid, M. D. , Carroll, J. D. , Sehitoglu, H. , and Lambros, J. , 2012, “ Slip Transfer and Plastic Strain Accumulation Across Grain Boundaries in Hastelloy X,” J. Mech. Phys. Solids, 60(6), pp. 1201–1220. [CrossRef]
Sangid, M. D. , Ezaz, T. , and Sehitoglu, H. , 2012, “ Energetics of Residual Dislocations Associated With Slip–Twin and Slip–GBs Interactions,” Mater. Sci. Eng.: A, 542, pp. 21–30. [CrossRef]
Warrington, D. H. , and Bufalini, P. , 1971, “ The Coincidence Site Lattice and Grain Boundaries,” Scr. Metall., 5(9), pp. 771–776. [CrossRef]
Sutton, A. P. , and Balluffi, R. W. , 1995, Interfaces in Crystalline Materials, Clarendon Press, Oxford, UK.
Britton, T. B. , Randman, D. , and Wilkinson, A. J. , 2009, “ Nanoindentation Study of Slip Transfer Phenomenon at Grain Boundaries,” J. Mater. Res., 24(03), pp. 607–615. [CrossRef]
Kumar, K. S. , Van Swygenhoven, H. , and Suresh, S. , 2003, “ Mechanical Behavior of Nanocrystalline Metals and Alloys,” Acta Mater., 51(19), pp. 5743–5774. [CrossRef]
Ovid'ko, I. A. , and Sheinerman, A. G. , 2009, “ Enhanced Ductility of Nanomaterials Through Optimization of Grain Boundary Sliding and Diffusion Processes,” Acta Mater., 57(7), pp. 2217–2228. [CrossRef]
Patriarca, L. , Abuzaid, W. , Sehitoglu, H. , and Maier, H. J. , 2013, “ Slip Transmission in bcc FeCr Polycrystal,” Mater. Sci. Eng.: A, 588, pp. 308–317. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Comparison of static MD calculated GB energy from Ref. [26] and average effective Burger's vector calculated for the [111] and [001] rotation axes for an fcc bicrystal

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Fig. 2

Average effective Burger's vector for the [111] rotation axis with CSL bicrystals showing the grain boundary transmission factor of the most active slip system at a nominal strain of 5%

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Fig. 3

Grain boundary misorientations determined using rotation matrices of each grain. The rotation matrices, R, were obtained by combining three successive rotations described by the Euler angles for each grain.

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Fig. 4

Microstructural polycrystal model with GB orientations indicated

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Fig. 5

(a) Normal stress and (b) GB residual dislocation-density at 3% nominal strain with maximum normal stress regions marked. Region 1 is a Σ7 CSL GB, and region 2 and region 3 are near triple junctions.

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Fig. 6

Behavior for the most active slip systems in grains A and B at 3% nominal strain: (a) immobile dislocation-density for (11¯1)[011], (b) GBTF for (11¯1)[011], (c) immobile dislocation-density for (1¯1¯1)[011], and (d) GBTF for (1¯1¯1)[011]

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Fig. 7

Normalized normal stress and grain boundary residual dislocation-density at the Σ7 CSL GB

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Fig. 8

Behavior at triple junction at 3% nominal strain: (a) GBTF for most active slip system (11¯1)[011], (b) grain boundary residual dislocation-density, (c) immobile dislocation-density for slip system (11¯1)[011], and (d) normal stress

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Fig. 9

Slip direction and immobile dislocation-density of the most active slip system of grains A, B, and C at the triple junction

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Fig. 10

Shear slip behavior: (a) near the TJ with sampling lines and CSL GBs indicated, (b) shear slip across Σ1 CSL GB, (c) shear slip across Σ13 CSL GB, and (d) shear slip across the Σ7 CSL GB

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