##
**Misorientation and grain boundary orientation dependent grain boundary response in polycrystalline plasticity.**
*(English)*
Zbl 1479.74021

Summary: This paper studies the evolution of intergranular localization and stress concentration in three dimensional micron sized specimens through the Gurtin grain boundary model [M. E. Gurtin, J. Mech. Phys. Solids 56, No. 2, 640–662 (2008; Zbl 1171.74314)] incorporated into a three dimensional higher-order strain gradient crystal plasticity framework [the first author et al., “Non-convex rate dependent strain gradient crystal plasticity and deformation patterning”, Int. J. Solids Struct. 49, No. 18, 2625–2636 (2012; doi:10.1016/j.ijsolstr.2012.05.029)]. The study addresses continuum scale dislocation-grain boundary interactions where the effect of crystal orientation mismatch and grain boundary orientation are taken into account through the grain boundary model in polycrystalline metallic specimens. Due to the higher-order nature of the model, a mixed finite element formulation is used to discretize the problem in which both displacements and plastic slips are considered as primary variables. For the treatment of grain boundaries within the solution algorithm, an interface element is formulated and implemented together with the bulk plasticity model. The capabilities of the framework is demonstrated through 3D polycrystalline examples considering grain boundary conditions, grain boundary strength, the orientation distribution and the specimen size. A detailed grain boundary condition and stress concentration analysis is presented. The advantages and the disadvantages of the model is discussed in detail through numerical examples.

### MSC:

74C20 | Large-strain, rate-dependent theories of plasticity |

74E15 | Crystalline structure |

74E20 | Granularity |

74M25 | Micromechanics of solids |

74S05 | Finite element methods applied to problems in solid mechanics |

### Keywords:

strain gradient plasticity; microforming; size effect; Gurtin grain boundary model; crystal plasticity; mixed finite element simulation### Citations:

Zbl 1171.74314
PDF
BibTeX
XML
Cite

\textit{T. Yalçinkaya} et al., Comput. Mech. 67, No. 3, 937--954 (2021; Zbl 1479.74021)

Full Text:
DOI

### References:

[1] | Geiger, M.; Kleiner, M.; Eckstein, R.; Tiesler, N.; Engel, U., Microforming, CIRP Ann, 50, 2, 445-462 (2001) |

[2] | Vollertsen, F.; Schulze Niehoff, H.; Hu, Z., State of the art in micro forming, Int J Mach Tools Manuf, 46, 11, 1172-1179 (2006) |

[3] | Abuzaid, WZ; Sangid, MG; Carroll, JD; Sehitoglu, H.; Lambros, J., Slip transfer and plastic strain accumulation across grain boundaries in hastelloy x, J Mech Phys Solids, 60, 6, 1201-1220 (2012) |

[4] | Bieler, TR; Eisenlohr, P.; Roters, F.; Kumar, D.; Mason, DE; Crimp, MA; Raabe, D., The role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals, Int J Plast, 25, 9, 1655-1683 (2009) |

[5] | Guery, A.; Hild, F.; Latourte, F.; Roux, S., Slip activities in polycrystals determined by coupling dic measurements with crystal plasticity calculations, Int J Plast, 81, 249-266 (2016) |

[6] | Guo, Y.; Britton, TB; Wilkinson, AJ, Slip band-grain boundary interactions in commercial-purity titanium, Acta Mater, 76, 1-12 (2014) |

[7] | Yalçinkaya, T.; Voyiadjis, G., Strain gradient crystal plasticity: thermodynamics and implementation, Handbook of nonlocal continuum mechanics for materials and structures, 1-32 (2017), Cham: Springer, Cham |

[8] | Yalçinkaya, T.; Özdemir, I.; Firat, AO; Tandogan, IT, Micromechanical modeling of inter-granular localization, damage and fracture, Procedia Struct Integr, 13, 385-390 (2018) |

[9] | Yalçinkaya, T.; Özdemir, I.; Simonovski, I., Micromechanical modeling of intrinsic and specimen size effects in microforming, Int J Mater Form, 11, 729-741 (2018) |

[10] | Yalçinkaya, T.; Özdemir, I.; Firat, AO, Inter-granular cracking through strain gradient crystal plasticity and cohesive zone modeling approaches, Theor Appl Fract Mech, 103, 102306 (2019) |

[11] | Güler, B.; Simsek, Ü.; Yalçinkaya, T.; Efe, M., Grain-scale investigations of deformation heterogeneities in aluminum alloys, AIP Conf Proc, 1960, 170005 (2018) |

[12] | Ma, A.; Roters, F.; Raabe, D., On the consideration of interactions between dislocations and grain boundaries in crystal plasticity finite element modeling - theory, experiments, and simulations, Acta Mater, 54, 8, 2181-2194 (2006) |

[13] | Ng, KS; Ngan, AHW, Deformation of micron-sized aluminium bi-crystal pillars, Philos Mag, 89, 33, 3013-3026 (2009) |

[14] | Zaefferer, S.; Kuo, JC; Zhao, Z.; Winning, M.; Raabe, D., On the influence of the grain boundary misorientation on the plastic deformation of aluminum bicrystals, Acta Mater, 51, 4719-4735 (2003) |

[15] | Zhao, Z.; Ramesh, M.; Raabe, D.; Cuitino, AM; Radovitzky, R., Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal, Int J Plast, 24, 12, 2278-2297 (2008) |

[16] | Zhang, Z.; Lunt, D.; Abdolvand, H.; Wilkinson, AJ; Preuss, M.; Dunne, FPE, Quantitative investigation of micro slip and localization in polycrystalline materials under uniaxial tension, Int J Plast, 108, 88-106 (2018) |

[17] | Lim, H.; Carroll, JD; Corbett, CB; Boyce, BL; Weinberger, CR, Quantitative comparison between experimental measurements and cp-fem predictions of plastic deformation in a tantalum oligocrystal, Int J Mech Sci, 92, 98-108 (2015) |

[18] | Acar, P.; Ramazani, A.; Sundararaghavan, V., Crystal plasticity modeling and experimental validation with an orientation distribution function for ti-7al alloy, Metals, 7, 11, 459 (2017) |

[19] | Doquet, V.; Barkia, B., Combined AFM, SEM and crystal plasticity analysis of grain boundary sliding in titanium at room temperature, Mech Mater, 103, 18-27 (2016) |

[20] | Liang, H.; Dunne, FPE, Gnd accumulation in bi-crystal deformation: crystal plasticity analysis and comparison with experiments, Int J Mech Sci, 51, 326-333 (2009) |

[21] | Mello, AW; Nicolas, A.; Lebensohn, RA; Sangid, MD, Effect of microstructure on strain localization in a 7050 aluminum alloy: comparison of experiments and modeling for various textures, Mater Sci Eng A, 661, 187-197 (2016) |

[22] | Pinna, C.; Lan, Y.; Kiu, MF; Efthymiadis, P.; Lopez-Pedrosa, M.; Farrugia, D., Assessment of crystal plasticity finite element simulations of the hot deformation of metals from local strain and orientation measurements, Int J Plast, 73, 24-38 (2015) |

[23] | Sachtleber, M.; Zhao, Z.; Raabe, D., Experimental investigation of plastic grain interaction, Mater Sci Eng A, 336, 1, 81-87 (2002) |

[24] | Tasan, CC; Hoefnagels, JPM; Diehl, M.; Yan, D.; Roters, F.; Raabe, R., Strain localization and damage in dual phase steels investigated by coupled in-situ deformation experiments and crystal plasticity simulations, Int J Plast, 63, 198-210 (2014) |

[25] | Roters, F., Application of crystal plasticity fem from single crystal to bulk polycrystal, Comput Mater Sci, 32, 3, 509-517 (2005) |

[26] | Luccarelli, PG; Pataky, GJ; Sehitoglu, H.; Foletti, S., Finite element simulation of single crystal and polycrystalline haynes 230 specimens, Int J Solids Struct, 115-116, 3, 270-278 (2017) |

[27] | Gurtin, ME, A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation, J Mech Phys Solids, 56, 640-662 (2008) |

[28] | Özdemir, I.; Yalçinkaya, T., Modeling of dislocation-grain boundary interactions in a strain gradient crystal plastictiy framework, Comput Mech, 54, 255-268 (2014) |

[29] | Yalçinkaya, T.; Brekelmans, WAM; Geers, MGD, Non-convex rate dependent strain gradient crystal plasticity and deformation patterning, Int J Solids Struct, 49, 2625-2636 (2012) |

[30] | Yalcinkaya, T.; Brekelmans, WAM; Geers, MGD, Deformation patterning driven by rate dependent non-convex strain gradient plasticity, J Mech Phys Solids, 59, 1-17 (2011) |

[31] | Özdemir I, Yalçinkaya T (2017) Strain gradient crystal plasticity: intergranular microstructure formation. In: Voyiadjis G (eds) Handbook of nonlocal continuum mechanics for materials and structures, pp 1035-1065 |

[32] | van Beers, PRM; McShane, GJ; Kouznetsova, VG; Geers, MGD, Grain boundary interface mechanics in strain gradient crystal plasticity, J Mech Phys Solids, 61, 12, 2659-2679 (2013) |

[33] | van Beers, PRM; Kouznetsova, VG; Geers, MGD; Tschopp, MA; McDowell, DL, A multiscale model of grain boundary structure and energy: from atomistics to a continuum description, Acta Mater, 82, 12, 513-529 (2015) |

[34] | Gottschalk, D.; McBride, A.; Reddy, BD; Javili, A.; Wriggers, P.; Hirschberger, CB, Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation, Comput Mater Sci, 111, 443-459 (2016) |

[35] | Bayerschen, E.; McBride, AT; Reddy, BD; Böhlke, T., Review on slip transmission criteria in experiments and crystal plasticity models, J Mater Sci, 51, 5, 2243-2258 (2016) |

[36] | Alipour, A.; Reese, S.; Wulfinghoff, S., A grain boundary model for gradient-extended geometrically nonlinear crystal plasticity: theory and numerics, Int J Plast, 118, 17-35 (2019) |

[37] | Wulfinghoff, S., A generalized cohesive zone model and a grain boundary yield criterion for gradient plasticity derived from surface- and interface-related arguments, Int J Plast, 92, 57-78 (2017) |

[38] | Evers, LP; Brekelmans, WAM; Geers, MGG, Non-local crystal plasticity model with intrinsic ssd and gnd effects, J Mech Phys Solids, 52, 2379-2401 (2004) |

[39] | Klusemann, B.; Yalcinkaya, T., Plastic deformation induced microstructure evolution through gradient enhanced crystal plasticity based on a non-convex helmholtz energy, Int J Plast, 48, 168-188 (2013) |

[40] | Rys, M.; Petryk, H., Gradient crystal plasticity models with a natural length scale in the hardening law, Int J Plast, 111, 168-187 (2018) |

[41] | Bittencourt, E., Interpretation of the size effects in micropillar compression by a strain gradient crystal plasticity theory, Int J Plast, 116, 280-296 (2019) |

[42] | Kuroda, M., Interfacial microscopic boundary conditions associated with backstress-based higher-order gradient crystal plasticity theory, J Mech Mater Struct, 12, 193-218 (2017) |

[43] | Spannraft, L.; Ekh, M.; Larsson, F.; Runesson, K.; Steinmann, P., Grain boundary interaction based on gradient crystal inelasticity and decohesion, Comput Mater Sci, 178, 109604 (2020) |

[44] | Gurtin, ME, On the plasticity of single crystals: free energy, microforces, plastic-strain gradients, J Mech Phys Solids, 48, 989-1036 (2000) |

[45] | Gurtin, ME, A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations, J Mech Phys Solids, 50, 5-32 (2002) |

[46] | Arsenlis, A.; Parks, DM; Becker, R.; Bulatov, VV, On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals, J Mech Phys Solids, 52, 1213-1246 (2004) |

[47] | Bayley, CJ; Brekelmans, WAM; Geers, MGD, A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity, Int J Solids Struct, 43, 7268-7286 (2006) |

[48] | Evers, LP; Brekelmans, WAM; Geers, MGD, Scale dependent crystal plasticity framework with dislocation density and grain boundary effects, Int J Solids Struct, 41, 5209-5230 (2004) |

[49] | Yefimov, S.; Groma, I.; van der Giessen, E., A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations, J Mech Phys Solids, 52, 279-300 (2004) |

[50] | Yalçinkaya, T.; Özdemir, I.; Firat, AO, Three dimensional grain boundary modeling in polycrystalline plasticity, AIP Conf Proc, 1960, 170019 (2018) |

[51] | Huang Y (1991) A user-material subroutine incorporating single crystal plasticity in the abaqus finite element program: mech. report 178. Technical Report, Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts |

[52] | Kysar JW (1997) Addendum to a user-material subroutine incorporating single crystal plasticity in the abaqus finite element program: mech. report 178. Technical Report, Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts |

[53] | Acharya, A.; Bassani, JL, Lattice incompatibility and a gradient theory of crystal plasticity, J Mech Phys Solids, 48, 156-1595 (2000) |

[54] | Dunne, FPE; Rugg, D.; Walker, A., Lengthscale-dependent, elastically anisotropic, physically-based hcp crystal plasticity: Application to cold-dwell fatigue in ti alloys, Int J Plast, 23, 1061-1083 (2007) |

[55] | Han, CS; Gao, H.; Huang, Y.; Nix, WD, Mechanism-based strain gradient crystal plasticity-i. theory, J Mech Phys Solids, 53, 1188-1203 (2005) |

[56] | Han, CS; Gao, H.; Huang, Y.; Nix, WD, Mechanism-based strain gradient crystal plasticity-ii. analysis, J Mech Phys Solids, 53, 1204-1222 (2005) |

[57] | Borg, U., A strain gradient crystal plasticity analysis of grain size effects in polycrystals, Eur J Mech A Solid, 26, 313-324 (2007) |

[58] | Klusemann, B.; Yalçinkaya, T.; Geers, MGD; Svendsen, B., Application of non-convex rate dependent gradient plasticity to the modeling and simulation of inelastic microstructure development and inhomogeneous material behavior, Comput Mater Sci, 80, 51-60 (2013) |

[59] | Bargmann, S.; Ekh, M.; Runesson, K.; Svendsen, B., Modeling of polycrystals with gradient crystal plasticity: a comparison of strategies, Philos Mag, 90, 1263-1288 (2010) |

[60] | Bittencourt, E.; Needleman, A.; Gurtin, ME; Van der Giessen, E., A comparison of nonlocal continuum and discrete dislocation plasticity predictions, J Mech Phys Solids, 51, 281-310 (2003) |

[61] | Ekh, M.; Grymer, M.; Runesson, K.; Svedberg, T., Gradient crystal plasticity as part of the computational modelling of polycrystals, Int J Numer Methods Eng, 72, 197-220 (2007) |

[62] | Okumura, D.; Higashi, Y.; Sumida, K.; Ohno, N., A homogenization theory of strain gradient single crystal plasticity and its finite element discretization, Int J Plast, 23, 1148-1166 (2007) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.