Skip to main content

From Single Crystal to Polycrystal Plasticity: Overview of Main Approaches

  • Reference work entry
  • First Online:
Handbook of Damage Mechanics
  • 5361 Accesses

Abstract

This chapter provides a brief overview of the different continuum mechanics approaches used to describe the deformation behavior of either single crystals or individual grains in polycrystalline metallic materials. The crucial role that physics-based crystal plasticity approaches may play in understanding the mechanisms of damage initiation and growth is addressed. This includes a discussion of the main strain gradient constitutive approaches used to describe size effects in crystalline solids. Finally, representative examples are given about the effect of the local stress and strain fields in the mechanisms of intergranular damage initiation and growth in FCC polycrystal materials.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 649.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • G. Abrivard, E.P. Busso, S. Forest, B. Appolaire, Phase field modelling of grain boundary motion driven by curvature and stored energy gradient. Part I – theory and numerical implementation. Philos. Mag. 92(28–30), 3618–3642 (2012)

    Article  Google Scholar 

  • A. Acharya, J.L. Bassani, Lattice incompatibility and a gradient theory of crystal plasticity. J. Mech. Phys. Solids 48, 1565–1595 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • A. Acharya, A.J. Beaudoin, Grain size effects in viscoplastic polycrystals at moderate strains. J. Mech. Phys. Solids 48, 2213–2230 (2000)

    Article  MATH  Google Scholar 

  • E.C. Aifantis, On the microstructural origin of certain inelastic models. J. Eng. Mater. Technol. 106, 326–330 (1984)

    Article  Google Scholar 

  • E.C. Aifantis, The physics of plastic deformation. Int. J. Plast. 3, 211–248 (1987)

    Article  MATH  Google Scholar 

  • L. Anand, M. Kothari, A computational procedure for rate independent crystal plasticity. J. Mech. Phys. Solids 44, 525–558 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • A. Arsenlis, D. Parks, Modeling the evolution of crystallographic dislocation density in crystal plasticity. J. Mech. Phys. Solids 50, 1979–2009 (2001)

    Article  Google Scholar 

  • R.J. Asaro, J.R. Rice, Strain localization in ductile single crystals. J. Mech. Phys. Solids 25, 309–338 (1977)

    Article  MATH  Google Scholar 

  • D.J. Bammann, A model of crystal plasticity containing a natural length scale. Mater. Sci. Eng. A 309–310, 406–410 (2001)

    Article  Google Scholar 

  • J.L. Bassani, Incompatibility and a simple gradient theory of plasticity. J. Mech. Phys. Solids 49, 1983–1996 (2001)

    Article  MATH  Google Scholar 

  • E. Bittencourt, A. Needleman, M. Gurtin, E. Van der Giessen, A comparison of nonlocal continuum and discrete dislocation plasticity predictions. J. Mech. Phys. Solids 51(2), 281–310 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • E.P. Busso, G. Cailletaud, On the selection of active slip systems in crystal plasticity. Int. J. Plast. 21, 2212–2231 (2005)

    Article  MATH  Google Scholar 

  • E.P. Busso, F. McClintock, A dislocation mechanics-based crystallographic model of a B2-type intermetallic alloy. Int. J. Plast. 12, 1–28 (1996)

    Article  Google Scholar 

  • E.P. Busso, F.T. Meissonnier, N.P. O’Dowd, Gradient-dependent deformation of two-phase single crystals. J. Mech. Phys. Solids 48, 2333–2361 (2000)

    Article  MATH  Google Scholar 

  • K.S. Cheong, E.P. Busso, Discrete dislocation density modelling of single phase FCC polycrystal aggregates. Acta Mater. 52, 5665–5675 (2004)

    Article  Google Scholar 

  • K.S. Cheong, E.P. Busso, Effects of lattice misorientations on strain heterogeneities in FCC polycrystals. J. Mech. Phys. Solids 54(4), 671–689 (2006)

    Article  MATH  Google Scholar 

  • K. Cheong, E. Busso, A. Arsenlis, A study of microstructural length scale effects on the behavior of FCC polycrystals using strain gradient concepts. Int. J. Plast. 21, 1797–1814 (2004)

    Article  Google Scholar 

  • J.D. Clayton, D.L. McDowell, D.J. Bammann, Modeling dislocations and disclinations with finite micropolar elastoplasticity. Int. J. Plast. 22, 210–256 (2006)

    Article  MATH  Google Scholar 

  • N.M. Cordero, A. Gaubert, S. Forest, E.P. Busso, F. Gallerneau, S. Kruch, Size effects in generalised continuum crystal plasticity for two-phase laminates. J. Mech. Phys. Solids 58, 1963–1994 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • N.M. Cordero, S. Forest, E.P. Busso, S. Berbenni, M. Cherkaoui, Grain size effects on plastic strain and dislocation density tensor fields in metal polycrystals. Comput. Mater. Sci. 52, 7–13 (2012a)

    Article  Google Scholar 

  • N.M. Cordero, S. Forest, E.P. Busso, Generalised continuum modelling of grain size effects in polycrystals. Comptes Rendus Mécanique 340, 261–264 (2012b)

    Article  Google Scholar 

  • M.A. Crisfield, Non-linear Finite Element Analysis of Solids and Structures, vols. 1 & 2, 4th edn. (Wiley, New York, 1997)

    Google Scholar 

  • D.N. Duhl, Directionally solidified superalloys, in Superalloys II – High Temperature Materials for Aerospace and Industrial Power, ed. by C.T. Sims, N.S. Stoloff, W.C. Hagel (Wiley, Toronto, 1987), pp. 189–214

    Google Scholar 

  • F.P.E. Dunne, D. Rugg, A. Walker, Length scale-dependent, elastically anisotropic, physically-based hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys. Int. J. Plast. 23, 1061–1083 (2007)

    Article  MATH  Google Scholar 

  • F.P.E. Dunne, R. Kiwanuka, A.J. Wilkinson, Crystal plasticity analysis of micro-deformation, lattice rotation and geometrically necessary dislocation density. Proc. R. Soc. A-Math. Phys. Eng. Sci. 468, 2509–2531 (2012)

    Article  Google Scholar 

  • A.C. Eringen, W.D. Claus, A micromorphic approach to dislocation theory and its relation to several existing theories, in Fundamental Aspects of Dislocation Theory, ed. by J.A. Simmons, R. de Wit, R. Bullough. National bureau of standards (US) special publication 317, II, 1970, pp. 1023–1062

    Google Scholar 

  • N.A. Fleck, J.W. Hutchinson, Strain gradient plasticity. Adv. Appl. Mech. 33, 295–361 (1997)

    Article  Google Scholar 

  • S. Forest, R. Sedlacek, Plastic slip distribution in two-phase laminate microstructures: dislocation-based vs. generalized-continuum approaches. Philos. Mag. A 83, 245–276 (2003)

    Article  Google Scholar 

  • S. Forest, F. Pradel, K. Sab, Asymptotic analysis of heterogeneous Cosserat media. Int. J. Solids Struct. 38, 4585–4608 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • N.M. Ghoniem, E.P. Busso, H. Huang, N. Kioussis, Multiscale modelling of nanomechanics and micromechanics: an overview. Philos. Mag. 83, 3475–3528 (2003)

    Article  Google Scholar 

  • M.E. Gurtin, A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50, 5–32 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • M.E. Gurtin, L. Anand, Thermodynamics applied to gradient theories involving the accumulated plastic strain: the theories of Aifantis and Fleck & Hutchinson and their generalization. J. Mech. Phys. Solids 57, 405–421 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • T.M. Hatem, M.A. Zikry, Dislocation density crystalline plasticity modeling of lath martensitic microstructures in steel alloys. Philos. Mag. 89(33), 3087–3109 (2009)

    Article  Google Scholar 

  • R. Hill, The Mathematical Theory of Plasticity, 4th edn. (Clarendon, Oxford, UK, 1950)

    MATH  Google Scholar 

  • N. Huber, C. Tsakmakis, Determination of constitutive properties from spherical indentation data using neural networks. Part II: plasticity with nonlinear isotropic and kinematic hardening. J. Mech. Phys. Solids 47, 1589–1607 (1999)

    Article  Google Scholar 

  • A. Hunter, M. Koslowski, Direct calculations of material parameters for gradient plasticity. J. Mech. Phys. Solids 56(11), 3181–3190 (2008)

    Article  MATH  Google Scholar 

  • S. Kalidindi, C. Bronkhorst, L. Anand, Crystallographic texture theory in bulk deformation processing of fcc metals. J. Mech. Phys. Solids 40, 537 (1992)

    Article  Google Scholar 

  • J.W. Kysar, Y. Saito, M.S. Oztop, D. Lee, W.T. Huh, Experimental lower bounds on geometrically necessary dislocation density. Int. J. Plast. 26(8), 1097–1123 (2010)

    Article  MATH  Google Scholar 

  • F. Meissonnier, E.P. Busso, N.P. O’Dowd, Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains. Int. J. Plast. 17(4), 601–640 (2001)

    Article  MATH  Google Scholar 

  • C.-W. Nan, D. Clarke, The influence of particle size and particle fracture on the elastic–plastic deformation of metal matrix composites. Acta Mater. 44, 3801–3811 (1996)

    Article  Google Scholar 

  • J.F. Nye, Some geometrical relations in dislocated crystals. Acta Metall. 1, 153–162 (1953)

    Article  Google Scholar 

  • B. Peeters, M. Seefeldt, C. Teodosiu, S.R. Kalidindi, P. VanHoutte, E. Aernoudt, Work-hardening/softening behaviour of B.C.C. polycrystals during changing strain paths: I. an integrated model based on substructure and texture evolution, and its prediction of the stress–strain behaviour of an IF steel during two-stage strain paths. Acta Mater. 49, 1607–1619 (2001)

    Article  Google Scholar 

  • E. Pouillier, A.F. Gourgues, D. Tanguy, E.P. Busso, A study of intergranular fracture in an aluminium alloy due to hydrogen embrittlement. Int. J. Plast. 34, 139–153 (2012)

    Article  Google Scholar 

  • G. Saada, Limite élastique et durcissement dessolutions solides. Pont à Mousson 16, 255–269 (1968)

    Google Scholar 

  • F. Schubert, G. Fleury, T. Steinhaus, Modelling of the mechanical behaviour of the SC Alloy CMSX-4 during thermomechanical loading. Model. Simul. Sci. Eng. 8, 947–957 (2000)

    Article  Google Scholar 

  • J.Y. Shu, Scale-dependent deformation of porous single crystals. Int. J. Plast. 14, 1085–1107 (1998)

    Article  MATH  Google Scholar 

  • J.Y. Shu, N.A. Fleck, E. Van der Giessen, and A. Needleman, Boundary layers in constrained plasticflow: com parison of non-local and discrete dislocation plasticity. J. Mech. Phys. Solids 49, 1361–1395 (2001)

    Google Scholar 

  • P. Steinmann, Views on multiplicative elastoplasticity and the continuum theory of dislocations. Int. J. Eng. Sci. 34, 1717–1735 (1996)

    Article  MATH  Google Scholar 

  • B. Svendsen, Continuum thermodynamic models for crystal plasticity including the effects of geometrically-necessary dislocations. J. Mech. Phys. Solids 50, 1297–1329 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Swadener, A. Misra, R. Hoagland, M. Nastasi, A mechanistic description of combined hardening and size effects. Scripta Met. 47, 343–348 (2002)

    Article  Google Scholar 

  • M.A. Zikry, M. Kao, Inelastic microstructural failure mechanisms in crystalline materials with high angle grain boundaries. J. Mech. Phys. Solids V 44(11), 1765–98 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Esteban P. Busso .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media New York

About this entry

Cite this entry

Busso, E.P. (2015). From Single Crystal to Polycrystal Plasticity: Overview of Main Approaches. In: Voyiadjis, G. (eds) Handbook of Damage Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5589-9_7

Download citation

Publish with us

Policies and ethics