Modeling Heterogeneous Intragrain Deformations Using Finite Element Formulations

  • Paul Dawson
  • Jobie Gerken
  • Tito Marin


Polycrystalline materials exhibit deformation patterns that are heterogeneous both between and within crystals. The deformation heterogeneity within crystals can arise from variations of the crystallographic slip due to spatial variations in the stress driven by interactions among neighboring crystals. Typically, misorientations develop across crystals if the slip is not homogeneous. Furthermore, dislocations may accumulate within crystals, causing lattice distortion (elastic straining) and contributing to the stress. In this chapter, we summarize basic and extended crystal elastoplasticity formulations to address these effects. Finite element methodologies for both formulations are presented and examples of their use are discussed.


Slip System Range Strain Orientation Distribution Function Lattice Orientation Fundamental Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Support for this work has been provided by the Office of Naval Research under contract N00014-06-1-0241. Large scale simulations were conducted at the Cornell Theory Center.


  1. Archarya A, Roy A (2006) Size effects and idealized dislocation microstructure at small scales: Predictions of phenomenological model of mesoscopic field dislocation mechanics: Part i, Journal of the Mechanics and Physics of Solids 54:1687–1710Google Scholar
  2. Ashby MF, Jones DRH (1980) Engineering Materials 1: An Introduction to their properties and applications. PergamonGoogle Scholar
  3. Barton NR, Dawson PR (2001a) A methodology for determining average lattice rotations and its application to the characterization of grain substructure. Metallurgical and Materials Transactions 32A:1967–1975Google Scholar
  4. Barton NR, Dawson PR (2001b) On the spatial arrangement of lattice orientations in hot rolled multiphase titanium. Modeling and Simulation in Materials Science and Engineering 9:433–463Google Scholar
  5. Bunge H (1982) Texture Analysis In Materials Science. Butterworth, LondonGoogle Scholar
  6. Dawson PR, Marin EB (1998) Computational mechanics for metal deformation processes using polycrystal plasticity. In: vander Giessen E, Wu TY (eds) Advances in Applied Mechanics, Academic, vol34, pp 78–169Google Scholar
  7. Dawson PR, Mika DP, Barton NR (2002) Finite element modeling of lattice misorientations in aluminum alloys. Scripta Materialia 47:713–717Google Scholar
  8. Dumoulin S, Tabourot L (2005) Experimental data on aluminium single crystals behaviour. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 219:1159–1167Google Scholar
  9. Frank F (1988) Orientation mapping. In: S KJ, Gottstein G (eds) Eighth International Conference on Textures of Materials, The Metallurgical Society, Warrendale, PA, pp 3–13Google Scholar
  10. Gerken JM, Dawson PR (2007) Bending of a single crystal thin foil material with slip gradient effects. Modeling and Simulation in Materials Science and Engineering 15:799–822Google Scholar
  11. Gerken JM, Dawson PR (2008a) A crystal plasticity model that incorporates stresses and strains due to slip gradients. Journal of the Mechanics and Physics of Solids 56:1651–1672Google Scholar
  12. Gerken JM, Dawson PR (2008b) A finite element formulation to solve a non-local constitutive model with stresses and strains due to slip gradients. Computer Methods in Applied Mechanics and Engineering 197:1343–1361Google Scholar
  13. Guruprasad PJ, Carter WJ, Berzerga AA (2008) A discrete dislocation analysis of the bauschinger effecit in microcrystals. Acta Materialia 56:5477–5491Google Scholar
  14. Hartley CS (2003) A method for linking thermally activated dislocation mechanisms of yielding with continuum plasticity theory. Philosophical Magazine 83:3783–3808Google Scholar
  15. Honeycombe R (1984) The Plastic Deformation of Metals, 2nd edn. Edward ArnoldGoogle Scholar
  16. Hosford WF (1993) The Mechanics of Crystals and Textured Polycrystals. Oxford Science PublicationsGoogle Scholar
  17. Kocks UF, Tome CN, Wenk HR (1998) Texture and Anisotropy. Cambridge University PressGoogle Scholar
  18. Kumar A, Dawson PR (2009) Dynamics of texture evolution in face-centered cubic polycrystals. Journal of the Mechanics and Physics of Solids 57:422–445Google Scholar
  19. Mach JC, Beaudoin AJ, Archarya A (2009) Continuity in the plastic strain rate and its influence on texture evolution submitted for publicationGoogle Scholar
  20. Marin EB, Dawson PR (1998a) Elastoplastic finite element analysis of metal deformations using polycrystal constititive models. Computer Methods in Applied Mechanics and Engineering 165:23–41Google Scholar
  21. Marin EB, Dawson PR (1998b) On modeling the elasto-viscoplastic response of metals using polycrystal plasticity. Computer Methods in Applied Mechanics and Engineering 165:1–21Google Scholar
  22. Marin T (2006) Elastoplasticity in polycrystalline metals: Experiments and computational modeling. PhD thesis, University of Parma (Italy)Google Scholar
  23. Mika DP, Dawson PR (1999) Polycrystal plasticity modeling of intracrystalline boundary textures. Acta Materialia 47(4):1355–1369Google Scholar
  24. Wenk HR (1985) Preferred Oreintations of Deformed Metals and Rocks: An Introduction to Modern Texture Analysis. AcademicGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Sibley School of Mechanical and Aerospace EngineeringCornell UniversityIthacaUSA

Personalised recommendations