Abstract
We review aspects of pattern formation in plastically deformed single crystals, in particular as described in the investigation of a copper single crystal shear experiment in [DDMR09]. In this experiment, the specimen showed a band-like microstructure consisting of alternating crystal orientations. Such a formation of microstructure is often linked to a lack of convexity in the free energy describing the system. The specific parameters of the observed bands, namely the relative crystal orientation as well as the normal direction of the band layering, are thus compared to the predictions of the theory of kinematically compatible microstructure oscillating between low-energy states of the non-convex energy. We conclude that this theory is suitable to describe the experimentally observed band-like structure. Furthermore, we link these findings to the models used in studies of relaxation and evolution of microstructure.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albin, N., Conti, S., Dolzmann, G.: Infinite-order laminates in a model in crystal plasticity. Proc. Roy. Soc. Edinburgh Sect. A 139(4), 685–708 (2009)
Anguige, K., Dondl, P.W.: Relaxation of the single-slip condition in strain-gradient plasticity. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 470(2169) (2014)
Bay, B., Hansen, N., Hughes, D., Kuhlmann-Wilsdorf, D.: Overview no-96 – evolution of FCC deformation structures in polyslip. Acta Metallurgica et Materialia 40(2), 205–219 (1992)
Ball, J.M., James, R.D.: Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal. 100(1), 13–52 (1987)
Conti, S., Dolzmann, G., Klust, C.: Relaxation of a class of variational models in crystal plasticity. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465(2106), 1735–1742 (2009)
Conti, S., Dolzmann, G., Kreisbeck, C.: Asymptotic behavior of crystal plasticity with one slip system in the limit of rigid elasticity. SIAM J. Math. Anal. 43(5), 2337–2353 (2011)
Conti, S., Dolzmann, G., Kreisbeck, C.: Relaxation and microstructure in a model for finite crystal plasticity with one slip system in three dimensions. Discrete Contin. Dyn. Syst. Ser. S 6(1), 1–16 (2013)
Conti, S., Dolzmann, G., Kreisbeck, C.: Relaxation of a model in finite plasticity with two slip systems. Math. Models Methods Appl. Sci. 23(11), 2111–2128 (2013)
Cermelli, P., Gurtin, M.E.: On the characterization of geometrically necessary dislocations in finite plasticity. Journal of the Mechanics and Physics of Solids 49(7), 1539–1568 (2001)
Dmitrieva, O., Dondl, P.W., Müller, S., Raabe, D.: Lamination microstructure in shear deformed copper single crystals. Acta Materialia 57(12), 3439–3449 (2009)
Dmitrieva, O., Svirina, J.V., Demir, E., Raabe, D.: Investigation of the internal substructure of microbands in a deformed copper single crystal: experiments and dislocation dynamics simulation. Modelling and Simulation in Materials Science and Engineering 18(8) (December 2010)
Hansen, N.: Cold deformation microstructures. Materials Science and Technology 6(11), 1039–1047 (1990)
Hansen, B.L., Bronkhorst, C.A., Ortiz, M.: Dislocation subgrain structures and modeling the plastic hardening of metallic single crystals. Modelling and Simulation in Materials Science and Engineering 18(5), 055001 (2010)
Hackl, K., Hoppe, U., Kochmann, D.M.: Generation and evolution of inelastic microstructures—an overview. GAMM-Mitt. 35(1), 91–106 (2012)
Hackl, K., Kochmann, D.M.: An incremental strategy for modeling laminate microstructures in finite plasticity—energy reduction, laminate orientation and cyclic behavior. In: de Borst, R., Ramm, E. (eds.) Multiscale Methods in Computational Mechanics. LNACM, vol. 55, pp. 117–134. Springer, Heidelberg (2011)
Jin, N., Winter, A.: Dislocation structures in cyclically deformed [001] copper crystals. Acta Metallurgica 32(8), 1173–1176 (1984)
Kochmann, D.M., Hackl, K.: The evolution of laminates in finite crystal plasticity: a variational approach. Contin. Mech. Thermodyn. 23(1), 63–85 (2011)
Kondo, K.: On the geometrical and physical foundations of the theory of yielding. In: Proc. 2nd Japan Nat. Congr. Applied Mechanics, pp. 41–47 (1952)
Miehe, C., Rosato, D., Frankenreiter, I.: Fast estimates of evolving orientation microstructures in textured bcc polycrystals at finite plastic strains. Acta Materialia 58(15), 4911–4922 (2010)
Nye, J.F.: Some geometrical relations in dislocated crystals. Acta Metallurgica 1(2), 153–162 (1953)
Ortiz, M., Repetto, E.A.: Nonconvex energy minimization and dislocation structures in ductile single crystals. J. Mech. Phys. Solids 47(2), 397–462 (1999)
Reina, C., Conti, S.: Kinematic description of crystal plasticity in the finite kinematic framework: a micromechanical understanding of F = F e F p. J. Mech. Phys. Solids 67, 40–61 (2014)
Rasmussen, K., Pedersen, O.: Fatigue of copper polycrystals at low plastic strain amplitudes. Acta Metallurgica 28(11), 1467–1478 (1980)
Rodney, D., Phillips, R.: Structure and strength of dislocation junctions: An atomic level analysis. Physical Review Letters 82(8), 1704–1707 (1999)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Dmitrieva, O., Raabe, D., Müller, S., Dondl, P.W. (2015). Microstructure in Plasticity, a Comparison between Theory and Experiment. In: Conti, S., Hackl, K. (eds) Analysis and Computation of Microstructure in Finite Plasticity. Lecture Notes in Applied and Computational Mechanics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-18242-1_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-18242-1_8
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18241-4
Online ISBN: 978-3-319-18242-1
eBook Packages: EngineeringEngineering (R0)