Microstructural Behavior and Fracture in Crystalline Materials: Overview

  • Pratheek Shanthraj
  • Mohammed A. Zikry
Reference work entry


A dislocation-density-based multiple-slip crystalline plasticity framework, which accounts for variant morphologies and orientation relationships (ORs) that are uniquely inherent to lath martensitic microstructures, and a dislocation-density grain-boundary (GB) interaction scheme, which is based on dislocation-density transmission and blockage at variant boundaries, are developed and used to predict stress accumulation or relaxation at the variant interfaces. A microstructural failure criterion, which is based on resolving these stresses on martensitic cleavage planes, and specialized finite-element (FE) methodologies using overlapping elements to represent evolving fracture surfaces are used for a detailed analysis of fracture nucleation and intergranular and transgranular crack growth in martensitic steels. The effects of block and packet boundaries are investigated, and the results indicate that the orientation of the cleavage planes in relation to the slip planes and the lath morphology are the dominant factors that characterize specific failure modes. The block and packet sizes along the lath long direction are the key microstructural features that affect toughening mechanisms, such as crack arrest and deflection, and these mechanisms can be used to control the nucleation and propagation of different failure modes.


Slip System Cleavage Plane Martensitic Steel Nominal Strain Active Slip System 
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 from both the US Office of Naval Research Multi-Disciplinary University Research Initiative on Sound and Electromagnetic Interacting Waves under grant number N00014-10-1-0958 and from the Office of Naval Research under grant number10848631 is gratefully acknowledged.


  1. R.J. Asaro, J.R. Rice, Strain localization in ductile single-crystals. J. Mech. Phys. Solids 25, 309–338 (1977)CrossRefMATHGoogle Scholar
  2. M. Ayada, M. Yuga, N. Tsuji, Y. Saito, A. Yoneguti, Effect of vanadium and niobium on restoration behavior after hot deformation in medium carbon spring steels. ISIJ Int. 38, 1022–1031 (1998)CrossRefGoogle Scholar
  3. A.A. Barani, F. Li, P. Romano, D. Ponge, D. Raabe, Design of high-strength steels by microalloying and thermomechanical treatment. Mater. Sci. Eng. A 463, 138–146 (2007)CrossRefGoogle Scholar
  4. M. de Koning, R. Miller, V.V. Bulatov, F. Abraham, Modelling grain-boundary resistance in intergranular slip transmission. Philos. Mag. A 82, 2511–2527 (2002)CrossRefGoogle Scholar
  5. B. Devincre, T. Hoc, L. Kubin, Dislocation mean free paths and strain hardening of crystals. Science 320, 1745–1748 (2008)CrossRefGoogle Scholar
  6. B. Dodd, Y. Bai, Width of adiabatic shear bands. Mater. Sci. Tech. 1, 38–40 (1985)CrossRefGoogle Scholar
  7. P. Franciosi, M. Berveiller, A. Zaoui, Latent hardening in copper and aluminum single-crystals. Acta Metall. 28, 273–283 (1980)CrossRefGoogle Scholar
  8. Z. Guo, C.S. Lee, J.W. Morris, On coherent transformations in steel. Acta Mater. 52, 5511–5518 (2004)CrossRefGoogle Scholar
  9. A. Hansbo, P. Hansbo, A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput. Methods Appl. Mech. Eng. 193, 3523–3540 (2004)MathSciNetCrossRefMATHGoogle Scholar
  10. T. Hatem, M.A. Zikry, Shear pipe effects and dynamic shear–strain localization in martensitic steels. Acta Mater. 57, 4558–4567 (2009)CrossRefGoogle Scholar
  11. A.A. Howe, Ultrafine grained steels: industrial prospects. Mater. Sci. Tech. 16, 1264–1266 (2000)CrossRefGoogle Scholar
  12. G.M. Hughes, G.E. Smith, A.G. Crocker, P.E.J. Flewitt, An experimental and modelling study of brittle cleavage crack propagation in transformable ferritic steel. Mater. Sci. Tech. 27, 767–773 (2011)CrossRefGoogle Scholar
  13. T. Inoue, S. Matsuda, Y. Okamura, K. Aoki, Fracture of a low carbon tempered martensite. Trans. Jpn. Inst. Metals 11, 36–43 (1970)CrossRefGoogle Scholar
  14. S. Jin, J.W. Morris, V.F. Zackay, Grain refinement through thermal cycling in an Fe–Ni–Ti cryogenic alloy. Met Trans. 6A, 141–149 (1975)CrossRefGoogle Scholar
  15. H. Kawata, K. Sakamoto, T. Moritani, S. Morito, T. Furuhara, T. Maki, Crystallography of ausformed upper bainite structure in Fe–9Ni–C alloys. Mater. Sci. Eng. A 438, 140–144 (2006)CrossRefGoogle Scholar
  16. H.J. Kim, Y.H. Kim, J.W. Morris, Thermal mechanisms of grain and packet refinement in a lath martensitic steel. ISIJ Int. 38, 1277–1285 (1998)CrossRefGoogle Scholar
  17. Y. Kimura, T. Inoue, F. Yin, K. Tsuzaki, Inverse temperature dependence of toughness in an ultrafine grain-structure steel. Science 320, 1057–1060 (2008)CrossRefGoogle Scholar
  18. G. Krauss, Martensite in steel: strength and structure. Mater. Sci. Eng. A 273–275, 40–57 (1999)CrossRefGoogle Scholar
  19. L. Kubin, B. Devincre, T. Hoc, Towards a physical model for strain hardening in fcc crystals. Mater. Sci. Eng. A 483–484, 19–24 (2008a)CrossRefGoogle Scholar
  20. L. Kubin, B. Devincre, T. Hoc, Modeling dislocation storage rates and mean free paths in face-centered cubic crystals. Acta Mater. 56, 6040–6049 (2008b)CrossRefGoogle Scholar
  21. T.C. Lee, I.M. Robertson, H.K. Birnbaim, An in situ transmission electron-microscope deformation study of the slip transfer mechanisms in metals. Metall. Trans. A 21, 2437–2447 (1990)CrossRefGoogle Scholar
  22. A. Ma, F. Roter, D. Raabe, Studying the effect of grain boundaries in dislocation density based crystal-plasticity finite element simulations. Int. J. Solids Struct. 43, 7287–7303 (2006)CrossRefMATHGoogle Scholar
  23. R. Madec, L.P. Kubin, Second order junctions and strain hardening in bcc and fcc crystals. Scripta Mater. 58, 767–770 (2008)CrossRefGoogle Scholar
  24. T. Maki, K. Tsuzaki, I. Tamura, The morphology of microstructure composed of lath martensites in steels. Trans. Iron Steel Inst. Jpn. 20, 207 (1980)Google Scholar
  25. S. Matsuda, Y. Okamura, T. Inoue, H. Mimura, Toughness and effective grain-size in heat-treated low-alloy high-strength steels. Trans. Iron Steel Inst. Jpn. 12, 325–333 (1972)Google Scholar
  26. K. Minaar, M. Zhou, An analysis of the dynamic shear failure resistance of structural metals. J. Mech. Phys. Solids 46, 2155–2170 (1998)CrossRefGoogle Scholar
  27. S. Morito, H. Tanaka, R. Konoshi, T. Furuhara, T. Maki, The morphology and crystallography of lath martensite in Fe–C alloys. Acta Mater. 51, 1789–1799 (2003)CrossRefGoogle Scholar
  28. S. Morito, X. Huang, T. Furuhara, T. Maki, N. Hansen, The morphology and crystallography of lath martensite in alloy steels. Acta Mater. 54, 5323–5331 (2006)CrossRefGoogle Scholar
  29. J.W. Morris, On the ductile–brittle transition in lath martensitic steel. ISIJ Int. 51, 1569–1575 (2011)CrossRefGoogle Scholar
  30. J.W. Morris, Z. Guo, C.R. Krenn, Y.H. Kim, The limits of strength and toughness in steel. ISIJ Int. 41, 599–611 (2011)CrossRefGoogle Scholar
  31. T. Ohmura, K. Tsuzaki, Plasticity initiation and subsequent deformation behavior in the vicinity of single grain boundary investigated through nanoindentation technique. J. Mater. Res. 42, 1728–1732 (2007)Google Scholar
  32. T. Ohmura, A.M. Minor, E.A. Starch, J.W. Morris, Dislocation-grain boundary interactions in martensitic steel observed through in situ nanoindentation in a transmission electron microscope. J. Mater. Res. 12, 3626–3632 (2004)CrossRefGoogle Scholar
  33. S. Queyreau, G. Monnet, B. Devincre, Slip systems interactions in alpha-iron determined by dislocation dynamics simulations. Int. J. Plast. 25, 361–377 (2009)CrossRefMATHGoogle Scholar
  34. P. Shanthraj, M.A. Zikry, Dislocation density evolution and interactions in crystalline materials. Acta Mater. 59, 7695–7702 (2011)CrossRefGoogle Scholar
  35. P. Shanthraj, M.A. Zikry, Dislocation-density mechanisms for void interactions in crystalline materials. Int. J. Plast. 34, 154–163 (2012a)CrossRefGoogle Scholar
  36. P. Shanthraj, M.A. Zikry, Optimal microstructures for martensitic steels. J. Mater. Res. 27, 1598–1611 (2012b)CrossRefGoogle Scholar
  37. A. Shibata, T. Nagoshi, M. Sone, S. Morito, Y. Higo, Evaluation of the block boundary and sub-block boundary strengths of ferrous lath martensite using a micro-bending test. Mater. Sci. Eng. A 29, 7538–7544 (2010)CrossRefGoogle Scholar
  38. R. Song, D. Ponge, D. Raabe, Mechanical properties of an ultrafine grained C–Mn steel processed by warm deformation and annealing. Acta Mater. 53, 4881–4892 (2005)CrossRefGoogle Scholar
  39. J.H. Song, M.A. Areias Pedro, T. Belytschko, A method for dynamic crack and shear band propagation with phantom nodes. Int. J. Numer. Methods Eng. 67, 868–893 (2006)CrossRefMATHGoogle Scholar
  40. S. Takaki, K. Kawasaki, Y. Kimura, Mechanical properties of ultra fine grains steels. J. Mater. Process. Technol. 117, 359–363 (2001)CrossRefGoogle Scholar
  41. N. Tsuji, Y. Ito, Y. Saito, Y. Minamino, Strength and ductility of ultrafine grained aluminum and iron produced by ARB and annealing. Scripta Mater. 47, 893–899 (2002)CrossRefGoogle Scholar
  42. N. Tsuji, Y. Ito, Y. Saito, Y. Minamino, Toughness of ultrafine grained ferritic steels fabricated by ARB and annealing process. Mater. Trans. 45, 2272–2281 (2004)CrossRefGoogle Scholar
  43. N. Tsuji, N. Kamikawa, R. Ueji, N. Takata, H. Koyama, D. Terada, Managing both strength and ductility in ultrafine grained steels. ISIJ int. 48, 1114–1121 (2008)CrossRefGoogle Scholar
  44. M.A. Zikry, An accurate and stable algorithm for high strain-rate finite strain plasticity. Comput. Struct. 50, 337–350 (1994)CrossRefMATHGoogle Scholar
  45. M.A. Zikry, M. Kao, Inelastic microstructural failure mechanisms in crystalline materials with high angle grain boundaries. J. Mech. Phys. Solids 44, 1765–1798 (1996)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringNorth Carolina State UniversityRaleighUSA
  2. 2.Department of Microstructure–Physics and Alloy DesignMax Planck Institut ür EisenforschungDüsseldorfGermany

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