The response of polycrystals to plastic deformation is studied at the level of variations within individual grains, and comparisons are made to theoretical calculations using crystal plasticity (CP). We provide a brief overview of CP and a review of the literature, which is dominated by surface observations. The motivating question asks how well does CP represent the mesoscale behavior of large populations of dislocations (as carriers of plastic strain). The literature shows consistently that only moderate agreement is found between experiment and calculation. We supplement this with a current example of microstructure evolution in the interior of a copper sample subjected to tensile deformation. Nondestructive measurements of orientation fields were performed using the near-field high-energy X-ray diffraction microscopy (nf-HEDM) technique at the Advanced Photon Source (APS). Starting at highly ordered grains, a single two-dimensional slice of microstructure containing ∼150 grains was followed through multiple strain states, where it tracked lattice rotations and defect accumulation of up to 14% elongation. In accord with the literature, at the scale of individual grains, comparison of observations with CP models indicates reasonable qualitative agreement but significant variations between simulation and experiment are apparent. The conclusion is that in order to be able to quantify the effects of microstructure on the distributions of slip, orientation change, and damage accumulation, the empirically derived constitutive relations used in continuum-scale simulations need to be improved. Equally important will be the development of large-scale simulations of polycrystals that directly model dislocations.


Article metrics loading...

Loading full text...

Full text loading...


Literature Cited

  1. Hirth JP, Lothe J. 1982. Theory of Dislocations New York: Wiley
  2. Xiang Y, Srolovitz DJ, Cheng LT, Weinan E. 2004. Acta Mater. 52:1745–60
  3. Kocks UF, Tomé CN, Wenk H-R. 2000. texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties Cambridge: Cambridge Univ. Press
  4. Kallend JS, Davies GJ. 1972. Philos. Mag. 25:2471–90
  5. Van Houtte P, Kanjarla AK, Van Bael A, Seefeldt M, Delannay L. 2006. Eur. J. Mech. A 25:4634–48
  6. Kocks UF, Argon AS, Ashby MF. 1975. Prog. Mater. Sci. 19:15
  7. Kubin L, Devincre B, Hoc T. 2008. Acta Mater. 56:206040–49
  8. Cottrell AH. 1953. Dislocation and Plastic Flow in Crystals Oxford: Clarendon Press
  9. Hughes DA, Liu Q, Chrzan DC, Hansen N. 1997. Acta Mater. 45:1105–12
  10. LeSar RA. 2013. Annu. Rev. Condens. Matter Phys In press
  11. Acharya A. 2011. J. Elast. 104:1–223–44
  12. Groma I. 2010. Multiscale Modelling of Plasticity and Fracture by Means of Dislocation Mechanics Vol. 522 Pippan R, Gumbsch P. 213–70 Vienna: Springer
  13. Zaiser M, Hochrainer T. 2006. Scr. Mater. 54:5717–21
  14. Crabtree GW, Sarrao JL. 2012. From Quanta to the Continuum: Opportunities for Mesoscale Science BESAC Tech. Rep. LAUR 13-26447. Washington, DC: US Dep. Energy
  15. Crabtree GW, Sarrao JL. 2012. Mater. Res. Soc. Bull. 37:107988
  16. Lei L, Marin JL, Koslowski M. 2013. Model. Simul. Mater. Sci. Eng. 21:2025009
  17. Li SF, Lind J, Hefferan CM, Pokharel R, Lienert U, Rollett AD, Suter RM. 2012. J. Appl. Crystallogr. 45:61098108
  18. Lebensohn RA. 2001. Acta Mater. 49:142723–37
  19. Lebensohn RA, Brenner R, Castelnau O, Rollett AD. 2008. Acta Mater. 56:153914–26
  20. Pokharel R, Li SF, Lind J, Hefferan CM, Lienert U et al. 2012. Mater. Sci. Forum 702:51518
  21. Taylor GI. 1938. J. Inst. Met. 62:307–24
  22. Rollett AD. 2013. Encyclopedia of Physical Metallurgy Laughlin DE. New York: Elsevier, 5th ed..
  23. Field JE, Bourne NK, Palmer SJP, Walley SM, Smallwood JM. 1992. Philos. Trans. R. Soc. A 339:1654269–83
  24. Miller PJ, Coffey CS, DeVost VF. 1986. J. Appl. Phys. 59:391316
  25. Papazian JM, Anagnostou EL, Engel SJ, Hoitsma D, Madsen J et al. 2009. Eng. Fract. Mech. 76:620–32
  26. da Vinci L. 1881–1891. Institut de France 3:40
  27. Bazant ZP. 1998. Fract. Mech. Concr. Struct. 3:1905–22
  28. Epstein B. 1948. J. Am. Stat. Assoc. 43:243403–12
  29. Freudenthal AM, Gumbel EJ. 1954. J. Am. Stat. Assoc. 49:267575–97
  30. Murakami Y, Beretta S. 1999. Extremes 2:2123–47
  31. Przystupa MA, Bucci RJ, Magnusen PE, Hinkle AJ. 1997. Int. J. Fatigue 19:9328588
  32. Przybyla CP, McDowell DL. 2012. Acta Mater. 60:1293–305
  33. Groh S, Zbib HM. 2009. J. Eng. Mater. Technol. 131:041209
  34. Deshpande VS, Needleman A, Van der Giessen E. 2003. Acta Mater. 51:11–15
  35. Brinckmann S, Van der Giessen E. 2007. Int. J. Fract. 148:2155–67
  36. Barbe F, Decker L, Jeulin D, Cailletaud G. 2001. Int. J. Plast. 17:4513–36
  37. Barbe F, Forest S, Cailletaud G. 2001. Int. J. Plast. 17:4537–63
  38. Diard O, Leclereq S, Rousselier G, Cailletaud G. 2005. Int. J. Plast. 21:4691–722
  39. Kanit T, Forest S, Galliet I, Mounoury V, Jeulin D. 2003. Int. J. Solids Struct. 40:13–143647–79
  40. Lewis AC, Suh C, Stukowski M, Geltmacher AB, Rajan K, Spanos G. 2008. Scr. Mater. 58:7575–78
  41. Rollett AD, Lebensohn RA, Groeber M, Choi Y, Li J, Rohrer GS. 2010. Model. Simul. Mater. Sci. Eng. 18:7074005
  42. Peirce D, Asaro RJ, Needleman A. 1982. Acta Metall. 30:61087–119
  43. Asaro RJ, Needleman A. 1985. Acta Metall. 33:6923–53
  44. Canova GR, Kocks UF, Jonas JJ. 1984. Acta Metall. 32:2211–26
  45. Bertin N, Capolungo L, Beyerlein IJ. 2013. Int. J. Plast. 49:119–44
  46. Tomé CN, Lebensohn RA. 2004. Continuum Scale Simulation of Engineering Materials: Fundamentals-Microstructures-Process Applications, ed. D Raabe, F Roters, F Barlat, L-Q Chen, pp. 473–499. Weinheim, Ger.: Wiley-VCH
  47. Franciosi P. 1985. Acta Metall. 33:91601–12
  48. Roters F, Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR, Raabe D. 2010. Acta Mater. 58:41152–211
  49. Kocks UF. 1987. Unified Constitutive Equations for Creep and Plasticity Miller AK. 188 New York: Elsevier
  50. Winther G, Margulies L, Schmidt S, Poulsen HF. 2004. Acta Mater. 52:102863–72
  51. Bishop JFW, Hill R. 1951. Philos. Mag. 42:327414–27
  52. Moulinec H, Suquet P. 1998. Comput. Methods Appl. Mech. Eng. 157:169–94
  53. Moulinec H, Suquet P. 2003. Phys. B 338:158–60
  54. Lebensohn RA, Kanjarla AK, Eisenlohr P. 2012. Int. J. Plast. 32:59–69
  55. Liu B, Raabe D, Roters F, Eisenlohr P, Lebensohn RA. 2010. Model. Simul. Mater. Sci. Eng. 18:8085005
  56. Allais L, Bornert M, Bretheau T, Caldemaison D. 1994. Acta Metall. Mater. 42:113865–80
  57. Kammers AD, Daly S. 2011. Meas. Sci. Technol. 22:12125501
  58. Raabe D, Sachtleber M, Zhao Z, Roters F, Zaefferer S. 2001. Acta Mater. 49:173433–41
  59. Schwartz AJ. 2009. Electron Backscatter Diffraction in Materials Science Dordrecht, Neth.: Kluwer Acad. Publ.
  60. Allain-Bonasso N, Wagner F, Berbenni S, Field DP. 2012. Mater. Sci. Eng. A 548:56–63
  61. Poulsen HF. 2004. Three-Dimensional X-Ray Diffraction Microscopy: Mapping Polycrystals and Their Dynamics Vol. 205 Berlin: Springer-Verlag
  62. Poulsen HF, Nielsen SF, Lauridsen EM, Søren Schmidt, Suter RM et al. 2001. J. Appl. Cryst. 34:6751–56
  63. Poulsen HF, Schmidt S. 2003. J. Appl. Cryst. 36:2319–25
  64. Ludwig W, Reischig P, King A, Herbig M, Lauridsen EM et al. 2009. Rev. Sci. Instrum. 80:3033905
  65. Bernier JV, Barton NR, Lienert U, Miller MP. 2011. J. Strain Anal. Eng. Des. 46:7527–47
  66. Hefferan CM, Li SF, Lind J, Lienert U, Rollett AD, Suter RM. Mater. Sci. Forum 715447–454
  67. Juul Jensen D, Schmidt S. 2009. Mater. Trans. 50:71655
  68. Oddershede J, Schmidt S, Poulsen HF, Sorensen HO, Wright J, Reimers W. 2010. J. Appl. Cryst. 43:3539–49
  69. Suter RM, Hennessy D, Xiao C, Lienert U. 2006. Rev. Sci. Instrum. 77:12123905
  70. Suter RM, Hefferan CM, Li SF, Hennessy D, Xiao C et al. 2008. J. Eng. Mater. Technol. 130:021007
  71. Li SF, Suter RM. 2013. J. Appl. Cryst. 46:2512–24
  72. Field DP, Magid KR, Mastorakos IN, Florando JN, Lassila DH, Morris JW Jr. 2010. Philos. Mag. 90:111451–64
  73. Hefferan CM, Lind J, Li SF, Lienert U, Rollett AD, Suter RM. 2012. Acta Mater. 60:104311–18
  74. Bart-Smith H, Bastawros A-F, Mumm DR, Evans AG, Sypeck DJ, Wadley HNG. 1998. Acta Mater. 46:103583–92
  75. Tong W. 1997. Exp. Mech. 37:4452–59
  76. Tatschl A, Kolednik O. 2003. Mater. Sci. Eng. A 339:1265–80
  77. Becker R, Panchanadeeswaran S. 1995. Acta Metall. Mater. 43:2701–19
  78. Panchanadeeswaran S, Doherty RD, Becker R. 1996. Acta Mater. 44:31233–62
  79. Lineau C, Rey C, Viaris de Lesegno P. 1997. Mater. Sci. Eng. A 234:853–56
  80. Delaire F, Raphanel JL, Rey C. 2000. Acta Mater. 48:51075–87
  81. Hoc T, Rey C. 2000. Scr. Mater. 42:111053–58
  82. Tatschl A, Kolednik O. 2003. Mater. Sci. Eng. A 356:1447–63
  83. Cheong K-S, Busso EP. 2006. J. Mech. Phys. Solids 54:4671–89
  84. Zhao Z, Ramesh M, Raabe D, Cuitino AM, Radovitzky R. 2008. Int. J. Plast. 24:122278–97
  85. Buchheit TE, Wellman GW, Battaile CC. 2005. Int. J. Plast. 21:2221–49
  86. Rehrl C, Völker B, Kleber S, Antretter T, Pippan R. 2012. Acta Mater. 60:52379–86
  87. Wu T-Y, Bassani JL, Laird C. 1991. Proc. R. Soc. A 435(1893):1–19
  88. Bassani JL, Wu T-Y. 1991. Proc. R. Soc. A 435(1893):21–41
  89. Turner TJ, Shade PA, Schuren JC, Groeber MA. 2013. Model. Simul. Mater. Sci. Eng. 21:1015002
  90. Zaefferer S, Kuo JC, Zhao Z, Winning M, Raabe D. 2003. Acta Mater. 51:164719–35
  91. Ma A, Roters F, Raabe D. 2006. Acta Mater. 54:82181–94
  92. Ma A, Roters F, Raabe D. 2006. Acta Mater. 54:82169–79
  93. Quey R, Dawson PR, Driver JH. 2012. J. Mech. Phys. Solids 60:3509–24
  94. Wang L, Barabash RI, Yang Y, Bieler TR, Crimp MA et al. 2011. Metall. Mater. Trans. A 42:3626–35
  95. Ice GE, Larson BC. 2000. Adv. Eng. Mater. 2:10643–46
  96. Sarma GB, Dawson PR. 1996. Acta Mater. 44:51937–53
  97. Lienert U, Han T-S, Almer J, Dawson PR, Leffers T et al. 2004. Acta Mater. 52:154461–67
  98. Miller MP, Park JS, Dawson PR, Han TS. 2008. Acta Mater. 56:153927–39
  99. Lind J. 2013. In-situ high-energy diffration mirosopy study of zironium under uniaxial tensile deformation. PhD thesis, Carnegie Mellon Univ., Pittsburgh, PA
  100. Pokharel R. 2013. Spatially resolved in-situ study of plastic deformation in polycrystalline copper using high-energy X-rays and full-field simulations. PhD thesis, Carnegie Mellon Univ., Pittsburgh, PA
  101. Lienert U, Li SF, Hefferan CM, Lind J, Suter RM et al. 2011. J. Miner. Met. Mater. Soc. 63:770–77
  102. Christodoulou N, Jonas JJ. 1984. Acta Metall. 32:1655–68
  103. Hefferan CM, Li SF, Lind J, Lienert U, Rollett AD et al. 2010. Comput. Mater. Contin. 14:3209–20
  104. Hefferan CM, Li SF, Lienert U, Suter RM. 2009. Bull. Am. Phys. Soc. 54:1
  105. Cho JH, Rollett AD, Oh KH. 2004. Metall. Mater. Trans. A 35:31075–86
  106. Winther G. 2008. Acta Mater. 56:91919–32
  107. Padilla HA, Smith CD, Lambros J, Beaudoin AJ, Robertson IM. 2007. Metall. Mater. Trans. A 38:122916–27
  108. Margulies L, Winther G, Poulsen HF. 2001. Science 291:55122392–94
  109. Turner TJ, Semiatin SL. 2011. Model. Simul. Mater. Sci. Eng. 19:065010
  110. Jiang J, Britton TB, Wilkinson AJ. 2012. Ultramicroscopy 125:1–9
  111. Kanjarla AK, Delannay L, Van Houtte P. 2011. Metall. Mater. Trans. A 42:3660–68
  112. Warren BE. 1969. X-Ray Diffraction Mineola, NY: Dover Publ.
  113. Merriman CC, Field DP, Trivedi P. 2008. Mater. Sci. Eng. A 494:1–228–35
  114. Oddershede J, Schmidt S, Poulsen HF, Margulies L, Wright J et al. 2011. Mater. Charact. 62:651–60
  115. Tome C, Canova GR, Kocks UF, Christodoulou N, Jonas JJ. 1984. Acta Metall. 32:1637–53
  116. Kalidindi SR, Bhattacharyya A, Doherty RD. 2004. Proc. R. Soc. A 460:20471935–56
  117. Zeghadi A, N’guyen F, Forest S, Gourgues A-F, Bouaziz O. 2007. Philos. Mag. 87:8–91401–24

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error