Experimental Mechanics

, Volume 59, Issue 5, pp 691–702 | Cite as

Investigation of the Relationship Between Microstructural Features and Strain Localization in Polycrystalline 316 L

  • L. BodelotEmail author


In this paper, strains are monitored in-situ at the surface of a polycrystalline 316 L sample loaded quasi-statically in uniaxial tension. Initial orientation data collected over thousands of grains is compared with the strain data evolution in order to investigate, with statistical significance, the relationship between the microstructural features and the strain localization patterns emerging at the grain scale. It is shown quantitatively that high values of strain appear early and primarily around grain boundaries, before growing into a network spanning several grains and grain boundaries. Strains are also heterogeneous within a grain, with the heterogeneity tending to be more pronounced in larger grains. Statistical analyses demonstrate that the usual microstructural descriptors—such as Taylor factors, average intragranular misorientation angles or intergranular misorientation angles—do not display any correlation with the localization network. Furthermore, higher Schmid factors, albeit exhibiting some weak correlation with higher strains, fail to systematically identify the grains that experience the largest strains. It is thus proposed to analyze three-dimensional descriptors of orientation expressed in the Rodrigues space and they are shown to help readily identify orientations that exhibit high strains early in the loading. Additionally, the study of the full three-dimensional misorientation information, expressed in the reduced Rodrigues space, clearly highlights the fact that some misorientations oppose localization at certain boundaries in the microstructure at hand. Hence, considering the full three-dimensional orientation (and misorientation) data instead of just scalar descriptors is demonstrated to be of great interest when investigating the relationship between microstructural features and strain localization.


EBSD  Mechanical characterization  Digital image correlation Austenitic stainless steel Plasticity  Orientation relationship 



Most of the work presented in this paper was conducted at the Graduate Aerospace Laboratory at the California Institute of Technology (GALCIT, Pasadena, California) and supported by the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613, which is gratefully acknowledged. The author also thanks Professor Sergio Pellegrino at GALCIT for granting access to the Instron machine in his lab, as well as Professors Guruswami Ravichandran and Michael Ortiz for fruitful discussions.

Supplementary material

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  1. 1.
    Taylor GI (1938) Plastic strains in metals. J Inst Met 62:307–324Google Scholar
  2. 2.
    Sachs G (1929) Zur Ableitung einer Fliessbedingung. Mitteilungen der deutschen Materialprüfungsanstalten. Springer, Berlin, Heidelberg
  3. 3.
    Khan AS, Huang S (1995) Continuum theory of plasticity. John Wiley & Sons, New YorkzbMATHGoogle Scholar
  4. 4.
    Asaro RJ (1983) Crystal Plasticity. J Appl Mech 50:921–934. CrossRefzbMATHGoogle Scholar
  5. 5.
    Cuitiño AM, Ortiz M (1992) Computational modelling of single crystals. Modelling Simul Mater Sci Eng 1:225–263. CrossRefGoogle Scholar
  6. 6.
    Barbe F, Descker L, Jeulin D, and Cailletaud G (2001) Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model. Int J Plasticity 17:513–536.
  7. 7.
    Lebensohn RA, Brenner R, Castelnau O, Rollett AD (2008) Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper. Acta Mater 56:3914–3926. CrossRefGoogle Scholar
  8. 8.
    Patra A, McDowell DL (2016) Crystal plasticity investigation of the microstructural factors influencing dislocation channeling in a model irradiated bcc material. Acta Mater 110:364–376. CrossRefGoogle Scholar
  9. 9.
    Abdolvand H, Wright JP, Wilkinson AJ (2018) On the state of deformation in a polycrystalline material in three-dimension: elastic strains, lattice rotations, and deformation mechanisms. Int J Plasticity 106:145–163. CrossRefGoogle Scholar
  10. 10.
    Groeber M, Ghosh S, Uchic MD, Dimiduk DM (2008) A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 1: Statistical characterization. Acta Mater 56:1257–1273. CrossRefGoogle Scholar
  11. 11.
    Groeber M, Ghosh S, Uchic MD, Dimiduk DM (2008) A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 2: Synthetic structure generation. Acta Mater 56:1274–1287. CrossRefGoogle Scholar
  12. 12.
    Qidwai SM, Turner DM, Niezgoda SR, Lewis AC, Geltmacher AB, Rowenhorst DJ, Kalidindi SR (2012) Estimating the response of polycrystalline materials using sets of weighted statistical volume elements. Acta Mater 60:5284–5299. CrossRefGoogle Scholar
  13. 13.
    Knezevic M, Drach B, Ardeljan M, Beyerlein IJ (2014) Three dimensional predictions of grain scale plasticity and grain boundaries using crystal plasticity finite element models. Comput Method Appl M 277:239–259. CrossRefzbMATHGoogle Scholar
  14. 14.
    Delaire F, Raphanel JL, Rey C (2000) Plastic heterogeneities of a copper multicrystal deformed in uniaxial tension: experimental study and finite element simulations. Acta Mater 48:1075–1087. CrossRefGoogle Scholar
  15. 15.
    Sachtleber M, Zhao Z, Raabe D (2002) Experimental investigation of plastic grain interaction. Mat Sci Eng A-Struct 336:81–87. CrossRefGoogle Scholar
  16. 16.
    Héripré E, Dexet M, Crépin J, Gélébart L, Roos A, Bornert M, Caldemaison D (2007) Coupling between experimental measurements and polycrystal finite element calculations for micromechanical study of metallic materials. Int J Plasticity 23:1512–1539. CrossRefzbMATHGoogle Scholar
  17. 17.
    Lewis AC, Jordan KA, Geltmacher AB (2008) Determination of Critical Microstructural Features in an Austenitic Stainless Steel Using Image-Based Finite Element Modeling. Metall Mater Trans A 39:1109–1117. CrossRefGoogle Scholar
  18. 18.
    Guery A, Hild F, Latourte F, Roux S (2016) Slip activities in polycrystals determined by coupling DIC measurements with crystal plasticity calculations. Int J Plasticity 81:249–266. CrossRefGoogle Scholar
  19. 19.
    Zhang N, Tong W (2004) An experimental study on grain deformation and interactions in an Al-0.5%Mg multicrystal. Int J Plasticity 20:523–542. CrossRefzbMATHGoogle Scholar
  20. 20.
    Zhao Z, Ramesh M, Raabe D, Cuitiño AM, Radovitzky R (2008) Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal. Int J Plasticity 24:2278–2297. CrossRefzbMATHGoogle Scholar
  21. 21.
    Di Gioacchino F, Quinta da Fonseca J (2013) Plastic Strain Mapping with Sub-micron Resolution Using Digital Image Correlation. Exp Mech 53:743–754. CrossRefGoogle Scholar
  22. 22.
    Patriarca L, Abuzaid W, Sehitoglu H, Maier HJ (2013) Slip transmission in bcc FeCr polycrystal. Mater Sci Eng A-Struct 588:308–317. CrossRefGoogle Scholar
  23. 23.
    Kammers AD, Daly S (2013) Digital Image Correlation under Scanning Electron Microscopy: Methodology and Validation. Exp Mech 53:1743–1761. CrossRefGoogle Scholar
  24. 24.
    Zhang Z, Lunt D, Abdolvand H, Wilkinson AJ, Preuss M, Dunne FPE (2018) Quantitative investigation of micro slip and localization in polycrystalline materials under uniaxial tension. Int J Plast 108:88–106. CrossRefGoogle Scholar
  25. 25.
    Tschopp MA, Bartha BB, Porter WJ, Murray PT, Fairchild SB (2009) Microstructure-Dependent Local Strain Behavior in Polycrystals through In-Situ Scanning Electron Microscope Tensile Experiments. Metall Mater Trans A 40:2363–2368. CrossRefGoogle Scholar
  26. 26.
    Efstathiou C, Boyce DE, Park JS, Lienert U, Dawson PR, Miller MP (2010) A method for measuring single-crystal elastic moduli using high-energy X-ray diffraction and a crystal-based finite element model. Acta Mater 58:5806–5819. CrossRefGoogle Scholar
  27. 27.
    Abuzaid WZ, Sangid MD, Carroll JD, Sehitoglu H, Lambros J (2012) Slip transfer and plastic strain accumulation across grain boundaries in Hastelloy X. J Mech Phys Solids 60:1201–1220. CrossRefGoogle Scholar
  28. 28.
    Littlewood PD, Wilkinson AJ (2012) Local deformation patterns in Ti-6Al-4V under tensile, fatigue and dwell fatigue loading. Int J Fatigue 43:111–119. CrossRefGoogle Scholar
  29. 29.
    Padilla HA, Lambros J, Beaudoin AJ, Robertson IM (2012) Relating inhomogeneous deformation to local texture in zirconium through grain-scale digital image correlation strain mapping experiments. Int J Solids Structures 49:18–31. CrossRefGoogle Scholar
  30. 30.
    Walley JL, Wheeler R, Uchic MD, Mills MJ (2012) In-Situ Mechanical Testing for Characterizing Strain Localization During Deformation at Elevated Temperatures. Exp Mech 52:405–416. CrossRefGoogle Scholar
  31. 31.
    Carroll JD, Clark BG, Buchheit TE, Boyce BL, Weinberger CR (2013) An experimental statistical analysis of stress projection factors in BCC tantalum. Mater Sci Eng A-Struct 581:108–118. CrossRefGoogle Scholar
  32. 32.
    Carroll JD, Abuzaid W, Lambros J, Sehitoglu H (2013) High resolution digital image correlation measurements of strain accumulation in fatigue crack growth. Int J Fatigue 57:140–150. CrossRefGoogle Scholar
  33. 33.
    Cho H, Bronkhorst CA, Mourad HM, Mayeur JR, Luscher DJ (2018) Anomalous plasticity of body-centered-cubic crystals with non-Schmid effect. Int J Solids Struct 139-140:138–149. CrossRefGoogle Scholar
  34. 34.
    Mishra SK, Pant P, Narasimhan K, Rollett AD, Samajdar I (2009) On the widths of orientation gradient zones adjacent to grain boundaries. Scripta Mater 61:273–276. CrossRefGoogle Scholar
  35. 35.
    Yoda R, Yokomaku T, Tsuji N (2010) Plastic deformation and creep damage evaluations of type 316 austenitic stainless steels by EBSD. Mater Charact 61:913–922. CrossRefGoogle Scholar
  36. 36.
    Allain-Bonasso N, Wagner F, Berbenni S, Field DP (2012) A study of the heterogeneity of plastic deformation in IF steel by EBSD. Mater Sci Eng A-Struct 548:56–63. CrossRefGoogle Scholar
  37. 37.
    Pokharel R, Lind J, Li SF, Kenesei P, Lebensohn RA, Suter RM, Rollett AD (2015) In-situ observation of bulk 3D grain evolution during plastic deformation in polycrystalline Cu. Int J Plasticity 67:217–234. CrossRefGoogle Scholar
  38. 38.
    Oxkford Instruments (2007) HKL Channel 5 ManualGoogle Scholar
  39. 39.
    Bodelot L, Ravichandran G (2014) Experimental determination of a representative texture and insight into the range of significant neighboring grain interactions via orientation and misorientation statistics. Int J Mater Res 105:117–129. CrossRefGoogle Scholar
  40. 40.
    Becker R, Panchanadeeswaran S (1989) Crystal Rotations Represented as Rodrigues Vectors. Texture Microstruct 10:167–194. CrossRefGoogle Scholar
  41. 41.
    Morawiec A, Field DP (1996) Rodrigues Parameterization for Orientation and Misorientation Distributions. Philos Mag A 73:1113–1130. CrossRefGoogle Scholar
  42. 42.
    Sutton MA, Orteu J, Schreier HW (2009) Image Correlation for Shape, Motion and Deformation Measurements. Basic Concepts, Theory and Applications. Springer, New YorkGoogle Scholar
  43. 43.
    Sutton MA, Yan JH, Tiwari V, Schreier HW, Orteu JJ (2008) The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. Opt Laser Eng 46:746–757. CrossRefGoogle Scholar
  44. 44.
    Schreier HW, Braasch JR, Sutton MA (2000) Systematic errors in digital image correlation caused by intensity interpolation. Opt Eng 39:2915–2921. CrossRefGoogle Scholar
  45. 45.
    Hild F, Roux S (2006) Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties - a Review. Strain 42:69–80. CrossRefGoogle Scholar
  46. 46.
    Bornert M, Brémand F, Doumalin P, Dupré J, Fazzini M, Grédiac M, Hild F, Mistou S, Molimard J, Orteu J, Robert L, Surrel Y, Vacher P, Wattrisse B (2009) Assessment of Digital Image Correlation Measurement Errors: Methodology and Results. Exp Mech 49:353–370. CrossRefGoogle Scholar
  47. 47.
    Doquet V, Barkia B (2016) Combined AFM, SEM and crystal plasticity analysis of grain boundary sliding in titanium at room temperature. Mech Mater 103:18–27. CrossRefGoogle Scholar
  48. 48.
    Schmid E, Boas W (1950) Plasticity of Crystals with Special Reference to Metals. F. A. Hughes, LondonGoogle Scholar
  49. 49.
    Bishop JFW (1953) A theoretical examination of the plastic deformation of crystals by glide. Philos Mag 44:51–64. MathSciNetCrossRefGoogle Scholar
  50. 50.
    Spearman C (1904) The Proof and Measurement of Association between Two Things. Am J Psychol 15:72–101CrossRefGoogle Scholar
  51. 51.
    Kurzydlowski KJ, Czerepko W (1994) On the localization of the plastic flow in polycrystals of austenitic stainless steel. Key Eng Mat 97(98):501–505. Google Scholar
  52. 52.
    Guilhem Y, Basseville S, Curtit F, Stéphan J, Cailletaud G (2018) Numerical analysis of the effect of surface roughness on mechanical fields in polycrystalline aggregates. Modelling Simul Mater Sci Eng 26:045004. CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2019

Authors and Affiliations

  1. 1.Laboratoire de Mécanique des Solides (LMS), Ecole Polytechnique, CNRS, IPParisPalaiseauFrance

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