Skip to main content

Spatiotemporal Thermal Inhomogeneities During Compression of Highly Textured Zirconium


Using a focal plane array infrared camera, the heat generated during large strain compression (at a rate of 1 s−1) is used to study the characteristics of plastic flow for hcp zirconium. Heat generation during plastic flow in a reference material, copper, was seen to develop uniformly both at the lower (40 μm/pixel) and higher (8 μm/pixel) magnifications used in this study. The thermomechanical response of Zr, however, was seen to depend on the loading direction with respect to the specimen texture. Highly textured zirconium compressed along nonbasal oriented grains results in a homogeneous thermal response at both scales. However, compression along basal (0001) oriented grains shows evidence of inhomogeneous deformation at small strains that lead to macroscale localization and failure at large strains. The conversion of plastic work into heat is observed to be a dynamic process, both in the time-dependent nature of the energy conversion, but also in the passage of waves and ‘bursts’ of plastic heating. Basal compression also showed evidence of small scale localization at strains far below macroscale localization, even below 10%. These localizations at the lower strain levels eventually dominate the response, and form the shear band that is responsible for the softening of the macroscopic stress–strain curve.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13


  1. 1.

    Zuev LB, Danilov VI (1999) A self-excited wave model of plastic deformation in solids. Philos Mag A 79(1):43–57

    Article  Google Scholar 

  2. 2.

    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(5):1075–1087

    Article  Google Scholar 

  3. 3.

    Bieler TR, Semiatin SL (2002) The origins of heterogeneous deformation during primary hot working of Ti-6Al-4 V. Int J Plast 18(9):1165–1189

    MATH  Article  Google Scholar 

  4. 4.

    Sachtleber M, Zhao Z, Raabe D (2002) Experimental investigation of plastic grain interaction. Mater Sci Eng A-Structural Materials Properties Microstructure and Processing 336(1–2):81–87

    Article  Google Scholar 

  5. 5.

    Schroeter DM, McDowell DL (2003) Measurement of deformation fields in polycrystalline OFHC copper. Int J Plast 19(9):1355–1376

    MATH  Article  Google Scholar 

  6. 6.

    Tatschl A, Kolednik O (2003) On the experimental characterization of crystal plasticity in polycrystals. Mater Sci Eng A-Structural Materials Properties Microstructure and Processing 342(1–2):152–168

    Article  Google Scholar 

  7. 7.

    Zhang N, Tong W (2004) An experimental study on grain deformation and interactions in an Al-0.5%Mg multicrystal. Int J Plast 20(3):523–542

    MathSciNet  Article  Google Scholar 

  8. 8.

    McDonald RJ, Efstathiou C, Kurath P (2009) The wavelike plastic deformation of single crystal copper. J Eng Mater Technol-Transactions of the Asme 131(3):7

    Google Scholar 

  9. 9.

    Aifantis EC (1987) The physics of plastic-deformation. Int J Plast 3(3):211–247

    MathSciNet  MATH  Article  Google Scholar 

  10. 10.

    Aifantis EC (1992) On the role of gradients in the localization of deformation and fracture. Int J Eng Sci 30(10):1279–1299

    MATH  Article  Google Scholar 

  11. 11.

    Beaudoin AJ, Mathur KK, Dawson PR, Johnson GC (1993) 3-Dimensional deformation process simulation with explicit use of polycrystal plasticity models. Int J Plast 9(7):833–860

    MATH  Article  Google Scholar 

  12. 12.

    Mika DP, Dawson PR (1999) Polycrystal plasticity modeling of intracrystalline boundary textures. Acta Mater 47(4):1355–1369

    Article  Google Scholar 

  13. 13.

    Miguel MC, Vespignani A et al (2001) Intermittent dislocation flow in viscoplastic deformation. Nature 410(6829):667–671

    Article  Google Scholar 

  14. 14.

    Weiss J, Marsan D (2003) Three-dimensional mapping of dislocation avalanches: clustering and space/time coupling. Science 299(5603):89–92

    Article  Google Scholar 

  15. 15.

    Richeton T, Weiss J et al (2005) Breakdown of avalanche critical behaviour in polycrystalline plasticity. Nat Mater 4(6):465–469

    Article  Google Scholar 

  16. 16.

    Weiss J, Richeton T, Louchet F (2007) Evidence for universal intermittent crystal plasticity from acoustic emission and high-resolution extensometry experiments. Phys Rev B 76(22)

  17. 17.

    Lebyodkin MA, Lebedkina TA, Chmelík F, Lamark TT, Estrin Y, Fressengeas C, Weiss J (2009) Intrinsic structure of acoustic emission events during jerky flow in an Al alloy. Phys Rev B 79(17)

  18. 18.

    Bernier J (2005) A direct method for determining the orientation-dependent lattice strain distribution function from diffraction strain pole figures, icotom 14: textures of materials, pts 1 and 2. Mater Sci Forum 495–497:1073–1078

    Article  Google Scholar 

  19. 19.

    Miller MP, Bernier JV, Park J-S, Kazimirov A (2005) Experimental measurement of lattice strain pole figures using synchrotron x rays. Rev Sci Instrum 76(11):113903–11

    Article  Google Scholar 

  20. 20.

    Haldrup K, Nielsen SF, Beckmann F, Wert JA (2006) Inhomogeneous plastic flow investigated by X-ray absorption microtomography of an aluminium alloy containing marker particles. J Microsc 222(1):28–35

    MathSciNet  Article  Google Scholar 

  21. 21.

    Padilla HA, Lambros J, Beaudoin A, Robertson IM (2010) Relating inhomogeneous deformation to local texture in zirconium through multiscale digital image correlation experiments. In review, Int J Solids Struct

  22. 22.

    Ait-Amokhtar H, Fressengeas C, Boudrahem S (2008) The dynamics of Portevin-Le Chatelier bands in an Al-Mg alloy from infrared thermography. Mater Sci Eng A-Structural Materials Properties Microstructure and Processing 488(1–2):540–546

    Article  Google Scholar 

  23. 23.

    Ranc N, Wagner D (2008) Experimental study by pyrometry of Portevin-Le Châtelier plastic instabilities—Type A to type B transition. Mater Sci Eng A-Structural Materials Properties Microstructure and Processing 474(1–2):188–196

    Article  Google Scholar 

  24. 24.

    Chrysochoos A, Wattrisse B et al (2009) Fields of stored energy associated with localized necking of steel. J Mech Mater Struct 4(2):245–262

    Article  Google Scholar 

  25. 25.

    Bodelot L, Sabatier L, Charkaluk E, Dufrénoy P (2009) Experimental setup for fully coupled kinematic and thermal measurements at the microstructure scale of an AISI 316L steel. Mater Sci Eng A-Structural Materials Properties Microstructure and Processing 501(1–2):52–60

    Article  Google Scholar 

  26. 26.

    Plekhov OA, Naimark OB (2009) Theoretical and experimental study of energy dissipation in the course of strain localization in iron. J Appl Mech Tech Phys 50(1):127–136

    Article  Google Scholar 

  27. 27.

    Jiang WH, Fan GJ, Liu FX, Wang GY, Choo H, Liaw PK (2008) Spatiotemporally inhomogeneous plastic flow of a bulk-metallic glass. Int J Plast 24(1):1–16

    Article  Google Scholar 

  28. 28.

    Guzman R, Melendez J, Aranda JM, Essa YE, López F, Pérez-Castellanos JL (2009) Measurement of temperature increment in compressive quasi-static and dynamic tests using infrared thermography. Strain 45(2):179–189

    Article  Google Scholar 

  29. 29.

    Zehnder AT, Guduru PR, Rosakis AJ, Ravichandran G (2000) Million frames per second infrared imaging system. Rev Sci Instrum 71(10):3762–3768

    Article  Google Scholar 

  30. 30.

    Mason JJ, Rosakis AJ, Ravichandran G (1994) On the strain and strain rate dependence of the fraction of plastic work converted to heat: an experimental study using high speed infrared detectors and the Kolsky bar. Mech Mater 17(2–3):135–145

    Article  Google Scholar 

  31. 31.

    Kapoor R, Nemat-Nasser S (1998) Determination of temperature rise during high strain rate deformation. Mech Mater 27(1):1–12

    Article  Google Scholar 

  32. 32.

    Padilla HA, Smith CD, Lambros J, Beaudoin A, Robertson IM (2007) Effects of deformation twinning on energy dissipation in high rate deformed zirconium. Metall Mater Trans A 38(12):2916–2927

    Article  Google Scholar 

  33. 33.

    Padilla HA (2008) Multiscale experimental study on the effect of texture and anisotropy on the thermomechanical response of zirconium. Mechanical Science and Engineering. Urbana, University of Illinois. PhD

  34. 34.

    Hodowany J, Ravichandran G, Rosakis AJ, Rosakis P (2000) Partition of plastic work into heat and stored energy in metals. Exp Mech 40(2):113–123

    Article  Google Scholar 

  35. 35.

    Rabin Y, Rittel D (2000) Infrared temperature sensing of mechanically loaded specimens: thermal analysis. Exp Mech 40(2):197–202

    Article  Google Scholar 

  36. 36.

    Tome CN, Maudlin PJ, Lebensohn RA, Kaschner GC (2001) Mechanical response of zirconium—I. Derivation of a polycrystal constitutive law and finite element analysis. Acta Mater 49(15):3085–3096

    Article  Google Scholar 

Download references


This work was supported by the U.S. Department of Energy under grant DEFG03-02-NA00072, which is administered by the Center for the Simulation of Advanced Rockets (CSAR) at the University of Illinois at Urbana, as well as grant DEFG52-06-NA26150. The microscopy was carried out with the assistance of James Mabon in the Center for Microanalysis of Materials, University of Illinois, which is partially supported by the U.S. Department of Energy under grant DEFG02-91-ER45439. The assistance of Dr. Gavin Horn with the performance of the thermal measurements is also greatly appreciated. The authors would also like to thank Dr. George Kaschner for many helpful discussions. Finally, the authors would like to acknowledge the excellent comments from the unknown reviewer, which considerably improved the final outcome of this effort.

Author information



Corresponding author

Correspondence to J. Lambros.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Padilla, H., Lambros, J., Beaudoin, A. et al. Spatiotemporal Thermal Inhomogeneities During Compression of Highly Textured Zirconium. Exp Mech 51, 1061–1073 (2011).

Download citation


  • Infrared
  • Multiscale
  • Plastic bursts
  • Highly textured Zr