Multiscale strain measurements of plastically deforming polycrystalline titanium: Role of deformation heterogeneities

C. Efstathiou, H. Sehitoglu, J. Lambros

Research output: Contribution to journalArticlepeer-review


The purpose of this work was to characterize the spatial distribution of residual deformation at the mesoscale (a few grains) and at the macroscale (hundreds of grains) in titanium subjected to cyclic tensile loading. Using ex situ digital image correlation, we compared the axial residual strain fields obtained at optical magnifications ranging from 3.2× to 50×. To compare the results obtained at different optical magnifications, numerous images at higher magnification had to be assembled to encompass the same field-of-view observed at lower magnifications. The strain fields at the highest optical magnification revealed deformation patterns that were not detectable at lower magnifications. These deformation patterns appeared as inclined slip bands near grain boundaries and grain boundary triple points, with the bands sometimes crossing into neighboring grain interiors. Measurements made at optical magnifications greater than 10× captured an underlying deformation pattern, however, considerably more detail within grains was obtained at 50× magnification. The strain fields obtained at 10× and 50× magnifications were subsequently used to estimate the length scale of a representative volume element (RVE) based on the standard deviation of the average residual strain. The estimated RVE length scale was nearly three times the average grain diameter if extracted from the 50× results. The estimate of the RVE length scale was smaller at lower magnification which was due to a homogenizing effect caused by the low measurement resolution. Thus, care must be taken when experimentally obtaining RVE length scale estimates.

Original languageEnglish (US)
Pages (from-to)93-106
Number of pages14
JournalInternational journal of plasticity
Issue number1
StatePublished - Jan 2010


  • Crystal plasticity
  • Grain boundaries
  • Inhomogeneous material
  • Polycrystalline material
  • Representative volume element (RVE)

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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