Plastic deformation of commercially-pure titanium: Experiments and modeling

Madhav Baral, Takayuki Hama, Erik Knudsen, Yannis P. Korkolis

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


The plastic behavior of commercially-pure titanium (CP-Ti) is assessed using a combination of experiments and analysis. A total of 23 (with three repetitions each) experiments were performed on a hot-rolled CP-Ti plate of 12.7 mm thickness. The experiments performed are uniaxial tension and uniaxial compression in-plane at 15° angles to the rolling direction (RD), and in the normal direction (ND), as well as plane-strain tension (PST) at 15° angles to the RD of the plate. The uniaxial tension and compression tests involve standard specimen geometries, except for the one in the ND, which required the creation of a custom, miniature tensile specimen. The PST specimen is a custom geometry to impose a constraint in the transverse direction, giving rise to the plane-strain condition. A procedure using finite element analysis is described to determine the axial stress in a PST test. The experiments reveal the deformation-induced anisotropy and tension-compression asymmetry of CP-Ti. The material strength is found to increase going from RD to transverse direction (TD) to ND. The experiments are then used to calibrate four constitutive models of increasing complexity: von Mises, Hill '48, KYL '12 and CPB '06. The calibrated models along with the experimental information are shown using three alternative approaches: biaxial tension-compression plane, Haigh-Westergaard or π-plane, and the one recently introduced by (Korkolis et al., 2017) that allows representation of stress states where the full stress tensor is active. Furthermore, the test results from off-axis experiments, not used in the calibration, are used to examine the performance of each model. The best performance in predicting the experiments was exhibited by the KYL '12 and CPB '06 models. It is expected that this improved understanding and representation of the plastic behavior of CP-Ti can lead to improved material models and numerical simulations of manufacturing and service.

Original languageEnglish
Pages (from-to)164-194
Number of pages31
JournalInternational Journal of Plasticity
StatePublished - Jun 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Ltd.


  • Commercially-pure titanium
  • Constitutive behavior
  • Experimental characterization
  • Plastic anisotropy
  • Tension-compression asymmetry
  • Yield criterion

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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