Continuum Mechanics and Thermodynamics

, Volume 20, Issue 8, pp 509–521 | Cite as

A physico-mechanical approach to modeling of metal forming processes—Part II: damage analysis in processes with plastic flow of metals

  • Maxim A. Zapara
  • Nikolay D. Tutyshkin
  • Wolfgang H. MüllerEmail author
  • Kerstin Weinberg
  • Ralf Wille
Original Article


A damage analysis is presented for the extrusion of a case-shaped cylindrical part by using a physico-mechanical approach for modeling metal forming processes. Two integral measures related to the hydrostatic and deviatoric parts of the damage tensor are used for the calculation of strain damage. The combined use of two damage measures in contrast to only one allows us to assess not only a risk of macro-fracture of the deformed material but also the stage of formation of large cavernous defects due to coalescence of ellipsoidal voids. Such a refined prediction of the actual quality of the material’s micro-structure is important when producing metalware that is supposed to operate under intense loading and thermal conditions. In case study of this paper the kinetic equations of damage are solved by using mutually consistent fields of stresses, flow velocities, and strains. It is shown that the predicted damage is less than its permissible value since a high hydrostatic pressure in the plastic zone heals the micro-defects, prevents their growth, and, thereby, increases the processing ductility of deformed metals during extrusion.


Plasticity Plastic flow Deformation Plastic strain and stress Slip line Velocity field Micro-structure Strain induced damage Meso-parameters Damage equation Metal forming Extrusion Case-shaped part 


81.40.Lm 81.20.Hy 46.35.+z 46.50.+a 62.20.F– 61.72.Qq 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Maxim A. Zapara
    • 1
  • Nikolay D. Tutyshkin
    • 1
  • Wolfgang H. Müller
    • 2
    Email author
  • Kerstin Weinberg
    • 3
  • Ralf Wille
    • 2
  1. 1.Department of Technological MechanicsTula State UniversityTulaRussia
  2. 2.Lehrstuhl für Kontinuumsmechanik und MaterialtheorieTechnische Universität BerlinBerlinGermany
  3. 3.Universität SiegenSiegenGermany

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