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A physico-mechanical approach to modeling of metal forming processes—part I: theoretical framework

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Abstract

A combined physico-mechanical approach to research and modeling of forming processes for metals with predictable properties is developed. The constitutive equations describing large plastic deformations under complex loading are based on both plastic flow theory and continuum damage mechanics. The model which is developed in order to study strongly plastically deformed materials represents their mechanical behavior by taking micro-structural damage induced by strain micro-defects into account. The symmetric second-rank order tensor of damage is applied for the estimation of the material damage connected with volume, shape, and orientation of micro-defects. The definition offered for this tensor is physically motivated since its hydrostatic and deviatoric parts describe the evolution of damage connected with a change in volume and shape of micro-defects, respectively. Such a representation of damage kinetics allows us to use two integral measures for the calculation of damage in deformed materials. The first measure determines plastic dilatation related to an increase in void volume. A critical amount of plastic dilatation enables a quantitative assessment of the risk of fracture of the deformed metal. By means of an experimental analysis we can determine the function of plastic dilatation which depends on the strain accumulated by material particles under various stress and temperature-rate conditions of forming. The second measure accounts for the deviatoric strain of voids which is connected with a change in their shape. The critical deformation of ellipsoidal voids corresponds to their intense coalescence and to formation of large cavernous defects. These two damage measures are important for the prediction of the meso-structure quality of metalware produced by metal forming techniques. Experimental results of various previous investigations are used during modeling of the damage process.

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Authors and Affiliations

  1. Department of Technological Mechanics, Tula State University, 300600, Tula, Russia

    Maxim A. Zapara & Nikolay D. Tutyshkin

  2. Institut für Mechanik-LKM, Technische Universitāt Berlin, Sekretariat MS 02, Einsteinufer 5, 10587, Berlin, Germany

    Wolfgang H. Müller & Ralf Wille

  3. Institut fūr Mechanik und Regelungstechnik - Mechatronik, AG Festkörpermechanik, Universitāt Siegen, Paul-Bonatz-Straße 9-11, 57076, Siegen, Germany

    Kerstin Weinberg

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  1. Maxim A. Zapara
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  2. Nikolay D. Tutyshkin
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  3. Wolfgang H. Müller
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  4. Kerstin Weinberg
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  5. Ralf Wille
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Correspondence to Wolfgang H. Müller.

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Communicated by S. Roux

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Zapara, M.A., Tutyshkin, N.D., Müller, W.H. et al. A physico-mechanical approach to modeling of metal forming processes—part I: theoretical framework. Continuum Mech. Thermodyn. 20, 231–254 (2008). https://doi.org/10.1007/s00161-008-0080-2

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  • DOI: https://doi.org/10.1007/s00161-008-0080-2

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