Identification of the cap model of elastoplasticity of non-compact media under compressive mean stress

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Abstract

A program of basic tests and a method for identifying a three-dimensional model of the elastoplastic behavior of an isotropic porous or powdery consolidated medium experiencing arbitrary quasi-static loading under compressive medium stress at room temperature are proposed. The medium under consideration under compressive medium stresses is compacted with increasing effective stress, which leads to a nonlinear change in elastic modules, hardening and dilatancy (coupling of shear and volumetric components of deformations) in the yield region. To describe this behavior, the cap model of DiMaggio and Sandler, which is present in application software packages, is considered. As basic tests, the free and constrained compression of a cylindrical sample is considered according to a special program containing the stages of loading and unloading with a sequential increase in the amplitude voltage. Samples with a given porosity for free compression tests are manufactured using a tight compression test rig. According to the initial slope of the discharge curves, the values of the elastic modulus for free and constrained compression are determined in a certain range of porosity changes, according to which the Poisson’s ratio is determined. The five constants of the cap model are correctly and explicitly determined by the deformation curve of the material under constrained compression over a wide range of changes in axial deformation (and density), the flow stress under free compression of the sample at some density, and the assumption that the coefficient of transverse deformation in the yield region is equal to the Poisson’s ratio. The elastic and plastic constants were determined according to the test data of powdered paraffin grade T1 with a fraction of 0.63 mm. The corresponding model is applicable for numerical simulation of extrusion processes and mold filling for casting by melting models, processes for manufacturing blanks of non-melting polymer composites by powder technology, stamping sealing elements from flexible graphite and other pressure treatment processes of non-compact media.

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About the authors

A. A. Adamov

Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science

Author for correspondence.
Email: adamov@icmm.ru
Russian Federation, Perm

I. E. Keller

Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science

Email: kie@icmm.ru
Russian Federation, Perm

S. G. Zhilin

Institute of Mechanical Engineering and Metallurgy of the Far Eastern Branch of the Russian Academy of Sciences

Email: zhilin@imim.ru
Russian Federation, Komsomolsk-on-Amur

N. A. Bogdanova

Institute of Mechanical Engineering and Metallurgy of the Far Eastern Branch of the Russian Academy of Sciences

Email: joyful289@inbox.ru
Russian Federation, Komsomolsk-on-Amur

References

  1. Kalashnik N.A., Ionov S.G. Mechanical and thermophysical properties of graphite foils based on low-density carbon materials // Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2017. V. 9. № 60. P. 11–16. [in Russian] https://doi.org/10.6060/tcct.2017609.4у
  2. Chung D.D.L. Flexible graphite for gasketing, adsorption, electromagnetic interference shielding, vibration damping, electrochemical applications, and stress sensing // Journal of Materials Engineering and Performance. 2000. № 9. P. 161–163. https://doi.org/10.1361/105994900770346105
  3. Dowell M.B., Howard R.A. Tensile and compressive properties of flexible graphite foils // Carbon. 1986. № 24. P. 311–323.
  4. Leng Y., Gu J., Cao W., Zhan T.Y. Influences of density and flake size on the mechanical properties of flexible graphite // Carbon. 1998. № 36. P. 875–881.
  5. Khelifa M., Fierro V., Macutkevic J., Celzard A. Nanoindentation of flexible graphite: Experimental versus simulation studies // Advanced Material Science. 2018. V. 3. № 2. P. 2–11. https://doi.org/10.15761/AMS.1000142
  6. Sapchenko I.G., Zhilin S.G., Komarov O.N. Controlling the structure and properties of porous combined removable models. Vladivistok: Dal’nauka, 2007. 138 p. [in Russian].
  7. Zhilin S.G., Bogdanova N.A., Komarov O.N. Influence of parameters of the compacting of powder body from wax-like material on the forming of residual stresses of pressing. Vestnik Chuvashskogo gosudarstvennogo pedagogicheskogo universiteta im. I.Ya. Yakovleva. Seriya: Mekhanika predel’nogo sostoyaniya. 2019. V. 3. № 41. P. 110–121. [in Russian]. https://doi.org/10.26293/chgpu.2019.41.3.009
  8. Zhilin S.G., Bogdanova N.A., Komarov O.N., Sosnin A.A. Decrease in the elastic response in compacting a paraffin-stearin powder composition // Russian Metallurgy (Metally). 2020. V. 1. P. 29–33. [in Russian]. https://doi.org/10.31044/1814-4632-2020-1-29-33
  9. Zhilin S.G., Bogdanova N.A., Komarov O.N. Porous wax patterns for high-precision investment casting // Izvestiya. Non-Ferrous Metallurgy. 2023. V. 3. № 29. P. 54–66. https://doi.org/10.17073/0021-3438-2023-3-54-66
  10. Pugachev A.K., Roslyakov O.A. Processing of Fluoroplastics into Products. L.: Khimiya, 1987. 168 p.
  11. Lyukshin B.A. et al. Dispersedly-Filled Polymer Composites for Technical and Medical Purposes. In: Plasticity of Pressure-Sensitive Materials, Engineering Materials (Ed. A.V. Gerasimov). Novosibirsk: Publishing House of the Siberian Branch of the Russian Academy of Sciences, 2017. 311 p.
  12. Aubertin M., Li L. A porosity-dependent inelastic criterion for engineering materials // Int. J. Plasticity. 2004. V. 12. № 20. P. 2179–2208. https://doi.org/10.1016/j.ijplas.2004.05.004
  13. Altenbach H., Bolchoun A., Kolupaev V.A. Phenomenological Yield and Failure Criteria // Plasticity of Pressure-Sensitive Materials, Engineering Materials. Eds. A. Öchsner, H. Altenbach. Berlin, Heidelberg: Springer. 2014. P. 49–152. https://doi.org/10.1007/978-3-642-40945-5_2
  14. Kolupaev V.A., Yu M.-H., Altenbach H. Fitting of the strength hypotheses // Acta Mechanica. 2016. V. 6. № 227. P. 1533–1556. https://doi.org/10.1007/s00707-016-1566-9
  15. Khoei A.R., DorMohammadi H. A three-invariant cap plasticity with isotropic–kinematic hardening rule for powder materials: Model assessment and parameter calibration // Computational Materials Science. 2007. № 41. P. 1–12. https://doi.org/10.1016/j.commatsci.2007.02.011
  16. Keller I.E., Petukhov D.S. Criteria of Strength and Plasticity. Perm: Perm National Research Polytechnical University Press, 2020. 157 p. [in Russian].
  17. DiMaggio F.L., Sandler I.S. Material models for granular soils // J. Eng. Mech. Div. ASCE. 1971. № 97. P. 935–950.
  18. Schwer L.E., Murray Y.D. A three-invariant smooth cap model with mixed hardening // Int. J. Num. Anal. Meth. Geomech. 1994. № 18. P. 657–688.
  19. LS-DYNA® Keyword User›s Manual. Volume II. Material Models. Version R10.0. Livermore Software Technology Corporation, 2017.
  20. Adamov A.A., Keller I.E., Podkina N.S. Basic experiments for identification of the cap model of flexible graphite plasticity // Bulletin of the Chuvash State Pedagogical University I.Ya. Yakovleva. Series: Mechanics of Limit State. 2020. V. 3. № 45. P. 131–142 [in Russia]. https://doi.org/10.37972/chgpu.2020.20.13.013

Supplementary files

Supplementary Files
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2. Fig. 1. Yield curve in the DiMaggio-Sandler model on the Buzhinsky diagram with the coefficient of adhesion equal to zero for two states of hardening and the direction of normals at the yield points under proportional loading

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3. Fig. 2a. Dependences of θ on R at v = 0.22

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4. Fig. 3. Test equipment for free (a) and constrained (b) compression

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5. Fig. 4a. Strain curves of samples under free compression. Stresses in MPa, density in g/cm3

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6. Fig. 5. Elastic moduli under free (red) and constrained (blue) compression depending on density. MPa is plotted along the vertical axis, g/cm3 along the horizontal axis.

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7. Fig. 6a. Strain curves under constrained compression: monotonic loading (blue - experiment, red - approximation). MPa are plotted along the vertical axis.

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8. Fig. 7. Curves of hardening under free (red) and constrained (blue) compression described by the model. MPa are plotted along the vertical axis.

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9. Fig. 8. Tangent of the angle of inclination of the direction of the deformation vector in the Buzhinsky plane depending on the ratio of compressive stresses under triaxial compression for two sets of constants (Table 2): the first is the red curve, the second is the blue curve

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10. Fig. 2b. Dependences of /f on R at v = 0.22

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11. Fig. 4b. Curves of unloading of samples under free compression. Stresses in MPa, density in g/cm3

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12. Fig. 6b. Strain curves under constrained compression: loading with unloading (blue - experiment, red - approximation). MPa are plotted along the vertical axis

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