Multilevel models of inelastic deformation of materials and their application for description of internal structure evolution
Source abstract
Abstract
The paper considers a general formulation of multilevel models of inelastic deformation of materials as applied to the description of their internal structure evolution. Key problems for further development of this class of models and their solutions are put forward. An original variant of making constitutive relations of differing scale (differently scaled one-type characteristics) consistent is proposed; the consistency simultaneously provides unambiguous description of macroscale geometric nonlinearity by specifying the Cauchy stress tensor derivative independent of the choice of a reference frame. The general formulation is used to construct a two-level model of polycrystalline metals and a three-level model of semi-crystalline polymers for which hardening and lattice rotation laws of lower scales are derived from physical analysis. Numerical experiments performed with the developed algorithms of multilevel models for simple loading are described and their results are analyzed.
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Research context
OpenAlex topics: Elasticity and Wave Propagation · Structural mechanics and materials · Material Properties and Failure Mechanisms
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References (47)
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1. V.V. Rybin, High Plastic Strains and Fracture of Metals, Metallurgiya, Moscow, 1986 (in Russian).
2. Ya.D. Vishnyakov, A.A. Babareko, S.A. Vladimirov, and I.V. Egiz, Theory of Texture Formation in Metals and Alloys, Nauka, Moscow, 1979 (in Russian).
3. V.E. Panin, The physical foundations of the mesomechanics of a medium with structure, Russ. Phys. J., 35, No. 4 (1992) 305.10.1007/BF00560066 ↗
4. P.V. Trusov, V.N. Ashikhmin, P.S. Volegov, and A.I. Shveykin, Constitutive relations and their application to the description of micro-structure evolution, Phys. Mesomech., 13, No. 1–2 (2010) 38.10.1016/j.physme.2010.03.005 ↗
5. P.V. Trussov, V.N. Ashikhmin, and A.I. Shveykin, Two-level model for polycrystalline materials elastoplastic deformation, J. Composite Mech. Design, 15, No. 3 (2009) 327.
6. G.I. Taylor, Plastic strain in metals, J. Inst. Metals, 2 (1938) 307.10.2320/jinstmet1937.2.5_A307 ↗
7. J.F. Bishop and R. Hill, A theory of the plastic distortion of a polycrystalline aggregate under combined stresses, Philos. Mag. Ser. 7, 42, No. 327 (1951)414.10.1080/14786445108561065 ↗
8. J.F.W. Bishop and R. Hill, A theoretical derivation of the plastic proporties of a polycrystalline face-centered metal, Philos. Mag. Ser. 7, 42, No. 334 (1951) 1298.10.1080/14786444108561385 ↗
9. T.H. Lin, Physical theory of plasticity, Adv. Appl. Mech., 11 (1971) 255.10.1016/S0065-2156(08)70344-2 ↗
10. V.A. Likhachev and VG. Malinin, Structural-Analytical Theory of Strength, Nauka, St. Petersburg, 1993 (in Russian).
11. Physical Mesomechanics of Heterogeneous Media and Computer-Aided Design of Materials, Ed. by V.E. Panin, Cambridge Interscience Publishing, Cambridge, V. 1,2 (1998).
12. P.V. Makarov, Microdynamic theory of plasticity and failure of structurally inhomogeneous media, Russ. Phys. J., 35, No. 4 (1992) 334.10.1007/BF00560068 ↗
13. P.V. Makarov, Modeling of deformation and fracture at the mesolevel, Izv. AN: Mekh. Tv. Tela, No. 5 (1999) 109 (in Russian).
14. P.V. Makarov, Simulation of mesoscale elastoplastic deformation and fracture of heterogeneous media, Phys. Mesomech., 6, No. 4 (2003) 99.
15. P.V. Trusov and A.I. Shveikin, Theory of Plasticity, Izd-vo PNIPU, Perm, 2011 (in Russian).
16. P.V. Trusov, V.N. Ashikhmin, P.S. Volegov, and A.I. Shveikin, Mathematical modelling of the evolution of polycrystalline materials structure under elastoplastic deformation, Uch. Zap. Kazan. Univers. Ser. Fiziko-Matemat. Nauki, 152, (2010) 225 (in Russian).
17. L. Anand, Single-crystal elasto-viscoplasticity: Application to texture evolution in polycrystalline metals at large strains, Comput. Method. Appl. M., 193 (2004) 5359.10.1016/j.cma.2003.12.068 ↗
18. D.L. McDowell, Viscoplasticity of heterogeneous metallic materials, Mat. Sci. Eng. R., 62 (2008) 67.10.1016/j.mser.2008.04.003 ↗
19. P. Van Houtte, S. Li, M. Seefeldt, and L. Delannay, Deformation texture prediction: from the Taylor model to the advanced Lamel model, Int. J. Plasticity, 21 (2005) 589.10.1016/j.ijplas.2004.04.011 ↗
20. P.V. Trusov and P.S. Volegov, Crystal plasticity theories and their applications to the description of inelastic deformations of materials. Part 1: Rigid-plastic and elastoplastic theories, Vestnik PGTU: Mechanics, No. 1 (2011) 5 (in Russian).
21. P.V. Trusov and P.S. Volegov, Crystal plasticity theories and their applications to the description of inelastic deformations of materials. Part 2: Viscoplastic and elastoviscoplastic theories, Vestnik PGTU: Mechanics, No. 2 (2011) 101 (in Russian).
22. P.V. Trusov and P.S. Volegov, Crystal plasticity theories and their applications to the description of inelastic deformations of materials. Part 3: Hardening theories, gradient theories, Vestnik PGTU: Mechanics, No. 3 (2011) 146 (in Russian).
23. P.V. Trusov and A.I. Shveykin, Multilevel physical models of single-and polycrystals. Statistical models, Phys. Mesomech., 16, No. 1 (2013) (in print).10.1134/S1029959913010037 ↗
24. P.V. Trusov and A.I. Shveykin, Multilevel physical models of single-and polycrystals. Direct models, Fiz. Mezomekh., 14, No. 5 (2011) 5 (in Russian).
25. A.A. Pozdeev, P.V. Trusov, and Yu.I. Nyashin, High Elastic-Plastic Strains: Theory, Algorithms, Applications, Nauka, Moscow, 1986 (in Russian).
26. C. Truesdell, A First Course in Rational Continuum Mechanics, Academic Press, New York, 1977.
27. V.N. Ashikhmin, P.V. Trusov, and A.I. Shveikin, A two-level model of stationary elasto-plastic deformation during metal forming processes. Part 1. Algorithm, Comp. Continuum Mechanics, 1, No. 3 (2008) 15.10.7242/1999-6691/2008.1.3.23 ↗
28. E.S. Nechaeva and P.V. Trusov, Constitutive model of semicrystal-line polymer material. Implementation algorithm for mesolevel model, Comp. Continuum Mech., 4, No. 1 (2011) 74.10.7242/1999-6691/2011.4.1.7 ↗
29. E.S. Nechaeva and P.V. Trusov, Constitutive model of semicrystal-line polymer material. Implementation algorithm for macrolevel representative volume, Comp. Continuum Mech., 4, No. 2 (2011) 82.10.7242/1999-6691/2011.4.2.16 ↗
30. E.S. Nechaeva and P.V. Trusov, Constitutive model of low pressure polyethylene with internal variables: General structure and deformation mechanisms, Vestnik PGTU: Mathematical Modeling of Systems and Processes, No. 16 (2008) 87 (in Russian).
31. E.F. Oleinik, Plasticity of semicrystalline flexible-chain polymers at the microscopic and mesoscopic levels, Polymer Sci., Ser. C, 45, No. 1 (2003) 17.
32. A.M. Habraken, Modelling the plastic anisotropy of metals, Arch. Comput. Method. E., 11, No. 1 (2004) 3.10.1007/BF02736210 ↗
33. V.N. Ashikhmin and P.V. Trusov, Direct modeling of elastoplastic behavior of polycrystals at mesolevel, Phys. Mesomech., 5, No. 3-1 (2002) 33.
34. D. Raabe and F. Roters, Using texture components in crystal plasticity finite element simulations, Int. J. Plasticity, 20 (2004) 339.10.1016/S0749-6419(03)00092-5 ↗
35. O. Diard, S. Leclercq, G. Rousselier, and G. Cailletaud, Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity. Application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries, Int. J. Plasticity, 21 (2005) 691.10.1016/j.ijplas.2004.05.017 ↗
36. P.V. Trusov, V.N. Ashikhmin, and A.I. Shveykin, Physical elastoplastic analysis of deformation of fcc metals, Phys. Mesomech., 14, No. 1–2 (2011) 40.10.1016/j.physme.2011.04.006 ↗
37. S. Balasubramanian and L. Anand, Elasto-viscoplastic constitutive equations for polycrystalline fcc materials at low homologous temperatures, J. Mech. Phys. Solids. 50 (2002) 101.10.1016/S0022-5096(01)00022-9 ↗
38. A.I. Shveykin, V.N. Ashikhmin, and P.V. Trusov, Lattice spin models in deformation of metals, Vestnik PGTU: Mechanics, No. 1 (2010) 111 (in Russian).
39. S. Nikolov, R.A. Lebensohn, and D. Raabe, Self-consistent modeling of large plastic deformation, texture and morphology evolution in semi-crystalline polymers, J. Mech. Phys. Solids, 54, No. 7 (2006) 1350.10.1016/j.jmps.2006.01.008 ↗
40. P.V. Trusov and P.S. Volegov, Internal variable constitutive relations and their application to description of hardening in single crystals, Phys. Mesomech., 13, No. 3–4 (2010) 152.10.1016/j.physme.2010.07.006 ↗
41. P.V. Trusov and P.S. Volegov, Physical theories of plasticity: application to the description of hardening in polycrystals, Tambov University Reports: Natural and Technical Sciences, 15, Iss. 3, P. 1 (2010) 983 (in Russian).
42. P.V. Trusov, P.S. Volegov, and A.I. Shveykin, Constitutive Elasto-viscoplastic Model of FCC-Crystals: Theory and Application Algorithms, LAP LAMBERT Academic Publ., Saarbrucken, 2011.
43. P.V. Trusov, P.S. Volegov, and A.Yu. Yants, Description of intra-granular and grain boundary hardening of single- and polycrystals, SPbSPU Sci. Tech. Bull.: Phys. Math. Sci., 98, No. 2 (2010) 110 (in Russian).
44. V.P. Trusov, P.S. Volegov, and A.Yu. Yants, Asymmetric physical theory of plasticity for the evolution of polycrystal microstructures, Phys. Mesomech., 15, No. 1–2 (2012) 58.10.1134/S1029959912010067 ↗
45. J.A.W. Van Dommelen, D.M. Parks, M.C. Boyce, W.A.M. Brekelmans, and F.P.T. Baaijens, Micromechanical modeling of the elastoviscoplastic behavior of semi-crystalline polymers, J. Mech. Phys. Solids, 51 (2003) 519.10.1016/S0022-5096(02)00063-7 ↗
46. Z. Bartczak, A.S. Argon, and R.E. Cohen, Deformation mechanisms and plastic resistance in single-crystal-textured high density polyethylene, Macromolecules, 25 (1992) 5036.10.1021/ma00045a034 ↗
47. Z. Bartczak, R.E. Cohen, and A.S. Argon, Evolution of the crystalline texture of high-density polyethylene during uniaxial compression, Macromolecules, 25, No. 18 (1992) 4692.10.1021/ma00044a034 ↗