Abstract
The problem of modelling extreme dynamic events for metallic materials including strain rates over 107 s-1 and temperatures reaching melting point is still vivid in theoretical, applied and computational mechanics. Such thermomechanical processes are highly influenced by elasto-viscoplastic wave effects (their propagation and interaction) and varying initial anisotropy caused by existing defects in metals structure like microcracks, microvoids, mobile and immobile dislocations densities being together a cause of overall induced anisotropy during deformation (from the point of view of meso-macro continuum mechanics approach). It should be emphasised, that the most reliable way for estimation of such processes needs nowadays a complex phenomenological models due to limitations of current experimental techniques (it is still not possible to measure the evolution of crucial quantities e.g. temperature for extreme dynamic processes) and computational capabilities.
Within this document we consider recent achievements of Perzyna's type viscoplasticity theory for metallic materials accounting for anisotropic description of damage suitable for modelling plastic strain localization and failure for large strain rates.
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Bibliography
Abaqus. Abaqus Version 6.12 Theory Manual. 2012.
R.K. Abu Al-Rub and G.Z. Voyiadjis. A finite strain plastic-damage model for high velocity impact using combined viscosity and gradient localization limiters: Part I - theoretical formulation. International Journal of Damage Mechanics, 15(4):293-334, 2006.
J.K. Dienes. On the analysis of rotation and stress rate in deforming bodies. Acta Mechanica, 32:217-232, 1979.
W. Dornowski. Influence of finite deformations on the growth mechanism of microvoids contained in structural metals. Archives of Mechanics, 51 (1):71-86, 1999.
W. Dornowski and P. Perzyna. Analysis of the influence of various effects on cycle fatigue damage in dynamic process. Archive of Applied Mechanics, 72:418-438, 2002.
W. Dornowski and P. Perzyna. Numerical investigation of localized fracture phenomena in inelastic solids. Foundations of Civil and Environmental Engineering, 7:7%116, 2006.
M.K. Duszek-Perzyna and P. Perzyna. Analysis of the influence of digerent eflects on criteria for adiabatic shear band localization in inelastic solids, volume 50, chapter Material Instabilities: Theory and Applications. ASME, New York, 1994.
A. Glema. Analysis of wave nature in plastic strain localization in solids, volume 379 of Rozprawy. Publishing House of Poznan University of Technology, 2004. (in Polish).
A. Glema, T. Lodygowski, W. Sumelka, and P. Perzyna. The numerical analysis of the intrinsic anisotropic microdamage evolution in elastoviscoplastic solids. International Journal of Damage Mechanics, 18(3): 205-231, 2009.
A. Glema, T. Lodygowski, and W. Sumelka. Towards the modelling of an anisotropic solids. Computational Methods in Science and Technology, 16(1):73-84, 2010a.
A. Glema, T. Lodygowski, and W. Sumelka. Nowacki's double shear test in the framework of the anisotropic thermo-elast~vicsoplasticmaterial model. Journal of Theoretical and Applied Mechanics, 48(4):973-1001, 2010b.
H.A. Grebe, H.-R. P&, and Meyers M.A. Adiabatic shear localization in titanium and Ti-6 pct A1-4 pct V alloy. Metallurgical and Materials Transactions A, 16(5):761-775, 1985.
A.E. Green and P.M. Naghdi. A general theory of an elastic-plastic continuum. Archive for Rational Mechanics and Analysis, 18:251-281, 1965.
R. Hill. Aspects of invariance in solid mechanics. Advances in Applied Mechanics, 18:l-75, 1978.
G.A. Holzapfel. Nonlinear Solid Mechanics - A Continuum Approach for Engineering. Wiley, 2000.
J.R. Klepaczko. Constitutive relations in dynamic plasticity, pure metals and alloys. Advances in constitutive relations applied in computer codes. CISM, Udine, Italy, July 23-27 2007.
Th. Lehmann. Anisotrope plastische Formanderungen. Romanian J. Tech. Sci. Appl. Mech., 17:1077-1086, 1972.
P. Longere, A. Dragon, H. Trumel, and X. Deprince. Adiabatic shear banding-induced degradation in thermo-elastic/viscoplastic material under dynamic loading. International Journal of Impact Engineering, 32: 285-320, 2005.
J.E. Marsden and T.J.H Hughes. Mathematical Foundations of Elasticity. Prentice-Hall, New Jersey, 1983.
J.C. Nagtegaal and J.E. de Jong. Some aspects of non-isotropic workhardening in finite strain plasticity. In Lee E.H. and Mallet R.L., editors, Proceedings of the workshop on plasticity of metals at finite strain: theory, experiment and computation, pages 65-102. Stanford University, 1982.
R. Narayanasamy, N.L. Parthasarathi, and C.S. Narayanan. Effect of microstructure on void nucleation and coalescence during forming of three different HSLA steel sheets under different stress conditions. Materials and Design, 30:1310-1324, 2009.
S. Nemat-Nasser and W.-G. Guo. Thermomechanical response of HSLA-65 steel plates: experiments and modeling. Mechanics of Materials, 37: 379-405, 2005.
J.A. Nemes and J. Eftis. Several features of a viscoplastic study of plateimpact spallation with multidimensional strain. Computers and Structures, 38(3):317-328, 1991.
J.A. Nemes and J. Eftis. Constitutive modelling of the dynamic fracture of smooth tensile bars. International Journal of Plasticity, 9(2):243-270, 1993.
T. Lodygowski. Theoretical and numerical aspects of plastic strain localization, volume 312 of D.Sc. Thesis. Publishing House of Poznan University of Technology, 1996.
T. Lodygowskiand P. Perzyna. Localized fracture of inelastic polycrystalline solids under dynamic loading process. International Journal Damage Mechanics, 6:364-407, 1997a.
T. Lodygowski and P. Perzyna. Numerical modelling of localized fracture of inelastic solids in dynamic loading process. International Journal for Numerical Methods in Engineering, 40:4137-4158, 199713.
T. Lodygowski, A. Glema, and W. Sumelka. Anisotropy induced by evolution of microstructure in ductile material. In 8th World Congress on Computational Mechanics (WCCMt?), 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), Venice, Italy, June 30 - July 5 2008.
T. Lodygowski, A. Rusinek, T. Jankowiak, and W. Sumelka. Selected topics of high speed machining analysis. Engineering Transactions, 60(1):69- 96, 2012.
R.B. Pscherski, W.K. Nowacki, Z. Nowak, and P Perzyna. Effect of strain rate on ductile fracture. a new methodology. In Workshop, Dynamic Behaviour of Materials, In memory of our Friend and Colleague Prof. J.R. Klepaczko, pages 65-73, Metz, France, May 13-15 2009.
P. Perzyna. The constitutive equations for rate sensitive plastic materials. Quarterly of Applied Mathematics, 20:321-332, 1963.
P. Perzyna. Fundamental problems in viscoplasticity. Advances in Applied Mechanics, 9:243-377, 1966.
P. Perzyna. Termodynamika materiaFdw niesprciystych. PWN, Warszawa, 1978. (in Polish).
P. Perzyna. Internal state variable description of dynamic fracture of ductile solids. International Journal of Solids and Structures, 22:797-818, 1986a.
P. Perzyna. Constitutive modelling for brittle dynamic fracture in dissipative solids. Archives of Mechanics, 38:725-738, 198613.
P. Perzyna. Instability phenomena and adiabatic shear band localization in thermoplastic flow process. Acta Mechanica, 106:173-205, 1994.
P. Perzyna. Constitutive modelling of dissipative solids for localization and fracture. In Perzyna P., editor, Localization and fracture phenomena in inelastic solids, chapter 3, pages 99-241. Springer, 1998. (CISM course and lectures - No.386).
P. Perzyna. The thermodynamical theory of elasto-viscoplasticity. Engineering Transactions, 53:235-316, 2005.
P. Perzyna. The thermodynamical theory of elasto-viscoplasticity accounting for microshear banding and induced anisotropy effects. Mechanics, 27(1):25-42, 2008.
A. Rusinek and J.R. Klepaczko. Experiments on heat generated during plastic deformation and stored energy for trip steels. Materials and Design, 30(1):35-48, 2009.
Cz. Rymarz. Mechanika oirodkdw ciqgtych. PWN, Warszawa, 1993. (in Polish).
L. Seaman, D.R. Curran, and D.A. Shockey. Computational models for ductile and brittle fracture. Journal of Applied Physics, 47(11):4814- 4826, 1976.
S. Shima and M. Oyane. Plasticity for porous solids. International Journal of Mechanical Sciences, 18:285-291, 1976.
J-H Song, H. Wang, and T. Belytschko. A comparative study on finite element methods for dynamic fracture. Computational Mechanics, 42: 239-250, 2008.
W. Sumelka. The Constitutive Model of the Anisotropy Evolutionfor Metals with Microstructural Defects. Publishing House of Poznan University of Technology, Poznari, Poland, 2009.
W. Sumelka. The role of the covariance in continuum damage mechanics. ASCE Journal of Engineering Mechanics, 2013. (DOI:10.1061/(ASCE)EM.1943-7889.0000600).
W. Sumelka and A. Glema. The evolution of microvoids in elastic solids. In 17th International Conference on Computer Methods in Mechanics CMM-2007, pages 347-348, L6di-Spala, Poland, June 19-22 2007.
W. Sumelka and T. Lodygowski. The influence of the initial microdamage anisotropy on macrodamage mode during extremely fast thermomechanical processes. Archive of Applied Mechanics, 81(12):1973-1992, 2011.
W. Sumelka and T. Lodygowski. Reduction of the number of material parameters by ann approximation. Computational Mechanics, 2013a. (DOI: 10.1007/s00466-012-0812-9).
W. Sumelka and T. Lodygowski. Thermal stresses in metallic materials due to extreme loading conditions. ASME Journal of Engineering Materials and Technology, 2013b. (DOI: 10.1115/1.4023777).
D. Tikhomirov, R. Niekamp, and E. Stein. On three-dimensional microcrack density distribution. ZAMM - Journal of Applied Mathematics and Mechanics, 81(1):3-16, 2001.
G.Z. Voyiadjis and R.K. Abu Al-Rub. A finite strain plastic-damage model for high velocity impacts using combined viscosity and gradient localization limiters: Part I1 - numerical aspects and simulations. International Journal of Damage Mechanics, 15(4):335-373, 2006.
H. Xiao, O.T. Bruhns, and A. Meyers. Logarithmic strain, logarithmic spin and logarithmic rare. Acta Mechanica, 124:8%105, 1997a.
H. Xiao, O.T. Bruhns, and A. Meyers. Hypo-elasticity model based upon the logarithmic stress rate. Journal of Elasticity, 47:5148, 199713.
H. Xiao, O.T. Bruhns, and A. Meyers. Strain rates and material spin. Journal of Elasticity, 52:l-41, 1998.
S. Zaremba. Sur une forme perfectionke de la thkorie de la relaxation. Bull. Int. Acad. Sci. Cracovie, pages 594414, 1903.
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Łodygowski, T., Sumelka, W. (2014). Computer estimation of plastic strain localization and failure for large strain rates using viscoplasticity. In: Łodygowski, T., Rusinek, A. (eds) Constitutive Relations under Impact Loadings. CISM International Centre for Mechanical Sciences, vol 552. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1768-2_5
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