FE analysis on the formation of plastic instabilities in dynamically expanded copper rings

Vela, C.; Rodriguez-Martinez, J. A.; Rusinek, A.

Artykuł - szczegóły

Tytuł artykułu

FE analysis on the formation of plastic instabilities in dynamically expanded copper rings

Autorzy

Vela C. , Rodriguez-Martinez J. A. , Rusinek A.

Wybrane pełne teksty z tego czasopisma

http://et.ippt.gov.pl/

Identyfikatory

Warianty tytułu

Języki publikacji

Abstrakty

In this work the influence of the constitutive description in numerical simulations of the radial expansion of annealed OFHC copper rings has been studied. For that task, three physical-based constitutive models are implemented into the FE code ABAQUS/Explicit and applied to de?ne the thermo-viscoplastic behaviour of the material in the simulations. These are those due to Rusinek et al. [A. Rusinek, J.A. Rodr´ iguez–Mart´ inez, A. Arias, A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper, Int. J. Mech. Sci., 52, 120–135, 2010], Nemat–Nasser and Li [S. Nemat–Nasser, Y. Li, Flow stress of FCC polycrystals with application to OFHC Copper, Acta Mater., 46, 565–577, 1998] and Voyiadjis and Almasri [G. Z. Voyiadjis, A.H. Almasri, A physically based constitutive model for fcc metals with applications to dynamic hardness, Mech. Mater., 40, 549–563, 2008]. The attention is primarily focussed on analyzing the in?uence of the material description on the strain localization process. Notable differences are observed in the response of the specimen under loading depending on the constitutive relation used. The numerical study indicated that the constitutive model controls the low localization, defines the strain of instability and determines the number of necks formed. The causes which reside behind such decisive role played by the constitutive relation are investigated. It has been found that the rate sensitivity definition governs the models’ predictions for the strain localization process.

Słowa kluczowe

annealed OFHC copper fragmentation ring expansion constitutive description numerical simulation

miedź fragmentacja symulacja numeryczna

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

Engineering Transactions

Rocznik

2011

Tom

Vol. 59, iss. 3

Strony

211--233

Opis fizyczny

Bibliogr. 62 poz., rys., wykr.

Twórcy

autor

Vela C.

autor

Rodriguez-Martinez J. A.

autor

Rusinek A.

National Engineering School of Metz (ENIM) Laboratory of Mechanics, Biomechanics, Polymers and Structures (LaBPS) 1 route d’Ars Laquenexy, 57078 Metz Cedex 3, France, rusinek@enim.fr

Bibliografia

1. R. P. Papirno, J. F. Mescall, A. M. Hansen, Beyond the taylor test to fracture, [in:] Designing for extremes: Environment, loading, and structural behavior, Proceedings of the Army Symposium on Solid Mechanics, pp. 367–385, Watertown, MA, September 1980. Army Materials and Mechanics Research Center.
2. H. Couque, On the use of the symmetric Taylor test to evaluate dynamic ductile compression fracture properties of metals, Proceedings of the 5th International Conference on Structures Under Shock and Impact, pp. 579–589, Computational Mechanics Inc, Billerica, MA, USA, 1998.
3. A. Molinari, C. Musquar, G. Sutter, Adiabatic shear banding in high speed machining of Ti–6Al–4V: Experiments and modeling, Int. J. Plasticity, 18, 443–459, 2002.
4. M. K. Duszek, P. Perzyna, The localization of plastic deformation in thermoplastic solids, Int. J. Solids and Struct., 27, 1419–1443, 1991.
5. T. Łodygowski, M. Lengnick, P. Perzyna, E. Stein, Viscoplastic numerical analysis of dynamic plastic strain localization for a ductile material, Arch. Mech., 46, 4, 541–557, 1994.
6. P. Perzyna, Instability phenomena and adiabatic shear band localization in thermoplastic ﬂow processes, Acta Mechanica, 106, 173–205, 1994.
7. A. Glema, T. Łodygowski, P. Perzyna, Interaction of deformation waves and localization phenomena in inelastic solids, Comput. Methods Appl. Mech. Engrg., 183, 123–140, 2000.
8. F. Zhou, J. F. Molinari, K. T. Ramesh, An elasto-visco-plastic analysis of ductile expanding ring, Int. J. Impact Eng., 33, 880–891, 2006.
9. D. Rittel, G. Ravichandran, A. Venkert, The mechanical response of pure iron at high strain rates under dominant shear, Mat. Sci. Eng. A., 1–2, 191–201, 2006.
10. H. C. Mann, High-velocity tension-impact tests, Proc. ASTM, 36, 85, 1936.
11. J. R. Klepaczko, Generalized conditions for stability in tension test, Int. J. Mech. Sci., 10, 297–313, 1968.
12. A. M. Rajendran, I. M. Fyfe, Inertia eﬀects on the ductile failure of thin rings, Journal of Applied Mechanics, Transactions of the ASME, 49, 31-36, 1982.
13. R. J. Clifton, J. Duffy, K. A. Hartley, T. G. Shawki, On the critical conditions for shear band formation at high strain rates, Scripta Metall., 5, 443–448, 1984;.
14. R. C. Batra, C. H. Kim, Eﬀect of viscoplastic ﬂow rules on the initiation and growth of shear bands at high strain rate, J. Mech. Phys. Solids, 6, 859–874, 1990.
15. J. R. Klepaczko, Remarks on impact shearing, J. Mech. Phys. Solids, 35, 1028–1042, 1998.
16. Z. Xue, A. Vaziri, J.W. Hutchinson, Material aspects of dynamic neck retardation, J. Mech. Phys. Solids, 56, 93–113, 2008.
17. J. W. Hutchinson, K. W. Neale, Inﬂuence of strain rate sensitivity on necking under uniaxial tension, Acta Metall., 25, 839–846, 1977.
18. A. K. Ghosh, Tensile instability and necking in materials with strain hardening and strain-rate hardening, Acta Metall., 25, 1413–1424, 1977.
19. C. Fressengeas, A. Molinari, Instability and localization of plastic ﬂow in shear at high strain rates, J. Mech. Phys, Solids, 2, 185–211, 1987;.
20. C. Fressengeas, A. Molinari, The time development of Eulerian/Lagrangian perturbations to simple shear and its applications to shear banding, J. Mech. Phys. Solids, 8, 1735–1756, 1992.
21. F. L. Niordson, A unit for testing materials at high strain rates, Exp. Mech., 5, 29–32, 1965.
22. D. E. Grady, D. A. Benson, Fragmentation of metal rings by electromagnetic loading, Exp. Mech., 12, 393–400, 1983.
23. X. Hu, G. S. Daehn, Eﬀect of velocity on ﬂow localization in tension, Acta Mater., 44, 1021–1033, 1996.
24. M. Altynova, X. Hu, G. S. Daehn, Increased ductility in high velocity electromagnetic ring expansion, Metall. Trans. A, 27, 1837–1844, 1996.
25. H. Zhang, K. Ravi–Chandar, On the dynamics of necking and fragmentation – I. Realtime and post-mortem observations in Al 6061-O, Int. J. Fract., 142, 183–217, 2006.
26. H. Zhang, K. Ravi–Chandar, On the dynamics of necking and fragmentation – II. Eﬀect of material properties, geometrical constraints and absolute size, Int. J. Fract., 150, 3–36,2008.
27. S. Mercier, A. Molinari, Analysis of multiple necking in rings under rapid radial expansion, Int. J. Impact. Eng., 4, 403–419, 2004.
28. A. Rusinek, R. Zaera, Finite element simulation of steel ring fragmentation under radial expansion, Int. J. Impact. Eng., 34, 799–822, 2007.
29. U. F. Kocks, A. S. Argon, M. F. Ashby, Thermodynamics and kinetics of slip, [in:] Progress in Materials Science, vol. 19, Chalmers B., Christian J.W., Massalski T.B. [Eds.], Pergamon Press, Oxford, 1975.
30. F. J. Zerilli, R. W. Armstrong, Dislocation-mechanics-based constitutive relations for material dynamics calculations, J. Appl. Phys., 61, 1816–1825, 1987.
31. S. Nemat–Nasser, Y. Li, Flow stress of FCC polycrystals with application to OFHC Copper, Acta Mater., 46, 565–577, 1998.
32. A. Rusinek, J. R. Klepaczko, Shear testing of sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the ﬂow stress, Int. J. Plasticity, 17, 87–115, 2001.
33. S. Nemat–Nasser, W. G. Guo, Thermomechanical response of DH-36 structural steel over a wide range of strain rates and temperatures, Mech. Mat., 35, 1023–1047, 2003.
34. G. Z. Voyiadjis, F. H. Abed, Microstructural based models for bcc and fcc metals with temperature and strain rate dependency, Mechanics of Materials, 37, 355–378, 2005.
35. F. H. Abed, G. Z. Voyiadjis, Plastic deformation modeling of AL-6XN stainless steel at low and high strain rates and temperatures using a combination of bcc and fcc mechanisms of metals, Int. J. Plasticity, 21, 1618–1639, 2005.
36. G. Z. Voyiadjis, A. H. Almasri, A physically based constitutive model for fcc metals with applications to dynamic hardness, Mech. Mater., 40, 549–563, 2008.
37. A. Rusinek, J. A. Rodr´ıguez–Mart´ınez, R. Zaera, J. R. Klepaczko, A. Arias, C. Sauvelet, Experimental and numerical analysis of failure process of mild steel sheets subjected to perpendicular impact by hemispherical projectiles, Int. J. Impact. Eng., 36, 565–587, 2009.
38. A. Rusinek, J. A. Rodr´ıguez–Mart´ınez, A. Arias, A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper, Int. J. Mech. Sci., 52, 120–135, 2010.
39. M. C. Cai, L. S. Niu, X. F. Ma, H. J. Shi, A constitutive description of the strain rate and temperature eﬀects on the mechanical behavior of materials, Mech. Mat., 42, 774–781, 2010.
40. C. Y. Gao, L. C. Zhang, A constitutive model for dynamic plasticity of FCC metals, Materials Science and Engineering A., 527, 3138–3143, 2010.
41. A. Seeger, The mechanism of glide and work-hardening in face centered cubic and hexagonal close-packed metal, [in:] Dislocations and Mechanical Properties of Crystals, J. Wiley, New York, 1957.
42. U. F. Kocks, Realistic constitutive relations for metal plasticity, Mat. Sci. and Eng. A., 317, 181–187, 2001.
43. J. A. Rodr´ıguez–Mart´ınez, A. Rusinek, J. R. Klepaczko, Constitutive relation for steels approximating quasi-static and intermediate strain rates at large deformations, Mech. Res. Com., 4, 419–427, 2009.
44. J. R. Klepaczko, A general approach to rate sensitivity and constitutive modeling of FCC and BCC metals, [in:] Impact: Eﬀects of Fast Transient Loadings, Rotterdam, 3–35, 1998.
45. A. Rusinek, J. A. Rodr´ıguez–Mart´ınez, J. R. Klepaczko, R. B. Pecherski, Analysis of thermo-visco-plastic behaviour of six high strength steels, J. Mater. Des., 30, 1748–1761, 2009.
46. P. S. Follansbee, U. F. Kocks, A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable, Acta Metall., 1, 81–93, 1988.
47. J. R. Klepaczko, Thermally activated ﬂow and strain rate history eﬀects for some polycristalline f.c.c. metals, Materials Science and Engineering, 18, 121–135, 1975.
48. J. R. Klepaczko, B. Rezaig, A numerical study of adiabatic shear banding in mild steel by dislocation mechanics based constitutive relations, Mechanics of Materials, 24, 125–139, 1996.
49. R. Kapoor, S. Nemat–Nasser, Comparison between high strain-rate and low strain-rate deformation of tantalum, Metall. Mater. Trans., 31A, 815–823, 1999.
50. S. Nemat–Nasser, W. G. Guo, D. P. Kihl, Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures, J. Mech. Phys. Solids, 49, 1823–1846, 2001.
51. A. Rusinek, J. A. Rodriguez–Martinez, R. Pesci, J. Capelle, Experimental characterisation and modelling of thr thermo-viscoplastic behaviour of steel AISI 304 within wide ranges of strain rate at room temperature, Journal of Theoretical and Applied Mechanics, 2010 [in press].
52. O. Oussouaddi, J. R. Klepaczko, An analysis of transition from isothermal to adiabatic deformation in the case of a tube under torsion [in French], Proceedings Conf. DYMAT 91, Journal de Physique IV 1991, Coll. C3 (Suppl. III), C3–323.
53. A. Rusinek, R. Zaera, J. R. Klepaczko, Constitutive relations in 3-D for a wide range of strain rates and temperatures – application to mild steels, Int. J. Solids Struct., 44, 5611–5634, 2007.
54. P. S. Follansbee, High-strain-rate deformation of FCC metals and alloys, [in:] Metallurgical applications of shock-wave and high-strain-rate phenomena, pp. 451–479, 1986.
55. J. A. Zukas, D. R. Scheffler, Practical aspects of numerical simulations of dynamic events: eﬀects of meshing, Int. J. Impact Eng., 925–945, 2000.
56. M. Larson, A. Needlemen, V. Tvergaard, B. Storakers, Instability and failure of internally pressurized ductile metal cylinders, Internal report, Division of Engineering, Brown University, Providence, June 1981.
57. J. B. Han, V. Tvergaard, Eﬀect of inertia on the necking behaviour of ring specimens under rapid axial expansion, Eur. J. Mech. A/Solids, 14, 287–307, 1995.
58. N. J. Sorensen, L. B. Freund, Unstable neck formation in a ductile ring subjected to impulsive radial loading, Int. J. Solids Struct., 37, 2265–83, 2000.
59. G. Z. Voyiadjis, F. H. Abed, A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals, International Journal of Plasticity, 22, 1398–1431, 2006.
60. J. A. Nemes, J. Eftis, Constitutive modelling on the dynamic fracture of smooth tensile bars, International Journal of Plasticity, 9, 243–270, 1993.
61. R. Zaera, J. Fernandez–S ´ aez ´ , An implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and ﬁnite deformations, Int. J. Solids Struct., 43, 1594–1612, 2006.
62. N. Triantafyllidis, J. R. Waldenmyer, Onset of necking in electro-magnetically formed rings, J. Mech. Phys. Solids, 52, 2127–2148, 2004.

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Bibliografia

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