Evolution of plastic zones in dynamically loaded plates using different elastic-viscoplastic laws

International Journal of Solids and Structures

Volumn 41, Issue 24-25, 2004, Pages 6813-6830

  Stoffel, Marcus ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Dynamics; Elastic viscoplastic; Mechanical testing; Shock waves

Indexed keywords

COMPUTER SIMULATION; PLASTICITY; SHOCK WAVES; STRAIN; STRAIN RATE; STRESS ANALYSIS; VISCOPLASTICITY;

DYNAMICALLY LOADED PLATES; ELASTO-VISCOPLASTIC; PLASTIC STRAIN RATE; PLASTIC ZONES;

PLATES (STRUCTURAL COMPONENTS);

EID: 4544324823     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2004.05.060     Document Type: Article

References (53)

1. Andrade E.N., Da C. On the viscous flow of metals and allied phenomena. Proc. Roy. Soc. (A), London. 85:1910;A567.
2. Batra R.C., Jaber N.A., Malsbury M.E. Analysis of failure modes in an impact loaded thermoviscoplastic prenotched plate. Int. J. Plast. 19:2003;139-196.
3. Bodner S.R., Partom Y. Constitutive equations for elasto-viscoplastic strain-hardening materials. ASME J. Appl. Mech. 42:1975;385-389.
4. Bruhns O.T. Einige Bemerkungen zur Beschreibung inelastischer Prozesse im Bereich hoher Deformationsgeschwindigkeiten. ZAMM. 67:1987;T181-T183.
5. Chaboche J.L. Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plast. 5:1989;247-302.
6. Chan K.S., Bodner S.R., Lindholm U.S. Phenomenological modelling of hardening and thermal recovery in metals. J. Eng. Mat. Tech. 110:1988;1-8.
7. Colak O.U. A viscoplasticity theory applied to proportional and non-proportional cyclic loading at small strains. Int. J. Plast. 20:2004;1387-1401.
8. Cristescu N. Dynamic Plasticity. 1967;North-Holland, Amsterdam.
9. Doyle J.F. Wave Propagation in Structures. 1997;Springer-Verlag.
10. Eftis J., Carrasco C., Osegueda R.A. A constitutive-microdamage model to simulate hypervelocity projectile-target impact, material damage and fracture. Int. J. Plast. 2003;1321-1354.
11. Florence A.L. Circular plate under a uniformly distributed impulse. Int. J. Sol. Struct. 2:1966;37-47.
12. Gerard, G., 1956. A new experimental technique for applying impulse loads. In: Proc. Symp. on Impact Testing, Atlantic City.
13. Gurtin M.E. On a framework for small-deformation viscoplasticity: free energy, microforces, strain gradients. Int. J. Plast. 19:2003;47-90.
14. Haupt P., Kersten Th. On the modelling of anisotropic material behaviour in viscoplasticity. Int. J. Plast. 19:2003;1885-1915.
15. Häusler O., Schick D., Tsakmakis Ch. Description of plastic anisotropy effects at large deformations. Part II: The case of transverse isotropy. Int. J. Plast. 20:2004;199-223.
16. Imatani, S., Kokubo, K., Inoue, T., 1991. Rate dependent stress/strain response of a notched cylinder. In: Jono, M., Inoue, T. (Eds.), Proceedings of the Sixth International Conference on Mechanical Behaviour of Materials, 20.7.-2.8.1991, p. 793.
17. Idczak W., Rymarz Cz., Spychała A. Studies on shock-wave loaded, clamped circular plates. J. Tech. Phys. 22:1981;175-184.
18. Iyer S.K., Lissenden C.J. Multiaxial constitutive model accounting for the strength-differential in Inconel 718. Int. J. Plast. 19:2003;2055-2081.
19. Jones N. Structural Impact. 1989;Cambridge University Press.
20. Kajberg J., Sundin K.G., Melin L.G., Stahle P. High strain-rate tensile testing and viscoplastic parameter identification using microscopic high-speed photography. Int. J. Plast. 20:2004;561-575.
21. Kalthoff J.F. Modes of dynamic shear failure in solids. Int. J. Fract. 101:2000;1-31.
22. Kalthoff J.F., Winkler S. Failure mode transition at high rates of shear loading. Chiem C.Y., Kunze H.D., Meyer L.W. Impact Loading and Dynamic Behavior of Materials. vol. I:1987;185-195.
23. Klłosowski P., Woznica K., Weichert D. A comparative study of vibrations of elasto-viscoplastic shells and plates. Engng. Trans. 43:1995;183-204.
24. Kreja I., Schmidt R., Reddy J.N. Finite elements based on a first-order shear deformation moderate rotation shell theory with applications to the analysis of composite structures. Int. J. Non-Linear Mech. 32:1997;1123-1142.
25. Krempl E., Khan F. Rate (time)-dependent deformation behavior: an overview of some properties of metals and solid polymers. Int. J. Plast. 2003;1069-1095.
26. Krempl, E., McMahon, J.J., Yao, D., 1984. Viscoplasticity based on overstress with a differential growth law for equilibrium stress. In: Mechanics of Materials, 2nd Symp. on Non-linear Constitutive Relations for High temperature Applications, NASA, Cleveland, OH, vol. 5, p. 35.
27. Lehmann T. General frame for definition of constitutive laws for large nonisothermic elastic-plastic and elastic-viscoplastic deformations. The Constitutive Law in Thermoplasticity. CIMS Cours and Lectures. vol. 281:1984;Springer-Verlag, Wien, New York.
28. Lemaitre J., Chaboche J.L. Mechanics of Solid Materials. 1994;Cambridge University Press.
29. Lin R., Brocks W. On a finite strain viscoplastic theory based on a new internal dissipation inequality. Int. J. Plast. 20:2004;1281-1311.
30. Lubarda V.A., Benson D.J., Meyers M.A. Strain-rate effects in rheological models of inelastic response. Int. J. Plast. 19:2003;1097-1118.
31. Malvern L.E. Plastic wave propagation in a bar of material exhibiting a strain rate effect. Quart. Appl. Math. 8:1951;405-411.
32. Norton F.N. Creep of High Temperatures. 1929;McGraw-Hill Book Company, New York.
33. Palmerio A.F., Reddy J.N., Schmidt R. On a moderate rotation theory of laminated anisotropic shells, Part 1 - Theory, Part 2 - Finite element analysis. Int. J. Non-Linear Mech. 25:1990;687-714.
34. Perzyna P. The constitutive equations for rate sensitive plastic materials. Quart. Appl. Math. 20:1963;321-332.
35. Renard, J., Pennetier, O., 1996. Nonlinear dynamic response of plates submitted to an explosion, numerical and experimental study. In: Structural Dynamics-EURODYN'96, Balkema, Rotterdam, p. 689.
36. Rizzi E., Hähner P. On the Portevin-Le Chatelier effect. Int. J. Plast. 20:2004;121-165.
37. Schmidt R., Reddy J.N. A refined small strain moderate rotation theory of elastic anisotropic shells. ASME J. Appl. Mech. 55:1988;611-617.
38. Schmidt R., Weichert D. A refined theory of elastic-plastic shells at moderate rotations. ZAMM. 69:1989;11-21.
39. Schneidler M., Wright T.W. Classes of flow rules for finite viscoplasticity. Int. J. Plast. 19:2003;1119-1165.
40. Stoffel, M., 2000. Nichtlineare Dynamik von Platten. Ph.D. Thesis, RWTH, Aachen.
41. Stoffel M., Schmidt R., Weichert D. Vibrations of viscoplastic plates under impact load. Jones N., Talaslidis D.G., Brebbia C.A., Manolis G.D. Structures under Shock and Impact. vol. 5:1998;299-308 Computational Mechanics Publications, Southampton-Boston.
42. Stoffel M., Schmidt R., Weichert D. Experiment und Simulation stoßwellenbeanspruchter Platten. ZAMM. 81:2001;S231-S232.
43. Stoffel M., Schmidt R., Weichert D. Shock wave-loaded plates. Int. J. Solids Struct. 38:2001;7659-7680.
44. Stronge W.J., Yu T.X. Dynamic Models for Structural Plasticity. 1993;Springer-Verlag.
45. Tanimura S. A practical constitutive equation covering a wide range of strain rates. Int. J. Eng. Sci. 17:1979;997-1004.
46. Taylor, G.I., 1940. Propagation of earth waves from an explosion. In: British Official Report R.C. Vol. 70.
47. Tsakmakis Ch. Description of plastic anisotropy effects at large deformations. Part I: Restrictions imposed by the second law and the postulate of Il'iushin. Int. J. Plast. 20:2004;167-198.
48. Uenishi A., Teodosiu C. Constitutive modelling of the high strain rate behaviour of interstitial-free steel. Int. J. Plast. 20:2004;915-936.
49. von Kármán, T., 1942. On the propagation of plastic deformation in solids. In: N.D.R.C. Report, Nr. A-29 (O.S.R.D. Nr. 365).
50. Voyiadjis G.Z., Al-Rub R.K.A., Palazotto A.N. Thermodynamic frame work for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic loacalization problems using gradient theory. Int. J. Plast. 20:2004;981-1038.
51. Walker, K.P., 1981. Research and development program for non-linear structural modeling with advanced time-temperature dependent constitutive relationships. In: Report PWA-5700-50, NASA CR-165533.
52. Weichert D., Stoffel M. Theoretical and experimental investigations on plates under impulsive loading. Theocaris P.S., Fotiadis D.I., Massalas C.V. Proc. 5th National Congress on Mechanics. vol. 1:1998;72-83 University of Ioannina Press, Ioannina.
53. Wierzbicki T., Florence A.L. A theoretical and experimental investigation of impulsively loaded clamped circular viscoplastic plates. Int. J. Sol. Struc. 6:1970;553-568.