Abstract
We use the finite element code DYNA3D to analyze large thermomechanical deformations of a prenotched plate impacted on the notched side by a cylindrical projectile moving parallel to the axis of the notch. Both the projectile and the plate are assumed to be made of the same thermally softening but strain and strain-rate hardening material. It is found that the maximum speed imparted to points of the plate on the impact surface equals nearly 90% of the projectile speed, and the rise time depends upon the quasistatic yield stress of the material. Whereas deformations on the midsurface of the plate closely resemble a plane strain state of deformation, those on the traction free front and back surfaces are quite different. Thus measurements made on these surfaces may not describe well the deformations occurring in the interior of the plate.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Batra, R. C. and Adulla, C. (1995). Effect of prior quasistatic loading on the initiation and growth of dynamic adiabatic shear bands. Archives of Mechanics 47, 485–498.
Batra, R. C. and Gummalla, R. R. (2000). Effect of material and geometric parameters on deformations near the notch-tip of a dynamically loaded prenotched plate. International Journal of Fracture 101, 99–140.
Batra, R. C. and Jayachandran, R. (1992). Effect of constitutive models on steady state axisymmetric deformations of thermoelastic-viscoplastic targets. Internatioanl Journal of Impact Engineering 12, 209–226.
Batra, R. C. and Kim, K.H. (1990). Effect of viscoplastic flow rules on the initiation and growth of shear bands at high strain rates. Journal of the Mechanics and Physics of Solids 38, 859–874.
Batra, R. C. and Kim, C.H. (1991). Effect of thermal conductivity on the initiation, growth and bandwidth of adiabatic shear bands. International Journal of Engineering Science 29, 949–960.
Batra, R. C. and Kim, C.H. (1992). Analysis of shear bands in twelve materials. International Journal of Plasticity 8, 425–452.
Batra, R. C. and Nechitailo, N. V. (1997). Analysis of failure modes in impulsively loaded pre-notched plates. International Journal of Plasticity 13, 291–308.
Batra, R. C. and Rattazzi, D. (1997). Adiabatic shear banding in a thick-walled steel tube. Computational Mechanics 5, 442–426.
Batra, R. C. and Stevens, J. B. (1998). Adiabatic shear bands in axisymmetric impact and penetration problems. Computer Methods in Applied Mechanics and Engineering 151, 325–342.
Batra, R. C., Rajapakse, Y. D. S. and Rosakis, A. J. (eds.). (2000) Failure mode transitions under dynamic loading. International Journal of Fracture 101, 1–180.
Batra, R. C. and Chen, L. (2000). Effect of viscoplastic relations on the instability strain, shear band initiation strain, the strain corresponding to the minimum shear band spacing, and the band width in a thermoviscoplastic material (pending publication).
Chen, L. and Batra, R. C. (1998). Analysis of material instability at an impact loaded crack tip, Theoretical and Applied Fracture Mechanics 29, 213–217.
Curran, D. R., Seaman, L. and Shockey, D. A. (1987). Dynamic failure of solids. Physics Reports 147, 253–388.
Dowling, N. E. (1993). Mechanical Behavior of Materials, Prentice Hall, New York.
Johnson, G. R. and Cook, W. H. (1983). A constitutive model and data for metals subjected to large strains, high strain rates, and temperatures. Proceeding 7th International Symposium Ballistics, The Hague, The Netherlands, 1–7.
Kalthoff, J. F. (1987). Shadow optical analysis of dynamic shear fracture. SPIE, Photomechanics and Speckle Metrology 814, 531–538.
Kalthoff, J. F. and Winkler, S. (1987). Failure mode transition at high rates of shear loading. In: Impact Loading and Dynamic Behavior of Materials (Edited by Chiem, C.Y., Kunze, H.D. and Meyer, L.W.) Vol. 1, 185–195.
Kalthoff, J. F. (2000). Modes of dynamic shear failure in solids. International Journal of Fracture 101, 1–31.
Kim, C. H. and Batra, R.C. (1992). Effect of initial temperature on the initiation and growth of shear bands in a plain carbon-steel, International Journal of Nonlinear Mechanics 27, 279–291.
Klepaczko, J. R., Lipinski, P. and Molinari, A. (1987). An analysis of the thermoplastic catastrophic shear in some metals, in Chiem, C. Y., Junze, H. D. and Meyer, L. W. (eds.), Impact Loading and Dynamic Behavior of Materials, Verlag, 1, 695–704.
Lee, Y. J. and Freund, L.B. (1990). Fracture initiation due to asymmetric impact loading of an edge cracked plate. Journal of Applied Mechanics 57, 104–111.
Marchand, A. and Duffy, J. (1988). An experimental study of the formation process of adiabatic shear bands in a structural steel. Journal of the Mechanics and Physics of Solids 36, 251–283.
Mason, J. J., Rosakis, A.J. and Ravichandran, G. (1994). Full field measurements of the dynamic deformation field around a growing adiabatic shear band at the tip of a dynamically loaded crack or a notch. Journal of the Mechanics and Physics of Solids 42, 1679–1697.
Mason, J. J., Zimmerman, J. A. and Roessig, K. M. (1998). The effect of ageing condition on shear localization from the tip of a notch in maraging steel. Journal of Material Sciences 33, 1451–1460.
Needleman, A. and Tvergaard, V. (1995). Analysis of brittle-ductile transition under dynamic shear loading. International Journal of Solids and Structures 32, 2571–2590.
Perzyna, P. (1986). Constitutive modeling for brittle dynamic fracture in dissipative solids. Archive of Mechanics 38, 725–738.
Ravi-chandar, K., Lu, J., Yang, B. and Zhu, Z. (2000). Failure mode transitions in polymers under high strain loading. International Journal of Fracture 101, 33–72.
Ritchie, R. O., Knott, J.F. and Rice, J. R. (1973). On the relationship between critical tensile stress and fracture toughness in mild steel. Journal of the Mechanics and Physics of Solids 21, 395–410.
Roessig, K. M. and Mason, J. J. (1998). Adiabatic shear localization in the impact of edge-notched specimens. Experimental Mechanics 38, 196–203.
Taylor, G. I. and Quinney (1934). The latent energy remaining in a metal after cold working. Proceeding of the Royal Society A413, 307.
Tvergaard, V. and Needleman, A. (1984). Analysis of the cup-cone fracture in a round tensile bar. Acta Metallurgica 32, 157–169.
Vandergiessen, E., Vanderburg, M. W. D., Needleman, A. and Tvergaard, V. (1995). Void growth due to creep and grain-boundary diffusion at high triaxialities. Journal of the Mechanics and Physics of Solids 43, 123–165.
Whirley, R. C. and Hallquist, J. O. (1991). DYNA3D User's Manual (A nonlinear explicit three-dimensional finite element code for solid and structural mechanics), UCRL-MA-107254, University of California, Lawrence Livermore National Laboratory.
Zhou, M., Rosakis, A. J. and Ravichandran, G. (1996a). Dynamically propagating shear bands in prenotched plates: I - experimental investigations of temperature signatures and propagation speed. Journal of the Mechanics and Physics of Solids 44, 981–1006.
Zhou, M., Ravichandran, G. and Rosakis, A. J. (1996b). Dynamically propagating shear bands in prenotched plates: II - finite element simulations. Journal of the Mechanics and Physics of Solids 44, 1007–1032.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Batra, R., Ravinsankar, M. Three-dimensional numerical simulation of the Kalthoff experiment. International Journal of Fracture 105, 161–186 (2000). https://doi.org/10.1023/A:1007658224458
Issue Date:
DOI: https://doi.org/10.1023/A:1007658224458