Shock Waves

, Volume 29, Issue 3, pp 451–469 | Cite as

A new model for the time delay between elastic and plastic wave fronts for shock waves propagating in solids

  • M. HallajisanyEmail author
  • J. Zamani
  • M. Seyed Salehi
  • J. Albelda Vitoria
Original Article


A time delay is created between elastic and plastic wave fronts because of the difference between the elastic longitudinal sound speed and the plastic shock wave velocity. Over a short propagation distance, the time delay between the elastic and plastic wave fronts at the Hugoniot elastic limit (HEL) is nonlinear, while at larger distances, the time delay is linear. In this work, a new time delay model is introduced that is based on the distance traveled by the waves and using the Rayleigh–Hugoniot jump relations for elastic–perfectly plastic materials. The results of the model have shown in FCC metals the subsonic shock velocity is due to the reduction of shear stress in an unsteady wave being greater than the one in the steady wave. The reduction of the plastic shock wave speed and formation of the elastic shock at the moment of impact are found to result in the nonlinear relationship of the lag between elastic and plastic wave fronts. For calculating the nonlinear time delay in a relaxing material, the lower HEL must be used; the elastic shock is important when the difference between the longitudinal elastic sound speed and the plastic shock wave speed is very small or when the ratio of the HEL to the applied stress is high. In BCC metals, V, Cr, and W, a different behavior has been observed which is in contrast to FCC metals, Ag, Al, and Cu. Therefore, the different behavior is due to a different mechanism that occurs in BCC metals.


Elastic shock Plastic shock wave speed Longitudinal elastic sound speed Hugoniot elastic limit Time delay 



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Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringK. N. Toosi University of TechnologyTehranIslamic Republic of Iran
  2. 2.Faculty of Materials Science and EngineeringK. N. Toosi University of TechnologyTehranIslamic Republic of Iran
  3. 3.Department of Mechanical and Materials EngineeringUniversity Polytechnic of Valencia (UPV)ValenciaSpain

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