Abstract
The Hugoniot curve relates the pressure and volume behind a shock wave, with the temperature having been eliminated. This paper studies the Hugoniot curve behind a propagating sharp interface between two material phases for a solid in which an impact-induced phase transition has taken place. For a solid capable of existing in only one phase, compressive impact produces a shock wave moving into material, say, at rest in an unstressed state at the ambient temperature. If the specimen can exist in either of two material phases, sufficiently severe impact may produce a disturbance with a two-wave structure: a shock wave in the low-pressure phase of the material, followed by a phase boundary separating the low- and high-pressure phases. We use a theory of phase transitions in thermoelastic materials to construct the Hugoniot curve behind the phase boundary in this two-wave circumstance. The kinetic relation controlling the evolution of the phase transition is an essential ingredient in this process.
Similar content being viewed by others
References
Erskine D.J. and Nellis W.J. (1992). Shock-induced martensitic transformation of highly oriented graphite to diamond. J. Appl. Physi. 71: 4882–4886
Abeyaratne R. and Knowles J.K. (2006). Evolution of Phase Transitions: A Continuum Theory. Cambridge University Press, New York
Abeyaratne R. and Knowles J.K. (2000). On a shock-induced martensitic phase transition. J. App. Phys. 87: 1123–1134
Courant R. and Friedrichs K.O. (1948). Supersonic Flow and Shock Waves. Interscience, New York
Ahrens T.J. (1993). Equation of State. In: Asay, J.R. and Shahinpoor, M. (eds) High Pressure Shock Compression of Solids., pp 75–114. Springer, New York
Meyers M.A. (1994). Dynamic Behavior of Materials. Wiley, New York
Dunn J.E. and Fosdick R.L. (1988). Steady, structured shock waves. Part 1: Thermoelastic materials. Arch. Rat. Mech. Anal. 104: 295–365
Menikoff R. and Plohr B.J. (1989). The Riemann problem for fluid flow of real materials. Rev. Modern Phys. 61: 75–130
Duvall G.E. and Graham R.A. (1977). Phase transitions under shock-wave loading. Rev. Modern Phys. 49: 523–579
Swegle J.W. (1990). Irreversible phase transitions and wave propagation in silicate geologic materials. J. Appl. Phys. 68: 1563–1579
Carlson, D.E.: Linear thermoelasticity. In: Truesdell, C. (ed.) Handbuch der Physik, vol. VIa/2 C, pp. 297–345. Springer, Berlin (1972)
Clifton R.J. (1993). Failure waves in glasses. Appl. Mech. Rev. 46: 540
Marsh S.P. (1980). LASL Shock Hugoniot Data. University of California Press, Berkeley
Escobar, J.C.: Plate impact induced phase transformations in CuAlNi single crystals, Ph.D. dissertation. Brown University, Providence, RI (1995)
Escobar J.C. and Clifton R.J. (1993). On pressure-shear plate impact for studying the kinetics of stress-induced phase transformations. J. Mater. Sci. Eng. A170: 125–142
Escobar J.C. and Clifton R.J. (1995). Pressure-shear impact-induced phase transitions in C-14.4 Al-4.19 Ni single crystals. SPIE 2427: 186–197
Gupta S.C. and Sikka S.K. (1996). Some investigations on shock wave induced phase transitions. Shock Waves 6: 345–359
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by N. Thadhani.
Rights and permissions
About this article
Cite this article
Knowles, J.K. On the structure of the Hugoniot relation for a shock-induced martensitic phase transition. Shock Waves 17, 421–432 (2008). https://doi.org/10.1007/s00193-008-0119-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00193-008-0119-0