Shock jump equations for unsteady wave fronts of finite rise time

Abstract

Compression and shear wave measurements to characterize the shocked state in silicon carbideFirst, generalized Rankine-Hugoniot equations for unsteady wave fronts of finite width are derived. It is clarified from these jump equations for particle velocity, stress, and specific internal energy that shock jump conditions involve the effects of rise time of the front or the change in its velocity with time, in addition to that of strain rate and acceleration, and that the treatment in the previous study ͓Sano, J. Appl. Phys. 82, 5382 ͑1997͔͒ where the rise time is reduced to an infinitesimal eliminates the terms of this change in the jump equations. Furthermore, the jump equations of the general form derived here support this elimination. Next, the influence of the rise time on the three jumps at the impacted surface of a lithium fluoride single crystal is calculated based on its experimental data and shown to be negligibly small. However, its influence, calculated for sandstone in a similar manner, is great. Finally, a parametric investigation of the influence is carried out for specific strain waves.

Solitary waves and supersonic reaction front in metastable solids

“…For example the Chapman-Jouguet process yields a constant value for the velocity of the reaction front with respect to the unreacted phase. Sano and Miyamoto [33] have developed an unsteady state Rankine-Hugoniot theory and point out the deficiencies of the steady state theories. But arguably the greatest shortcoming of the theory to account for the above mentioned experiments is the lack of detailed description of events that occur on the microscopic level.…”

Generalized smooth and weak-discontinuous unsteady waves

“…It was recently clarified that the effects of the strain rate and strain acceleration induce smooth or weak-discontinuous unsteady wave fronts in those materials and they are responsible for anomalous stress-particle velocity and stress-strain paths. [5][6][7][8][9][10][11][12][13][14][15] In addition, Rankine-Hugoniot jump conditions 16,17 can only be applied insufficiently to some unsteady wave fronts that induce nonzero strain accelerations. 13,14 Use of these jump conditions in translating particle velocity into stress is one of the factors that causes the precursor decay anomaly in single-crystal lithium fluoride.…”

“…[5][6][7][8][9][10][11][12][13][14][15] In addition, Rankine-Hugoniot jump conditions 16,17 can only be applied insufficiently to some unsteady wave fronts that induce nonzero strain accelerations. 13,14 Use of these jump conditions in translating particle velocity into stress is one of the factors that causes the precursor decay anomaly in single-crystal lithium fluoride. 15 The unsteady wave fronts have been analyzed using only the conservation equations without using the constitutive relations because it is difficult to determine the function f in this case.…”

“…where b ii 0 and c iiϩ1 0; iϭ1,2,...,n. This generalization of the previous plane wave theory [5][6][7][8][9][10][11][12][13][14][15] using the conservation equations of mass and momentum also considers that B, C, and d depend on ũ, x, and t, respectively. The fundamental theorem demonstrates the theoretical existence of a smooth wave and a weak-discontinuous wave in a generalized wave.…”