Lateral release waves in shocked solids

Various shock and detonation experiments and applications are affected by lateral release waves; however, we’re unaware that any simple method has been offered by which shock erosion can be quickly and easily quantified. We present for this purpose the geometric equation derived by Dennis Hayes in the late 1970s, which he never published. We wish to honor Dennis by doing so in his name, at this, the first SCCM meeting following his death in January 2023. The Hayes equation gives the angle, θ, that the release-wave leading-edge traces as it moves along the initially undisturbed shock toward the charge center. To evaluate θ, salient equation of state information must also be specified. For this purpose we derive an equation for the isentropic bulk modulus, Ks, in which we make the common assumption that the shock speed, U, and shock-induced particle velocity, u, are linearly related via the Hugoniot equation U = c0 + su. One must further specify the functional dependence of the Grüneisen parameter, Γ; for this we make the common assumption that Γ ρ=constant, and employ the Dugdale-MacDonald result for Γ0. Our final result expresses θ in terms of shock Mach number, M, and the Hugoniot slope, s. Under the same assumption, the shock pressure, P, can likewise be simply expressed in terms of M and s, plus parameters c0 and ρ0 (the initial density). Thus may θ [P] be plotted parametrically in terms of M. Besides its mathematical tractability, the beauty of the present analysis is that ρ0, c0, and s have been measured for most important inert and energetic materials.