Experimental and theoretical observations on the relationship between dislocation cell size, dislocation density, residual hardness, peak pressure and pulse duration in shock-loaded nickel

Abstract

Dislocation density and dislocation cell sizes have been measured along with residual hardness in nickel shockloaded with peak pressures ranging from 80 to 460 kbar at a constant pulse duration of 2 μs, and similarly for 0.5 to 6 μs shock pulse duration at a constant peak pressure of 250 kbar. The dislocation cell size was found to be inversely proportional to the square root of the dislocation density ( d√ ρ ≅ 15), consistent with the “principle of similitude”, as well as to the peak pressure (i.e. P = k d ) in accordance with a widely observed empirical law. The residual dislocation cell size and dislocation density were observed to remain essentially constant in the range of 1–6 μs pulse duration, suggesting that the rate at which dislocations can move into cell configurations lies somewhat below this value. The residual hardness increases with decreasing cell size, but not linearly, and saturates over the range of shock pulse durations investigated at constant peak pressure. When these measurements are evaluated in terms of the mesh-length theory of work-hardening, an apparently good agreement is found and the data reveal a high degree of internal consistency within the limits of experimental error. However, the effective resolved shear stress on the active glide systems is found to be a constant but unexpectedly low fraction of the peak pressure, namely about 1 1/2%. Moreover. at the very high shock pressures used, the Peierls-Nabarro stress might have been too high to permit dislocations to move into the observed sub-boundary configurations. Consistent explanations for all of the observations are possible whether or not the Peierls stress under pressure should have been high. In the former case, the dislocation cells formed only at the very end of the shock, when the shock pressures were already well below their peak values. The low value of the computed flow stress arises because the shock generated an essentially hydrostatic pressure. There should have in fact been no slip if it had not been for small deviations from hydrostatic pressure conditions. The rate of work hardening appears to have been 3–4 times higher than for the same strain in tensile testing. Imperfect cell formation and a high rate of dislocation retention is believed to be responsible.