Optimization of shaped charges

Efficient design of shaped charges requires a full calculation of all three basic processes involved: liner collapse, jet fragmentation, and subsequent penetration in the target. Claims have been made [S. S. Grigoryan and N. S. Sanasaryan, Mekh. Zhidkosti Gaza 6, 9 (1974); N. S. Sanasaryan, ibid. 6, 151 (1975)] that for given standoff distance, a certain initial jet velocity profile exists that corresponds to maximum penetration at this distance. We demonstrate that no such profile exists. In fact, the velocity profile yielding maximum penetration depth corresponds to infinite strain and is therefore of no practical interest. We abandon the ‘‘moving tank’’ representation of the jet formation adopted by previous authors, and treat the initial axial profiles of jet velocity and strain rate as independent quantities that are intrinsically related only through the shaped charge design. A general relationship is derived between initial axial profiles of jet velocity, strain rate, and total strain for a jet fragmenting exactly in the bottom of the crater it produces. The result is applied to two different fragmentation models of the jet, and the resulting constraints imposed on quantities associated with the initial jet is derived. We indicate how analytical relationships of this sort may help to improve liner geometries by identifying those parts of the liner where the ‘‘optimum’’ requirement of fragmentation in the crater bottom is least satisfied. Crude arguments indicate that the use of variable angle—variable thickness liners can improve penetration depths by typically a few tens of percent relative to conventional, straight conical liners.