The Mott Fragmentation Model and the Vpl break-up parameter

It is shown that the Mott fragmentation model and the Hirsch formula for the shaped charge jet break-up time complete one another to yield a unified model. This model is consistant with the microscopic picture of internal flow splitting in the metal, into shear bands undergoing a strain larger than the average and the metal between them which undergoes a strain which is smaller than the average. This splitting reduces the deformation energy dissipated by the metal while elongating. It corresponds to the splitting of the stress versus strain characteristics of the metal into the isothermic and adiabatic curves as measured by Johnson and Cook. The parameter V_plwhich describes the break-up process according to the Hirsch model, is identified with the expression (dσ_m/ϱ)^1/2 where dσ_m is the difference in yield strength between the isothermic and adiabatic curves where the adiabatic characteristic becomes a maximum. The comparison with available experimental measurements of this prediction shows a very encouraging agreement. The weak dependence of V_pl on the strain rate on the one hand and the observed increase of the jet break-up time in slowly elongating jets on the other hand are also explained using energy considerations. The recent recovery of jet particles by Zernow yields supportive evidence of the proposed theory which may be extended to all semi steady metal plastic flow phenomena. The final break-up, according to this model is due to the separation between the two sides of shear bands where the slide motion went on during the whole deformation process.