Elastic-plastic impact (some persistent misconceptions)

摘要

The first rational model of elastic-plastic impact was presented about 37 years ago (J. W. Taylor and M. H. Rice, 1963). They showed that the magnitude of the then mysterious "elastic precursor" is simply the dynamic yield stress; and their model eliminated the mythic "plastic waves"; an incorrect part of the earlier literature. They showed that impact of one flat solid on another produces uniaxial elastic waves traveling with the longitudinal wave speed, and containing both shear and dilatational strain energies. The shear stresses larger than the yield stress get absorbed by plastic deformation; the hydrostatic stresses do not. Thus the uniaxial wave soon becomes two waves; one of lower amplitude travelling at the elastic longitudinal wave speed, and the other of higher amplitude travelling at the slower speed of pressure waves. Both waves are elastic. There are no "plastic waves", although references to them still appear in the literature. Several misconceptions (of more, or less, persistence in each case) regarding elastic-plastic impacts include: 1. Elastic and plastic deformations can be treated as if they are equivalent (they are not equivalent since they are conservative, and non-conservative, respectively; 2. Plastic deformation is rate independent; 3. There is an equation-of-state for plastic deformation (not valid); 4. Impact is a hydrodynamic process; 5. Dislocation effective masses are a function of velocity (this fallacy is based on incorrect solutions of the equations of motion; 6. Dislocation multiplication is a kinetically zero order process (wrong! Koehler's multiplication process is first order); 7. The expression for the plastic deformation-rate contains a multiplication-rate term (not true because the displacements associated with dislocations are finite); 8. Dislocations can propagate supersonically (the equations that indicate this are incorrect, as are existing molecular-dynamic simulations).