By John D. Campbell
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Extra info for Dynamic Plasticity of Metals: Course Held at the Department for Mechanics of Deformable Bodies, July 1970
27. - __ ...... 0 -- ---- --------"'7"10 Shear pre-strain so that a discontinuity is formed. r. 2) where ~g is the discontinuity in the strain. 3) 1 Cs Equations f ~(} = 9M. 3) may be Shock waves 43 applied to the propagation of a wave under conditions of uniaxial stress or of uniaxial strain. Much of the experimental work on shock waves on solids has been carried out in uniaxial strain conditions with very high compressive stresses produced by explosives. Under these conditions the stress-strain relation is effectively linear up to the dynamic compressive yield stress Py but for higher stresses the relation is such thatd5/de increases with increasing compressive strain.
This effect has been explained in terms of a rate-dependent constitutive relation based on dislocation dynamics  . Chap. 80x 104 em/sec. 45x Icf em/sec 3 X(cm) Fig. 28. Cartesian plot of the Hugoniot elastic wave free-8Urface velocity for annealed Armco iron. The parameter u 0 is the initial impact velocity. [ 42] Chapter 3. Experimental Methods and Results. 1. Tests at Medium Strain Rates. dependent materials have been discussed by Cooper and Campbell  . The observed behaviour depends on the interaction of the specimen and test machine, which is largely determined by their relative stiffnesses.
This may be shown by a perturbation method i for uniaxial tension or compression loading, the wave speed is