Part II – February 1968 - Communication - Crystallography of Shock Compression

PREVIOUS studies of the shock loading of randomly oriented polycrystalline aggregates have firmly established that, after rather short load duration, hydrostatic compression closely approximates the shocked state.' However, McQueen deduced from pressure measurements with good time resolution that, during shock loading, metals begin to undergo a stress relaxation at the yield stress. He suggested that the relaxation is due to plastic deformation accompanying the change from a one-dimensional compression to a three-dimensional, hydrostatic, compression.' Stress relaxation may occur faster as stress is increased above the yield stress, but the existence of unidirectionally compressed states for finite times suggests that the concept of a unidirectionally distorted lattice should furnish considerable insight into the mechanical behavior of materials subjected to shock loading. Here, a crystallographic analysis is presented for the hypothetical situation where atom motion may be considered as unidirectional which, as indicated above, is a useful extension of the macroscopic concept of shock loading to the microscopic domain. Only motion caused by the com-pressive forces is treated; i.e., lattice vibrations upon which this motion is superimposed, as discussed by Fitzgerald, are ignored.3 The purpose of the analysis to be presented is to develop a description for single crystals of the lattice rotations that occur for idealized uniaxial strain deformation. The usefulness of such an analysis in realistic deformation is to give a method of specification of those properties of an initially distorted lattice which would affect the subsequent deformation. Non-axial complications that arise experimentally, such as off-axis rarefaction waves, must be treated in proper context. Consider the material element shown in Fig. 1 and let the compression be uniform at all regions of the element. Then, any interior point of the element is displaced in proportion to its distance from the base of the element. Accordingly, if the top of a unit element is displaced by an amount, (-K), with respect to the base, a point P(X, Y) will be displaced by (-KY). Crystal planes are, therefore, rotated by the compression. Analysis of this rotation may be accomplished from the geometry shown in Fig. 1 where the line OP is the edge of the plane {hkl} and N is its normal. The orientation of the crystal plane with respect to the shock direction is specified by the angle, before deformation. After deformation the edge of plane {hkl}