One-dimensional dislocations IV. Dynamics

Abstract

Tho equations of motion of the one-dimensional dislocation model are studied, and all solutions representing disturbances propagated without change of form are obtained. These comprise: (i) dislocations, and regular sequences of the same, either of like or of alternating sign, travelling with velocity less than c , the characteristic wave velocity of the system; (ii) an iddislocations, and sequences of the spme, travelling with velocity greater than c; and (iii) waves of infinitesimal amplitude, belonging to two branches travelling respectively with velocities less than and greater than c . Only dislocations or sequences of dislocations of like sign, and waves of velocity less than c , correspond to stable equilibria. The dislocations exhibit ‘relativistic’ behaviour. The relevance of anti-dislocations to very fast slip in solids is considered, and rejected.