THE CONTINUOUSLY DISLOCATED CONTINUUM: ELASTIC PLASTIC PLANE BENDING OF A SINGLE CRYSTAL.
Annual technical rept. no. 1, 1 Feb 68-31 Jan 69,
FLORIDA UNIV GAINESVILLE DEPT OF ENGINEERING SCIENCE AND MECHANICS
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The elastic-plastic bending of a single crystal beam has been analyzed using both continuum plasticity and dislocation theory. A simple prismatic beam bent by couples applied to both ends is considered. The elastic solution is obtained for both isotropic beams and a particular orientation of an anisotropic beam. Both linear work-hardening and perfectly plastic models of material behavior are employed. It is demonstrated that phenomenalogical coefficients appearing in the plasticity solution can be rationalized in terms of dislocation content and distribution. The results of continuum dislocation theory are checked by direct integration and direct summation of the stress fields of individual dislocations in a continuously distributed array and a discrete array. Author