On Bending of a Crystal to a Cylindrical Surface

[+] Author and Article Information
K. S. Havner

Department of Civil Engineering, North Carolina State University, Raleigh, N. C.

J. Appl. Mech 41(1), 184-188 (Mar 01, 1974) (5 pages) doi:10.1115/1.3423220 History: Received October 01, 1972; Revised March 01, 1973; Online July 12, 2010


This paper is concerned with macroscopic aspects of (large deformation) bending of a crystal to a cylindrical surface via slip in a single family of glide planes. The analysis rests upon the involute geometry of bent configurations and upon the adoption of an extended Schmid law. General stress fields required to bend the crystal are investigated considering possible phenomenological effects of (gross) glide plane curvature on local crystal hardening. In the case of linear (easy-glide) hardening of the glide system, an overall, nonlinear moment-curvature relation is developed. This general analytical equation, evaluated for zinc crystals, predicts a critical moment for large deformations and a finite moment with infinite rate of change at maximum bending.

Copyright © 1974 by ASME
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