INTRODUCTION

For pencil glide, the five independent slip variable necessary to produce an arbitrary shape change can be the amount of slip in a given direction and the orientation of the plane (angle of rotation about the direction). There are two possibilities for five systems: Either three or four active slip directions can be active. Chin and Mammel [1] used a Taylor type analysis for combined slip on {110}, {123}, and {112} planes, finding that Mav for axially symmetric flow = 2.748 (Figure 10.1). Hutchinson [2] approximated pencil glide by assuming slip on a large, but finite number of slip planes. Both of these analyses used the least work approach of Taylor. Penning [3] described a least-work solution considering the possibility of both three and four active slip directions. Parniere and Sauzay [4] described a least work solution.

METHOD OF CALCULATION

Piehler et al [5, 7, 8] used a Bishop and Hill-type approach, by considering the stress states capable of activating enough slip systems. Explicit expressions were derived for the stress states in the case of four active slip directions. Instead of explicit solutions for the case of three active slip directions, a limited number of specific cases were considered. The stress states are: