Flattening in shear zones under constant volume: a theoretical evaluation

This paper presents a theoretical model based on strain energy and work rat e calculations that evaluates the possible degrees of flattening in P finit e, ductile shear zones with rigid and deformable walls under constant volum e conditions. The principal parameters governing the ratio of bulk flatteni ng and shear rates (S-r = epsilon (b)/gamma (b)) in shear zones with rigid walls are found to be: (1) the length to width ratio (D-f ; measured in the normal section parallel to the extrusion direction), and (2) the inclinati on of shear zone normal (alpha) with the bulk compression direction. Narrow and long shear zones (D-f > 10) are characterized by low S, ratios, implyi ng little flattening in the shear zone even when Ce is low (in the order of a few degrees). Accordingly, the kinematical vorticity number W-k is close to one when D-f is large (> 10) or a is high (> 20 degrees), and is much l ess than one if D-f or a are low. The stretching rate of shear zone walls r elative to the shear zone (R-f) is an additional parameter that controls th e degree of flattening in shear zones with deformable walls. For given D-f and a values the flattening rate increases with increasing relative stretch ing rate R-f, and is significant at large values of R-f. Likewise the kinem atical vorticity number W-k shows an inverse relation with the relative str etching rate of shear zone walls. (C) 2001 Elsevier Science Ltd. All rights reserved.