Flattening in shear zones under constant volume: a theoretical evaluation

Abstract

This paper presents a theoretical model based on strain energy and work rate calculations that evaluates the possible degrees of flattening in finite, ductile shear zones with rigid and deformable walls under constant volume conditions. The principal parameters governing the ratio of bulk flattening and shear rates (S_r = ε_b/γ_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 inclination of shear zone normal (α ) with the bulk compression direction. Narrow and long shear zones (D_f>10) are characterized by low S_r ratios, implying little flattening in the shear zone even when a is low (in the order of a few degrees). Accordingly, the kinematical vorticity number Wk is close to one when D_f is large (>10) or a is high (>20°), and is much less than one if D_f or a are low. The stretching rate of shear zone walls relative to the shear zone (R_f) is an additional parameter that controls the degree of flattening in shear zones with deformable walls. For given D_f and a values the flattening rate increases with increasing relative stretching rate R_f, and is significant at large values of R_f. Likewise the kinematical vorticity number W_k shows an inverse relation with the relative stretching rate of shear zone walls.