Analytical solutions for material line and plane in triple slip, with inverse solutions for the slips from a finite deformation experiment on iron crystals

Abstract

Triple-slip analytical solutions are derived for rotation and extension of crystal material lines and planes relative to the underlying lattice, applicable to any crystal class. An algebraic inverse solution is then developed for the amounts of slip on the three systems (two collinear) in terms of initial and final positions of material line and plane. The solutions are applied to a finite deformation experiment (from the recent literature) on a bcc iron crystal in uniaxial compression, considering both {110} and {112} slip-planes. The respective slips and areal and length changes are determined from the initial and final experimental positions of the compression plane and an edge line. Such analyses can assist in assessment of relative hardening rates of the slip systems.