Past exam of the materials science course of the University of Cambridge 2016 Paper 1 5 c Solution 2026-10-20
A second slip system begins to operate as the tensile-axis rotation makes its resolved shear stress comparable to that on the primary system. Dislocations on intersecting planes interact much more strongly, giving the transition from easy single slip to rapid work hardening. The standard geometric estimate neglects differences between the evolving critical stresses of the two systems.
The primary direction is . Single-slip shear carries the line joining the specimen ends, expressed in crystal coordinates, alongThe initial fundamental sector has . Its first reached boundary is , at , giving . At that orientation and have equal Schmid factors. Since the component perpendicular to the primary slip direction is unchanged by that shear, the length ratio follows directly:ThereforeThe corresponding logarithmic strain is . This is an ideal equal-critical-stress geometric onset estimate. Real secondary slip can start earlier or later because of latent hardening, nonuniform deformation and grip constraints; the problem supplies no hardening law that would determine that shift.[ref]
Applied Mechanics of Solids by A. F. Bower. §3.12.2, points10–12: tensile-axis rotation, secondary slip and stages of hardening