Review of the Taylor ambiguity and the relationship between rate-independent and rate-dependent full-constraints Taylor models

摘要

A comprehensive review of the Taylor ambiguity is given. An improved algorithm for efficient quadratic programming is suggested and the use of the very efficient singular value decomposition to obtain quadratic minimum solutions is extended to the rigid plastic case. It is found that using strain rate dependent critical resolved shear stresses with strain rate sensitivities m less than about 0.15 provides a solution which coincides with a rate insensitive solution with minimum of L~(1+m) norm of slip rates as a constraint. Rolling texture predictions change very little in this range of the strain rate sensitivities, while the shape of the yield locus changes considerably. It is shown how this range is increased by the presence of an athermal stress component. It is argued that strain rate insensitive solutions obtained by minimizing the sum of the square of the slip rates not only give the best texture predictions for rolling, but also have a physical meaning as being an approximation to a physically-based strain rate sensitive theory. This allows implementing rate-dependency by use of efficient quadratic optimization methods without having to deal with nonlinear iterations.