Plastic Spin

In the classical (rate-independent)
theory of metal plasticity, the plastic spin has been an issue of
research and debate for about thirty years. Judging by the content
of current publications on the topic (regarding modeling
possibilities, consequences and applications), it seems that the
concept has acquired a certain degree of acceptance, although no
rigorous justification, at theoretical level, has ever been provided.
In the attached preprint this matter is investigated starting from
crystal level and going up to the macro-level (of an aggregate of
many crystals) by employing Hill's averaging techniques and his
differential invariant.

The emphasis is on rigorous deduction
and the only phenomenology employed is Taylor's widely accepted
description of plastic deformation at crystal level (reformulated
later in a general elastic-plastic context by Hill and Rice 1972). It
is found that the evolution law assigned to the slip systems of a
constituent crystal has a considerable effect on the resulting
constitutive equations at macro-level, these being the genes of the
macro-model. Specifically, among the many plausible evolution
laws (Hill and Rice 1972, Asaro and Rice 1977) there exists one for
which the macro-model acquires the classical form: a yield surface
controls yielding of the macro-particle, the macro-rate of plastic
deformation is along its exterior normal (at the current stress
state) and is related to an objective stress-rate and the macro-rate
of deformation by an appropriate tensor of instantaneous moduli. In
particular, in this macro-model the plastic spin does not
appear as macro-variable. This happens if one assumes that slip
directions and normals to slip planes convect with the motion (of the
lattice).

Any other type of evolution (e.g.,
rigidly rotating slip systems) induces a deviation of the macro-rate
of plastic deformation from the above normality rule. Nevertheless,
in all cases the flow rule is associated (to the yield surface).
Only part of this deviation can be “alleviated” by the
introduction of a plastic (macro-)spin, which may be interpreted as
the spin of a macro-rotation of the yield surface. Thus, the plastic
spin is always accompanied by a deviation from the normality rule
(contrary to the established practice, where the plastic spin is
employed in conjunction with the normality rule).