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Plasticity and non-Schmid effects

If slip is the only mechanism of
plastic deformation of a crystal and Schmid law governs the slip
activity, the overall response of an aggregate of such crystals
features the normality rule of classical plasticity, see
node/15347
for a rigorous recent proof. Any deviation from Schmid law is
referred to as a non-Schmid effect. In general, these effects may be
of two kinds: in addition to the resolved shear stress (on a slip
system), other stress components may influence slip activity or/and
the hardening of a slip system (representative examples for each kind
are described, for example, in Qin and Bassani(1992) and Spitzig
and Richmond(1984), respectively). Then, naturally, one is led to the
following question: what is the “essential” structure of the
constitutive relations describing the overall response of a
polycrystal aggregate of constituents featuring non-Schmid effects ?

The current point of view is that the
normality rule doe not hold for such aggregates, and that the
direction of plastic deformation is determined by an additional
constitutive element in the form of a plastic potential, distinct
from the yield surface. Some theoretical support for these ideas is
provided by Rice's (1971) paper, where arguments for the existence of
a plastic potential are presented. On the other hand, in the attached
preprint the old Bishop-Hill (1951) argument is extended and employed
in the search for an answer to the above question. It is found that,
contrary to the current belief, even when non-Schmid effects are
present at constituent level the macro flow rule is still associated
(to the yield surface)
. However, the macro-direction of plastic
deformation is no longer along the exterior normal to the yield
surface; its deviation can be described by an additional constitutive
element in the form of a symmetric second order tensor.

  

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Comments

A corrected version of this preprint has been published in Proceedings of the Royal Soc. A (doi: 10.1098/rspa.2013.0440).

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