  The current form of the effective yield criterion that is used to describe
non-Schmid behavior of dislocations in crystalline materials is not invariant
under the simultaneous change of the slip direction and the slip plane normal
as dictated by crystallography. Here, we explore the consequences of this
symmetry on the derivation of the effective stress. This is defined by a linear
combination of six stress functions that are represented by their Maclaurin
series. Only the lowest order terms that obey this symmetry are retained, which
results in a homogeneous effective stress of order two. It is shown that the
quadratic terms can be further eliminated by resolving the respective stresses
into another coordinate system in the zone of the slip direction. The
application of the ensuing linear yield criterion to body-centered cubic and
hexagonal close-packed metals shows under which conditions the non-Schmid
stress terms become significant in predicting the onset of yielding. In the
special case, where the contributions of all non-Schmid stresses vanish, this
model reduces to the maximum shear stress theory of Tresca.
