  We report the first-ever complete measurement of MAOStress material
functions, which reveal that stress can be more fundamental than strain or
strain rate for understanding linearity limits as a function of Deborah number.
The material used is a canonical viscoelastic liquid with a single dominant
relaxation time: Polyvinyl alcohol (PVA) polymer solution crosslinked with
tetrahydroborate (Borax) solution. We outline experimental limit lines and
their dependence on geometry and test conditions. These MAOStress measurements
enable us to observe the frequency dependence of the weakly nonlinear deviation
as a function of stress amplitude. The observed features of MAOStress material
functions are distinctly simpler than MAOStrain, where the frequency dependence
is much more dramatic. The strain-stiffening transient network model (SSTNM)
was used to derive a model-informed normalization of the nonlinear material
functions that accounts for their scaling with the linear material properties.
Moreover, we compare the frequency-dependence of the critical stress, strain,
and strain-rate for the linearity limit, which are rigorously computed from the
MAOStress and MAOStrain material functions. While critical strain and
strain-rate change by orders of magnitude throughout the Deborah number range,
the critical stress changes by a factor of about two, showing that stress is a
more fundamental measure of nonlinearity strength. This work extends the
experimental accessibility of the weakly nonlinear regime to stress-controlled
instruments and deformations, which reveal material physics beyond linear
viscoelasticity but at conditions that are accessible to theory and detailed
simulation.
