The yield stress tensor

Yield stress materials are known to possess a certain threshold property, a strength, that must be overcome in order for flow to occur. This strength is commonly conceived as a scalar representation of the stress tensor at the yielding point, here called the yield stress tensor. The recognition of the importance of elastic, thixotropic, and other effects not predicted by ideal viscoplastic models is becoming more and more present in the study of yield stress materials. Nevertheless, the paradigm built by the theoretical analysis of inelastic viscoplastic models has a strong influence in the literature. For example, the common denomination of the shear component of the stress tensor at the yielding point as the yield stress of the material. This nomenclature is so spread in the literature that is explicitly employed even in articles where elastic effects are investigated. Viscometric rheometry is the most widely imposed kinematics used to probe the material, and the flow curve is considered the most useful single information about the material related to flow. However, even for this fixed kinematics, the conditions at the yielding point are not uniquely determined by the shear stress component. Although the existence of normal stress differences are known to be present in a variety of yield stress materials, and virtually all yielding criteria are dependent on the invariants of the deviatoric stress tensor at the yield point, the components of the yield stress tensor other than the yield shear stress are ignored altogether. In the present work, we measure not only the shear stress component of the yield stress tensor, but also the normal stress differences at the yielding point for eight yield stress materials, in order to determine the full deviatoric yield stress tensor in viscometric flow. To this end, besides creep tests performed to find the yield shear stress, cone-plate as well as plate-plate geometries are employed to determine, respectively, the first normal stress difference, N1, and the difference of normal stress differences, N1−N2. A low-slope shear stress ramp is imposed and the normal stress differences are plotted as a function of the shear stress, in order to determine their values at the yield shear stress. In most of the cases, it is found that the normal stresses of the deviatoric yield stress tensor are significant when compared to the yield shear stress component. Therefore, in general all the yield stress tensor components can contribute significantly to the composition of a yield criterion. This fact imposes the need for reliable measurements to determine the full yield stress tensor of the material.