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The large amplitude oscillatory shear (LAOS) has been extensively studied forunderstanding the rheological responses of yield stress fluids. However, theemployed methodology for determining the yield stress remains uncertain albeitthe fact that many classical or plausible methods exist in the literature.Along these lines, herein, based on Fourier transform (FT) rheology, stressdecomposition, and stress bifurcation, a new straightforward method termed asalgebraic stress bifurcation was developed. More specifically, the main goalwas to determine the yield stress and investigate the solid-liquid transitionof fluids in LAOS. A simple and efficient mathematical framework wasestablished and verified by the KVHB, Saramito, Giesekus models, and FTrheology. The main strength of this approach is that only the data from thestress/strain sweep are required instead of Lissajous curves. Alternativecurves based on the first harmonic were constructed to demonstrate thenon-critical role of both higher harmonics and phenomenological Lissajouscurves in determining yield stress. The determined start and end yield pointsin the solid-liquid transition were compared with the already existing methods.Furthermore, the resulting solid-liquid transition region was analyzed by FTrheology, stress decomposition, and sequence of the physical process to obtaininformation on nonlinearity and intracycle/intercycle yielding. Our workprovides fruitful insights for explaining and reducing the complexities of thestress bifurcation technique by using an easy-to-understand and implementformat. Therefore, a concise theoretical framework was introduced forunderstanding the concept of yield stress, the intercycle yielding process, andthe rational choice of yield stress measurement techniques.

Demonstration of a Facile and Efficient Strategy for Yield Stress Determination in Large Amplitude Oscillatory Shear: Algebraic Stress Bifurcation