Yielding and bifurcated aging in nanofibrillar networks

Although phenomenologically simple to define, the yield stress is often difficult to quantify unambiguously in practice, especially for thixotropic materials with complex shear histories. Here, we identify a stress-controlled bifurcation in the yielding response of cellulose nanofibril gels, which we show can rigorously localize the yield stress in disordered materials with time-dependent behavior. After an initial yielding event, the fibrillar networks subsequently yield faster and at lower magnitudes of stress. For low stresses, the time to yielding increases with waiting time ${t}_{w}$ and diverges once the network has restored sufficient entanglement density to support the stress. For higher stresses, the yield time instead plateaus at a finite value because the developed network density is insufficient to support the applied stress. We quantitatively relate the yielding and aging behavior of the network to the competition between stress-induced disentanglement and dynamic fluctuations of the fibrils rebuilding the network. The critical stress ${\ensuremath{\sigma}}_{c}$ that bifurcates the response of the material between these two states identifies the intrinsic yield stress in these disordered materials, independent of aging, thixotropic effects, or shear history.