Bifurcated yielding response of aging fibrillar networks

Yielding in disordered materials occurs with a remarkably broad variety of characteristics and remains a poorly understood phenomenon. Here, we investigate the yielding and aging behavior of disordered fibrillar networks of cellulose nanofibrils (CNF), micron-sized semiflexible fibers with aspect ratios >100. At high concentrations, CNF form dense physical networks that support finite stresses and in which terminal relaxations are suppressed. We observe a strong decrease in the yield strain of the networks with increasing volume fraction (γ_y ∼ φ^-2). Further, we observe a strong aging response of the system after an initial yielding event. Subsequent yielding occurs at a time t_y that depends sensitively on the magnitude of applied stress and the aging time t_w between initial yielding and reapplication of stress. The yield time diverges at finite waiting times for small stresses and asymptotes towards a finite yield time at large stresses, with bifurcation around a critical stress that is similar to the yield stress of the system. The waiting time at which the yield time diverges increases with applied stress below the critical stress, indicating that the bifurcation is rooted in the rate of thermally driven network restructuring relative to stress-driven de-structuring.