Crack Initiation in Viscoelastic Materials

Abstract

In viscoelastic materials, individually short-lived bonds collectively result in a mechanical resistance which is long lived but finite as, ultimately, cracks appear. Here, we provide a microscopic mechanism by which a critical crack length emerges from the nonlinear local bond dynamics. Because of this emerging length scale, macroscopic viscoelastic materials fracture in a fundamentally different manner from microscopically small systems considered in previous models. We provide and numerically verify analytical equations for the dependence of the critical crack length on the bond kinetics and applied stress.

Crosslinker mobility weakens transient polymer networks

“…Why is the network lifetime with mobile linkers drastically smaller than with static linkers, even though the average linker lifetime and bond-bond distance are similar? To investigate this paradox, we need to look beyond the mean field properties as rupture is a stochastic phenomenon, initiated by the emergence and growth of cracks due to local fluctuations [11,13,23,38,39]. Plotting the distribution of bound linker distances at steady state reveals a crucial difference between immobile and mobile linkers: whereas their mean values are comparable, the bond-bond distance is significantly more widely distributed for mobile than for immobile linkers (figure 2b).…”

“…Different from previous transient network models [6,[28][29][30][31][32][33], this model acknowledges that the applied stress is distributed inhomogeneously over the bonds on basis of their spatial distribution [34][35][36]. As a result of this inhomogeneous force distribution, cracks stochastically initiate and subsequently propagate due to fluctuations in the local bond density [13]. However, this model was specific for the case of immobile linkers.…”

“…In this work, we compare a network connected by mobile linkers to a network connected by immobile linkers. For immobile linkers, we use a model that was introduced in reference [13]. Here, we briefly summarize its salient features for clarity, and afterwards explain how we extend this model to the case of mobile linkers.…”

“…dn steady dt = 0 = k on · (N − n steady ) − k off (σ) · n steady (7) where k on · (N − n steady ) is the total rate of linker binding and k off (σ) · n steady is the total rate of linker unbinding within the network. As k L-increases linearly with the gap size, whereas k L+ increases exponentially, gaps will always become unstable for large enough L as unbinding occurs significantly more rapidly than re-binding [13]. We are interested in the length L unstable at which gaps become unstable and propagate.…”

“…However, viscoelastic materials can resist mechanical stress only for a limited time, after which the system suddenly loses its mechanical percolation, a process which is known as fracturing [8][9][10][11]. Crack initiation of viscoelastic materials occurs stochastically [1,11] due to fluctuations in the local density of bound linkers [12,13], which eventually results in fracture due to rapid crack propagation [14]. In order to understand the fracturing behavior of transient networks, one needs to understand the linker dynamics.…”