Stationary crack propagation in a two-dimensional visco-elastic network model

Abstract

We investigate crack propagation in a simple two-dimensional visco-elastic model and find a scaling regime in the relation between the propagation velocity and energy release rate or fracture energy, together with lower and upper bounds of the scaling regime. On the basis of our result, the existence of the lower and upper bounds is expected to be universal or model-independent: the present simple simulation model provides generic insight into the physics of crack propagation, and the model will be a first step towards the development of a more refined coarse-grained model. Relatively abrupt changes of velocity are predicted near the lower and upper bounds for the scaling regime and the positions of the bounds could be good markers for the development of tough polymers, for which we provide simple views that could be useful as guiding principles for toughening polymer-based materials.

Crack propagation under static and dynamic boundary conditions

“…2 (b) and (c), we show that the above results is not special to the standard parameter set and that the results obtained at a small velocity U which satisfies Eq. (6) well possess the following properties, which the results in the static test were confirmed to satisfy in our previous study [10,11]…”

“…2 where c 1 is approximately 2.3 for all the data shown in Fig. 2. (The constant c 1 seems weekly dependent on N but takes the same value for the two simulation models for a given N ; in the previous studies [10,11], c 1 is approximately 2.4 in the two simulation models for N = 200, which is about ten times larger than present values of N . )…”

“…Here, we elucidate this relation through a numerical study. We use two simple viscoelastic models appropriate for examining crack propagation [10,11]. One model is a spring-bead model based on Voigt model.…”

Crack propagation in porous polymer sheets with different pore sizes

“…[16] The structural size-effect is also verified with numerical simulations; it has been shown that, by changing the mesh size of a network model for elastic sheets, the failure stress of a sheet with a crack can be tuned. [17] For crack propagation, in a numerical simulation [18] and a theoretical model, [12] it is confirmed that mesh size affects crack velocities. In summary, recent works have implied that certain structural sizes of polymer sheets such as foam size and distance between cross-linking points, which correspond to the mesh size in theory and simulations, affect crack propagation and strength.…”

Visco- and plastoelastic fracture of nanoporous polymer sheets

“…Accordingly, active studies have been performed on mechanical and fracture mechanical properties, focusing on an important parameter for cellular solids, the volume fraction of the matrix material φ [1]. However, studies on velocity dependent properties of their fracture are relatively limited, compared with intensive studies that have been performed on other materials such as adhesive [6][7][8][9][10], laminar [11], viscoelastic [12,13], weakly cross-linked [14,15], biopolymer gel [16], and biological composite [17] materials, including recent active experimental [18][19][20], numerical [21,22], and theoretical [23,24] studies on the velocity jump in crack propagation in elastomers.…”