A model for stable interfacial crack growth

Abstract

We present a model for stable crack growth in a constrained geometry. The morphology of such cracks show scaling properties consistent with self affinity. Recent experiments show that there are two distinct self-affine regimes, one on small scales whereas the other at large scales. It is believed that two different physical mechanisms are responsible for this. The model we introduce aims to investigate the two mechanisms in a single system. We do find two distinct scaling regimes in the model.

Local dynamics of a randomly pinned crack front: a numerical study

“…In order to follow the crack front as the breakdown process develops, we implement the "conveyor belt" technique [21,34]. We illustrate this technique in Figure 2.…”

“…By refining the model proposed by Batrouni et al [20] and Gjerden et al [21], consisting of fibers clamped between a hard and a soft block and with a gradient in the breaking thresholds, we have identified two scaling regimes for the roughness of the advancing crack front [22]. On large scales we recover the roughness seen in the reanalysis of experimental data by Santucci et al [8], ζ + = 0.39 ± 0.04, consistent with the fluctuating line model.…”

“…This idea in turn has its origin in the proposal by Bouchaud et al [17] that the crack front does not advance not only due to a competition between effective elastic forces and pinning forces at the front, but also by coalescence of damage in front of the crack with the advancing crack itself. The coalescence By refining the model proposed by Batrouni et al [18,19], consisting of fibers clamped between a hard and a soft block and with a gradient in the breaking thresholds, we have identified two scaling regimes for the roughness of the advancing crack front [20]. On large scales we recover the roughness seen in the reanalysis of experimental data by Santucci et al [8], ζ = 0.39 ± 0.04, consistent with the fluctuating line model, whereas on small scales with identify a gradient percolation process, leading to ζ = 2/3 [21], which is also consistent with Santucci et al reanalysis.…”

Soft-Clamp Fiber Bundle Model and Interfacial Crack Propagation: Comparison Using a Non-linear Imposed Displacement

“…In order to keep the process zone around the fracture tip away from the boundaries, we used the "conveyor belt" technique [34]. Since only the surviving fibers matter in the force field calculations and fibers fail irreversibly, we remove the first broken (i.e., left side in Figure 3) row from our calculations and add a fully intact one at the last (i.e., right side) row.…”

Universality Classes in Constrained Crack Growth

“…This makes it possible to follow the advancing crack front indefinitely. The implementation has been described in detail in [24]. Figure 1 shows two examples of typical crack fronts representative of a stiff (high e = 0.8) and a soft system (low e = 2 × 10 −3 ).…”