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

Arne Stormo,Olivier Lengliné,Alex Hansen,Jean Schmittbuhl

doi:10.3389/fphy.2016.00018

Abstract

We compare experimental observations of a slow interfacial crack propagation along an heterogeneous interface to numerical simulations using a soft-clamped fiber bundle model. The model consists of a planar set of brittle fibers between a deformable elastic half-space and a rigid plate with a square root shape that imposes a non linear displacement around the process zone. The non-linear square-root rigid shape combined with the long range elastic interactions is shown to provide more realistic displacement and stress fields around the crack tip in the process zone and thereby significantly improving the predictions of the model. Experiments and model are shown to share a similar self-affine roughening of the crack front both at small and large scales and a similar distribution of the local crack front velocity. Numerical predictions of the Family-Viscek scaling for both regimes are discussed together with the local velocity distribution of the fracture front.

Highlights

Crack propagation in heterogeneous media is a rich problem which involves the interplay of various physical processes
Previous experimental studies reported that an interfacial crack front in the present configuration is self-affine with a roughness exponent ζ ≃ 0.6 [e.g., 8, 28]
More recent data extracted from numerous experiments and at various scales show that two distinct regimes emerge depending on the scale of investigation: at small scales the scaling regime is characterized by a roughness exponent ζ − ≃ 0.60 while at large scale the exponent is lower and is found around ζ + ≃ 0.35 [12]

Summary

Introduction

Crack propagation in heterogeneous media is a rich problem which involves the interplay of various physical processes. The problem has been intensively investigated theoretically, numerically, and experimentally, but a unifying model capturing all the experimental features has not been entirely achieved [1, 2] despite its broad range of implications in engineering and Earth sciences problems [3, 4]. During most regular fracture experiments, the fracture surface can only be observed post mortem [5]. Since Mandelbrot’s discovery [6] of fracture surfaces in metal that display fractal properties, there have been many attempts to understand the scaling relations of fracture [5]. The self-affine nature of fracture surfaces have come under much scrutiny. A self-affine surface h(x) has the following scaling relation [7]

Methods

Results

Discussion

Conclusion