Magic Angles and Cross-Hatching Instability in Hydrogel Fracture

Abstract

The full 2D analysis of roughness profiles of fracture surfaces resulting from quasi-static crack propagation in gelatin gels reveals an original behavior characterized by (i) strong anisotropy with maximum roughness at V -independent symmetry-preserving angles, (ii) a sub-critical instability leading, below a critical velocity, to a cross-hatched regime due to straight macrosteps drifting at the same magic angles and nucleated on crack-pinning network inhomogeneities.Step height values are determined by the width of the strain-hardened zone, governed by the elastic crack blunting characteristic of soft solids with breaking stresses much larger that low strain moduli.PACS numbers: 62.20. Mk, 83.80.Kn Over the past two decades, considerable effort has been devoted to characterizing and understanding the statistical properties of the roughness of fracture surfaces in linear elastic disordered materials. Investigation of a wide variety of systems, ranging from brittle silica glass to ductile metallic alloys, has revealed the ubiquity of wide roughness spectra exhibiting self-affine characteristics on sizeable wavelength ranges. On the basis of analysis of height-height correlation functions in a single direction, E. Bouchaud et al.[1] first conjectured a fully universal behavior summed up into a single Hurst exponent. The discrepancies between the predictions of various subsequent theoretical models have pointed toward the importance of also investigating possible anisotropies of the scaling properties [2]. Work along this line indeed reveals different scaling exponents along the crack propagation direction and the (orthogonal) crack front one. From this, Ponson et al. [3] conclude that the self-affinity of the roughness is described by a Family-Vicsek scaling, hence by a set of two exponents. Within their new analysis, full universality is no longer the case since they evidence the existence of at least two classes of materials.However, on the basis of their theoretical work, Bouchbinder et al. [4] have recently raised several new issues. In particular, they point to the necessity of a full 2D analysis of the correlations and find, when reexamining some experimental data, that a host of up to now unidentified exponents appear. They insist on the need to focus on the effects of departures from linear elasticity in the fracture process.In this spirit we report here on the nature of surface morphologies resulting from the fracture of gelatin, a highly compliant thermally reversible hydrogel, in the strongly subsonic regime. We show that these surfaces present very striking anisotropic features. Namely, the rms roughness R(θ), measured along a direction at angle θ from the propagation one Ox, exhibits two symmetrypreserving maxima for θ = ±θ m . For gels with a fixed gelatin concentration, this "magic angle" θ m is constant over more than one decade of both crack velocity V and solvent viscosity η. Moreover, below a critical, η-dependent, velocity V c a new regime develops, characterized by a cross-hatched (CH) mo...

Crack tip fields in soft elastic solids subjected to large quasi-static deformation — A review

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Recent developments in dynamic fracture: some perspectives

“…The importance of a length scale proportional to Γ/E has also been highlighted in experiments on the quasi-static fracture of hydrogels, where it was shown to play a decisive role in a mode I cross-hatching instability [106], in a wetting-induced branching instability [107] and in a mixed-mode I+III (mode III corresponds to antiplane shear fracture)échelon instability [108]. We suspect that the incorporation of intrinsic length scales into fracture theory may be essential to developing equations of motion for crack tips/fronts and to understanding dynamic instabilities.…”

“…There are several other basic phenomena that necessitate a 3D framework of fracture dynamics. In the quasi-static regime, simulations coupled with analytic work [111][112][113][114][115] has shed light on a crack front instability under mixed-mode I+III conditions.Recently, helical perturbations have been shown, in 3D simulations, to develop into segmented crack fronts [116][117][118].Related segmented crack front structures have been observed in mode I [106,119] and mixedmode I+III fracture of of both "standard" [120][121][122][123][124][125] and soft materials [108].…”

Fractographic aspects of crack branching instability using a phase-field model

“…This difference can be attributed to the self-interaction of a crack with itself that is induced by periodic boundary conditions. Hence under pure mode I loading, the localized branching event can induce front fragmentation similarly to what is observed under mixed mode (I + III) loading [29,31,32]. The existence of various morphologies within the same loading conditions leads to the question of pattern selection by the system.…”