Micromechanics of fracture in elastomers

Gent, A. N.; Pulford, C. T. R.

doi:10.1007/bf00552273

Cited by 32 publications

(37 citation statements)

References 17 publications

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“…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) morphology analogous to those observed previously on a covalently cross-linked hydrogel [5,6] and on various elastomers, swollen or not [7]. It is due to straight "macroscopic" steps, here of heights a few 100 µm, emerging from the above-described coexistent micrometric roughness.…”

supporting

confidence: 57%

“…The defect topology thus involves a material overhang ABC I D I . Note that this topology is the equivalent, for a widely open crack, of that identified in [5] and [7]. As the front proceeds, the fold A I C I D I B I ultimately collapses, leaving two complementary steps on the crack faces.…”

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confidence: 81%

“…With G 0 ≈ 2.5 J.m −2 , E ≈ 10 kPa, we get δ ≈ 150 µm, in excellent agreement with the experimental value. For slow cracks in elastomers as studied in [7], G 0 and the relaxed E are respectively of order a few 10 J.m −2 and a few MPa, leading to step heights δ in the 10 µm range. This agrees with Gent's findings, lending further support to our picture.…”

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Magic Angles and Cross-Hatching Instability in Hydrogel Fracture

et al. 2008

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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...

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Magic Angles and Cross-Hatching Instability in Hydrogel Fracture

et al. 2008

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“…In the past, it has been shown that observing the stretched crack tip by scanning electron microscopy (SEM) is an interesting way to investigate these mechanisms. 5,[10][11][12] Nevertheless, no such study was proposed for noncrystallisable elastomers.…”

Section: Introductionmentioning

confidence: 99%

Failure analysis of carbon black filled styrene butadiene rubber under fatigue loading conditions

Cam¹,

Huneau²,

Verron³

2014

Plastics, Rubber and Composites

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International audienceThe present paper deals with the fatigue crack growth in a carbon black-filled styrene butadiene rubber (CB-SBR) under fully relaxing loading conditions. More precisely, it is devoted to the determination of the scenario of crack growth. For that purpose, an original ‘microcutting’ technique, previously applied by the authors on natural rubber (NR), is used to observe microscopic phenomena involved in fatigue crack growth thanks to scanning electron microscopy (SEM). Results show that the crack tip grows following a tearing line by generating ligaments; it explains the differences between fatigue responses of crystallisable and non-crystallisable rubbers during crack propagation. So, contrary to crystallisable elastomers such as NR, the microstructure of SBR is similar at crack tip and in the bulk material, and the crack tip does not resist crack propagation. Moreover, the morphology of fracture surfaces only depends on particles encountered by the fatigue crack during its propagation

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“…Cracks show a strong tendency for instability, creating non-smooth surfaces with rich structure. Crack instabilities and their associated structure exhibit a strong dependence on crack velocity: slow tensile cracks (v c R , where c R is the Rayleigh wave speed) are prone to nucleate steps which drift along the crack front and divide the fracture surface into facets [1][2][3][4][5][6]; faster tensile cracks are unstable to the formation of micro-branches -microscopic cracks that branch off the main crack front [7][8][9][10][11]. Linear perturbation theory, however, predicts that any initial disturbance to a tensile crack front should either decay as the crack progresses [12][13][14] or disperse as outgoing waves [15,16].…”

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Nonlinear Focusing in Dynamic Crack Fronts and the Microbranching Transition

2017

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Cracks in brittle materials produce two types of generic surface structures: facets at low velocities and micro-branches at higher ones. Here we observe a transition from faceting to micro-branching in polyacrylamide gels that is characterized by nonlinear dynamic localization of crack fronts. To better understand this process we derive a first-principles nonlinear equation of motion for crack fronts in the context of scalar elasticity. Its solution shows that nonlinear focusing coupled to rate-dependence of dissipation governs the transition to micro-branching.Fracture is typically an irregular process. Cracks show a strong tendency for instability, creating non-smooth surfaces with rich structure. Crack instabilities and their associated structure exhibit a strong dependence on crack velocity: slow tensile cracks (v c R , where c R is the Rayleigh wave speed) are prone to nucleate steps which drift along the crack front and divide the fracture surface into facets [1-6]; faster tensile cracks are unstable to the formation of micro-branches -microscopic cracks that branch off the main crack front [7][8][9][10][11]. Linear perturbation theory, however, predicts that any initial disturbance to a tensile crack front should either decay as the crack progresses [12][13][14] or disperse as outgoing waves [15,16]. Current linear theories are therefore incapable of reproducing the observed fracture surfaces.In recent non-perturbative approaches to fracture, such as lattice models [17,18] and phase-field models [19][20][21], localized crack branching arises naturally, regardless of the specific dissipative process. Both approaches predict that micro-branching is governed by the microscopic dissipation length-scale and that instability initiates at v c ∼ 0.7c R . This critical velocity is significantly higher than that observed in experiments, and predicted from energy considerations in the theory of 2D branching [22,23]. In addition, micro-branch dimensions typically exceed the process zone size by a few orders of magnitude. It therefore remains unclear what component or mechanism is missing in the existing models.In polyacrylamide gels [6] cracks exhibit a transition between facet formation and micro-branching at v ∼ 0.05 − 0.1c R . The transition is not sharp, and both types of structures may coexist in the transition region. A typical fracture surface (for v ∼ 0.06c R ) shown in Fig.

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Micromechanics of fracture in elastomers

Cited by 32 publications

References 17 publications

Magic Angles and Cross-Hatching Instability in Hydrogel Fracture

Magic Angles and Cross-Hatching Instability in Hydrogel Fracture

Failure analysis of carbon black filled styrene butadiene rubber under fatigue loading conditions

Nonlinear Focusing in Dynamic Crack Fronts and the Microbranching Transition

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