A complete three-dimensional continuum model of wing-crack growth in granular brittle solids

    Research output: Contribution to journalArticleScientificpeer-review

    11 Citations (Scopus)

    Abstract

    Failure of brittle materials containing embedded three dimensional pre-cracks and subjected to uniaxial compressive and tensile loading is considered here. The sliding crack (wing-crack) model of Ashby and Sammis (1990) is extended and further developed to formulate a 3D anisotropic continuum damage model.First, a frictional sliding condition of pre-cracks is formulated in three dimensions and a crack interaction function is proposed. To introduce inelastic strains due to cracking, crack opening displacements are derived from Castigliano's second theorem. Finally, a strain-stress relation is obtained from the Gibbs energy density equation.The model was implemented in Abaqus/Explicit finite element software. Material inhomogeneity was considered assuming that the pre-cracks are lognormally distributed between integration points.While testing the proposed model against experimental results of granular ice, the numerical simulations were in good agreement both under uniaxial compression and tension as a function of grain size and temperature-dependent kinetic friction. The model was able to predict qualitatively and quantitatively the brittle failure modes and strength both under compression and under tension. Due to the modelled inhomogeneity, the scatter in simulated strengths corresponded to that of the test results. Besides non-simultaneous and non-uniform damaging, the model revealed important phenomena observed during the experiments; e.g. under compression the sliding of the pre-cracks resembled "stick-slip" motion, and secondary cracks were observed to grow in a jerky manner. The effect of specimen end conditions on both the failure stress and failure mode was addressed in the simulations.
    Original languageEnglish
    Pages (from-to)27-42
    Number of pages16
    JournalInternational Journal of Solids and Structures
    Volume115-116
    DOIs
    Publication statusPublished - 2017
    MoE publication typeA1 Journal article-refereed

    Fingerprint

    Crack Growth
    Continuum Model
    wings
    Crack propagation
    Crack
    cracks
    continuums
    Cracks
    Three-dimensional
    sliding
    failure modes
    Compression
    Failure Mode
    Inhomogeneity
    Failure modes
    inhomogeneity
    kinetic friction
    Model
    brittle materials
    End Conditions

    Keywords

    • brittle failure
    • sliding crack
    • wing crack
    • stick slip
    • anisotropic damage
    • ice failure

    Cite this

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    abstract = "Failure of brittle materials containing embedded three dimensional pre-cracks and subjected to uniaxial compressive and tensile loading is considered here. The sliding crack (wing-crack) model of Ashby and Sammis (1990) is extended and further developed to formulate a 3D anisotropic continuum damage model.First, a frictional sliding condition of pre-cracks is formulated in three dimensions and a crack interaction function is proposed. To introduce inelastic strains due to cracking, crack opening displacements are derived from Castigliano's second theorem. Finally, a strain-stress relation is obtained from the Gibbs energy density equation.The model was implemented in Abaqus/Explicit finite element software. Material inhomogeneity was considered assuming that the pre-cracks are lognormally distributed between integration points.While testing the proposed model against experimental results of granular ice, the numerical simulations were in good agreement both under uniaxial compression and tension as a function of grain size and temperature-dependent kinetic friction. The model was able to predict qualitatively and quantitatively the brittle failure modes and strength both under compression and under tension. Due to the modelled inhomogeneity, the scatter in simulated strengths corresponded to that of the test results. Besides non-simultaneous and non-uniform damaging, the model revealed important phenomena observed during the experiments; e.g. under compression the sliding of the pre-cracks resembled {"}stick-slip{"} motion, and secondary cracks were observed to grow in a jerky manner. The effect of specimen end conditions on both the failure stress and failure mode was addressed in the simulations.",
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    A complete three-dimensional continuum model of wing-crack growth in granular brittle solids. / Kolari, Kari.

    In: International Journal of Solids and Structures, Vol. 115-116, 2017, p. 27-42.

    Research output: Contribution to journalArticleScientificpeer-review

    TY - JOUR

    T1 - A complete three-dimensional continuum model of wing-crack growth in granular brittle solids

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    AB - Failure of brittle materials containing embedded three dimensional pre-cracks and subjected to uniaxial compressive and tensile loading is considered here. The sliding crack (wing-crack) model of Ashby and Sammis (1990) is extended and further developed to formulate a 3D anisotropic continuum damage model.First, a frictional sliding condition of pre-cracks is formulated in three dimensions and a crack interaction function is proposed. To introduce inelastic strains due to cracking, crack opening displacements are derived from Castigliano's second theorem. Finally, a strain-stress relation is obtained from the Gibbs energy density equation.The model was implemented in Abaqus/Explicit finite element software. Material inhomogeneity was considered assuming that the pre-cracks are lognormally distributed between integration points.While testing the proposed model against experimental results of granular ice, the numerical simulations were in good agreement both under uniaxial compression and tension as a function of grain size and temperature-dependent kinetic friction. The model was able to predict qualitatively and quantitatively the brittle failure modes and strength both under compression and under tension. Due to the modelled inhomogeneity, the scatter in simulated strengths corresponded to that of the test results. Besides non-simultaneous and non-uniform damaging, the model revealed important phenomena observed during the experiments; e.g. under compression the sliding of the pre-cracks resembled "stick-slip" motion, and secondary cracks were observed to grow in a jerky manner. The effect of specimen end conditions on both the failure stress and failure mode was addressed in the simulations.

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