Fracture mechanics solutions for interfacial cracks between compressible thin layers and substrates

Roberta Massabò*, Konstantin Ustinov, Luca Barbieri, Christian Berggreen

*Corresponding author for this work

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    The decohesion of coatings, thin films, or layers used to protect or strengthen technological and structural components causes the loss of their functions. In this paper, analytical, computational, and semi-analytical 2D solutions are derived for the energy release rate and mode-mixity phase angle of an edge-delamination crack between a thin layer and an infinitely deep substrate. The thin layer is subjected to general edge loading: axial and shear forces and bending moment. The solutions are presented in terms of elementary crack tip loads and apply to a wide range of material combinations, with a large mismatch of the elastic constants (isotropic materials with Dundurs’ parameters −1≤α≤1 and −0.4≤β≤0.4 ). Results show that for stiff layers over soft substrates ( α→1 ), the effects of material compressibility are weak, and the assumption of substrate incompressibility is accurate; for other combinations, including soft layers over stiff substrates ( α→−1 ), the effects may be relevant and problem specific. The solutions are applicable to edge- and buckling-delamination of thin layers bonded to thick substrates, to mixed-mode fracture characterization test methods, and as benchmark cases.
    Original languageEnglish
    Article number152
    JournalJournal of Coatings Technology and Research
    Issue number3
    Number of pages19
    Publication statusPublished - 2019

    Bibliographical note

    © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (


    • Coatings
    • Delamination
    • Interfaces
    • Linear elastic fracture mechanics
    • Mixed-mode fracture
    • Phase angle
    • Sandwich
    • Soft materials substrates


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