Abstract
To quantify the gain in strength of a layered heterogeneous structure caused by the elastic contrast between the layers, especially if no crack deflection is observed at the interface, two original mechanisms baptized “step-over” and “jump-through” were proposed in Part I. They addressed the ability of a crack to pass through an interface and were applied to a bimaterial structure; whereas part II is dedicated to a homogeneous beam embedding a thin stiff film. The asymptotic expansions differ significantly since the small parameter is now the layer thickness. Unlike the first part where it was difficult to evidence the gain in toughness due to the superposition of two effects: a simultaneous increase in stiffness and in toughness, here it is possible to characterize the strength enhancement in using a single parameter. A discussion of the possibility to repeat the effect by multiplying the thin films is presented at the end.
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References
Chai H, Ravichandran G (2007) Transverse fracture in multilayers from tension and line-wedge indentations. Int J Fract 145: 299–312
Gudmundsson A (2009) Deflection of dykes into sills at discontinuities and magma-chamber formation. Tectonophysics 500(1–4): 50–64
He MY, Hutchinson JW (1989) Crack deflection at an interface between dissimilar elastic materials. Int J Solids Struct 25: 1053–1067
Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech A Solids 21: 61–72
Leguillon D, Lacroix C, Martin E (2000) Matrix crack deflection at an interface between a stiff matrix and a soft inclusion. C R Acad Sci Paris (série IIb) 328: 19–24
Leguillon D, Quesada D, Putot C, Martin E (2007) Size effects for crack initiation at blunt notches or cavities. Eng. Fract. Mech. 74: 2420–2436
Leguillon D, Martin E (2012a, to appear) Crack nucleation at stress concentration points in composite materials—application to the crack deflection by an interface. In: Mantic V (ed) Mathematical methods and models in composites. Computational and experimental methods in structures. Imperial College Press, London
Leguillon D, Martin E (2012b, in preparation) The strengthening effect caused by an elastic contrast—part I: the bimaterial case
Leguillon D, Sanchez-Palencia E (1987) Computation of singular solutions in elliptic problems and elasticity. Wiley, New York
Leguillon D, Sanchez-Palencia E (1992) Fracture in heterogeneous materials, weak and strong singularities. In: Ladevèze P, Zienkiewicz O (eds). Proceedings of the European conference on new advances in computational structural mechanics. Elsevier, Amsterdam, pp 229–236
Okumura K, de Gennes P-G (2001) Why is nacre strong? Elastic theory and fracture mechanics for biocomposites with stratified structures. Eur Phys J E4:121–127
Simon P (2009) Approche multi-échelle du comportement mécanique du bois dans le plan transverse. PhD thesis, INSA Lyon, Villeurbanne
Xia S, Ponson L, Ravichandran G, Bhattacharya K (2012, to appear) Toughening and asymmetry in peeling of heterogeneous adhesives. Phys Rev Letter
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Leguillon, D., Martin, E. The strengthening effect caused by an elastic contrast—part II: stratification by a thin stiff layer. Int J Fract 179, 169–178 (2013). https://doi.org/10.1007/s10704-012-9785-0
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DOI: https://doi.org/10.1007/s10704-012-9785-0