From telephone cords to branched buckles: A phase diagram

Abstract

International audienceThin films with low adhesion and large residual stresses may buckle and delaminate from their substrates. This delamination often results in oscillating patterns known as ‘telephone cords’. Other configurations can be observed as well, such as entangled networks of blisters. The present study aims at elucidating how these networks are generated through branching. A model coupling a geometrically non-linear plate model and a cohesive zone with mode dependent interfacial toughness is used. Previous work on the early stage delamination of initially circular blisters during interfacial crack front propagation are revisited and extended to the remote post-critical regime to capture front branching. We also build a partial phase diagram of buckling driven delamination morphologies. An intrinsic critical stress parameter is proposed which can be used to predict delamination morphology and to define ‘safe’ conditions where buckle propagation can be avoided. This critical stress also defines an intrinsic lengthscale which plays the role of a minimum nucleation siz

Configurational stability of a crack propagating in a material with mode-dependent fracture energy - Part I: Mixed-mode I+III

“…A quadratic variation of the fracture energy with mode mixity -κ = 2 -would be the most natural assumption, as it corresponds to the leading term in a development of the even function G c (ρ) for small values of ρ; such a value is generally chosen to describe the variations of G c with the ratio K II /K I in interfacial fracture, see e.g. Faou et al (2017). But we choose here to keep κ as a free parameter so as not to restrict the generality of the stability analysis.…”

Configurational stability of a crack propagating in a material with mode-dependent fracture energy – Part II: Drift of fracture facets in mixed-mode I+II+III

“…Even more recently, following a different line of thought, Leblond et al (2019) revisited Leblond et al (2011)'s stability analysis by accounting for a new physical mechanism: instead of assuming the fracture energy to be a constant, they introduced a possible dependence of this energy upon the local mixity ratio. This new heuristic hypothesis was motivated indirectly by Freund et al (2003)'s and Faou et al (2017)'s observation that interfacial 1 fracture energy significantly increases with the amount of plane shear applied (mode II) , and more straightforwardly by the toughening observed in the presence of anti-plane shear (mode III) by Liu et al (2004) and Davenport and Smith (1993) , for PMMA, Lin et al (2010), for Homalite, and Suresh and Tschegg (1987), for alumina. A material parameter γ characterizing the toughening induced by anti-plane shear was thus introduced.…”

Spontaneous formation and morphology of telephone cord blisters in thin films: The Ω formulae

“…In the second exercise, the accuracy of Eqs. (8) and (11) is examined for predicting the two local morphology parameters, namely, the TCB half-width R and height x A , by using experimental data from Refs. [12,19,24,31].…”

“…Among many others, Refs. [6][7][8][9][10][11] report studies on buckling-driven straight blisters [6,8,10], circular blisters [6,7], elliptical blisters [6], telephone cord blisters (TCBs) [9], and branched blisters [11]. Among these different types of blisters, the TCB is the most interesting and challenging one, and predicting TCB morphology has attracted the attention of many researchers worldwide.…”

“…Based on Refs. [6][7][8][9][10][11] and many others, there are also two stages of blister growth in the buckling-driven approach: During the first stage, the separation nucleates and grows without bending-away from the substrate resulting in zero energy release rate at the separation edge.…”