Compressively stressed thin films with low adhesion frequently buckle and delaminate simultaneously into telephone cords. Although these buckles have been studied for decades, no complete understanding of their propagation has so far been presented. In this study, we have coupled a nonlinear plate deformation with a cohesive zone model to simulate the kinematics of a propagating telephone cord buckle in very close agreement with experimental observations. Proper inclusion of the dependence of an adhesion upon the mode mixity proved to be central to the success of the approach. The clarification of the mechanism promises better understanding of buckle morphologies.

a b s t r a c tThis paper, the second of two parts, presents three novel finite element case studies to demonstrate the importance of normal-tangential coupling in cohesive zone models (CZMs) for the prediction of mixed-mode interface debonding. Specifically, four new CZMs proposed in Part I of this study are implemented, namely the potential-based MP model and the non-potential-based NP1, NP2 and SMC models. For comparison, simulations are also performed for the well established potential-based Xu-Needleman (XN) model and the non-potential-based model of van den Bosch, Schreurs and Geers (BSG model). Case study 1: Debonding and rebonding of a biological cell from a cyclically deforming silicone substrate is simulated when the mode II work of separation is higher than the mode I work of separation at the cell-substrate interface. An active formulation for the contractility and remodelling of the cell cytoskeleton is implemented. It is demonstrated that when the XN potential function is used at the cell-substrate interface repulsive normal tractions are computed, preventing rebonding of significant regions of the cell to the substrate. In contrast, the proposed MP potential function at the cell-substrate interface results in negligible repulsive normal tractions, allowing for the prediction of experimentally observed patterns of cell cytoskeletal remodelling. Case study 2: Buckling of a coating from the compressive surface of a stent is simulated. It is demonstrated that during expansion of the stent the coating is initially compressed into the stent surface, while simultaneously undergoing tangential (shear) tractions at the coating-stent interface. It is demonstrated that when either the proposed NP1 or NP2 model is implemented at the stent-coating interface mixed-mode over-closure is correctly penalised. Further expansion of the stent results in the prediction of significant buckling of the coating from the stent surface, as observed experimentally. In contrast, the BSG model does not correctly penalise mixed-mode over-closure at the stent-coating interface, significantly altering the stress state in the coating and preventing the prediction of buckling. Case study 3: Application of a displacement to the base of a bi-layered composite arch results in a symmetric sinusoidal distribution of normal and tangential traction at the arch interface. The traction defined mode mixity at the interface ranges from pure mode II at the base of the arch to pure mode I at the top of the arch. It is demonstrated that predicted debonding patterns are highly sensitive to normal-tangential coupling terms in a CZM. The NP2, XN, and BSG models exhibit a strong bias towards mode I separation at the top of the arch, while the NP1 model exhibits a bias towards mode II debonding at the base of the arch. Only the SMC model provides mode-independent behaviour in the early stages of debonding. This case study provides a practical example of the importance of the behaviour of CZMs under conditions of traction controlled mode mixity, foll...

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Thin films deposited on substrates are usually submitted to large residual compression stresses, causing delamination and buckling of the film into various patterns. The present study is focused on the different equilibria arising on strip-shaped delaminated areas. The three most common types of buckling patterns observed on such strips are known as the straight-sided wrinkles, bubble pattern, and telephone cord blisters. The stability of those equilibria as a function of the two stress components of the loading is investigated. The Föppl-Von Karman model for elastic plates is used for theoretical aspects. The post-critical equilibrium paths of the buckling patterns are investigated numerically by means of the finite-element method. The substrate is assumed to be rigid and the contact to be frictionless. The equilibrium solutions can be classified into families of homologous equilibria allowing the identification of dimensionless parameters for the study of stability. A mapping of the different stable post-critical equilibria is given. It is shown that the straight-sided wrinkles and the bubbles are associated with anisotropy of stresses and/or of elastic properties, whereas the telephone cords are stable at high isotropic stresses. The morphological transitions are experimentally evidenced by in situ atomic force microscopy observations of a nickel 50-nm-thick film under stress.

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Structural quality and stability of nanocrystals are fundamental problems that bear important consequences for the performances of small-scale devices. Indeed, at the nanoscale, their functional properties are largely influenced by elastic strain and depend critically on the presence of crystal defects. It is thus of prime importance to be able to monitor, by noninvasive means, the stability of the microstructure of nano-objects against external stimuli such as mechanical load. Here we demonstrate the potential of Bragg coherent diffraction imaging for such measurements, by imaging in 3D the evolution of the microstructure of a nanocrystal exposed to in situ mechanical loading. Not only could we observe the evolution of the internal strain field after successive loadings, but we also evidenced a transient microstructure hosting a stable dislocation loop. The latter is fully characterized from its characteristic displacement field. The mechanical behavior of this small crystal is clearly at odds with what happens in bulk materials where many dislocations interact. Moreover, this original in situ experiment opens interesting possibilities for the investigation of plastic deformation at the nanoscale.