Closed-form solutions for bonded elasticallycompressible layers

Compression of elastic layers between parallel plates often finds applications in the mechanical characterization of soft materials or the transfer-printing of nanomembranes with rubber stamps. In addition, annular rubbery gaskets and sealers are often under uniaxial compression during service. Analysis of elastic layers under compression has been focused on incompressible materials, and empirical assumptions of displacements were adopted for simplicity. For compressible materials, solutions obtained by the method of averaged equilibrium are sufficient for effective compression modulus but inaccurate for the displacement or stress fields, whereas solutions obtained by the method of series expansion are considerably complicated. In this article, we report full field, closed-form solutions for bonded elastic layers (disks, annuli, annuli with rigid shafts, infinitely long strips) in compression using separation of variables without any preassumed deformation profile. Our solutions can satisfy the exact forms of the equilibrium equations and all the essential boundary conditions as well as the weak form of the natural boundary conditions. Therefore, the predicted stress, displacement, and effective modulus have found excellent agreement with finite element modeling (FEM) results over a wide range of Poisson’s ratio and aspect ratio. Our analytical and FEM solutions of the stress, displacement, and effective modulus are highly sensitive to Poisson’s ratio, especially near 0.5. Therefore, we also propose a viable means to simultaneously measure the intrinsic Young’s modulus and Poisson’s ratio of elastically compressible layers without camera settings. When Poisson’s ratio approaches 0.5, our solutions can degenerate to classical solutions for incompressible elastic layers

Extraction of rate-dependent traction–separation relations

Methods for characterizing and predicting crack growth in linearly or nonlinearly elastic materials are well established both theoretically and experimentally. However, fundamental work relating to fracture in polymers and other time dependent materials is relatively limited. Complexity in characterizing crack development, growth, and propagation in viscoelastic media stems from two different yet unique challenges. Firstly, typical energy-based methods, widely used in characterizing traction separation relationships in elastic media, are not applicable anymore because of inherent bulk energy dissipation, a characteristic of viscoelastic media. Furthermore, the load dependent response of viscoelastic materials makes it difficult to quantify any independent parameters which would be indicative of fracture process. For example, loss of stiffness at particular load level in an elastic body can be very well attributed to crack development/propagation, whereas the same cannot be hypothesized for a viscoelastic material. The primary objective of this study is to establish a theoretical framework for developing a simple experimental procedure aimed at quantifying traction–separation relations, a vital fracture parameter used in numerical modeling of cohesive or interfacial cracks in viscoelastic media. The procedure combines the pseudo strain concepts of Schapery with the field projection method of Kim to extract traction–separation relationships for both cohesive and adhesive cracks, without making any assumptions on their form. It was found that test problems for the interaction integrals could be chosen so as to greatly reduce the number of measurements that are required. Numerical experiments were carried out on two strips of polyvinyl acetate bonded together and conclusive results produced demonstrate the efficiency of the framework developed in this study

Failure by Simultaneous Grain Growth, Strain Localization, and Interface Debonding in Metal Films on Polymer Substrates

In a previous paper, we have demonstrated that a microcrystalline copper film well bonded to a polymer substrate can be stretched beyond 50% without cracking. The film eventually fails through the co-evolution of necking and debonding from the substrate. Here we report much lower strains to failure (around 10%) for polymer-supported nanocrystalline metal films, whose microstructure is revealed to be unstable under mechanical loading. We find that strain localization and deformation-associated grain growth facilitate each other, resulting in an unstable deformation process. Film/substrate delamination can be found wherever strain localization occurs. We therefore propose that three concomitant mechanisms are responsible for the failure of a plastically deformable but microstructurally unstable thin metal film: strain localization at large grains, deformation-induced grain growth and film debonding from the substrate.Engineering and Applied Science

Competing Multiferroic Phases in NiI2_{2} Mono- and Few-layers

A recent experiment reported type-II multiferroicity in monolayer (ML) NiI$_{2}$ based on a presumed spiral magnetic configuration (Spiral-B), which is, as we found here, under debate in the ML limit. Freestanding ML NiI$_{2}$ breaks its C$_{3}$ symmetry, as it prefers a striped antiferromagnetic order (AABB-AFM) along with an intralayer antiferroelectric (AFE) order. However, substrate confinement may preserve the C$_{3}$ symmetry and/or apply tensile strain to the ML. This leads to another spiral magnetic order (Spiral-$IV^X$), while 2L shows a different order (Spiral-$V^Y$) and Spiral-B dominates in thicker layers. Thus, three multiferroic phases, namely, Spiral-B+FE, Spiral-$IV^X$ +FE, Spiral-$V^Y$+FE, and an anti-multiferroic AABB-AFM+AFE one, show layer-thickness-dependent and geometry-dependent dominance, ascribed to competitions among thickness-dependent Kitaev, biquadratic, and Heisenberg spin-exchange interactions and single-ion magnetic anisotropy. Our theoretical results clarify the debate on the multiferroicity of ML NiI$_{2}$ and shed light on the role of layer-stacking-induced changes in noncollinear spin-exchange interactions and magnetic anisotropy in thickness-dependent magnetism.Comment: 14 pages, 4 figures and an SI file of 25 pages appende

Islands stretch test for measuring the interfacial fracture energy between a hard film and a soft substrate

We present a technique for measuring the interfacial fracture energy, $\Gamma_i$, between a hard thin film and a soft substrate. A periodic array of hard thin islands is fabricated on a soft substrate, which is then subjected to uniaxial tension under an optical microscope. When the applied strain reaches a critical value, delamination between the islands and the substrate starts from the edge of the islands. As the strain is increased, the interfacial cracks grow in a stable fashion. At a given applied strain, the width of the delaminated region is a unique function of the interfacial fracture energy. We have calculated the energy release rate driving the delamination as a function of delamination width, island size, island thickness, and applied strain. For a given materials system, this relationship allows determination of the interfacial fracture energy from a measurement of the delamination width. The technique is demonstrated by measuring the interfacial fracture energy of plasma-enhanced chemical vapor deposition SiNx islands on a polyimide substrate. We anticipate that this technique will find application in the flexible electronics industry where hard islands on soft substrates are a common architecture to protect active devices from fracture.Engineering and Applied Science