Finite-distance singularities in the tearing of thin sheets

We investigate the interaction between two cracks propagating quasistatically in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. A single tear propagates in a straight line independently of its position in the sheet. In contrast, we find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.     

Stress defocusing in anisotropic compaction of thin sheets

We address the crumpling of thin sheets in between large scale curved cylinders. In contrast with the usual crushing of a paper ball, one curvature of the sheet is fixed here by the cylinders radius, yielding an anisotropic compaction. As compaction proceeds, it is found that sheets first develop singular folds involving ridges or developable cones, but eventually turn to regular folds free of any geometrical singularities, without ever having entered the plastic regime. This surprising uncrumpling transition corresponds to a stress defocusing. It is understood from a balance between bending and stretching energies on regular states.     

Dissipation in turbulent plasma due to reconnection in thin current sheets

We present in situ measurements in a space plasma showing that thin current sheets the size of an ion inertial length exist and are abundant in strong and intermittent plasma turbulence. Many of these current sheets exhibit the microphysical signatures of reconnection. The spatial scale where intermittency occurs corresponds to the observed structures. The reconnecting current sheets represent a type of dissipation mechanism, with observed dissipation rates comparable to or even dominating over collisionless damping rates of waves at ion inertial length scales (x100), and can have far reaching implications for small-scale dissipation in all turbulent plasmas.     

Small-scale fracture toughness of ceramic thin films: the effects of specimen geometry,ion beam notching and high temperature on chromium nitride toughness evaluation

For the implementation of thin ceramic hard coatings into intensive application environments, the fracture toughness is a particularly important material design parameter. Characterisation of the fracture toughness of small-scale specimens has been a topic of great debate, due to size effects, plasticity, residual stress effects and the influence of ion penetration from the sample fabrication process. In this work, several different small-scale fracture toughness geometries (single-beam cantilever, double-beam cantilever and micro-pillar splitting) were compared, fabricated from a thin physical vapour-deposited ceramic film using a focused ion beam source, and then the effect of the gallium-milled notch on mode I toughness quantification investigated. It was found that notching using a focused gallium source influences small-scale toughness measurements and can lead to an overestimation of the fracture toughness values for chromium nitride (CrN) thin films. The effects of gallium ion irradiation were further studied by performing the first small-scale high-temperature toughness measurements within the scanning electron microscope, with the consequence that annealing at high temperatures allows for diffusion of the gallium to grain boundaries promoting embrittlement in small-scale CrN samples. This work highlights the sensitivity of some materials to gallium ion penetration effects, and the profound effect that it can have on fracture toughness evaluation.     

Correlating flame geometry in opposed-flow flame spread over thin fuels

Numerical analysis and scale analysis are combined in a novel manner in this work to develop closed-form expressions for flame geometry in opposed-flow flame spread over condensed fuels. A scale analysis is used to relate different geometric attributes to appropriate non-dimensional parameters. A comprehensive numerical model is then used to generate a large set of numerical data for flame height, flame length, and pyrolysis length as functions of different fuel and oxidizer parameters for flame spread in the thermal, kinetic, and radiative regimes. The numerical data is then correlated to scaled expressions and the unknown coefficients are numerically determined. It is shown that flame length, flame height, and pyrolysis length can be expressed in terms of the preheat length in different regimes of flame spread. An experimental approach is outlined to measure the preheat length necessary for accurately predicting the flame structure. Experimental images obtained from interferometry in two different regimes – downward spreading configuration and quiescent microgravity environment – are consistent with the proposed flame height correlation.     

Diffraction of electromagnetic waves in thin screens with variable geometry

Odessa Electronics-Technical Institute of Communications. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 2, pp. 226–230, February, 1990.     

Scaling effect on the mixed-mode fracture path of rock materials

In this paper, a new approach is presented to predict the crack growth path in the rock materials by taking into account the size effect. The proposed approach is an incremental method in which the crack initiation angle for each step is determined from the modified forms of the maximum tangential stress criterion. These modified maximum tangential stress criteria take into account the influence of the higher order terms of the stress series at the crack tip in addition to the singular terms. As an important parameter in the proposed method, the critical distance r _c is also assumed to be size dependent. Finally the incremental method is evaluated by experimental results obtained from Guiting limestone and CJhorveh marble specimens reported in the previous studies. It is shown that the proposed approach can predict the fracture trajectory of cracked specimens with different sizes in good agreement with the experimental results when three terms of Williams series expansion are considered for characterizing the stress field around the crack tip.     

Cracks and crazes: on calculating the macroscopic fracture energy of glassy polymers from molecular simulations

We combine molecular dynamics simulations of deformation at the submicron scale with a simple continuum fracture mechanics model for the onset of crack propagation to calculate the macroscopic fracture energy of amorphous glassy polymers. Key ingredients in this multiscale approach are the elastic properties of polymer crazes and the stress at which craze fibrils fail through chain pullout or scission. Our results are in quantitative agreement with dimensionless ratios that describe experimental polymers and their variation with temperature, polymer length, and polymer rigidity.     

Measurement of transport mean-free path of light in thin systems

We extensively investigate in-plane light diffusion in systems with thicknesses larger than but comparable with the transport mean free path. By exploiting amplified spontaneous emission from dye molecules placed in the same holder of the sample, we obtain a directional probe beam precisely aligned to the sample plane. By comparing spatial intensity distribution of laterally leaking photons with predictions from random walk simulations, we extract accurate values of transport mean free path, opening the way to the investigation of a previously inaccessible kind of sample.     

Effective material parameter retrieval for thin sheets: Theory and application to graphene,thin silver films,and single-layer metamaterials

An important tool in the field of metamaterials is the extraction of effective material parameters from simulated or measured scattering parameters of a sample. Here we discuss a retrieval method for thin-film structures that can be approximated by a two-dimensional scattering sheet. We determine the effective sheet conductivity from the scattering parameters and we point out the importance of the magnetic sheet current to avoid an overdetermined inversion problem. Subsequently, we present two applications of the sheet retrieval method. First, we determine the effective sheet conductivity of thin silver films and we compare the resulting conductivities with the sheet conductivity of graphene. Second, we apply the method to a cut-wire metamaterial with an electric dipole resonance. The method is valid for thin-film structures such as two-dimensional metamaterials and frequency-selective surfaces and can be easily generalized for anisotropic or chiral media.     

How geometry controls the tearing of adhesive thin films on curved surfaces

Flaps can be detached from a thin film glued on a solid substrate by tearing and peeling. For flat substrates, it has been shown that these flaps spontaneously narrow and collapse in pointy triangular shapes. Here we show that various shapes, triangular, elliptic, acuminate, or spatulate, can be observed for the tears by adjusting the curvature of the substrate. From combined experiments and theoretical models, we show that the flap morphology is governed by simple geometric rules.     

Energy dissipation and path instabilities in dynamic fracture of silicon single crystals

Brittle fracture usually proceeds at crack driving forces which are larger than those needed to create the new fracture surfaces. This surplus can lead to faster crack propagation or to the onset of additional dissipation mechanisms. Dynamic fracture experiments on silicon single crystals reported here show several distinct transitions between different dissipation mechanisms. Cleavage fracture is followed by the propagation of a faceted crack front, which is finally followed by a path instability and the propagation of multiple cracks. The fracture surface qualitatively corresponds to the mirror, mist, and hackle morphology of amorphous materials. However, the corresponding fracture mechanisms, which remain largely unknown in the amorphous materials, can clearly be identified here.     

On the multiple-root problem when solving directly the nonlinear coupled-wave equations for two-wave mixing in a reflection geometry

A detailed analysis is given of the properties of the algebraic equations obtained when solving directly the nonlinear coupled-wave equations for degenerate two-wave mixing in a reflection geometry. An efficient method is developed for computing the appropriate root only amongst the multiple roots of these algebraic equations.     

Cracks in random brittle solids:

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.     

Opposed flow flame spread over an array of thin solid fuel sheets in a microgravity environment

In this work a numerical study has been carried out to gain physical insight into the phenomena of opposed flow flame spread over an array of thin solid fuel sheets in a microgravity environment. The two-dimensional (2D) simulations show that the flame spread rates for the multiple-fuel configuration are higher than those for the flame spreading over a single fuel sheet. This is due to reduced radiation losses from the flame and increased heat feedback to the solid fuel. The flame spread rate exhibits a non-monotonic variation with decrease in the interspace distance between the fuel sheets. Higher radiation heat feedback primarily as gas/flame radiation was found to be responsible for the increase in the flame spread rate with the reduction of the interspace distance. It was noted that as the interspace distance between the fuel sheets was reduced below a certain value, no steady solution could be obtained. However, at very small interspace distances, steady state spread rates were obtained. Here, due to oxygen starvation the flame spread rate decreased and eventually at some interspace distance the flame extinguished. With fuel emittance (equal to absorptance) reduced to ‘0’ the flame spread rate was nearly independent of the interspace distance, except at very small distances where the flame spread rate dropped due to oxygen starvation. A flame extinction plot with the extinction oxygen level was constructed for the multiple-fuel configuration at various interspace distances. The default fuel with an emittance of 0.92 was found to be more flammable in the multiple-fuel configuration than in a single fuel sheet configuration. For a fuel emittance equal to zero, the extinction oxygen limit decreases for both the single and the multiple fuel sheet configurations. However, the two flammability curves cross over at a certain fuel separation distance. The multiple-fuel configurations become less flammable compared to the single fuel sheet configuration below a certain separation distance.     

Terahertz electromagnetic wave transmission through random arrays of single rectangular holes and slits in thin metallic sheets

We report on the observation of terahertz transparency in random arrays of the single rectangular holes and slits with the areal coverage of only 12%. The terahertz transparency occurs at the fundamental shape resonance of the rectangular holes and confirms the theoretical predictions of earlier works of García-Vidal et al. [Phys. Rev. Lett. 95, 103901 (2005)] on single rectangular holes and of Ruan and Qiu [Phys. Rev. Lett. 96, 233901 (2006)] on random arrays of holes.