Session X52: Focus Session: Extreme Mechanics - Fracture, Friction, and Frequencies

Geometry of Tearing: crack propagation in brittle sheets

We experiment the fracture of thin object everyday when trying to open a packaging. From a physics point of vew, the propagation of cracks in thin brittle elastic sheets appears to be remarkably reproducible, with very regular crack path. We will present some examples where the crack path can be predicted using classical arguments in fracture and geometrical tools: this is another example where geometry plays a central role in the mechanics of thin sheets.   

Spiral and croissant crack in drying thin films

Drying mud or crazing in ceramics glaze leads to familiar hierarchical cracks network where a new crack connects perpendicularly to older ones. We report unusual spirals and croissants crack patterns in methylsiloxane drying thin films moderately adhering on a substrate. Such cracks are also observed in a very different situation when magnetron sputtering multilayers are under external tension. The amplitude and wavelength of the pattern are robusts and are orders of magnitude larger than the thickness of the layer. The propagation of the spiral and croissant cracks occurs in a narrow range of adhesion energy between the film and the substrate and strain in the film. We will show how the propagation is driven by a cooperation between fracture and adhesion.   

Rupture of a highly stretchable acrylic dielectric elastomer

Dielectric elastomers have found widespread application as energy harvesters, actuators, and sensors. In practice these elastomers are subject to large tensile stretches, which potentially can lead to mechanical fracture. In this study, we have examined fracture properties of the commercial acrylic elastomer VHB 4905. We have found that inserting a pre-cut into the material drastically reduces the stretch at rupture from $\lambda _{rup}$ = 9.43$\pm $1.05 for pristine samples down to only $\lambda _{rup}$ = 3.63$\pm $0.45 for the samples with a pre-cut. Furthermore, using ``pure-shear'' test specimens with a pre-crack, we have measured the fracture energy and stretch at rupture as a function of the sample geometry. The stretch at rupture was found to decrease with sample height, which agrees with an analytical prediction. Additionally, we have measured the fracture energy as a function of stretch-rate. The apparent fracture energy was found to increase with stretch-rate from $\Gamma \approx $1500 J/m$^{2}$ to $\Gamma \approx $5000 J/m$^{2}$ for the investigated rates of deformation. This phenomenon is due to viscoelastic properties of VHB 4905, which result in an apparent stiffening for sufficiently large stretch-rates.   

How does adhesion impact the formation of telephone cord buckles?

Compressively stressed thin films with low adhesion frequently buckle into telephone cords. Although telephone cord buckles have been studied for decades, no complete understanding of their origin and propagation has so far been presented. Here, using Finite Element Analysis, we have coupled non-linear plate deformation with a cohesive zone model to simulate the kinematics of a propagating telephone cord buckle. On the experimental side, we have developped model thin films with a precise adjustment of both adhesion and residual stresses. From the comparison of the simulations with some experimental observations, we propose a generic mechanism for the formation of telephone cord buckles. Proper inclusion of the dependence of interfacial toughness upon mode mixity proved to be central to the success of the approach so that this clarification of the mechanism of telephone cord formation promises better understanding of interfacial toughness through the analysis of buckle morphology.   

Nonlinear modal interactions in a microcantilever

We study the nonlinear interactions between vibrational modes in a microcantilever. The flexural-flexural, torsional-torsional and torsional-flexural modal interactions are investigated theoretically and experimentally. In a cantilever, the nonlinearity arising from geometrical and inertial effects couples the different modes. The motion of one mode influences the resonance frequency of the other modes. We show that depending on the amplitude of one mode, both frequency stiffening and weakening of the other mode occurs. The modal interactions in clamped-clamped beam resonators is recently studied, and several applications have been proposed. Microcantilevers are frequently used in instrumentation, and the modal interactions presented here enable such schemes, including Q-factor tuning and self-detection.   

Effects of Roughness and Inertia on Precursors to Frictional Sliding

Experiments show that when a PMMA block on a surface is normally loaded and driven by an external shear force, contact at the interface is modified in discrete precursor slips prior to steady state sliding.[1] Our simulations use an atomistic model of a rough two-dimensional block in contact with a flat surface to investigate the evolution of stress and displacement along the contact between surfaces. The talk will show how local and global stress conditions govern the initiation of interfacial cracks as well as the spatial extension of the cracked region. Inertia also plays an important role in determining the number and size of slips before sliding and influences the distribution of stresses at the interface. Finally, the geometry of surface asperities also influences the interfacial evolution and the total friction force. The relationship between the interfacial stress state and rupture velocity will also be discussed. [1] S.M. Rubinstein, G. Cohen and J. Fineberg, PRL 98, 226103 (2007)   

Scratch test as a fracture process: from soft to hard materials

The scratch test consists of driving a probe, at a certain depth, through a material and is most likely the oldest technique for the mechanical characterization of materials. Although it is widely used in strength testing, the presence of residual chips during the process suggests that a fracture mechanism is at play. We investigate the link between the material fracture properties, the probe geometry and the resulting forces using a combination of precision experiments and Linear Elastic Fracture Mechanics analysis. An analytical model is developed that is applicable both at the macro and micro scale, and that can take into account different probe geometries. Rationalizing the mechanics involved allows us to introduce a novel experimental technique to accurately determine the fracture toughness from scratch tests. Application of this technique to mechanical testing on metals, polymers and ceramics yields values for the fracture toughness that are in excellent agreement with conventional methods such as the three-point bending test, albeit in a way that is less destructive and more scalable. As such, our method to determine materials fracture properties represents an important new development in the field of mechanical micro-characterization.   

Sliding on a Nanotube: Interplay of Friction, Deformations and Defects

Carbon nanotubes (CNT) have applications as composite material reinforcements and components in nanodevices due to their exceptional physical properties. However, CNTs have structural defects that can change their mechanical properties. For applications, CNTs have to be in contact with other surfaces, thus it is important to understand how defects change their frictional properties. Here, we show that defects can impact the frictional properties of supported Arc Discharge (AD) and Chemical Vapor Deposition (CVD) grown CNTs by sliding an AFM tip along (longitudinal) and across (transverse) the CNT axis. Larger friction coefficient is found during transverse sliding due to a lateral CNT deformation (called hindered rolling) that causes extra friction dissipation which is absent during longitudinal sliding.[1] A friction anisotropy, defined as the ratio of shear strength measured during both sliding directions, can be as high as 13.7 for AD CNTs but less than 6 for CVD CNTs. Extra defects in CVD CNTs couple both sliding motions, resulting in more energy dissipation and higher longitudinal friction. A simple analytical model is developed to explain the observed experimental behavior. Our finding provides a better understanding of tribological properties of individual CNT at the nanoscale. [1] M. Lucas et al., Nature Mater. 8, 876 (2009)   

Graphene Morphology on Nano-Patterned Electronic Substrates

In order to get high quality of graphene for the application in electronic devices, good transfer of graphene prepared by mechanical exfoliation or chemical vapor deposition is always required and substrate with flat surface is preferred to avoid the crack and destruction of the thin sheets. Here, we studied the graphene morphology on nano-patterned electronic substrates by transferring graphene grown from chemical vapor deposition onto the gold nano pillar patterns on silicon substrate. The adhesion between the graphene and the gold surface makes the flexible thin membrane conform to the substrate geometry and form a series of blisters. By measuring the blister radius and height, the adhesion energy of graphene and gold substrate can be deduced. In the meantime, the morphology of graphene on the pillar patterns was found to strongly related to the adhesion energy, the height and separation of pillars. By changing these parameters, the blisters may decrease size or expand to coalesce. The critical separation between pillars and the critical height of pillars were predicted to avoid the coalescence of the blisters when the adhesion energy was fixed. The results obtained here can be useful to increase the performance and the durability of the graphene based device.   

Graphene Blister Adhesion Mechanics

We describe graphene blister configurations to study the elasticity of mono- and multi-layer graphene as well as the adhesion of the blister to an SiO2 substrate. We create blisters by depositing graphene on a chip containing etched cavities of a prescribed volume. The chip is placed in a high-pressure chamber where the cavities are charged to a prescribed pressure. When the chip is removed from the chamber the pressure difference across the membrane causes it to bulge, while the number of gas molecules in the chamber remains constant. As the pressure is increased the membrane continues to bulge and at a critical pressure can delaminate (in a stable or unstable manner) permitting extraction of the adhesion energy from a combination of theory and measurements of the deformed blister configuration. We describe these experiments and develop a thermodynamic model of the system that identifies interesting nonlinear effects as the membranes deform including instabilities, delamination, and adhesion hysteresis, depending on the configurational parameters. We use the theory and experiments together to determine for the first time the adhesion energy between graphene and SiO2, as well as explore the interesting mechanics that occur.   

Novel method for simulation of structural post buckling

A new FEM-based method for simulating the onset of buckling instabilities and the post-buckling evolution is developed. The method consists of creating a random spatial perturbation of the elastic modulus and applying a step-by-step loading to approach the critical state and beyond. Prior to buckling, the non-uniform modulus triggers micro bending and lateral deformation. As the compressive load progresses, the micro displacement grows non-linearly causing the system to be biased toward the mode that minimizes energy. The system buckles in that mode and the post-buckling deformation can be examined. The technique has been applied to several buckling cases. The results show quantitative agreement with theory and experiments. For problems with continuously-distributed buckling modes and critical values that are close from one to another, the method is able to automatically select the correct critical configuration. Unlike other perturbation methods that are inspired by either Eigen vectors or experimental data, the current method does not need a priori knowledge of the expected buckling mode. This is especially useful in complex problems (e.g. wrinkling of stretched films) for which linear eigenvalue analysis cannot predict the critical conditions.   

Buckling morphologies of crystalline shells with frozen defects

The crumpling of spherical crystalline lattices where the topological defects are frozen is studied. The geometry of the crumpled membrane is found to depend on the set of topological defects and more exotic defect sets can result in crumpled shapes resembling that of the Platonic and Archimedean solids. The phase diagram of the crumpled spheres can be categorized by two dimensionless numbers $h/R$ (aspect ratio) and $R/a$ (lattice ratio), where $h$ is the thickness of the shell, $R$ is the radius of the initial sphere and $a$ is the average bond length of the triangulation. The shapes of the crumpled membrane can be understood using rotationally invariant quantities formed from spherical harmonics coefficients and a Landau free energy can be written, involving quadratic and cubic rotational invariants. Shells with different topological defects have qualitatively different hysteresis behaviors and the transitions appear to be first order in general.   

Do tidal stresses trigger large earthquakes early?

The effect of tidal or other periodic stresses on the timing of large earthquakes is a hotly debated topic in geophysics and rock-friction or granular physics communities. I discuss a simple probabilistic model which captures the main qualitative features of several rock-friction or granular experiments and may resolve some outstanding discrepancies between different experimental results. With sufficiently accurate measurements, quantitative predictions for real experiments are possible, including the number of measured events needed to detect correlations between periodic stresses and large slip events for given amplitudes and frequencies.   

Tattoo-Like Strain Gauges Based on Silicon Nano-Membranes

This talk reports the in vivo measurement of tissue deformation through adhesive-free, conformable lamination of a tattoo-like elastic strain gauge consisted of piezoresistive silicon nano-membranes strategically integrated with tissue-like elastomeric substrates. The mechanical deformation in soft tissues cannot yet be directly quantified due to the lack of enabling tools. While stiff strain gauges for structural health monitoring have long existed, biological tissues are soft, curvilinear and highly deformable in contrast to civil or aerospace structures. An ultra-thin, ultra-soft, tattoo-like strain gauge that can conform to the convoluted surface of human body and stay attached during locomotion will be able to directly quantify tissue deformation without affecting the mechanical behavior of the tissue. While single crystalline silicon is known to have the highest gauge factor and best elastic response, it is intrinsically stiff and brittle. To achieve strain gauges with high compliance, high stretchability and reasonable sensitivity, single crystalline silicon nano-membranes will be transfer-printed onto polymeric support through carefully engineered stamps. The thickness and length of the Si strip will be chosen according to theoretical and numerical mechanics analysis which takes into account for the tradeoff between stretchability and sensitivity.