Lower Length Scale Research Articles

Nonlinear elasticity tailoring and failure mode manipulation of functionally graded honeycombs under large deformation

Design of lattice metamaterials with tailored mechanical properties at a relatively higher (macro) length scale by architecting lower (micro) length scale geometric and material configurations leads to achieving unprecedented mechanical properties for fulfilling advanced multi-functional structural demands. In the design space of innovative microstructural configurations, we propose a novel class of lattice metamaterials with cell walls made of optimally designed functionally graded intrinsic materials. Under different modes of remotely applied mechanical stresses, two different intuitive architectures of functional gradations for the intrinsic cell wall materials are proposed. The large-deformation nonlinear lattices result in broadband modulation of effective stiffness, and an unprecedented manipulation capability of failure modes and corresponding strengths covering ductile and brittle types depending on architected material gradation. For estimating the nonlinear elasticity and microstructural stresses as a measure of failure mode for the proposed functionally graded lattices undergoing large deformation, a multi-scale mechanics-based semi-analytical framework is developed. Geometrically nonlinear functionally graded beams with generalized material gradation, integrated with unit cell architectures, are analyzed through iterative variational energy principle-based Ritz approach. Based on the developed physically insightful computational framework, effective nonlinear elastic properties and failure modes of the functionally graded honeycomb lattices are tailored as a function of the intrinsic material gradation at the lower length scale. The proposed novel class of lattices with optimally designed functionally graded intrinsic materials and coupled unit cell architectures would open up innovative avenues for designing advanced multi-functional engineering structures and mechanical systems.

Percolation versus depinning transition: The inherent role of damage hardening during quasibrittle failure.

The intermittent damage evolution preceding the failure of heterogeneous brittle solids is well described by scaling laws. In deciphering its origins, failure is routinely interpreted as a critical transition. However at odds with expectations of universality, a large scatter in the value of the scaling exponents is reported during acoustic emission experiments. Here we numerically examine the precursory damage activity to reconcile the experimental observations with critical phenomena framework. Along with the strength of disorder, we consider an additional parameter that describes the progressive damageability of material elements at mesoscopic scale. This hardening behavior encapsulates the microfracturing processes taking place at lower length scales. We find that damage hardening can not only delay the final failure but also affect the preceding damage accumulation. When hardening is low, the precursory activity is strongly influenced by the strength of the disorder and is reminiscent of damage percolation. On the contrary, for large hardening, long-range elastic interactions prevail over disorder, ensuring a rather homogeneous evolution of the damage field in the material. The power-law statistics of the damage bursts is robust to the strength of the disorder and is reminiscent of the collective avalanche dynamics of elastic interfaces near the depinning transition. The existence of these two distinct universality classes also manifests as different values of the scaling exponent characterizing the divergence of the precursor size on approaching failure. Our finding sheds new light on the connection between the level of quasibrittleness of materials and the statistical features of the failure precursors. Finally, it also provides a more complete description of the acoustic precursors and thus paves the way for quantitative techniques of damage monitoring of structures-in-service.

Two-way coupled modeling of dislocation substructure sensitive crystal plasticity and hydrogen diffusion at the crack tip of FCC single crystals

Dislocation substructure-sensitive crystal plasticity (DSS-CP) modeling accounts for the evolution of mesoscale structures using dislocation-based parameters informed by experiments and computation at various lower length scales. To a first-order approximation, DSS-CP model parameters are affected by hydrogen (H) concentration, accounting for both H-dependent yield strength and strain hardening rate. This H-affected DSS-CP model is two-way coupled with H-diffusion to explore both effects of plastic deformation on H-diffusion and effects of H on yield strength and strain hardening in the DSS-CP model. Crack tip simulations are performed for face-centered cubic (FCC) metals under monotonic loading conditions with and without H. Enhanced maximum plastic deformation in the vicinity of the crack tip (i.e., localization or intensification of plastic strain) and crack tip opening displacement (CTOD) are predicted in the presence of H, consistent with experimental observations. In spite of increased initial strength due to H, subsequent reduction of the rate of strain hardening in the presence of H is shown to enhance localization of crack tip plasticity. Furthermore, this modeling framework predicts that higher H-diffusivity (leading to a larger H-affected zone) will enhance the crack tip plasticity, making use of the two-way coupling algorithm implemented in this work. On the other hand, we find that the H-sensitivity of crack tip strain localization response, based only on modification of model parameters, is too weak to explain typical experimental observations. This points to the need to develop more advanced DSS-CP constitutive relations that consider highly complex dislocation interactions with point defects.

A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism.

We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure-property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius-Duhem inequality. The kinetic framework employs a stress-strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model's results showing good correlations.

Multi-Scale Characterization of Porosity and Cracks in Silicon Carbide Cladding after Transient Reactor Test Facility Irradiation

Silicon carbide (SiC) ceramic matrix composite (CMC) cladding is currently being pursued as one of the leading candidates for accident-tolerant fuel (ATF) cladding for light water reactor applications. The morphology of fabrication defects, including the size and shape of voids, is one of the key challenges that impacts cladding performance and guarantees reactor safety. Therefore, quantification of defects’ size, location, distribution, and leak paths is critical to determining SiC CMC in-core performance. This research aims to provide quantitative insight into the defect’s distribution under multi-scale characterization at different length scales before and after different Transient Reactor Test Facility (TREAT) irradiation tests. A non-destructive multi-scale evaluation of irradiated SiC will help to assess critical microstructural defects from production and/or experimental testing to better understand and predict overall cladding performance. X-ray computed tomography (XCT), a non-destructive, data-rich characterization technique, is combined with lower length scale electronic microscopic characterization, which provides microscale morphology and structural characterization. This paper discusses a fully automatic workflow to detect and analyze SiC-SiC defects using image processing techniques on 3D X-ray images. Following the XCT data analysis, advanced characterizations from focused ion beam (FIB) and transmission electron microscopy (TEM) were conducted to verify the findings from the XCT data, especially quantitative results from local nano-scale TEM 3D tomography data, which were utilized to complement the 3D XCT results. In this work, three SiC samples (two irradiated and one unirradiated) provided by General Atomics are investigated. The irradiated samples were irradiated in a way that was expected to induce cracking, and indeed, the automated workflow developed in this work was able to successfully identify and characterize the defects formation in the irradiated samples while detecting no observed cracking in the unirradiated sample. These results demonstrate the value of automated XCT tools to better understand the damage and damage propagation in SiC-SiC structures for nuclear applications.

Experimental characterization of quasi-2-dimension nanoporous gold ultra-thin film from nano to micro length scale

Quasi-2D nanoporous gold ultra-thin films have been elaborated and investigated by specific surface approaches. Three different microscopy techniques (Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM), and Atomic Force Microscopy (AFM)) have been used for the characterizations. A careful statistical analysis of experimental images has been done, thanks to the development of a dedicated image analysis software. It reveals that the inhomogeneous gold nanomesh at low length scale becomes homogeneous at a length scale larger than the biggest pores size of about 2 μm, with a constant opacity reaching 35%. At such a scale, the ligaments present an average diameter of 20 nm and an average length of 70 nm. While TEM and SEM present similar results, AFM overestimates the geometric characteristics due to tip convolution effect. However, the topology of the nanomesh is not affected. This study also reveals pores with a much larger size in the quasi 2D nanoporous ultra-thin film than in its bulk counterpart for similar ligaments diameters, which could play an important role in its mechanical properties.

Fracture toughness of Ca‐, Sr‐, and Ba‐aluminoborosilicate glasses

AbstractThe field strength effect on fracture toughness was tested for three alkaline earth (AE) aluminoborosilicate (ABS) glasses. This work explores the impact of modifier field strength (FS) on macro‐mechanical properties in line with previous works which examined the FS effect on structure, hardness, crack resistance, and elastoplastic properties of alkali and AE‐ABS glasses. Fracture toughness (KIcVNB) was found to increase as modifier FS increased; and the elastoplastic ratio (HV/E) correlated well with plasticity, hardness, and fracture toughness. The purpose of this work is to examine the mechanical response of AE‐ABS glasses at a larger length scale in order to determine whether the field strength effect is active as was observed at lower length scales in previous works. The observed increase and decrease of the KIcVNB and HV/E, respectively, with increasing modifier FS, suggest a strong correlation between increasing fracture toughness and crack resistance with increasing plasticity for the AE‐ABS glasses studied.

Role of crystallographic orientation in material behaviour under nanoindentation: Molecular Dynamics study

Abstract The mechanical properties of materials can be analysed under deformation conditions by various laboratory tests. However, such experimental investigations become extremely complicated and often even impossible at the lower length scales where the arrangement of the atomic planes is considered. In this case, computational materials science is a robust alternative to extend the capabilities of laboratory tests. Therefore, the molecular dynamics technique was selected in the current work to evaluate the role of the local grain crystallographic orientation during nanoindentation testing. A pure aluminium sample was selected as a case study. For the sake of clarity, two distinctively different crystallographic orientations cube {100}<001> and hard {110}<011> were investigated in a set of arrangements: monocrystalline, bicrystalline, and polycrystalline. The influence of the substrate and the neighbouring grains on the material response to local deformation was evaluated. The research used two types of indenters: spherical and sharp-tipped. Results obtained were analysed with respect to the arrangement of atoms and load-displacement curves. This research proved that the role of crystallographic orientation in material behaviour under nanoindentation should not be neglected during the interpretation of data from this test.

MULTISCALE MODELING OF HYDROGEN-AFFECTED CRACK TIP DAMAGE USING FULLY COUPLED CHEMO-MECHANICAL CRYSTAL PLASTICITY FRAMEWORK FOR AUSTENITIC STAINLESS STEEL

Hydrogen embrittlement is a long-standing issue in engineering structural applications with a multitude of competing hypotheses and theories. Despite advances in experimental and computational capabilities, common understanding of contributing phenomena has not yet been achieved. Accordingly, models are varied and limited in scope, even for a given material system. A more complete understanding of hydrogen-related damage across multiple length and time scales is still an open challenge. In the present report, lower length scale simulations and arguments are used to motivate a mesoscale crystal plasticity model that can inform crack tip field evolution and fatigue crack growth rates. The fully coupled chemo-mechanical framework describes and simulates the complex interplay between hydrogen, hydrogen traps, vacancies, dislocations, vacancy complex stabilization by hydrogen, and damage in the form of nanovoid sheets. The model is implemented at a crack tip using a finite element framework to simulate the influence of hydrogen on deformation and fatigue damage development of face-centered cubic (FCC) austenitic stainless steel 316L (SS316L), a structural material important in energy applications. Accounting for hydrogen and hydrogen-related damage across multiple length scales in this way facilitates study of hydrogen embrittlement that can be related to experimental observations and historical attributions of hydrogen effects on deformation and damage in FCC metals and alloys.

Conductive polymer based hydrogels and their application in wearable sensors: a review.

Hydrogels have been attracting increasing attention for application in wearable electronics, due to their intrinsic biomimetic features, highly tunable chemical-physical properties (mechanical, electrical, etc.), and excellent biocompatibility. Among many proposed varieties of hydrogels, conductive polymer-based hydrogels (CPHs) have emerged as a promising candidate for future wearable sensor designs, with capability of realizing desired features using different tuning strategies ranging from molecular design (with a low length scale of 10-10 m) to a micro-structural configuration (up to a length scale of 10-2 m). However, considerable challenges remain to be overcome, such as the limited strain sensing range due to the mechanical strength, the signal loss/instability caused by swelling/deswelling, the significant hysteresis of sensing signals, the de-hydration induced malfunctions, and the surface/interfacial failure during manufacturing/processing. This review aims to offer a targeted scan of recent advancements in CPH based wearable sensor technology, from the establishment of dedicated structure-property relationships in the lab to the advanced manufacturing routes for potential scale-up production. The application of CPHs in wearable sensors is also explored, with suggested new research avenues and prospects for CPHs in the future also included.

Spectral induced polarization monitoring of induced calcite precipitation in subsurface sediments

SUMMARY Co-precipitation of contaminants within the crystalline structure of calcite is a promising natural attenuation or remedial technology being considered at contaminated sites. We explore the sensitivity of the spectral induced polarization (SIP) method to induced calcite precipitation in natural sediments as a path forward to non-invasively monitor these sites. We performed time-lapse column experiments using phased (I–IV) injections over 40 d on natural sediments from the Hanford Site (WA, USA). In the phased injections, abiotic calcite precipitation was induced and confirmed to have occurred. Previous work on glass beads and homogeneous sand was limited to high frequency detection of calcite, however in this work we observed the development of two polarization mechanisms, one at high frequency (>100 Hz) and one at low frequency (<100 Hz). Based on the characteristic frequencies from the SIP high and low frequency regimes, characteristic length scales (L) were computed where the adsorption mode of Na+ versus Ca2+ was compared by using diffusion coefficients corresponding to Na+ versus an arithmetically averaged value for Na+ and Ca2+. Using the diffusion coefficient of Na+, the high frequency L was found to correlate well with the size of the calcite crystals. The low frequency L correlated well with the individual natural sediment grain sizes within the columns. During late experimental times (day 36 and 40), the characteristic low frequency in two of the experimental columns shifted to lower frequencies (<0.001 Hz) which may signify SIP sensitivity of the formed calcite with the sediment grains. In field applications, the development of a low frequency polarization length scale to monitor calcite precipitation is promising for field monitoring applications, however further laboratory work needs to be performed to examine the SIP sensitivity of calcite formation in the presence of natural sediments.

A micromorphic filter for determining stress and deformation measures from direct numerical simulations of lower length scale behavior

AbstractA micromorphic filter is presented for the extraction of stress and deformation measures from underlying direct numerical simulation (DNS) of microstructural mechanical response. The filter is consistent with the micromorphic continuum theory of Eringen and Suhubi (1964), and allows the interrogation of a DNS to generate higher order constitutive models. The filter adopts aspects of the overlap coupling techniques for atomistic‐continuum scale‐bridging in order to update the nodal degrees of freedom of the finite‐element‐based filter. Two methods for the extraction of quantities of interest from the underlying DNS are presented. The first is a least squares fitting technique which is appropriate for finite‐element‐style macro‐scale domains, and the second is a variationally based approach which generalizes the method to any macro‐scale domain which has a variational form. No restrictions on the form of the micro‐scale simulation are inherent to the approach, provided that the required quantities (stress, position, etc.) can be provided. The filter is applied to a simple homogeneous medium undergoing homogeneous deformation to demonstrate the recovery of a classical continuum response, what we call the null case. We then apply the framework to the same homogeneous medium with a central and edge penny‐shaped crack to show micromorphic effects. We demonstrate that varying the size of the filter causes the micromorphic behaviors to arise and then dissipate as the filter becomes smaller than the crack's length scale. We also show the effect of filter size on a chiral element network along with a plate perforated with evenly spaced and perturbed holes through the thickness. The micromorphic effects are shown to be present for the chiral elements under any loading but become most pronounced when a single element is located within each averaging domain. Micromorphic effects become pronounced for the plate upon the onset of localization.

Analysis of wake properties and meandering under different cases of atmospheric stability: a large eddy simulation study

Large eddy simulations (LES) with the solver Meso-NH are performed to analyse a single wind turbine wake. In the first part of this work, four algorithms to determine the instantaneous wake centre (wake tracking) from the literature are compared. A data-processing method is also proposed to improve the results of these algorithms. In the second part, three different atmospheric conditions are simulated to assess the effect of inflow conditions on the wake. The focus is on the 2-dimensional wake width, the maximum deficit, the maximum added turbulence and the amount of wake meandering in the lateral and vertical directions. The three formers are computed in both the Moving and Fixed Frames of Reference (MFOR and FFOR). Results in the MFOR are shown to be sensitive to the wake tracking algorithm, in particular for turbulence. The flowfield in the MFOR is found to be independent of atmospheric conditions for the two cases with similar operating conditions and length scales larger than two diameters of the rotor. The third case with lower length scales and turbulence intensity behaves differently.

Mesoscale modeling of ballistic impact experiments on a single layer of plain weave composite

To gain fundamental understanding of energy absorbing mechanisms during high velocity impact of plain weave S-2 glass/epoxy composites, single layer composites are ballistically tested and modeled. To avoid boundary condition effects, targets were 0.6 m by 0.6 m with free boundaries. Targets were perforated by 17 grain, 0.22 caliber fragment simulating projectiles . Experiments focused on determining ballistic limit velocity and the associated damage modes. The experiments were simulated with a continuum finite element model with effective plain weave properties that predicted the ballistic limit velocity with 6% error. A mesoscale model that incorporates the woven fabric architecture and lower length scale energy absorbing mechanisms was also developed. The mesoscale model includes accurate geometry and fiber volume fraction , rate-dependent matrix behavior, and important damage mechanisms including tow-tow delamination , tow pullout and frictional sliding . The mesoscale model predicted ballistic limit velocity with 1% error and more accurately predicts the deformation modes during ballistic impact and penetration than the continuum modeling approach. The mesoscale model indicated two phases of penetration, the first dominated by momentum transfer and the second dominated by tow tension and pullout. In a materials-by-design framework, the mesoscale model was used to quantify energy dissipation and identify important damage mechanisms that could be optimized to provide improved ballistic penetration resistance .

Mesoscale Simulation-Based Parametric Study of Damage Potential in Brain Tissue Using Hyperelastic and Internal State Variable Models.

Two-dimensional mesoscale finite element analysis (FEA) of a multilayered brain tissue was performed to calculate the damage-related average stress triaxiality and local maximum von Mises strain in the brain. The FEA was integrated with rate-dependent hyperelastic and internal state variable (ISV) models, respectively, describing the behaviors of wet and dry brain tissues. Using the finite element results, a statistical method of design of experiments (DOE) was utilized to independently screen the relative influences of seven parameters related to brain morphology (sulcal width/depth, gray matter (GM) thickness, cerebrospinal fluid (CSF) thickness and brain lobe) and loading/environment conditions (strain rate and humidity) with respect to the potential damage growth/coalescence in the brain tissue. The results of the parametric study illustrated that the GM thickness and humidity were the two most crucial parameters affecting average stress triaxiality. For the local maximum von Mises strain at the depth of brain sulci, the brain lobe/region was the most influential factor. The conclusion of this investigation gives insight for the future development and refinement of a macroscale brain damage model incorporating information from lower length scale.

Physics-based modelling and validation of inter-granular helium behaviour in SCIANTIX

In this work, we propose a new mechanistic model for the treatment of helium behaviour at the grain boundaries in oxide nuclear fuel. The model provides a rate-theory description of helium inter-granular behaviour, considering diffusion towards grain edges, trapping in lenticular bubbles, and thermal re-solution. It is paired with a rate-theory description of helium intra-granular behaviour that includes diffusion towards grain boundaries, trapping in spherical bubbles, and thermal re-solution. The proposed model has been implemented in the meso-scale software designed for coupling with fuel performance codes SCIANTIX. It is validated against thermal desorption experiments performed on doped UO2 samples annealed at different temperatures. The overall agreement of the new model with the experimental data is improved, both in terms of integral helium release and of the helium release rate. By considering the contribution of helium at the grain boundaries in the new model, it is possible to represent the kinetics of helium release rate at high temperature. Given the uncertainties involved in the initial conditions for the inter-granular part of the model and the uncertainties associated to some model parameters for which limited lower-length scale information is available, such as the helium diffusivity at the grain boundaries, the results are complemented by a dedicated uncertainty analysis. This assessment demonstrates that the initial conditions, chosen in a reasonable range, have limited impact on the results, and confirms that it is possible to achieve satisfying results using sound values for the uncertain physical parameters.

Bulk and surface diffusion of neodymium in alpha-uranium: Ab initio calculations and kinetic Monte Carlo simulations

• A Nd interstitial is found to be intrinsically unstable in alpha- U . • The binding between the substitutional Nd and the U vacancy in strong in alpha- U . • Nd atoms migrate in bulk alpha- U via the vacancy mechanism. • Radiation can significantly accelerate the bulk diffusivity of Nd in alpha- U . • Diffusion of Nd adatoms via pore surfaces is much faster than bulk diffusion. A fundamental understanding of lanthanide transport in metallic fuels is critical for high fidelity modeling of the fuel-cladding chemical interaction (FCCI) phenomenon, which can lead to the formation of brittle intermetallic compounds and premature failure of the cladding. Here we report a combined ab initio density functional theory (DFT) and kinetic Monte Carlo (KMC) study of the bulk diffusivity of Nd in α-U , fully taking into account the effect of radiation enhanced diffusion. The vacancy mechanism is considered to be the dominant mechanism for the bulk diffusion of Nd since a Nd interstitial is found to be intrinsically unstable in α-U . The surface diffusivity of a Nd adatom on α-U (001) surface has been further predicted using KMC simulations parameterized by DFT calculations. The present study suggests that Nd transport via the surface diffusion mechanism can be many orders of magnitude faster than bulk diffusion. Furthermore, the results from the present lower length scale study can be used to inform mesoscale phase-field simulations to determine the effective diffusion coefficient of Nd through α-U with a porous microstructure.

Improvement of the BISON U3Si2 modeling capabilities based on multiscale developments to modeling fission gas behavior

• The recommended models for analyzing U 3 Si 2 fuel behavior with BISON are provided. • Lower-length scale methods have been used to reduce uncertainty in fission gas modeling of U 3 Si 2 . • Comparisons to PIE measurements of U 3 Si 2 fueled rodlets are acceptable. Uranium silicide ( U 3 Si 2 ) is a concept explored as a potential alternative to UO 2 fuel used in light water reactors (LWRs) since it may improve accident tolerance and economics due to its higher thermal conductivity and increased uranium density. U 3 Si 2 has been previously used in research reactors in the form of dispersion fuel which operates at lower temperatures than commercial LWRs. The research reactor data illustrated that significant gaseous swelling occurs as the fuel burnup increases. Therefore, it is imperative to understand the fission gas behavior of U 3 Si 2 under higher temperature LWR operating conditions. In this work, molecular dynamics and phase-field modeling techniques are used to reduce the uncertainty in select modeling assumptions made in developing the fission gas behavior model for U 3 Si 2 in the BISON fuel performance code. To support the implementation of a U 3 Si 2 fission gas model in BISON, cluster dynamics simulations of irradiation enhanced Xe diffusion have been carried out. Similarly, MD simulations were used to predict the athermal contribution due to atomic mixing during ballistic damage cascades. By combining our results with literature DFT data for thermal equilibrium diffusion, Xe diffusivity has been described over a wide range of temperatures for in-reactor conditions. These lower length scale informed models are then utilized in the assessment of BISON U 3 Si 2 modeling capabilities by simulating the ATF-1 experiments irradiated in the Advanced Test Reactor (ATR). Sensitivity analysis (SA) and uncertainty quantification (UQ) are included as part of the assessment process to identify where further experiments and lower length scale modeling would be beneficial. The multiscale modeling approach utilized in this work can be applied to new fuel concepts being explored for both LWRs and advanced reactors (e.g., uranium nitride , uranium carbide).

Where is the hydrodynamic limit?

ABSTRACT In this paper, the classical hydrodynamic theory is compared to molecular dynamics simulation data using two different dynamical modes, namely, the transverse and longitudinal modes. The comparison is based on the dynamics of the equilibrium fluctuations for four different systems, the Lennard-Jones system, model liquids for butane, toluene, and water. Using an error estimator limit of 1%, it is found that for the transverse dynamics the classical hydrodynamic theory holds down to 5–14 nm depending on the fluidic system. For the longitudinal dynamics, this characteristic length scale is approximately doubled. From the dispersion relations, it is furthermore concluded that classical hydrodynamics qualitatively accounts for the dominating processes at even lower length scales.

Confined buckling in thin sheets and its correlation to ripplocations: A deformation mechanism in layered solids

Recently, we have established that, when loaded in compression, edge-on, atomic layers in layered solid can fail by buckling. The resulting structure is termed a ripplocation. When more than one layer buckles, they outline standing waves with boundaries that we labeled ripplocation boundaries that are nearly fully recoverable. In this paper, we examine buckling of layers at the centimeter level to explore continuum buckling theory and its applicability to atomic layers. Specifically, we examine buckling by confining and cyclically loading thin steel sheets, edge-on, determining that increasing confining pressure, sheet thickness, and/or decreasing the number of layers increases the buckling load. Concomitantly, the resulting wavelengths and amplitudes are reduced. A nonlinear, folding mechanics model, which accounts for frictional bending and foundation energies, is adapted and verified on our experimental results. We also demonstrate that Coulombic friction between the layers can account for the energy dissipated per cycle. The predicted values of buckling nucleation loads and number of modes from the model are in good agreement---at low levels of confinement---with continuum and atomistic scale results. The wavelength estimates from the model correlate surprisingly well with the continuum buckling results; however, likely due to the complex mechanics at the lower length scales and limiting theoretical assumptions in the derivation, the accuracy decreases at the atomistic scale and at higher confining pressures.