A compressed stiff film on a soft substrate may exhibit wrinkles and, under increased compressive... more A compressed stiff film on a soft substrate may exhibit wrinkles and, under increased compressive strain, post-buckling instabilities as well. We numerically analyze wrinkling behaviors of graphene attached on a polydimethylsiloxane (PDMS) substrate under lateral compression. The finite element method is used to simulate the equilibrium shape of the wrinkles as a function of compressive strain. Two-dimensional stretching and bending properties of graphene are obtained by density functional theory analysis, which are then converted to equivalent elastic properties of a continuum film with finite effective thickness. The PDMS is described using an Ogden or a neo-Hookean material model. Wrinkles first appear at extremely small strain. As the lateral compression increases, due to the nonlinear elasticity of the PDMS, sequential period-doubling bifurcations of the wrinkle mode are activated until the bifurcation stops and the film folds. We show that the bifurcations are consequences of a delicate balance between the deformations of the film and the substrate to minimize the total energy.
Bulletin of the American Physical Society, Mar 12, 2008
The strength characterization of Al/Si interfaces with a hybrid nanoindentation/FEM method SHUMAN... more The strength characterization of Al/Si interfaces with a hybrid nanoindentation/FEM method SHUMAN XIA, Division of Engineering, Brown University, YUE QI, THOMAS A. PERRY, GM Research & Development Center, KYUNG-SUK KIM, Division of Engineering, Brown University -The mechanical property characterization of the reinforcement/matrix interface in a metal matrix composite (MMC) is entailed for tailoring the interface in the microstructure design of the composite. In this work we developed a hybrid method to characterize the interface strength of an MMC, combining a nanoindentation experiment and a finite element analysis. The nanoindentation experiment was carried out by indenting individual reinforcement particles on a free surface with a nanoindenter. The dependence of indentation response on the interface properties was systematically studied through the finite element analysis with cohesive zone modeling of the interface failure. The interface strength could then be extracted from the comparison between the experimental and FEM results. With this method, the shear strength of an Al/Si interface was measured approximately 240MPa which compares well with the lower bound of an atomistic simulation with a modified EAM potential. The intrinsic fracture toughness of the interface crack tip surrounded by densely populated dislocations was measured 0.25 J/m2. We also studied the effect of the strontium modification on the interface strength with this hybrid method.
Bulletin of the American Physical Society, Mar 16, 2016
Phonon softening and mechanical failure of graphene under tensile strain JEONGWOON HWANG, JISOON ... more Phonon softening and mechanical failure of graphene under tensile strain JEONGWOON HWANG, JISOON IHM, Seoul Natl Univ, KYUNG-SUK KIM, MOON-HYUN CHA, Brown Univ -Phonon softening of graphene under tensile strain is investigated based on ab initio density functional theory calculations. From calculated phonon band structures, we show that the Kohn anomaly point shifts from a high symmetry K point to a lower symmetry one as a consequence of the Dirac point shift in the electronic band structure. We demonstrate that, over a wide range of tensile strain directions, the strain-induced enhancement of phonon softening can give rise to phonon instabilities resulting in a mechanical failure of graphene at lower strains. It is shown that there are two types of instabilities associated with phonons near K and Γ points, respectively, which induce symmetry-breaking structural distortions, and both of them lead to mechanical failure prior to the elastic failure commonly expected when the structural symmetry is retained.
Here, we report an experimental characterization of a new subcritical graphene nanostructure term... more Here, we report an experimental characterization of a new subcritical graphene nanostructure termed a crinkle ruga. Multilayer graphene forms crinkles as a periodic mode of buckling if the ratio of periodic buckling span to thickness is smaller than a critical value. Otherwise, it forms wrinkles. The crinkles have sawtooth-shaped profiles with their faces perfectly flat and the tips of the peaks and valleys highly curved. Our AFM measurements show that the width of the curvature focusing band at the tip is very narrow, e.g. smaller than 16 nm for a 6o crinkle, indicating a strong influence of flexoelectric coupling in crinkle formation. We also found that concavity or convexity of crinkle tips, i.e. parity of the crinkle, can be controlled. Due to the flexoelectric coupling, the concave tip at the crinkle valley is positively charged, and the convex tip at the crinkle peak negatively charged. In addition, here, we demonstrate that the charges at the crinkle tips can attract macromol...
When an elastic thin-film/substrate bilayer is cyclically compressed with a large plane-strain st... more When an elastic thin-film/substrate bilayer is cyclically compressed with a large plane-strain stroke, various surface morphologies develop either reversibly or irreversibly with cyclic hysteresis. Here, we examine the cyclic morphology evolution with extensive finite-element analyses and present a generic irreversibility map on the primary bilayer Ruga-phase diagram (PB-RPD). The term “PB” refers to a system of a film on a substrate, both of which are incompressible neo-Hookean, while the term “Ruga-phase” refers to the classification of corrugated surface morphologies. Our generic map reveals two configurational irreversibility types of Ruga-phases during a loading and unloading cycle. One, localization irreversibility, is caused by unstable crease localization and the other, modal irreversibility, by unstable mode transitions of wrinkle-Ruga configurations. While the instability of crease localization depends mainly on smoothness of the creasing surface or interface, the instabil...
How friction affects adhesion is addressed. The problem is considered in the context of a very st... more How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson–Kendall–Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A simple model for the interaction of friction and adhesion is utilized, in which some of the work done against frictional resistance is assumed to be stored reversibly. This behavior is cons...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
We present the mechanics of folding surface-layer wrinkles on a soft substrate, i.e. inter-touchi... more We present the mechanics of folding surface-layer wrinkles on a soft substrate, i.e. inter-touching of neighbouring wrinkle surfaces without forming a cusp. Upon laterally compressing a stiff layer attached on a finite-elastic substrate, certain material nonlinearities trigger a number of bifurcation processes to form multi-mode wrinkle clusters. Some of these clusters eventually develop into folded wrinkles. The first bifurcation of the multi-mode wrinkles is investigated by a perturbation analysis of the surface-layer buckling on a pre-stretched neo-Hookean substrate. The post-buckling equilibrium configurations of the wrinkles are then trailed experimentally and computationally until the wrinkles are folded. The folding process is observed at various stages of wrinkling, by sectioning 20–80 nm thick gold films deposited on a polydimethylsiloxane substrate at a stretch ratio of 2.1. Comparison between the experimental observation and the finite-element analysis shows that the Ogde...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1999
A micromechanical dislocation model of frictional slip between two asperities is presented. The m... more A micromechanical dislocation model of frictional slip between two asperities is presented. The model suggests that when the contact radius is smaller than a critical value, the friction stress is constant, of the order of the theoretical shear strength, in agreement with reported atomic force microscope (AFM) friction experiments. However, at the critical value there is a transition beyond which the friction stress decreases with increasing area, until it reaches the second transition where the friction stress gradually becomes independent of the contact size. This is in contrast to previous theories, which assume that the friction stress is always independent of the size. The present model also predicts that the mechanisms of slip are size dependent. Before the first transition, the constant friction stress is associated with concurrent slip without the aid of dislocation motion. The first transition corresponds to the minimum contact size at which a single dislocation loop is nucleated and sweeps through the whole contact interface, resulting in a single-dislocation-assisted (SDA) slip. This mechanism is predicted to prevail for a wide range of contact sizes, from 10 nm to 10 µm in radius for typical dry adhesive contacts; however, there are no available experimental data in this size range. The second transition is found to be caused by the effective Peierls stress, which stabilizes the dislocation loop within the contact region, resulting in dislocation pile-ups. Beyond the second transition, slip is assisted by cooperative glide of dislocations in the pile-up. For sufficiently large contacts the mechanism of cooperative glide induces a size-independent friction stress, in agreement with observations in surface force apparatus (SFA) friction experiments. This paper (Part I) addresses the first transition: from concurrent slip to SDA slip. The second transition is analysed in a companion paper (Part II).
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011
We report that a graphene sheet has an unusual mode of atomic-scale fracture owing to its structu... more We report that a graphene sheet has an unusual mode of atomic-scale fracture owing to its structural peculiarity, i.e. single sheet of atoms. Unlike conventional bond-breaking tensile fracture, a graphene sheet can be cut by in-plane compression, which is able to eject a row of atoms out-of-plane. Our scale-bridging molecular dynamics simulations and experiments reveal that this compressive atomic-sheet fracture is the critical precursor mechanism of cutting single-walled carbon nanotubes (SWCNTs) by sonication. The atomic-sheet fracture typically occurs within 200 fs during the dynamic axial buckling of a SWCNT; the nanotube is loaded by local nanoscale flow drag of water molecules caused by the collapse of a microbubble during sonication. This is on the contrary to common speculations that the nanotubes would be cut in tension, or by high-temperature chemical reactions in ultrasonication processes. The compressive fracture mechanism clarifies previously unexplainable diameter-depe...
Journal of the Mechanics and Physics of Solids, 1998
The energy fluxes upon shrinkage of the contact area are calculated for a pair of spheres in adhe... more The energy fluxes upon shrinkage of the contact area are calculated for a pair of spheres in adhesion. Various notions of energy release rate are introduced and analyzed for correlating the external work parameters and the work of adhesion. Decomposition of the energy release rate into reversible and irreversible parts shows that the reversible part is the work of adhesion and it can be described by the cohesive response purely at the contact zone-edge. This result justifies the use of local zone-edge quantities for modeling the interaction of adhesion and friction. For specific quantitative analysis, adhesion is represented by the Dugdale model, uniform cohesive traction up to a limited separation, as an approximation to more exact inter-surface forces. Exact results are given for the entirely reversible energy release rate to the edge of the contact and the energy release rate to the cohesive zone. The latter is named the strain energy release rate and found to depend on the path in loading parameter space, while the reversible energy release rate is independent of the loading path. The solution for shear of the contact is given as well. Energy released reversibly to be converted into surface energy is identified in contrast to energy released due to slip which will be partially or totally dissipated as heat. The relevance of the results for friction is discussed and contrasted with their significance for the mixed mode fracture of a circular joint.
A new transverse‐displacement inteferometer (TDI) is described. This interferometer makes use of ... more A new transverse‐displacement inteferometer (TDI) is described. This interferometer makes use of intensity variations of a beam obtained by superposition of two beams diffracted symmetrically from a diffraction grating copied onto a plane surface. The TDI is used to monitor the ...
Here, we report the dynamic fracture toughness as well as the cohesive parameters of a bicontinuo... more Here, we report the dynamic fracture toughness as well as the cohesive parameters of a bicontinuously nanostructured copolymer, polyurea, under an extremely high crack-tip loading rate, from a deep-learning analysis of a dynamic big-data-generating experiment. We first invented a novel Dynamic Line-Image Shearing Interferometer (DL-ISI), which can generate the displacement-gradient time profiles along a line on a sample’s back surface projectively covering the crack initiation and growth process in a single plate impact experiment. Then, we proposed a convolutional neural network (CNN) based deep-learning framework that can inversely determine the accurate cohesive parameters from DL-ISI fringe images. Plate-impact experiments on a polyurea sample with a mid-plane crack have been performed, and the generated DL-ISI fringe image has been inpainted by a Conditional Generative Adversarial Networks (cGAN). For the first time, the dynamic cohesive parameters of polyurea have been success...
The polyurea coating is found very useful in strengthening structures ranging from helmets to con... more The polyurea coating is found very useful in strengthening structures ranging from helmets to concrete structures under impact or blast loading. We believe that the hierarchical architecture of nano and microstructures is the bases of the strengthening mechanism, which provides scale-dependent stress laxation and energy dissipation. Here, a challenge is to characterize the strengthening mechanisms not only in the bulk of the copolymer but also at the coating/substrate interface. To this end, we have found that the tapping-mode images of an atomic-force-microscope (AFM) are ideal markers for digital image correlation (DIC) analysis of nano/micro-scale deformation. The tapping-mode images typically exhibit clustered hierarchical structures of hard and soft domains that can trace multiscale deformation mechanisms. To study the role of the hierarchical deformation mechanisms in dynamic toughening, we have developed a line-image shearing interferometer (L-ISI) for plate impact experiments of dynamic fracture testing. The L-ISI measures the variation of the normal-displacementgradient over time along a line on the back surface of a pre-cracked specimen loaded by plate impact. The time history of the displacement gradient forms fringes on the streak-camera image, and the fringes are inverted to determine the time history of the crack speed and the dynamic toughness.
In experimental fracture studies of viscoelastic polymers presently available optical measurement... more In experimental fracture studies of viscoelastic polymers presently available optical measurement methods need to be modified to account for the rate sensitivity of the physical properties. Here, photoviscoelastic behavior is examined for the purpose of determining the mechanical state of stress and strain at the tip of a crack moving through a viscoelastic solid. The linearly opto-mechanical constitutive relation is
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Here, we report the closure resistance of a soft-material bilayer orifice increases against exter... more Here, we report the closure resistance of a soft-material bilayer orifice increases against external pressure, along with ruga-phase evolution, in contrast to the conventional predictions of the matrix-free cylindrical-shell buckling pressure. Experiments demonstrate that the generic soft-material orifice creases in a threefold symmetry at a limit-load pressure of p / μ ≈ 1.20, where μ is the shear modulus. Once the creasing initiates, the triple crease wings gradually grow as the pressure increases until the orifice completely closes at p / μ ≈ 3.0. By contrast, a stiff-surface bilayer orifice initially wrinkles with a multifold symmetry mode and subsequently develops ruga-phase evolution, progressively reducing the orifice cross-sectional area as pressure increases. The buckling-initiation mode is determined by the layer's thickness and stiffness, and the pressure by two types of the layer's instability modes—the surface-layer-wrinkling mode for a compliant and the ring-...
We report closed-form formulas to calculate the incremental-deposition stress, the elastic relaxa... more We report closed-form formulas to calculate the incremental-deposition stress, the elastic relaxation stress, and the residual stress in a finite-thickness film from a wafer-curvature measurement. The calculation shows how the incremental deposition of a new stressed layer to the film affects the amount of the film/wafer curvature and the stress state of the previously deposited layers. The formulas allow the incremental-deposition stress and the elastic relaxation to be correctly calculated from the slope of the measured curvature versus thickness for arbitrary thicknesses and biaxial moduli of the film and the substrate. Subtraction of the cumulative elastic relaxation from the incremental-deposition stress history results in the residual stress left in the film after the whole deposition process. The validities of the formulas are confirmed by curvature measurements of electrodeposited Ni films on substrates with different thicknesses.
Proceedings, annual meeting, Electron Microscopy Society of America
A novel approach to quantitative deformation characterization of high-resolution electron microsc... more A novel approach to quantitative deformation characterization of high-resolution electron microscopy (HREM) defect images has been developed. The essential principle of this technique, called Computational Fourier Transform Deformation (CFTD) analysis, is to extract an accurate displacement field about a defect from its HREM image using Fourier transformation procedures. The methodology's unique feature is to digitize the defect image and compute the Moire pattern, from which the displacement field is obtained, without the need for an external reference lattice image, normally associated with the interference phenomena. Details of the image processing steps are described elsewhere. The motivation is that from this data, the displacement gradient can be calculated which yields much information on the experimental deformation mechanics of some solid undergoing a specific growth process or mechanical testing. One question that has arisen is whether different imaging conditions of t...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
As a sequel of part I (Kothari et al. 2018 Proc. R. Soc. A 474 , 20180054), we present a general ... more As a sequel of part I (Kothari et al. 2018 Proc. R. Soc. A 474 , 20180054), we present a general thermodynamic framework of flexoelectric constitutive laws for multi-layered graphene (MLG), and apply these laws to explain the role of crinkles in peculiar molecular adsorption characteristics of highly oriented pyrolytic graphite (HOPG) surfaces. The thermodynamically consistent constitutive laws lead to a non-local interaction model of polarization induced by electromechanical deformation with flexoelectricity–dielectricity coupling. The non-local model predicts curvature and polarization localization along crinkle valleys and ridges very close to those calculated by density functional theory (DFT). Our analysis reveals that the non-local model can be reduced to a simplified uc-local or e-local model (Kothari et al. 2018 Proc. R. Soc. A 474 , 20180054) only when the curvature distribution is uniform or highly localized. For the non-local model, we calibrated and formulated the layer-...
A compressed stiff film on a soft substrate may exhibit wrinkles and, under increased compressive... more A compressed stiff film on a soft substrate may exhibit wrinkles and, under increased compressive strain, post-buckling instabilities as well. We numerically analyze wrinkling behaviors of graphene attached on a polydimethylsiloxane (PDMS) substrate under lateral compression. The finite element method is used to simulate the equilibrium shape of the wrinkles as a function of compressive strain. Two-dimensional stretching and bending properties of graphene are obtained by density functional theory analysis, which are then converted to equivalent elastic properties of a continuum film with finite effective thickness. The PDMS is described using an Ogden or a neo-Hookean material model. Wrinkles first appear at extremely small strain. As the lateral compression increases, due to the nonlinear elasticity of the PDMS, sequential period-doubling bifurcations of the wrinkle mode are activated until the bifurcation stops and the film folds. We show that the bifurcations are consequences of a delicate balance between the deformations of the film and the substrate to minimize the total energy.
Bulletin of the American Physical Society, Mar 12, 2008
The strength characterization of Al/Si interfaces with a hybrid nanoindentation/FEM method SHUMAN... more The strength characterization of Al/Si interfaces with a hybrid nanoindentation/FEM method SHUMAN XIA, Division of Engineering, Brown University, YUE QI, THOMAS A. PERRY, GM Research & Development Center, KYUNG-SUK KIM, Division of Engineering, Brown University -The mechanical property characterization of the reinforcement/matrix interface in a metal matrix composite (MMC) is entailed for tailoring the interface in the microstructure design of the composite. In this work we developed a hybrid method to characterize the interface strength of an MMC, combining a nanoindentation experiment and a finite element analysis. The nanoindentation experiment was carried out by indenting individual reinforcement particles on a free surface with a nanoindenter. The dependence of indentation response on the interface properties was systematically studied through the finite element analysis with cohesive zone modeling of the interface failure. The interface strength could then be extracted from the comparison between the experimental and FEM results. With this method, the shear strength of an Al/Si interface was measured approximately 240MPa which compares well with the lower bound of an atomistic simulation with a modified EAM potential. The intrinsic fracture toughness of the interface crack tip surrounded by densely populated dislocations was measured 0.25 J/m2. We also studied the effect of the strontium modification on the interface strength with this hybrid method.
Bulletin of the American Physical Society, Mar 16, 2016
Phonon softening and mechanical failure of graphene under tensile strain JEONGWOON HWANG, JISOON ... more Phonon softening and mechanical failure of graphene under tensile strain JEONGWOON HWANG, JISOON IHM, Seoul Natl Univ, KYUNG-SUK KIM, MOON-HYUN CHA, Brown Univ -Phonon softening of graphene under tensile strain is investigated based on ab initio density functional theory calculations. From calculated phonon band structures, we show that the Kohn anomaly point shifts from a high symmetry K point to a lower symmetry one as a consequence of the Dirac point shift in the electronic band structure. We demonstrate that, over a wide range of tensile strain directions, the strain-induced enhancement of phonon softening can give rise to phonon instabilities resulting in a mechanical failure of graphene at lower strains. It is shown that there are two types of instabilities associated with phonons near K and Γ points, respectively, which induce symmetry-breaking structural distortions, and both of them lead to mechanical failure prior to the elastic failure commonly expected when the structural symmetry is retained.
Here, we report an experimental characterization of a new subcritical graphene nanostructure term... more Here, we report an experimental characterization of a new subcritical graphene nanostructure termed a crinkle ruga. Multilayer graphene forms crinkles as a periodic mode of buckling if the ratio of periodic buckling span to thickness is smaller than a critical value. Otherwise, it forms wrinkles. The crinkles have sawtooth-shaped profiles with their faces perfectly flat and the tips of the peaks and valleys highly curved. Our AFM measurements show that the width of the curvature focusing band at the tip is very narrow, e.g. smaller than 16 nm for a 6o crinkle, indicating a strong influence of flexoelectric coupling in crinkle formation. We also found that concavity or convexity of crinkle tips, i.e. parity of the crinkle, can be controlled. Due to the flexoelectric coupling, the concave tip at the crinkle valley is positively charged, and the convex tip at the crinkle peak negatively charged. In addition, here, we demonstrate that the charges at the crinkle tips can attract macromol...
When an elastic thin-film/substrate bilayer is cyclically compressed with a large plane-strain st... more When an elastic thin-film/substrate bilayer is cyclically compressed with a large plane-strain stroke, various surface morphologies develop either reversibly or irreversibly with cyclic hysteresis. Here, we examine the cyclic morphology evolution with extensive finite-element analyses and present a generic irreversibility map on the primary bilayer Ruga-phase diagram (PB-RPD). The term “PB” refers to a system of a film on a substrate, both of which are incompressible neo-Hookean, while the term “Ruga-phase” refers to the classification of corrugated surface morphologies. Our generic map reveals two configurational irreversibility types of Ruga-phases during a loading and unloading cycle. One, localization irreversibility, is caused by unstable crease localization and the other, modal irreversibility, by unstable mode transitions of wrinkle-Ruga configurations. While the instability of crease localization depends mainly on smoothness of the creasing surface or interface, the instabil...
How friction affects adhesion is addressed. The problem is considered in the context of a very st... more How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson–Kendall–Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A simple model for the interaction of friction and adhesion is utilized, in which some of the work done against frictional resistance is assumed to be stored reversibly. This behavior is cons...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
We present the mechanics of folding surface-layer wrinkles on a soft substrate, i.e. inter-touchi... more We present the mechanics of folding surface-layer wrinkles on a soft substrate, i.e. inter-touching of neighbouring wrinkle surfaces without forming a cusp. Upon laterally compressing a stiff layer attached on a finite-elastic substrate, certain material nonlinearities trigger a number of bifurcation processes to form multi-mode wrinkle clusters. Some of these clusters eventually develop into folded wrinkles. The first bifurcation of the multi-mode wrinkles is investigated by a perturbation analysis of the surface-layer buckling on a pre-stretched neo-Hookean substrate. The post-buckling equilibrium configurations of the wrinkles are then trailed experimentally and computationally until the wrinkles are folded. The folding process is observed at various stages of wrinkling, by sectioning 20–80 nm thick gold films deposited on a polydimethylsiloxane substrate at a stretch ratio of 2.1. Comparison between the experimental observation and the finite-element analysis shows that the Ogde...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1999
A micromechanical dislocation model of frictional slip between two asperities is presented. The m... more A micromechanical dislocation model of frictional slip between two asperities is presented. The model suggests that when the contact radius is smaller than a critical value, the friction stress is constant, of the order of the theoretical shear strength, in agreement with reported atomic force microscope (AFM) friction experiments. However, at the critical value there is a transition beyond which the friction stress decreases with increasing area, until it reaches the second transition where the friction stress gradually becomes independent of the contact size. This is in contrast to previous theories, which assume that the friction stress is always independent of the size. The present model also predicts that the mechanisms of slip are size dependent. Before the first transition, the constant friction stress is associated with concurrent slip without the aid of dislocation motion. The first transition corresponds to the minimum contact size at which a single dislocation loop is nucleated and sweeps through the whole contact interface, resulting in a single-dislocation-assisted (SDA) slip. This mechanism is predicted to prevail for a wide range of contact sizes, from 10 nm to 10 µm in radius for typical dry adhesive contacts; however, there are no available experimental data in this size range. The second transition is found to be caused by the effective Peierls stress, which stabilizes the dislocation loop within the contact region, resulting in dislocation pile-ups. Beyond the second transition, slip is assisted by cooperative glide of dislocations in the pile-up. For sufficiently large contacts the mechanism of cooperative glide induces a size-independent friction stress, in agreement with observations in surface force apparatus (SFA) friction experiments. This paper (Part I) addresses the first transition: from concurrent slip to SDA slip. The second transition is analysed in a companion paper (Part II).
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011
We report that a graphene sheet has an unusual mode of atomic-scale fracture owing to its structu... more We report that a graphene sheet has an unusual mode of atomic-scale fracture owing to its structural peculiarity, i.e. single sheet of atoms. Unlike conventional bond-breaking tensile fracture, a graphene sheet can be cut by in-plane compression, which is able to eject a row of atoms out-of-plane. Our scale-bridging molecular dynamics simulations and experiments reveal that this compressive atomic-sheet fracture is the critical precursor mechanism of cutting single-walled carbon nanotubes (SWCNTs) by sonication. The atomic-sheet fracture typically occurs within 200 fs during the dynamic axial buckling of a SWCNT; the nanotube is loaded by local nanoscale flow drag of water molecules caused by the collapse of a microbubble during sonication. This is on the contrary to common speculations that the nanotubes would be cut in tension, or by high-temperature chemical reactions in ultrasonication processes. The compressive fracture mechanism clarifies previously unexplainable diameter-depe...
Journal of the Mechanics and Physics of Solids, 1998
The energy fluxes upon shrinkage of the contact area are calculated for a pair of spheres in adhe... more The energy fluxes upon shrinkage of the contact area are calculated for a pair of spheres in adhesion. Various notions of energy release rate are introduced and analyzed for correlating the external work parameters and the work of adhesion. Decomposition of the energy release rate into reversible and irreversible parts shows that the reversible part is the work of adhesion and it can be described by the cohesive response purely at the contact zone-edge. This result justifies the use of local zone-edge quantities for modeling the interaction of adhesion and friction. For specific quantitative analysis, adhesion is represented by the Dugdale model, uniform cohesive traction up to a limited separation, as an approximation to more exact inter-surface forces. Exact results are given for the entirely reversible energy release rate to the edge of the contact and the energy release rate to the cohesive zone. The latter is named the strain energy release rate and found to depend on the path in loading parameter space, while the reversible energy release rate is independent of the loading path. The solution for shear of the contact is given as well. Energy released reversibly to be converted into surface energy is identified in contrast to energy released due to slip which will be partially or totally dissipated as heat. The relevance of the results for friction is discussed and contrasted with their significance for the mixed mode fracture of a circular joint.
A new transverse‐displacement inteferometer (TDI) is described. This interferometer makes use of ... more A new transverse‐displacement inteferometer (TDI) is described. This interferometer makes use of intensity variations of a beam obtained by superposition of two beams diffracted symmetrically from a diffraction grating copied onto a plane surface. The TDI is used to monitor the ...
Here, we report the dynamic fracture toughness as well as the cohesive parameters of a bicontinuo... more Here, we report the dynamic fracture toughness as well as the cohesive parameters of a bicontinuously nanostructured copolymer, polyurea, under an extremely high crack-tip loading rate, from a deep-learning analysis of a dynamic big-data-generating experiment. We first invented a novel Dynamic Line-Image Shearing Interferometer (DL-ISI), which can generate the displacement-gradient time profiles along a line on a sample’s back surface projectively covering the crack initiation and growth process in a single plate impact experiment. Then, we proposed a convolutional neural network (CNN) based deep-learning framework that can inversely determine the accurate cohesive parameters from DL-ISI fringe images. Plate-impact experiments on a polyurea sample with a mid-plane crack have been performed, and the generated DL-ISI fringe image has been inpainted by a Conditional Generative Adversarial Networks (cGAN). For the first time, the dynamic cohesive parameters of polyurea have been success...
The polyurea coating is found very useful in strengthening structures ranging from helmets to con... more The polyurea coating is found very useful in strengthening structures ranging from helmets to concrete structures under impact or blast loading. We believe that the hierarchical architecture of nano and microstructures is the bases of the strengthening mechanism, which provides scale-dependent stress laxation and energy dissipation. Here, a challenge is to characterize the strengthening mechanisms not only in the bulk of the copolymer but also at the coating/substrate interface. To this end, we have found that the tapping-mode images of an atomic-force-microscope (AFM) are ideal markers for digital image correlation (DIC) analysis of nano/micro-scale deformation. The tapping-mode images typically exhibit clustered hierarchical structures of hard and soft domains that can trace multiscale deformation mechanisms. To study the role of the hierarchical deformation mechanisms in dynamic toughening, we have developed a line-image shearing interferometer (L-ISI) for plate impact experiments of dynamic fracture testing. The L-ISI measures the variation of the normal-displacementgradient over time along a line on the back surface of a pre-cracked specimen loaded by plate impact. The time history of the displacement gradient forms fringes on the streak-camera image, and the fringes are inverted to determine the time history of the crack speed and the dynamic toughness.
In experimental fracture studies of viscoelastic polymers presently available optical measurement... more In experimental fracture studies of viscoelastic polymers presently available optical measurement methods need to be modified to account for the rate sensitivity of the physical properties. Here, photoviscoelastic behavior is examined for the purpose of determining the mechanical state of stress and strain at the tip of a crack moving through a viscoelastic solid. The linearly opto-mechanical constitutive relation is
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Here, we report the closure resistance of a soft-material bilayer orifice increases against exter... more Here, we report the closure resistance of a soft-material bilayer orifice increases against external pressure, along with ruga-phase evolution, in contrast to the conventional predictions of the matrix-free cylindrical-shell buckling pressure. Experiments demonstrate that the generic soft-material orifice creases in a threefold symmetry at a limit-load pressure of p / μ ≈ 1.20, where μ is the shear modulus. Once the creasing initiates, the triple crease wings gradually grow as the pressure increases until the orifice completely closes at p / μ ≈ 3.0. By contrast, a stiff-surface bilayer orifice initially wrinkles with a multifold symmetry mode and subsequently develops ruga-phase evolution, progressively reducing the orifice cross-sectional area as pressure increases. The buckling-initiation mode is determined by the layer's thickness and stiffness, and the pressure by two types of the layer's instability modes—the surface-layer-wrinkling mode for a compliant and the ring-...
We report closed-form formulas to calculate the incremental-deposition stress, the elastic relaxa... more We report closed-form formulas to calculate the incremental-deposition stress, the elastic relaxation stress, and the residual stress in a finite-thickness film from a wafer-curvature measurement. The calculation shows how the incremental deposition of a new stressed layer to the film affects the amount of the film/wafer curvature and the stress state of the previously deposited layers. The formulas allow the incremental-deposition stress and the elastic relaxation to be correctly calculated from the slope of the measured curvature versus thickness for arbitrary thicknesses and biaxial moduli of the film and the substrate. Subtraction of the cumulative elastic relaxation from the incremental-deposition stress history results in the residual stress left in the film after the whole deposition process. The validities of the formulas are confirmed by curvature measurements of electrodeposited Ni films on substrates with different thicknesses.
Proceedings, annual meeting, Electron Microscopy Society of America
A novel approach to quantitative deformation characterization of high-resolution electron microsc... more A novel approach to quantitative deformation characterization of high-resolution electron microscopy (HREM) defect images has been developed. The essential principle of this technique, called Computational Fourier Transform Deformation (CFTD) analysis, is to extract an accurate displacement field about a defect from its HREM image using Fourier transformation procedures. The methodology's unique feature is to digitize the defect image and compute the Moire pattern, from which the displacement field is obtained, without the need for an external reference lattice image, normally associated with the interference phenomena. Details of the image processing steps are described elsewhere. The motivation is that from this data, the displacement gradient can be calculated which yields much information on the experimental deformation mechanics of some solid undergoing a specific growth process or mechanical testing. One question that has arisen is whether different imaging conditions of t...
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
As a sequel of part I (Kothari et al. 2018 Proc. R. Soc. A 474 , 20180054), we present a general ... more As a sequel of part I (Kothari et al. 2018 Proc. R. Soc. A 474 , 20180054), we present a general thermodynamic framework of flexoelectric constitutive laws for multi-layered graphene (MLG), and apply these laws to explain the role of crinkles in peculiar molecular adsorption characteristics of highly oriented pyrolytic graphite (HOPG) surfaces. The thermodynamically consistent constitutive laws lead to a non-local interaction model of polarization induced by electromechanical deformation with flexoelectricity–dielectricity coupling. The non-local model predicts curvature and polarization localization along crinkle valleys and ridges very close to those calculated by density functional theory (DFT). Our analysis reveals that the non-local model can be reduced to a simplified uc-local or e-local model (Kothari et al. 2018 Proc. R. Soc. A 474 , 20180054) only when the curvature distribution is uniform or highly localized. For the non-local model, we calibrated and formulated the layer-...
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Papers by Kyung-Suk Kim