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, 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-...
The shear force required to emit circular dislocation loops from the edge of a circular adhesive-... more The shear force required to emit circular dislocation loops from the edge of a circular adhesive-contact zone is calculated analytically as a function of contact-zone radii. The emission condition is based on the balance of the configurational force and the Peierls force on a dislocation loop initiated at the edge of the adhesive contact zone. The analysis suggests that there is a transition, for a nanometer-scale single-asperity contact, from concurrent (mobile- dislocation-free) slip to single-dislocation-assisted (SDA) slip. The nanometer-scale friction stress (shear force required for slip/contact area), which experimentally is observed independent of normal loading and contact-zone size, is believed to be the stress required for concurrent slip. The analysis also predicts a second transition from SDA slip to multiple-dislocation-cooperated (MDC) slip at the scale of tens of micrometers in contact size. The friction stress at this large length scale has also been observed experi...
The practice of forming electrical conduction paths in an insulating material by filling cylindri... more The practice of forming electrical conduction paths in an insulating material by filling cylindrical holes with molten metal can result in high residual stresses when the metal cools. Residual stress is greatest near the metal-insulator interface, and stress relaxation by means of de-adhesion is possible. Another failure mode that poses greater practical difficulties is the growth of cracks along paths which spiral away from the interface into the brittle material. Such cracks may occur singly or in pairs, and their lengths can be sufficiently great to provide links with adjacent conduction paths. Such cracks are considered from the fracture mechanics point of view. The residual stress field is relaxed by the growth of spiral cracks which are modeled as continuous distributions of dislocations. It is assumed that these cracks grow so that the stress state on the prospective fracture plane just ahead of the crack tip is purely tensile. The paths are determined by means of an incremen...
ABSTRACTA novel approach to quantitative interpretation of high-resolution electron microscopy im... more ABSTRACTA novel approach to quantitative interpretation of high-resolution electron microscopy images of defects in materials has been developed. The emphasis of this paper is on the methodology, which has been named Computational Fourier Transform Moiré Analysis. The essential principle of this technique is to extract an accurate displacement field about a defect from its near-atomic-resolution picture using digital Fourier transformation procedures. From this data, the displacement gradient can be calculated which yields much information on the experimental deformation mechanics of the material under investigation. As a by-product, we produce the computational Moiré pattern without the need of an external perfect reference lattice image normally associated with the interference phenomena. This method is illustrated using a bounding Frank partial dislocation for a Frank loop of the vacancy type. Results are presented on its strain field, Burgers vector and dislocation core shape an...
A novel diamagnetic lateral force calibrator ͑D-LFC͒ has been developed to directly calibrate ato... more A novel diamagnetic lateral force calibrator ͑D-LFC͒ has been developed to directly calibrate atomic force microscope ͑AFM͒ cantilever-tip or-bead assemblies. This enables an AFM to accurately measure the lateral forces encountered in friction or biomechanical-testing experiments at a small length scale. In the process of development, deformation characteristics of the AFM cantilever assemblies under frictional loading have been analyzed and four essential response variables, i.e., force constants, of the assembly have been identified. Calibration of the lateral force constant and the "crosstalk" lateral force constant, among the four, provides the capability of measuring absolute AFM lateral forces. The D-LFC is composed of four NdFeB magnets and a diamagnetic pyrolytic graphite sheet, which can calibrate the two constants with an accuracy on the order of 0.1%. Preparation of the D-LFC and the data processing required to get the force constants is significantly simpler than any other calibration methods. The most up-to-date calibration technique, known as the "wedge method," calibrates mainly one of the two constants and, if the crosstalk effect is properly analyzed, is primarily applicable to a sharp tip. In contrast, the D-LFC can calibrate both constants simultaneously for AFM tips or beads with any radius of curvature. These capabilities can extend the applicability of AFM lateral force measurement to studies of anisotropic multiscale friction processes and biomechanical behavior of cells and molecules under combined loading. Details of the D-LFC method as well as a comparison with the wedge method are provided in this article.
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, 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-...
The shear force required to emit circular dislocation loops from the edge of a circular adhesive-... more The shear force required to emit circular dislocation loops from the edge of a circular adhesive-contact zone is calculated analytically as a function of contact-zone radii. The emission condition is based on the balance of the configurational force and the Peierls force on a dislocation loop initiated at the edge of the adhesive contact zone. The analysis suggests that there is a transition, for a nanometer-scale single-asperity contact, from concurrent (mobile- dislocation-free) slip to single-dislocation-assisted (SDA) slip. The nanometer-scale friction stress (shear force required for slip/contact area), which experimentally is observed independent of normal loading and contact-zone size, is believed to be the stress required for concurrent slip. The analysis also predicts a second transition from SDA slip to multiple-dislocation-cooperated (MDC) slip at the scale of tens of micrometers in contact size. The friction stress at this large length scale has also been observed experi...
The practice of forming electrical conduction paths in an insulating material by filling cylindri... more The practice of forming electrical conduction paths in an insulating material by filling cylindrical holes with molten metal can result in high residual stresses when the metal cools. Residual stress is greatest near the metal-insulator interface, and stress relaxation by means of de-adhesion is possible. Another failure mode that poses greater practical difficulties is the growth of cracks along paths which spiral away from the interface into the brittle material. Such cracks may occur singly or in pairs, and their lengths can be sufficiently great to provide links with adjacent conduction paths. Such cracks are considered from the fracture mechanics point of view. The residual stress field is relaxed by the growth of spiral cracks which are modeled as continuous distributions of dislocations. It is assumed that these cracks grow so that the stress state on the prospective fracture plane just ahead of the crack tip is purely tensile. The paths are determined by means of an incremen...
ABSTRACTA novel approach to quantitative interpretation of high-resolution electron microscopy im... more ABSTRACTA novel approach to quantitative interpretation of high-resolution electron microscopy images of defects in materials has been developed. The emphasis of this paper is on the methodology, which has been named Computational Fourier Transform Moiré Analysis. The essential principle of this technique is to extract an accurate displacement field about a defect from its near-atomic-resolution picture using digital Fourier transformation procedures. From this data, the displacement gradient can be calculated which yields much information on the experimental deformation mechanics of the material under investigation. As a by-product, we produce the computational Moiré pattern without the need of an external perfect reference lattice image normally associated with the interference phenomena. This method is illustrated using a bounding Frank partial dislocation for a Frank loop of the vacancy type. Results are presented on its strain field, Burgers vector and dislocation core shape an...
A novel diamagnetic lateral force calibrator ͑D-LFC͒ has been developed to directly calibrate ato... more A novel diamagnetic lateral force calibrator ͑D-LFC͒ has been developed to directly calibrate atomic force microscope ͑AFM͒ cantilever-tip or-bead assemblies. This enables an AFM to accurately measure the lateral forces encountered in friction or biomechanical-testing experiments at a small length scale. In the process of development, deformation characteristics of the AFM cantilever assemblies under frictional loading have been analyzed and four essential response variables, i.e., force constants, of the assembly have been identified. Calibration of the lateral force constant and the "crosstalk" lateral force constant, among the four, provides the capability of measuring absolute AFM lateral forces. The D-LFC is composed of four NdFeB magnets and a diamagnetic pyrolytic graphite sheet, which can calibrate the two constants with an accuracy on the order of 0.1%. Preparation of the D-LFC and the data processing required to get the force constants is significantly simpler than any other calibration methods. The most up-to-date calibration technique, known as the "wedge method," calibrates mainly one of the two constants and, if the crosstalk effect is properly analyzed, is primarily applicable to a sharp tip. In contrast, the D-LFC can calibrate both constants simultaneously for AFM tips or beads with any radius of curvature. These capabilities can extend the applicability of AFM lateral force measurement to studies of anisotropic multiscale friction processes and biomechanical behavior of cells and molecules under combined loading. Details of the D-LFC method as well as a comparison with the wedge method are provided in this article.
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Papers by Kyung-Suk Kim