Surface Strain Energy Research Articles

Control of the preferential orientation and properties of HiPIMS and DCMS deposited chromium coating based on bias voltage

This study investigates the effects of varying bias voltages on the crystallographic orientation and properties of DCMS + HiPIMS-deposited chromium coatings. Under bias voltages varying from 100 to 500 V, dense Cr coatings were obtained, and the deposition rate decreased by 13 %. The bias voltage significantly impacts the hardness, crystallographic orientation, electrical conductivity, and bonding strength of the coating. As the bias voltage increases, the hardness of the Cr coating gradually increases. The crystallographic orientation of the coating is governed collectively by surface energy, strain energy, and sputtering effects. The preferential crystallographic orientation of the Cr coating transitions from (222) to (110), subsequently changing to a mixed preferential crystallographic orientation of (110), (211), and (222). Under the combined influence of thermal effects and ion bombardment, a (110) preferential crystallographic orientation was obtained at a bias voltage of 300 V, featuring moderate hardness and optimal wear resistance. This study establishes that the electrical characteristics of the coatings have a significant correlation with bias voltage levels.

Mechanical behavior of nanocircular plates under coupled surface and nonlocal effects by using molecular dynamics simulations

The equations of control for a circular thin plate under simple support are obtained by coupling the surface effect and non-local effect using the equilibrium method. Molecular dynamics simulations were used to calculate the residual surface strain energies at different crystal orientations. Different crystal orientations of the same material would affect its surface energy and thus result in different mechanical behaviors. The effects of residual surface strain energy and non-local parameters on the mechanical behavior of circular thin plates were analyzed. The analysis reveals that the surface effect and non-local effect on the deflection of the nanoplates are significant. The surface effect parameter of tensile stress increases the deflection, while the opposite is true for the surface effect parameter of compressive stress, and the non-local parameter decreases the deflection. The influence of surface effect and non-local effect is significant for smaller thicknesses and weakens for larger thicknesses.

A phase field fracture model for ultra-thin micro-/nano-films with surface effects

Surface effects usually remarkably affect the mechanical response of ultra-thin micro-/nano-structures. However, the mechanisms of surface effects on the fracture characteristics of ultra-thin films are still not fully understood. To this end, this paper develops a modeling framework to investigate the fracture of ultra-thin films at microscales or below. Such a framework couples the Gurtin–Murdoch theory with a phase-field fracture model, in which the former is adopted to introduce the surface effects, i.e., the surface residual stress and surface elasticity of a thin film, and the latter is able to model crack evolution without requiring predefined crack paths or any criteria. Furthermore, a novel crack driving force is introduced, which encompasses the tensile components of both bulk elastic energy and surface elastic energy. Several numerical examples including the biaxial tension test as well as the single-edge notched tension/shear test are performed. The simulation results indicate that the surface strain energy plays a major role in the total elastic strain energy of an ultra-thin film when its thickness is at a micro level, thus demonstrating the significance of surface effects. Moreover, the mode-I fracture test shows that the surface elasticity and surface residual stress have a remarkable influence on the displacement at failure, while for the mode-II fracture test, the surface residual stress significantly influences the fracture characteristics such as the crack path and failure displacement. The developed model paves the way for revealing the fracture mechanisms of ultra-thin micro-/nano-films and conducting their safety assessment.

Discussion of the linearized version of the Steigmann-Ogden surface model in plane deformation and its application to inclusion problems

We re-examine two linearized versions of the Steigmann-Ogden model of a general elastic cylindrical surface under plane deformation. The first version appears quite commonly in the literature and is distinguished by the fact that the bending moment of the surface is defined by the nominal curvature of the deformed surface (which is independent of the change in the length scale of the surface during deformation). The second version is a modified version in which the bending moment is defined by the actual curvature of the deformed surface. In both versions, the tangential force of the surface is determined by its stretch during deformation. We demonstrate from an energetic point of view that the first version is self-consistent while the second is not in that it does not yield a unique positive-definite surface strain energy density. Accordingly, we propose a refined and self-consistent linearized version of the Steigmann-Ogden model in which the bending moment of a material surface remains dependent on the actual curvature of the deformed surface while the corresponding tangential force relies on the stretch of the surface, the initial curvature of the surface and the actual curvature of the deformed surface. We formulate, in the context of the complex variable formalism of elasticity, the boundary condition corresponding to this refined version for an elastic composite system with an arbitrary curved interface (including the case of an arbitrarily-shaped inclusion embedded within an elastic matrix) under plane deformation. Some additional formulae are also given for the analysis of the boundary value problem corresponding to an arbitrarily-shaped inclusion subjected to the proposed refined boundary condition.

Identifying USP1 Inhibitors with Allosteric Effect on Its Triple Catalytic Center through Virtual Screening

Previous studies have shown that downregulation of ubiquitin-specific protease 1 (USP1) can inhibit cell proliferation and promote apoptosis, indicating that targeting USP1 with drugs is a potential treatment for cancer, especially breast and ovarian cancer. In this study, we performed virtual screening on a database containing about 1.37 million molecules using the pharmacophore model, multiple precision molecular docking algorithms, molecular mechanics/generalized born surface area (MM/GBSA), strain energy, and ADMET screening methods. We found that Z28551960, Z423064076, Z1037335610, and Z1129923146 compounds showed excellent performance in terms of binding energy with USP1, ADMET property evaluation, and binding dynamics with USP1, had high potential as USP1 inhibitors, and were identified as hits in virtual screening. In addition, we demonstrated for the first time through molecular dynamics simulations that those molecules can enhance the structural flexibility of the USP1 protein and reduce its structural compactness, providing a basis for protein conformational changes. In summary, our discovery of potential USP1 inhibitors with novel scaffolds provides a theoretical basis for further development of USP1 inhibitors.

Reorientation Mechanisms of Graphene Coated Copper {001} Surfaces

Engineering the surface orientation of face-centered cubic (fcc) metals to the close-packed {111} plane can significantly enhance their oxidation resistance. However, owing to the synergetic effect of surface energy density (γ˙) and strain energy density (ω), such close-packed surface orientation can currently only be achieved by atomic-level thin film epitaxy or monocrystallization of polycrystalline metals. In this study, we characterized the microstructures of pure copper (Cu) foil and two types of graphene-coated Cu (Gr/Cu) foils and observed a 12~14 nm thick reconstructed surface layer with the {111} orientation in the high-temperature deposited Gr/{001} Cu surface. Combining the statistical results with thermodynamic analysis, we proposed a surface melting-solidification mechanism for the reconstruction of the Cu surface from {001} orientation to {111} orientation. This process is dominated by Gr/Cu interfacial energy and is particularly promoted by high-temperature surface melting. We also validated such a mechanism by examining Cu surfaces coated by h-BN (hexagonal boron nitride) and amorphous carbon. Our findings suggest a possible strategy to enhance the surface properties of fcc metals via engineering surface crystallography.

Molecular dynamics simulation and thermodynamics calculation on surface segregation in Ni-Cu nano-films under stress

The surface segregation of Cu atoms in a Ni-Cu system was investigated using molecular dynamics simulations. Thermodynamic calculations were performed to verify the results of the molecular dynamics simulations. For the thermodynamic calculations, a model for evaluating the influence of stress on surface segregation was developed using the modified Darken model in combination with the broken-bond model. Using molecular dynamics simulations, it was found that the enrichment of Cu atoms occurred for a free-standing Ni-10 at.% Cu film consisting of 20 layers. Simultaneously, the stress distribution across the Ni-Cu thin film is obtained. The thermodynamic calculation results show that the influence of stress on the surface segregation cannot be ignored because of the considerable surface stress. Surface tension stress promotes the surface segregation of copper in Cu-Ni alloys due to the larger lattice parameter of copper than nickel, which leads to the reduction of surface strain energy. When the thickness is greater than 31 nm (or the number of layers exceeds 89), the size effect disappears, i.e., the surface concentration doesn’t increase with the increase of thickness. The calculation results obtained by the Bragg-William equation used for the surface segregation in equilibrium are in good agreement with the thermodynamic calculation and molecular dynamics simulation results.

Predicting and explaining crystallographic orientation relationships of exsolved precipitates in garnet using the edge‐to‐edge matching model

AbstractRelative alignments of mineral exsolutions and their host crystals can be described by crystallographic orientation relationships (COR). Exsolved phases in garnet from high‐grade metamorphic rocks and igneous rocks may have COR, but the complexity of COR distributions has thus far restricted their use to identifying exsolved phases. Classification of COR also remains mineral‐specific, leaving doubt as to what information COR preserve. To test how COR may be standardized, we calculated mismatch of low‐index crystallographic planes (d‐value ratios) and crystallographic directions (rows of atoms) between precipitates and garnet and defined search criteria for structural alignments likely to be energetically favourable. We analysed published electron backscatter diffraction (EBSD) data for apatite, rutile, ilmenite, corundum, and quartz precipitates in garnet (ntot = 1,296) for the presence of these alignments. Our method predicts between 88% and 98% of observed alignments across the studied minerals and requires only calculations using unit cell parameters. We further show that each exsolved mineral forms COR predicted by the edge‐to‐edge matching model which was developed to describe unambiguous exsolution textures in alloys. Edge‐to‐edge matching aligns atoms at the host–precipitate interface by parallelism or near‐parallelism of crystallographic planes of similar spacing and parallelism of crystallographic directions (rows of atoms) of similar length on the edges of those planes. Edge‐to‐edge matches likely facilitate coherent to semi‐coherent interfaces by lowering surface free energy and strain energy, stabilizing precipitates. These matches are defined by criteria applicable to all minerals, making them an ideal tool for classifying, discovering and interpreting COR of diverse precipitates in garnet. This approach may also predict COR in other geological mineral pairs (e.g., exsolved feldspars). We find that edge‐to‐edge matching may explain the stability of the needle‐shaped morphologies commonly observed for exsolution textures in garnet. Edge‐to‐edge matching COR distributions can be tested as proxies of the state of the host rock at the time of exsolution to evaluate factors such as temperature, cooling rate, degree of undercooling, and/or strain. Patterns of edge‐to‐edge matching COR may be paired with geothermobarometry and/or petrochronology to provide a powerful new tool for studying the histories of granulite and eclogite facies metamorphic and igneous rocks.

Element segregation and thermal stability of Ni–Rh nanoparticles

A new angular-dependent potential (ADP) of Ni–Rh system was obtained by fitting the experimental data and first principle data, and the effectiveness of the potential was tested. Then, the element segregation characteristics and thermal stability of Ni–Rh nanoparticles were studied by Monte Carlo and molecular dynamics. The results show that the chemical ordering pattern of Ni1-xRhx nanoparticles is the result of the competition of surface energy, strain energy, interface energy and bond energy. With the increase of x, Rh atoms are preferentially segregated to the surface and dispersed. The concentration of Rh atoms in the surface decreases with the increase of size or temperature. With the increase of x, the melting point of Ni1-xRhx nanoparticle first gradually increased, reached the highest near x ​= ​0.1, then gradually decreased, reached the lowest near x ​= ​0.5, and then gradually increased. The above results theoretically explain the reason why doping a small amount of Rh can improve the coking-resistance and sintering-resistance ability of Ni catalyst.

In-situ construction of high-modulus nanospheres on elastomer fibers for linearity-tunable strain sensing

A flexible strain sensor is developed via one-step in-situ construction of stiff PVDF nanospheres on the surface of TPU fibers via polymeric phase and morphology control technology. It enables tunable linear sensing to strain thanks to the restricting of quick crack propagation. • Flexible fiber mat strain sensors of heterogeneous structures are developed. • The heterogeneous structure is consisted of stiff PVDF nanospheres on TPU fibers. • The structure can restrict quick micro-crack propagation throughout fiber surface. • The sensor with high-density nanospheres shows very good linearity. Wearable strain sensors with high sensitivity and linear resistance signal response to strain are urgently demanded for human–machine interface, which can be tuned by introducing uneven surface mechanics distribution onto fiber surfaces via structural heterogeneity for fibrous elastomer fiber mat sensors. Yet it is still of great challenge to build micro- or nano-scale heterogeneous structures on fiber surfaces in a facile and scalable way without using templates. Herein, we report a plastic nanosphere-decorated elastomer fiber mat strain sensor with a zoned surface strain energy release characteristic, designed based on analysis of material match and structural mechanics. Surface mechanics analysis confirms that the as-designed sensor shows a controllable strain energy release area, significantly improving sensing stability thanks to effective restriction of micro-crack propagation in conductive pathways. In particular, fibrous mat sensor with high-density nanospheres shows very low fluctuation in strain sensitivity variation (±0.05 for strain ≤ 30 %), i.e., good linearity in the resistance response to strain, while that for the control sensor is ± 10.0 for strain ≤ 16 %. Such a fiber mat strain sensor can not only be applied for real-time sensing of object deformations for human–machine interface and intelligent control, but also in hydrophobic porous elastomeric packaging materials and triboelectric devices.

The biomechanics of autoinjector-skin interactions during dynamic needle insertion

Autoinjector devices are rapidly becoming the preferred method of drug delivery for a wide array of pharmaceuticals such as monoclonal antibodies. Yet, our understanding of injection biomechanics is limited, but is crucially important to create autoinjectors that lead to the least amount of pain, penetrate the skin to a desired depth, produce small lesions that minimize back flow of drug, and operate robustly even given the variability in the skin mechanics among individuals. We propose a finite element model of needle insertion coupled to the dynamic model of an autoinjector. The finite element model is embedded with a cohesive zone plane to capture crack initiation and propagation within an energy-based fracture mechanics framework. The cohesive zone model is supported by experimental observations of a mode I crack during the needle insertion into the soft tissue. Model calibration against force curves from needle insertion experiments leads to estimated material and fracture properties that match values reported in independent experiments from the literature. With the calibrated model we explore the effect of change in the material properties and device parameters on the insertion dynamics. One of the most interesting findings is that pre-compression of skin from the autoinjector base plate can regulate the stress field near the skin surface and add strain energy that is available for crack formation.

Influence of bilayers period on mechanical properties of TaNx/TaCx multilayers obtained by direct current magnetron sputtering

In this paper, the mechanical properties of TaNx/TaCx bilayers obtained by direct current magnetron sputtering are studied. The materials were manufactured by stacking bilayers formed by the periodic alternation TaN and TaC. Initially, samples of 40 bilayers were produced varying the deposition temperature (200, 300, 400 and 500°C), finding the best mechanical properties for the sample grown at 500°C; after that, the number of bilayers was varied, taking values of 10, 20, 40, 80 and 160. Transmission electron microscopy images show the layers formation and thicknesses between 1.2 and 1.6 µm. In addition, X-ray diffraction patterns were acquired to observe the crystalline structure of samples produced varying the number of bilayers. Hardness was related to the preferential orientation and the competition between surface free energy and strain energy. The sample exhibiting the greatest hardness was obtained with 40 bilayers, in which, there is an equilibrium between both energies.

Anti-plane surface and interfacial waves influenced by layer reinforcement in Piezo-Electro-Magnetic structures with surface energy

The electro-magnetic coupling parameter which is absent in monolithic piezoelectric materials is a unique property of the composite Piezo-Electro-Magnetic(PEM) materials that enhance the applicability of these composites in magnetic field probes, electric packaging, biotechnological applications, etc. In surgical process of joining bones, the freshly developed bone is softer than the mature bone, and thus the mechanical properties of this soft bone becomes important in the success of the surgery. Hence, these kinds of structures having a soft material reinforced at the surface or interface are the prime motivation of this study. In the present work, the propagation of Anti-plane wave is discussed in two models, namely a PEM half-space with a thin elastic layer reinforced at the free surface - Model $$-1$$ and two imperfectly bonded PEM half-spaces with a thin elastic layer reinforced at the interface - Model $$-2$$ . The presence of imperfectness(mechanical, electrical, and magnetic) at the interface gives rise to the discontinuity of displacement and electric & magnetic potential which result in imperfect signal communications affecting the performance of sensing devices. The Gurtin−Murdoch approach is used to derive the surface strain energy density, surface stress tensor, and surface kinetic energy density accounting for the reinforced elastic layer. Admissible boundary/interface conditions relating to the propagation of Anti-plane wave are defined for Electrically Open-Magnetically Open (EOMO) and Electrically Short-Magnetically Short (ESMS) boundaries/interfaces. Using these conditions, the dispersion relation for the propagating Anti-plane wave in both models and the mechanical-electro-magnetic boundaries/interfaces are derived. The impact of the electro-magnetic coupling parameter, imperfectness parameter, and reinforcement of soft & stiff elastic layer on the dispersion relation of Anti-plane wave is numerically computed and portrayed graphically. The data of two dissimilar PEM composites and surface/interface elastic layer of Iron, Gold, and Aluminum with different crystallographic directions constituting soft and stiff reinforcement are considered for numerical and graphical purposes. The electromechanical efficiency of the models are discussed through electromechanical coupling parameter. Moreover, the Cut-Off frequencies of both the models are portrayed graphically for the three data of soft reinforcement of surface/interface layer.

On weak solutions of boundary value problems within the surface elasticity of Nth order

AbstractA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining the weak solution. In order to characterize the smoothness of such solutions, certain energy functional spaces of Sobolev type are introduced. Compared with the solutions obtained in classical linear elasticity, weak solutions for solids with surface stresses are smoother on the boundary; more precisely, a weak solution belongs to where and .

Effect of Particle Spreading Dynamics on Powder Bed Quality in Metal Additive Manufacturing

Powder spreading precedes creation of every new layer in powder bed additive manufacturing (AM). The powder spreading process can lead to powder layer defects such as porosity, poor surface roughness and particle segregation. Therefore, the creation of homogeneous layers is the first task for optimal part printing. Discrete element methods (DEM) powder spreading simulations are typically limited to a single layer and/or small number of particles. Therefore, results from such model configurations may not be generalized to multiple layer processes. In this study, a computationally efficient multi-layer powder spreading DEM simulation model is proposed. The model is calibrated experimentally using static Angle of Repose measurements. The adhesion model parameter, cohesive energy density is related to adhesive surface energy and strain energy release rate parameters. The model results show that interaction between particle and the powder spreading rake leads to noticeable variation in packing density, surface roughness, dynamic angle of repose (AOR), particle size distribution, and particle segregation. The powder model is experimentally validated using a recoater spreading rig to measure the dynamic AOR at spreading speeds consistent with recoating speeds and layer heights used in AM processes.

Anisotropic Grain Growth in (111) Nanotwinned Cu Films by DC Electrodeposition.

We have reported a method of fabricating (111)-orientated nanotwinned copper (nt-Cu) by direct current electroplating. X-ray analysis was performed for the samples annealed at 200 to 350 °C for an hour. X-ray diffraction indicates that the (200) signal intensity increases while (111) decreases. Abnormal grain growth normally results from transformation of surface energy or strain energy density. The average grain size increased from 3.8 µm for the as-deposited Cu films to 65–70 µm after the annealing at 250 °C for 1 h. For comparison, no significant grain growth behavior was observed by random Cu film after annealing for an hour. This research shows the potential for its broad electric application in interconnects and three-dimensional integrated circuit (3D IC) packaging.

Efficient large amplitude primary resonance in in-extensional nanocapacitors: Nonlinear mean curvature component

In general, the impact of geometric nonlinearity, which arises from geometric relationships governing the motion of constituent particles of elastic mediums, becomes critically important while the system operates under large deformations. In this case, the influence of different physics governing the system dynamics might be coupled with the impact of geometric nonlinearity. Here, for the first time, the non-zero component of the mean curvature tensor is nonlinearly expressed in terms of the middle-axis curvature of a cantilevered beam. To this aim, the concept of local displacement field together with inextensibility condition are employed. A nanowire-based capacitor is assumed to be excited by the electrostatic load that is composed of both DC and AC voltages. The main concern is on the case, in which it is necessary to polarize the electrodes with large amplitude voltages. Other physics, including surface strain energy, size-dependency, and dispersion force are modeled to predict the system response more accurately. Hamilton’s principle is used to establish the motion equation, and the Galerkin method is applied to exploit a set of nonlinear ordinary differential equations (ODEs). Implementing a combination of shooting and arc-length continuation scheme, the frequency and force-displacement behaviors of the capacitor are captured near its primary resonance. The coupled effects of the nonlinear impact factor, surface elasticity and size parameters on the bifurcation point’s loci and dynamic pull-in instability are studied.

Strongly anisotropic surface elasticity and antiplane surface waves.

Within the new model of surface elasticity, the propagation of anti-plane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic long flexible beams. Physically, the model was motivated by deformations of surface coatings consisting of aligned bar-like elements as in the case of hyperbolic metasurfaces. Using the least action variational principle, we derive the dynamic boundary conditions. The linearized boundary-value problem is also presented. In order to demonstrate the peculiarities of the problem, the dispersion relations for surface anti-plane waves are analysed. We have shown that the bending stiffness changes essentially the dispersion relation and conditions of anti-plane surface wave propagation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.

Link adjustment for spatial multi-loop deployable structures considering redundant constraints based on multi-objective discrete optimization

Because of the existence of link errors, assembly deviations, and redundant constraints, link adjustments for deployable structures must be implemented during the assembly process to ensure accurate performance and deployable reliability. Thus, this study proposes an optimization method to conduct quantitative link adjustments for spatial multi-loop deployable structures considering redundant constraints. First, the equations of the deformation compatibility are derived based on static analysis. Second, by formulating the objective functions of surface accuracy and strain energy, a multiobjective discrete optimization model of link adjustment, subjected to the equations of the deformation compatibility and adjustable scopes of the support links, is established accordingly. Third, the optimization model is solved using the successive Taguchi approach, which uses the grey relational analysis coupled with principal component analysis as the multicriteria decision-making model, leading to the optimal adjustment for each link. Finally, a numerical example is presented to verify the validity of the proposed method.

Effects of Size, Surface Energy and Casimir Force on the Superharmonic Resonance Characteristics of a Double-Layered Viscoelastic NEMS Device Under Piezoelectric Actuations

This paper investigates the nonlinear characteristics of a double-layered viscoelastic nanoelectromechanical system (NEMS) in the vicinity of superharmonic resonance. Two nanobeams are made of piezoelectric material and coupled through a visco-Pasternak medium in between. Modified couple-stress theory together with Gurtin–Murdoch surface elasticity theory is utilized to take into account the effects of size-dependency and surface energy for the nanosized structure. Kelvin–Voigt model is also implemented to consider the impact of viscoelasticity. The differential equations of motion are established based on Hamilton’s principle and decomposed to a set of nonlinear ordinary differential equations via Galerkin discretization method. Arclength continuation technique is schemed to capture the frequency–response curves near superharmonic resonance of the system. The influence of the couple-stress parameter, surface strain energy and dispersion force on the nonlinear behavior of the system near superharmonic resonance has been studied. It is observed, that the hardening and softening behaviors of the system are remarkably affected by the size and surface parameters, and interatomic Casimir force. Finally, considering all the mentioned effects, the influence of the DC and AC voltage loads on the dynamic pull-in behavior of the NEMS device is investigated. For these cases, some frequency ranges are addressed as the pull-in band in which the lower nanobeam collapses.